Flexible resource aggregation and scheduling method and system based on power distribution network operation safety domain

Abstract

The application discloses a flexible resource aggregation scheduling method and system based on power distribution network operation safety domain, and relates to the technical field of power system energy management. Through the cooperative collection of operation parameters of transferable loads and delayable loads by a load aggregator and a home energy management system, the loads are grouped by using a k-means++ clustering algorithm, an equivalent aggregation model is constructed to reduce the optimization dimension; in combination with a voltage stability safety domain and a thermal stability safety domain, a safe and feasible injection power space of the power distribution network is established; a mixed integer nonlinear optimization model containing generation cost, power abandonment penalty and demand response incentive is constructed with the minimum total operation cost as the target, and safety domain constraints and aggregation load characteristics are embedded; efficient collaborative scheduling of distributed resources is realized, and the operation safety and economy of the power distribution network are improved.

Description

Technical Field

[0001] This application relates to a flexible resource aggregation and scheduling method and system based on the distribution network operation security domain, belonging to the field of power system energy management technology. Background Technology

[0002] In modern smart distribution networks, with the widespread integration of distributed power sources, electric vehicles, and various adjustable loads, demand-side resources are gradually becoming a crucial force in system regulation. To achieve effective integration and unified scheduling of massive, dispersed, flexible loads, current technologies generally employ load aggregators (LAs) as intermediary entities. These LAs collect power consumption characteristics and operating status information from user-side equipment, construct equivalent aggregation models, and incorporate them into the upper-level scheduling optimization system. Mainstream methods typically categorize loads based on simple rule classification or weighted averaging to generate representative power curves or response capability indicators, which then participate in day-ahead or real-time scheduling decisions. Meanwhile, in the scheduling modeling process, some studies introduce AC power flow constraints to improve accuracy, but these often employ simplified linearization methods to handle nonlinear elements and frequently model network constraints and load regulation potential separately, lacking in-depth consideration of their coupling effect.

[0003] However, when residential loads (typically smaller in capacity) actively participate in system dispatch, the impact of individual loads is often limited, resulting in a smaller impact on individual interests. To effectively utilize the dispatch potential of these loads, load aggregation becomes a key strategy. Load aggregators, acting as a bridge between distribution network operators (DSOs) and small consumers, incentivize consumer participation in demand response (DR) programs, thereby enabling the effective management and utilization of these small-scale resources.

[0004] Existing aggregation scheduling methods have significant limitations when dealing with large-scale heterogeneous flexible resources. On the one hand, traditional clustering strategies do not fully consider the differences in time flexibility, power characteristics, and user preferences among different load types (such as transferable and deferred loads), leading to distorted aggregation models that fail to accurately reflect actual regulation potential. On the other hand, most scheduling models ignore physical constraints such as voltage overruns and line overloads, or implicitly include safety boundaries in iterative verification, easily resulting in infeasible solutions. Furthermore, the lack of explicit modeling and embedding mechanisms for the distribution network's operational safety domain causes optimization results to deviate from safety boundaries under complex operating conditions, affecting system stability. Therefore, how to construct a collaborative scheduling framework that balances load behavior diversity and distribution network physical feasibility while ensuring computational efficiency has become a key bottleneck issue in improving demand-side resource utilization efficiency. Summary of the Invention

[0005] The purpose of this application is to address the shortcomings of the aforementioned background technology by proposing a flexible resource aggregation and scheduling method and system based on the safety domain of the distribution network. This method realizes the aggregation and scheduling of flexible resources based on the safety domain, unifies and coordinates resources on the supply side and demand side, and improves the system's economy and regulation capability.

[0006] To achieve the above objectives, the technical solution adopted in this application is as follows:

[0007] Firstly, this application provides a flexible resource aggregation and scheduling method based on the distribution network operation security domain, including:

[0008] Based on the information interaction between the load aggregator and the home energy management system, the operating parameters of the transferable and deferred loads of multiple users are obtained. The operating parameters include rated power, available time window, minimum continuous operating time, maximum allowable number of interruptions, and user comfort preferences.

[0009] The k-means++ clustering algorithm is used to cluster the operating parameters of the transferable and delayable loads of multiple users, and an aggregated load model consisting of equivalent power range, total energy demand and start-stop logic is constructed.

[0010] A model of operational safety domain, including voltage stability safety domain and voltage stability safety domain, is established by combining voltage stability constraints and thermal stability constraints of the distribution network. The voltage stability safety domain is derived from the relationship between node injected power and line voltage drop, while the thermal stability safety domain is transformed into a quadratic inequality constraint on active and reactive power based on the condition that the branch current does not exceed the corresponding thermal limit. Together, they define a safe and feasible injected power space.

[0011] A mixed-integer nonlinear optimization model is established with the goal of minimizing the total operating cost. It comprehensively considers the generation cost, renewable energy curtailment penalty, and demand response incentive cost. The aggregated load model and the safety domain model are used as model inputs. Under the premise of satisfying the AC power flow equation, unit ramp rate, distributed power output limit, and network operation boundary, the optimal scheduling scheme is solved.

[0012] Based on the optimal scheduling scheme, the global optimization result is obtained. After the global optimization result is sent to each load aggregator, each load aggregator decomposes the reference scheduling instruction locally and allocates it to the individual loads under its jurisdiction. The individual loads prioritize satisfying high-priority loads and minimize the deviation between actual power consumption and the plan.

[0013] As a further improvement to this application, the transferable load includes dishwashers, microwave ovens, vacuum cleaners, dryers, sensors, and irons; the deferred load is the charging load of an electric vehicle in G2V mode.

[0014] As a further improvement of this application, the voltage stability safety domain is derived based on the relationship between node injected power and line voltage drop, and the thermal stability safety domain is transformed into a quadratic inequality constraint on active and reactive power based on the condition that the branch current does not exceed the corresponding thermal limit. Together, they define a safe and feasible injected power space, including:

[0015] By utilizing the relationship between node-injected active / reactive power and line resistance and reactance, and combining it with the root node voltage reference, a linearized voltage deviation constraint is established.

[0016] Based on the premise that the branch current amplitude does not exceed the corresponding thermal limit, Ohm's law is transformed into a quadratic cone constraint on the downstream injected power.

[0017] The intersection of the voltage stability domain and the thermal stability security domain is used as the safe and feasible injection power space for distribution network operation.

[0018] As a further improvement of this application, the voltage stability safety domain considers a power distribution system that ignores phase angle. The voltage difference between any two nodes is determined by the node voltage amplitude, line transmission power, line resistance and reactance. The line transmission power is approximately simplified. Based on the relationship between the node voltage and the root node voltage, a voltage stability safety domain is constructed to ensure that all node voltages are within the upper and lower limits. Based on Ohm's law, the branch current amplitude is determined by the node injected power and line parameters.

[0019] As a further improvement to this application, the method employs the k-means++ clustering algorithm to cluster the operating parameters of multiple users' transferable and deferred loads, constructing an aggregated load model consisting of equivalent power range, total energy demand, and start-stop logic; including:

[0020] The k-means++ clustering algorithm is used to cluster the operating parameters of the transferable and delayable loads of multiple users. The load aggregator performs aggregation based on the information submitted by consumers. The centroid-based k-means clustering algorithm is used to group the loads to form an equivalent aggregated load model.

[0021] Loads are partitioned based on their similar available time; after load partitioning, profiles are constructed based on the power requirements of the loads during the corresponding time intervals of their operating time.

[0022] In the process of grouping the load using the centroid-based k-means clustering algorithm, the first centroid is randomly selected, and subsequent centroids are selected according to a probability distribution proportional to the square of the distance to their nearest existing centroid. Euclidean distance is used as the similarity criterion, and the multidimensional feature vectors are normalized.

[0023] As a further improvement to this application, the voltage stability safety domain is:

[0024]

[0025]

[0026] In the formula, n The number of nodes P h , Q h They are nodes h Active and reactive power; The voltage magnitude at the root node; node s For nodes j With nodes k The node number of the first intersection of the upstream branch; , The equivalent impedance parameter represents the impedance from the root node to the node. i and nodes h The equivalent impedance on the common path; Active power at the upper limit of voltage safety P h Sensitivity, Active power at the upper limit of voltage safety Q h Sensitivity; Active power at the lower boundary of voltage safety P h Sensitivity, Active power at the lower boundary of voltage safety Q h Sensitivity; u M , u m These are the upper and lower limits of the voltage. , These are the upper and lower limits of the voltage, respectively.

[0027] As a further improvement to this application, the thermal stability safety domain is:

[0028]

[0029]

[0030] In the formula, branch road ij Thermal stability current limit; α k The active power mapping coefficient, β k These are reactive power mapping coefficients used to determine node positions. k Does the load flow through the branch? ij ; express j The set of downstream branch nodes of a node; Let d be the voltage amplitude of the root node, and d be the set of downstream branch nodes of node j.

[0031] As a further improvement to this application, the objective function for the total operating cost includes the sum of power generation fuel cost, wind and solar curtailment penalty cost, and demand response incentive cost; the power generation fuel cost, wind and solar curtailment penalty cost, and demand response incentive cost are all calculated by multiplying the maximum absolute deviation between the actual dispatched power of each aggregation group and the reference plan by the time-of-use incentive price; specifically:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] In the formula, OF is the objective function; b g This represents the power generation cost coefficient for distributed generators. P g This refers to the active power of the distributed generator; VW curt This represents the penalty cost coefficient for wind power curtailment; VS curt This refers to the cost coefficient for photovoltaic curtailment. The cost of responding to demand; T Total time period; C This represents the total number of clusters capable of handling load transfer. For a transferable load balancing cluster c exist t Fixed power at any given time; For the first c Equivalent scheduling power of a transferable load cluster; Indicates the first i DR quantity of each transferable load; D The total number of clusters that can defer load; For Deferred Load Cluster d exist t Fixed power at any given time; For the first d Equivalent scheduling power of a delayable load cluster; For the first dEquivalent scheduling power of a transferable load cluster; Indicates the first i The amount of DR that can defer the load; G For generator sets; For generator g exist t Active power at any given moment; for t Time of the first n Wind power wastage on a single busbar; for t Time of the first n The amount of solar energy wasted by the busbar; for t The cost of responding to demand at any given moment; They are respectively in t Time connection to the first n Active power generation of wind turbines via bus; They are respectively in t Time connection to the first n Active power generation of the bus-mounted solar generator; In order to be in t Always connected to the bus n Inelastic active load; In order to be in t Always connected to the bus n Inelastic reactive load; for t Time bus n and m The positive trend between them; for t Time bus n and m The reactive current between them; They are respectively in t Bus at time n The availability of wind energy at the location; They are respectively in t Bus at time n The availability of solar energy at the location; busbars n Total wind power generation capacity, busbars n Total solar power generation capacity, M For the set of busbars, Let be the amount of wind energy wasted on the nth bus at time t. Let be the amount of solar power wasted by the nth bus at time t;

[0039] Other related constraints include: line flow, line limits, voltage amplitude and angle limits, DG operating range and ramp;

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] In the formula: Indicates the first c A portable load balancing cluster in time t The state is 1 if scheduled, and 0 otherwise; Minimum power for the cluster This represents the maximum power of the cluster. For the first c Each cluster t The start indicator of the interruptible period of time; This is the status indicator of the c-th transferable load cluster at time t; For the c-th transferable load cluster at time t -1 status indicator; For the first c Each cluster t The stop indicator for the interruptible period of time; The duration of the time interval; For the first c The equivalent working time of a transferable load cluster represents the total time that the cluster needs to run continuously. For the first d The energy requirements of a cluster can be postponed; These are the behavioral attributes corresponding to availability. The maximum number of DR events per day; For each load cluster d Arrival time, For each load cluster d departure time; x d,t For the first d A DL cluster in time t Switch status indicator, This is the stop indicator for the c-th transferable load cluster during the interruptible period at time h. For the first d The rated power of a load cluster that can be deferred.

[0049] As a further improvement to this application, when each load aggregator decomposes the reference dispatch instructions locally, it prioritizes meeting the power demand of users with high comfort levels and minimizes individual dispatch deviations.

[0050] Secondly, this application provides a flexible resource aggregation and scheduling method based on the distribution network operation security domain, including:

[0051] The parameter acquisition module is used to acquire the operating parameters of multiple users' transferable and deferred loads based on the information interaction between the load aggregator and the home energy management system. The operating parameters include rated power, available time window, minimum continuous operating time, maximum allowable number of interruptions, and user comfort preferences.

[0052] The model building module is used to cluster the operating parameters of the transferable and delayable loads of multiple users using the k-means++ clustering algorithm, and to build an aggregated load model consisting of equivalent power range, total energy demand and start-stop logic.

[0053] The safety domain establishment module is used to establish an operational safety domain model that includes a voltage stability safety domain and a voltage stability safety domain, by combining the voltage stability constraints and thermal stability constraints of the distribution network. The voltage stability safety domain is derived based on the relationship between node injected power and line voltage drop, while the thermal stability safety domain is transformed into a quadratic inequality constraint on active and reactive power based on the condition that the branch current does not exceed the corresponding thermal limit. Together, they define a safe and feasible injected power space.

[0054] The model solving module is used to establish a mixed-integer nonlinear optimization model with the goal of minimizing the total operating cost. It comprehensively considers the generation cost, renewable energy curtailment penalty and demand response incentive cost, and takes the aggregated load model and the safety domain model as model inputs. Under the premise of satisfying the AC power flow equation, unit ramp rate, distributed power output limit and network operation boundary, it solves the optimal scheduling scheme.

[0055] The load scheduling module is used to obtain the global optimization result based on the optimal scheduling scheme. After the global optimization result is sent to each load aggregator, each load aggregator decomposes the reference scheduling instruction locally and allocates it to the individual loads under its jurisdiction. The individual loads prioritize satisfying high-priority loads and minimize the deviation between actual power consumption and the plan, thus completing the closed-loop control from centralized decision-making to distributed execution.

[0056] The beneficial effects of the technical solution proposed in this application are:

[0057] To achieve effective scheduling of numerous small-scale distributed resource clusters in a distribution network, this application proposes a user-side resource aggregation scheduling method based on the distribution network's operational safety domain. This method establishes a flexible resource potential model considering distribution network operational constraints by aggregating transferable and deferred loads. By constructing voltage stability and thermal stability safety domains, it ensures a safe and feasible power injection space for the distribution network without violating thermal and voltage constraints. The method utilizes k-means clustering to group loads, forming an equivalent aggregated load model, simplifying the scheduling problem while preserving the main technical attributes and consumer preferences of the original loads. Through decomposition steps, the scheduling plan of aggregated loads is decomposed into scheduling plans for individual loads, ensuring that the scheduling plan for each flexible load meets consumer preferences and constraints, while minimizing scheduling deviations and interruptions. Compared with traditional methods, this application can more accurately assess the network's operational status, ensuring the network operates within the safety boundary, improving computational efficiency and the accuracy of calculating the safety domain boundary in high-dimensional space. This method effectively solves the concurrent scheduling problem of large-scale flexible energy devices and small distributed resource clusters, improving scheduling flexibility and efficiency.

[0058] This application effectively solves the problems of dimensionality curse, model distortion, and physical infeasibility in large-scale distributed flexible resource concurrent scheduling by constructing a four-stage collaborative architecture of "load characteristic clustering—dual security domain modeling—multi-objective optimization—scheduling instruction decomposition." The k-means++ clustering algorithm is used to scientifically group transferable loads (SL) and deferred loads (DL), significantly reducing the complexity of the scheduling problem while preserving the essential characteristics of user electricity consumption behavior. For the first time, the voltage stability domain and thermal stability domain are jointly constructed as a safe and feasible injected power space for distribution network operation, achieving prior compliance assurance of scheduling schemes in terms of voltage exceedance and line overload. By establishing a mixed-integer nonlinear optimization model that integrates generation costs, renewable energy curtailment penalties, and demand response incentives, the supply-side and demand-side resources are coordinated in a unified manner, improving system economy and regulation capabilities. The entire framework balances modeling accuracy, computational efficiency, and engineering practicality, supporting closed-loop control from centralized optimization to local execution, and is applicable to various typical scenarios such as urban residential areas and industrial parks. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of a flexible resource aggregation and scheduling method based on the distribution network operation security domain.

[0060] Figure 2 This is a schematic diagram of a flexible resource aggregation and scheduling system based on the distribution network operation safety domain. Detailed Implementation

[0061] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0062] In the description of this application, unless otherwise expressly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0063] Terminology Explanation:

[0064] ACOPF: Alternating Current Optimal Power Flow;

[0065] BCVSR: Voltage Stability Region Considering Boundary Crises;

[0066] Bonmin: Basic Open-source Nonlinear Mixed Integer Programming;

[0067] CPLEX: CPLEX Optimization Studio, CPLEX optimization solver;

[0068] DG: Distributed Generator;

[0069] DER: Distributed Energy Resources;

[0070] DN: Distribution Network;

[0071] DL: Deerrable Load;

[0072] DR: Demand Response;

[0073] DSO: Distribution System Operator;

[0074] EV: Electric Vehicle;

[0075] FL: Flexible Load;

[0076] G2V: Grid to Vehicle (mode).

[0077] Gurobi: Gurobi Optimizer;

[0078] HEMS: Home Energy Management System;

[0079] Ipopt: Interior Point OPTimizer;

[0080] ITMAX: Maximum Number of Iterations;

[0081] LA: Load Aggregator;

[0082] MATLAB: Matrix Laboratory (software);

[0083] MINLP: Mixed-Integer Nonlinear Programming;

[0084] OF: Objective Function;

[0085] OPF: Optimal Power Flow;

[0086] Pyomo: Pyomo Optimization Modeling Language, Pyomo optimization modeling framework;

[0087] Python: Python Programming Language;

[0088] SL: Shiftable Load;

[0089] SVSR: Steady-State Voltage Stability Region;

[0090] VScurt: Solar Curtailment Penalty Cost Coefficient;

[0091] VWcurt: Wind Curtailment Penalty Cost Coefficient.

[0092] This application provides a flexible resource aggregation and scheduling method based on the operational safety domain of a distribution network. This method collects operational data of user-side controllable loads and distributed energy resources, and combines this data with grid topology and physical constraints to achieve coordinated and optimized scheduling of demand-side resources. The method includes the following steps:

[0093] Based on the information interaction between the load aggregator (LA) and the home energy management system (HEMS), the operating parameters of the transferable load (SL) and deferred load (DL) of multiple users are obtained. The operating parameters include rated power, available time window, minimum continuous operating time, maximum allowable number of interruptions and user comfort preferences.

[0094] The k-means++ clustering algorithm is used to group loads with similar characteristics and construct an aggregated load model consisting of equivalent power range, total energy demand and start-stop logic, so as to reduce the dimensionality of the scheduling problem and retain the technical attributes and user behavior characteristics of the original load.

[0095] A model of operational safety domain, including voltage stability safety domain and voltage stability safety domain, is established by combining voltage stability constraints and thermal stability constraints of the distribution network. The voltage stability safety domain is derived from the relationship between node injected power and line voltage drop, and is used to ensure that the voltage amplitude of each node is within the range. The thermal stability safety domain is transformed into a quadratic inequality constraint on active and reactive power based on the condition that the branch current does not exceed the corresponding thermal limit. Together, they define a safe and feasible injected power space.

[0096] A mixed-integer nonlinear optimization model is established with the goal of minimizing total operating cost. It comprehensively considers generation cost, renewable energy curtailment penalty and demand response incentive cost. The aggregated load model and safety domain constraints are used as model inputs. Under the premise of satisfying AC power flow equation, unit ramp rate, distributed power output limit and network operation boundary, the optimal scheduling scheme is solved.

[0097] After the global optimization results are sent to each load aggregator, the aggregator decomposes the reference scheduling instructions locally and distributes them to the individual loads under its jurisdiction. The individual loads prioritize high-priority loads and minimize the deviation between actual power consumption and the plan, thus completing the closed-loop control from centralized decision-making to distributed execution.

[0098] This application uses the k-means clustering algorithm to cluster transferable loads (SL) and deferred loads (DL), forming an equivalent aggregated load model. SL and DL have different operating characteristics and consumer preferences. The clustering algorithm groups loads with similar characteristics, simplifying the scheduling problem while preserving the main technical attributes and consumer preferences of the original loads. Voltage stability and thermal stability security domains are constructed to describe the safe and feasible power injection space of the distribution network without violating thermal and voltage constraints. The voltage stability security domain is defined by the relationship between node voltage and root node voltage, while the thermal stability security domain is based on the upper limit of branch current to ensure the thermal stability of the system. With the goal of minimizing system operating costs, the application considers network topology, the operating constraints of distributed energy resources (DER), and the scheduling requirements of flexible loads. The scheduling model is based on AC optimal power flow (ACOPF), analyzes the impact of aggregated demand response (DR) on the system level, and ensures that the scheduling plan meets network constraints.

[0099] The load aggregator (LA) and home energy management system (HEMS) are involved: the LA acts as an intermediary between flexible loads (FL) and distribution network operators (DSOs) through the HEMS. Consumers can interact with the HEMS through a dedicated application / tool. Demand flexibility sources: The framework considers two sources of demand flexibility: transferable loads (SL) and deferred loads (DL). SLs are considered to be independent of continuous tasks, uninterrupted, and have continuous consumption levels, such as dishwashers, microwave ovens, vacuum cleaners, dryers, sensors, irons, etc.

[0100] This application clarifies two typical equipment types for flexible loads, reflecting practical application scenarios. Dishwashers, dryers, and other appliances with fixed and uninterrupted task cycles meet the characteristics of SL (Sustainable Load). Electric vehicles, after being connected, can flexibly adjust their charging periods before leaving the site, exhibiting the characteristics of DL (Dependent Load). In practical applications, SL can also be extended to non-continuously operating appliances such as washing machines and air conditioners, and DL can also cover household energy storage systems; however, this application does not limit these aspects.

[0101] The rated power, available time window, minimum running time, and user priority weight are obtained for each load. These parameters are the basic inputs for building an accurate load model. Rated power determines the energy consumption level, available time window defines the scheduling degrees of freedom, minimum running time reflects the rigid constraints of the task, and user priority weight is used to formulate differentiated response strategies. This information is collected through the HEMS user interface to ensure that the aggregated model takes into account both technical feasibility and user experience. In practical applications, data can be automatically read through smart sockets or energy management systems; this application embodiment does not limit this.

[0102] DL refers to electric vehicles (EVs) in a grid-to-vehicle (G2V) model with discrete consumption levels. Load aggregation: LA performs aggregation based on information submitted by consumers to reduce the dimensionality of the problem while maintaining overall flexibility. A centroid-based k-means clustering algorithm is used to group loads, forming an equivalent aggregated load model. This approach reduces the constraints and the size of control variables in the scheduling problem, making it more manageable while preserving the main technical attributes of the original loads and consumer preferences.

[0103] Furthermore, the cooperation model: The proposed framework is based on a cooperation model, with the LA acting as the entity cooperating with the DSO. The distribution network (DN) can purchase energy from the upper-level grid to meet demand, and it is assumed that the DN has some traditional distributed generation facilities. Problem formulation: This includes three steps: load aggregation, optimization, and decomposition. The aggregation step involves grouping, aggregating, and formulating an equivalent aggregated load model for SLs and DLs. SLs are grouped according to availability, while DLs are not grouped because they are inserted when idle, with availability time only between the arrival and departure of EVs. After grouping, representative parameters are extracted from each cluster, which form the basis of the equivalent model. Optimized scheduling: Performed by the DSO to minimize the system operating costs considering network, LA, and distributed energy resource (DER) operational constraints. The scheduling result includes a decision vector, i.e., a reference schedule for optimal energy allocation to DERs and LAs. Decomposition: After scheduling, the LA calculates the maximum absolute deviation from the reference schedule to alleviate the computational burden on the DSO.

[0104] As an alternative, transferable loads (SL) and deferred loads (DL) are grouped using the k-means clustering algorithm to form an equivalent aggregated load model. The k-means clustering algorithm is used to aggregate the loads. k-means++ is used to select the seed to eliminate the drawback of k-means relying on centroid initialization.

[0105] Among them, k-means++ is an improved version of the traditional k-means clustering algorithm. It optimizes the initial centroid selection strategy and selects the initial centroid in a probabilistic manner, avoiding the problems of unstable clustering results and easy getting trapped in local optima caused by the random selection of initial centroids in traditional k-means. Ultimately, it improves the clustering quality and convergence efficiency, and is especially suitable for grouping scenarios of high-dimensional data (such as multi-parameter load characteristic data).

[0106] SL Load Model: SL is independent of continuous tasks, uninterrupted, and has a continuous consumption level. The model ensures that the load power equals the rated power required for operation, the operating time is sufficient, and the minimum runtime requirement is met. The aggregation model consists of the algebraic summation of SL vectors, and is transformed into an equivalent model to support optimal scheduling and decomposition.

[0107] DL Model: DL can be interrupted and transferred in time, but is limited by the maximum available time. The model ensures that the energy storage charging capacity matches the discharging capacity within a cycle.

[0108] Considering a power distribution system neglecting phase angle, the voltage difference between any two nodes is determined by the node voltage amplitude, line transmission power, and line resistance and reactance. Line transmission power can be approximated and simplified. Based on the relationship between node voltage and root node voltage, a voltage stability safety region is constructed to ensure that all node voltages remain within their upper and lower limits. Based on Ohm's law, the branch current amplitude is determined by the node injected power and line parameters. A thermal stability safety region is constructed to ensure that branch currents do not exceed their upper limits, maintaining system thermal stability.

[0109] This model aims to minimize total operating cost, comprehensively considering generation costs as well as the costs of wind and solar power reduction. Demand response costs are incorporated to incentivize flexible user-side resource allocation. Regarding constraints, the model ensures a balance between active and reactive power, preventing grid instability caused by power imbalances. Simultaneously, wind and solar power reductions are limited to reduce renewable energy waste. Line flow limits are strictly enforced to ensure safe grid operation. Furthermore, the model maintains node voltage and angle within safe ranges to prevent voltage collapse and other issues. Finally, the operating range and slope limitations of distributed generation units are considered to ensure stable operation of these units.

[0110] In the k-means clustering algorithm based on centroids to group loads, the first centroid is randomly selected, and subsequent centroids are selected according to a probability distribution proportional to the square of the distance to their nearest existing centroid. This is the core initialization mechanism of the k-means++ algorithm, designed to avoid the slow convergence or getting trapped in local optima caused by uneven initial centroid distribution in traditional k-means. A probability-weighted approach guides new centroids away from already selected points, improving clustering quality and stability. This method significantly improves the accuracy of segmenting heterogeneous load groups and enhances the representativeness of the aggregation model. In practical applications, other optimization initialization strategies, such as the maximum-minimum distance method, can also be used; this application does not limit this approach.

[0111] Euclidean distance is used as the similarity criterion to normalize the multidimensional feature vectors. Euclidean distance is suitable for measuring the similarity of continuous variables and can effectively reflect the comprehensive differences of different loads in dimensions such as power, time, and energy consumption. To eliminate the influence of the dimensions, the original data is preprocessed using Z-score or Min-Max normalization before calculation. This design ensures the scientific validity and robustness of the clustering results. In practical applications, time-series matching methods such as Dynamic Time Warping (DTW) can be introduced according to the characteristics of load behavior; this application does not limit this approach.

[0112] Furthermore, the number of clusters, k, is dynamically determined based on the total load and computing resources, with a value ranging from 3 to 10. Too small a number of clusters, k, leads to strong heterogeneity within groups and distortion of the aggregation model; too large a number prevents effective dimensionality reduction. Experiments show that in typical residential power distribution scenarios, dividing thousands of devices into 5 to 8 clusters can balance modeling accuracy and computational efficiency. The k value can be automatically optimized using the Elbow Method or the contour coefficient method. In practical applications, the k value can be adaptively adjusted according to seasonal changes and electricity consumption habits; this embodiment does not limit this.

[0113] By utilizing the relationship between node-injected active / reactive power and line resistance and reactance, and combining it with the root node voltage reference, a linearized voltage deviation constraint is established. Based on the premise that the branch current amplitude does not exceed the corresponding thermal limit, Ohm's law is transformed into a quadratic cone constraint regarding downstream injected power. The intersection of the voltage stability domain and the thermal stability safety domain is taken as the safe and feasible injected power space for distribution network operation. A single safety domain can only prevent certain types of risks, while the joint boundary can comprehensively cover the dual threats of voltage exceeding limits and line overload. By simultaneously satisfying voltage and thermal stability constraints, the generated scheduling scheme is physically feasible. This design improves the overall safety and robustness of the system. In practical applications, the safety margin can be dynamically adjusted according to the operating status to achieve flexible switching between conservative and aggressive strategies; this application does not limit this. The total operating cost includes the sum of three parts: power generation fuel cost, wind and solar curtailment penalty cost, and demand response incentive cost. The objective function comprehensively considers the economics of the supply side and the willingness of the demand side to participate. Power generation cost reflects the operating expenses of conventional units; curtailment penalty reflects the pressure of new energy consumption; and DR incentive cost quantifies the social value brought about by user adjustment behavior. The weighted average of these three factors constitutes the global optimization objective, promoting coordinated optimization of power generation, grid, and load. In practical applications, the weighting coefficients can be dynamically adjusted based on market electricity prices or policy guidance; this application's embodiments do not impose such limitations.

[0114] Optionally, the cost item is the maximum absolute deviation between the actual dispatched power of each aggregation group and the reference plan, multiplied by the time-of-use incentive price. Demand response cost measures the inconvenience caused by changes in users' electricity plans; the greater the deviation, the higher the compensation. This design incentivizes active user participation while limiting excessive deviations, ensuring comfort. Time-of-use price Higher values ​​can be set during peak hours to guide peak shaving and valley filling. In practical applications, satisfaction indices or credit scoring mechanisms can also be introduced for personalized pricing, but this application does not limit this approach.

[0115] Constraints include active / reactive power balance, renewable energy output limits, distributed generation ramp rates, and flexible load start-stop logic. These constraints collectively constitute the complete system operating conditions. Power balance ensures real-time supply and demand matching; wind and solar output limits reflect resource availability; DG ramp rates simulate physical response capabilities; and load start-stop logic ensures safe equipment operation. All constraints are integrated into the MINLP model, ensuring the scheduling results are engineering-executable. In practical applications, constraint items can be added or removed according to specific projects; this application's embodiments do not limit this.

[0116] Furthermore, this application can utilize MATLAB to call the CPLEX or Gurobi solvers, or use Python combined with the Pyomo framework for modeling and optimization. Commercial solvers (such as CPLEX and Gurobi) support mixed-integer nonlinear programming (MINLP) and possess high convergence speed and stability; open-source toolchains (such as Python + Pyomo + Ipopt / Bonmin) provide flexibility and low-cost deployment paths. Both methods can achieve efficient solutions to complex scheduling models. In practical applications, distributed algorithms such as Benders decomposition or ADMM can also be used to improve parallel performance; this application does not limit this approach.

[0117] During the local decomposition phase, priority is given to meeting the electricity needs of users with high comfort levels, while minimizing individual dispatch deviations. The decomposition process must balance fairness and control precision. High-priority users (such as hospitals and data centers) should have their power supply guaranteed first; LA implements differentiated strategies according to contractual agreements to enhance user stickiness. In practical applications, game theory mechanisms can be introduced to achieve multi-party negotiated decomposition, but this application embodiment does not limit this approach. The method is applicable to typical power distribution system scenarios such as urban residential areas, industrial parks, and campus microgrids. The framework of this application has good versatility and portability, and its applicability has been verified in various typical scenarios. Urban residential areas are mainly composed of flexible residential loads, suitable for large-scale aggregation; industrial parks have the advantage of centralized management, facilitating the coordination of high-power equipment; campus microgrids integrate photovoltaics, energy storage, and electric vehicles, serving as an integrated demonstration platform for "source-grid-load-storage". In practical applications, it can also be extended to commercial buildings, transportation hubs, and other fields, but this application embodiment does not limit this approach.

[0118] The following is in conjunction with the appendix Figure 1This application will be described in further detail. This embodiment provides a flexible resource aggregation scheduling method based on the distribution network operation safety domain. The flexible resource aggregation scheduling operation framework based on the distribution network operation safety domain includes: Flexible load aggregation framework: Through the collaboration of load aggregator (LA) and home energy management system (HEMS), transferable load (SL) and delayable load (DL) are integrated, and the k-means++ clustering algorithm is used to realize the equivalent modeling of load flexibility and reduce the scheduling dimension. Flexible resource aggregation model: For SL, the load model is constructed and the cluster parameters are extracted based on the available time grouping model; for DL, the interruptible discrete model is established based on the maximum available time constraint to support dynamic power adjustment. (3) Distribution network safety domain model: Combining the voltage stability domain (node ​​voltage amplitude constraint) and the thermal stability safety domain (branch current amplitude limit), the power space for safe and feasible injection of power is defined to ensure that the scheduling scheme does not exceed the limit. (4) Flexible resource operation scheduling model: With the goal of minimizing the total system cost, the safety domain constraint and mixed integer nonlinear optimization are integrated, and the efficient concurrent scheduling of distributed resources is realized through the "aggregation-optimization-decomposition" process. The specific implementation is described as follows.

[0119] (1) The flexible load aggregation framework for optimized operation of the distribution network is described in detail below:

[0120] Load aggregators (LAs) act as intermediaries between flexible loads (FLs) and distribution network operators (DSOs) through home energy management systems (HEMS), leveraging the ability of small consumers in a geographic area to adjust their consumption at certain times of the day in response to their willingness to receive monetary rewards. Consumers can interact with HEMS through dedicated applications / tools.

[0121] For day-ahead scheduling, HEMS: (i) acquires information submitted by FL consumers; (ii) monitors the consumption of individual appliances; (iii) supports information flow between consumers and LA; and (iv) controls the load based on the reference scheduling allocated by the LA. This framework considers two sources of demand flexibility: SL and DL. Transferable loads (SL) in this application are considered independent of continuous tasks, uninterrupted, and have continuous consumption levels. SL consists of loads such as dishwashers, microwave ovens, vacuum cleaners, dryers, sensors, and irons. Electric vehicles are considered as deferred loads (DL) in a grid-to-vehicle (G2V) mode with discrete consumption levels. FLs have different slack levels depending on consumer comfort. To mitigate the complexity caused by the participation of different loads, LA attempts to reduce the dimensionality of the problem while maintaining overall flexibility. To this end, LA performs aggregation based on consumer-submitted information and shares the aggregated demand data with the DSO. In this application, a centroid-based k-means clustering algorithm is used to represent load flexibility because it is suitable for comprehensive analysis and effective on large-scale datasets. Cluster-based aggregation reduces the constraints and size of control variables in the scheduling problem, making the problem more tractable. Furthermore, it retains the original descriptions of FL and their main technical properties and preferences, in contrast to direct aggregation and approximate models.

[0122] The proposed framework is based on a cooperative model, where LA is assumed to be an entity cooperating with DSO. The distribution network (DN) can purchase energy from the upstream grid to meet demand. For simplicity, it is assumed that the DN has some traditional distributed generation facilities.

[0123] A detailed overview of the problem formulation includes three steps: load aggregation, optimization, and decomposition. The aggregation step involves grouping, aggregating, and formulating an equivalent aggregated load model for SLs and DLs. Typically, SLs are not always inserted in residential environments, and the availability of SLs used to perform tasks may vary. Therefore, SLs are grouped according to availability to achieve effective management of these loads and reflect actual behavior. DLs are not grouped because they are assumed to be inserted once parked; therefore, the corresponding availability time is only between the arrival and departure of EVs. However, without loss of generality, the grouping step can be performed on both categories of load. After load partitioning, representative parameters are extracted from each obtained cluster. These parameters form the basis of the equivalent model. Optimal scheduling is performed by the DSO with (OF1) as the objective to minimize the system operating cost considering operational constraints of the network, LA, and DER. The result of the DSO scheduling involves a decision vector, the optimal energy allocation to the DER, and the reference schedule LA. The decomposition of the comprehensive decision, i.e., obtaining the reference schedule after scheduling, is then performed. The maximum absolute deviation from the reference schedule is calculated by the LA to alleviate the computational burden on the DSO.

[0124] (2) Establish a flexible resource aggregation model that combines the operational constraints of the distribution network, as detailed below:

[0125] This application presents the mathematical formulas for the load model to aggregate FL, and then proposes an equivalent model using the obtained parameters.

[0126] SL aggregation is performed in two steps. In the first step, loads are partitioned based on their similar availability. After load partitioning, profiles are constructed based on the power requirements of each load during corresponding time intervals of its operating time. This profile has the following attributes: availability, power requirements, operating time requirements, and start-stop time. The k-means clustering algorithm is used to aggregate the profiles to obtain clusters. c ), making | C |<| I The k-means algorithm starts with an arbitrary set of cluster centers, so k-means++ is used to select a seed around which clusters are formed. It eliminates the drawback of k-means relying on centroid initialization. At any given time, let... D ( X i ) indicates from X i To the nearest already selected X c The shortest distance.

[0127] The step-by-step process of obtaining cluster representativeness and membership weights using k-means++ seed selection is as follows:

[0128] Step 1. From the consumption vector X i The initial centroid is selected uniformly and randomly. X c ;

[0129] Step 2. Select Next X c ,choose X c = ∈ χ probability ;

[0130] Step 3. Repeat step 2 until a selection is made. k The center of mass;

[0131] Step 4. Based on Euclidean distance, divide each X i Assigned to the nearest X c To obtain k One cluster;

[0132] Step 5. Calculate the new X c As all that is assigned to it X i The average value;

[0133] Step 6. Repeat steps 5 and 6 until distance minimization no longer improves, or until the fixed number of iterations of ITMAX is completed;

[0134] Step 7. For each X i :turn up X c And X i Assign to this cluster;

[0135] Step 8. For each cluster c = 1...k, after the update X c =All assigned to this cluster X i The average value;

[0136] Step 9. Output has X c The final clustering is based on membership degree.

[0137] The cluster FL obtained from the above steps has approximate available time, operating time, and power distribution represented by the centroid. These parameters are crucial for optimizing cluster scheduling. They can be used to represent the flexibility of load shifting, while the profile represents the demand that has a significant impact on the scheduling process. To achieve optimal cluster scheduling, the operating time and demand distribution of the cluster obtained above need to be optimized.

[0138] 1. The SL load model considers SLs that are independent of continuous tasks and cannot be interrupted or adjusted before the operation ends. However, these loads can be shifted within a certain available timeframe. If Indicates a single load i DR capacity (kW), operating time is The behavioral attribute corresponding to availability is The single load model of SL can be represented as follows:

[0139] (1)

[0140] (2)

[0141] (3)

[0142] In the formula: Rated power (kW) when operating under transferable loads; The start / stop time (h) for transferable loads; Indicates the first i A transferable load in time t The state; if scheduled, it is 1, otherwise it is 0.

[0143] Equation (1) ensures the load i The power should be equal to the rated power required for operation, and equation (2) ensures sufficient operating time. For a load to complete its operation, the minimum operating time requirement is met by equation (3). Here, for continuous independent loads participating in DR, is a positive integer.

[0144] For the set of numbers of SL , i ∈ (1, 2, ..., I), the aggregate power of each load is equal to the sum of the power of all loads in the set. ;

[0145] (4)

[0146] (5)

[0147] (6)

[0148] In the formula, For the first c Energy requirements (kWh) for a mobile cluster; For transferable load i A separate load; Affected by individual load constraints and aggregation parameters, and By a separate load vector composition.

[0149] Corresponding to equation (4), in equation (5) it represents the use of having i Clustering of SL c The clustering model obtained is agglomerated. The agglomerated model consists of the algebraic summation of SL vectors, which is transformed into an equivalent model to support optimal scheduling and decomposition, and presents as a continuous power range as shown in Equation (6). The transformed parameters Limited by the lower and upper limits of power, and within the available time. Internal binary variables Control. Total energy is limited by The updated connection time is This equivalent model is considered for a given cluster. c Scheduling of all loads under [the specified load].

[0150] Improved model in equation (6) The power is limited to / Within, and obtain updated working hours, making (gather c The equivalent working time does not exceed the set c (Working hours). Here. To assist in selection in a way that meets energy requirements at an appropriate number of intervals. At the same time, the on-time requirements of each load must be met during the decomposition process. Otherwise, if all loads are connected simultaneously, If a load is considered power-limited, then in this case, power might be dispatched within a single interval to save energy. For loads with time requirements exceeding one interval, this dispatching would be contradictory, as the power in the next dispatch interval might be less than the minimum power requirement. Therefore, for effective decomposition, the reference schedule should meet the minimum working time requirement of the load, which can be achieved by using... , and TLONc restrictions This also proves the model equivalence of each SL cluster and can be obtained by decomposing the reference timeline ( To verify.

[0151] 2. DL Model: These loads can be interrupted and transferred in time, but are limited by the maximum available time; for example, EV charging loads can be interrupted and serviced before the last trigger. For a given time range t The DR capacity (kW) is Each load j and arrival-departure time ( , The individual load model of DL is represented by equation (7):

[0152] (7)

[0153] (8)

[0154] In the formula: For the first j The energy demand (kWh) of a deferable cluster.

[0155] In equation (7) j The set of feasible regions can be represented as , To postpone load j Individual load vectors. For a set n Load aggregation quantity j∈(1,2,..., J The aggregate power should be equal to the set The sum of the power of all individual loads, and = .

[0156] (9)

[0157] (10)

[0158] In the formula: For the first d The energy demand (kWh) of a deferable cluster.

[0159] For any DL cluster d The aggregated load model can be represented by equation (9). The total load model in equation (9) is transformed into the equivalent load model with discrete power range proposed in equation (10) for load scheduling. The improved model describes how, before the latest departure time, the DL cluster scheduling can be adjusted by discontinuous power range to meet load demand. The modified parameters... (Deferred load set) d The equivalent power is limited by the cluster. d Maximum power demand during cluster arrival and departure times In the formula, The lower bound is zero because DL demand is interruptible and can be served in the next interval. Total energy demand must be met during arrival and departure times.

[0160] (3) Construction of the security domain model for distribution network operation, detailed as follows:

[0161] The security domain used in this application consists of voltage stability and thermal stability security domains, which are used to describe the safe and feasible power injection space for all nodes.

[0162] 1) Voltage stability safety domain

[0163] This application considers a power distribution system where phase angle is negligible. Therefore, the voltage difference between any two nodes can be described as:

[0164] (11)

[0165] In the formula: U i and U j Representing nodes respectively i With nodes j The voltage amplitude; P and Q They represent the lines respectively. ijThe line transmission power; R and X They represent the lines respectively. ij The line resistance and reactance.

[0166] Meanwhile, since line losses are relatively small compared to the load, the line transmission power can be approximated as:

[0167] (12)

[0168] (13)

[0169] In the formula, This represents the set of downstream branch nodes of node j.

[0170] Substituting formulas (12) and (13) into formula (11), we get:

[0171] (14)

[0172] Applying equation (14) to all branches, while considering that the node voltage of each node is similar to that of the root node, the relationship between the voltage of each node and that of the root node can be given as follows:

[0173] (15)

[0174] (16)

[0175] In the formula, The voltage magnitude at the root node; node s For nodes j With nodes k The node number of the first intersection of the upstream branch; , The equivalent impedance parameter represents the impedance from the root node to the node. i and nodes h The equivalent impedance on the common path.

[0176] Substituting the upper / lower limit of the node voltage into the node voltage formula shown in equation (15), we can obtain the voltage stability safe region as follows:

[0177] (17)

[0178] (18)

[0179] In the formula, n The number of nodes P h , Q h For nodes hActive and reactive power; nodes s For nodes j With nodes k The node number of the first intersection of the upstream branch; , The equivalent impedance parameter represents the impedance from the root node to the node. i and nodes h The equivalent impedance on the common path; , The standardized sensitivity parameter for the upper boundary of voltage safety. Corresponding active power P h Sensitivity, Corresponding active power Q h Sensitivity; , These are the standardized sensitivity parameters for the lower boundary of voltage safety. Corresponding active power P h Sensitivity, Corresponding active power Q h Sensitivity; u M , u m Upper and lower limits of voltage , These are the upper and lower limits of the voltage, respectively.

[0180] 2) Thermal stability safety domain

[0181] Based on Ohm's law, branches in a radial power grid ij Current amplitude I It can be represented as:

[0182] (19)

[0183] Substituting formulas (12) and (13) into formula (13), we get:

[0184] (20)

[0185] Since the node voltage of each node is close to the root node voltage, the upper limit of the branch current is set accordingly. Substituting into formula (20), we can obtain the thermal stability safety region as follows:

[0186] (twenty one)

[0187] (twenty two)

[0188] In the formula, n The number of nodes P k , Q k For nodes h Active and reactive power; branch road ij Thermal stability current limit; α k and β k These are power and current mapping coefficients, binary variables used to determine nodes. k Does the load flow through the branch? ij ; express j The set of downstream branch nodes of a node. express j The set of downstream branch nodes of a node; Let d be the voltage amplitude of the root node, and d be the set of downstream branch nodes of node j.

[0189] (4) Establish a flexible resource operation scheduling model that combines the operational constraints of the distribution network, as detailed below:

[0190] Considering grid operation constraints and line limitations, the objective function (23) minimizes the total cost of power generation, which is the sum of the costs of energy production from all distributed generator (DG) units and the costs associated with wind (VWcurt) and solar curtailment (VScurt) when maximum power generation is available. The cost of load transfer is derived from formula (24).

[0191] (twenty three)

[0192] (twenty four)

[0193] (25)

[0194] (26)

[0195] (27)

[0196] (28)

[0197] In the formula, OF is the objective function; b g This represents the power generation cost coefficient for distributed generators. P g This refers to the active power of the distributed generator; VWcurt This represents the penalty cost coefficient for wind power curtailment; VS curt This refers to the cost coefficient for photovoltaic curtailment. The cost of demand response (DR); T Total time period; C This represents the total number of clusters capable of handling load transfer. For a transferable load balancing cluster c exist t Fixed power at any given time; For the first c The equivalent dispatch power of a transferable load cluster is a decision variable in the optimization model, representing the total power required from the cluster at a given moment. Indicates the first i DR quantity of each transferable load; D The total number of clusters that can defer load; For Deferred Load Cluster d exist t Fixed power at any given time; For the first d The equivalent scheduling power of a delayable load cluster represents the total charging power required from that cluster at a given moment. Indicates the first i The amount of DR that can defer the load; G For generator sets; For generator g exist t Active power at any given moment; / for t Time of the first n The amount of wind / solar energy wasted by the busbar; for t The cost of responding to demand at any given moment; In order to be in t Time connection to the first n Active power generation of wind / solar generators via bus; / In order to be in t Always connected to the bus n Inelastic active / reactive loads; / for t Time bus n and m The active / reactive current flow between them; / exist t Bus at time n The availability of wind / solar energy at the location; / busbar n Total wind / solar power generation capacity. Let be the amount of wind energy wasted on the nth bus at time t. Let t be the amount of solar energy wasted by the nth bus at time t.

[0198] The constraints listed in Equations (25)-(28) correspond to active and reactive power flow balance, wind power reduction, minimum-maximum available wind power, hourly solar power reduction, and available solar power generation, respectively. Since load remodeling at the LA location also affects network operation, other relevant constraints are considered, including: line flow, line limits, voltage amplitude and angle limits, DG operating range, and ramp.

[0199] (29)

[0200] (30)

[0201] (31)

[0202] (32)

[0203] (33)

[0204] (34)

[0205] (35)

[0206] (36)

[0207] In the formula: Indicates the first c A portable load balancing cluster in time t The state is 1 if scheduled, and 0 otherwise; P c For clusters c The power; For the first c Each cluster t Start / stop indicators for interruptible time periods; The duration of the time interval (h); No. c The equivalent working time of a transferable load cluster represents the total time that the cluster needs to run continuously. For the first d Energy requirements (kWh) of a deferable cluster; These are the behavioral attributes corresponding to availability. The maximum number of DR events per day; , For each load cluster d Arrival-departure time; x d,t Indicates the first d A DL cluster in time t The switch status indicator. No. c The equivalent working time of a transferable load cluster represents the total time that the cluster needs to run continuously. For the first d The energy requirements of a cluster can be postponed. This is the stop indicator for the c-th transferable load cluster during the interruptible period at time h. For the first d The rated power of a load cluster that can be deferred.

[0208] The number of DRs provided by SL is limited by equation (29). This is the reference plan for DSO. The start-stop decision for cluster scheduling is determined by binary variables. Give, and It is an on / off status indicator. When formula (30) represents the correlation of binary variables; when When changing from 0 to 1, It becomes 1; when When it changes from 1 to 0, It becomes 1. Equation (31) gives the way to avoid start and stop indicators at any interval. t The binary relations overlap. When equation (32) is constrained... Set the work time to 1 to update the work time ( ), making ( ≤ ), as shown in the equivalent model (6). For daily DR events (N DR The maximum number of ) should be such that the start indicator is higher, as shown in equation (33). Stop indicator ( The update time for the cluster, as shown in (34), will become 1. For equations (29)-(34), the time ( t ) is limited to available time ( To maintain consumer preference. Constraints related to DL clusters are given by equations (35)-(36). The total load after planning is determined by This corresponds to equation (23). The energy constraint is represented by equation (36). Binary variables... It is an on / off status indicator, and It is limited by the maximum power of the DL cluster.

[0209] Considering the constraints (35)-(36) above along with the flexible load modeling constraints (1)-(10), solve the objective (OF) of the operation scheduling model. This model is a mixed-integer nonlinear problem that can be solved using the MATLAB solver.

[0210] This model aims to minimize total operating cost, comprehensively considering generation costs as well as the costs of wind and solar power reduction. Demand response costs are incorporated to incentivize flexible user-side resource allocation. Regarding constraints, the model ensures a balance between active and reactive power, preventing grid instability caused by power imbalances. Simultaneously, wind and solar power reductions are limited to reduce renewable energy waste. Line flow limits are strictly enforced to ensure safe grid operation. Furthermore, the model maintains node voltage and angle within safe ranges to prevent voltage collapse and other issues. Finally, the operating range and slope limitations of distributed generation units are considered to ensure stable operation of these units.

[0211] In summary, the method proposed in this application can tap the adjustment potential of demand-side prosumers and consumers, more accurately describe the operating state range of the distribution network under the condition of not violating the security domain constraints, and help solve the concurrent scheduling problem of a large number of small-scale distributed resource clusters in the distribution network.

[0212] like Figure 2 As shown, the second objective of this application is to provide a flexible resource aggregation and scheduling system based on the distribution network operation safety domain. Based on the aforementioned flexible resource aggregation and scheduling method based on the distribution network operation safety domain, the method includes:

[0213] The flexible resource potential model building module is used to build a flexible resource potential model under the constraints of distribution network operation, taking user-side flexible resources as the object.

[0214] The flexible resource adjustment model establishment module is used to determine the feasible operating range of the distribution network without violating any operating constraints by introducing the quadratic terms of active and reactive power injected by the nodes using the security domain analysis method, thus obtaining a flexible resource adjustment model that combines the operating constraint boundary of the distribution network.

[0215] The user-side resource aggregation model construction module constructs a user-side resource aggregation model that considers the distribution network operation safety domain, based on the flexible resource potential model under the distribution network operation constraints and the flexible resource adjustment model combined with the distribution network operation constraint boundary.

[0216] The solution module is used to solve the user-side resource aggregation model that considers the safety domain of the distribution network operation, and to perform user-side resource aggregation scheduling based on the solution results.

[0217] A third objective of this application is to provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned flexible resource aggregation and scheduling method based on the power distribution network operation security domain. The device also includes a communication interface and a bus.

[0218] A fourth objective of this application is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned flexible resource aggregation and scheduling method based on the power distribution network operation security domain.

[0219] A fifth objective of this application is to provide a computer program product comprising computer instructions that instruct a computer to execute the aforementioned flexible resource aggregation and scheduling method based on the power distribution network operation security domain.

[0220] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0221] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0222] This application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, readable storage media, optical storage, etc.) containing computer-usable program code.

[0223] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0224] Obviously, the described embodiments are only some, not all, of the embodiments in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort should fall within the scope of protection of this application.

[0225] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A flexible resource aggregation and scheduling method based on the operational security domain of a distribution network, characterized in that, include: Based on the information interaction between the load aggregator and the home energy management system, the operating parameters of the transferable and deferred loads of multiple users are obtained. The operating parameters include rated power, available time window, minimum continuous operating time, maximum allowable number of interruptions, and user comfort preferences. The k-means++ clustering algorithm is used to cluster the operating parameters of the transferable and delayable loads of multiple users, and an aggregated load model consisting of equivalent power range, total energy demand and start-stop logic is constructed. A safe operating domain model is established by combining the voltage stability constraints and thermal stability constraints of the distribution network, including the voltage stability safe domain and the thermal stability safe domain. The voltage stability safe domain is derived from the relationship between node injected power and line voltage drop, while the thermal stability safe domain is transformed into a quadratic inequality constraint on active and reactive power based on the condition that the branch current does not exceed the corresponding thermal limit. Together, they define a safe and feasible injected power space. A mixed-integer nonlinear optimization model is established with the goal of minimizing the total operating cost. It comprehensively considers the generation cost, renewable energy curtailment penalty, and demand response incentive cost. The aggregated load model and the safety domain model are used as model inputs. Under the premise of satisfying the AC power flow equation, unit ramp rate, distributed power output limit, and network operation boundary, the optimal scheduling scheme is solved. Based on the optimal scheduling scheme, the global optimization result is obtained. After the global optimization result is sent to each load aggregator, each load aggregator decomposes the reference scheduling instruction locally and allocates it to the individual loads under its jurisdiction. The individual loads prioritize satisfying high-priority loads and minimize the deviation between actual power consumption and the plan.

2. The flexible resource aggregation and scheduling method based on the distribution network operation security domain according to claim 1, characterized in that, The transferable loads include dishwashers, microwave ovens, vacuum cleaners, dryers, sensors, and irons; the deferred loads are the charging loads of electric vehicles in G2V mode.

3. The flexible resource aggregation and scheduling method based on the distribution network operation security domain according to claim 1, characterized in that, The voltage stability safety domain is derived based on the relationship between node injected power and line voltage drop. The thermal stability safety domain is based on the condition that the branch current does not exceed the corresponding thermal limit, which is transformed into a quadratic inequality constraint on active and reactive power. Together, they define a safe and feasible injected power space, including: By utilizing the relationship between node-injected active / reactive power and line resistance and reactance, and combining it with the root node voltage reference, a linearized voltage deviation constraint is established. Based on the premise that the branch current amplitude does not exceed the corresponding thermal limit, Ohm's law is transformed into a quadratic cone constraint on the downstream injected power; The intersection of the voltage stability domain and the thermal stability security domain is used as the safe and feasible injection power space for distribution network operation.

4. The flexible resource aggregation and scheduling method based on the distribution network operation security domain according to claim 1, characterized in that, The voltage stability safety domain considers a power distribution system that ignores phase angle, where the voltage difference between any two nodes is determined by the node voltage amplitude, line transmission power, line resistance and reactance. The line transmission power is approximately simplified. Based on the relationship between the node voltage and the root node voltage, a voltage stability safety domain is constructed to ensure that the voltage of all nodes is within the upper and lower limits. Based on Ohm's law, the amplitude of the branch current is determined by the node injected power and the line parameters.

5. The flexible resource aggregation and scheduling method based on the distribution network operation security domain according to claim 1, characterized in that, The k-means++ clustering algorithm is used to cluster the operating parameters of the transferable and delayable loads of multiple users, and to construct an aggregated load model consisting of equivalent power range, total energy demand and start-stop logic. include: The k-means++ clustering algorithm is used to cluster the operating parameters of the transferable and delayable loads of multiple users. The load aggregator performs aggregation based on the information submitted by consumers. The centroid-based k-means clustering algorithm is used to group the loads to form an equivalent aggregated load model. Loads are partitioned based on their similar available time; after load partitioning, profiles are constructed based on the power requirements of the loads during the corresponding time intervals of their operating time. In the process of grouping the loads using the centroid-based k-means clustering algorithm, the first centroid is randomly selected, and subsequent centroids are selected according to a probability distribution proportional to the square of the distance to their nearest existing centroid. Euclidean distance is used as the similarity criterion, and the multidimensional feature vectors are normalized.

6. The flexible resource aggregation and scheduling method based on the distribution network operation security domain according to claim 1, characterized in that, The voltage stability safe range is: In the formula, n The number of nodes P h , Q h They are nodes h Active and reactive power; The voltage magnitude at the root node; node s For nodes j With nodes k The node number of the first intersection of the upstream branch; , The equivalent impedance parameter represents the impedance from the root node to the node. i and nodes h The equivalent impedance on the common path; Active power at the upper limit of voltage safety P h Sensitivity, Reactive power at the upper limit of voltage safety Q h Sensitivity; Active power at the lower boundary of voltage safety P h Sensitivity, Reactive power at the lower boundary of voltage safety Q h Sensitivity; u M , u m These are the upper and lower limits of the voltage. , These are the upper and lower limits of the voltage, respectively.

7. The flexible resource aggregation and scheduling method based on the distribution network operation security domain according to claim 6, characterized in that, The thermal stability safety domain is: In the formula, branch road ij Thermal stability current limit; α k The active power mapping coefficient, β k These are reactive power mapping coefficients used to determine node positions. k Does the load flow through the branch? ij ; express j The set of downstream branch nodes of a node; Let d be the voltage magnitude of the root node, and d be the downstream branch node of node j.

8. The flexible resource aggregation and scheduling method based on the distribution network operation security domain according to claim 1, characterized in that, The objective function for the total operating cost includes the sum of power generation fuel cost, wind and solar curtailment penalty cost, and demand response incentive cost; the power generation fuel cost, wind and solar curtailment penalty cost, and demand response incentive cost are all calculated by multiplying the maximum absolute deviation between the actual dispatched power of each aggregation group and the reference plan by the time-of-use incentive price; specifically: In the formula, OF is the objective function; b g This represents the power generation cost coefficient for distributed generators. P g This refers to the active power of the distributed generator; VW curt This represents the penalty cost coefficient for wind power curtailment; VS curt This refers to the cost coefficient for photovoltaic curtailment. The cost of responding to demand; T Total time period; C This represents the total number of clusters capable of handling load transfer. For a transferable load balancing cluster c exist t Fixed power at any given time; For the first c Equivalent scheduling power of a transferable load cluster; Indicates the first i Demand response DR for each transferable load; D The total number of clusters that can defer load; For Deferred Load Cluster d exist t Fixed power at any given time; For the first d Equivalent scheduling power of a delayable load cluster; For the first d Equivalent scheduling power of a transferable load cluster; Indicates the first i The amount of DR that can defer the load; G For generator sets; For generator g exist t Active power at any given moment; for t Time of the first n Wind power wastage on a single busbar; for t Time of the first n The amount of solar energy wasted by the busbar; for t The cost of responding to demand at any given moment; In order to be in t Time connection to the first n Active power generation of wind turbines via bus; In order to be in t Time connection to the first n Active power generation of the bus-mounted solar generator; In order to be in t Always connected to the bus n Inelastic active load; In order to be in t Always connected to the bus n Inelastic reactive load; for t Time bus n and m The positive trend between them; for t Time bus n and m The reactive current between them; In order to be in t Bus at time n The availability of wind energy at the location; They are respectively in t Bus at time n The availability of solar energy at the location; busbar n Total wind power generation capacity, busbar n Total solar power generation capacity, M For the set of busbars, Let be the amount of wind energy wasted on the nth bus at time t. Let be the amount of solar power wasted by the nth bus at time t; Other related constraints include: line flow, line limits, voltage amplitude and angle limits, DG operating range and ramp; In the formula: Indicates the first c A portable load balancing cluster in time h The state is 1 if scheduled, and 0 otherwise; Minimum power for the cluster This represents the maximum power of the cluster. For the first c Each cluster t The start indicator of the interruptible period of time; This is the status indicator of the c-th transferable load cluster at time t; For the c-th transferable load cluster at time t -1 status indicator; For the first c Each cluster t The stop indicator for the interruptible period of time; The duration of the time interval; For the first c The equivalent working time of a transferable load cluster represents the total time that the cluster needs to run continuously. For the first d The energy requirements of a cluster can be postponed; These are the behavioral attributes corresponding to availability. The maximum number of DR events per day; For each load cluster d Arrival time, For each load cluster d departure time; x d,t For the first d A DL cluster in time t Switch status indicator, This is the stop indicator for the c-th transferable load cluster during the interruptible period at time h. For the first d The rated power of a load cluster that can be deferred.

9. The flexible resource aggregation and scheduling method based on the distribution network operation security domain according to claim 1, characterized in that, When each load aggregator decomposes the reference dispatch instructions locally, it prioritizes meeting the power demand of users with high comfort levels and minimizes individual dispatch deviations.

10. A flexible resource aggregation and scheduling system based on the operational security domain of a distribution network, characterized in that, include: The parameter acquisition module is used to acquire the operating parameters of multiple users' transferable and deferred loads based on the information interaction between the load aggregator and the home energy management system. The operating parameters include rated power, available time window, minimum continuous operating time, maximum allowable number of interruptions, and user comfort preferences. The model building module is used to cluster the operating parameters of the transferable and delayable loads of multiple users using the k-means++ clustering algorithm, and to build an aggregated load model consisting of equivalent power range, total energy demand and start-stop logic. The safety domain establishment module is used to establish an operational safety domain model that includes a voltage stability safety domain and a thermal stability safety domain by combining the voltage stability constraints and thermal stability constraints of the distribution network. The voltage stability safety domain is derived based on the relationship between node injected power and line voltage drop, while the thermal stability safety domain is transformed into a quadratic inequality constraint on active and reactive power based on the condition that the branch current does not exceed the corresponding thermal limit. Together, they define a safe and feasible injected power space. The model solving module is used to establish a mixed-integer nonlinear optimization model with the goal of minimizing the total operating cost. It comprehensively considers the generation cost, renewable energy curtailment penalty and demand response incentive cost, and takes the aggregated load model and the safety domain model as model inputs. Under the premise of satisfying the AC power flow equation, unit ramp rate, distributed power output limit and network operation boundary, it solves the optimal scheduling scheme. The load scheduling module is used to obtain the global optimization result based on the optimal scheduling scheme. After the global optimization result is sent to each load aggregator, each load aggregator decomposes the reference scheduling instruction locally and allocates it to the individual loads under its jurisdiction. The individual loads prioritize satisfying high-priority loads and minimize the deviation between actual power consumption and the plan.

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