A reactive power and voltage hierarchical control method and device based on optimal control objective

Abstract

This invention belongs to the field of voltage level control technology, specifically relating to a reactive power voltage level control method and device based on optimal control objectives. The steps include: acquiring actual data during the reactive power voltage control process; analyzing the correlation between voltage influence factors, reactive power control modes, and reactive power configuration, forming judgment indicators from a quantitative perspective, and completing reactive power voltage leveling; considering the operating cost of reactive power voltage control, the number of switching operations of capacitor banks and on-load tap-changing transformers, and line active power transmission losses, establishing a reactive power voltage optimization model based on optimal control objectives; dynamically adjusting the sub-objective weights of the reactive power voltage optimization model using game theory weighting according to the reactive power voltage leveling situation; and solving the reactive power voltage optimization model using the NSGA-II algorithm within a set time period to obtain the optimal solution of the reactive power voltage level control method based on optimal control objectives. This invention can achieve multi-level reactive power voltage control, stabilizing the voltage within a safe range.

Description

Technical Field

[0001] This invention belongs to the field of voltage graded control technology, specifically relating to a reactive voltage graded control method and device based on optimal control objectives. Background Technology

[0002] In power systems, reactive power and voltage control are crucial for ensuring the safe, stable, and economical operation of the power grid. However, with the increasing complexity of the power grid structure, especially the high proportion of large-scale distributed renewable energy sources (such as wind power and photovoltaics) being integrated, the intermittency and volatility of their output have significantly increased the uncertainty of the system. At the same time, the diversification of load types has further amplified the dynamic range of system voltage changes, making voltage fluctuation problems more prominent.

[0003] Traditional reactive power and voltage control methods, such as hierarchical switching based on fixed rules or optimization strategies that focus on a single objective, face severe challenges: insufficient control accuracy, difficulty in matching complex operating conditions, poor adaptability, difficulty in dealing with strong uncertainties, and difficulty in effectively synergistically optimizing multiple objectives such as voltage safety, minimum network loss, and fewer equipment operations, resulting in low control efficiency.

[0004] While the currently widely used conventional automatic voltage control (AVC) system has improved the level of control, it often relies on experience or simple rules when dividing control areas, grouping equipment, or setting priorities. The classification and grading are highly subjective and lack dynamic quantitative indicators. More importantly, the process of generating control strategies fails to effectively combine the quantitative analysis results of the above-mentioned influencing factors with the needs of multi-objective comprehensive optimization, and the strategies lack adaptive adjustment capabilities.

[0005] Therefore, existing technologies have significant shortcomings in achieving refined hierarchical control and efficient collaborative optimization of multiple objectives. There is an urgent need to develop an advanced reactive voltage control method that can systematically quantify influencing factors, achieve refined hierarchical control, deeply integrate multi-objective optimization, and possess high adaptability. Summary of the Invention

[0006] In view of the shortcomings of the prior art, the purpose of the present invention is to provide a reactive voltage hierarchical control method and device based on the optimal control objective. Considering conditions such as reactive voltage hierarchical control and optimal control objective, it can realize multi-level reactive voltage control and stabilize the voltage within a safe range.

[0007] To achieve the above objectives, this invention provides a reactive power and voltage hierarchical control method based on optimal control objectives, comprising the following steps: S1. Obtain actual data during the reactive power and voltage control process, including voltage and load data of each node, location and capacity of reactive power compensation equipment, location and power generation data of distributed power sources, and impedance parameters of transmission lines; S2. Based on the acquired actual data, analyze the correlation between voltage influence factors, reactive power control mode, and reactive power configuration, and form judgment indicators from a quantitative perspective to complete the reactive power voltage classification. S3. Considering the operating cost of reactive voltage control, the number of switching operations of capacitor banks and on-load tap-changing transformers, and the active power transmission loss of the line, establish a reactive voltage optimization model based on the optimal control objective and set its constraints. S4. Based on the reactive voltage classification, use game theory weighting method to dynamically adjust the sub-objective weights of the reactive voltage optimization model. S5. Within a set time period, use the NSGA-II algorithm to solve the reactive voltage optimization model and obtain the optimal solution of the reactive voltage hierarchical control method based on the optimal control objective.

[0008] As a preferred embodiment of the present invention, in S2, the region is divided based on the control area. For a certain region in the reactive voltage control process, the influence of the load in the region on the reactive voltage sensitivity of the node voltage is considered to form a voltage influence factor. ; ; In the formula, Let be the voltage influence factor of node i at time t; The importance of the load on node i; Let be the voltage deviation at node i at time t; Let N be the reactive power-voltage sensitivity of node j to node i at time t; N is the number of nodes in the region where node i is located. , , , Both represent Jacobian block matrices. , These represent the degree of influence of the change in node voltage amplitude at time t on the reactive power and active power balance of the node, respectively. , These represent the degree of influence of the change in node voltage phase angle at time t on the balance of node reactive power and active power, respectively. The reactive power control mode is divided into three layers. The first layer is local control, which relies on local distributed power sources to complete reactive power and voltage compensation. The second layer is line control, which calls reactive power compensation equipment including capacitor banks (CB) and on-load tap changers (OLTC) to complete reactive power and voltage compensation. The third layer is global control, which calls reactive power compensation equipment including static var compensators (SVC) and synchronous condensers (SC) to complete reactive power and voltage compensation. For reactive power configurations, the reactive power output of distributed generation is approximately replaced by active power: ; In the formula, The reactive power injected into node i at time t by the local distributed power source; Let be the active power output of the distributed power source at node i at time t; The angle representing the maximum power factor of the distributed power source at time t; The output of the reactive power compensation device is represented as follows: ; ; ; ; ; In the formula, The reactive power injected into node i by the line control reactive power compensation device at time t; To determine the reactive power injected into node i at time t by the global control reactive power compensation device; Let be the switching capacity of the c-th CB at time t; Let d be the variable capacity of the OLTC at time t; Let be the reactive power output of the a-th SVC at time t; Let be the reactive power output of the b-th SC at time t; , , , The quantities of CB, OLTC, SVC, and SC devices are respectively. , , , These are the indicators for CB, OLTC, SVC, and SC being in use, respectively. 0 indicates that they are not in use, and 1 indicates that they are in use. Let be the number of capacitors at node i at time t; Let be the reactive power output of a single capacitor at node i at time t; , Let be the actual voltages at node i and node j at time t, respectively; Let be the ratio of OLTC at node j at time t; Let be the impedance between node i and node j at time t; Let be the actual voltage of the a-th SVC at time t; Let be the reactance parameter of the a-th SVC.

[0009] As a preferred embodiment of the present invention, in step S2, by comparing the quantitative relationship between the node voltage deviation and the reactive voltage compensation, a correlation model of voltage influence factor, reactive power control mode, and reactive power configuration is established, expressed as follows: ; In the formula, , , These are the activation signals for the first, second, and third levels of reactive power control, respectively, with 1 representing activation and 0 representing deactivation. Let be the voltage deviation at node i at time t; Let be the rated voltage of node i at time t; The model output is for node i; T is the total number of time points. The NSGA-II algorithm is used to obtain the output results of the correlation model. At the same time, the K-means clustering algorithm is used to cluster the output results of the correlation model and classify the reactive power and voltage in descending order.

[0010] As a preferred embodiment of the present invention, the reactive power voltage optimization model in S3 is expressed as follows: ; ; ; ; In the formula, The optimal control objective for node i; Let $t$ be the operating cost of reactive voltage control at node $i$ at time $t$. Let t be the number of times CB and OLTC are switched at node i at time t; Let t be the active power transmission loss that injects power into node i at time t; , , They are respectively , , Weighting coefficients; The unit operating cost of distributed power sources; Let x be the output of the x-th distributed power source at time t; The unit operating cost of reactive voltage control; Let r be the output of the reactive power compensation device at time t; , These represent the action states of the c-th CB at times t and t+1, where 1 indicates action and 0 indicates no action. , These represent the action states of the d-th OLTC at times t and t+1, respectively, where 1 indicates action and 0 indicates no action. , Let be the voltage amplitudes at nodes m and n of the y-th line at time t, respectively; , Let be the voltage phases of nodes m and n of the y-th line at time t, respectively; Let be the resistance value of the y-th transmission line; This refers to the number of transmission lines. The number of distributed power sources participating in the reactive voltage control of node i; The number of reactive power compensation devices participating in reactive power voltage control at node i; T is the total number of moments. The constraints of the reactive voltage optimization model include voltage amplitude constraints, SVC / SC output power constraints, CB switching constraints, OLTC tap constraints, line transmission capacity constraints, and power balance constraints.

[0011] As a preferred embodiment of the present invention, the constraints of the reactive power voltage optimization model are specifically as follows: Voltage amplitude constraint, expressed as: ; In the formula, , These are the upper and lower limits of the voltage amplitude at the i-th node, respectively. SVC output power constraint is expressed as: ; In the formula, , These are the upper and lower limits of the SVC output power, respectively. The SC output power constraint is expressed as: ; In the formula, , These are the upper and lower limits of the SC output power, respectively; CB switching constraint, expressed as: ; ; In the formula, Let c be the number of times the capacitor of the c-th CB is switched on and off. , These are the upper and lower limits of the number of times the capacitor of the c-th CB can be switched on and off, respectively. OLTC gear position constraints are represented as: ; ;

[0012] In the formula, For the d-th OLTC gear; , These are the upper and lower limits of the gear for the d-th OLTC, respectively. This is the upper limit of the gear adjustment for the d-th OLTC; Line transmission capacity constraints are expressed as: ; In the formula, Let y be the transmission capacity of the y-th transmission line; , These are the upper and lower limits of the transmission capacity of the y-th line, respectively; Power balance constraints are expressed as: ; In the formula, , These represent the active and reactive power injected at node i at time t, respectively. , These represent the active and reactive loads at node i at time t, respectively. The reactive power injected by the reactive power compensation device at node i at time t; , and represent the conductance and susceptance of the y-th line, respectively.

[0013] As a preferred embodiment of the present invention, in S2, the output results of the three-level control modes participating in reactive voltage classification at the same node are obtained, and the priority of the control modes is determined according to the magnitude of the values, wherein the mode with the largest value is the optimal control mode. In S3, the weight corresponding to the optimal control mode is increased.

[0014] As a preferred embodiment of the present invention, the specific steps of the game theory weighting method in S4 are as follows: S4.1 Construct a sub-target judgment matrix based on the output results of the association model. , Middle elements This represents the degree of importance between sub-objectives u and v; right A consistency check is performed, expressed as: ; In the formula, For consistency calculation indicators; The average proportion of consistency; for The largest eigenvalue; for The order of; This is an average consistency index; S4.2, Use The average value of the column vectors is used to approximate the subjective weights of the sub-objectives. , is represented as: ; In the formula, for The element in the middle represents the importance between sub-targets k and v; S4.3 Constructing the Sub-Objective Evaluation Matrix , Middle elements The z-th evaluation score represents the u-th sub-objective; right Normalization is performed: ; In the formula, To represent the normalized result ; for The z-th evaluation score in each column; for The minimum value in the column; for The difference between the maximum and minimum values ​​in the column; S4.4 Establish volatility indicators and opposing indicators, analyze and determine the trend of weight changes; comprehensively consider volatility indicators and opposing indicators to solve for the objective weights of sub-objectives. : ; ; In the formula, is the volatility index of the z-th evaluation score, which measures the degree of dispersion of different evaluation scores; , is the opposition indicator of the z-th evaluation score, which measures the correlation differences between different evaluation scores; for The number of indicators in each column; for middle The average evaluation score of the column; for The correlation between the z-th evaluation score in each column and other evaluation scores; S4.5 Construct a game theory weight combination objective, and solve for the combination coefficients by minimizing the weight deviation, thereby obtaining the sub-objective weights: ; ; In the formula, The objective is to minimize the weight bias; L represents the number of weight optimization methods. For the first Combination coefficients of the weight optimization method; For the first The sub-objective weights determined by the weight optimization method; The final sub-objective weights include , , ; For the first The weight of the u-th sub-objective under the weight optimization method.

[0015] As a preferred embodiment of the present invention, in step S5, an improved NSGA-II algorithm is used for solving the problem, and the steps are as follows: S5.1 Randomly generate a temporary population of twice the size, and dynamically select distributed power sources or reactive power compensation devices according to different reactive power control modes. Calculate the fitness of individuals in the temporary population, use fast non-dominated sorting to divide the temporary population by fitness, prioritize retaining individuals with high fitness rankings, and construct the target population. S5.2 Introduce an inverse weighting mechanism that considers a density threshold to calculate individual density, and combine it with the objective function value of the individual to adjust the overall population crowding to avoid getting stuck in local convergence; for individuals with crowding less than the set crowding threshold, introduce random noise to avoid forming densely crowded areas. S5.3. Obtain the offspring population by solving the crossover and variation of individual positions, and merge the parent and offspring populations; in the mixed population of two generations, obtain the new population by non-dominated sorting and crowding degree calculation. S5.4 Detect population diversity and dynamically adjust the elite retention ratio using linear interpolation based on the diversity level; based on the elite retention ratio, sort the individuals according to non-dominance level and crowding degree, and select elite individuals to form a new population: ; ; In the formula, This is the time decay factor; As a diversity regulator; This represents the current iteration number; O represents the total number of iterations; O represents the population diversity. , These represent the upper and lower limits of the elite retention ratio, respectively. Indicates the percentage of elites retained; S5.5 Determine if the maximum number of iterations has been reached. If yes, output the optimal solution; otherwise, go to step S5.2.

[0016] As a preferred embodiment of the present invention, in S5.2, the inverse weighting mechanism considering the density threshold is expressed as follows: ; ; ; In the formula, For individual h density; Let be the distance between the nearest neighbors of individuals h and f; K is the nearest neighbor search coefficient. Crowding level adjusted for individual h; The crowding level before adjustment for individual h; The objective function value for individual h+1; The objective function value for individual h-1; The objective function value; Density threshold; Crowding degree after introducing random noise into individual h.

[0017] A reactive voltage hierarchical control device based on optimal control objectives includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The processor executes the program to implement the above-mentioned method.

[0018] The beneficial effects of this invention are: This invention starts with quantitative indicators, comprehensively considers the impact of node load and reactive power-voltage sensitivity, and establishes a correlation model of voltage influence factor, control mode, and reactive power configuration. It studies the comprehensive impact of load, control mode, and reactive power compensation device on reactive power and voltage, overcoming the extensiveness of traditional methods that rely on experience-based adjustments, and providing a basis for hierarchical control of reactive power and voltage. This invention incorporates multiple sub-objectives such as operating cost, number of equipment operations, and line loss into a unified reactive power and voltage control framework, and dynamically adjusts the weights of each sub-objective based on the hierarchical results using a game theory-based combined weighting method. This allows the control model to prioritize the sub-objectives corresponding to the optimal control mode while ensuring voltage quality, thus achieving comprehensive optimal control of reactive power and voltage. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the principle of this invention; Figure 2 This is a flowchart of the reactive voltage classification process in Embodiment 1 of the present invention; Figure 3 This is the IEEE 33-node topology diagram in Embodiment 1 of the present invention; Figure 4 This is a flowchart of the game theory weighting method for solving the control weights of control sub-objectives in Embodiment 1 of the present invention; Figure 5 This is a flowchart of the improved NSGA-II algorithm for solving the reactive voltage hierarchical control method in Embodiment 1 of the present invention; Figure 6 These are the optimal control target results under different weight optimization methods in Embodiment 1 of the present invention; Figure 7 This is the reactive voltage control result of IEEE 33 node in Embodiment 1 of the present invention; Figure 8 The results of voltage distribution and deviation under reactive voltage control in Embodiment 1 of the present invention are shown. (a) in Figure (8) is a box plot of voltage distribution, and (b) in Figure (8) is a box plot of voltage deviation. Detailed Implementation

[0020] The embodiments of the present invention will be further described below with reference to the accompanying drawings: Example 1: As Figure 1 As shown, a reactive power voltage hierarchical control method based on optimal control objective includes the following steps: S1. Obtain actual data during the reactive power and voltage control process, including voltage and regional load data of each node, location and capacity of reactive power compensation equipment, location and power generation data of distributed power sources, and transmission line impedance parameters (obtained by the power grid dispatching system, distribution automation system or field monitoring device). S2. Based on the acquired actual data, analyze the correlation between voltage influence factors, reactive power control mode, and reactive power configuration, and form judgment indicators from a quantitative perspective to complete the reactive power voltage classification. S3. Considering the operating cost of reactive voltage control, the number of switching operations of capacitor banks and on-load tap-changing transformers, and the active power transmission loss of the line, establish a reactive voltage optimization model based on the optimal control objective and set its constraints. S4. Based on the reactive voltage classification, use game theory weighting method to dynamically adjust the sub-objective weights of the reactive voltage optimization model. S5. Within a set time period, use the NSGA-II algorithm to solve the reactive voltage optimization model and obtain the optimal solution of the reactive voltage hierarchical control method based on the optimal control objective.

[0021] like Figure 2 As shown in S2, the region is divided based on the control console area. For a certain region in the reactive voltage control process, the voltage influence factor is formed by considering the influence of the load in the region on the reactive voltage sensitivity of the node voltage. ; ; In the formula, Let be the voltage influence factor of node i at time t; The importance of the load at node i is determined (normal loads are usually assigned a value of 1, important loads are assigned a value of 1.1 to 1.5, loads belonging to the first or second level of power supply reliability or load interruptions that would cause personal safety risks or significant social impacts are determined to be important loads, and all other cases are determined to be normal loads). Let be the voltage deviation at node i at time t; Let N be the reactive power-voltage sensitivity of node j to node i at time t; N is the number of nodes in the region where node i is located. , , , Both represent Jacobian block matrices. , These represent the degree of influence of the change in node voltage amplitude at time t on the reactive power and active power balance of the node, respectively. , These represent the degree of influence of the change in node voltage phase angle at time t on the balance of node reactive power and active power, respectively. The reactive power control mode is divided into three layers. The first layer is local control, which relies on local distributed power sources to complete reactive power and voltage compensation. The second layer is line control, which calls reactive power compensation equipment including capacitor banks (CB) and on-load tap changers (OLTC) to complete reactive power and voltage compensation. The third layer is global control, which calls reactive power compensation equipment including static var compensators (SVC) and synchronous condensers (SC) to complete reactive power and voltage compensation. For reactive power configurations, the reactive power output of distributed generation is approximately replaced by active power: ; In the formula, The reactive power injected into node i at time t by the local distributed power source; Let be the active power output of the distributed power source at node i at time t; The angle representing the maximum power factor of the distributed power source at time t; The output of the reactive power compensation device is represented as follows: ; ; ; ; ; In the formula, The reactive power injected into node i by the line control reactive power compensation device at time t; To determine the reactive power injected into node i at time t by the global control reactive power compensation device; Let be the switching capacity of the c-th CB at time t; Let d be the variable capacity of the OLTC at time t; Let be the reactive power output of the a-th SVC at time t; Let be the reactive power output of the b-th SC at time t; , , , The quantities of CB, OLTC, SVC, and SC devices are respectively. , , , These are the indicators for CB, OLTC, SVC, and SC being in use, respectively. 0 indicates that they are not in use, and 1 indicates that they are in use. Let be the number of capacitors at node i at time t; Let be the reactive power output of a single capacitor at node i at time t; , Let be the actual voltages at node i and node j at time t, respectively; Let be the ratio of OLTC at node j at time t; Let be the impedance between node i and node j at time t; Let be the actual voltage of the a-th SVC at time t; Let be the reactance parameter of the a-th SVC.

[0022] By comparing the quantitative relationship between node voltage deviation and reactive power compensation, a correlation model is established for voltage influence factor, reactive power control mode, and reactive power configuration, expressed as: ; In the formula, , , These are the activation signals for the first, second, and third levels of reactive power control, respectively, with 1 representing activation and 0 representing deactivation. Let be the voltage deviation at node i at time t; Let be the rated voltage of node i at time t; The model output is for node i; T is the total number of time points. The NSGA-II algorithm is used to obtain the output results of the correlation model (which can be solved using the NSGA-II algorithm of the formula or the improved NSGA-II algorithm similar to S5). At the same time, the K-means clustering algorithm is used to cluster the output results of the correlation model and classify the reactive power and voltage in descending order. The reactive power and voltage control capabilities are classified as Level 1 and the reactive power and voltage control capabilities are classified as Level 3.

[0023] Figure 3 This is an IEEE 33-node topology diagram. Based on the method of this embodiment, under the IEEE 33-node model, the reactive voltage classification results are shown in Table 1: Table 1 Reactive voltage classification results

[0024] In S3, the reactive voltage optimization model is expressed as follows: ; ; ; ; In the formula, The optimal control objective for node i; Let $t$ be the operating cost of reactive voltage control at node $i$ at time $t$. Let t be the number of times CB and OLTC are switched at node i at time t; Let t be the active power transmission loss that injects power into node i at time t; , , They are respectively , , Weighting coefficients; The unit operating cost of distributed power sources; Let x be the output of the x-th distributed power source at time t; The unit operating cost of reactive voltage control; Let r be the output of the reactive power compensation device at time t; , These represent the action states of the c-th CB at times t and t+1, where 1 indicates action and 0 indicates no action. , These represent the action states of the d-th OLTC at times t and t+1, respectively, where 1 indicates action and 0 indicates no action. , Let be the voltage amplitudes at nodes m and n of the y-th line at time t, respectively; , Let be the voltage phases of nodes m and n of the y-th line at time t, respectively; Let be the resistance value of the y-th transmission line; This refers to the number of transmission lines. The number of distributed power sources participating in the reactive voltage control of node i; The number of reactive power compensation devices participating in reactive power voltage control at node i; T is the total number of moments. The constraints of the reactive voltage optimization model include voltage amplitude constraints, SVC / SC output power constraints, CB switching constraints, OLTC tap constraints, line transmission capacity constraints, and power balance constraints.

[0025] The specific constraints of the reactive voltage optimization model are as follows: Voltage amplitude constraint, expressed as: ; In the formula, , These are the upper and lower limits of the voltage amplitude at the i-th node, respectively. SVC output power constraint is expressed as: ; In the formula, , These are the upper and lower limits of the SVC output power, respectively. The SC output power constraint is expressed as: ; In the formula, , These are the upper and lower limits of the SC output power, respectively; CB switching constraint, expressed as: ; ; In the formula, Let c be the number of times the capacitor of the c-th CB is switched on and off. , These are the upper and lower limits of the number of times the capacitor of the c-th CB can be switched on and off, respectively. OLTC gear position constraints are represented as: ; ;

[0026] In the formula, For the d-th OLTC gear; , These are the upper and lower limits of the gear for the d-th OLTC, respectively. This is the upper limit of the gear adjustment for the d-th OLTC; Line transmission capacity constraints are expressed as: ; In the formula, Let y be the transmission capacity of the y-th transmission line; , These are the upper and lower limits of the transmission capacity of the y-th line, respectively; Power balance constraints are expressed as: ; In the formula, , These represent the active and reactive power injected at node i at time t, respectively. , These represent the active and reactive loads at node i at time t, respectively. The reactive power injected by the reactive power compensation device at node i at time t; , and represent the conductance and susceptance of the y-th line, respectively.

[0027] In S2, the output results of the three-level control modes participating in reactive power voltage classification at the same node are obtained. The priority of the control modes is determined based on their numerical values, with the mode with the largest value being the optimal control mode. In S3, the weight corresponding to the optimal control mode is increased. For example, when local control is the optimal control mode, the weight is increased. The proportion increases when the line control is in the optimal control mode. The proportion increases when global control is in the optimal control mode. The proportion; like Figure 4 As shown, in S4, the specific steps of the game theory weighting method are as follows: S4.1 Construct a sub-target judgment matrix based on the output results of the association model. , Middle elements This represents the degree of importance between sub-targets u and v; the element importance scale is shown in Table 2: Table 2. Scale for Determining the Importance of Matrix Elements

[0028] right A consistency check is performed to ensure that the weights calculated subsequently can be applied, expressed as: ; In the formula, For consistency calculation indicators; The average proportion of consistency; for The largest eigenvalue; for The order of; For example, the average consistency index The corresponding value is 0.36; S4.2, when satisfied When <0.1, use The average value of the column vectors is used to approximate the subjective weights of the sub-objectives. , is represented as: ; In the formula, for The element in the middle represents the importance between sub-targets k and v; S4.3 Constructing the Sub-Objective Evaluation Matrix , Middle elements The z-th evaluation score represents the u-th sub-objective; right Normalization is performed: ; In the formula, To represent the normalized result ; for The z-th evaluation score in each column; for The minimum value in the column; for The difference between the maximum and minimum values ​​in the column; S4.4 Establish volatility indicators and opposing indicators, analyze and determine the trend of weight changes; comprehensively consider volatility indicators and opposing indicators to solve for the objective weights of sub-objectives. : ; ; In the formula, is the volatility index of the z-th evaluation score, which measures the degree of dispersion of different evaluation scores; , is the opposition indicator of the z-th evaluation score, which measures the correlation differences between different evaluation scores; for The number of indicators in each column; for middle The average evaluation score of the column; for The correlation between the z-th evaluation score in each column and other evaluation scores; S4.5 Construct a game theory weight combination objective, and solve for the combination coefficients by minimizing the weight deviation, thereby obtaining the sub-objective weights: ; ; In the formula, To minimize the weight bias objective; L is the number of weight optimization methods (subjective weight method in S4.2 and objective weight method in S4.4, L=2); For the first The combination coefficients of the weight optimization method (used to adjust the proportion of subjective / objective weights in the final combined weights); For the first The sub-objective weights determined by the weight optimization method ( When =1, it represents subjective weight. When the value is 2, it represents the objective weight. The final sub-objective weights include , , ; For the first Under this weight optimization method, the weight of the u-th sub-objective is, for example... Indicating subjective weights The weights; the superscript T indicates transpose.

[0029] Taking an 8-node system in the IEEE 33-bus system as an example, the optimal control mode for this node is global control, and all three control modes participate in reactive power and voltage classification. The judgment matrix for relevant sub-objectives... Sub-objective evaluation matrix The final sub-objective weights are as follows: ; like Figure 5 As shown, in S5, the improved NSGA-II algorithm is used for solving, and the steps are as follows: S5.1 Randomly generate a temporary population of twice the size, and dynamically select distributed power sources or reactive power compensation devices according to different reactive power control modes. Calculate the fitness of individuals in the temporary population, use fast non-dominated sorting to divide the temporary population by fitness, prioritize retaining individuals with high fitness rankings, and construct the target population. S5.2. Introduce an inverse weighting mechanism that considers a density threshold to calculate individual density, and combine it with the individual's objective function value to adjust the overall population crowding to avoid getting stuck in local convergence; for individuals with crowding less than 0.01, introduce random noise to avoid forming densely crowded regions. ; ; ; In the formula, For individual h density; Let be the distance between the nearest neighbors of individuals h and f; K is the nearest neighbor search coefficient. n1 is the number of individuals; Crowding level adjusted for individual h; The crowding level before adjustment for individual h; The objective function value for individual h+1; The objective function value for individual h-1; The objective function value ; Density threshold; Crowding degree after introducing random noise into individual h; S5.3. Obtain the offspring population by solving the crossover and variation of individual positions, and merge the parent and offspring populations; in the mixed population of two generations, obtain the new population by non-dominated sorting and crowding degree calculation. S5.4 Detect population diversity and dynamically adjust the elite retention ratio using linear interpolation based on the diversity level; based on the elite retention ratio, sort the individuals according to non-dominance level and crowding degree, and select elite individuals to form a new population: ; ; In the formula, This is the time decay factor; As a diversity regulator; This represents the current iteration number; O represents the total number of iterations; O represents the population diversity. , These represent the upper and lower limits of the elite retention ratio, respectively; clip is the truncation function; Indicates the percentage of elites retained; S5.5 Determine if the maximum number of iterations has been reached. If yes, output the optimal solution; otherwise, go to step S5.2.

[0030] For example, the population size is set to 250, the crossover and mutation probabilities are 0.85 and 0.05 respectively, the upper and lower limits of the elite retention ratio are 0.5 and 0.1 respectively, the population density threshold is 0.7, and the number of iterations is 300. The optimal control objective results under different weight optimization methods are as follows: Figure 6 As shown, overall, the dynamic weight optimization method outperforms the fixed weight optimization method on most nodes, indicating that under the current parameter settings or scenarios, dynamic weight configuration can more stably improve the reactive power and voltage control performance of the system than fixed adjustment. Further analysis of the relationship between control modes and node levels reveals that all first-level nodes (such as nodes 8 and 18) adopt a "global control" mode, while third-level nodes (such as nodes 11 and 33) correspond to "local control." This allocation aligns with engineering logic, where nodes with stronger control capabilities undertake global coordination tasks, while nodes with relatively weaker capabilities focus on local regulation. Second-level node control strategies show differentiation, including both "global control" and "line control," reflecting the transitional and hybrid characteristics of this level of nodes.

[0031] The reactive voltage control results of IEEE 33-node are as follows: Figure 7As shown, dynamic weight optimization significantly improves the overall voltage level and distribution uniformity of the system. With fixed weight optimization, the overall voltage is mostly concentrated between 1.02 pu and 1.05 pu, operating close to the upper limit, and some node voltages even equal the allowable upper limit of 1.05 pu, posing a risk of voltage exceeding the limit. With dynamic weight optimization, the voltage curve shifts downward, closer to 1 pu, and all node voltages are strictly controlled within a reasonable range of 0.95 pu to 1.05 pu, fully satisfying the upper and lower voltage limits. This indicates that dynamic weight control effectively improves voltage quality and operational stability, avoids localized high-voltage problems, and provides a good foundation for the safe and economical operation of the system.

[0032] Voltage distribution and deviation under reactive voltage control are as follows: Figure 8 As shown, the dynamic weighted voltage optimization effect is significant in terms of overall distribution and fluctuation suppression. During dynamic weighted optimization, the overall voltage level is effectively improved, with the mean voltage decreasing from 1.0273 pu in fixed weighted optimization to 1.0033 pu. Simultaneously, the voltage distribution box position shifts significantly downwards and expands in range, indicating that the voltage at each node is effectively reduced and closer to the ideal operating voltage. Regarding voltage stability, the mean voltage deviation during dynamic weighted optimization decreases from 0.0412 pu to 0.0278 pu, and the box height in the box plot decreases, indicating improved voltage stability at the nodes and a significant reduction in the risk of exceeding limits. Overall, the dynamic weighted optimization scheme not only improves the average voltage level but also effectively suppresses voltage fluctuations, providing a reliable basis for achieving safe, economical, and high-quality power supply.

[0033] Example 2: Based on Example 1, in the dynamic adjustment process of the elite retention ratio in S5.4, a distribution network fault transient state sensing mechanism is introduced to dynamically correct the upper and lower limit thresholds of the elite retention ratio. Specifically, the following steps are included: Real-time monitoring of distribution network operation status: Real-time voltage data of distribution network nodes are collected through phasor measurement units to identify fault transient scenarios such as voltage dips and voltage oscillations, and to extract voltage dip depth, voltage recovery rate, and transient duration as fault transient characteristic parameters. Calculating the transient adaptation factor: The transient characteristic parameters of the fault are graded and quantified according to their severity, with voltage drop depth having the highest weight, followed by voltage recovery rate, and transient duration having the lowest weight. The transient adaptation factor is obtained by weighted summation of the three factors. , The value range is [0,1], and the more severe the fault, the higher the value. The closer to 1; Dynamically adjusted threshold range: based on transient adaptation factor Adjust the upper and lower thresholds for the elite retention rate, when (When there are no obvious faults or slight fluctuations) maintain the original fixed threshold. , ;when (In the case of a moderate transient fault) Increase by 10% to 20% Increase by 5% to 10% to increase the number of elite individuals retained; when In the event of a severe transient failure, Increase by 20%~30% Increase by 10%~15%, while shortening the threshold update cycle to 50% of the original cycle, accelerating the iteration of high-quality individuals; Perform dynamic elite retention: Substitute the modified upper and lower thresholds into the original clip function, and calculate the elite retention ratio by combining the time decay factor and population diversity. Elite individuals are selected according to this ratio to enter the next generation of the population until the algorithm converges.

[0034] This improvement can increase the convergence speed of the algorithm in the transient scenario of distribution network faults, and avoid the loss of high-quality individuals or insufficient population diversity due to fixed thresholds. At the same time, in severe faults with voltage drop depths exceeding 10%, the reactive power regulation scheme obtained can shorten the voltage recovery time and significantly improve the transient voltage stability of the distribution network.

[0035] Example 3: A reactive voltage hierarchical control device based on optimal control objective, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method in Example 1 or Example 2.

Claims

1. A reactive power and voltage hierarchical control method based on optimal control objective, characterized in that... Includes the following steps: S1. Obtain actual data during the reactive power and voltage control process, including voltage and load data of each node, location and capacity of reactive power compensation equipment, location and power generation data of distributed power sources, and impedance parameters of transmission lines; S2. Based on the acquired actual data, analyze the correlation between voltage influence factors, reactive power control mode, and reactive power configuration, and form judgment indicators from a quantitative perspective to complete the reactive power voltage classification. S3. Considering the operating cost of reactive voltage control, the number of switching operations of capacitor banks and on-load tap-changing transformers, and the active power transmission loss of the line, establish a reactive voltage optimization model based on the optimal control objective and set its constraints. S4. Based on the reactive voltage classification, use game theory weighting method to dynamically adjust the sub-objective weights of the reactive voltage optimization model. S5. Within a set time period, use the NSGA-II algorithm to solve the reactive voltage optimization model and obtain the optimal solution of the reactive voltage hierarchical control method based on the optimal control objective.

2. The reactive power and voltage hierarchical control method based on optimal control objective according to claim 1, characterized in that, In S2, the control area is divided into regions. For a certain region in the reactive voltage control process, the influence of the load in the region on the reactive voltage sensitivity of the node voltage is considered to form a voltage influence factor. ； ； In the formula, Let be the voltage influence factor of node i at time t; The importance of the load on node i; Let be the voltage deviation at node i at time t; Let N be the reactive power-voltage sensitivity of node j to node i at time t; N is the number of nodes in the region where node i is located. , , , Both represent Jacobian block matrices. , These represent the degree of influence of the change in node voltage amplitude at time t on the reactive power and active power balance of the node, respectively. , These represent the degree of influence of the change in node voltage phase angle at time t on the balance of node reactive power and active power, respectively. The reactive power control mode is divided into three layers. The first layer is local control, which relies on local distributed power sources to complete reactive power and voltage compensation. The second layer is line control, which calls reactive power compensation equipment including capacitor banks (CB) and on-load tap changers (OLTC) to complete reactive power and voltage compensation. The third layer is global control, which calls reactive power compensation equipment including static var compensators (SVC) and synchronous condensers (SC) to complete reactive power and voltage compensation. For reactive power configurations, the reactive power output of distributed generation is approximately replaced by active power: ； In the formula, The reactive power injected into node i at time t by the local distributed power source; Let be the active power output of the distributed power source at node i at time t; The angle representing the maximum power factor of the distributed power source at time t; The output of the reactive power compensation device is represented as follows: ； ； ； ； ； In the formula, The reactive power injected into node i by the line control reactive power compensation device at time t; To determine the reactive power injected into node i at time t by the global control reactive power compensation device; Let be the switching capacity of the c-th CB at time t; Let d be the variable capacity of the OLTC at time t; Let be the reactive power output of the a-th SVC at time t; Let be the reactive power output of the b-th SC at time t; , , , The quantities of CB, OLTC, SVC, and SC devices are respectively. , , , These are the indicators for CB, OLTC, SVC, and SC being in use, respectively. 0 indicates that they are not in use, and 1 indicates that they are in use. Let be the number of capacitors at node i at time t; Let be the reactive power output of a single capacitor at node i at time t; , Let be the actual voltages at node i and node j at time t, respectively; Let be the ratio of OLTC at node j at time t; Let be the impedance between node i and node j at time t; Let be the actual voltage of the a-th SVC at time t; Let be the reactance parameter of the a-th SVC.

3. The reactive power and voltage hierarchical control method based on optimal control objective according to claim 2, characterized in that, In S2, by comparing the quantitative relationship between node voltage deviation and reactive power compensation, a correlation model is established for voltage influence factor, reactive power control mode, and reactive power configuration, expressed as: ； In the formula, , , These are the activation signals for the first, second, and third levels of reactive power control, respectively, with 1 representing activation and 0 representing deactivation. Let be the voltage deviation at node i at time t; Let be the rated voltage of node i at time t; The model output is for node i; T is the total number of time points. The NSGA-II algorithm is used to obtain the output results of the correlation model. At the same time, the K-means clustering algorithm is used to cluster the output results of the correlation model and classify the reactive power and voltage in descending order.

4. The reactive power and voltage hierarchical control method based on optimal control objective according to claim 2, characterized in that, In S3, the reactive power voltage optimization model is expressed as follows: ； ； ； ； In the formula, The optimal control objective for node i; Let $t$ be the operating cost of reactive voltage control at node $i$ at time $t$. Let t be the number of times CB and OLTC are switched at node i at time t; Let t be the active power transmission loss that injects power into node i at time t; , , They are respectively , , Weighting coefficients; The unit operating cost of distributed power sources; Let x be the output of the x-th distributed power source at time t; The unit operating cost of reactive voltage control; Let r be the output of the reactive power compensation device at time t; , These represent the action states of the c-th CB at times t and t+1, where 1 indicates action and 0 indicates no action. , These represent the action states of the d-th OLTC at times t and t+1, respectively, where 1 indicates action and 0 indicates no action. , Let be the voltage amplitudes at nodes m and n of the y-th line at time t, respectively; , Let be the voltage phases of nodes m and n of the y-th line at time t, respectively; Let be the resistance value of the y-th transmission line; This refers to the number of transmission lines. The number of distributed power sources participating in the reactive voltage control of node i; The number of reactive power compensation devices participating in reactive power voltage control at node i; T is the total number of moments. The constraints of the reactive voltage optimization model include voltage amplitude constraints, SVC / SC output power constraints, CB switching constraints, OLTC tap constraints, line transmission capacity constraints, and power balance constraints.

5. The reactive power and voltage hierarchical control method based on optimal control objective according to claim 4, characterized in that, The specific constraints of the reactive voltage optimization model are as follows: Voltage amplitude constraint, expressed as: ； In the formula, , These are the upper and lower limits of the voltage amplitude at the i-th node, respectively. SVC output power constraint is expressed as: ； In the formula, , These are the upper and lower limits of the SVC output power, respectively. The SC output power constraint is expressed as: ； In the formula, , These are the upper and lower limits of the SC output power, respectively; CB switching constraint, expressed as: ； ； In the formula, Let c be the number of times the capacitor of the c-th CB is switched on and off. , These are the upper and lower limits of the number of times the capacitor of the c-th CB can be switched on and off, respectively. OLTC gear position constraints are represented as: ； ； ； In the formula, For the d-th OLTC gear; , These are the upper and lower limits of the gear for the d-th OLTC, respectively. This is the upper limit of the gear adjustment for the d-th OLTC; Line transmission capacity constraints are expressed as: ； In the formula, Let y be the transmission capacity of the y-th transmission line; , These are the upper and lower limits of the transmission capacity of the y-th line, respectively; Power balance constraints are expressed as: ； In the formula, , These represent the active and reactive power injected at node i at time t, respectively. , These represent the active and reactive loads at node i at time t, respectively. The reactive power injected by the reactive power compensation device at node i at time t; , and represent the conductance and susceptance of the y-th line, respectively.

6. The reactive power and voltage hierarchical control method based on optimal control objective according to claim 4, characterized in that, In S2, the output results of the three-level control modes participating in reactive power voltage classification at the same node are obtained. The priority of the control modes is determined according to the magnitude of the values, with the largest value being the optimal control mode. In S3, the weight corresponding to the optimal control mode is increased.

7. The reactive power and voltage hierarchical control method based on optimal control objective according to claim 6, characterized in that, In S4, the specific steps of the game theory weighting method are as follows: S4.1 Construct a sub-target judgment matrix based on the output results of the association model. , medium elements This represents the degree of importance between sub-objectives u and v; right A consistency check is performed, expressed as: ； In the formula, For consistency calculation indicators; The average proportion of consistency; for The largest eigenvalue; for The order of; This is the average consistency index; S4.2, Use The average value of the column vectors is used to approximate the subjective weights of the sub-objectives. , is represented as: ； In the formula, for The element in the middle represents the importance between sub-targets k and v; S4.3 Constructing the Sub-Objective Evaluation Matrix , medium elements The z-th evaluation score represents the u-th sub-objective; right Normalization is performed: ； In the formula, To represent the normalized result ; for The z-th evaluation score in each column; for The minimum value in the column; for The difference between the maximum and minimum values ​​in the column; S4.4 Establish volatility indicators and opposing indicators, analyze and determine the trend of weight changes; comprehensively consider volatility indicators and opposing indicators to solve for the objective weights of sub-objectives. : ； ； In the formula, is the volatility index of the z-th evaluation score, which measures the degree of dispersion of different evaluation scores; , is the opposition indicator of the z-th evaluation score, which measures the correlation differences between different evaluation scores; for The number of indicators in each column; for middle The average evaluation score of the column; for The correlation between the z-th evaluation score in each column and other evaluation scores; S4.5 Construct a game theory weight combination objective, and solve for the combination coefficients by minimizing the weight deviation, thereby obtaining the sub-objective weights: ； ； In the formula, The objective is to minimize the weight bias; L represents the number of weight optimization methods. For the first Combination coefficients of the weight optimization method; For the first The sub-objective weights determined by the weight optimization method; The final sub-objective weights include , , ; For the first The weight of the u-th sub-objective under the weight optimization method.

8. The reactive power and voltage hierarchical control method based on optimal control objective according to claim 1, characterized in that, In S5, the improved NSGA-II algorithm is used for solving, and the steps are as follows: S5.1 Randomly generate a temporary population of twice the size, and dynamically select distributed power sources or reactive power compensation devices according to different reactive power control modes. Calculate the fitness of individuals in the temporary population, use fast non-dominated sorting to divide the temporary population by fitness, prioritize retaining individuals with high fitness rankings, and construct the target population. S5.2 Introduce an inverse weighting mechanism that considers a density threshold to calculate individual density, and combine it with the objective function value of the individual to adjust the overall population crowding to avoid getting stuck in local convergence; for individuals with crowding less than the set crowding threshold, introduce random noise to avoid forming densely crowded areas. S5.

3. Obtain the offspring population by solving the crossover and variation of individual positions, and merge the parent and offspring populations; in the mixed population of two generations, obtain the new population by non-dominated sorting and crowding degree calculation. S5.4 Detect population diversity and dynamically adjust the elite retention ratio using linear interpolation based on the diversity level; based on the elite retention ratio, sort the individuals according to non-dominance level and crowding degree, and select elite individuals to form a new population: ； ； In the formula, This is the time decay factor; As a diversity regulator; This represents the current iteration number; O represents the total number of iterations; O represents the population diversity. , These represent the upper and lower limits of the elite retention ratio, respectively. Indicates the percentage of elites retained; S5.5 Determine if the maximum number of iterations has been reached. If yes, output the optimal solution; otherwise, go to step S5.

2.

9. A reactive power voltage hierarchical control method based on optimal control objective according to claim 8, characterized in that, In S5.2, the inverse weighting mechanism considering the density threshold is expressed as follows: ； ； ； In the formula, For individual h density; Let be the distance between the nearest neighbors of individuals h and f; K is the nearest neighbor search coefficient. Crowding level adjusted for individual h; Crowding level before adjustment for individual h; The objective function value for individual h+1; The objective function value for individual h-1; The objective function value; Density threshold; Crowding degree after introducing random noise into individual h.

10. A reactive power voltage hierarchical control device based on optimal control objective, characterized in that: It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any one of claims 1-9.

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