Active power distribution network day-ahead and intra-day two-stage optimal scheduling method

Abstract

The active power distribution network day-ahead-intra-day two-stage optimization scheduling method solves the problem of how to suppress the voltage deviation and network loss caused by the intermittence and volatility of photovoltaic output, and belongs to the field of optimization scheduling of distributed photovoltaic power distribution network. The application comprises: based on the photovoltaic output and load prediction data in the future day, taking the switching group number of discrete reactive power compensation device as the decision variable, taking the minimum degree of voltage deviation of each node in the power distribution network from the reference value and the voltage fluctuation amount of adjacent period as the objective function, the switching plan of the discrete reactive power compensation device in each hour in the future day is solved; based on the switching plan and the photovoltaic output and load prediction data updated every 15 minutes, taking the active power output and reactive power output of the continuous reactive power compensation device as the decision variable, the scheduling instruction of each 15 minutes is solved. And through the optimization of the objective function and the constraint condition, the reactive power output between the static reactive power generator and the photovoltaic grid-connected system is automatically allocated.

Description

Technical Field

[0001] This application relates to a two-stage optimization scheduling method for active distribution networks, specifically day-ahead and intraday scheduling, and belongs to the field of optimization scheduling for distributed photovoltaic distribution networks. Background Technology

[0002] With the large-scale integration of distributed photovoltaic (PV) systems into distribution networks, the power flow of these networks is shifting from a traditional unidirectional radial distribution to a multidirectional interactive distribution. This leads to more complex node voltage distribution characteristics and a significant increase in voltage limit exceedance risks and network losses. Particularly in low-voltage distribution areas, the large number of small-capacity residential PV systems, dispersed connection points, and frequent single-phase grid connection result in high R / X ratios, making active power injection prone to causing voltage rises at the line ends. Currently, reactive power and voltage control in distribution networks primarily employs the following technologies:

[0003] (1) Control method based on discrete reactive power compensation device

[0004] This method employs capacitor banks and reactor banks as the primary control means, providing stepped reactive power compensation through group switching. However, discrete devices suffer from slow response speeds, limited adjustment frequency, and an upper limit to the number of actions. When photovoltaic output fluctuates rapidly, discrete devices require frequent switching to track voltage changes, but this frequent operation accelerates equipment aging and increases maintenance costs. Furthermore, the discreteness of the switching actions makes it difficult to match the continuous fluctuations in photovoltaic output, often resulting in compensation lag or overcompensation, causing repeated voltage exceedances, persistently high network losses, and an inability to effectively mitigate voltage deviations.

[0005] (2) Local control methods for photovoltaic power generation systems

[0006] Photovoltaic power generation systems are often set to operate at a fixed power factor (e.g., 0.95) or employ simple reactive power-voltage droop control based on grid connection voltage. In fixed power factor mode, the inverter cannot adjust reactive power according to actual voltage demand, leading to significant voltage deviations. Simple Q(U) droop control relies solely on local voltage information and cannot coordinate multiple photovoltaic power plants and static var generators (SVAs), often resulting in reverse regulation by different devices and reactive power circulation. These phenomena not only fail to effectively suppress voltage fluctuations but also increase line losses and may even trigger voltage oscillations, adversely affecting the power quality of the distribution network.

[0007] (3) Reactive power optimization scheduling method with a single time scale

[0008] One type of method employs day-ahead offline optimization, formulating action plans for discrete devices based on forecast data. Another type relies solely on real-time local control (such as fast response of static var generators). Day-ahead optimization suffers from significant discrepancies between actual and forecasted photovoltaic (PV) output. When forecast deviations occur on a given day (e.g., a sharp rise or fall in PV output), the pre-set switching plans cannot adapt, leading to severe voltage deviations from safe ranges during localized periods, resulting in prominent voltage offset issues. While real-time control can suppress some fluctuations, it lacks adequate day-ahead coordination for discrete devices. During drastic changes in PV output, the real-time control phase often faces insufficient reactive power capacity or limited adjustment methods, forcing the system to take extreme measures to reduce PV active power output, resulting in power generation losses, and voltage offset remains uncontrolled.

[0009] (4) Fixed-priority reactive power coordination control method

[0010] The static var generator (SVR), photovoltaic (PV) power generation system, and capacitor bank are coordinated according to a fixed priority order (e.g., SVR first, PV second, and capacitors last). When the system operating status changes (e.g., PV output fluctuations, load changes), the fixed priority cannot adaptively adjust, often resulting in low-priority equipment being idle while high-priority equipment is overloaded. This leads to insufficient utilization of reactive power resources, unstable voltage regulation, and ineffective reduction of network losses. In scenarios with high-frequency fluctuations in PV output, fixed priority control easily causes frequent start-ups and shutdowns of equipment, further exacerbating voltage fluctuations and resulting in poor voltage smoothing effects.

[0011] (5) Solution methods for conventional multi-objective optimization algorithms

[0012] Multi-objective particle swarm optimization (MOPSO) or genetic algorithm (GA) are used to solve optimization models that aim to minimize active power loss and node voltage deviation. These algorithms are prone to premature convergence in the later stages of iteration, with particles clustering near local optima. This results in an uneven distribution of the final Pareto optimal front, deviating significantly from the true global optimal front. In practical applications, the optimized switching plans or output commands often lead to situations where the system has acceptable voltage but high network loss during certain periods, or low network loss but frequent voltage exceedances. It is difficult to provide a diverse set of optimal decision schemes that achieve an ideal balance between network loss and voltage quality, resulting in an unsatisfactory overall effect in mitigating voltage deviation and reducing network loss.

[0013] Therefore, there is an urgent need for a scheduling method that can adapt to photovoltaic fluctuations, coordinate multiple types of reactive resources, and optimize time scale coordination in order to effectively mitigate voltage deviations and reduce network losses. Summary of the Invention

[0014] To address the issues of voltage deviation and network losses caused by the intermittency and fluctuation of photovoltaic power output, this application provides a two-stage optimization scheduling method for active distribution networks, from day-ahead to intraday.

[0015] This application discloses a two-stage optimization scheduling method for active distribution networks, encompassing both day-ahead and intraday scheduling, including:

[0016] The pre-execution phase of reactive power optimization is as follows: with the first preset time scale as the scheduling cycle, based on the photovoltaic output forecast data and load forecast data for the next day, with the number of discrete reactive power compensation devices to be switched on as the decision variable, and with the objective function of minimizing the degree of voltage deviation from the reference value of each node in the distribution network and the voltage fluctuation of adjacent time periods, the switching plan of each discrete reactive power compensation device at the first preset time scale for the next day is obtained.

[0017] Execution of intraday rolling short-term scheduling phase: with a second preset time scale less than the first preset time scale as the scheduling cycle, based on the switching plan and the photovoltaic output forecast data and load forecast data updated according to the second preset time scale, the active power output and reactive power output of the continuous reactive power compensation device are used as decision variables to solve for the scheduling instructions of each second preset time scale.

[0018] Among them, the continuous reactive power compensation device includes a static var generator and a photovoltaic grid-connected system. During the intraday rolling short-term scheduling phase, the reactive power output allocation between the static var generator and the photovoltaic grid-connected system is determined by an adaptive priority weight model. The adaptive priority weight model calculates the priority weight based on the response speed, unit adjustment marginal cost and voltage sensitivity of each continuous reactive power compensation device, and uses the day-ahead forecast error of photovoltaic output to correct the priority weight in real time.

[0019] Preferably, the first preset time scale is 1 hour, and the second preset time scale is 15 minutes. Preferably, the objective function for the intraday rolling short-term scheduling phase is:

[0020]

[0021] The objective function value; This is a function representing the intraday voltage deviation from the reference value. This is a function of voltage fluctuations between adjacent time periods within a day. and These are functions representing intraday voltage deviation from reference values. Voltage fluctuation function in adjacent time periods within the day Weighting coefficients; For continuous reactive power compensation device Adjustment cost item for reactive power output; For balance coefficient, ; This represents the total number of continuous reactive power compensation devices.

[0022] As a preferred option, for each continuous reactive power compensation device Calculate its priority weight:

[0023]

[0024] in For continuous reactive power compensation device Sensitivity coefficient to critical node voltage. To adjust marginal cost per unit, For response time coefficient, , , The preset weighting coefficients satisfy the following conditions: ;

[0025] Calculate the day-ahead forecast error for photovoltaic power output:

[0026]

[0027] in Based on photovoltaic power output forecast data for the next day, Current actual measurement data for photovoltaic power output This refers to the rated capacity of the photovoltaic system.

[0028] The priority weights are adjusted in real time using the day-ahead forecast error of photovoltaic output:

[0029]

[0030] in, The preset correction strength coefficient, For continuous reactive power compensation device The prediction error sensitivity coefficient;

[0031] The revised priority weight As a continuous reactive power compensation device The weighted coefficient of the reactive power output adjustment cost term is incorporated into the objective function of the intraday rolling short-term scheduling stage, so that the objective function tends to select continuous reactive power compensation devices with smaller adjustment cost coefficients to undertake reactive power adjustment tasks during the solution process.

[0032] The beneficial effects of this application are that it further analyzes the regulation characteristics of existing discrete reactive power compensation devices such as capacitors and reactors, explores the regulation potential of the remaining capacity of photovoltaic grid-connected systems, and constructs a two-stage reactive power coordination optimization scheduling strategy. This strategy aims to minimize the node voltage deviation and fluctuation over the next 24 hours, using the number of capacitor and reactor groups switched on and off in the next 24 hours as control variables. It also includes a two-stage intraday rolling short-term scheduling strategy, aiming to minimize the node voltage deviation and fluctuation at the current moment, using the active and reactive power output of the photovoltaic power generation system and the reactive power output of the static var generator every 15 minutes as control variables. In the day-ahead stage, with a 1-hour cycle, the switching plans of discrete devices such as capacitors and reactors are optimized using predicted data, with the goal of minimizing voltage deviation and fluctuation. This arrangement allows slow-speed devices to be pre-configured with basic reactive power compensation, suppressing trend voltage drift caused by daily variations in photovoltaic output (e.g., generally higher voltage at noon and lower voltage at night), thereby reducing the overall deviation and hourly fluctuations of the voltage throughout the day. The intraday phase operates on a 15-minute cycle, using ultra-short-term forecast data to continuously optimize the output of static var generators (SVRs) and photovoltaic (PV) systems. This two-stage division of labor ensures that slower-moving equipment executes according to plan, while faster-moving equipment tracks fluctuations in real time, with complementary time scales. During the intraday rolling phase, SVRs and PV systems no longer employ fixed priorities (e.g., SVRs always have priority). Instead, an adaptive weighting model is constructed: response speed, marginal cost, and voltage sensitivity are quantified and weighted, with the reciprocal of the weights used as the adjustment cost embedded in the optimization objective. When voltage fluctuates rapidly, the SVR's response speed has a high weight and a low cost coefficient, so reactive power regulation is automatically allocated to it, utilizing its millisecond-level response to quickly suppress instantaneous overloads. When voltage changes slowly or requires continuous support, the PV's marginal cost weight takes precedence, and the system mobilizes the PV's reactive power capacity to share the regulation task, preventing long-term overload of the SVR. This dynamic weighting mechanism enables the distribution network to adjust with the most appropriate resources under different fluctuation characteristics. It ensures the speed of voltage tracking, avoids resource idleness or overload, and makes the voltage curve more stable. At the same time, due to local compensation and reduction of long-distance reactive power transmission, network losses are significantly reduced compared with fixed priority schemes. Attached Figure Description

[0033] Figure 1 This is a schematic diagram illustrating the principle of the scheduling method in this application;

[0034] Figure 2 This is a schematic diagram showing the adjustable power range under various operating conditions;

[0035] Figure 3 This is a diagram of the IEEE 33-node system architecture.

[0036] Figure 4 The network loss result diagram;

[0037] Figure 5 This represents the lowest voltage under each compensation method.

[0038] Figure 6 Voltage stability indicators under various compensation methods;

[0039] Figure 7 The simulation results are for DTLZ2 and ZDT2, where (a) is DTLZ2 and (b) is ZDT2.

[0040] Figure 8 Comparison of Pareto fronts under different multi-objective particle swarm optimization algorithms;

[0041] Figure 9 For IEEE 33-node system;

[0042] Figure 10 The image shows the predicted daily and hourly photovoltaic output and load power of a typical port area.

[0043] Figure 11 The capacitor and reactor switching plan is given, where (a) is the number of capacitor groups to be switched on, and (b) is the number of reactor groups to be switched on.

[0044] Figure 12 The figures are voltage fluctuation curves of typical nodes in the distribution network before and after day-ahead coordinated reactive power optimization, where (a) is the voltage amplitude 24 hours before the implementation of day-ahead coordinated reactive power optimization, and (b) is the voltage amplitude 24 hours after the implementation of day-ahead coordinated reactive power optimization.

[0045] Figure 13 The photovoltaic output and load power prediction curves for a typical day in a port area are shown every 15 minutes.

[0046] Figure 14 The figures show the voltage fluctuation curves of typical nodes in the distribution network before and after the intraday rolling short-term dispatch, where (a) is the voltage amplitude 24 hours before the intraday rolling short-term dispatch and (b) is the voltage amplitude 24 hours after the intraday rolling short-term dispatch. Detailed Implementation

[0047] 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, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0048] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0049] The present application will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the application.

[0050] Based on differences in operating modes and regulation characteristics, reactive power compensation devices in distribution networks can be categorized into two types: discrete reactive power compensation devices and continuous reactive power compensation devices. As typical representatives of discrete reactive power compensation devices, group-switched capacitors and reactors typically operate on a slower timescale, making them unsuitable for the rapid response requirements of dynamic reactive power regulation. Continuous reactive power compensation devices, such as photovoltaic grid-connected systems and static var generators, possess the ability to dynamically adjust reactive power in real time. In accordance with the requirements of multi-period optimized operation, this application includes discrete reactive power compensation devices within the scope of day-ahead coordinated reactive power optimization, and uses continuous compensation devices for intraday rolling short-term dispatch. Based on the three typical operating modes of photovoltaic power generation systems, this application provides a two-stage reactive power coordinated optimization dispatch strategy, specifically including day-ahead reactive power coordinated optimization with a first preset timescale as the dispatch period within the next day, and intraday rolling short-term dispatch with a second preset timescale less than the first preset timescale as the dispatch period. Its structure is as follows: Figure 1 As shown. Specifically, the first preset time scale can be selected as 1 hour, and the second preset time scale can be selected as 15 minutes.

[0051] The active distribution network day-day / intraday two-stage optimized scheduling method of this embodiment includes:

[0052] The pre-execution coordination reactive power optimization phase: with a 1-hour scheduling cycle, based on the photovoltaic output forecast data and load forecast data for the next day, with the number of discrete reactive power compensation device switching groups as the decision variable, and with minimizing the degree of voltage deviation of each node from the reference value and the voltage fluctuation of adjacent time periods as the optimization objective, the switching plan of each first preset time scale discrete reactive power compensation device for the next day is obtained.

[0053] The data to be collected in advance includes: the grid structure of the distribution network, the grid connection location and rated capacity of distributed photovoltaics, the installation location and capacity parameters of discrete reactive power compensation devices, and the photovoltaic output and load power forecast data for the next day. Combined with day-ahead coordinated reactive power optimization, discrete reactive power compensation devices such as capacitor banks and reactor banks that are switched in groups are taken as the main control objects. The optimal operating plan of discrete reactive power compensation devices in the distribution network for the next day is solved in a centralized manner, which serves as a reference for subsequent intraday rolling short-term scheduling.

[0054] Execution of intraday rolling short-term scheduling phase: with a scheduling cycle of 15 minutes, based on the switching plan and the photovoltaic output forecast data and load forecast data updated according to the second preset time scale, the active power output and reactive power output of the continuous reactive power compensation device are used as decision variables to solve for the scheduling instructions of each second preset time scale.

[0055] Due to biases in the day-ahead forecasting process, relying solely on day-ahead reactive power optimization is often insufficient to simultaneously achieve both economic efficiency and safety in distribution network operation. Therefore, an intraday correction process is necessary in addition to the day-ahead plan. In intraday dispatching, a rolling optimization cycle of 15 minutes is used to update short-term forecast data on grid structure, grid connection location and rated capacity of distributed photovoltaic (PV) systems, and PV output and load power in real time. Continuous reactive power compensation devices include static var generators (SVMs) and PV grid-connected systems. Based on the discrete reactive power compensation device operation plan determined by day-ahead optimization, and with the goal of economical and safe distribution network operation, SVMs and PV grid-connected systems are treated as key control objects. Their active and reactive power outputs are optimized in a coordinated manner, thereby achieving precise control of the distribution network voltage.

[0056] In the intraday rolling short-term scheduling phase of this implementation, the reactive power output allocation between the static var generator (SGFG) and the photovoltaic grid-connected system is determined using an adaptive priority weight model. This model calculates priority weights based on the response speed, unit adjustment marginal cost, and voltage sensitivity of each continuous reactive power compensation device, and uses the day-ahead forecast error of the photovoltaic output to correct the priority weights in real time. Specifically:

[0057] For each continuous reactive power compensation device Calculate its priority weight:

[0058]

[0059] in For continuous reactive power compensation device The sensitivity coefficient to critical node voltage reflects the effect of the continuous reactive power compensation device's output per unit of reactive power on the critical node voltage. It is calculated in real-time through sensitivity analysis based on the current network topology and operating status. The better the adjustment effect, the greater the weight and the higher the priority for its application. The marginal cost of unit adjustment reflects the economic cost of activating the continuous reactive power compensation device to generate reactive power compensation. The marginal cost of the static var generator is the lowest (only equipment losses), followed by photovoltaic reactive power (increased inverter losses), and photovoltaic active power has the highest derating cost (generation loss). This application directly includes this cost item in the adaptive priority weight model, enabling the autonomous selection of low-cost adjustment methods. The response time coefficient reflects the time response capability of the reactive power output. Static var generators (SGFGs) have the fastest response, followed by photovoltaic (PV) power generation systems. This application introduces a response speed constraint in the adaptive priority weight model to ensure that the allocated adjustment amount does not exceed the response capability of the device. The faster the response, the greater the weight. , , The preset weighting coefficients satisfy the following conditions: ;

[0060] Calculate the day-ahead forecast error for photovoltaic power output:

[0061]

[0062] The normalized deviation (ranging from -1 to 1) between the day-ahead forecast and the actual intraday measurement of photovoltaic power output is used to reflect the uncertainty of the day-ahead forecast for the current period. Based on photovoltaic power output forecast data for the next day, Current actual measurement data for photovoltaic power output This refers to the rated capacity of the photovoltaic system.

[0063] The priority weights are adjusted in real time using the day-ahead forecast error of photovoltaic output:

[0064]

[0065] in, The preset correction intensity coefficient controls the degree to which prediction error affects priority. For continuous reactive power compensation device Prediction error sensitivity coefficient; Static var generator =0.5, which is less affected by prediction errors because its output does not depend on the photovoltaic prediction value. The photovoltaic power generation system... =1.0, directly affected by prediction error, because the available reactive power capacity of photovoltaics depends on the current active power output prediction.

[0066] The revised priority weight The weighted coefficients, representing the adjustment cost, are incorporated into the optimization objective of the intraday rolling short-term scheduling model. This causes the optimization objective to favor continuous reactive power compensation devices with smaller adjustment cost coefficients during the solution process, with the following logic:

[0067] when When the value is positive, it indicates that the recent forecast was too high, the actual output was insufficient, the available reactive power capacity of photovoltaics was lower than expected, the priority of photovoltaic power generation system decreased, and the system tended to call more static var generators.

[0068] when When the value is negative, it indicates that the previous forecast was lower than expected, the actual output exceeded expectations, the available reactive power capacity of photovoltaics was higher than expected, the priority of photovoltaic power generation system increased, and the system tends to make full use of photovoltaic reactive power to reduce the pressure on the static var generator.

[0069] This application automatically determines whether to prioritize the use of the static var generator (SVR) or the photovoltaic (PV) power generation system based on the real-time system status, avoiding resource waste caused by fixed priorities when marginal costs are inverted. Through a prediction error correction factor, the coordination strategy becomes adaptive to prediction uncertainties, reducing intraday voltage fluctuations. Under the premise of ensuring voltage safety, the application prioritizes the use of the SVR with the lowest marginal cost, followed by PV reactive power, and finally considers PV active power derating to minimize curtailment losses. This upgrades the optimization from a single voltage quality optimization to a multi-objective collaborative optimization of voltage quality and economic efficiency.

[0070] The optimization objectives and constraints for the reactive power optimization phase in this implementation are as follows:

[0071] Under the timescale used in the previous optimization, this application selects the number of switching groups of capacitors and reactors as the variables to be optimized, with the optimization objective being to minimize the voltage deviation and voltage fluctuation of each node within the next day. The core task of the optimization is to solve for the optimal configuration scheme of each discrete reactive power compensation device within the next day, and its objective function is:

[0072]

[0073] in, and They are nodes In the Hour and the Hourly voltage amplitude, Here, n is the voltage reference value, and n is the total number of nodes in the distribution network.

[0074] The objective function considers both the degree of node voltage deviation from the reference value and the stability of voltage changes between adjacent time points; therefore, it can be regarded as being derived from the voltage deviation function. With voltage fluctuation function The multi-objective model, which is formed by these factors, can be uniformly expressed as follows:

[0075]

[0076] in, and The sum of the two is 1.

[0077] The constraints include power flow constraints, discrete reactive power compensation device operation constraints, and power grid safe operation constraints.

[0078] (1) Current constraints

[0079] Considering the distribution network operation characteristics after distributed photovoltaic (PV) integration, power flow constraints need to simultaneously satisfy active power balance and reactive power balance requirements, which are mathematically expressed as follows:

[0080]

[0081]

[0082] in, and Let be the total active power and total reactive power of node i, respectively. and These represent the active and reactive power injected by the generator into the node, respectively. and These represent the active and reactive power outputs of the distributed power source, respectively. and These represent the active and reactive power absorbed by the load from the power grid, respectively. and These are branch conductance and branch susceptance, respectively. For phase difference, Let be the voltage amplitude at node i.

[0083] (2) Action constraints of discrete reactive power compensation devices

[0084] a. Capacitor bank action constraints: The number of capacitor banks switched on and off at each node in each time period shall not exceed the maximum number of capacitor banks allowed to be connected to the corresponding node, and the number of capacitor bank actions in a single scheduling cycle shall not exceed the preset maximum number of capacitor bank actions.

[0085] The operating state of the capacitor is determined by the number of switching groups, and the specific constraints are as follows:

[0086]

[0087] in, Let represent the number of capacitor banks deployed at node i at time t. This is a critical decision quantity in day-ahead optimization. This refers to the reactive power capacity that a single capacitor bank can provide. This is the total amount of reactive power compensation. This represents the maximum number of groups allowed to access the network.

[0088] The number of times a capacitor can be switched within a scheduling cycle must also be limited, and the switching frequency constraint is as follows:

[0089]

[0090] in, This is the upper limit on the number of actions a capacitor is allowed to take within a single scheduling cycle.

[0091] b. Reactor group action constraints: The number of reactor groups put into operation at each node in each time period shall not exceed the maximum number of groups allowed to be connected to the corresponding node, and the number of reactor group actions in a single scheduling cycle shall not exceed the preset maximum number of reactor group actions.

[0092] Similar to capacitors, the operating state of reactors is also characterized by the number of switching groups, and the specific constraints are as follows:

[0093]

[0094] in, The number of reactor groups put into operation at node i at time t is also a day-ahead optimization variable. The reactive power absorption capacity of a single reactor Let be the total reactive power absorbed by node i at the corresponding time. This represents the maximum number of reactor groups that node i is allowed to connect to.

[0095] The switching operation of the reactor is also limited by the number of operations, and the constraint is as follows:

[0096]

[0097] in, This represents the maximum number of times the reactor is allowed to operate within a single scheduling cycle.

[0098] (3) Constraints on safe operation of power grid

[0099] a. Node voltage constraint: The voltage amplitude of each node in each time period is between the preset lower voltage limit and the upper voltage limit;

[0100] To ensure that each node operates within a safe voltage range, it is necessary to limit the node voltage amplitude. The specific form of this constraint is as follows:

[0101]

[0102] This constraint is used to limit the operating voltage range of the voltage amplitude at node i, while and These represent the lower and upper limits of the allowed voltage for that node, respectively.

[0103] b. Branch current constraint: The current value of each branch in each time period shall not exceed the maximum allowable current value of the corresponding branch;

[0104] Due to the limited current-carrying capacity of the line, the branch current cannot exceed its safety threshold. The specific constraints are as follows:

[0105]

[0106] in, Let k be the actual current in the k-th branch between node i and node j. This is the maximum allowable current for this branch.

[0107] c. Branch power constraint: The active power transmitted by each branch in each time period shall not exceed the upper limit of the active power allowed for the corresponding branch.

[0108] In addition to current limitations, branch transmission power must also be controlled within permissible limits, with the specific constraints being:

[0109]

[0110] in, Let be the active power transmitted along the k-th branch between node i and node j. This is the maximum allowed active power for this branch.

[0111] Therefore, the objective function and the aforementioned constraints together constitute a complete mathematical model for day-ahead coordinated reactive power optimization. By solving this model, the optimal setpoints for discrete reactive power compensation devices can be obtained for the next day, thereby maintaining the basic voltage quality of the distribution network while reducing drastic fluctuations in node voltage over time.

[0112] The optimization objectives and constraints for the intraday rolling short-term scheduling phase in this implementation are as follows:

[0113] The previous coordinated reactive power optimization phase provided a switching plan for discrete reactive power compensation devices for the next day. The intraday rolling short-term scheduling phase further corrects for deviations caused by short-term forecast errors. This phase uses a 15-minute scheduling cycle, with the goal of minimizing voltage deviations and fluctuations at each node within the current time period. Unlike the previous coordinated reactive power optimization phase, the control variables are no longer the switching states of capacitors and reactors, but rather the active power output, reactive power output, and reactive power output of the static var generator (SVM) of the photovoltaic grid-connected system. The corresponding objective function is:

[0114]

[0115] The objective function value; This is a function representing the intraday voltage deviation from the reference value. This is a function of voltage fluctuations between adjacent time periods within a day. and These are functions representing intraday voltage deviation from reference values. Voltage fluctuation function in adjacent time periods within the day Weighting coefficients; For continuous reactive power compensation device Adjustment cost item for reactive power output; For balance coefficient, ; This represents the total number of continuous reactive power compensation devices.

[0116] The constraints include the operating constraints of the photovoltaic grid-connected system and the operating constraints of the static var generator;

[0117] i. Operational constraints of photovoltaic grid-connected systems:

[0118] Based on the current grid operating status and photovoltaic active power output level, this application divides the control mode of the photovoltaic grid-connected system into three operating modes, within the limitation of the inverter's rated capacity. Coordinated switching between these three modes achieves synergistic regulation of active and reactive power. Figure 2 The adjustable power range corresponding to each operating state shown, and the inverter's rated capacity S pv Represented by a semi-circular arc, in the division of the operating area, the arc segment Defined as high power factor mode, arc segment and Defined as low power factor mode, arc segment and It is defined as an active power reduction mode.

[0119] High power factor mode: arc The defined area corresponds to the high power factor operating mode. In this mode, the power factor of the photovoltaic inverter is set between 0.95 lagging and 0.95 leading, and control is applied to voltage over-limit situations at local nodes in the distribution network based on its output reactive power. The reactive power output range of the photovoltaic grid-connected system in this state is:

[0120]

[0121] Among them, Q pv1 P represents the reactive power output range of a photovoltaic grid-connected system in high power factor mode. pv The active power output is S, the rated capacity is φ. min Q is the angle of maximum power factor. min1 and Q max1 These are the lower and upper bounds of reactive power output in high power factor mode.

[0122] Low power factor mode: arc and The defined range corresponds to the low power factor operating mode. If the reactive power support applied in the previous state is insufficient to maintain the distribution network voltage within the safety boundary, the system needs to switch to this state to implement further voltage regulation. Using only the rated capacity as its output boundary, the reactive power output range of the photovoltaic grid-connected system is:

[0123]

[0124] Among them, Q pv2 Q represents the reactive power output range of a photovoltaic grid-connected system in low power factor mode. min2 and Qmax2 These are the lower and upper bounds of reactive power output under low power factor mode, respectively.

[0125] Active power reduction mode: arc and The defined range corresponds to the active power derating mode. If the reactive power support in the first two states cannot sufficiently maintain the distribution network voltage within the safety boundary, the system will trigger the active power derating mode for further regulation. In this operating mode, by appropriately reducing the active power output of the photovoltaic grid-connected system, the inverter capacity is released, thereby expanding the adjustable range of reactive power. At this time, the active and reactive power output ranges of the photovoltaic grid-connected system are:

[0126]

[0127] in, and These represent the active power output range and reactive power output range of the photovoltaic grid-connected system in active power derating mode, respectively. min3 and Q max3 These are the lower and upper bounds of reactive power output under the active power reduction mode, respectively.

[0128] During intraday rolling dispatch, photovoltaic inverters sequentially enter three operating states based on the severity of the grid connection voltage: high power factor mode (state one), low power factor mode (state two), and active power derating mode (state three). Traditional schemes use fixed voltage thresholds for state transitions (e.g., the node voltage threshold for transitioning from state one to state two, and from state two to state three). However, the intermittency and volatility of photovoltaic output can lead to discrepancies between day-ahead forecasts and actual intraday measurements. Fixed thresholds cannot accommodate these discrepancies: when actual output is lower than expected, the system may switch too late due to a high threshold, causing a voltage drop; when actual output is higher than expected, the system may switch too early due to a low threshold, resulting in unnecessary curtailment. The core idea of ​​this strategy is that the photovoltaic grid-connected system switches its operating state in a progressive sequence from high power factor mode to low power factor mode and active power derating mode. The first switching voltage threshold between high power factor and low power factor modes, and the second switching voltage threshold between low power factor and active power derating modes, are adaptively corrected in real time based on the day-ahead prediction error. This adaptive correction is as follows: when the day-ahead prediction error is positive, the first and second switching voltage thresholds are lowered; when the day-ahead prediction error is negative, the first and second switching voltage thresholds are raised. This allows the progressive control to actively adapt to prediction deviations, thereby more accurately mitigating voltage shifts while reducing curtailment losses and network losses. Specifically, this includes:

[0129] (1) Calculate the relative prediction error for the current period.

[0130] At the start of each daily scheduling cycle (e.g., every 15 minutes), the system acquires two sets of data: the day-ahead forecast of photovoltaic (PV) output for that period and the actual measured PV output for that period. By comparing the two, the relative forecast error is obtained. A positive error indicates that the day-ahead forecast is too high; a negative error indicates that the day-ahead forecast is too low; and a zero error indicates that the forecast is unbiased.

[0131] (2) Smoothing the prediction error

[0132] To avoid drastic threshold fluctuations caused by noise from a single measurement, the system exponentially smooths the real-time relative prediction error. Specifically, the current relative prediction error is weighted proportionally with the mean error of historical data for the same period (same time point, similar weather type) to obtain a smoothed effective prediction error. The error for the same period in history was obtained by offline statistical analysis of historical data.

[0133] (3) Calculate the adaptive correction factor

[0134] Based on the smoothed effective prediction error Calculate a correction factor. This factor is linearly related to the prediction error: the larger the prediction error, the larger the correction factor; the smaller the prediction error, the smaller the correction factor. The correction factor is usually limited to a reasonable range, such as between 0.5 and 1.5, to avoid over-correction.

[0135] The correction factor is ,in This is the preset correction factor.

[0136] (4) Dynamically adjust the switching voltage threshold

[0137] First switching voltage threshold The second switching voltage threshold is the voltage threshold value for switching from state one to state two. This is the voltage threshold for switching from state two to state three;

[0138] The base thresholds for the first and second switching voltage thresholds are set as follows: and descent step size and ;

[0139] The first switching voltage threshold is ;

[0140] The second switching voltage threshold is ;

[0141] When the prediction error is positive, it indicates that the prediction is too high and the actual output is insufficient. A value greater than 1 indicates that the switching voltage threshold is lowered. This means that the system will switch from state one to state two, and from state two to state three in advance when the grid connection point voltage is still relatively low, thereby releasing more reactive power capacity in advance and preventing voltage drops caused by insufficient actual active power.

[0142] When the prediction error is negative, it indicates that the prediction is too low and the actual output exceeds expectations. The correction factor is less than 1, and the switching voltage threshold is increased. This means that the system requires a higher voltage to trigger the state switch, thereby avoiding premature entry into the active power derating mode and reducing unnecessary curtailment losses.

[0143] When the prediction error is zero, the correction factor equals 1, and the threshold is restored to the base threshold.

[0144] (5) Perform progressive switching

[0145] During each scheduling cycle, the system monitors the grid connection point voltage in real time and compares it with the adjusted switching voltage threshold.

[0146] If the grid connection point voltage The photovoltaic grid-connected system operates in state one (high power factor mode), outputting only limited reactive power.

[0147] If the current grid connection point voltage If it is currently in state one, it will switch to state two and release the full reactive power regulation capability.

[0148] If the current grid connection point voltage If the reactive power in state two has been exhausted and the voltage rise still cannot be suppressed, then switch to state three, gradually reduce the active power output to release more reactive capacity, until the voltage at the grid connection point drops.

[0149] Once the grid connection point voltage is restored, the return sequence is reversed step by step.

[0150] (6) Rolling updates

[0151] At the start of each new scheduling cycle (15 minutes), repeat (1) to (5) to recalculate the prediction error for the current period and update the switching voltage threshold so that the threshold is always dynamically adjusted to follow the changes in the prediction error.

[0152] When a grid-connected photovoltaic system suddenly reduces its output due to cloud cover, the day-ahead forecast is often too high. In this situation: the correction factor increases, the first and second switching voltage thresholds decrease, and the system enters state two or even state three earlier than expected, before the voltage drops significantly. Preemptively deploying more reactive power or even slightly reducing active power can quickly replenish voltage support and prevent the voltage from falling below the lower limit. The minimum voltage value is raised, the voltage drop is reduced, and voltage deviation is suppressed.

[0153] When photovoltaic (PV) output suddenly increases due to improved weather, the day-ahead forecast is often underestimated. At this time: the correction factor decreases, the switching voltage threshold increases, and the system delays entering states two and three. In the initial stage of voltage increase, limited reactive power regulation in state one is prioritized to avoid premature active power reduction, thus maximizing active power generation while ensuring voltage does not exceed limits. The voltage peak is reduced but not excessively, avoiding unnecessary curtailment, while simultaneously reducing voltage fluctuations. Under cloudy weather, PV output fluctuates multiple times within a short period, causing frequent changes in the sign and magnitude of the forecast error. The adaptive threshold is dynamically adjusted accordingly.

[0154] When a downward trend in power output occurs, the threshold is automatically lowered to reserve reactive power capacity in advance.

[0155] When an upward trend in output occurs, the threshold automatically increases, delaying the rate reduction.

[0156] The switching action of this application is smoother, avoiding repeated switching (oscillation) that may occur under a fixed threshold, resulting in a more stable voltage curve and a significant improvement in voltage fluctuation indicators.

[0157] Given that the active power output of distributed photovoltaic (PV) systems is affected by both sunlight conditions and ambient temperature, voltage control through active power regulation typically requires reducing PV active power output. Reducing active power output leads to increased curtailment during power generation periods, thus diminishing the investment returns of PV projects. Therefore, the third operating mode should be avoided as a reactive power regulation method whenever possible. The third operating mode should only be switched to when reactive power regulation methods under the first two operating modes are insufficient to prevent voltage exceedances or even threaten the safe operation of the distribution network. This is to ensure the safe and stable operation of the distribution network. During peak PV output periods, the PV grid-connected system in this application follows a coordinated principle of prioritizing voltage support while considering operational economics. Specifically, it prioritizes utilizing the remaining capacity of PV inverters, static var generators, and discrete reactive power compensation devices for voltage regulation. Only when the system still faces the risk of voltage exceedances and reactive power regulation capacity approaches its capacity limit will PV active power output be moderately reduced to free up more reactive power support space. While this strategy may result in some power generation revenue loss during certain periods, it effectively avoids greater operational costs caused by voltage exceeding limits, frequent equipment operation, and increased grid losses, thus achieving a comprehensive balance between safety and economy. When the photovoltaic grid-connected system is in high power factor mode, the active and reactive power outputs and power factor constraints of the photovoltaic grid-connected system are as follows:

[0158]

[0159] in, The reactive power output range of the photovoltaic grid-connected system at node i during system operation. Its power factor angle, and These are the lower and upper bounds of reactive power output during high power factor mode operation, respectively.

[0160] When the photovoltaic grid-connected system is in low power factor mode, the active and reactive power outputs and power factor constraints of the photovoltaic grid-connected system are as follows:

[0161]

[0162] in, S represents the active power output range of the photovoltaic grid-connected system at node i during system operation, where S is the rated power value. and These are the lower and upper bounds of reactive power output during low power factor mode operation, respectively.

[0163] When the photovoltaic grid-connected system is in active power derating mode, the active power, reactive power output, and power factor constraints of the photovoltaic grid-connected system are as follows:

[0164]

[0165] in, and These are the lower and upper bounds of reactive power output during active power derating mode operation, respectively. The original active power output before the implementation of active power reduction.

[0166] ii. Static Var Generator (SVA) Operating Constraints: Node voltages are divided into unqualified, qualified, and ideal zones. When a node voltage is in the unqualified zone, the SVA performs maximum reactive power compensation at its rated capacity. When a node voltage is in the qualified zone but exceeds the ideal zone, the SVA performs continuous reactive power regulation to maintain the node voltage close to the reference value. When the node voltage is within the ideal zone, the SVA maintains its current reactive power output. Specifically:

[0167] When the node voltage exceeds the allowable range, to prevent severe voltage exceedance, the static var generator performs reactive power compensation at its maximum capacity, with the specific constraints as follows:

[0168]

[0169] in, Let i be the capacity of the static var generator at node i. Let be the rated capacity of the static var generator at node i.

[0170] When the node voltage is within the acceptable range but deviates from the ideal range, the static var generator (SVA) performs continuous reactive power regulation based on the principle of "voltage stabilization priority," with the following specific constraints:

[0171]

[0172] in, =1.0pu, the meaning of this constraint is: when At this time, the static var generator tends to absorb reactive power to suppress voltage rise. At that time, the static var generator tends to generate reactive power to support the voltage recovery.

[0173] When the node voltage is within the ideal range, the static var generator maintains a constant reactive power output:

[0174] Determining the weights of the objective function is a crucial step in both the day-ahead coordinated reactive power optimization phase and the intraday rolling short-term scheduling phase. This application employs a judgment matrix method to assign weights to each optimization objective, thereby transforming a multi-objective model into a single-objective model. This method not only reflects the differences in importance between objectives but also indicates a preference for specific objectives during the decision-making process. Specifically, a judgment matrix is ​​established by comparing different objectives pairwise, and a 1-9 scale is used for quantification. Table 1 provides the specific definition of this scaling method. Scale value and The target for comparison.

[0175] Based on the meanings of scale values ​​1 to 9 in Table 1, pairwise comparisons are performed on each target to obtain the judgment matrix A, whose expression is:

[0176]

[0177] in, for Compared to Importance scale value =1. Table 1: Meaning of each scale value.

[0178]

[0179] The importance of each objective in the optimization problem can be calculated based on its numerical value. Specifically:

[0180]

[0181] This leads to the weight of each objective relative to the total objective. The value of is calculated using the following formula:

[0182]

[0183] This implementation also proposes a multi-objective particle swarm optimization algorithm that integrates niche mechanisms and Pareto external archives to solve the objective functions of the day-ahead coordinated reactive power optimization stage and the intraday rolling short-term scheduling stage, including:

[0184] Step A: Generate multiple typical photovoltaic power output scenarios and assign the probability of occurrence for each scenario. Each scenario corresponds to a photovoltaic power output curve and a load curve.

[0185] Based on historical photovoltaic (PV) output data and weather forecast information, multiple typical PV output scenarios are generated, covering possible fluctuation patterns. Each scenario... A corresponding 24-hour photovoltaic power output curve is generated, and an occurrence probability is assigned. (Based on historical statistics or subjective experience). Typical scenarios include:

[0186] Scenario 1 (Typical sunny day): The output curve is smooth, reaching its peak at noon, with a probability of... =0.6;

[0187] Scenario 2 (Typical Cloudy): The power output curve fluctuates multiple times, with a relatively low peak value. =0.3;

[0188] Scenario 3 (Typical Rainy Day): Overall output is low and fluctuates drastically, with a high probability of... =0.1;

[0189] At the same time, a corresponding load forecast curve is generated independently for each scenario.

[0190] Step B: Initialize the particle swarm and external files. Each particle represents a set of decision variables. The decision variables for the day-ahead coordinated reactive power optimization stage are the sequence of switching groups of discrete reactive power compensation devices, and the decision variables for the intraday rolling short-term scheduling stage are the active power output and reactive power output sequences of continuous reactive power compensation devices. In the day-ahead coordinated reactive power optimization stage, the particle encoding also includes an auxiliary variable: the preset maximum action step size, which represents the change in the number of switching groups between adjacent time periods.

[0191] Taking the day-ahead coordinated reactive power optimization stage as an example, each particle represents a set of discrete reactive power compensation device switching plans for the day-ahead 24 hours (24 time periods). Traditional coding directly concatenates the number of switching groups for the 24 time periods into a one-dimensional vector. The improved coding adds an auxiliary variable to the coding to reflect the changes in actions between adjacent time periods, guiding the algorithm to generate a smooth switching sequence.

[0192] Specific coding structure (taking capacitor banks as an example, the same applies to reactor banks):

[0193] Main variables: (node During the period (Number of capacitor banks connected);

[0194] Auxiliary variables: (Changes between adjacent time periods) );

[0195] During particle updates, a penalty constraint is imposed on the auxiliary variable: if Then the objective function will have a larger penalty term added (e.g. ,in This is the penalty coefficient. This helps to suppress solutions with excessively large actions during the optimization process.

[0196] Step C: Divide particles into niches based on the crowding distance between them. When the distance between two particles is less than a preset threshold, they are divided into the same niche. The crowding distance is calculated based on the coordinate difference of each particle in each dimension.

[0197] Initialize the particle swarm: The main variable for each particle is randomly generated within its allowed range (satisfying the upper limit of the number of drop groups in a single time period), and the auxiliary variables are calculated based on the main variables.

[0198] The existing niche grouping method is adopted: particles are grouped according to their crowding distance, and those with a distance less than a preset threshold are grouped into the same niche. The initial threshold is set to a relatively large value (e.g., 0.5), which decays exponentially to 0.05 with the number of iterations, thus achieving adaptive grouping.

[0199] Step D: Calculate the fitness value of each particle. The fitness value is the weighted sum of the objective function values ​​under each scenario, where the weight is the probability of occurrence of each scenario. The objective function value under each scenario is determined according to the objective function of the day-ahead coordinated reactive power optimization stage or the intraday rolling short-term scheduling stage. In the day-ahead coordinated reactive power optimization stage, if the absolute value of the change in the number of switching groups in adjacent time periods exceeds the preset maximum action step size, a penalty term is added to the fitness value.

[0200] This method is improved by recognizing that the fitness of each particle is no longer the objective function value under a single scenario, but rather a weighted sum of the objective function values ​​under all scenarios. This weighted sum approach reflects the performance of probabilistic averaging. This scheme employs the weighted sum approach.

[0201] For particles Its adaptability The calculation is as follows:

[0202]

[0203] in, In the scene The objective function value of the current day's coordinated reactive power optimization stage. The calculation needs to be tailored to the scenario. A complete forward-backward power flow calculation is performed based on the predicted load and photovoltaic output curves to obtain the node voltages at each time period, and then the objective function is calculated.

[0204] To improve computational efficiency, parallel computing is possible. The trend of each scenario is analyzed, and the historical best solution caching technology is used to avoid redundant calculations.

[0205] Step E: Store the non-dominated solutions generated by the iteration into the external archive. If the number of non-dominated solutions in the external archive has not reached the capacity limit, store them directly. If the number of non-dominated solutions in the external archive reaches the capacity limit, if the new non-dominated solution dominates the existing solutions in the external archive, replace the dominated solution with the new non-dominated solution. The dominance relationship is compared based on the fitness vectors in each scenario.

[0206] The multi-scene fitness vector of each particle As the objective vector for multi-objective optimization.

[0207] Non-inferior solutions are stored in external archives: solutions Dominant Solution If and only if for all scenarios , And at least one is strictly unequal.

[0208] The file update rules are consistent with the original algorithm: if the capacity is not full, the file is stored directly; if the capacity is full, the new solution replaces some solutions in the file if they dominate the new solution; otherwise, the file is discarded.

[0209] When multiple solutions exist that are independent of each other, the solution with the most balanced performance across different scenarios should be retained first.

[0210] Step F: When a non-dominated solution in the external archive is removed and that non-dominated solution was previously used as the global optimal position of some particles, the newly stored non-dominated solution is used as the updated global optimal position of some particles.

[0211] Step G: Update the velocity and position of each particle according to the particle swarm velocity and position update formula, and constrain the updated decision variables. Simultaneously, locally correct the switching changes exceeding the maximum action step size in the day-ahead coordinated reactive power optimization phase. Velocity updates use the standard PSO formula, but after position updates, constraints need to be applied to both the main and auxiliary variables.

[0212] (1) Clamp the main variable to the allowed range And round down (the number of cut groups is an integer).

[0213] (2) Recalculate the auxiliary variables based on the updated main variables. .

[0214] (3) If the change in motion during a certain period exceeds the maximum allowable step length. If so, the number of cut groups for that time period and its adjacent time periods will be locally adjusted: for example, the excess portion will be evenly distributed to the preceding and following time periods, or a random fine-tuning will be performed and then re-checked.

[0215] (4) This repair step ensures that the cutting plan meets the equipment action rate constraints, while not destroying the original optimization direction of the particles.

[0216] Step H, repeat steps C to G until the preset maximum number of iterations is reached or the convergence condition is met, and output the Pareto optimal solution set.

[0217] The iteration ends when the preset maximum number of iterations is reached (e.g., 200 generations), or when the external archive has not been updated for 30 consecutive generations and the optimal fitness of the population has not improved.

[0218] Output all non-dominated solutions from the external archive, i.e., the Pareto optimal front. Each solution corresponds to a set of switching plans, along with its objective function value and overall weighted fitness for each scenario.

[0219] The intermittency and volatility of photovoltaic power output mainly affect the distribution network by exacerbating voltage timing fluctuations and causing spatial voltage distribution imbalances, which in turn lead to increased network losses. This implementation method uses a multi-objective particle swarm optimization algorithm to specifically address these problems through the following three mechanisms.

[0220] (1) In particle coding, the change in the number of switching groups in adjacent time periods is introduced as an auxiliary variable, and a large penalty term is applied to changes exceeding the preset maximum action step size (such as a maximum of 2 groups per switch) in the fitness function; this forces the switching plan generated by the algorithm to transition smoothly in time, avoiding abrupt changes. The voltage fluctuation amplitude in adjacent time periods is directly reduced; the probability of voltage exceeding the limit decreases, because excessively fast switching actions often lead to voltage overshoot or under-adjustment.

[0221] (2) Generate multiple typical photovoltaic power output scenarios (sunny, cloudy, rainy), assign an occurrence probability to each scenario, and the fitness of the particles is no longer the objective function value under a single scenario, but the weighted sum of the objective function values ​​under all scenarios; the comparison of non-dominated solutions in the external archive is based on the multi-scenario fitness vector—solution Dominant Solution If and only if in all scenarios The target value is not worse than Furthermore, at least one scenario is strictly optimal; Results: The final selected switching plan maintains good voltage quality under various weather conditions, rather than being suitable only for a single mode; When the actual weather deviates from the daytime forecast (e.g., sunny weather turns cloudy), the system can still maintain the voltage within the acceptable range, avoiding drastic voltage fluctuations caused by scenario switching. The worst-case scenario of network loss is suppressed because the algorithm weighs the loss levels under various scenarios during optimization.

[0222] (3) The niche distance threshold adaptively decreases with the number of iterations: the threshold is large in the early stage, and the particle grouping is coarse, maintaining global diversity and avoiding premature convergence; the threshold is small in the later stage, and the grouping is fine, promoting local fine search; the external archive is linked with the global optimal position: when a solution is removed from the archive, the global optimal position of the particle it served is updated to the new solution to prevent the optimization direction from being lost. Effect: It is easier to find the global Pareto front, so that the two objectives of voltage deviation and voltage fluctuation can be optimized at the same time. The switching plan is more balanced in all 24 time periods of the day, and there will be no abnormal deviation in local time periods.

[0223] Simulation verification:

[0224] Figure 3 The IEEE 33-node system architecture diagram shows that a 0.5MW photovoltaic power station is configured at nodes 16, 21, and 30, with a corresponding inverter capacity of 0.6MVar. Static var generators (SVG) are installed at nodes 5, 15, and 31, with a single unit compensation capacity of 0.6MVar. In addition, 20 capacitor banks (C) are installed at node 25, each with a compensation capacity of 0.25MVar. The acceptable voltage fluctuation range of the system is [0.95, 1.05] pu.

[0225] This implementation scheme selects four configuration schemes for simulation: photovoltaic (PV), PV+C (PV and capacitor bank combined), PV+SVG (PV and static var generator combined), and PV+SVG+C (PV, static var generator, and capacitor bank combined). The network loss, minimum node voltage, and voltage stability index values ​​are recorded for each time period. The corresponding relationships are shown in [see attached diagram]. Figure 4 , Figure 5 and Figure 6 .

[0226] Among the four compensation methods, the network loss is significantly lower when PV+SVG and PV+SVG+C are used for compensation compared to methods that only configure PV or PV+C. In the operating scenario using the PV+SVG+C coordinated control strategy, the maximum reduction in network loss can reach 0.029MW, demonstrating good energy-saving effects.

[0227] Depend on Figure 5 The simulation results show that when the PV+SVG+C combination is used for reactive power compensation, the minimum voltage value of the system in each time period is significantly increased and is closer to the ideal voltage level of 1.0 pu, thus effectively avoiding the problem of voltage exceeding the lower limit caused by insufficient reactive power at the end of the distribution network.

[0228] The Voltage Stability Index (LCPI) assesses the voltage stability of various nodes in a distribution network under distributed photovoltaic (PV) grid-connected conditions. The closer the LCPI value is to zero, the better the system's stability. Figure 6It is evident that relying solely on the photovoltaic system for reactive power compensation results in weak compensation and consequently, poor voltage stability. Furthermore, capacitor banks struggle to achieve continuous adjustment during switching operations, leading to voltage surges that further degrade voltage stability. Static var generators (SVG) possess the capability for continuous reactive power adjustment, enabling photovoltaic and capacitor bank combined systems to achieve superior voltage stability. The system exhibits the most outstanding voltage stability when employing a combination of photovoltaics, SVG, and capacitor banks.

[0229] Simulation analysis of the multi-objective particle swarm optimization algorithm in this application:

[0230] In this embodiment, DTLZ2 and ZDT2 are selected as test functions. Simulations are performed using the Multi-Objective Particle Swarm Optimization (MOPSO), the Improved Gray Wolf (MOGWO) algorithm, and the Multi-Objective Particle Swarm Optimization (NPAMOPSO) algorithm of this application, respectively. The GD and SP performance indicators are calculated to verify the superiority of the improved algorithm.

[0231]

[0232]

[0233] The DTLZ2 and ZDT2 functions were simulated for the three algorithms mentioned above. The simulation results were compared with the actual optimal solutions as follows: Figure 7 As shown in Table 2. From Figure 7 As shown in Table 2, the NPAMOPSO algorithm of this application is significantly better than the MOPSO and MOGWO algorithms in both SP and GD metrics. The obtained non-dominated solution sets are all located on the true Pareto optimal front, and the convergence performance is excellent.

[0234] Simulations were conducted using three algorithms: MOPSO, MOGWO, and NPAMOPSO (as proposed in this application). The Pareto optimal solutions for network loss and voltage deviation were compared, for example... Figure 8 As shown.

[0235] Table 2 Comparison of Algorithm Test Function Indicators

[0236]

[0237] Depend on Figure 8 Simulation results show that the solution set obtained by the NPAMOPSO algorithm in this application exhibits better convergence characteristics than the MOPSO and MOGWO algorithms, fully verifying the performance advantages of the improved algorithm in this application. Table 3 shows the optimal results of reactive power optimization calculated by simulation. As can be seen from the table, the improved NPAMOPSO algorithm in this application has better optimization effects on system network loss and node voltage deviation.

[0238] Table 3 Optimal Results of Reactive Power Optimization

[0239]

[0240] Simulation verification of the day-ahead and intraday two-stage reactive power coordination and optimization scheduling strategy was performed on the IEEE 33-bus system.

[0241] The load is scaled by multiplying the standard load of each node by the per-unit value of the corresponding time period, and the photovoltaic active power is injected into the system by multiplying the installed capacity by the per-unit value of the corresponding time period, such as... Figure 9 As shown, a discrete voltage regulation device combining capacitors and reactors is configured at nodes 4, 8, 12, and 18, with a single unit capacity of ±0.05×10kVar. At nodes 8 and 14, a 2MW photovoltaic power station is connected to each. At nodes 16 and 18, SVG reactive power compensation devices are connected to each, with a single unit capacity of 1.5MVar. To improve the voltage margin at the end of the distribution network, the voltage of the balancing node 1 is set to 1.05pu (indicating that the voltage of the upstream grid is at a relatively high operating level). At the same time, the voltage deviation evaluation is still based on 1.0pu to ensure that the optimization target is consistent with the nominal voltage of the distribution network.

[0242] (1) The effect of recent coordination on reactive power optimization

[0243] The predicted hourly photovoltaic output and load power for a typical port area on a given day are as follows: Figure 10 As shown in Table 4, the actual load at any node at a certain moment is obtained by multiplying the standard load value by the per-unit value for that period, while the active power output of the photovoltaic system is determined by converting the rated capacity and the per-unit value for the corresponding period.

[0244] Table 4. Typical Daily Hourly Photovoltaic Output and Load Power Forecast Data for a Port Area

[0245]

[0246] The switching plan for the discrete compensation device, obtained after recent coordinated reactive power optimization calculations, is as follows: Figure 11 As shown.

[0247] Depend on Figure 11It can be seen that the recently optimized discrete reactive power regulation scheme exhibits a clear "capacitor-dominated, reactor-assisted" characteristic: capacitors undertake the main task of voltage support during most periods, while reactors are mainly put into operation during periods of high photovoltaic output or increased risk of voltage overshoot, to absorb excess reactive power, suppress excessive voltage rise, and mitigate voltage fluctuations. From periods 1 to 18, capacitor switching at each compensation node is generally dispersed, but its operation significantly increases from periods 19 to 24, especially with a large number of clusters being concentrated at multiple compensation points from periods 20 to 23. This indicates that as photovoltaic output weakens or even approaches zero and the load level relatively increases, the undervoltage trend at the system's end becomes more prominent, requiring increased capacitive reactive power injection to achieve voltage rise and voltage deviation convergence. Correspondingly, reactor switching is mainly concentrated from periods 10 to 16, with more reactors at node 18, and some at nodes 8 and 12 during certain periods. From periods 19 to 24, reactor operation is generally lower, indicating that the system primarily focuses on undervoltage compensation during this stage, with a relatively lower need to suppress overvoltage.

[0248] Capacitors and reactors complement each other on the time scale. Capacitors are used to boost voltage, improve undervoltage, and reduce voltage deviation, while reactors are used to absorb reactive power, constrain overvoltage, and smooth fluctuations during periods of high photovoltaic output. This achieves overall optimization of voltage levels and improvement of timing stability while meeting voltage constraints.

[0249] Using reference node 1, connecting nodes 5 and 9, photovoltaic power station access nodes 8, 14 and 18, and feeder terminal node 33 as the analysis objects, voltage analysis is conducted on representative nodes in the distribution network. The 24-hour voltage changes of these nodes before and after the implementation of day-ahead coordinated reactive power optimization are shown in the distribution curves below. Figure 12 As shown.

[0250] The 24-hour voltage distribution curves of typical nodes before day-ahead reactive power optimization show significant temporal fluctuations and spatial differences in system voltage throughout the day. During periods 1-8 and 19-24, photovoltaic output is low, and voltage is mainly affected by load levels, showing a decreasing trend as load increases. The voltage at end nodes (such as node 33) remains consistently low, with a minimum value of approximately 0.91 pu. At night, the voltage at nodes 14 and 18 can also drop to approximately 0.93 pu, indicating a significant deviation from per-unit values. During periods 9-18, voltage rises significantly and peaks between 10-16, with some nodes reaching a peak of approximately 1.07 pu. This indicates that photovoltaic active power injection plays a supporting role in improving node voltage levels, but it also increases the risk of system overvoltage. Before optimization, the node voltage distribution curves show significant fluctuations during the photovoltaic ramp-up and pullback phases, resulting in poor supply voltage quality stability. The 24-hour voltage distribution curves of typical nodes after day-ahead reactive power optimization show that day-ahead optimization significantly improves system voltage levels and temporal stability. During periods 1-8 and 19-24, low-voltage nodes were effectively improved: the lowest voltage at node 33 increased from approximately 0.91 pu to approximately 0.98 pu, and the voltage differences between nodes converged significantly, with node voltages mostly concentrated in the range of approximately 0.98-1.05 pu. During periods 9-18, the optimized voltage peak was effectively reduced, and no significant trend of exceeding the upper limit was observed, indicating that discrete reactive power switching effectively constrained the voltage rise caused by high photovoltaic output. The optimized voltage curves of typical nodes were smoother, and the intraday fluctuation amplitude was significantly reduced, improving the voltage quality and operational safety of the distribution network under photovoltaic fluctuation scenarios. Table 5 shows the statistical results of the average hourly voltage deviation of each node. As can be seen from the table, before day-ahead coordinated reactive power optimization, the average hourly voltage deviation per node in the distribution network was 0.0488, and the voltage fluctuation at the same time scale was 0.0108. After day-ahead coordinated reactive power optimization, both indicators decreased to 0.0217 and 0.0028, respectively. Therefore, it can be seen that the day-ahead coordinated reactive power optimization proposed in this application can significantly reduce the voltage deviation and voltage fluctuation of the distribution network. Specifically, the average hourly voltage deviation per node is reduced by 55.5%, and the average hourly voltage fluctuation per node is reduced by 74.1%, which shows that the method can effectively improve the power supply quality of the distribution network.

[0251] Table 5 shows the average hourly voltage deviation and fluctuation of each node before and after reactive power optimization.

[0252]

[0253] (2) Intraday rolling short-term scheduling effect

[0254] The predicted photovoltaic output and load power every 15 minutes on a typical day in a port area are as follows: Figure 13As shown, the actual load value of any node at a given moment is obtained by multiplying the standard load value corresponding to that node by the per-unit value of the current time period. The active power output of the photovoltaic system is determined based on its rated capacity and by referring to the per-unit value of the corresponding time period.

[0255] Based on the calculation results of reactive power coordination optimization, intraday rolling short-term dispatch calculations were carried out. According to the PV three-state output regulation strategy, the voltage distribution of each node in the distribution network during the dynamic change over time was obtained. To intuitively demonstrate the improvement effect of intraday rolling short-term dispatch on voltage regulation, reference node 1, connecting nodes 5 and 9, PV power plant access nodes 8, 14 and 18, and feeder end node 33 were selected as typical analysis objects. The 24-hour voltage distribution curves of these nodes before and after the implementation of intraday rolling short-term dispatch are shown below. Figure 14 As shown.

[0256] The 24-hour voltage distribution curves of typical nodes before the intraday rolling short-term dispatch show that during the high-output period of photovoltaic power generation (33-72), the node voltage generally increases, with the highest voltage at the end nodes 14 and 18 reaching 1.06 pu, while nodes 8 and 9 remain around 1.05 pu. During periods 1-32 and 73-96, the voltage generally decreases, with most nodes ranging from 0.98 to 1.02 pu. The weakest end node, 33, drops to a low of around 0.98 pu during the evening off-peak period. Overall, the voltage level is quite sensitive to changes in photovoltaic output, with the midday peak period closer to the upper limit, resulting in a contraction in voltage operating margin.

[0257] The 24-hour voltage distribution curves of typical nodes after intraday rolling short-term scheduling show that the voltage curves of typical nodes converge significantly. During the high-output photovoltaic period (33-72), the rise in node voltage is significantly weakened, with the peak voltage of terminal nodes 14 and 18 dropping from approximately 1.06 pu to 1.01 pu, and nodes 8 and 9 also concentrated at 1.02 pu. During the low-output photovoltaic periods (1-32 and 73-96), the voltage generally remains within a range closer to the per-unit value. The voltage at terminal node 33 rises during the evening low-valley period and remains at 1.00 pu, exhibiting an overall "peak shaving and valley filling" effect. The voltage difference between nodes is significantly reduced, and the operating margin is increased.

[0258] Table 6 presents the statistical results of the average voltage deviation and fluctuation of each node every 15 minutes before and after the intraday rolling short-term dispatch. As shown in the table, before the intraday rolling short-term dispatch, the average voltage deviation per node per 15 minutes in the distribution network was 0.0274, and the voltage fluctuation at the same time scale was 0.0193. After the intraday rolling short-term dispatch, both indicators decreased to 0.0014 and 0.0006, respectively, representing further reductions of 29.6% and 57.1%. The results indicate that the intraday rolling short-term dispatch proposed in this application can significantly improve the voltage operation status of the distribution network, with both voltage deviation and voltage fluctuation being significantly suppressed, and the reliability of power supply quality greatly improved.

[0259] Table 6 shows the average voltage deviation and fluctuation of each node every 15 minutes before and after the intraday rolling short-term scheduling.

[0260]

[0261] While this application has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other embodiments.

Claims

1. A two-stage optimization scheduling method for active distribution networks, characterized in that, include: The pre-execution day coordination reactive power optimization phase: with the first preset time scale as the scheduling cycle, based on the photovoltaic output forecast data and load forecast data for the next day, with the number of discrete reactive power compensation device switching groups as the decision variable, and with minimizing the degree of voltage deviation from the reference value of each node in the distribution network and the voltage fluctuation amount in adjacent time periods as the objective function, the switching plan of the discrete reactive power compensation device for each first preset time scale in the next day is obtained. Execution of intraday rolling short-term scheduling phase: with a second preset time scale less than the first preset time scale as the scheduling cycle, based on the switching plan and the photovoltaic output forecast data and load forecast data updated according to the second preset time scale, the active power output and reactive power output of the continuous reactive power compensation device are used as decision variables to solve for the scheduling instructions of each second preset time scale. The continuous reactive power compensation device includes a static var generator (SVA) and a photovoltaic grid-connected system. During the intraday rolling short-term scheduling phase, the reactive power output allocation between the SVA and the photovoltaic grid-connected system is determined using an adaptive priority weight model. The adaptive priority weight model calculates the priority weight based on the response speed, unit adjustment marginal cost, and voltage sensitivity of each continuous reactive power compensation device, and uses the day-ahead forecast error of photovoltaic output to correct the priority weight in real time.

2. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 1, characterized in that, For each continuous reactive power compensation device Calculate its priority weight: ； in For continuous reactive power compensation device Sensitivity coefficient to critical node voltage. To adjust marginal cost per unit, For response time coefficient, , , The preset weighting coefficients satisfy the following conditions: ; Calculate the day-ahead forecast error for photovoltaic power output: ； in The photovoltaic power output forecast data is based on the forecast data for the next day. Current actual measurement data for photovoltaic power output This refers to the rated capacity of the photovoltaic system. The priority weights are corrected in real time using the day-ahead forecast error of photovoltaic output: ； in, The preset correction strength coefficient, For continuous reactive power compensation device The prediction error sensitivity coefficient; The revised priority weight As a continuous reactive power compensation device The weighted coefficient of the reactive power output adjustment cost term is incorporated into the objective function of the intraday rolling short-term scheduling stage, so that the objective function tends to select continuous reactive power compensation devices with smaller adjustment cost coefficients to undertake reactive power adjustment tasks during the solution process.

3. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 2, characterized in that, The objective function for the intraday rolling short-term scheduling phase is: ； The objective function value; This is a function of intraday voltage deviation from the reference value; This is a function of voltage fluctuations between adjacent time periods within a day. and These are functions representing intraday voltage deviation from reference values. Voltage fluctuation function in adjacent time periods within the day Weighting coefficients; For continuous reactive power compensation device Adjustment cost item for reactive power output; For balance coefficient, ; This represents the total number of continuous reactive power compensation devices.

4. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 2, characterized in that, The constraints of the intraday rolling short-term scheduling phase include photovoltaic system operating constraints: The photovoltaic grid-connected system switches its operating state in a progressive order of high power factor mode, low power factor mode and active power derating mode. The first switching voltage threshold between high power factor mode and low power factor mode and the second switching voltage threshold between low power factor mode and active power derating mode are adaptively corrected in real time based on the day-ahead prediction error. The adaptive correction is as follows: when the current day's prediction error is positive, the first switching voltage threshold and the second switching voltage threshold are reduced; When the prediction error is negative, the first switching voltage threshold and the second switching voltage threshold are increased.

5. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 4, characterized in that, The constraints of the intraday rolling short-term scheduling phase also include static var generator (SVM) operation constraints: The node voltage is divided into three regions: unqualified, qualified, and ideal. When the node voltage is in the unqualified area, the static var generator performs maximum reactive power compensation at its rated capacity. When the node voltage is in the acceptable range but exceeds the ideal range, the static var generator performs continuous reactive power regulation according to the principle of maintaining the node voltage close to the reference value. When the node voltage is within the ideal range, the static var generator maintains its current reactive power output.

6. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 1, characterized in that, The constraints for the current reactive power optimization phase include: Capacitor bank operation constraints: The number of capacitor banks switched on and off by each node in each time period shall not exceed the maximum number of capacitor banks allowed to be connected by the corresponding node, and the number of capacitor bank operations in a single scheduling cycle shall not exceed the preset maximum number of capacitor bank operations. Reactor group operation constraints: The number of reactor groups put into operation at each node in each time period shall not exceed the maximum number of groups allowed to be connected to the corresponding node, and the number of reactor group operations in a single scheduling cycle shall not exceed the preset maximum number of reactor group operations. Node voltage constraint: The voltage amplitude of each node in each time period is between the preset lower voltage limit and the upper voltage limit; Branch current constraint: The current value of each branch in each time period shall not exceed the maximum allowable current value of the corresponding branch; Branch power constraint: The active power transmitted by each branch in each time period shall not exceed the upper limit of the active power allowed for the corresponding branch.

7. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 1, characterized in that, Both the day-ahead coordinated reactive power optimization stage and the intraday rolling short-term scheduling stage are solved using a multi-objective particle swarm optimization algorithm that integrates niche mechanisms and Pareto external archives, including: Step A: Generate multiple typical photovoltaic power output scenarios and assign the probability of occurrence for each scenario. Each scenario corresponds to a photovoltaic power output curve and a load curve. Step B: Initialize the particle swarm and external files. Each particle represents a set of decision variables. The decision variables for the day-ahead coordinated reactive power optimization stage are the sequence of switching groups of discrete reactive power compensation devices, and the decision variables for the intraday rolling short-term scheduling stage are the active power output and reactive power output sequences of continuous reactive power compensation devices. In the day-ahead coordinated reactive power optimization stage, the particle encoding also includes an auxiliary variable: the preset maximum action step size, which represents the change in the number of switching groups between adjacent time periods. Step C: Divide particles into microhabitats based on the crowding distance between them. When the distance between two particles is less than a preset threshold, they are divided into the same microhabitat. The crowding distance is calculated based on the coordinate difference of each particle in each dimension. Step D: Calculate the fitness value of each particle. The fitness value is the weighted sum of the objective function values ​​under each scenario, where the weight is the probability of occurrence of each scenario. The objective function value under each scenario is determined according to the objective function of the day-ahead coordinated reactive power optimization stage or the intraday rolling short-term scheduling stage. In the day-ahead coordinated reactive power optimization stage, if the absolute value of the change in the number of switching groups in adjacent time periods exceeds the preset maximum action step size, a penalty term is added to the fitness value. Step E: Store the non-dominated solutions generated by the iteration into the external archive. If the number of non-dominated solutions in the external archive has not reached the capacity limit, store them directly. If the number of non-dominated solutions in the external archive reaches the capacity limit, if the new non-dominated solution dominates the existing solutions in the external archive, replace the dominated solution with the new non-dominated solution. The dominance relationship is compared based on the fitness vectors in each scenario. Step F: When a non-dominated solution in an external file is removed and that non-dominated solution was previously used as the global optimal position of some particles, the newly stored non-dominated solution is used as the updated global optimal position of the aforementioned particles. Step G: Update the velocity and position of each particle according to the particle swarm velocity and position update formula, and constrain the updated decision variables. At the same time, make local corrections to the switching changes that exceed the maximum action step size in the day-ahead coordinated reactive power optimization stage. Step H, and repeat steps C through G until the preset maximum number of iterations is reached or the convergence condition is met, then output the Pareto optimal solution set.

8. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 7, characterized in that, The scenarios include typical sunny, typical cloudy, typical cloudy, and typical rainy.

9. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 1, characterized in that, The first preset time scale is 1 hour, and the second preset time scale is 15 minutes.

10. The active distribution network day-day / intraday two-stage optimized scheduling method according to claim 9, characterized in that, The objective function for the current reactive power optimization phase is: ； in, and They are nodes The voltage amplitude at hour t and hour t-1 Here, n is the voltage reference value, and n is the total number of nodes in the distribution network. The weighting factor for voltage deviation from the reference value within the next day; This is the weighting factor for voltage fluctuations in adjacent time periods within the next day.

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