A power distribution network reactive power optimization method, system, device, medium and product based on a BES-QPSO hybrid algorithm

Abstract

The application discloses a power distribution network reactive power optimization method, system, equipment, medium and product based on a BES-QPSO hybrid algorithm, relates to the technical field of power system operation and control, and comprises the following steps: a power distribution network multi-objective reactive power optimization model is established with the minimum comprehensive economic cost, the minimum voltage deviation and the maximum voltage stability margin as targets; the model is subjected to multi-objective aggregation, and a comprehensive objective function is constructed; a hybrid algorithm population is initialized, the comprehensive objective function is used as an adaptability function, the hybrid algorithm of the bald eagle search and quantum behavior particle swarm optimization is used to iteratively optimize the population, and a global optimal solution is output and issued to a target power distribution network for execution. Through the synergistic complementation of the two algorithms, the application can stably converge to a high-quality solution in a high-dimensional nonlinear multi-constrained power distribution network scene, significantly reduces the comprehensive economic cost, improves the voltage quality and improves the system stability.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, and in particular to a method, system, equipment, medium and product for reactive power optimization of distribution networks based on the BES-QPSO hybrid algorithm. Background Technology

[0002] With the large-scale integration of distributed power sources and flexible loads, distribution networks are transforming from traditional passive radial networks into active, bidirectional interactive complex systems. Their operational characteristics are becoming increasingly complex, placing higher demands on the precision and efficiency of reactive power optimization. Reactive power optimization, as a key means to ensure the safe, economical, and high-quality operation of distribution networks, focuses on coordinating and controlling various reactive resources within the network to minimize network losses, improve voltage quality, and enhance system stability. However, reactive power optimization in active distribution networks is essentially a high-dimensional, nonlinear, and multi-constrained multi-objective optimization problem. Its decision variables encompass various types of regulation methods, and conflicts often exist between sub-objectives. Traditional methods struggle to simultaneously achieve both solution accuracy and computational efficiency.

[0003] Among existing solution methods, traditional mathematical programming-based methods, while offering advantages in model accuracy, suffer from inherent limitations when dealing with discrete variables and complex constraints in active distribution networks. These limitations include difficulties in achieving precise linearization of the model and a weak ability to handle discrete variables. While swarm intelligence methods based on classical intelligent algorithms possess some global search capabilities, they are prone to premature convergence to local optima due to loss of population diversity when solving high-dimensional multi-objective optimization problems. This makes it difficult to balance optimization accuracy and convergence speed, failing to meet the dual requirements of optimization quality and real-time performance in practical engineering. In recent years, emerging metaheuristic algorithms have made breakthroughs in global exploration capabilities, but generally suffer from insufficient local refinement capabilities. Other algorithms that enhance convergence by introducing quantum mechanical models are sensitive to the quality of the initial population and are prone to getting trapped in suboptimal solutions under complex constraints. The difficulty of achieving an effective balance between exploration and refinement by a single algorithm limits its performance when solving high-dimensional nonlinear multi-constraint optimization problems. Summary of the Invention

[0004] This invention provides a method, system, equipment, medium, and product for reactive power optimization of distribution networks based on the BES-QPSO hybrid algorithm, which solves the problem that existing single metaheuristic algorithms are difficult to efficiently solve the active reactive power optimization problem of distribution networks due to the imbalance between global exploration and local development capabilities.

[0005] The first aspect of this invention provides a reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm, comprising:

[0006] A multi-objective reactive power optimization model for distribution networks is established with the optimization objectives of minimizing overall economic cost, minimizing voltage deviation, and maximizing voltage stability margin.

[0007] The multi-objective reactive power optimization model of the power distribution network is aggregated to construct a comprehensive objective function;

[0008] Initialize the hybrid algorithm population, use the comprehensive objective function as the fitness function, and iteratively optimize the hybrid algorithm population using a hybrid algorithm of vulture search and quantum behavior particle swarm optimization to output the global optimal solution;

[0009] The global optimal solution is used as the optimal reactive power control scheme and sent to the target distribution network for execution.

[0010] Optionally, the step of performing multi-objective aggregation on the multi-objective reactive power optimization model of the distribution network to construct a comprehensive objective function includes:

[0011] In the multi-objective reactive power optimization model of the power distribution network, multiple optimization objectives are taken as sub-objectives to be processed, and each sub-objective to be processed is the objective function term of the decision variable vector.

[0012] Obtain the sub-target baseline value corresponding to each of the sub-targets to be processed;

[0013] The analytic hierarchy process (AHP) is used to determine the sub-target weight coefficients corresponding to each sub-target to be processed according to the preset sub-target priority order.

[0014] The weighted coefficient method is used to divide each objective function term by the corresponding sub-objective benchmark value, and then multiply the ratio result by the corresponding sub-objective weight coefficient to obtain the weighted sub-objective term corresponding to each sub-objective to be processed;

[0015] The weighted sub-objectives are summed to construct a comprehensive objective function, which is the objective function of the single-objective optimization problem after the transformation of the multi-objective reactive power optimization model of the distribution network.

[0016] Optionally, the initialization of the hybrid algorithm population, using the comprehensive objective function as the fitness function, iteratively optimizes the hybrid algorithm population using a hybrid algorithm combining vulture search and quantum behavior particle swarm optimization to output the global optimal solution, including:

[0017] Chaotic sequences are generated using the Tent chaotic map;

[0018] The chaotic sequence is used to initialize the hybrid algorithm population. Each individual in the hybrid algorithm population is a decision variable vector. The decision variable vector includes the reactive power output of each distributed power source, the reactive power output of each static var compensator, and the number of switching groups of each parallel capacitor.

[0019] Using the comprehensive objective function as the fitness function, the individual fitness of the hybrid algorithm population is evaluated, and the set of historical best positions and global best positions of individuals are determined based on the evaluation results.

[0020] Based on the set of the individual's historical best positions and the global best position, the hybrid algorithm of vulture search and quantum behavior particle swarm optimization is used to iteratively optimize the hybrid algorithm population until the maximum number of iterations is reached, and the global best solution is output.

[0021] Optionally, the step of iteratively optimizing the hybrid algorithm population based on the individual's historical best position set and the global best position using a hybrid algorithm of eagle search and quantum behavior particle swarm optimization until the maximum number of iterations is reached, and outputting the global best solution, includes:

[0022] The hybrid algorithm population is globally explored using a vulture search strategy to obtain a globally updated population.

[0023] Calculate the historical average optimal position of the population and the random attraction point of each individual corresponding to the global update population;

[0024] Substituting the historical average optimal position of the population and the random attraction point of each individual into the quantum motion equation, the position of each individual in the globally updated population is updated to obtain the locally updated population.

[0025] Using the comprehensive objective function as the fitness function, the fitness value of each individual in the local update population is calculated, and the set of historical best positions and the global best position of the individual are updated according to the fitness value. The decision variable vector corresponding to the global best position is synchronously updated to the global best solution.

[0026] Determine if the maximum number of iterations has been reached;

[0027] If the target is not reached, proceed to the step of using the vulture search strategy to perform a global exploration of the hybrid algorithm population to obtain a globally updated population.

[0028] If the optimal solution is reached, the iteration is terminated and the current global optimal solution is output. The optimal reactive power control scheme includes the reactive power output of each distributed power source, the output of the static var compensator, and the number of switching groups of each parallel capacitor.

[0029] Optionally, the vulture search strategy includes region selection and spiral search operations. The step of using the vulture search strategy to globally explore the hybrid algorithm population and obtain a globally updated population includes:

[0030] For each individual in the hybrid algorithm population, the region selection operation and the spiral search operation are performed sequentially to obtain a globally updated population;

[0031] The region selection operation specifically involves randomly selecting a search region for each individual in the hybrid algorithm population using the vulture search selection probability, and updating the population individual position based on the current global optimal position and random individual perturbation.

[0032] The spiral search operation specifically involves performing a spiral descent search within the selected search area for each individual in the population after the region selection operation is updated. This search incorporates the population average position and the previous position of the individual's current position, thus updating the individual's position.

[0033] Optionally, the model constraints of the multi-objective reactive power optimization model of the distribution network include node power balance equation constraints, node voltage amplitude upper and lower limit constraints, distributed power reactive power output upper and lower limit constraints, parallel capacitor switching group number upper and lower limit constraints, static var compensator reactive power output upper and lower limit constraints, photovoltaic traditional power active power output upper and lower limit constraints, wind power traditional power active power output upper and lower limit constraints, and traditional power active power output upper and lower limit constraints.

[0034] The second aspect of this invention provides a reactive power optimization system for distribution networks based on the BES-QPSO hybrid algorithm, comprising:

[0035] The model building module is used to establish a multi-objective reactive power optimization model for the distribution network with the optimization objectives of minimizing the overall economic cost, minimizing the voltage deviation, and maximizing the voltage stability margin.

[0036] The comprehensive objective function construction module is used to aggregate multiple objectives in the multi-objective reactive power optimization model of the power distribution network and construct a comprehensive objective function.

[0037] The hybrid algorithm iterative optimization module is used to initialize the hybrid algorithm population, use the comprehensive objective function as the fitness function, and use a hybrid algorithm of vulture search and quantum behavior particle swarm optimization to iteratively optimize the hybrid algorithm population and output the global optimal solution.

[0038] The control command issuing module is used to take the global optimal solution as the optimal reactive power control scheme and issue it to the target distribution network for execution.

[0039] The third aspect of the present invention provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the power distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm as described above.

[0040] The fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed, it implements the reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm as described above.

[0041] The fifth aspect of the present invention provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, wherein, when the program instructions are executed by a computer, the computer performs the power distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm as described above.

[0042] As can be seen from the above technical solutions, the present invention has the following advantages:

[0043] This invention provides a method, system, equipment, medium, and product for reactive power optimization in distribution networks based on the BES-QPSO hybrid algorithm. First, a multi-objective reactive power optimization model for the distribution network is established, with the optimization objectives of minimizing overall economic cost, minimizing voltage deviation, and maximizing voltage stability margin. Based on this, the multi-objective reactive power optimization model is aggregated to construct a comprehensive objective function, transforming the multi-objective problem into a single-objective optimization problem, unifying the optimization evaluation criteria, and simplifying the solution complexity. Then, a hybrid algorithm population is initialized, and using the comprehensive objective function as the fitness function, a hybrid algorithm combining eagle search and quantum behavior particle swarm optimization is used to iteratively optimize the population. Through the collaborative search of the two algorithms, an effective balance is achieved between global exploration and local exploitation, avoiding premature local optima while ensuring fine-grained search capabilities near the optimal region. Finally, the globally optimal solution is output and distributed as the optimal reactive power control scheme to the target distribution network for execution. This invention achieves a balance between search breadth and convergence accuracy when solving high-dimensional, nonlinear, and multi-constrained active distribution network reactive power optimization problems through hierarchical collaboration and information interaction between vulture search and quantum behavior particle swarm optimization. It overcomes the premature convergence or search stagnation problems caused by the capacity imbalance of single algorithms, effectively reduces the overall economic cost, improves voltage quality, enhances system stability, and achieves significant comprehensive optimization results. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart illustrating the steps of a reactive power optimization method for a distribution network based on the BES-QPSO hybrid algorithm, provided in Embodiment 1 of the present invention.

[0046] Figure 2This is a flowchart illustrating the steps of a reactive power optimization method for a distribution network based on the BES-QPSO hybrid algorithm, provided in Embodiment 2 of the present invention.

[0047] Figure 3 This is an improved IEEE-33 node topology diagram provided in Embodiment 2 of the present invention;

[0048] Figure 4 This is a comparison chart of network losses provided in Embodiment 2 of the present invention;

[0049] Figure 5 This is a voltage offset comparison diagram provided in Embodiment 2 of the present invention;

[0050] Figure 6 This is a comparison chart of voltage stability indicators provided in Embodiment 2 of the present invention;

[0051] Figure 7 This is a comparison chart of fitness function values ​​for different algorithms provided in Embodiment 2 of the present invention;

[0052] Figure 8 This is a structural block diagram of a power distribution network reactive power optimization system based on the BES-QPSO hybrid algorithm provided in Embodiment 3 of the present invention;

[0053] Figure 9 This is a structural block diagram of an electronic device provided in Embodiment 4 of the present invention. Detailed Implementation

[0054] This invention provides a method, system, device, medium, and product for reactive power optimization of distribution networks based on the BES-QPSO hybrid algorithm, which addresses the shortcomings of existing single metaheuristic algorithms that are difficult to efficiently solve active reactive power optimization problems in distribution networks due to the imbalance between global exploration and local development capabilities.

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] Please see Figure 1 , Figure 1 The flowchart illustrates the steps of a reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm, as provided in Embodiment 1 of the present invention.

[0057] This invention provides a reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm, comprising:

[0058] Step 101: Establish a multi-objective reactive power optimization model for the distribution network with the optimization objectives of minimizing the overall economic cost, minimizing the voltage deviation, and maximizing the voltage stability margin.

[0059] In this embodiment of the invention, the topology, line parameters, node load data, and technical parameters of each reactive power regulation device of the distribution network are first obtained. Then, the decision variables are selected, namely the output or switching status of each controllable reactive power source (including distributed power sources, static var compensators, and parallel capacitors). Based on this, expression functions for three optimization objectives—minimizing comprehensive economic cost, minimizing voltage deviation, and maximizing voltage stability margin—are constructed respectively. Node power balance equation constraints and various equipment operation limit inequality constraints are set to form a complete multi-objective reactive power optimization model for the distribution network.

[0060] Step 102: Perform multi-objective aggregation on the multi-objective reactive power optimization model of the distribution network to construct a comprehensive objective function.

[0061] In this embodiment of the invention, three optimization objectives—comprehensive economic cost, voltage deviation, and voltage stability margin—are defined as sub-objectives to be processed. Each sub-objective is expressed as a function of the decision variable vector. Then, the comprehensive economic cost, voltage deviation, and L-index of the distribution network system before optimization are obtained and used as the baseline values ​​for each sub-objective. These baseline values ​​remain constant throughout the iterative optimization process. Using the analytic hierarchy process (AHP), the weight coefficients of the three sub-objectives are determined according to the priority order of comprehensive economic cost over voltage deviation, and voltage deviation over voltage stability margin, with the sum of the three equal to 1. Finally, the function values ​​of each sub-objective are divided by their corresponding baseline values ​​to achieve dimensionless processing, and then multiplied by their respective weight coefficients and summed to construct the comprehensive objective function. This function is the objective function of the single-objective optimization problem transformed from the original multi-objective optimization problem.

[0062] Step 103: Initialize the hybrid algorithm population. Using the comprehensive objective function as the fitness function, iteratively optimize the hybrid algorithm population using a hybrid algorithm of vulture search and quantum behavior particle swarm optimization, and output the global optimal solution.

[0063] In this embodiment of the invention, key parameters of the hybrid algorithm are first set, including population size, maximum number of iterations, vulture search selection probability, and contraction / expansion coefficients of quantum behavior particle swarm optimization. A chaotic sequence is generated using the Tent chaotic map. This chaotic sequence is used to initialize the hybrid algorithm population within the upper and lower bounds of the decision variables, ensuring that the initial individuals are uniformly distributed in the solution space. Then, the constructed comprehensive objective function is used as the fitness function to calculate the fitness value of each individual, and the position of the individual with the lowest fitness is set as the global optimum. Based on this, an iterative optimization loop is entered: first, the vulture search strategy is executed for global exploration, updating the positions of the individuals in the population; then, the updated population is used as input to execute the quantum behavior particle swarm optimization strategy for local development, further updating the individual positions; after each iteration, the fitness value is recalculated and the global optimum position is updated. When the preset maximum number of iterations is reached, the iteration terminates, and the decision variable vector corresponding to the current global optimum position is output as the global optimum solution.

[0064] Step 104: Use the global optimal solution as the optimal reactive power control scheme and send it to the target distribution network for execution.

[0065] In this embodiment of the invention, after the iterative optimization terminates, the output global optimal solution is decoded to obtain the reactive power output of each distributed power source, the reactive power output of each static var compensator (SVC), and the number of switching groups of each parallel capacitor bank, forming the optimal reactive power control scheme. Then, this scheme is distributed to each field execution terminal, including distributed power source inverters, SVCs, and parallel capacitor switches, through the distribution network energy management system, completing the closed-loop control of the reactive power and voltage of the distribution network. After execution, the distribution network operates in an optimized state with the lowest overall economic cost, the smallest voltage deviation, and the largest voltage stability margin.

[0066] Comprehensive Economic Cost: The comprehensive economic cost encompasses the economic losses corresponding to distribution network losses, i.e., the network loss cost, and the generation cost of various power sources. Voltage Deviation: Voltage deviation characterizes the degree to which the voltage at each node in the distribution network deviates from the reference value. It is obtained by dividing the deviation of the voltage amplitude at each node from the reference voltage by the difference between its upper and lower limits, taking the absolute value, and summing the results. Voltage Stability Margin: Voltage stability margin is quantified using the L-index. A lower L-index indicates better system voltage stability. This index is calculated based on the voltage amplitude at the branch head, the active and reactive power at the branch end, the branch resistance and reactance, and impedance. Multi-Objective Reactive Power Optimization Model for Distribution Networks: The multi-objective reactive power optimization model for distribution networks aims to minimize the comprehensive economic cost, minimize the voltage deviation, and maximize the voltage stability margin. It includes node power balance equation constraints and inequality constraints for various reactive power regulation devices. Multi-Objective Aggregation: Multi-objective aggregation refers to the process of transforming multiple optimization objectives into a single-objective optimization problem through normalized weighted summation using the analytic hierarchy process (AHP) and weighted coefficient method. **Comprehensive Objective Function:** The comprehensive objective function is the objective function of a single-objective optimization problem constructed after multi-objective aggregation of the multi-objective reactive power optimization model of the distribution network. It is obtained by dividing each sub-objective function value by its corresponding baseline value to achieve dimensionlessness, multiplying by the corresponding weight coefficient, and then summing the results. **Hybrid Algorithm Population:** The hybrid algorithm population refers to a set of individuals, each representing a decision variable vector, serving as the basic object for iterative optimization in the hybrid algorithm combining Eagle Search and Quantum Behavioral Particle Swarm Optimization. **Fitness Function:** The fitness function, also known as the comprehensive objective function, evaluates the performance of each individual in the hybrid algorithm population. A smaller fitness value indicates better overall performance of the reactive power control scheme corresponding to that individual. **Hybrid Algorithm of Eagle Search and Quantum Behavioral Particle Swarm Optimization:** This hybrid algorithm is a hierarchical collaborative optimization algorithm. It first uses the Eagle Search strategy for global exploration, then uses the Quantum Behavioral Particle Swarm Optimization strategy for local refinement. The two strategies achieve an effective balance between global exploration and local refinement through population relay and information interaction. Iterative optimization: Iterative optimization refers to the process of repeatedly executing vulture search for global exploration and quantum behavior particle swarm optimization for local development, continuously updating the positions of individuals in the population and optimizing their fitness values ​​until the convergence condition is met. Global optimal solution: The global optimal solution is the decision variable vector corresponding to the position of the individual with the lowest fitness in the hybrid algorithm population at the termination of iterative optimization. Decoding this decision variable vector yields the optimal reactive power control scheme. Optimal reactive power control scheme: The optimal reactive power control scheme refers to a set of specific control commands obtained after decoding the global optimal solution, including the reactive power output of each distributed power source, the reactive power output of each static var compensator, and the number of switching groups for each parallel capacitor, used to issue to the target distribution network for execution.Target distribution network: The target distribution network refers to the active distribution network system to be optimized for reactive power, including distributed generation, static var compensators, parallel capacitors and other reactive power regulation equipment.

[0067] In this invention, firstly, a multi-objective reactive power optimization model is established with comprehensive economic cost, voltage deviation, and voltage stability margin as optimization objectives. This model covers three core dimensions of distribution network operation: economy, safety, and power supply quality, providing a comprehensive evaluation system for subsequent optimization. The multi-objective problem is then aggregated into a single-objective comprehensive objective function, preserving the physical meaning of each sub-objective while avoiding the complex Pareto front solution process in multi-objective optimization, effectively reducing the difficulty of solving the optimization problem. Based on this, iterative optimization is performed using a hybrid algorithm combining Eagle Search and Quantum Behavior Particle Swarm Optimization. Through Tent chaotic mapping initialization and a hierarchical collaborative mechanism between the two algorithms, the global exploration capability of the Eagle Search algorithm and the local development capability of the Quantum Behavior Particle Swarm Optimization algorithm are fully utilized, achieving an effective balance between search breadth and convergence depth, and stably converging to a high-quality global optimal solution. Finally, the global optimal solution is decoded into specific reactive power control commands and executed, completing a seamless connection from optimization calculation to engineering implementation. Therefore, this invention can efficiently solve multi-objective reactive power optimization problems in active distribution network scenarios, effectively reduce overall economic costs, improve voltage quality, enhance system stability, and achieve significant comprehensive optimization results.

[0068] Please see Figure 2 , Figure 2 The flowchart illustrates the steps of a reactive power optimization method for a distribution network based on the BES-QPSO hybrid algorithm, as provided in Embodiment 2 of the present invention.

[0069] This invention provides a reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm, comprising:

[0070] Step 201: Establish a multi-objective reactive power optimization model for the distribution network with the optimization objectives of minimizing the overall economic cost, minimizing the voltage deviation, and maximizing the voltage stability margin.

[0071] In this embodiment of the invention, the topology, line impedance parameters, node load data, and connection locations and technical parameters of each reactive power regulation device (including distributed generation, static var compensators, parallel capacitors, etc.) of the target distribution network are first obtained. The decision variables are selected as the reactive power output of each distributed generation, the reactive power output of each static var compensator, and the number of switching groups of each parallel capacitor. Based on this, objective functions for three optimization objectives are constructed respectively:

[0072] (a) Comprehensive economic cost target

[0073] The comprehensive economic cost encompasses the economic losses (network loss cost) corresponding to distribution network losses and the generation costs of various power sources, and its expression is as follows:

[0074] ;

[0075] In the formula, To take into account the overall economic costs, For network loss costs, This represents the total cost of electricity generation.

[0076] The formula for calculating network loss cost is:

[0077] ;

[0078] In the formula, The total active power network loss of the distribution network. For the calculation period (h). This refers to the unit price for electricity purchase and sale.

[0079] The calculation method for the total active power network loss of the distribution network is as follows:

[0080] ;

[0081] In the formula, This represents the total number of branches in the distribution network. branch road electrical conductivity, They are nodes With nodes voltage amplitude, For nodes With nodes The phase angle difference between them.

[0082] Considering the cost difference between distributed power sources (photovoltaics, wind power) and traditional power sources, the expression for the total power generation cost is:

[0083] ;

[0084] In the formula, This represents the total number of distributed power sources. The cost of generating electricity from traditional power sources, For the first The generation cost of distributed power sources varies, with photovoltaic (PV) and wind power using different cost models. Specifically, the generation cost of PV power... The calculation formula is:

[0085] ;

[0086] In the formula, Contributing to photovoltaic power generation This represents the fixed cost coefficient for photovoltaic power generation. This represents the variable cost coefficient for photovoltaic power generation.

[0087] The cost of generating electricity from wind power The calculation formula is:

[0088] ;

[0089] In the formula, For active power output of wind power. This represents the fixed cost coefficient for wind power generation. Variable cost factor for wind power generation.

[0090] Cost of generating electricity from traditional power sources Using a linear cost model:

[0091] ;

[0092] In the formula, For traditional power sources, active power output, This represents the unit power generation cost of traditional power sources.

[0093] (ii) Voltage offset target

[0094] The voltage offset target is quantified using the normalized cumulative sum of the voltage deviations from the reference value at each node, and its expression is as follows:

[0095] ;

[0096] In the formula, The total number of distribution network nodes. For nodes voltage amplitude, For nodes The reference voltage, They are nodes The upper and lower limits of the voltage amplitude.

[0097] (III) Voltage stability margin target

[0098] Voltage stability margin adopted Quantification of indices A lower exponent indicates better system voltage stability, and its expression is:

[0099] ;

[0100] In the formula, For voltage stability margin index, This represents the total number of branches in the distribution network. For the first node of the branch road voltage amplitude, These are the end nodes of the branch. Active power and reactive power, These are the resistance, reactance, and impedance of the branch, respectively. The apparent power of the branch terminal node and .

[0101] In addition, constraints are set for the multi-objective reactive power optimization model of the distribution network, including constraints on the node power balance equation, as well as upper and lower limits constraints on node voltage amplitude, reactive power output of distributed generation sources, number of parallel capacitor banks, reactive power output of static var compensators, active power output of photovoltaic traditional power sources, active power output of wind power traditional power sources, and active power output of traditional power sources. These objective functions and constraints together constitute the multi-objective reactive power optimization model of the distribution network.

[0102] (a) Equality constraints (nodal power balance constraints)

[0103] The active and reactive power injected at each node must satisfy the power balance equation, expressed as follows:

[0104] ;

[0105] In the formula, They are nodes Injected active power and reactive power, They are nodes With nodes voltage amplitude, The nodal admittance matrices are respectively the first... Line number The real and imaginary parts of column elements, For nodes With nodes Voltage phase angle difference between them This represents the total number of nodes in the distribution network.

[0106] (ii) Inequality constraints

[0107] Inequality constraints cover system operating safety limits and output boundaries of various reactive power regulation devices, specifically including:

[0108] Node voltage amplitude upper and lower limit constraints:

[0109] ;

[0110] In the formula, They are nodes The lower and upper limits of voltage amplitude, It is a set of distribution network nodes.

[0111] Distributed power generation reactive power output upper and lower limit constraints:

[0112] ;

[0113] In the formula, For the first The reactive power injected into the node by a distributed power source The first The lower and upper limits of reactive power output of a distributed power source. It is a set of distributed power supply access nodes.

[0114] Upper and lower limits on the number of parallel capacitor banks to be switched:

[0115] ;

[0116] In the formula, For the first Number of parallel capacitor banks switched on / off (or reactive power compensation capacity). The first The lower and upper limits of the number of parallel capacitor banks that can be switched. This is the set of nodes connected to parallel capacitors.

[0117] Static var compensator reactive power output upper and lower limit constraints:

[0118] ;

[0119] In the formula, For the first The reactive power output of a static var compensator The first The lower and upper limits of reactive power output of a static var compensator. This is the set of nodes connected to the static var compensator.

[0120] Upper and lower limits of active power output constraints for photovoltaic power sources:

[0121] ;

[0122] In the formula, For the active power output of photovoltaic power sources, These represent the lower and upper limits of the active power output of photovoltaic power sources, respectively.

[0123] Upper and lower limits of active power output constraints for wind power sources:

[0124] ;

[0125] In the formula, For the active power output of wind power sources, These represent the lower and upper limits of the active power output of wind power sources, respectively.

[0126] Traditional power supply has upper and lower limits for active power output:

[0127] ;

[0128] In the formula, For the active power output of traditional power sources, These represent the lower and upper limits of the active power output of a traditional power source, respectively.

[0129] In all the constraints mentioned above, the feasible domain boundaries of each variable (i.e., each upper and lower limit value) are predetermined by the equipment parameters and operating procedures of the target distribution network and remain constant during the optimization iteration process.

[0130] Model constraints: Model constraints refer to the equality and inequality restrictions that the optimization variables and state variables in the multi-objective reactive power optimization model of the distribution network must satisfy. These include nodal power balance equality constraints and various operational safety limits and equipment output boundaries. Nodal power balance equality constraints: Nodal power balance equality constraints refer to the power flow balance equations that the active and reactive power injected into each node in the distribution network must satisfy. These are the fundamental physical constraints for power system operation. Various upper and lower limit constraints: Various upper and lower limit constraints include upper and lower limit constraints on node voltage amplitude, upper and lower limit constraints on reactive power output of distributed generation sources, upper and lower limit constraints on the number of parallel capacitor banks, upper and lower limit constraints on reactive power output of static var compensators, upper and lower limit constraints on active power output of photovoltaic power sources, upper and lower limit constraints on active power output of wind power sources, and upper and lower limit constraints on active power output of traditional power sources. These upper and lower limit values ​​are predetermined by the equipment parameters and operating procedures of the target distribution network.

[0131] Step 202: Perform multi-objective aggregation on the multi-objective reactive power optimization model of the distribution network to construct a comprehensive objective function.

[0132] Furthermore, step 202 may include the following sub-steps:

[0133] S11. In the multi-objective reactive power optimization model of the distribution network, multiple optimization objectives are taken as sub-objectives to be processed, and each sub-objective to be processed is the objective function term of the decision variable vector.

[0134] In this embodiment of the invention, the three optimization objectives included in the multi-objective reactive power optimization model of the distribution network established in step 201—namely, minimizing the comprehensive economic cost, minimizing voltage deviation, and maximizing voltage stability margin—are first determined as sub-objectives to be processed. Each sub-objective to be processed is expressed as an objective function term about the decision variable vector, i.e., the comprehensive economic cost term. Voltage offset term and voltage stability margin Index Term All three sub-objective functions use a decision variable vector as their independent variable. This decision variable vector is composed of the reactive power output of each distributed power source, the reactive power output of each static var compensator, and the number of switching groups of each parallel capacitor.

[0135] S12. Obtain the baseline value of each sub-target to be processed.

[0136] In this embodiment of the invention, the comprehensive economic cost, voltage deviation, and other parameters of the target distribution network system before optimization are obtained respectively. The index value is used as the benchmark value for each sub-objective to be processed. Specifically, in the initial operating state without any reactive power optimization adjustment, the comprehensive economic cost value of the system before optimization is calculated according to the objective function expressions established in step 201. Voltage offset value and Index value These serve as the baseline values ​​for the three sub-objectives. Once determined, these baseline values ​​remain constant throughout the iterative optimization process and are used for subsequent dimensionless processing of each sub-objective.

[0137] S13. Using the analytic hierarchy process (AHP), determine the sub-target weight coefficients corresponding to each sub-target to be processed according to the preset sub-target priority order, and the sum of all sub-target weight coefficients is equal to 1.

[0138] In this embodiment of the invention, the weight coefficients of each sub-objective are determined using the Analytic Hierarchy Process (AHP). Based on the actual engineering requirements for distribution network operation optimization, the priority order of the sub-objectives is set as follows: comprehensive economic cost has a higher priority than voltage deviation, and voltage deviation has a higher priority than voltage stability margin. Based on this priority order, the weight coefficients of comprehensive economic cost are determined through pairwise comparisons and judgment matrix solving in the AHP. Weighting factor for voltage offset Weighting factor for voltage stability margin All three weighting coefficients mentioned above are positive numbers and satisfy the following condition: This reflects the dominant role of economic objectives in optimization, while also taking into account voltage quality and system stability.

[0139] S14. Using the weighting coefficient method, divide each objective function term by the corresponding sub-objective benchmark value, and multiply the ratio result by the corresponding sub-objective weighting coefficient to obtain the weighted sub-objective term corresponding to each sub-objective to be processed.

[0140] In this embodiment of the invention, a weighting coefficient method is used to normalize and weight each sub-objective. Specifically, the comprehensive economic cost objective function term is divided by its corresponding benchmark value to obtain the dimensionless ratio of the comprehensive economic cost; the voltage offset objective function term is divided by its corresponding benchmark value to obtain the dimensionless ratio of the voltage offset; and so on. Dividing the exponential objective function term by its corresponding benchmark value yields the dimensionless ratio of the voltage stability margin. Then, multiplying these three dimensionless ratios by their respective weighting coefficients yields the weighted sub-objective terms for each sub-objective to be processed.

[0141] S15. Sum the weighted sub-objectives to construct a comprehensive objective function. The comprehensive objective function is the objective function of the single-objective optimization problem after the transformation of the multi-objective reactive power optimization model of the distribution network.

[0142] In this embodiment of the invention, the three weighted sub-objectives obtained in S14 are summed to construct a comprehensive objective function, the expression of which is:

[0143] ;

[0144] In the formula, This is the value of the comprehensive objective function.

[0145] The aforementioned comprehensive objective function is the objective function of the single-objective optimization problem transformed from the original multi-objective reactive power optimization model of the distribution network. This function unifies three sub-objectives with different dimensions and priorities into a single scalar evaluation index, allowing the subsequent hybrid algorithm to simply minimize the comprehensive objective function during iterative optimization to balance the multi-dimensional optimization requirements of economy, security, and power supply quality. The smaller the value of the comprehensive objective function, the better the overall performance of the corresponding reactive power control scheme.

[0146] Sub-objectives to be processed: These are the three optimization objectives in the multi-objective reactive power optimization model for the distribution network: comprehensive economic cost, voltage deviation, and the L-index corresponding to voltage stability margin. Decision variable vector: This is a multi-dimensional vector composed of the decision variables of all controllable reactive power regulation devices in the distribution network, including the reactive power output of each distributed source, the reactive power output of each static var compensator, and the number of switching groups of each parallel capacitor. Objective function term: This is the mathematical expression of each sub-objective to be processed with respect to the decision variable vector. Sub-objective benchmark values: These are the comprehensive economic cost, voltage deviation, and L-index values ​​of the target distribution network system before optimization, calculated under the initial operating state without any reactive power optimization. These benchmark values ​​remain constant throughout the iterative optimization process. Analytic Hierarchy Process (AHP): The AHP is a multi-objective decision-making method that determines the weight coefficients of each sub-objective by constructing a judgment matrix and calculating a weight vector. In this scheme, the weights are determined according to the priority order: comprehensive economic cost takes precedence over voltage deviation, and voltage deviation takes precedence over voltage stability margin. Sub-objective priority order: The sub-objective priority order refers to the ranking of the importance of each sub-objective according to the actual engineering needs of distribution network operation optimization. Specifically, comprehensive economic cost has a higher priority than voltage deviation, and voltage deviation has a higher priority than voltage stability margin. Sub-objective weight coefficients: Sub-objective weight coefficients refer to the weight values ​​of each sub-objective determined using the analytic hierarchy process (AHP). The weight coefficient for comprehensive economic cost is 0.7, for voltage deviation it is 0.2, and for voltage stability margin it is 0.1, with a sum of 1. Weighting coefficient method: The weighting coefficient method involves dividing each objective function term by its corresponding sub-objective benchmark value to achieve dimensionless processing, multiplying the ratio by the corresponding sub-objective weight coefficient, and finally summing all weighted results to construct the comprehensive objective function. Weighted sub-objective term: A weighted sub-objective term is the product term obtained by dividing each objective function term by its corresponding sub-objective benchmark value to obtain a dimensionless ratio, and then multiplying it by the corresponding sub-objective weight coefficient. Single-objective optimization problem: A single-objective optimization problem refers to transforming the multiple optimization objectives in the original multi-objective reactive power optimization model of the distribution network into an optimization problem with a comprehensive objective function as the sole objective through multi-objective aggregation. The algorithm only needs to minimize the comprehensive objective function to take into account the multi-dimensional optimization requirements.

[0147] Step 203: Generate a chaotic sequence using Tent chaotic mapping.

[0148] In this embodiment of the invention, the key parameters of the hybrid algorithm are first set, including the population size. Maximum number of iterations Vulture search selection probability And the contraction and expansion coefficients of quantum behavior particle swarm optimization Subsequently, the Tent chaotic mapping is used to generate chaotic sequences. The Tent mapping has the advantages of a wide traversal range and uniform sequence generation, effectively improving the uniformity and ergodicity of the initial population distribution in the solution space. The iterative formula for the Tent chaotic mapping is:

[0149] ;

[0150] In the formula, For the first The chaotic number generated in the next iteration For the first The chaos number is generated in the next iteration. Using the above iterative formula, the chaos number is generated. There are n chaotic numbers, among which Let be the total dimension of the decision variables. Each chaos number takes values ​​in the range [0, 1] and is uniformly distributed throughout the chaotic sequence.

[0151] Step 204: Initialize the hybrid algorithm population using chaotic sequences. Each individual in the hybrid algorithm population is a decision variable vector, which includes the reactive power output of each distributed power source, the reactive power output of each static var compensator, and the number of switching groups of each parallel capacitor.

[0152] In this embodiment of the invention, the chaotic sequence generated in step 203 is used to initialize each dimension of the variable of each individual in the hybrid algorithm population. Specifically, for the first individual in the population... Individual, the first dimensional decision variables, their initial positions Calculate using the following formula:

[0153] ;

[0154] In the formula, For the first The individual in the first The initial position of the dimension. and The first Lower and upper bounds of decision variables. For the first generation generated by the Tent chaotic map The individual in the first The chaotic number of dimensions.

[0155] Each individual in the population represents a complete vector of decision variables. The vector consists of three parts: the first part is the reactive power output of each distributed power source (photovoltaic, wind power). Its upper and lower bounds are respectively The second part is the reactive power output of each static var compensator. Its upper and lower bounds are respectively The third part is the number of switching groups for each parallel capacitor. Its upper and lower bounds are respectively The upper and lower bounds for each dimension are derived from the inequality constraints of the multi-objective reactive power optimization model of the distribution network established in step 201. This is achieved by analyzing all population data... Each individual performs the above initialization operation one by one to complete the initialization of the hybrid algorithm population, thus obtaining the hybrid algorithm population. This initialization method ensures the diversity and traversal of the algorithm's search starting point, providing a high-quality initial population for subsequent iterative optimization.

[0156] Step 205: Using the comprehensive objective function as the fitness function, evaluate the individual fitness of the hybrid algorithm population, and determine the set of historical best positions and the global best position of each individual based on the evaluation results.

[0157] In this embodiment of the invention, the comprehensive objective function constructed in step 202 is used as the fitness function to evaluate the hybrid algorithm population obtained in step 204. Fitness is assessed for each individual in the population. Specifically, for the first individual in the population... individual The initial fitness value of the individual is calculated by substituting its decision variable vector into the comprehensive objective function. The smaller the fitness value, the better the overall performance of the reactive power control scheme corresponding to that individual.

[0158] After calculating the fitness of all individuals, the current position of each individual is set as its historical best position, i.e. The individual historical best positions of all individuals together constitute the set of individual historical best positions. Then, select the individual with the smallest fitness value from all individuals and set its position as the global optimum. ,Right now:

[0159] ;

[0160] In the formula, The global optimal position is the position of the individual with the smallest fitness value in the hybrid algorithm population. The decision variable vector corresponding to this global optimal position is the initial global optimal solution. This completes the initialization of the set of individual historical optimal positions and the global optimal position, providing initial guiding information for subsequent iterative optimization.

[0161] Tent Chaotic Mapping: Tent chaotic mapping is a chaotic mapping characterized by its wide traversal range and uniform sequence generation. It uses a piecewise linear iterative method to generate chaotic numbers, which are used to generate uniformly distributed chaotic sequences to initialize the population. Chaotic Sequence: A chaotic sequence refers to the sequence of chaotic numbers generated iteratively through Tent chaotic mapping. Each chaotic number takes values ​​between 0 and 1, and is used to map individual positions to the actual value range of decision variables. Individual Historical Best Position Set: The individual historical best position set refers to the set of positions with the lowest fitness found by each individual in the hybrid algorithm population since the start of iteration. These historical best positions are updated during iteration as individuals discover better positions. Global Best Position: The global best position is the individual position with the lowest fitness among all historical best positions of all individuals in the entire hybrid algorithm population.

[0162] Step 206: Based on the individual historical best position set and the global best position, use the hybrid algorithm of vulture search and quantum behavior particle swarm optimization to iteratively optimize the hybrid algorithm population until the maximum number of iterations is reached, and output the global best solution.

[0163] Furthermore, step 206 may include the following sub-steps:

[0164] S21. Use the vulture search strategy to conduct a global exploration of the hybrid algorithm population to obtain a globally updated population.

[0165] Furthermore, the bald eagle search strategy includes region selection operation and spiral search operation. For each individual in the hybrid algorithm population, the region selection operation and spiral search operation are performed sequentially to obtain a globally updated population.

[0166] The region selection operation is specifically to randomly select a search region for each individual in the hybrid algorithm population using the vulture search selection probability, and update the population individual position based on the current global optimal position and random individual perturbation.

[0167] The spiral search operation involves performing a spiral descent search within the selected search area for each individual in the population after the region selection operation, using the population average position and the previous position of the individual's current position as inputs, to update the individual's position.

[0168] In this embodiment of the invention, the bald eagle search strategy includes a region selection operation and a spiral search operation, which are performed sequentially on each individual in the hybrid algorithm population. Specifically:

[0169] Region selection operation: for each individual Based on the probability of selection by vulture search Randomly select a search region, based on the current global best position. The individual position is updated by random individual perturbation, and the position update formula is:

[0170] ;

[0171] In the formula, After the region selection operation The new position of each individual This is the current globally optimal position. To control the parameters of the search step size, A random number in the range [0, 1] This represents the position of an individual randomly selected from the current population. This operation encourages individuals to explore towards the global optimum while introducing random perturbations to expand the search range.

[0172] Spiral search operation: For each individual updated by the region selection operation, a spiral descent search is performed within the selected search region, incorporating the population average position and the individual's previous position. The position update formula is as follows:

[0173] ;

[0174] In the formula, For the first spiral search operation The new position of each individual This represents the current position of the individual. For the first The position of each individual in the previous iteration step This represents the average position of the current population. The value is a random number within the range [0, 1]. This strategy enhances the population's ability to explore local areas near potential optimal regions.

[0175] After all individuals complete the above region selection and spiral search operations in sequence, the updated individual positions form a globally updated population.

[0176] S22. Calculate the population historical average optimal position and the random attraction point of each individual corresponding to the global update population.

[0177] In this embodiment of the invention, the globally updated population obtained after global exploration via the S21 vulture search is used as the input for the quantum behavior particle swarm optimization stage. First, the historical average optimal position of the population is calculated using the following formula:

[0178] ;

[0179] In the formula, This represents the historical average optimal position of the population. For the first The individual's historical best position.

[0180] Then, the random attraction point for each individual is calculated using the following formula:

[0181] ;

[0182] In the formula, For the first The random attraction point of each individual on the th The components of the dimension, For the first The individual's historical best position is in the th The components of the dimension, The globally optimal position is at the th The components of the dimension, is a random number uniformly distributed within [0, 1].

[0183] S23. Substitute the historical average optimal position of the population and the random attraction point of each individual into the quantum motion equation to update the position of each individual in the global updated population, thus obtaining the locally updated population.

[0184] In this embodiment of the invention, the population historical average optimal position calculated in S22 is used. And the random attraction points of each individual Substituting into the quantum motion equation, we update the position of each individual in the global update population. The quantum motion equation is:

[0185] ;

[0186] In the formula, For the first The individual in the first During the nth iteration The position of the dimension For the first Each individual at the current iteration step The position of the dimension For the first The random attraction point of each individual on the th The components of the dimension, The population's historical average best position is at the 1st The components of the dimension, The coefficient of contraction and expansion. for The random numbers are uniformly distributed within the population, and the signs "±" are selected with equal probability. After all individuals complete the above quantum motion equation update, a locally updated population is obtained.

[0187] S24. Using the comprehensive objective function as the fitness function, calculate the fitness value of each individual in the local update population, and update the set of historical best positions and the global best position of the individual according to the fitness value. The decision variable vector corresponding to the global best position is synchronously updated to the global best solution.

[0188] In this embodiment of the invention, the fitness function is calculated using the comprehensive objective function as the fitness function, and the fitness value of each individual in the locally updated population obtained in S23 is calculated. For the first... Each individual, with its current fitness value The fitness value corresponding to its individual historical best position Comparison: If Then, the individual's historical best position is updated to the current position, i.e. Simultaneously, the position of the individual with the lowest fitness value in the current population is compared with the globally optimal position. Compare the corresponding fitness values: if the individual's fitness value is less than... Then the global optimal position will be updated to the individual's position, i.e. At the same time, the decision variable vector corresponding to the global optimal position is updated to the global optimal solution.

[0189] S25. Determine whether the maximum number of iterations has been reached.

[0190] In this embodiment of the invention, it is determined whether the current iteration count has reached the preset maximum iteration count.

[0191] S26. If not achieved, proceed to the step of using the vulture search strategy to perform a global exploration of the hybrid algorithm population and obtain a globally updated population.

[0192] In this embodiment of the invention, if the current iteration number has not reached the maximum iteration number, the process returns to S21 and enters the next iteration, continuing to perform hierarchical collaborative optimization of global exploration by vulture search and local development of quantum behavior particle swarm optimization.

[0193] S27. If the target is reached, the iteration is terminated and the current global optimal solution is output. The optimal reactive power control scheme includes the reactive power output of each distributed power source, the output of the static var compensator, and the number of switching groups of each parallel capacitor.

[0194] In this embodiment of the invention, if the current iteration count has reached the preset maximum iteration count, the iterative optimization process is terminated. The decision variable vector corresponding to the current global optimal position is output as the global optimal solution. This global optimal solution includes the reactive power output of each distributed power source, the reactive power output of each static var compensator, and the number of switching groups of each parallel capacitor, which is the optimal reactive power control scheme.

[0195] Vulture Search Strategy: The vulture search strategy is a global exploration strategy that simulates the behavior of vultures searching for prey in a vast space. It includes two sub-stages: region selection and spiral search. Individual positions are updated by moving towards the global optimum and spiraling downwards. Global Update Population: The global update population refers to the population formed by the updated individual positions of all individuals in the hybrid algorithm population after they have successively completed the region selection and spiral search operations of the vulture search strategy. Population Historical Average Optimal Position: The population historical average optimal position is the arithmetic mean of the historical optimal positions of all individuals in the hybrid algorithm population. It is used to calculate the quantum motion step size of particles in quantum behavior particle swarm optimization. Random Attraction Point: The random attraction point is the local attraction point of each particle in quantum behavior particle swarm optimization. This attraction point is located at a random position between the particle's historical optimal position and the global optimum, obtained by weighting the two positions with random weights. Quantum Equation of Motion: The quantum equation of motion refers to the equation used to update particle positions in quantum behavior particle swarm optimization. Centered on a random attraction point, it constructs a search step size based on the absolute value of the difference between the population's historical average best position and the current position. New positions are generated using a shrinking / expanding coefficient that decreases with the number of iterations and random numbers. Locally Updated Population: A locally updated population refers to the population obtained by updating the position of each individual in the globally updated population by substituting it into the quantum equation of motion.

[0196] Region Selection Operation: The region selection operation is the first sub-stage of the vulture search strategy. Individuals randomly select a search region with the vulture search selection probability, and update their positions based on the current globally optimal position and random individual perturbation. Spiral Search Operation: The spiral search operation is the second sub-stage of the vulture search strategy. Individuals perform a spiral descent search within the search region selected in the region selection operation, updating their positions by introducing the population average position and the difference between their current and previous positions. Vulture Search Selection Probability: The vulture search selection probability is a key parameter in the vulture search strategy, used to control the probability of an individual performing the region selection operation. This probability is preset during initialization and remains constant throughout the iteration. Random Individual Perturbation: Random individual perturbation refers to randomly selecting an individual position from the current population in the vulture search region selection operation and introducing it into the position update formula to expand the search range and maintain population diversity. Population Average Position: The population average position is the arithmetic mean of the positions of all individuals in the current population, used in the vulture search spiral search operation to guide individuals towards the population center. The position of an individual at the previous moment before its current position refers to the position of the individual in the previous iteration step. Together with the current position, it forms the position difference term, which is used for inertial guidance in the spiral search operation of the vulture search.

[0197] Step 207: Use the global optimal solution as the optimal reactive power control scheme and send it to the target distribution network for execution.

[0198] In this embodiment of the invention, after the iterative optimization terminates, the global optimal solution output in step 206 is decoded, and its dimensional values ​​are restored to specific control commands for the actual physical variables. Specifically, the global optimal solution is a set of decision variable vectors, including the reactive power output setpoints of each distributed power source (photovoltaic, wind power), the reactive power output setpoints of each static var compensator, and the switching group setpoints of each parallel capacitor. The above control commands are sent to each field execution terminal through the distribution network energy management system, including distributed power source inverters, static var compensator controllers, and parallel capacitor switching devices, to complete the closed-loop control of the reactive power and voltage of the distribution network. After execution, the target distribution network operates in an optimized operating state with the lowest overall economic cost, the smallest voltage deviation, and the largest voltage stability margin, realizing the economic, safe, and high-quality coordinated control of reactive power resources in the active distribution network. Thus, the complete process of the distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm in Embodiment 1 of the present invention has been completed. This embodiment combines the global exploration capability of the Bald Eagle Search algorithm with the local development capability of the Quantum Behavior Particle Swarm Optimization algorithm, along with the Tent chaotic mapping initialization and multi-objective aggregation strategy, to stably obtain high-quality global optimal solutions. In practical power distribution networks, it effectively reduces overall economic costs, improves voltage quality, and enhances system stability, demonstrating significant engineering practical value.

[0199] This invention has the following advantages:

[0200] 1. This invention constructs a multi-objective reactive power optimization model with the core objectives of minimizing comprehensive economic cost, minimizing voltage deviation, and maximizing voltage stability margin. It integrates network loss cost and generation costs of various power sources into a unified comprehensive economic cost index, better aligning with the economic needs of actual distribution network operation. By employing the analytic hierarchy process (AHP) and weighted coefficient method, the multi-objective optimization problem is scientifically transformed into a single-objective optimization problem. Through reasonable weight setting, the primary objective of economic operation is highlighted while also considering voltage quality and system stability, achieving multi-dimensional synergistic optimization of distribution network economy, security, and high-quality power supply.

[0201] 2. This invention proposes a hierarchical collaborative optimization framework combining vulture search and quantum behavior particle swarm optimization. The vulture search phase employs extensive global exploration through region selection and spiral search operations to avoid getting trapped in local optima; the quantum behavior particle swarm optimization phase utilizes a quantum potential well model for refined development within potential optimal regions, accelerating convergence. Through population relay and information interaction, the two approaches effectively balance search breadth and convergence accuracy, significantly improving the solution efficiency and robustness of complex high-dimensional optimization problems.

[0202] 3. This invention employs Tent chaotic mapping to initialize the initial population, effectively improving the ergodicity and diversity of the solution space and laying a good foundation for global optimization. Secondly, in the quantum behavior particle swarm optimization stage, a non-uniform mutation mechanism with adaptive decay over iterations is introduced. This enhances global exploration capabilities in the early stages of iteration and assists in local refinement in the later stages, thereby significantly suppressing premature convergence and improving the algorithm's ability to escape local extrema. Simultaneously, the penalty function method transforms complex inequality constraints such as node voltage amplitude upper and lower limits, distributed power source reactive power output upper and lower limits, parallel capacitor switching group number upper and lower limits, static var compensator reactive power output upper and lower limits, photovoltaic power source active power output upper and lower limits, wind power source active power output upper and lower limits, and traditional power source active power output upper and lower limits into penalty terms and incorporates them into the comprehensive objective function. This guides the search process towards the feasible region, ensuring the engineering practicality and stability of the solution.

[0203] 4. The multi-objective reactive power optimization model for distribution networks constructed in this invention explicitly considers the operational constraints of various reactive power regulation devices such as distributed generation sources, parallel capacitors, and static var compensators, effectively adapting to modern active distribution network scenarios with a high proportion of distributed generation sources. This model provides an integrated optimization scheme for the coordinated control of multiple types of reactive power resources, supports the overall optimization of the output of various devices, and enhances the applicability and scalability of the method in actual complex distribution network environments.

[0204] Application example:

[0205] To verify the effectiveness and superiority of the distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm proposed in this invention, this application example uses an improved IEEE 33-bus system for simulation testing and analysis, and combines... Figures 3-7 The optimization results are visualized and compared for evaluation.

[0206] This application example uses an improved IEEE 33-bus distribution system as the test system, and its topology is as follows: Figure 3 As shown. The system contains 33 bus nodes, with a reference voltage U. B =12.66kV, reference power S B =10MV·A. The system is equipped with various reactive power regulation devices: 800kvar static var compensators are connected to nodes 15 and 30 respectively; capacitor banks 1 and 2, each with a capacity of 10kvar, are connected to nodes 9 and 32 respectively, each containing 20 switchable capacitor banks with a maximum switching frequency of 10 times; photovoltaic (PV) power is connected to nodes 21 and 25, each with a maximum active power output of 500kW; wind power (WT) is connected to nodes 18 and 33, each with a maximum active power output of 600kW. In addition, a conventional backup power supply is connected to node 1, with a maximum active power capacity of 800kW.

[0207] The algorithm parameters are set as follows: population size N=30, maximum number of iterations T. max =100, the probability of vulture search selection q bes =0.5, the contraction-expansion coefficient β of quantum behavior particle swarm optimization decreases linearly from 1.0 to 0.5. In the comprehensive objective function, the weighting coefficients of comprehensive economic cost, voltage deviation, and voltage stability margin are set to λ1=0.7, λ2=0.2, and λ3=0.1, respectively. Wind power cost coefficient a WT =0.25 yuan / (MW·h), b WT =0.04 yuan / (MW) 2 ·h); Unit power generation cost ρ of traditional power sources conv =0.8 yuan / (MW·h); Electricity purchase and sale price ρ elec =0.6 yuan / (MW·h); calculation period τ=24τ hours.

[0208] To comprehensively evaluate the performance of the method of this invention, reactive power optimization simulations were performed on the above test system using the Particle Swarm Optimization (PSO) method, the Bald Eagle Search (BES) method, the Quantum Behavior Particle Swarm Optimization (QPSO) method, and the BES-QPSO hybrid algorithm proposed in this invention. The optimization effects of each algorithm were then compared.

[0209] Analysis of comprehensive economic cost optimization results:

[0210] The overall economic costs of each optimized algorithm are shown in the table below:

[0211]

[0212] Therefore, the overall economic cost of the system before optimization was 12864.0 yuan. After optimization with the PSO algorithm, it decreased to 8260.8 yuan; after optimization with the BES algorithm, it decreased to 8025.6 yuan; after optimization with the QPSO algorithm, it decreased to 7814.4 yuan; and after optimization with the BES-QPSO algorithm of this invention, it decreased to 6912.0 yuan. The above results show that the BES-QPSO hybrid algorithm proposed in this invention has the most significant effect in reducing the overall economic cost, reducing it by 46.27% compared to before optimization. It also shows significant improvement compared to the PSO, BES, and QPSO algorithms, indicating that the method of this invention can more effectively search for more economical reactive power control schemes through hierarchical collaborative optimization.

[0213] Analysis of network loss optimization results:

[0214] Network loss after optimization of each algorithm at different time periods, such as Figure 4 As shown in the figure, the horizontal axis represents time (0-24 hours), and the vertical axis represents the active power loss value (unit: MW). The daily variation curves of network loss before optimization and after optimization using four algorithms: PSO, BES, QPSO, and BES-QPSO are presented. It can be seen from the figure that throughout the 24-hour period, the network loss value of the BES-QPSO algorithm is basically the same as that of the PSO and QPSO algorithms, and both are lower than that of the BES algorithm. Taking the midday peak load period (12:00) as an example, the network loss before optimization was 0.120MW, which decreased to 0.050MW after optimization using the PSO algorithm, 0.055MW after optimization using the BES algorithm, 0.050MW after optimization using the QPSO algorithm, and also decreased to 0.050MW after optimization using the BES-QPSO algorithm. Taking the evening peak period (20:00) as an example, the network loss before optimization was 0.190MW. After optimization with the PSO algorithm, it was reduced to 0.090MW; after optimization with the BES algorithm, it was reduced to 0.095MW; after optimization with the QPSO algorithm, it was reduced to 0.085MW; and after optimization with the BES-QPSO algorithm, it was also reduced to 0.085MW. The loss reduction effect of BES-QPSO during this period was better than PSO and BES, and on par with QPSO. Considering all time periods throughout the day, the method of this invention can stably and effectively reduce network loss under different operating scenarios, verifying the effective loss reduction capability of the BES-QPSO hybrid algorithm.

[0215] Analysis of voltage offset optimization results:

[0216] The node voltage offset after optimization by each algorithm is as follows: Figure 5 As shown in the figure, the horizontal axis represents time (0~24 hours), and the vertical axis represents the voltage offset at per-unit values. The figure presents the daily variation curves of voltage offset before optimization and after optimization using four different algorithms. Figure 5 It can be seen that the daily voltage offset curves of the PSO, BES, and QPSO algorithms completely overlap, while the voltage offset optimized by the BES-QPSO algorithm is significantly lower than that of the three comparative algorithms in all time periods. Regarding the magnitude of voltage offset optimization, statistical calculations show that the PSO algorithm reduced voltage offset by 45.15% after optimization, the BES algorithm by 42.84%, the QPSO algorithm by 44.79%, and the BES-QPSO algorithm of this invention by 54.99%. The above comparison demonstrates that the method of this invention has the best optimization effect in improving voltage quality, verifying the effectiveness and superiority of the BES-QPSO hybrid algorithm in handling voltage safety constraints.

[0217] Analysis of voltage stability optimization results:

[0218] The L-exponential optimization results of each algorithm at different time periods are as follows: Figure 6As shown in the figure, the L-index of BES-QPSO is lower than that of the three comparison algorithms, PSO, BES, and QPSO, throughout all time periods of the day, with a significant advantage. Especially during the high-load period from 8:00 to 20:00, the L-index of BES-QPSO is about 0.010-0.015 lower than that of PSO, and about 0.010-0.020 lower than that of BES and QPSO (both with identical values), further verifying the superiority of the method of this invention in improving voltage stability.

[0219] Algorithm convergence performance comparison and analysis:

[0220] The convergence curves of the fitness functions of each algorithm are as follows: Figure 7 As shown in the figure, the horizontal axis represents the number of iterations (0-100), and the vertical axis represents the fitness function value. The figure presents the fitness values ​​of the BES, QPSO, and BES-QPSO algorithms as a function of the number of iterations. It can be seen from the figure that the BES algorithm converges relatively quickly in the early stages of iteration, with the fitness value dropping to around 0.57 after about 20 iterations. However, due to its insufficient local optimization capability, the convergence curve becomes relatively flat in the later stages of iteration (after about 20 iterations), and the fitness value eventually stabilizes at about 0.565, falling into a local optimum. The QPSO algorithm converges relatively slowly, with the fitness value decreasing gradually in the early stages of iteration, only gradually approaching convergence after about 50 iterations, and the final fitness value is slightly lower than that of the BES algorithm. In contrast, the proposed BES-QPSO hybrid algorithm exhibits excellent search performance in the early stages of iteration. From the beginning of iteration to about 30 iterations, the fitness value drops rapidly, and then continues to optimize steadily until it converges at about 70 iterations, with the final fitness value stabilizing at about 0.460. Throughout the entire iteration process, the convergence curve of the BES-QPSO algorithm remained below that of the BES and QPSO algorithms, and its final fitness value was significantly lower than that of BES and QPSO. This fully verifies that the method of this invention achieves an effective balance between global exploration and local development, and has better convergence accuracy and optimization ability.

[0221] In summary, this application example comprehensively evaluates the improved IEEE 33-bus system from multiple dimensions, including overall economic cost, network loss, voltage deviation, voltage stability margin, and convergence performance, through simulation testing. The results show that the reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm proposed in this invention outperforms the PSO, BES, and QPSO algorithms in reducing overall economic cost, decreasing network loss, improving voltage quality, and enhancing system stability. This verifies the effectiveness and superiority of the proposed method in handling multi-objective reactive power optimization problems in active distribution networks, and it can better meet the economic, safe, and high-quality operation requirements of distribution networks with a high proportion of distributed energy resources.

[0222] Please see Figure 8, Figure 8 This is a structural block diagram of a power distribution network reactive power optimization system based on the BES-QPSO hybrid algorithm, provided in Embodiment 3 of the present invention.

[0223] This invention provides a reactive power optimization system for distribution networks based on the BES-QPSO hybrid algorithm, comprising:

[0224] Model building module 801 is used to establish a multi-objective reactive power optimization model for the distribution network with the optimization objectives of minimizing comprehensive economic cost, minimizing voltage deviation and maximizing voltage stability margin.

[0225] The comprehensive objective function construction module 802 is used to perform multi-objective aggregation on the multi-objective reactive power optimization model of the distribution network and construct a comprehensive objective function.

[0226] The hybrid algorithm iterative optimization module 803 is used to initialize the hybrid algorithm population, use the comprehensive objective function as the fitness function, and use the hybrid algorithm of vulture search and quantum behavior particle swarm optimization to iteratively optimize the hybrid algorithm population and output the global optimal solution.

[0227] The control command issuing module 804 is used to take the global optimal solution as the optimal reactive power control scheme and issue it to the target distribution network for execution.

[0228] Since the above is a system corresponding to a distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm, its implementation principle is the same as that of a distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm. For the sake of convenience and brevity, those skilled in the art can clearly understand that the specific working process of the system and modules described above can be referred to the corresponding process in the aforementioned method embodiments, and will not be repeated here.

[0229] Please see Figure 9 , Figure 9 This is a structural block diagram of an electronic device provided in Embodiment 4 of the present invention.

[0230] An electronic device according to an embodiment of the present invention includes: a memory 901 and a processor 902. The memory 901 stores a computer program. When the computer program is executed by the processor 902, the processor 902 executes the power distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm as described in the above embodiment.

[0231] Memory 901 may be an electronic memory such as flash memory, EEPROM (Electrically Erasable Programmable Read-Only Memory), EPROM, hard disk, or ROM. Memory 901 has storage space 903 for program code 913 for performing any of the method steps described above. For example, storage space 903 for program code may include various program codes 913 for implementing the various steps in the methods described above. These program codes may be read from or written to one or more computer program products. These computer program products include program code carriers such as hard disks, CDs, memory cards, or floppy disks. The program code may be compressed, for example, in a suitable form. When run by a computing processing device, this code causes the computing processing device to perform the various steps in the methods described above. These program codes may be read from or written to one or more computer program products. These computer program products include program code carriers such as hard disks, CDs, memory cards, or floppy disks. The program code may be compressed, for example, in a suitable form. When this code is run by a computing device, it causes the computing device to perform the various steps in the distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm described above.

[0232] Embodiment 5 of the present invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm as described in the above embodiments.

[0233] Embodiment 6 of the present invention also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, wherein when the program instructions are executed by a computer, the computer executes the power distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm as described in the above embodiments.

[0234] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0235] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between apparatuses or units, and may be electrical, mechanical, or other forms.

[0236] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0237] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0238] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0239] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm, characterized in that, include: A multi-objective reactive power optimization model for distribution networks is established with the optimization objectives of minimizing overall economic cost, minimizing voltage deviation, and maximizing voltage stability margin. The multi-objective reactive power optimization model of the power distribution network is aggregated to construct a comprehensive objective function; Initialize the hybrid algorithm population, use the comprehensive objective function as the fitness function, and iteratively optimize the hybrid algorithm population using a hybrid algorithm of vulture search and quantum behavior particle swarm optimization to output the global optimal solution; The global optimal solution is used as the optimal reactive power control scheme and sent to the target distribution network for execution.

2. The reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm according to claim 1, characterized in that, The process of performing multi-objective aggregation on the multi-objective reactive power optimization model of the distribution network to construct a comprehensive objective function includes: In the multi-objective reactive power optimization model of the power distribution network, multiple optimization objectives are taken as sub-objectives to be processed, and each sub-objective to be processed is the objective function term of the decision variable vector. Obtain the sub-target baseline value corresponding to each of the sub-targets to be processed; The analytic hierarchy process (AHP) is used to determine the sub-target weight coefficients corresponding to each sub-target to be processed according to the preset sub-target priority order. The weighted coefficient method is used to divide each objective function term by the corresponding sub-objective benchmark value, and then multiply the ratio result by the corresponding sub-objective weight coefficient to obtain the weighted sub-objective term corresponding to each sub-objective to be processed; The weighted sub-objectives are summed to construct a comprehensive objective function, which is the objective function of the single-objective optimization problem after the transformation of the multi-objective reactive power optimization model of the distribution network.

3. The reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm according to claim 1, characterized in that, The initialization of the hybrid algorithm population, using the comprehensive objective function as the fitness function, iteratively optimizes the hybrid algorithm population using a hybrid algorithm of vulture search and quantum behavior particle swarm optimization, outputting the global optimal solution, including: Chaotic sequences are generated using the Tent chaotic map; The chaotic sequence is used to initialize the hybrid algorithm population. Each individual in the hybrid algorithm population is a decision variable vector. The decision variable vector includes the reactive power output of each distributed power source, the reactive power output of each static var compensator, and the number of switching groups of each parallel capacitor. Using the comprehensive objective function as the fitness function, the individual fitness of the hybrid algorithm population is evaluated, and the set of historical best positions and global best positions of individuals are determined based on the evaluation results. Based on the set of the individual's historical best positions and the global best position, the hybrid algorithm of vulture search and quantum behavior particle swarm optimization is used to iteratively optimize the hybrid algorithm population until the maximum number of iterations is reached, and the global best solution is output.

4. The reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm according to claim 3, characterized in that, The process involves iteratively optimizing the hybrid algorithm population based on the individual's historical optimal position set and the global optimal position using a hybrid algorithm combining eagle search and quantum behavior particle swarm optimization until the maximum number of iterations is reached, outputting the global optimal solution, including: The hybrid algorithm population is globally explored using a vulture search strategy to obtain a globally updated population. Calculate the historical average optimal position of the population and the random attraction point of each individual corresponding to the global update population; Substituting the historical average optimal position of the population and the random attraction point of each individual into the quantum motion equation, the position of each individual in the globally updated population is updated to obtain the locally updated population. Using the comprehensive objective function as the fitness function, the fitness value of each individual in the local update population is calculated, and the set of historical best positions and the global best position of the individual are updated according to the fitness value. The decision variable vector corresponding to the global best position is synchronously updated to the global best solution. Determine if the maximum number of iterations has been reached; If the target is not reached, proceed to the step of using the vulture search strategy to perform a global exploration of the hybrid algorithm population to obtain a globally updated population. If the optimal solution is reached, the iteration is terminated and the current global optimal solution is output. The optimal reactive power control scheme includes the reactive power output of each distributed power source, the output of the static var compensator, and the number of switching groups of each parallel capacitor.

5. The reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm according to claim 4, characterized in that, The vulture search strategy includes region selection and spiral search operations. The process of using the vulture search strategy to globally explore the hybrid algorithm population and obtain a globally updated population includes: For each individual in the hybrid algorithm population, the region selection operation and the spiral search operation are performed sequentially to obtain a globally updated population; The region selection operation specifically involves randomly selecting a search region for each individual in the hybrid algorithm population using the vulture search selection probability, and updating the population individual position based on the current global optimal position and random individual perturbation. The spiral search operation specifically involves performing a spiral descent search within the selected search area for each individual in the population after the region selection operation is updated. This search incorporates the population average position and the previous position of the individual's current position, thus updating the individual's position.

6. The reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm according to any one of claims 1-5, characterized in that, The model constraints of the multi-objective reactive power optimization model of the distribution network include node power balance equation constraints, node voltage amplitude upper and lower limit constraints, distributed power reactive power output upper and lower limit constraints, parallel capacitor switching group number upper and lower limit constraints, static var compensator reactive power output upper and lower limit constraints, photovoltaic traditional power active power output upper and lower limit constraints, wind power traditional power active power output upper and lower limit constraints, and traditional power active power output upper and lower limit constraints.

7. A reactive power optimization system for distribution networks based on the BES-QPSO hybrid algorithm, characterized in that, include: The model building module is used to establish a multi-objective reactive power optimization model for the distribution network with the optimization objectives of minimizing the overall economic cost, minimizing the voltage deviation, and maximizing the voltage stability margin. The comprehensive objective function construction module is used to aggregate multiple objectives in the multi-objective reactive power optimization model of the power distribution network and construct a comprehensive objective function. The hybrid algorithm iterative optimization module is used to initialize the hybrid algorithm population, use the comprehensive objective function as the fitness function, and use a hybrid algorithm of vulture search and quantum behavior particle swarm optimization to iteratively optimize the hybrid algorithm population and output the global optimal solution. The control command issuing module is used to take the global optimal solution as the optimal reactive power control scheme and issue it to the target distribution network for execution.

8. An electronic device, characterized in that, The device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform the steps of the power distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it implements the reactive power optimization method for distribution networks based on the BES-QPSO hybrid algorithm as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, wherein when the program instructions are executed by a computer, the computer performs the power distribution network reactive power optimization method based on the BES-QPSO hybrid algorithm as described in any one of claims 1-6.

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