Power distribution network voltage reactive robust prediction control method and system considering communication delay

Abstract

The application relates to the field of power system automation, and discloses a power distribution network voltage and reactive power robust prediction control method and system considering communication time delay. The method comprises the following steps: estimating the communication time delay based on time-stamped neighbor operation data, and performing time mapping alignment; constructing a delay embedded extended state containing a time delay feature, and realizing local and neighbor operation state fusion estimation; adaptively adjusting a prediction step length according to the time delay level, and combining a source and load prediction and a power flow prediction model to generate a voltage and reactive power prediction trajectory; further combining source and load prediction errors and time delay fluctuations into a joint uncertainty set, tightening voltage safety range and reactive power capacity constraints through an uncertainty envelope, and solving a tube robust optimization problem to obtain a reactive power control reference value; and finally, performing feedforward correction based on a time delay compensation gain and issuing a control instruction. Therefore, the safety, robustness and real-time adaptability of power distribution network voltage and reactive power control under the conditions of communication time delay and source and load disturbance can be improved.

Description

Technical Field

[0001] This invention relates to the field of power system automation technology, and in particular to a robust predictive control method and system for voltage and reactive power in distribution networks that takes into account communication delay. Background Technology

[0002] In the process of transmitting and distributing electrical energy, distribution networks need to maintain the voltage levels of each node within a reasonable range and improve voltage deviation, reduce line losses, and enhance operational economy through reactive power regulation. With the continuous integration of distributed photovoltaic, wind power, energy storage, and electric vehicles into the distribution side, the power flow direction and node voltage distribution of the distribution network exhibit greater randomness and dynamism, and local nodes may experience significant voltage fluctuations in a short period. Traditional distribution networks typically rely on on-load tap-changing transformers, capacitor banks, and line voltage regulators for voltage / reactive power regulation. While these devices are mature in engineering applications, their operation is usually discrete and has a relatively slow response, making it difficult to fully adapt to the frequent and rapid voltage regulation demands following the integration of a high proportion of distributed energy resources.

[0003] In recent years, smart inverters and distributed reactive power compensation devices with rapid reactive power response capabilities have gradually become important resources for voltage regulation in distribution networks. By coordinating multiple distributed controllable devices, local voltage deviations can be improved to a certain extent, and the distribution network's adaptability to source-load fluctuations can be enhanced. Correspondingly, distribution network voltage and reactive power control has gradually evolved from local regulation by single devices to a collaborative control mode combining centralized, hierarchical, distributed, or locally autonomous methods, aiming to achieve a comprehensive balance among voltage quality, reactive power allocation, network losses, and equipment operation.

[0004] However, the effectiveness of distribution network coordinated control depends not only on the regulation capabilities of the electrical equipment itself, but also on the communication network, sampling synchronization, and data transmission reliability. Centralized or hierarchical control typically requires the collection of operational information over a large area and the issuance of unified control commands, placing high demands on communication bandwidth, transmission delay, and data integrity. While local or distributed control can reduce communication dependence, it often relies primarily on local measurements for adjustment, making it difficult to fully reflect the electrical coupling relationships between different nodes and the overall network operating status. In situations where distributed energy output changes rapidly, load fluctuates significantly, or line impedance distribution is uneven, all control methods may be affected by information lag, local judgment bias, or insufficient coordination.

[0005] In particular, in actual power distribution communication environments, phenomena such as communication delays, data packet loss, link congestion, and asynchronous sampling have a certain degree of randomness, which may cause the operating status acquired by the controller to lag behind the actual physical state of the power grid. When this information lag is superimposed on source load prediction errors, equipment response constraints, and node voltage coupling relationships, timing deviations can easily occur between control commands and actual operating states, thereby affecting the timeliness, coordination, and stability of voltage regulation. Summary of the Invention

[0006] The purpose of this invention is to overcome the deficiencies of the prior art and provide a robust predictive control method, system, storage medium, computer program product, and electronic device for distribution network voltage and reactive power considering communication delay. This invention aims to at least solve the problem of insufficient adaptability and stability of distribution network voltage and reactive power coordinated control under non-ideal communication conditions in the prior art, and improve the safety, robustness, and real-time adaptability of distribution network voltage and reactive power control under communication delay and source-load disturbance conditions.

[0007] In a first aspect, the present invention provides a robust predictive control method for voltage and reactive power in a distribution network that considers communication delay, comprising the following steps: estimating communication delay based on timestamped neighbor operating data and performing time mapping alignment; constructing a delay embedding extended state containing delay features to achieve fusion estimation of local and neighbor operating states; adaptively adjusting the prediction step size according to the delay level, and generating voltage and reactive power prediction trajectories by combining source load prediction and power flow prediction models; further combining source load prediction errors and delay fluctuations into a joint uncertainty set. By tightening the voltage safety range and reactive power capacity constraints through the uncertainty envelope, the reactive power control reference value is obtained by solving the robust optimization problem of the control bundle; finally, feedforward correction is performed based on the time delay compensation gain and control commands are issued.

[0008] Optionally, the above-described robust predictive control method for voltage and reactive power in distribution networks considering communication delay includes the following steps: acquiring local real-time operating data and local source-load prediction data of the distribution network node to be processed in the current control cycle, and receiving neighbor operating data with timestamps sent by each neighbor node; calculating the estimated communication delay with each neighbor node based on the timestamps and the reception time of the neighbor operating data; performing time mapping alignment processing on the neighbor operating data according to the estimated communication delay to obtain aligned neighbor operating data; constructing a delay embedding extended state vector containing the estimated communication delay; and... The local real-time operating data and the aligned neighbor operating data are fused to perform delay embedding state estimation to obtain a current estimated state containing dynamic delay characteristics. The model prediction step size is adaptively adjusted based on the communication delay estimate. Using the current estimated state, the local source-load prediction data, and the aligned neighbor operating data, a power flow prediction model is used to generate a voltage prediction trajectory and a reactive power prediction trajectory within the prediction time domain, determined by the model prediction step size. The power flow prediction model is constructed based on the voltage-to-reactive-power sensitivity coefficient to characterize the dynamic changes in node voltage with local reactive power control increments, neighbor operating states, and source-load variations. The evolution relationship is determined based on the local source load prediction data, and the delay fluctuation set is determined based on the change of the communication delay estimate in adjacent control cycles. The local source load prediction error set and the delay fluctuation set are combined into a joint uncertainty set. Combining the voltage prediction trajectory and the reactive power prediction trajectory, under the conditions of minimizing voltage deviation and reactive power control increment, and satisfying the preset safe voltage range and equipment reactive power capacity constraints, an uncertainty envelope is introduced to construct a bundle robust optimization problem, and the bundle robust optimization problem is solved to obtain the reactive power control reference value. The uncertainty envelope determines the upper bound of the state deviation based on the joint uncertainty set, and performs constraint tightening processing on the safe voltage range and the reactive power capacity constraint of the equipment based on the upper bound of the state deviation, so that the actual evolution trajectory remains within the safe voltage range and the reactive power capacity constraint of the equipment under the disturbance corresponding to the joint uncertainty set; based on the preset time delay compensation gain and the communication time delay estimate, the reactive power control reference value is subjected to feedforward time delay correction to generate reactive power control command, and the reactive power control command is sent to the voltage and reactive power regulation equipment corresponding to the distribution network node to be processed to perform voltage and reactive power coordinated control.

[0009] Optionally, the step of calculating the estimated communication delay with each of the neighboring nodes based on the timestamp and the reception time of the neighboring running data, and performing time mapping alignment processing on the neighboring running data according to the estimated communication delay to obtain aligned neighboring running data, includes: For each neighbor node, extract the transmission timestamp generated based on a unified time base from the received neighbor operation data, and calculate the continuous time communication delay by combining it with the reception time of the neighbor operation data. Based on the discrete sampling period of the power distribution network control system, the continuous-time communication delay is normalized and mapped to a communication delay estimate, and the communication delay estimate is decomposed into an integer delay step and a fractional delay weight. Determine whether the estimated communication delay is less than a preset effective delay threshold; If the delay is less than the effective delay threshold, then extract the historical neighbor running data of the two adjacent historical control cycles corresponding to the integer delay steps from the locally maintained sliding historical data cache queue, and use the fractional delay weight to perform a dynamic window interpolation algorithm on the two adjacent historical neighbor running data to calculate the aligned neighbor running data of the current control cycle. If the delay is not less than the effective delay threshold, the corresponding communication link is determined to be in a timeout state and a zero-order hold strategy is triggered. The most recent reliable historical neighbor running data that satisfies the delay being less than the effective delay threshold is extracted from the sliding historical data cache queue and used as the aligned neighbor running data for the current control cycle.

[0010] Optionally, the step of constructing a delay embedding extended state vector containing the communication delay estimate, and fusing the local real-time running data with the aligned neighbor running data to perform delay embedding state estimation to obtain a current estimated state containing dynamic delay features, includes: For the distribution network node to be processed, the estimated communication delay values ​​with each neighbor node are combined into a delay feature vector. Based on the equivalent delay steps determined by the delay feature vector, the corresponding delayed reactive power output value is extracted from the local historical control cache. In this way, a delay embedding extended state vector containing the node's real-time voltage measurement value, the delayed reactive power output value, and the delay feature vector is constructed. Based on the nonlinear system state transition function considering time delay characteristics, the prior state estimate of the current control cycle is calculated using the posterior state estimate of the previous control cycle and the reactive power control input variable. The prior error covariance matrix is ​​calculated by combining the preset system process noise covariance matrix and the time delay perception state transition Jacobian matrix obtained by taking the partial derivative with respect to the time delay state. Calculate the measurement Jacobian matrix that maps the extended state space to the observation space, and calculate the Kalman gain matrix by combining the preset measurement noise covariance matrix and the prior error covariance matrix. The local real-time running data and the neighborhood measurement features extracted from the aligned neighbor running data are combined to construct the actual measurement vector. The Kalman gain matrix is ​​used to perform residual correction measurement update for the difference between the actual measurement vector and the predicted output of the measurement function, so as to output the current estimated state and simultaneously update the posterior error covariance matrix for use in the next control cycle iteration.

[0011] Optionally, the step of adaptively adjusting the model prediction step size based on the communication delay estimate, and using the current estimation state, the local source-load prediction data, and the aligned neighbor operating data to generate the voltage prediction trajectory and reactive power prediction trajectory in the prediction time domain determined by the model prediction step size through the power flow prediction model, includes: Obtain the historical communication delay estimates of the distribution network nodes to be processed within the past preset time window, and calculate the smoothed average delay using a moving average filter. Based on the nominal prediction step size under ideal communication conditions, the model prediction step size of the current control cycle is dynamically adjusted according to the smoothed average time delay using a negative exponential decay penalty mechanism, and combined with the minimum prediction step size to maintain the robust and stable operation of the system, lower limit boundary protection is performed. The filtered node voltage and equivalent reactive power state are extracted from the current estimated state as the initial boundary conditions for the forward rolling derivation. Within the prediction time domain determined by the model prediction step size, the power flow prediction model containing delay coupling terms is used to perform multi-step forward rolling deduction. Based on the power flow sensitivity matrix of the nominal operating point of the distribution network, the local single-step reactive power control increment to be solved, the neighbor reactive power splicing increment embedded with dynamic time delay features, and the active power change corresponding to the source load prediction data are mapped to the corresponding influence components on the local voltage and superimposed to generate the voltage prediction trajectory. The single-step reactive power control increment is also accumulated simultaneously to generate the reactive power prediction trajectory. Specifically, when the forward inference time step does not exceed the integer delay step, the neighbor reactive power splicing increment with embedded dynamic delay features calls the actual historical reactive power control increment determined by the aligned neighbor running data and the sliding historical data cache queue; when the inference time step exceeds the integer delay step, the reactive power prediction trajectory sequence broadcast by the corresponding neighbor node in the previous control cycle is called as a substitute estimate.

[0012] Optionally, by combining the voltage prediction trajectory and the reactive power prediction trajectory, and under the conditions of minimizing voltage deviation and reactive power control increment, and satisfying preset safe voltage range and equipment reactive power capacity constraints, an uncertainty envelope is introduced to construct a robust optimization problem for the control tubes, and the robust optimization problem for the control tubes is solved to obtain reactive power control reference values, including: Using the linear matrix inequality method, the robust positive invariant error set that keeps closed under the disturbance corresponding to the joint uncertainty set of the system error is calculated, and the geometric boundary of the set is projected and mapped as the upper bound of voltage state deviation and the upper bound of reactive power state deviation, respectively. For the nominal predicted state, the Minkowski difference operation is used to subtract the corresponding upper bound of the voltage state deviation and the upper bound of the reactive state deviation from the initial safe voltage range and the equipment reactive capacity constraint, respectively, to generate nominal voltage constraint pipelines and nominal capacity constraint pipelines with tightened internal space. Within the robust feasible region defined by the nominal voltage constraint pipe and the nominal capacity constraint pipe, a minimax optimization problem with dynamic time delay decay weight is constructed as a bundle robust optimization problem; the objective function of the bundle robust optimization problem is constructed based on the weighted sum of the voltage deviation penalty term and the reactive power increment penalty term under the worst disturbance condition in the joint uncertainty set. The predicted communication delay is obtained by extrapolating historical communication delay estimates. The dynamic delay attenuation weight is constructed by combining the predicted communication delay with a preset weight attenuation factor. The dynamic delay attenuation weight is inversely proportional to the predicted communication delay. The minimum-maximization optimization problem is solved in a rolling manner to obtain the optimal decision sequence, and the reactive power value of the first step reactive power control increment in the sequence is extracted and superimposed on the reactive power value of the current state to generate the reactive power control reference value output in the current control cycle.

[0013] Optionally, the step of performing feedforward delay correction on the reactive power control reference value based on a preset delay compensation gain and the estimated communication delay value to generate reactive power control commands includes: Extract the target value of the reactive power control reference value in the current control cycle and the historical reference value in the previous control cycle, and combine the discrete sampling cycle with the first-order difference mapping to approximate the prediction derivative term that characterizes the transient dynamic evolution trend of reactive power regulation. The transmission delay of the instruction sent locally to the voltage and reactive power regulation equipment is estimated as the equivalent execution communication delay, and a preset delay compensation gain coefficient characterizing the physical response features of the voltage and reactive power regulation equipment is extracted. Based on the delay compensation gain coefficient, the equivalent execution communication delay, and the prediction derivative term, the feedforward compensation increment is calculated; the feedforward compensation increment is used to introduce an adjustment change corresponding to the transmission lag time in advance during the control command transmission process. The feedforward compensation increment is superimposed and corrected with the target value, and a preset anti-saturation limiting function is used in conjunction with the physical upper and lower boundaries of the equipment's reactive power capacity to perform limiting constraint processing, so as to generate a reactive power control command that ensures physical feasibility.

[0014] Optionally, the step of acquiring the local real-time operating data and local source-load prediction data of the distribution network node to be processed in the current control cycle, and receiving the neighbor operating data with timestamps sent by each neighbor node, includes: In each control cycle, extract the real-time voltage measurement value and reactive power output value of the node at the current moment, and obtain the voltage record value and reactive power record value cached locally when the communication broadcast was successfully triggered last time; The absolute deviation between the measured value at the current moment and the cached recorded value are calculated respectively. The voltage absolute deviation and reactive absolute deviation are linearly weighted by the preset voltage deviation normalization weight coefficient and reactive power deviation normalization weight coefficient to construct an event-triggered evaluation function based on local state fluctuations. Determine whether the event trigger evaluation function is greater than a preset comprehensive trigger threshold; If the value exceeds the comprehensive trigger threshold, the local running data carrying the sending timestamp generated based on the unified time base will be encapsulated to generate a status update packet, and asynchronously broadcast to the topology neighbor nodes. At the same time, the measurement data at the current moment will be synchronously updated to the locally cached record data. If the fluctuation is not greater than the comprehensive trigger threshold, it is determined that the local state fluctuation is within the preset silent range, and the communication at the sending end remains silent. If the distribution network node to be processed does not hear a new state update packet sent by the first neighbor node among the neighbor nodes in the current control cycle, the alignment state corresponding to the last effective communication time of the first neighbor node is extracted as the initial value for inference, and the open-loop time step extrapolation is performed based on the locally maintained power flow prediction model to generate the corresponding rolling state estimate, and the rolling state estimate is used as the completed neighbor operation data.

[0015] Secondly, the present invention provides a robust predictive control system for voltage and reactive power in a distribution network that considers communication delay, comprising: a data alignment unit, configured to acquire local real-time operating data and local source-load prediction data of the distribution network node to be processed in the current control cycle, and receive neighbor operating data carrying timestamps sent by each neighbor node, calculate an estimated communication delay with each neighbor node based on the timestamps and the reception time of the neighbor operating data, and perform time mapping alignment processing on the neighbor operating data according to the estimated communication delay to obtain aligned neighbor operating data; and a state estimation unit, configured to construct a delay-embedded extended state vector containing the estimated communication delay. The system calculates and integrates the local real-time operating data with the aligned neighbor operating data to perform delay embedding state estimation, thereby obtaining a current estimated state containing dynamic delay characteristics. A trajectory prediction unit is used to adaptively adjust the model prediction step size based on the communication delay estimate, and utilizes the current estimated state, the local source-load prediction data, and the aligned neighbor operating data to generate a voltage prediction trajectory and a reactive power prediction trajectory in the prediction time domain, determined by the model prediction step size, through a power flow prediction model. The power flow prediction model is constructed based on the voltage-to-reactive-power sensitivity coefficient to characterize the dynamic changes in node voltage with local reactive power control increments, neighbor operating states, and source-load variations. Evolutionary relationship; Set construction unit, used to determine the local source load prediction error set based on the local source load prediction data, and to determine the delay fluctuation set based on the change of the communication delay estimate in adjacent control cycles, and to combine the local source load prediction error set and the delay fluctuation set into a joint uncertainty set; Robust optimization unit, used to combine the voltage prediction trajectory and the reactive power prediction trajectory, under the conditions of minimizing voltage deviation and reactive power control increment, and satisfying the preset safe voltage range and equipment reactive power capacity constraints, to introduce an uncertainty envelope to construct a bundle robust optimization problem, and to solve the bundle robust optimization problem to obtain a reactive power control reference value; The uncertainty envelope determines the upper bound of the state deviation based on the joint uncertainty set, and performs constraint tightening processing on the safe voltage range and the reactive power capacity constraint of the equipment based on the upper bound of the state deviation, so that the actual evolution trajectory remains within the safe voltage range and the reactive power capacity constraint of the equipment under the disturbance corresponding to the joint uncertainty set; the instruction generation unit is used to perform feedforward delay correction on the reactive power control reference value based on the preset delay compensation gain and the communication delay estimate, so as to generate a reactive power control instruction, and send the reactive power control instruction to the voltage and reactive power regulation equipment corresponding to the distribution network node to be processed, so as to perform voltage and reactive power coordinated control.

[0016] Thirdly, the present invention provides an electronic device comprising: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the distribution network voltage reactive power robust predictive control method considering communication delay according to any embodiment of the present application.

[0017] Fourthly, the present invention provides a storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the robust predictive control method for voltage reactive power of a distribution network that takes into account communication delay, according to any embodiment of the present application.

[0018] Fifthly, the present invention provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of the robust predictive control method for reactive power distribution network voltage considering communication delay according to any embodiment of the present application.

[0019] The technical solution of the robust predictive control method and system for reactive power in power distribution networks that takes into account communication delay, as proposed in this invention, can produce at least the following technical effects: (1) By performing timestamp parsing and communication delay estimation on the neighbor node's operating data, and further using the communication delay estimate for time mapping alignment of the neighbor's operating data and delay embedding state estimation, the state variables involved in predictive control within the current control cycle can simultaneously reflect the local real-time operating state, the timing alignment state of neighbor nodes, and the dynamic delay characteristics of the communication link. As a result, when making voltage and reactive power regulation decisions, the controller no longer relies solely on local instantaneous measurements or uncorrected neighbor data, but can form an extended state expression that matches the current control cycle, improving the timing consistency and global correlation of state perception in distributed collaborative control, thereby providing a more accurate initial state basis for subsequent voltage trajectory prediction and reactive power control quantity optimization.

[0020] (2) The model prediction step size is adaptively adjusted based on the communication delay estimate, and combined with the power flow prediction model constructed based on the voltage-to-reactive-power sensitivity coefficient, the voltage prediction trajectory and reactive-power prediction trajectory in the prediction time domain are generated. At the same time, the local source-load prediction error set and the delay fluctuation set are combined into a joint uncertainty set, and a bundle robust optimization problem is constructed based on this joint uncertainty set. Thus, the predictive control process can not only reasonably plan the coverage of future state evolution according to the communication delay change, but also cope with the superimposed influence of source-load fluctuation and delay fluctuation on the actual trajectory during the optimization solution stage. Furthermore, by tightening the safety voltage range and equipment reactive capacity constraints based on the uncertainty envelope, the final reactive power control reference value can meet the nominal optimization objective while reserving sufficient safety margin for uncertain disturbances in actual operation, effectively improving the safety reliability and engineering feasibility of the voltage and reactive power control results.

[0021] (3) Through this technical solution, communication delay is transformed from an external, uncontrollable interference factor into a core control variable that can be estimated, embedded, predicted, and compensated. This enables the distribution network voltage and reactive power predictive control to form a complete closed-loop control link encompassing delay-aware state estimation, adaptive trajectory prediction, joint uncertainty robust optimization, and feedforward delay correction. With this control link, the timing matching between reactive power control commands and actual physical operating states can be significantly enhanced, effectively offsetting the state offset impact during the issuance and execution of control commands. Thus, in the distribution network operating environment characterized by rapid fluctuations in a high proportion of distributed energy resources and dynamic changes in communication network conditions, more timely, coordinated, and stable voltage and reactive power collaborative control can be achieved. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart is shown as an example of a robust predictive control method for voltage reactive power in a distribution network that takes into account communication delay, according to an embodiment of this application. Figure 2 A flowchart illustrating an example of determining the voltage prediction trajectory and reactive power prediction trajectory in the prediction time domain according to an embodiment of this application is shown. Figure 3 A flowchart illustrating an example of obtaining reactive power control reference values ​​by solving a robust optimization problem for a tube bundle according to an embodiment of this application is shown. Figure 4This illustration shows a schematic diagram of the system operation mechanism of an example of a robust predictive control method for voltage reactive power in a distribution network that takes into account communication delay, according to an embodiment of this application. Figure 5 A comparative experimental simulation diagram shows an example of voltage time-domain tracking and constraint protection using different methods under dynamic time delay abrupt changes and source load disturbances; Figure 6 A comparative experimental simulation diagram shows an example of the cumulative voltage deviation distribution under multiple random disturbances and time delays. Figure 7 A schematic diagram of the comparative experimental simulation results of different methods in evaluating system performance trade-offs and control costs is shown. Figure 8 A structural block diagram of an example of a robust predictive control system for voltage reactive power in a distribution network that takes into account communication delay, according to an embodiment of this application, is shown. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] With the increasing integration of flexible resources such as distributed photovoltaics, wind power, energy storage, and electric vehicles into distribution networks, the distribution network is gradually transforming from a traditional one-way power receiving network into a two-way interactive network between power sources and loads. Affected by fluctuations in renewable energy output, concentrated charging and discharging of electric vehicles, and changes in load timing, the voltage and power injection at distribution network nodes exhibit more pronounced time-varying, random, and spatial variability. To address these operational scenarios, relevant technologies have developed control systems such as VVC (Volt / VAR Control) and VVO (Volt / VAR Optimization). These systems typically improve node voltage distribution and reduce network losses by adjusting resources such as inverters, capacitor banks, on-load tap changers, and static var compensators.

[0026] To reduce the computational complexity of reactive power optimization in large-scale distribution networks, current technologies often employ network partitioning, regional autonomous control, or hierarchical coordinated control. For example, some methods divide the distribution network into regions based on static electrical distances, node voltage sensitivity, line impedance relationships, or typical operating sections, enabling coordinated regulation of reactive power resources within each region on a relatively independent scale. While these methods simplify the controlled objects and improve local regulation efficiency, their partitioning criteria and control weights typically reflect preset operating conditions or local electrical relationships, making it difficult to adapt promptly to continuous changes in distributed power output, electric vehicle charging and discharging loads, and the available capacity of controllable reactive power resources.

[0027] Regarding the flexible participation of resources in voltage regulation, current technologies incorporate EVs (Electric Vehicles), energy storage systems, and smart inverters into the distribution network voltage control process. For example, some EV / V2G (Vehicle-to-Grid) regulation methods alleviate local node voltage deviations through orderly charging and discharging or active-reactive power coordinated regulation; some MPC (Model Predictive Control) methods utilize short-term predictive information to optimize voltage deviations and equipment actions within a certain future time domain. Compared to traditional local control, these methods offer better foresight and coordination, but their control objectives are mostly focused on local voltage quality, equipment economy, or regional autonomy within the distribution network, with limited consideration given to the operational impact between networks of different voltage levels.

[0028] On the other hand, with the integration of a high proportion of power electronic equipment, distribution network voltage problems are no longer limited to steady-state voltage deviations, but may also manifest as short-term voltage fluctuations, uncoordinated control responses, and amplified dynamic disturbances under weakly damped operating conditions. To enhance dynamic voltage support capabilities, current technologies often employ STATCOM (Static Synchronous Compensator), SVG (Static Var Generator), smart inverters, and AVC (Automatic Voltage Control) systems to rapidly regulate the voltage of the PCC (Point of Common Coupling) or local critical nodes. While these devices can improve reactive power support capabilities and voltage recovery speed in local areas, their regulation process typically focuses on voltage control within the local substation, feeder, or distribution area. Their adaptability to changes in the operating status of a larger power grid remains limited by control boundaries and the scope of information acquisition.

[0029] Overall, existing voltage and reactive power control technologies for distribution networks have been able to play a role in local regulation, regional optimization, and rapid reactive power support. However, under complex operating conditions with a high proportion of distributed resources, the coordination difficulties between different control levels, different regulating devices, and different time scales continue to increase. Especially in scenarios with frequent source-load fluctuations, a high proportion of power electronic equipment, and enhanced interaction between the distribution network and the upper-level network, control methods relying solely on static zoning, local autonomy, or single-level optimization are insufficient to fully reflect the continuous impact of changes in operating conditions on voltage stability. Therefore, improving the adaptability and stability of distribution network voltage and reactive power control under complex source-load fluctuations and multi-device coordinated regulation conditions has become an important area of ​​ongoing focus in this field.

[0030] It should be understood that the above description of the relevant technologies is intended only to help the public better understand the inventive spirit and motivation of this application, and is not intended to limit this application. Furthermore, the technical solutions described in the above-mentioned relevant technologies are not prior art, and may also be undisclosed technical solutions, such as those under research or in the laboratory stage.

[0031] The technical solutions in this application, including the collection, storage, use, processing, transmission, provision, and disclosure of users' personal information, comply with relevant laws and regulations and do not violate public order and good morals.

[0032] Figure 1 A flowchart illustrating an example of a robust predictive control method for reactive power in distribution networks, considering communication delays, according to an embodiment of this application, is provided. This method can be applied to distribution network operation scenarios with a high proportion of distributed resource access, such as industrial park distribution networks, rural feeder distribution networks, or urban transformer distribution networks equipped with rooftop photovoltaic systems, electric vehicle charging stations, energy storage converters, smart inverters, static var generators, and conventional loads. In such scenarios, distributed photovoltaic systems may experience rapid power output fluctuations due to cloud cover, electric vehicles may be concentratedly charged or participate in orderly charging and discharging during evening peak hours, and energy storage and inverters may frequently participate in reactive power support, resulting in strong time-varying characteristics in node voltage and reactive power.

[0033] In some embodiments, the distribution network node to be processed can be a bus node in a feeder, a distributed photovoltaic grid-connected node, an energy storage access node, an electric vehicle charging station access node, a reactive power compensation device access node, or other nodes with voltage and reactive power regulation requirements. This distribution network node to be processed can be configured with a local controller, edge computing unit, distribution automation terminal, or station control device to collect local operating status, receive neighbor node status, perform predictive optimization calculations, and issue control commands to the corresponding voltage and reactive power regulation equipment. Neighbor nodes can be nodes that are electricalally adjacent to the distribution network node to be processed, related in the control area, or can directly interact in the communication topology.

[0034] In practical deployments, nodes can transmit operational data through information networks composed of fiber optic private networks, 4G / 5G private networks, wireless mesh, industrial Ethernet, or a combination of multiple communication methods. Due to varying degrees of queuing, congestion, jitter, packet loss and retransmission, or sampling asynchrony in communication links, the data received by the controller from neighboring nodes often does not strictly correspond to the current physical time. Therefore, this application embodiment incorporates communication delay estimation, state estimation, predictive control, and feedforward compensation into the same control closed loop, enabling distribution network nodes to achieve voltage and reactive power coordinated control under conditions of asynchronous communication and coexisting source-load disturbances.

[0035] like Figure 1 As shown, in step S110, the local real-time operation data and local source-load prediction data of the distribution network node to be processed in the current control cycle are obtained, and the neighbor operation data with timestamps sent by each neighbor node are received. Based on the timestamps and the receiving time of the neighbor operation data, the estimated communication delay between the node and each neighbor node is calculated, and the time mapping alignment processing of the neighbor operation data is performed according to the estimated communication delay to obtain the aligned neighbor operation data.

[0036] Here, local real-time operational data can include voltage amplitude, current, active power, reactive power, power factor, current output of reactive power regulation equipment, available equipment capacity, and equipment operating status of the distribution network nodes to be processed. Local source-load forecast data can include load forecasts for the next short timescale, distributed photovoltaic output forecasts, wind power output forecasts, energy storage charging and discharging plans, electric vehicle aggregated charging load forecasts, and user-side flexible load forecasts. For example, in a park distribution network that includes rooftop photovoltaics and electric vehicle charging piles, local source-load forecast data can include photovoltaic output curves, office building load forecast curves, and charging pile aggregated charging power forecast curves for the next control time domain.

[0037] Neighbor operational data can include voltage amplitude, active power, reactive power, equipment regulation status, available reactive power capacity, control reference values ​​generated by neighboring nodes, or other data reflecting the operational status of the neighborhood. To enable the receiving end to identify the generation time of the neighbor data, each neighboring node can carry a transmission timestamp based on a unified time reference in its data packets. This unified time reference can be provided by the clock synchronization mechanism of the distribution automation system, the station-area time synchronization mechanism, or other synchronization methods that meet the accuracy requirements of the control cycle.

[0038] At the receiving end, the distribution network node to be processed calculates an estimated communication delay between the corresponding neighbor node and the node itself, based on the transmission timestamp carried in the neighbor's operational data and the time it receives the neighbor's operational data locally. This estimated communication delay may differ for different neighbor nodes. For example, within the same control cycle, a photovoltaic inverter node closer to the controller may experience only a small communication delay, while a charging station node located at the end of the feeder may experience a larger communication delay due to wireless link congestion. By calculating the estimated communication delay link by link, the degree of lag in information from different neighbors can be characterized more precisely.

[0039] After obtaining the communication delay estimate, the distribution network node to be processed performs time mapping alignment processing on the neighbor's operating data based on this estimate. This time mapping alignment processing refers to converting neighbor operating data with different generation and arrival times to a unified time segment corresponding to the current control cycle. Specifically, based on locally maintained historical data caches, historical operating data of neighbor nodes, or short-term state prediction results, time-series compensation can be performed on lagging neighbor data to obtain aligned neighbor operating data. For example, when the voltage and reactive power data sent by a neighbor node lag behind the current control cycle, the controller can map it to an equivalent neighbor operating state that can be used for control calculations in the current control cycle, based on the recent state change trend of that neighbor node.

[0040] This avoids directly using raw, delayed data for collaborative control, reducing timing mismatches caused by multi-source asynchronous data. Especially when there are significant differences in communication delays among multiple neighboring nodes, it enables local nodes to use neighborhood states with relatively consistent time bases in subsequent control calculations, thereby improving the input quality for state estimation and prediction optimization.

[0041] In step S120, a delay embedding extended state vector containing communication delay estimates is constructed, and delay embedding state estimation is performed by fusing local real-time running data with aligned neighbor running data to obtain the current estimated state containing dynamic delay features.

[0042] In some implementations, the delayed embedding extended state vector can simultaneously include electrical state quantities and communication delay state quantities of the distribution network nodes. Electrical state quantities can include the voltage, reactive power, and equipment output status of the distribution network node to be processed; communication delay state quantities can be composed of estimated communication delays with neighboring nodes within the current control cycle, or delay characteristics formed by these delay estimates. Thus, when describing the current operating state, the system considers not only the voltage and reactive power states on the physical side of the power grid, but also the transmission lag states on the information side.

[0043] It should be noted that in the industrial park distribution network or the distribution network of a transformer substation, voltage fluctuations at certain nodes may be caused by changes in local load, or indirectly by reactive power regulation of nearby photovoltaic inverters or changes in the load of charging stations. If the controller only uses local voltage measurements for state estimation, it is difficult to reflect the impact of changes in neighboring nodes on the voltage of the local node; if neighbor data without time delay processing is used directly, outdated information may be introduced. Therefore, this embodiment fuses local real-time operating data with aligned neighbor operating data and embeds the communication delay estimate into the state representation, so that the current estimated state can reflect the combined effects of local operating state, neighborhood coupling state, and communication delay state.

[0044] For example, delayed embedded state estimation can be implemented based on a distribution network state evolution model and a measurement model. The state evolution model describes the trends of node voltage, reactive power, and related state quantities as a function of the control cycle; the measurement model describes the correspondence between local measurement data, neighborhood measurement characteristics, and extended states. Through state deduction and measurement correction, the current estimated state can be obtained even in the presence of measurement noise, communication delay, and lag in neighboring data. For instance, when a neighboring node experiences short-term communication congestion, the state estimation process can utilize aligned neighboring data, local real-time measurements, and delay characteristics to jointly correct the state estimation result, preventing the controller from over-adjusting due to a single abnormal data point.

[0045] In step S130, the model prediction step size is adaptively adjusted based on the communication delay estimate. Using the current estimated state, local source-load prediction data, and aligned neighbor operating data, the power flow prediction model generates the voltage and reactive power prediction trajectories for the future prediction time domain, determined by the model prediction step size. Here, the power flow prediction model is constructed based on the voltage-reactive power sensitivity coefficient to characterize the dynamic evolution of node voltage with local reactive power control increments, neighbor operating states, and source-load changes.

[0046] It should be noted that in model predictive control, the prediction step size determines the time range for the controller to observe the future. If communication is good and neighbor node data arrives in a timely manner, a longer prediction time domain allows the controller to identify the impact of changes in photovoltaic output, increased electric vehicle load, or changes in energy storage plans on voltage in advance, and generate a smoother reactive power regulation strategy. If communication delay increases significantly, long-term predictions will rely more on lagging neighbor data and uncertain states, and the prediction reliability will decrease. Therefore, this embodiment adaptively adjusts the model prediction step size based on the communication delay estimate, enabling the controller to maintain strong foresight when communication quality is good, and appropriately shrink the prediction time domain when communication quality deteriorates, in order to reduce the impact of unreliable long-term information on current control decisions.

[0047] For example, under normal communication conditions, the controller can plan ahead for changes in inverter reactive power output based on a longer prediction time domain to smoothly cope with the increase in electric vehicle load during the evening peak. However, when local communication links are congested, the controller can shorten the prediction time domain, focusing on ensuring voltage safety within the near-end control cycle and avoiding over-adjustment based on unreliable distant neighbor information. In this way, the model prediction step size can adapt to the current communication health status, achieving a balance between real-time performance and foresight in predictive control.

[0048] In terms of predictive trajectory generation, power flow prediction models can be constructed based on the voltage sensitivity coefficient to reactive power. This sensitivity coefficient characterizes the degree of impact of reactive power changes on node voltage. During the prediction process, the current estimated state serves as the starting state for forward rolling extrapolation. Local source-load prediction data is used to provide future load and distributed generation trends, while aligned neighbor operating data reflects the impact of neighboring node states on the local node voltage. The power flow prediction model can incorporate local reactive power control increments, neighbor operating state changes, and source-load changes into the voltage evolution relationship to generate a voltage prediction trajectory in the prediction time domain.

[0049] Meanwhile, the reactive power prediction trajectory is used to reflect the potential output state of the reactive power regulation equipment in each future control step. By simultaneously generating voltage and reactive power prediction trajectories, the controller can determine in subsequent optimization stages whether a certain reactive power regulation strategy will lead to voltage over-limit risks, equipment capacity saturation risks, or excessive reactive power changes. This not only improves the controller's ability to perceive future voltage change trends but also provides a calculable predictive basis for subsequent robust optimization of the control system.

[0050] In step S140, a local source load prediction error set is determined based on local source load prediction data, and a time delay fluctuation set is determined based on the change of communication delay estimate in adjacent control cycles. The local source load prediction error set and the time delay fluctuation set are combined into a joint uncertainty set.

[0051] It should be noted that while local source-load forecast data can reflect future operating trends, it inevitably contains forecast errors. For example, rooftop photovoltaic systems may experience a short-term drop in output when clouds rapidly obscure the sky; electric vehicle charging loads may deviate from the plan due to random user connections; and energy storage devices may change their charging and discharging behavior due to upper-level scheduling strategies or local state constraints. Therefore, a set of local source-load forecast errors can be determined based on historical forecast error statistics, forecast model confidence intervals, operating scenario boundaries, or preset safety margins. This set describes the range within which the source-load power may deviate from the nominal forecast value in the future forecast time domain.

[0052] On the other hand, communication latency itself also exhibits dynamic uncertainty. For example, during normal operation, neighbor node state packets may arrive relatively quickly; however, when a large amount of charging pile status data is uploaded centrally, the wireless link is interfered with, or the network forwarding path changes, latency may fluctuate significantly between adjacent control cycles. Based on the changes in the estimated communication latency within adjacent control cycles, a latency fluctuation set can be determined to characterize the range by which the communication latency in the future control time domain may deviate from the current estimate. This latency fluctuation set reflects information-side uncertainty, which affects the temporal position of neighbor states in the prediction model and the actual effective time of control commands.

[0053] By combining the local source-load prediction error set and the delay fluctuation set into a joint uncertainty set, this embodiment can simultaneously consider physical-side source-load disturbances and information-side communication disturbances under a unified disturbance boundary. In other words, the controller, in subsequent optimization, does not only consider a single factor such as "potential deviation in photovoltaic output" or "potential change in communication delay," but rather the combined impact of the two on voltage and reactive power control. For example, in scenarios where photovoltaic output drops sharply and neighbor node information transmission delays increase, the joint uncertainty set can provide a disturbance boundary that more closely reflects actual operational risks for robust optimization. This provides a clear uncertainty description for robust optimization, enabling subsequent control strategies to reserve control margins for source-load prediction errors and communication delay fluctuations, thereby enhancing the robustness of the control strategy under complex operating conditions.

[0054] In step S150, combining the voltage prediction trajectory and the reactive power prediction trajectory, under the conditions of minimizing voltage deviation and reactive power control increment, and satisfying the preset safe voltage range and equipment reactive power capacity constraints, an uncertainty envelope is introduced to construct a robust optimization problem for the tube bundle, and the robust optimization problem for the tube bundle is solved to obtain the reactive power control reference value.

[0055] Here, the uncertainty envelope determines the upper bound of the state deviation based on the joint uncertainty set, and performs constraint tightening processing on the safe voltage range and equipment reactive capacity constraints based on the upper bound of the state deviation, so that the actual evolution trajectory remains within the safe voltage range and equipment reactive capacity constraints under the disturbance effect corresponding to the joint uncertainty set.

[0056] In some implementations, the generated voltage prediction trajectory and reactive power prediction trajectory can be used as nominal prediction trajectories. The nominal prediction trajectory describes the future operating state of the system under nominal source load prediction and current communication delay estimation conditions. However, in actual operation, source load prediction errors and delay fluctuations can cause the actual operating trajectory to deviate from the nominal prediction trajectory. Therefore, this embodiment constructs an uncertainty envelope based on a joint uncertainty set to describe the possible deviation range of the actual trajectory relative to the nominal prediction trajectory, and determines the upper bound of the state deviation accordingly.

[0057] Subsequently, constraint tightening can be applied to the safe voltage range and equipment reactive power capacity constraints based on the upper bound of the state deviation. Taking voltage constraints as an example, if the distribution network operation procedures require node voltages to remain within a preset safe range, the feasible voltage range can be tightened inward during nominal optimization to reserve margin for absorbing the effects of source load errors and time delay fluctuations. For reactive power capacity constraints, adjustment margins can also be reserved within the upper and lower limits of equipment physical output to avoid the nominal control strategy from approaching the equipment boundary excessively. The above constraint tightening does not change the physical capabilities of the equipment itself, but rather applies a more conservative safety boundary to the nominal trajectory at the optimization level, ensuring that the actual trajectory still has a margin within the original safety constraints under disturbances.

[0058] Within the tightened feasible range, the robust optimization problem of the control bundle can be solved with the objectives of minimizing voltage deviation and reactive power control increment. The voltage deviation objective aims to make the node voltage in the prediction time domain as close as possible to the reference level, while the reactive power control increment objective aims to reduce equipment stress and voltage oscillation risks caused by excessive, rapid, or frequent control actions. By solving the optimization problem under the condition of considering the uncertainty envelope, the reactive power control reference value for the current control cycle can be obtained. This reactive power control reference value is not a control quantity obtained only for a single nominal scenario, but a robust control reference generated after considering the source load error and time delay fluctuation disturbance boundary.

[0059] For example, within a certain control cycle, if it is predicted that a local decrease in photovoltaic output may cause a voltage drop, and communication delay fluctuations may lead to a lag in reactive power support information from neighboring nodes, then the constraint robust optimization will select a reactive power reference value with a certain safety margin within the feasible region after the constraints are tightened. In this way, even if the actual photovoltaic output is lower than the predicted value or the neighbor information arrives with a further lag, the actual voltage trajectory is more likely to remain within the original safety constraints, thereby reducing the risks of voltage exceeding limits, reactive power equipment saturation, and control oscillations.

[0060] In step S160, based on the preset time delay compensation gain and communication time delay estimate, the reactive power control reference value is fed forward time delay correction to generate a reactive power control command, and the reactive power control command is sent to the voltage and reactive power regulation equipment corresponding to the distribution network node to be processed to perform voltage and reactive power coordinated control.

[0061] In some implementations, the output reactive power control reference value is a target value calculated by the controller within the current control cycle. However, when this target value is sent from the controller to the smart inverter, energy storage converter, static var generator, static var compensator, or other voltage and reactive power regulation equipment, and actually applied to the distribution network, it may still experience downlink communication delays and equipment response processes. If the lag in this execution link is not considered, the voltage state when the control command actually takes effect may differ from the calculation time, resulting in delayed, over-compensated, or under-compensated reactive power regulation actions.

[0062] Therefore, this embodiment performs feedforward delay correction on the reactive power control reference value based on the estimated communication delay and a preset delay compensation gain. Feedforward delay correction can appropriately compensate for the reactive power control reference value in advance, based on the changing trend of the reactive power control reference value, the magnitude of the communication delay, and the response characteristics of the corresponding voltage reactive power regulation equipment. This makes the final generated reactive power control command closer to the control quantity required when it actually arrives and acts on the equipment. For example, when the reactive power control reference value shows a continuous upward trend and the downlink communication delay is large, the feedforward delay correction can appropriately increase the pre-compensation component in the issued command to reduce the regulation lag after the command arrives; when the communication delay is small or the reference value changes relatively smoothly, the feedforward correction amplitude can be reduced accordingly to avoid unnecessary control overshoot.

[0063] After generating a reactive power control command, the distribution network node to be processed sends the command to the corresponding voltage and reactive power regulation equipment. For photovoltaic smart inverters, the command can be used to adjust their reactive power output; for energy storage converters, it can be used to change their reactive power support status; for static var generators or static var compensators, it can be used to quickly provide or absorb reactive power. By executing the reactive power control command through these devices, voltage and reactive power coordinated control is achieved within the distribution network node to be processed and its surrounding area.

[0064] The embodiments of this application establish a closed-loop control process consisting of data acquisition, delay estimation, data alignment, delay embedding state estimation, adaptive prediction, joint uncertainty modeling, constraint robust optimization, and feedforward compensation execution. This process can improve the state perception accuracy, prediction reliability, constraint safety, and execution timeliness of distribution network voltage and reactive power control under conditions of communication delay, link jitter, source load prediction errors, and equipment capacity constraints. It is particularly suitable for distribution network operation scenarios with high requirements for real-time voltage regulation and robustness under high proportion of distributed resource access.

[0065] Regarding the implementation details of the data acquisition operation in step S110, in some examples of the embodiments of this application, in the actual operation of a distributed distribution network, if each node adopts a fixed-period time-triggered communication method, that is, forcibly broadcasts local operating data in each communication cycle, a large amount of repetitive state data transmission is likely to occur in scenarios with a large number of nodes, limited communication link carrying capacity, or large fluctuations in wireless link quality. For example, in a park distribution network including rooftop photovoltaics, energy storage converters, and electric vehicle charging piles, some nodes have small changes in voltage and reactive power over a period of time. If periodic broadcasting continues, it will occupy a lot of communication bandwidth and may increase the queuing time for critical state update data packets. To reduce the impact of redundant communication on link latency, the embodiments of this application can adopt an asynchronous event-triggered communication method based on local state fluctuations in the data acquisition stage.

[0066] Specifically, in each control cycle Extract the real-time voltage measurement value of the node at the current moment. With reactive power output value And retrieve the voltage record value cached locally when the communication broadcast was last successfully triggered. With reactive power recording value The voltage and reactive power records are used to characterize the local state baseline of the node when it last broadcast to neighboring nodes. By comparing the current measurement value with the last broadcast record value, it can be determined whether the voltage and reactive power state of the local node has changed in a way that is sufficient to affect the neighborhood coordinated control.

[0067] Then, the absolute deviation between the measured value at the current moment and the cached recorded value are calculated respectively, and the absolute voltage deviation and absolute reactive power deviation are linearly weighted by the preset voltage deviation normalization weight coefficient and reactive power deviation normalization weight coefficient to construct an event-triggered evaluation function based on local state fluctuations.

[0068] For example, an event-triggered evaluation function It can be expressed by the following formula: Equation (1); In the formula, This represents the event trigger evaluation value of the distribution network node to be processed in the current control cycle. This represents the real-time voltage measurement value of the node at the current moment. This represents the reactive power output value at the current moment. This represents the voltage record value cached when the communication broadcast was last successfully triggered. This represents the reactive power record value cached when the communication broadcast was last successfully triggered. Indicates the voltage normalization reference. Indicates the reactive power normalization benchmark. and These represent the preset voltage deviation normalization weighting coefficient and reactive power deviation normalization weighting coefficient, respectively. The voltage normalization reference can be the node rated voltage, the per-unit reference voltage, or a preset voltage scale value; the reactive power normalization reference can be the rated reactive power capacity of the corresponding voltage reactive power regulation equipment, the node reactive power reference value, or a preset reactive power scale value. Through the above normalization process, the unreasonable dominance of large reactive power values ​​on the event trigger evaluation results can be avoided.

[0069] In some implementations, if the voltage measurement value and reactive power output value have been pre-converted to per-unit values ​​or have undergone dimensionless processing, the above event-triggered evaluation function can also be simplified as follows: Equation (2); To ensure that the event-triggered evaluation value reflects the relative importance of voltage deviation and reactive power deviation, the normalized weighting coefficients for voltage deviation and reactive power deviation can satisfy the following constraints: Equation (3); The above constraints indicate that voltage deviation and reactive power deviation participate in the judgment according to a preset ratio in the event-triggered evaluation function. For feeder ends, weak voltage nodes, or nodes with a high risk of voltage exceeding limits, the constraints can be appropriately increased. The value of makes it easier for this type of node to trigger state update broadcasts when there is a significant voltage shift; for nodes where changes in reactive power regulation have a significant impact on the neighborhood voltage, the value can be appropriately increased. The value of allows changes in reactive power output to be perceived by neighboring nodes more promptly.

[0070] Afterwards, the event-triggered evaluation function is obtained. Subsequently, the evaluation function is triggered by the event judgment of the distribution network node to be processed. Is it greater than the preset comprehensive trigger threshold? This comprehensive trigger threshold is used to define the boundary for determining whether a change in local state needs to trigger a communication broadcast.

[0071] On the one hand, if it exceeds the comprehensive trigger threshold, i.e. Then, the local running data carrying the sending timestamp generated based on a unified time base will be encapsulated to generate a status update packet, and asynchronously broadcast to the topology neighbor nodes. At the same time, the measurement data at the current moment will be synchronously updated to the locally cached record data.

[0072] It should be noted that, This indicates that the voltage or reactive power of the local node has changed significantly compared to the previous broadcast state within the current control cycle. At this time, the distribution network node to be processed encapsulates its local operating data, including the transmission timestamp generated based on a unified time base, into a status update packet and asynchronously broadcasts it to its topology neighbors. The status update packet may include the node identifier, transmission timestamp, current voltage measurement value, current active power value, current reactive power output value, available equipment capacity, current control input, or other data used for neighborhood collaborative control. After broadcasting, the distribution network node to be processed updates its current voltage measurement value and reactive power output value to the new recorded voltage and reactive power values. and This serves as the local cache benchmark for determining the event trigger in the next control cycle.

[0073] On the other hand, if it is not greater than the comprehensive trigger threshold, i.e. If the local state fluctuation is within the preset silent range, then the communication at the sending end will remain silent.

[0074] It should be noted that, This indicates that the local state has changed little compared to the previous broadcast state within the current control cycle. The distribution network node to be processed can determine that the local state fluctuation is within a preset quiet range and maintain silent communication at the sending end. In this case, the node does not send new state update packets to neighboring nodes, thereby reducing repeated broadcasts when voltage and reactive power changes are small. Through this process, nodes with small state changes can reduce their occupation of communication links, while nodes with significant state changes can promptly send updated data to neighboring nodes, thus reducing the communication load caused by large-scale simultaneous periodic broadcasts.

[0075] Furthermore, if the distribution network node to be processed does not receive a new state update packet from its first neighbor node within the current control cycle, the aligned state corresponding to the first neighbor node at the last valid communication time is extracted as the initial value for deduction. This is then extrapolated using an open-loop time step based on the locally maintained power flow prediction model to generate a corresponding rolling state estimate. This rolling state estimate is used as the completed neighbor operating data, which can be input into the delayed embedded state estimation stage to maintain the temporal continuity of the system control calculation process. In this way, the temporal continuity of the neighbor operating data sequence can be maintained under asynchronous communication conditions, while avoiding long-term complete reliance on failed data.

[0076] For example, open-loop time step extrapolation can be expressed in the following recursive form: Equation (4); In the formula, Indicates the current control cycle generated neighbor nodes The estimated value of the rolling state, Indicates the neighboring node corresponding to the previous control cycle. The estimated state value. At the initial missing time, It can be determined by the alignment state corresponding to the last valid communication time of the neighboring node. Representing neighboring nodes The control input carried during the last valid broadcast or that can be obtained from the local cache. This represents the mapping function of the locally maintained power flow prediction model. This power flow prediction model can be established based on node voltage, power injection, reactive power regulation, and neighborhood electrical relationships, and is used to extrapolate short-term trends in the states of neighboring nodes in the absence of current measurement feedback.

[0077] Rolling state estimate generated by open-loop time step extrapolation This supplemented neighbor operational data can be used as input to the delayed embedded state estimation process. Through this process, even if some neighbor nodes do not send new state update packets in the current control cycle, the distribution network node to be processed can still obtain neighborhood state inputs usable for current control calculations, thus avoiding incomplete state estimation inputs due to missing neighbor data. This supplemented neighbor operational data does not replace the priority of valid communication data; when new valid communication data arrives, the time-mapped and aligned real neighbor operational data is still used as the priority input.

[0078] Through the above implementation methods, the distribution network nodes under processing can adaptively decide whether to broadcast data based on the degree of local voltage and reactive power state changes, reducing redundant communication transmissions when state changes are small, and enabling nodes with significant state changes to send update information in a timely manner. Simultaneously, in the absence of current state update packets from neighboring nodes, rolling state estimates can be generated using the last effective alignment state of the neighboring node, the last known control input, and the power flow prediction model to supplement the neighboring operational data required for the current control cycle. Therefore, while reducing communication load, this improves the adaptive capability and timing consistency of the distributed system in complex information environments such as asynchronous communication, link jitter, and short-term data loss.

[0079] Regarding the implementation details of the time mapping and alignment processing of data in step S110, in some examples of the embodiments of this application, the local controller typically performs state sampling, prediction calculation, and control command generation according to a fixed discrete sampling period. However, the transmission delay of neighbor node data packets in the underlying communication network is usually a continuous time quantity and may change due to network congestion, link jitter, or data queuing. If randomly arriving neighbor running data is directly input into the discrete controller, the physical time corresponding to the neighbor data may be inconsistent with the current control period, resulting in a misalignment of the neighborhood state on the time axis. Therefore, the embodiments of this application can convert the neighbor running data into an aligned state usable in the current control period through continuous delay calculation, discrete sampling mapping, and data interpolation alignment.

[0080] First, for each neighbor node, the transmission timestamp generated based on a unified time base is extracted from the received neighbor operation data. Combined with the reception time of the neighbor operation data, the continuous-time communication delay is calculated. The transmission timestamp can be generated based on a unified time base, such as through distribution automation system time synchronization, IEEE 1588 precision clock synchronization, satellite time synchronization, or other clock synchronization methods that meet control accuracy requirements. For example, the continuous-time communication delay can be expressed as: Equation (5); In the formula, Indicates the distribution network node to be processed. With the The continuous time communication delay between neighboring nodes This indicates the time when the neighbor operation data recorded by the distribution network node to be processed was received. This represents the transmission timestamp carried in the neighbor's operational data. Through the above calculation, the transmission time from sending to receiving the neighbor's operational data can be obtained in the continuous time domain, providing a time basis for data mapping in subsequent discrete control cycles.

[0081] Then, based on the discrete sampling period of the distribution network control system The continuous-time communication delay is normalized and mapped to a communication delay estimate. The communication delay estimate is decomposed into integer delay steps and fractional delay weights.

[0082] For example, it can be represented as: Equation (6); Equation (7); Equation (8); In the formula, This represents the normalized communication delay estimate. Represents the integer delay steps. Indicates the score delay weight. This indicates rounding down to the nearest integer. Because... The number of complete sampling periods that characterize the lag of neighbor data relative to the current control period, while Characterizing the degree of offset between adjacent discrete sampling points, the above decomposition can convert continuous communication delay into a time index and interpolation weight that can be handled by the discrete control system.

[0083] Next, determine the estimated communication delay value. Is it less than the preset effective delay threshold? .in, A sampling step threshold with the same scale as the normalized communication delay estimate can be used to characterize the maximum information lag range that the system is allowed to perform alignment processing using interpolation.

[0084] On the one hand, if the estimated communication delay is less than the effective delay threshold, i.e. This indicates that the lag in the current neighbor's operational data is within an acceptable range, and interpolation alignment can be performed based on the locally maintained sliding historical data cache queue. Specifically, the distribution network node to be processed can extract the integer delay steps from the locally maintained sliding historical data cache queue. The historical neighbor operation data of two adjacent historical control cycles are used, and fractional delay weights are applied. A dynamic window interpolation algorithm is performed on the running data of two adjacent historical neighbors to calculate the current control cycle. Aligned neighbor running data .

[0085] For example, the neighbor runs data It can be expressed by the following formula: Equation (9); In the formula, Indicates the current control cycle The corresponding aligned neighbor running data, This indicates a backward offset in the sliding history data cache queue. Historical neighbor running data for each discrete sampling period Indicates backward offset The historical neighbor running data for each discrete sampling period. The meaning of the above interpolation process is that when the actual data generation time corresponding to the continuous delay is between two adjacent discrete sampling points, a weighted reconstruction can be performed between adjacent historical states based on the fractional delay weight, thereby obtaining a neighbor state estimate that is closer to the continuous generation time.

[0086] In some implementations, neighbor operating data may include one or more state variables such as voltage, active power, reactive power, control reference values, or equipment status. When the neighbor operating data is a multi-dimensional vector, the aforementioned time mapping alignment processing can be performed on each state variable in the multi-dimensional vector separately, or interpolation operations can be performed uniformly on the entire state vector. Through the above processing methods, data from different neighbor nodes can have a more consistent time reference when entering the controller, reducing cross-cycle deviations caused by the mismatch between continuous time delay and discrete sampling period.

[0087] On the other hand, if it is not less than the effective delay threshold, i.e. If the corresponding communication link is in a timeout state, the zero-order hold strategy is triggered. The most recent reliable historical neighbor running data that satisfies the delay being less than the effective delay threshold is extracted from the sliding historical data cache queue and used as the aligned neighbor running data for the current control cycle.

[0088] For example, it can be set For the current control cycle The most recent time I was satisfied The effective communication period, and For the reliable aligned neighbor running data corresponding to this valid communication period, it can be represented as follows in the timeout state: Equation (10); in, This represents the aligned neighbor operating data obtained using the zero-order hold strategy in the current control cycle. In equation (10), when the current neighbor data exceeds the effective delay range, the controller no longer uses this timed-out data for interpolation reconstruction, but instead maintains the most recent reliable alignment state. This reduces the impact of severely delayed data on the current control calculation and ensures that the neighbor operating data remains basically continuous during communication anomalies.

[0089] In some implementations, if the communication link is in a timeout state for a long time, the data reliability of the neighboring node can be marked by combining a preset timeout count threshold, and the weight of the neighboring node's running data in the state estimation or prediction calculation can be reduced when the data reliability is low. When neighbor running data that meets the effective delay threshold condition is received again, the time mapping alignment process can be performed again and the reliable alignment state can be updated, which can provide different levels of data protection between short-term jitter and long-term anomalies in the communication link.

[0090] Through the embodiments of this application, the distribution network node to be processed can accurately convert continuous-time communication delay into integer delay steps and fractional delay weights within a discrete control cycle, and perform time mapping alignment on neighbor operating data based on this decomposition result. When the communication delay is within an effective range, dynamic window interpolation can significantly improve the alignment accuracy of neighbor data on the discrete control time axis and reduce sub-cycle errors; when the communication delay exceeds the effective range, the zero-order hold strategy combined with the credibility marking mechanism can effectively suppress severely lagging data from entering the control calculation. Thus, the timing misalignment of neighbor states caused by asynchronous communication and random transmission delays is eliminated from the bottom layer, improving the availability, consistency, and overall system anti-disturbance stability of the neighborhood operating data within the current control cycle.

[0091] Regarding the implementation details of estimating the current estimated state containing dynamic delay characteristics in step S120, in actual distribution network control systems, the neighbor operating data received by the distribution network nodes to be processed may have varying degrees of communication lag. If the state estimation process only processes electrical quantities such as node voltage and reactive power, without considering the impact of communication delay on data timing, the state estimation result is prone to deviating from the actual operating state corresponding to the current control cycle. Therefore, in some examples of embodiments of this application, the communication delay estimate is incorporated as extended state information into the state estimation process to improve the ability of the current estimated state to jointly represent the electrical state and the information transmission state.

[0092] First, for the distribution network nodes to be processed The estimated communication delays between each neighboring node are combined into a delay feature vector. For example, when the distribution network node to be processed... When there are multiple neighboring nodes, the delay feature vector can be composed of the estimated communication delay of each neighboring link in the current control cycle, which is used to describe the overall delay status of the node receiving neighborhood information in the current control cycle.

[0093] Meanwhile, based on the time delay feature vector Given a defined equivalent delay step number, extract the delayed reactive power output value corresponding to that equivalent delay step number from the local historical control cache. This is used to construct a system containing real-time voltage measurements of nodes. Delayed reactive power output value and time delay feature vector Delayed embedding extended state vector Delayed reactive power output value This is used to characterize the reactive power output that actually participates in the state evolution under the influence of communication delay.

[0094] Based on the above information, a system containing real-time node voltage measurements can be constructed. Delayed reactive power output value and time delay feature vector The delayed embedding extended state vector. For example, the delayed embedding extended state vector can be represented as: , Equation (11); In the formula, Indicates the distribution network node to be processed. In the current control cycle The delayed embedding extended state vector, This represents the real-time voltage measurement value of the node. This represents the delayed reactive power output value extracted based on the equivalent delay steps. This represents the communication delay feature vector. Through the extended state vector described above, the state estimation process can simultaneously utilize electrical quantities and communication delay quantities, enabling the impact of communication lag on reactive power output state and neighborhood information timing to be incorporated into a unified state space description.

[0095] Then, based on the nonlinear system state transition function considering time delay characteristics The prior state estimate for the current control cycle is calculated using the posterior state estimate from the previous control cycle and the reactive power control input variable. Next, combining the preset system process noise covariance matrix and the time-delay-aware state transition Jacobian matrix obtained by taking the partial derivative with respect to the time delay state, the prior error covariance matrix is ​​calculated. .

[0096] In some embodiments, the state transition function of a nonlinear system It can be constructed based on the power flow relationship of the distribution network, the reactive power regulation response of the nodes, the communication delay state changes, and the impact of local control input on the node state, and is used to describe the evolution relationship of the extended state vector between adjacent control cycles.

[0097] For example, the prior state estimate can be calculated using the following formula: Equation (12); In the formula, Indicates the current control cycle The prior state estimate, Indicates the previous control cycle The posterior state estimate, This represents the reactive power control input variable from the previous control cycle. (In the formula...) This indicates that the zero-mean process noise assumption is adopted when extrapolating the prior state, that is, the mean of the process noise is zero, and its uncertainty is characterized by the system process noise covariance matrix.

[0098] Simultaneously with prior state estimation, the prior error covariance matrix of the current control cycle can be calculated. Therefore, we first calculate the delay-aware state transition Jacobian matrix, which includes the component with respect to the partial derivative with respect to the delay state. And combined with the posterior error covariance matrix of the previous control cycle and the preset system process noise covariance matrix This yields the prior error covariance matrix. For example, it can be represented as: Equation (13); , Equation (14); In the formula, This represents the prior error covariance matrix of the current control cycle. This represents the posterior error covariance matrix of the previous control cycle. Represents the system process noise covariance matrix. This represents the state transition Jacobian matrix calculated at the previous posterior state estimate and the previous reactive power control input variable. Since the extended state vector contains a time delay eigenvector, the state transition Jacobian matrix can include partial derivative terms related to the time delay state, thus enabling error covariance propagation to reflect the impact of communication delay variations on the uncertainty of the state estimate.

[0099] Next, the measurement Jacobian matrix that maps the extended state space to the observation space is calculated. And combined with the preset measurement noise covariance matrix and prior error covariance matrix Calculate the Kalman gain matrix .

[0100] For example, measuring the Jacobian matrix and Kalman gain matrix It can be calculated using the following formula: Equation (15); , Equation (16); In the formula, Represents the measurement function. The measurement Jacobian matrix represents the measurement of the current control cycle. Represents the measurement noise covariance matrix. This represents the Kalman gain matrix. The measurement function can be used to describe the correspondence between local real-time running data, aligned neighbor running data, and their neighborhood measurement features, and the delayed embedding extended state vector. Through the above Kalman gain calculation, the degree of influence of measurement residuals on state correction can be determined based on prior estimation uncertainty and measurement uncertainty.

[0101] Furthermore, the local real-time operational data is combined with the neighborhood measurement features extracted from the aligned neighbor operational data to construct the actual measurement vector. Using the Kalman gain matrix for actual measurement vectors The difference between the measured state and the predicted output of the measurement function is used to perform residual correction measurement updates to output the current estimated state. The posterior error covariance matrix is ​​updated synchronously for use in the next control cycle iteration.

[0102] Here, local real-time operational data can include local measurement information such as node real-time voltage and reactive power output; neighborhood measurement features can include neighbor node voltage, neighbor node reactive power, neighborhood power changes, or other coupling state information extracted from aligned neighbor operational data. Based on actual measurement vectors Measurement function Predicted output and Kalman gain matrix in the prior state It can perform residual correction measurement updates to obtain the posterior state estimate for the current control cycle.

[0103] For example, the current estimated state It can be obtained through the following formula: , Equation (17); Meanwhile, the posterior error covariance matrix It can be updated using the following formula: Equation (18); In the formula, This represents the posterior state estimate of the current control cycle, which is the current estimated state in this embodiment that includes dynamic delay characteristics; This represents the measurement residual between the actual measurement vector and the predicted measurement output; This represents the identity matrix. Through measurement residual correction, the current estimated state can simultaneously incorporate local real-time measurement information and aligned neighborhood measurement information, and reflect the impact of communication delay on state evolution and state uncertainty during the estimation process.

[0104] In some implementations, when the communication link is stable and measurement noise is low, the corrective effect of the actual measurement vector on the state update can be relatively enhanced. When measurement noise is high or the reliability of some neighborhood data decreases, the state estimation process can rely more on the prior deduction results provided by the system state transition function. This processing can obtain a relatively smooth and time-consistent current estimated state when measurement noise, neighbor data lag, and communication delay fluctuations coexist.

[0105] Through the embodiments of this application, the distribution network node to be processed can simultaneously characterize node voltage, delayed reactive power output, and communication delay characteristics in the extended state vector, and accurately obtain the current estimated state using a closed-loop mechanism of prior state deduction and multi-source measurement residual correction. This processing abandons the traditional approach of treating delay as merely an external interference, bridging the discrepancy between asynchronous delay and physical evolution from an internal dynamic mechanism perspective. This allows the current estimated state to not only filter out random measurement noise, but also to sensitively perceive and smooth communication link delay jitter. At the same time, the nonlinear recursion of error covariance fully quantifies the uncertainty of state estimation, providing a high-confidence, high-time-fidelity global state foundation for the system in complex and harsh communication-physical fusion environments.

[0106] Figure 2 A flowchart illustrating an example of determining the voltage prediction trajectory and reactive power prediction trajectory in the prediction time domain according to an embodiment of this application is shown.

[0107] like Figure 2 As shown, in step S210, the estimated historical communication delay of the distribution network node to be processed within the past preset time window is obtained, and the smoothed average delay is calculated by moving average filtering.

[0108] It should be noted that in actual power distribution network communication networks, data transmission between nodes may be achieved through dedicated fiber optic networks, 4G / 5G, or power wireless networks. Communication latency is usually not a fixed value but fluctuates with network load, link quality, and packet queuing. If the instantaneous communication latency estimate of the current control cycle is directly used to adjust the model prediction step size, the prediction step size may change frequently in adjacent control cycles, thus affecting the smoothness of the prediction trajectory. Therefore, the embodiments of this application can perform a moving average filter on the historical communication latency estimates within a preset time window to obtain a smooth average latency that reflects the recent trend of communication link status changes.

[0109] In some implementations, the node-level equivalent communication delay estimate of the distribution network node to be processed in the current control cycle can be determined first based on the estimated communication delay between the node to be processed and each of its neighboring nodes. The node-level equivalent communication delay estimate can be determined based on the average, maximum, weighted average, or preset aggregation rule of the communication delays of each neighboring link. Subsequently, a smoothed average delay is calculated based on the node-level equivalent communication delay estimates within a preset time window. For example, the smoothed average delay... It can be calculated using the following formula: , Equation (19); In the formula, Indicates the distribution network node to be processed. In the current control cycle Smooth average delay, Indicates the preset sliding window length. Indicates the distribution network node to be processed. In the past The node-level equivalent communication delay estimate corresponding to each control cycle. Through the above moving average filtering process, the impact of occasional communication glitches on the prediction step size adjustment can be reduced, so that the prediction step size is mainly adjusted according to the continuous change trend of the communication state.

[0110] In step S220, based on the nominal prediction step size under ideal communication conditions, the model prediction step size of the current control cycle is dynamically adjusted according to the smoothed average time delay using a negative exponential decay penalty mechanism, and lower limit boundary protection is performed in combination with the minimum prediction step size to maintain robust and stable operation of the system.

[0111] In model predictive control, the prediction step size is used to determine the time range from the current control cycle to the future. A longer prediction step size is beneficial for identifying the impact of source load changes on voltage in advance. However, when the communication delay is large, long-term predictions will rely more on lagging neighbor information, which may increase the uncertainty of the prediction results. Therefore, the embodiments of this application adaptively adjust the model prediction step size based on the smoothed average delay, so that the prediction time domain can change with the communication status.

[0112] For example, the model prediction step size It can be determined by the following formula: Equation (20); In the formula, Indicates the distribution network node to be processed. In the current control cycle The model predicts the step size. This represents the nominal prediction step size under ideal communication conditions. This indicates the preset minimum prediction step size. This indicates the preset time delay sensitivity adjustment coefficient. This indicates rounding down to the nearest integer. If The time delay is the normalized value based on the discrete sampling period. It can be set as a dimensionless adjustment coefficient; if If continuous time delay is used as the representation, then It can be set as an adjustment factor corresponding to the reciprocal of time.

[0113] In equation (20), when the smoothed average delay is small, the negative exponential decay term approaches a large value, and the model prediction step size approaches the nominal prediction step size; when the smoothed average delay increases, the negative exponential decay term decreases, and the model prediction step size shortens accordingly. The outer lower limit boundary protection is used to ensure that the model prediction step size is not lower than the preset minimum prediction step size, avoiding the prediction time domain being too short to form an effective rolling prediction. In this way, the controller can maintain sufficient foresight when the communication status is good, and reduce the dependence on long-term uncertain predictions when the communication status is poor.

[0114] In step S230, the filtered node voltage and equivalent reactive power state are extracted from the current estimated state as the initial boundary conditions for the forward rolling derivation.

[0115] In some implementations, the current estimated state can be a posterior state estimate obtained through delayed embedded state estimation. This current estimated state integrates local real-time operating data, aligned neighbor operating data, and communication delay characteristics, and better reflects the electrical operating state of the distribution network node to be processed under the current control cycle compared to the unprocessed raw measurements. Therefore, before performing multi-step forward rolling inference, filtered node voltage and equivalent reactive power states can be extracted from the current estimated state as the initial states for the voltage prediction trajectory and reactive power prediction trajectory, respectively.

[0116] For example, the node voltage components in the current estimated state can be used as the initial predicted voltage values. The reactive power-related components in the current estimated state are used as the initial predicted reactive power values. By using the voltage and reactive power states corrected by state estimation as the starting point for forward extrapolation, the impact of measurement noise, neighbor data lag, and timing misalignment on the initial state of the predicted trajectory can be reduced, thereby improving the initial consistency of the predicted trajectory within the current control cycle.

[0117] In step S240, within the prediction time domain determined by the model prediction step size, a multi-step forward rolling deduction is performed using a power flow prediction model that includes a delay coupling term. Based on the power flow sensitivity matrix of the nominal operating point of the distribution network, the local single-step reactive power control increment to be solved, the neighbor reactive power splicing increment embedded with dynamic time delay features, and the active power change corresponding to the source load prediction data are mapped to the corresponding influence components on the local voltage and superimposed to generate a voltage prediction trajectory. Simultaneously, the single-step reactive power control increment is accumulated to generate a reactive power prediction trajectory.

[0118] Here, the reactive power splicing increment of the neighbor embedded with dynamic delay features, when the forward extrapolation time step does not exceed the integer delay step, calls the actual historical reactive power control increment determined by the aligned neighbor running data and the sliding historical data cache queue; when the extrapolation time step exceeds the integer delay step, it calls the reactive power prediction trajectory sequence broadcast by the corresponding neighbor node in the previous control cycle as the alternative estimate.

[0119] In practical implementation, the power flow prediction model can be constructed based on the power flow sensitivity matrix at the nominal operating point of the distribution network. The power flow sensitivity matrix can be used to describe the impact of local reactive power control increments, reactive power changes at neighboring nodes, and local active power changes on the voltage of the distribution network nodes to be addressed. Compared to solving the nonlinear AC power flow equations completely in each control cycle, the prediction model based on power flow sensitivity can reduce the online computational complexity and is suitable for distribution network control scenarios that require rolling predictions within shorter control cycles.

[0120] For example, in the prediction time domain Within this framework, the predicted trajectories for voltage and reactive power can be generated recursively: , Equation (21); Equation (22); In the formula, Indicates the current control cycle The predicted future Step voltage value, Indicates the current control cycle The predicted future Step reactive power value, This represents the local single-step reactive power control increment to be solved. Indicates the distribution network node to be processed. The set of neighboring nodes, Indicates the local reactive power control increment to the node Voltage sensitivity coefficient, Representing neighboring nodes reactive power changes on nodes Voltage sensitivity coefficient, Indicates the local active power change to the node Voltage sensitivity coefficient, This represents the change in active power corresponding to the local source-load forecast data. This represents the reactive power splicing increment of the neighboring node, which incorporates dynamic delay features.

[0121] In the recursive model described above, within each prediction step, the node voltage change is jointly influenced by the local reactive power control increment, the reactive power changes of neighboring nodes, and the active power changes of local source loads. Specifically, the local reactive power control increment describes the voltage regulation effect of the control actions of the distribution network node itself; the neighboring reactive power splicing increment describes the impact of neighboring control actions on the node's voltage via electrical coupling; and the local source load active power change describes the impact of load or distributed power generation output changes on the voltage. The reactive power prediction trajectory is obtained by progressively accumulating the single-step reactive power control increments.

[0122] To address the timing gaps in reactive power information from neighboring nodes caused by communication delays, embodiments of this application construct neighbor reactive power splicing increments embedded with dynamic delay features. The neighbor reactive power splicing increment can be segmented and reconstructed based on the relationship between the inferred time step and the corresponding integer delay step, using a zero-order hold strategy and the neighbor prediction sequence obtained from the most recent effective communication. For example, it can be represented as: Equation (23); In the formula, Represents a node with neighboring nodes Integer delay steps between This represents the actual historical reactive power control increment at the time of the last valid communication, determined by the aligned neighbor operating data. Representing neighboring nodes At the last valid communication time (i.e., time) The corresponding prediction increment in the reactive power prediction trajectory sequence broadcast.

[0123] In the above equation (23), a piecewise expression is used. When the simulation time step does not exceed the integer delay step corresponding to the communication delay, the reactive power change of the neighbor node at the corresponding time can be determined by the aligned historical data or historical cached data. When the simulation time step exceeds the integer delay step, the neighbor node at the corresponding time enters the prediction range that needs to be estimated in the current control cycle, and the reactive power prediction trajectory sequence broadcast by the neighbor node in the previous control cycle can be used as a substitute estimate. Through this processing, the temporal continuity of the neighbor's reactive power input can be maintained in multi-step forward rolling simulation, and the loss of neighbor reactive power information caused by asynchronous communication can be reduced.

[0124] Through the embodiments of this application, the distribution network node to be processed can adaptively determine the model prediction step size based on the recent trend of communication delay changes, and perform forward rolling extrapolation of voltage and reactive power based on the initial state corrected by state estimation. Moving average filtering helps reduce the impact of instantaneous communication delay spikes on the prediction step size; the negative exponential decay rule causes the prediction step size to shrink as communication delay increases; the recursive model based on power flow sensitivity can characterize the impact of local control, neighbor coupling, and source-load changes on voltage with lower computational cost; and the neighbor reactive power splicing increment can supplement the timing gap of neighbor reactive power information when communication delay exists. Therefore, the time consistency and availability of the prediction trajectory under communication delay fluctuation conditions can be improved.

[0125] Figure 3 A flowchart illustrating an example of obtaining reactive power control reference values ​​by solving a robust optimization problem for a tube bundle according to an embodiment of this application is shown.

[0126] like Figure 3 As shown, in step S310, the linear matrix inequality method is used to calculate the robust positive invariant error set that remains closed under the disturbance action corresponding to the joint uncertainty set of the system error dynamics, and the geometric boundary of the set is projected and mapped to the upper bound of voltage state deviation and the upper bound of reactive power state deviation, respectively.

[0127] It should be noted that the joint uncertainty set This can be used to characterize the combined disturbance caused by local source-load prediction errors and communication delay fluctuations on the predicted trajectory. Due to this disturbance, the actual system state typically deviates from the nominal predicted state generated by the power flow prediction model. To quantify this deviation, the error between the actual state and the nominal predicted state can be defined as... The evolution of the error between control cycles is dynamically described based on the linearization error.

[0128] For example, the dynamics of the system error can be expressed as: , Equation (24); In the formula, This indicates the state error of the current control cycle. This indicates the state error for the next control cycle. Represents the error state transition matrix. Represents the perturbation input matrix. This represents the perturbation variable belonging to the joint uncertainty set. Error states can include voltage state errors, reactive power state errors, or other state errors related to the prediction model. The error state transition matrix can be determined based on the linearization results of the power flow prediction model near the nominal operating point.

[0129] To ensure that the error remains within a boundable range under the perturbation corresponding to the joint uncertainty set, the robust positive invariant error set can be solved using the linear matrix inequality method. For example, the robust positive invariant error set satisfies the following inclusion relationship: Equation (25); In the formula, Minkowski and, Represents a set The set after mapping by the error state transition matrix, This represents the set of joint uncertainties mapped by the perturbation input matrix. The above inclusion relationship indicates that when the error state is located... The internal and perturbation variables belong to At that time, the error state of the next control cycle is still in Inside. Therefore, it can be... This is the error envelope of the actual trajectory relative to the nominal predicted trajectory.

[0130] In some embodiments, robust positive invariant error set It can be represented using ellipsoidal sets, polyhedral sets, or other convex set forms suitable for optimization solutions. When using the linear matrix inequality method, it can be achieved through constraint sets. By determining the closure property under dynamic error conditions, the error set parameters that satisfy the preset disturbance boundary are obtained. Furthermore, by projecting this robust positive invariant error set onto the voltage state dimension and the reactive power state dimension respectively, the upper bound of the voltage state deviation can be obtained. Upper bound of reactive state deviation .in, Used to characterize the possible range of deviation between the actual voltage state and the nominal voltage prediction value. Used to characterize the possible range of deviation between the actual reactive power state and the nominal reactive power prediction value.

[0131] In step S320, for the nominal predicted state, the Minkowski difference operation is used to subtract the corresponding upper bound of voltage state deviation and upper bound of reactive state deviation from the initial safe voltage range and equipment reactive capacity constraint, respectively, to generate nominal voltage constraint pipeline and nominal capacity constraint pipeline with tightened internal space.

[0132] For example, the initial safe voltage range can be expressed as It is used to limit the physical safety boundaries that the voltage at distribution network nodes must meet; the reactive power capacity constraint of equipment can be expressed as It is used to limit the available reactive power output range of voltage reactive power regulation equipment. Since the actual trajectory may deviate from the nominal predicted trajectory under the joint uncertainty set disturbance, if the nominal predicted trajectory is close to the original safety boundary, the actual trajectory may go beyond the original boundary due to the disturbance deviation. Therefore, the nominal feasible region can be tightened based on the obtained upper bound of the deviation.

[0133] For example, the constraint tightening process can be represented as: , Equation (26); Equation (27); In the formula, This indicates the nominal voltage constraint pipe after tightening. This indicates the tightened nominal capacity constraint pipeline. This represents the Minkowski difference operation. The above formula indicates that, during nominal prediction optimization, a certain disturbance margin is reserved inward between the original safe voltage range and the original reactive power capacity constraints of the equipment. This disturbance margin is determined by the upper bound of the voltage state deviation and the upper bound of the reactive power state deviation, and is used to absorb the trajectory deviation caused by source load prediction errors and time delay fluctuations in actual operation.

[0134] Through the above constraint tightening process, as long as the nominal voltage prediction trajectory is located within... Within, and the nominal reactive state or control variable is located Within this range, the actual trajectory can still be constrained to the original position under the influence of disturbance deviation. and Within this range, this processing can reduce the occurrence of nominal optimization results that excessively approximate physical boundaries, and improve the feasibility of control variables under disturbance conditions.

[0135] In step S330, within the robust feasible region defined by the nominal voltage constraint pipe and the nominal capacity constraint pipe, a minimax optimization problem with dynamic time delay decay weights is constructed as a bundle robust optimization problem. Here, the objective function of the bundle robust optimization problem is constructed based on the weighted sum of the voltage deviation penalty term and the reactive power increment penalty term under the worst disturbance condition within the joint uncertainty set.

[0136] For example, the robust optimization problem of the control bundle can be expressed by the following formula: Equation (28); And satisfy the following constraints: Equation (29); Equation (30); In the formula, This represents the sequence of decisions to be optimized in the prediction time domain, consisting of single-step reactive power control increments. Denotes a set of joint uncertainties. This indicates the value of the disturbance variable within the set of joint uncertainties. Indicates the disturbance variable The predicted voltage state under the action, Indicates the voltage reference value. and These represent the preset positive definite penalty matrices, Indicates the dynamic delay decay weight. This indicates the model prediction step size for the current control cycle.

[0137] The aforementioned minimax optimization problem states that the controller selects a reactive power control increment sequence within the tightened nominal feasible region such that the weighted cost of the voltage deviation penalty and the reactive power increment penalty is minimized under adverse disturbances within the joint uncertainty set. Specifically, the voltage deviation penalty is used to constrain the predicted voltage to approach the voltage reference value, while the reactive power increment penalty is used to suppress excessively large or rapidly changing reactive power adjustments. By introducing worst-case disturbance values ​​into the objective function, the obtained control reference value can be made applicable not only to the nominal prediction scenario but also to the disturbance boundaries corresponding to source load errors and time delay fluctuations.

[0138] In step S340, a predicted communication delay value in the prediction time domain is obtained by extrapolation based on historical communication delay estimates. A dynamic delay attenuation weight is constructed using a preset weight attenuation factor and the predicted communication delay value. Here, the dynamic delay attenuation weight has an inversely proportional attenuation relationship with the predicted communication delay value, which is used to reduce the weight of the cost term at the corresponding prediction time step when the predicted delay value increases in the long term.

[0139] For example, dynamic delay decay weight It can be defined as: , Equation (31); In the formula, This indicates the preset weight decay factor. This represents the predicted future time domain based on extrapolated historical communication delay estimates. The estimated communication delay for each step. When using normalized time delay representation, It can be a dimensionless coefficient; when When using continuous time delay representation, It can be set as a coefficient with the reciprocal dimension of time.

[0140] The aforementioned weighting function indicates that the larger the estimated communication delay, the smaller the weight of the cost term for the corresponding prediction time step. Thus, when the communication delay corresponding to a long-term prediction step is large, the influence of that prediction time step in the objective function is reduced, preventing low-confidence long-term prediction terms from having an excessive impact on current control decisions. Conversely, when the estimated communication delay is small, the corresponding prediction time step retains a higher weight, allowing the controller to fully utilize prediction information when communication conditions are good. This processing enables the objective function to respond differently to the information confidence levels of different time steps within the prediction time domain.

[0141] In step S350, the minimax optimization problem is solved in a rolling manner to obtain the optimal decision sequence. And extract the first step reactive power control increment from the sequence. reactive power value superimposed on the current state To generate the reactive power control reference value output in the current control cycle. .

[0142] For example, the reactive power control reference value for the current control cycle can be expressed as: Equation (32); In the formula, This represents the reactive power value extracted from the current estimated state. This represents the reactive power control increment in the first step of the optimal decision sequence. Although the optimization solution yields an optimal decision sequence covering the entire prediction time domain. However, in the current control cycle, only the first step of reactive power control increment is used to generate the reactive power control reference value. When entering the next control cycle, the optimization problem can be solved again based on the reacquired operating data, communication delay estimate, and predicted trajectory. This rolling solution method enables the reactive power control reference value to be updated with the latest operating and communication status.

[0143] Through the embodiments of this application, the upper bound of the state deviation of the distribution network node to be processed can be accurately derived based on the joint uncertainty set. Furthermore, by tightening constraints based on Minkowski difference operations, sufficient disturbance rejection margin is reserved for the nominal optimization trajectory, eliminating the risk of system instability due to exceeding limits at the underlying mechanism. Simultaneously, the minimax optimization problem with dynamic delay decay weights can intelligently find a balance between voltage deviation tracking and reactive power operation costs, considering the worst-case disturbance combination. This improves the physical feasibility and reliability of the reactive power control reference value under conditions of sudden changes in source load prediction and communication delay jitter.

[0144] Regarding the implementation details of generating reactive power control commands in the embodiments of this application, in actual power distribution network control systems, reactive power control reference values ​​are typically calculated by local controllers or edge control units. However, voltage and reactive power regulation devices such as smart inverters, energy storage converters, static var generators, and static var compensators are distributed at different access locations. When the reactive power control reference value is sent from the controller to the corresponding device and actually takes effect, it may be affected by downlink communication transmission delay, device receiving and processing delay, and device response characteristics. If the uncorrected reactive power control reference value is directly sent to the device, the power grid state at the time the control command actually takes effect may have changed relative to the calculation time, resulting in a lag in reactive power regulation actions.

[0145] To mitigate the impact of the aforementioned execution delay, this embodiment performs feedforward delay correction on the reactive power control reference value before generating the reactive power control command. In some examples of this application's embodiments, firstly, the target value of the reactive power control reference value in the current control cycle is extracted. and historical reference values ​​from the previous control cycle Furthermore, by combining the discrete sampling period, the first-order difference mapping is used to approximate the prediction derivative term that characterizes the transient dynamic evolution trend of reactive power regulation. .

[0146] For example, predicting the derivative term It can be expressed by the following formula: Equation (33); In the formula, This represents the estimated rate of change of the reactive power control reference value within the current control cycle. This represents the reactive power control reference value for the current control cycle. This represents the reactive power control reference value from the previous control cycle. This represents the discrete sampling period of the control system. The predictive derivative term characterizes the trend of reactive power control reference values ​​between adjacent control periods. A large change in the reactive power control reference value between adjacent control periods indicates a significant change in the current operating state's demand for reactive power regulation; conversely, a small change in the reactive power control reference value between adjacent control periods indicates a relatively gradual demand for reactive power regulation.

[0147] Next, the transmission delay of the command sent locally to the voltage and reactive power regulation equipment is estimated as the equivalent execution communication delay. And extract the preset time delay compensation gain coefficient that characterizes the physical response features of the voltage reactive power regulation equipment. The equivalent execution communication delay can be determined based on the estimated communication delay of the current control cycle, the historical downlink delay record, or the transmission delay statistics of the device communication interface; the delay compensation gain coefficient can be preset based on the response speed of the voltage and reactive power regulation equipment, the characteristics of the control interface, the reactive power output variation capability, and the system setting requirements.

[0148] Then, using the aforementioned delay compensation gain coefficient The equivalent execution communication delay and the predicted derivative term Calculate the feedforward compensation increment .

[0149] For example, feedforward compensation increment It can be calculated using the following formula: , Equation (34); In the formula, This represents the feedforward compensation increment for the current control cycle. This represents the delay compensation gain coefficient. Indicates the equivalent execution communication delay. This represents the estimated rate of change of the reactive power control reference value.

[0150] In equation (34), the equivalent execution communication delay characterizes the time offset between the generation and actual effect of the control command, and the prediction derivative term characterizes the trend of the reactive power reference value changing over time. Both are used together to estimate the possible change in reactive power control demand during this time offset. The delay compensation gain coefficient is used to adjust the compensation magnitude according to the equipment response characteristics and control tuning requirements. Through this processing, the issued reactive power control command can have a certain amount of advance correction relative to the uncompensated reactive power control reference value, thereby reducing the control action lag caused by the command transmission delay.

[0151] Then, the feedforward compensation increment will be... With target value Superposition correction is performed, and a preset anti-saturation limiting function is used in conjunction with the physical upper and lower boundaries of the equipment's reactive power capacity to perform limiting constraint processing, so as to generate reactive power control commands that ensure physical feasibility.

[0152] It should be noted that, since voltage reactive power regulation equipment has physical upper and lower output limits, if the compensated theoretical reactive power control quantity obtained through superposition correction exceeds the equipment's allowable range, the equipment may be unable to execute the command or trigger protection constraints. Therefore, this embodiment utilizes a preset anti-saturation limiting function, combined with the physical upper and lower boundaries of the equipment's reactive power capacity, to perform limiting processing on the compensated theoretical reactive power control quantity to generate a reactive power control command. .

[0153] For example, the clipping process can be expressed by the following formula: , Equation (35); In the formula, This represents the theoretical reactive power control quantity obtained after superimposing the feedforward compensation increment. This indicates the final generated reactive power control command. Represents the anti-saturation limiting function. and These represent the upper and lower limits of the reactive power that the corresponding voltage reactive power regulation equipment is allowed to output. For smart inverters or energy storage converters, the upper and lower limits of reactive power can also be dynamically determined based on the rated capacity of the equipment, the current active power output, and operational safety constraints; for static var generators or static var compensators, the upper and lower limits of reactive power can be determined based on the rated reactive power capacity of the equipment or the current available capacity.

[0154] Through the above limiting process, when the compensated theoretical reactive power control quantity is within the allowable range of the equipment, it can be directly used as a reactive power control command; when it exceeds the upper limit of the equipment's reactive power output or falls below the lower limit of the equipment's reactive power output, it is restricted to the corresponding physical boundary. This retains the compensating effect of feedforward delay correction on command lag, while avoiding the feedforward compensation increment causing the control command to exceed the equipment's executable range.

[0155] In some implementations, if the equivalent execution communication delay is small or the reactive power control reference value changes slowly, the feedforward compensation increment obtained from the above formula is small, and the reactive power control command is mainly determined by the reactive power control reference value. If the equivalent execution communication delay is large and the reactive power control reference value changes rapidly, the feedforward compensation increment is increased accordingly to compensate for the lag in command execution time. This compensation method, which is related to delay and reference change trends, can improve the matching degree between reactive power control commands and the actual effective time of the equipment.

[0156] Through the embodiments of this application, the distribution network node to be processed can calculate the feedforward compensation increment based on the changing trend of the reactive power control reference value in adjacent control cycles, combined with the equivalent execution communication delay and delay compensation gain coefficient, before the reactive power control reference value is issued, thereby reducing the impact of command execution lag caused by the downlink communication link. Simultaneously, by using an anti-saturation limiting function based on the physical boundaries of the equipment, the theoretical reactive power control quantity after superimposed feedforward compensation is constrained, ensuring that the final generated reactive power control command remains within the executable range of the equipment. This improves the matching degree between the reactive power control command and the actual effective time of the equipment, and reduces the risk that feedforward compensation will cause the control command to exceed the reactive power capacity boundary of the equipment.

[0157] Figure 4 A schematic diagram illustrating the system operation mechanism of an example of a robust predictive control method for voltage reactive power in a distribution network that takes into account communication delay, according to an embodiment of this application, is shown.

[0158] like Figure 4 As shown, the distribution network control system first acquires current operating data through a local real-time acquisition module and receives asynchronous data from neighboring nodes. To address the random communication delays present in the underlying network, the system performs dynamic delay alignment processing on lagging data across nodes to eliminate timing misalignments in multi-source data. Subsequently, the aligned neighborhood data is fused with local measurement data and input into the delay embedding state estimation stage. This process filters out measurement noise while reconstructing the current estimated state, which includes dynamic communication delay characteristics.

[0159] Based on the acquired estimated state, the system invokes an adaptive prediction model, adaptively adjusts the prediction step size according to the communication delay estimate, and performs forward rolling extrapolation to generate the voltage and reactive power evolution trajectories in the prediction time domain. This prediction trajectory is then input into the robust optimization module. This module comprehensively considers the joint uncertainty constituted by physical source-load prediction errors and information delay fluctuations, provides disturbance rejection margin to the system through nominal constraint tightening operations, and solves for the optimal reactive power control reference value that satisfies safety constraints within the tightened feasible region.

[0160] Finally, the system enters the time-delay compensation control stage at the output end, performing feedforward time-delay correction with anti-saturation limiting on the reactive power control reference value, generating the final control command, and sending it to the distribution network equipment for physical execution. Furthermore, the system's underlying data interaction relies on an event-triggered mechanism to form a closed-loop feedback, enabling nodes to adaptively determine asynchronous communication broadcast actions based on the amplitude of local state fluctuations. This ensures the effectiveness of multi-node device collaborative execution while achieving on-demand allocation and efficient flow of communication bandwidth resources.

[0161] To verify the effectiveness and engineering feasibility of the robust predictive control method for voltage and reactive power in distribution networks considering communication delay proposed in this application, a cyber-physical coupling simulation platform was built based on an improved IEEE 33-node distribution network system. Distributed photovoltaic resources were integrated into the simulation network at a high proportion, with a photovoltaic penetration rate set at 120%, and the corresponding smart inverter capacity was uniformly configured to 1.0 MVar. Simultaneously, a real load fluctuation sequence containing Gaussian white noise was superimposed on each node to highly replicate the highly random real physical operating environment.

[0162] Considering the dynamic uncertainties of underlying communication in real-world power distribution IoT, the simulation experiments abandoned the assumption of a single ideal delay distribution and introduced a Markov chain delay model to simulate three dynamically switching network states: a normal communication state with a delay distribution of 20 ms to 50 ms, a network congestion state with a delay distribution of 100 ms to 300 ms, and an occasional packet loss state equivalent to extremely long communication delays. Furthermore, the discrete sampling period (i.e., the basic control step size) of the system's underlying controller was uniformly set to 50 ms to fully stimulate and present the real impact of step quantization error and asynchronous delay effects on the system's collaborative control.

[0163] To comprehensively evaluate the technical advantages of the proposed scheme, three control strategies were set up in parallel as comparison benchmarks. Strategy A adopts traditional droop control, representing a static feedback control mode that is completely independent of communication and relies solely on local measurements; Strategy B adopts standard distributed model predictive control (D-MPC), representing a conventional online optimization control mode that relies on neighbor communication but does not perform delay modeling and deep compensation at the underlying level; Strategy C adopts the method proposed in the embodiments of this application, which is a cooperative predictive control architecture that fully integrates delay embedded state estimation, delay adaptive prediction step size adjustment, joint uncertainty-bound robust optimization, and end-feedforward delay correction mechanism.

[0164] Figure 5 This diagram illustrates a comparative simulation of voltage time-domain tracking and constraint protection using different methods under dynamic time delay abrupt changes and source load disturbances. The upper subplot of this comparative simulation shows the real-time communication delay that dynamically changes over time, while the lower subplot shows the node voltage fluctuation trajectory under different control strategies after the system is disturbed. The two parallel red dashed lines mark the upper and lower safety limits of 1.05 pu and 0.95 pu, respectively.

[0165] like Figure 5 As shown, the simulation test introduced a severe network congestion condition between the 5th and 8th seconds, causing the communication latency to spike to 300 ms instantaneously, accompanied by a sudden drop in photovoltaic output. The figure reveals that Strategy A (traditional droop control), lacking global neighborhood coordination capabilities, exhibited a significant static deviation in the face of severe disturbances, causing the local node voltage to drop below the safe lower limit of 0.95 pu in the initial stage of the disturbance. While Strategy B (standard distributed model predictive control) possesses global optimization capabilities, the direct use of outdated historical data in real-time online optimization without time-delay alignment and filtering resulted in a severe timing misalignment between control commands and the actual physical system state. This led to typical integral saturation and control oscillations, causing severe fluctuations in the voltage trajectory and multiple crossings of the safety threshold.

[0166] In contrast, the voltage evolution trajectory using the method (Strategy C) of this application exhibits good stability. This method achieves accurate perception of dynamic delay through delayed embedded state estimation and generates the bundle safety envelope (blue shaded area) shown in the figure based on the joint uncertainty set of source load and communication. Even under the dual extreme impact of severe communication lag of up to 300 ms and photovoltaic drop, the system actively uses the tightened nominal constraint pipeline for forward control inference, ensuring that the final actual voltage evolution trajectory (blue solid line) is always strictly bound within the dynamic envelope and never touches the physical safety boundaries of 0.95 pu and 1.05 pu. This result intuitively and fully verifies that this method has transient disturbance resistance and voltage safety constraint guarantee performance in complex disturbance environments with deep cyber-physical coupling.

[0167] Figure 6 This diagram illustrates a comparative simulation of the cumulative voltage deviation distribution using different methods in an example scenario involving multiple random disturbances and time delays. The cumulative distribution function (CDF) curve is statistically plotted based on 500 experimental scenarios involving interleaved random communication time delay fluctuations and source-load disturbances. The horizontal axis represents the absolute value (pu) of the voltage deviation at the distribution network nodes, and the vertical axis represents the cumulative probability. The tail region from 90% to 99.999% is logarithmically stretched to provide a clear and rigorous representation of the system's reliability under extreme boundary conditions.

[0168] In actual operation of distribution networks, the security of system coordinated control often depends not on average performance, but on the extremely rare and severe operating conditions, i.e., tail reliability. For example... Figure 6 The statistical curves shown reveal a significant dividing line between the two control strategies in the tail region (i.e., the interval where the cumulative probability is greater than 99%), representing the superposition of extremely poor communication and severe disturbances. Strategy B (standard distributed model predictive control), failing to build an isolation defense against uncertainty in its underlying optimization logic, achieved a maximum voltage deviation of 0.12 pu at the 99.99th percentile, leading to severe grid over-limit violations. This indicates that conventional predictive control poses a significant risk of system instability when facing extreme operating conditions coupled with long time delays and strong disturbances.

[0169] In contrast, the voltage deviation cumulative probability curve using the method of this application (Strategy C) exhibits extremely superior boundary convergence. By leveraging the proposed joint uncertainty set modeling and robust constraint tightening mechanism, this method pre-reserves sufficient disturbance rejection margin in the nominal optimization space, successfully locking the extreme deviation at the 99.99th quantile within the boundary of 0.045 pu. The simulation results demonstrate that the method of this application not only maintains high-precision voltage tracking under normal operating conditions but also provides strong robustness and reliable safety assurance for the distribution network under harsh environments with nondeterministic time delays and extreme source-load disturbances.

[0170] Figure 7 This diagram illustrates a comparative simulation of different methods in evaluating system performance trade-offs and control costs. The simulation is presented as a dual Y-axis bar chart. The left Y-axis represents the reactive power margin, which measures the physical cost of the system, while the right Y-axis represents the time required to solve a single control cycle, which measures the computational cost. Since introducing any robust control mechanism inevitably incurs additional physical and computational overhead, this diagram objectively evaluates the comprehensive trade-off cost of using the method described in this application (Strategy C) compared to traditional droop control (Strategy A) and standard distributed model predictive control (Strategy B).

[0171] like Figure 7 As shown, from the perspective of computational cost, since the method in this embodiment requires online solution of the optimization problem considering the joint uncertainty set and the tightening of the constraint, the average solution time per control cycle increases to about 28ms, which is higher than the 8ms of strategy B and the minimal solution time of strategy A (<1ms). Although the computing power overhead on the edge side has increased, the solution time is still strictly within the set 50ms discrete sampling control cycle, which fully demonstrates the engineering real-time feasibility of this scheme under the existing edge computing capabilities of the power distribution terminal. From the perspective of physical resources, in order to effectively cope with the joint uncertainty of communication delay and source load fluctuation, the method in this embodiment performs internal constraint contraction processing on the control feasible domain at the mathematical level. This constraint tightening operation causes the system to call up part of the reactive power capacity in advance as a disturbance rejection safety base under the same load level, resulting in the reactive power adjustment margin of this method (strategy C) being reduced to 80%, which sacrifices about 5% of the physical capacity margin compared to strategy B (85%) without robust processing.

[0172] The simulation comparison results above show that this "conservatism" at the physical and computational levels is an inherent and reasonable system cost for achieving robust control. The method in this application, by reasonably relinquishing a small amount of computational resources at the edge of the distribution terminal and a small amount of reactive power margin for the regulating equipment, successfully ensures that the global voltage of the distribution system remains within a safe range under extremely harsh communication and strong disturbance environments. This achieves a better engineering performance trade-off between computational real-time performance, physical economy, and reliability and security in distribution network collaborative control.

[0173] In summary, this application proposes a robust predictive control method for reactive power in distribution networks that considers communication delay, effectively overcoming the system voltage instability problem caused by neglecting network communication delay and source load uncertainty in traditional control strategies. This method incorporates communication delay as an endogenous state into the system model, relying on delay-embedded state estimation to achieve accurate perception of complex delays. Simultaneously, through a closed-loop architecture that integrates delay-adaptive trajectory extrapolation and robust constraint optimization, strict constraint tightening is performed within the nominal feasible region. Furthermore, by combining feedforward delay correction at the output end with an asynchronous event-triggered communication mechanism at the underlying level, the method significantly reduces communication bandwidth load while mitigating execution lag during command issuance from the control layer.

[0174] Simulation and experimental results fully demonstrate that, compared to traditional local feedback control and conventional distributed predictive control, the method proposed in this application can still tightly lock the voltage of distribution network nodes within safe and reliable physical boundaries even under severe operating conditions such as extreme network congestion, severe latency jitter, and superimposed uncertainties from both source and load. This technical solution not only achieves a reasonable system trade-off between computational real-time performance, physical capacity margin, and control reliability and security, but also provides a high-fidelity and robust engineering-based collaborative control solution for future smart distribution networks and novel microgrid systems with widespread high-proportion distributed energy access, complex dynamic topologies, and limited communication conditions.

[0175] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of combined actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Secondly, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application. In the above embodiments, the descriptions of each embodiment have their own emphasis; for parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0176] Figure 8 A structural block diagram of an example of a robust predictive control system for voltage reactive power in a distribution network that takes into account communication delay, according to an embodiment of this application, is shown.

[0177] like Figure 8 As shown, the robust predictive control system 800 for voltage and reactive power of distribution networks considering communication delay includes a data alignment unit 810, a state estimation unit 820, a trajectory prediction unit 830, an ensemble construction unit 840, a robust optimization unit 850, and an instruction generation unit 860.

[0178] The data alignment unit 810 is used to acquire the local real-time operation data and local source-load prediction data of the distribution network node to be processed in the current control cycle, and receive the neighbor operation data with timestamps sent by each neighbor node. Based on the timestamps and the reception time of the neighbor operation data, it calculates the estimated communication delay with each neighbor node, and performs time mapping alignment processing on the neighbor operation data according to the estimated communication delay to obtain the aligned neighbor operation data.

[0179] The state estimation unit 820 is used to construct a delay embedding extended state vector containing the communication delay estimate, and to perform delay embedding state estimation by fusing the local real-time running data with the aligned neighbor running data to obtain the current estimated state containing dynamic delay features.

[0180] The trajectory prediction unit 830 is used to adaptively adjust the model prediction step size according to the communication delay estimate, and use the current estimated state, the local source load prediction data and the aligned neighbor operation data to generate the voltage prediction trajectory and reactive power prediction trajectory in the prediction time domain determined by the model prediction step size through the power flow prediction model; the power flow prediction model is constructed based on the voltage sensitivity coefficient to reactive power, and is used to characterize the dynamic evolution relationship of node voltage with local reactive power control increment, neighbor operation state and source load changes.

[0181] The set construction unit 840 is used to determine a local source load prediction error set based on the local source load prediction data, and to determine a delay fluctuation set based on the change of the communication delay estimate in adjacent control cycles, and to combine the local source load prediction error set and the delay fluctuation set into a joint uncertainty set.

[0182] The robust optimization unit 850 combines the voltage prediction trajectory and the reactive power prediction trajectory to construct a robust optimization problem by introducing an uncertainty envelope, aiming to minimize voltage deviation and reactive power control increment, and satisfying preset safe voltage range and equipment reactive power capacity constraints. The unit then solves this problem to obtain a reactive power control reference value. The uncertainty envelope determines an upper bound for the state deviation based on the joint uncertainty set, and performs constraint tightening on the safe voltage range and equipment reactive power capacity constraints based on this upper bound, ensuring that the actual evolution trajectory remains within the safe voltage range and equipment reactive power capacity constraints under the disturbances corresponding to the joint uncertainty set.

[0183] The instruction generation unit 860 is used to perform feedforward delay correction on the reactive power control reference value based on the preset delay compensation gain and the estimated communication delay value, so as to generate a reactive power control instruction and send the reactive power control instruction to the voltage and reactive power regulation equipment corresponding to the distribution network node to be processed, so as to perform voltage and reactive power coordinated control.

[0184] In some embodiments, this application provides a non-volatile computer-readable storage medium storing one or more programs including execution instructions. The execution instructions can be read and executed by electronic devices (including but not limited to computers, servers, or network devices) to perform the steps of any of the above-described distribution network voltage reactive power robust predictive control methods considering communication delays.

[0185] In some embodiments, this application also provides a computer program product, the computer program product including a computer program stored on a non-volatile computer-readable storage medium, the computer program including program instructions, which, when executed by a computer, cause the computer to perform the steps of any of the above-described distribution network voltage reactive power robust predictive control methods considering communication delay.

[0186] In some embodiments, this application also provides an electronic device comprising: at least one processor and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of a robust predictive control method for voltage reactive power in a distribution network that takes into account communication delays.

[0187] The above-described product can perform the methods provided in the embodiments of this application, and has the corresponding functional modules and beneficial effects for performing the methods. Technical details not described in detail in this embodiment can be found in the methods provided in the embodiments of this application.

[0188] The electronic devices in this application can exist in various forms, including but not limited to: mobile communication devices, ultra-mobile personal computer devices, portable entertainment devices, or other airborne electronic devices with data interaction functions.

[0189] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0190] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented using software plus a general-purpose hardware platform, or of course, using hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the related technology, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0191] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A power distribution network voltage and reactive power robust prediction control method considering communication time delay, characterized in that, Includes the following steps: Based on timestamped neighbor operation data, communication delay is estimated and time mapping alignment is performed: local real-time operation data and local source-load prediction data of the distribution network node to be processed in the current control cycle are obtained, and neighbor operation data with timestamps sent by each neighbor node are received. Based on the timestamps and the reception time of the neighbor operation data, the estimated communication delay between the node and each neighbor node is calculated, and time mapping alignment processing is performed on the neighbor operation data according to the estimated communication delay to obtain aligned neighbor operation data. Construct a delay embedding extended state containing delay features to achieve fusion estimation of local and neighbor operating states: Construct a delay embedding extended state vector containing the communication delay estimate, and perform delay embedding state estimation by fusing the local real-time operating data and the aligned neighbor operating data to obtain the current estimated state containing dynamic delay features; The prediction step size is adaptively adjusted based on the latency level, and voltage and reactive power prediction trajectories are generated by combining source load prediction and power flow prediction models: The model prediction step size is adaptively adjusted based on the communication latency estimate, and the current estimated state, the local source load prediction data, and the aligned neighbor operating data are used to generate voltage and reactive power prediction trajectories in the prediction time domain determined by the model prediction step size through the power flow prediction model; The power flow prediction model is constructed based on the voltage sensitivity coefficient to reactive power to characterize the dynamic evolution relationship of node voltage with local reactive power control increments, neighbor operating states, and source load changes; Further, the source load prediction error and the delay fluctuation are combined into a joint uncertainty set: the local source load prediction error set is determined based on the local source load prediction data, and the delay fluctuation set is determined based on the change of the communication delay estimate in adjacent control cycles. The local source load prediction error set and the delay fluctuation set are combined into a joint uncertainty set. By tightening the voltage safety range and reactive power capacity constraints through an uncertainty envelope, a robust optimization problem is solved to obtain a reactive power control reference value. Combining the voltage prediction trajectory and the reactive power prediction trajectory, and under the conditions of minimizing voltage deviation and reactive power control increment while satisfying preset safety voltage range and equipment reactive power capacity constraints, an uncertainty envelope is introduced to construct a robust optimization problem, which is then solved to obtain the reactive power control reference value. Specifically, the uncertainty envelope determines the upper bound of the state deviation based on the joint uncertainty set, and performs constraint tightening processing on the safety voltage range and the equipment reactive power capacity constraints based on the upper bound of the state deviation, ensuring that the actual evolution trajectory remains within the safety voltage range and the equipment reactive power capacity constraints under the disturbances corresponding to the joint uncertainty set. Finally, feedforward correction is performed based on the time delay compensation gain and control commands are issued: based on the preset time delay compensation gain and the estimated communication time delay, feedforward time delay correction is performed on the reactive power control reference value to generate reactive power control commands, and the reactive power control commands are issued to the voltage and reactive power regulation equipment corresponding to the distribution network node to be processed to perform voltage and reactive power coordinated control. The step of calculating the estimated communication delay with each of the neighboring nodes based on the timestamp and the reception time of the neighboring operation data, and performing time mapping alignment processing on the neighboring operation data according to the estimated communication delay to obtain aligned neighboring operation data, includes: For each neighbor node, extract the transmission timestamp generated based on a unified time base from the received neighbor operation data, and calculate the continuous time communication delay by combining it with the reception time of the neighbor operation data. Based on the discrete sampling period of the power distribution network control system, the continuous-time communication delay is normalized and mapped to a communication delay estimate, and the communication delay estimate is decomposed into an integer delay step and a fractional delay weight. Determine whether the estimated communication delay is less than a preset effective delay threshold; If the delay is less than the effective delay threshold, then extract the historical neighbor running data of the two adjacent historical control cycles corresponding to the integer delay steps from the locally maintained sliding historical data cache queue, and use the fractional delay weight to perform a dynamic window interpolation algorithm on the two adjacent historical neighbor running data to calculate the aligned neighbor running data of the current control cycle. If the delay is not less than the effective delay threshold, the corresponding communication link is determined to be in a timeout state and a zero-order hold strategy is triggered. The most recent reliable historical neighbor running data that satisfies the delay being less than the effective delay threshold is extracted from the sliding historical data cache queue and used as the aligned neighbor running data for the current control cycle.

2. The robust predictive control method for reactive power in distribution networks considering communication delay as described in claim 1, characterized in that, The process of constructing a delay embedding extended state vector containing the communication delay estimate, and fusing the local real-time running data with the aligned neighbor running data to perform delay embedding state estimation to obtain a current estimated state containing dynamic delay features, includes: For the distribution network node to be processed, the estimated communication delay values ​​with each neighbor node are combined into a delay feature vector. Based on the equivalent delay steps determined by the delay feature vector, the corresponding delayed reactive power output value is extracted from the local historical control cache. In this way, a delay embedding extended state vector containing the node's real-time voltage measurement value, the delayed reactive power output value, and the delay feature vector is constructed. Based on the nonlinear system state transition function considering time delay characteristics, the prior state estimate of the current control cycle is calculated using the posterior state estimate of the previous control cycle and the reactive power control input variable. The prior error covariance matrix is ​​calculated by combining the preset system process noise covariance matrix and the time delay perception state transition Jacobian matrix obtained by taking the partial derivative with respect to the time delay state. Calculate the measurement Jacobian matrix that maps the extended state space to the observation space, and calculate the Kalman gain matrix by combining the preset measurement noise covariance matrix and the prior error covariance matrix. The local real-time running data and the neighborhood measurement features extracted from the aligned neighbor running data are combined to construct the actual measurement vector. The Kalman gain matrix is ​​used to perform residual correction measurement update for the difference between the actual measurement vector and the predicted output of the measurement function, so as to output the current estimated state and simultaneously update the posterior error covariance matrix for use in the next control cycle iteration.

3. The robust predictive control method for reactive power in distribution networks considering communication delay as described in claim 2, characterized in that, The step of adaptively adjusting the model prediction step size based on the communication delay estimate, and using the current estimation state, the local source-load prediction data, and the aligned neighbor operating data, to generate the voltage prediction trajectory and reactive power prediction trajectory in the prediction time domain determined by the model prediction step size through the power flow prediction model, includes: Obtain the historical communication delay estimates of the distribution network nodes to be processed within the past preset time window, and calculate the smoothed average delay using a moving average filter. Based on the nominal prediction step size under ideal communication conditions, the model prediction step size of the current control cycle is dynamically adjusted according to the smoothed average time delay using a negative exponential decay penalty mechanism, and combined with the minimum prediction step size to maintain the robust and stable operation of the system, lower limit boundary protection is performed. The filtered node voltage and equivalent reactive power state are extracted from the current estimated state as the initial boundary conditions for the forward rolling derivation. Within the prediction time domain determined by the model prediction step size, the power flow prediction model containing delay coupling terms is used to perform multi-step forward rolling deduction. Based on the power flow sensitivity matrix of the nominal operating point of the distribution network, the local single-step reactive power control increment to be solved, the neighbor reactive power splicing increment embedded with dynamic time delay features, and the active power change corresponding to the source load prediction data are mapped to the corresponding influence components on the local voltage and superimposed to generate the voltage prediction trajectory. The single-step reactive power control increment is also accumulated simultaneously to generate the reactive power prediction trajectory. Specifically, when the forward inference time step does not exceed the integer delay step, the neighbor reactive power splicing increment with embedded dynamic delay features calls the actual historical reactive power control increment determined by the aligned neighbor running data and the sliding historical data cache queue; when the inference time step exceeds the integer delay step, the reactive power prediction trajectory sequence broadcast by the corresponding neighbor node in the previous control cycle is called as a substitute estimate.

4. The robust predictive control method for reactive power in distribution networks considering communication delay as described in claim 3, characterized in that, The method combines the voltage prediction trajectory and the reactive power prediction trajectory, aiming to minimize voltage deviation and reactive power control increment, and satisfying preset safe voltage range and equipment reactive power capacity constraints. An uncertainty envelope is introduced to construct a robust optimization problem for the control tubes, and this problem is solved to obtain reactive power control reference values, including: Using the linear matrix inequality method, the robust positive invariant error set that keeps closed under the disturbance corresponding to the joint uncertainty set of the system error is calculated, and the geometric boundary of the set is projected and mapped as the upper bound of voltage state deviation and the upper bound of reactive power state deviation, respectively. For the nominal predicted state, the Minkowski difference operation is used to subtract the corresponding upper bound of the voltage state deviation and the upper bound of the reactive state deviation from the initial safe voltage range and the equipment reactive capacity constraint, respectively, to generate nominal voltage constraint pipelines and nominal capacity constraint pipelines with tightened internal space. Within the robust feasible region defined by the nominal voltage constraint pipe and the nominal capacity constraint pipe, a minimax optimization problem with dynamic time delay decay weight is constructed as a bundle robust optimization problem; the objective function of the bundle robust optimization problem is constructed based on the weighted sum of the voltage deviation penalty term and the reactive power increment penalty term under the worst disturbance condition in the joint uncertainty set. The predicted communication delay is obtained by extrapolating historical communication delay estimates. The dynamic delay attenuation weight is constructed by combining the predicted communication delay with a preset weight attenuation factor. The dynamic delay attenuation weight is inversely proportional to the predicted communication delay. The minimum-maximization optimization problem is solved in a rolling manner to obtain the optimal decision sequence, and the reactive power value of the first step reactive power control increment in the sequence is extracted and superimposed on the reactive power value of the current state to generate the reactive power control reference value output in the current control cycle.

5. The robust predictive control method for reactive power in distribution networks considering communication delay according to claim 4, characterized in that, The step of performing feedforward delay correction on the reactive power control reference value based on the preset delay compensation gain and the estimated communication delay value to generate reactive power control commands includes: Extract the target value of the reactive power control reference value in the current control cycle and the historical reference value in the previous control cycle, and combine the discrete sampling cycle with the first-order difference mapping to approximate the prediction derivative term that characterizes the transient dynamic evolution trend of reactive power regulation. The transmission delay of the instruction sent locally to the voltage and reactive power regulation equipment is estimated as the equivalent execution communication delay, and a preset delay compensation gain coefficient characterizing the physical response features of the voltage and reactive power regulation equipment is extracted. Based on the delay compensation gain coefficient, the equivalent execution communication delay, and the prediction derivative term, the feedforward compensation increment is calculated; the feedforward compensation increment is used to introduce an adjustment change corresponding to the transmission lag time in advance during the control command transmission process. The feedforward compensation increment is superimposed and corrected with the target value, and a preset anti-saturation limiting function is used in conjunction with the physical upper and lower boundaries of the equipment's reactive power capacity to perform limiting constraint processing, so as to generate a reactive power control command that ensures physical feasibility.

6. The robust predictive control method for reactive power in distribution networks considering communication delay as described in claim 1, characterized in that, The process of acquiring the local real-time operating data and local source-load prediction data of the distribution network node to be processed in the current control cycle, and receiving neighbor operating data with timestamps sent by each neighbor node, includes: In each control cycle, extract the real-time voltage measurement value and reactive power output value of the node at the current moment, and obtain the voltage record value and reactive power record value cached locally when the communication broadcast was successfully triggered last time; The absolute deviation between the measured value at the current moment and the cached recorded value are calculated respectively. The voltage absolute deviation and reactive absolute deviation are linearly weighted by the preset voltage deviation normalization weight coefficient and reactive power deviation normalization weight coefficient to construct an event-triggered evaluation function based on local state fluctuations. Determine whether the event trigger evaluation function is greater than a preset comprehensive trigger threshold; If the value exceeds the comprehensive trigger threshold, the local running data carrying the sending timestamp generated based on the unified time base will be encapsulated to generate a status update packet, and asynchronously broadcast to the topology neighbor nodes. At the same time, the measurement data at the current moment will be synchronously updated to the locally cached record data. If the fluctuation is not greater than the comprehensive trigger threshold, it is determined that the local state fluctuation is within the preset silent range, and the communication at the sending end remains silent. If the distribution network node to be processed does not hear a new state update packet sent by the first neighbor node among the neighbor nodes in the current control cycle, the alignment state corresponding to the last effective communication time of the first neighbor node is extracted as the initial value for inference, and the open-loop time step extrapolation is performed based on the locally maintained power flow prediction model to generate the corresponding rolling state estimate, and the rolling state estimate is used as the completed neighbor operation data.

7. A robust predictive control system for reactive power in a power distribution network that considers communication delay, characterized in that, A robust predictive control method for reactive power distribution network voltage considering communication delay, as described in any one of claims 1-6, includes: The data alignment unit is used to acquire the local real-time operation data and local source-load prediction data of the distribution network node to be processed in the current control cycle, and receive the neighbor operation data with timestamps sent by each neighbor node. Based on the timestamps and the receiving time of the neighbor operation data, it calculates the estimated communication delay with each neighbor node, and performs time mapping alignment processing on the neighbor operation data according to the estimated communication delay to obtain the aligned neighbor operation data. The state estimation unit is used to construct a delay embedding extended state vector containing the communication delay estimate, and to perform delay embedding state estimation by fusing the local real-time running data and the aligned neighbor running data to obtain the current estimated state containing dynamic delay features. The trajectory prediction unit is used to adaptively adjust the model prediction step size according to the communication delay estimate, and use the current estimated state, the local source load prediction data and the aligned neighbor operating data to generate the voltage prediction trajectory and reactive power prediction trajectory in the prediction time domain determined by the model prediction step size through the power flow prediction model; the power flow prediction model is constructed based on the voltage sensitivity coefficient to reactive power, and is used to characterize the dynamic evolution relationship of node voltage with local reactive power control increment, neighbor operating state and source load changes; The set construction unit is used to determine the local source load prediction error set based on the local source load prediction data, and to determine the delay fluctuation set based on the change of the communication delay estimate in adjacent control cycles, and to combine the local source load prediction error set and the delay fluctuation set into a joint uncertainty set; A robust optimization unit is used to combine the voltage prediction trajectory and the reactive power prediction trajectory, and under the conditions of minimizing voltage deviation and reactive power control increment, and satisfying the preset safe voltage range and equipment reactive power capacity constraints, introduce an uncertainty envelope to construct a robust optimization problem for the control system, and solve the robust optimization problem for the control system to obtain a reactive power control reference value; wherein, the uncertainty envelope determines the upper bound of the state deviation based on the joint uncertainty set, and performs constraint tightening processing on the safe voltage range and the equipment reactive power capacity constraints based on the upper bound of the state deviation, so that the actual evolution trajectory remains within the safe voltage range and the equipment reactive power capacity constraints under the disturbance corresponding to the joint uncertainty set; The instruction generation unit is used to perform feedforward delay correction on the reactive power control reference value based on a preset delay compensation gain and the estimated communication delay value, so as to generate a reactive power control instruction and send the reactive power control instruction to the voltage and reactive power regulation equipment corresponding to the distribution network node to be processed, so as to perform voltage and reactive power coordinated control.

8. An electronic device, comprising: At least one processor; as well as A memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the method as described in any one of claims 1-6.

9. A storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-6.

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