Unbalanced distribution network multi-time scale reactive power optimization method based on improved golden jackal algorithm

Abstract

The application relates to an unbalanced distribution network multi-time scale reactive power optimization method based on an improved golden cat algorithm, wherein the golden cat optimization algorithm is improved first, low-difference sequence generation and chaotic mapping traversal are combined to strengthen population initialization, and the traversal characteristics of the group in space are ensured; through design of a hyperbolic tangent-power law mixed attenuation model, global exploration is maintained and local development is enhanced; a leadership dynamic weighting mechanism is proposed to enhance the guiding role of the optimal individual and avoid falling into local optimization; considering the three-phase voltage imbalance of the distribution network and the discrete characteristics of the regulating equipment, a day-ahead reactive power-voltage optimization model is established, and the improved golden cat optimization algorithm is used to solve the day-ahead optimization model; the equipment action scheme obtained through day-ahead optimization is used as the basis for intraday optimization, a three-phase unbalanced distribution network intraday reactive power-voltage optimization model considering continuous equipment is established, and the reactive power and voltage are adjusted; the improved golden cat optimization algorithm is used for solving, so that the second-stage optimization is completed.

Description

Technical Field

[0001] This invention belongs to the field of power grid control technology, and in particular to a multi-time-scale reactive power optimization method for unbalanced distribution networks based on an improved Golden Jackal algorithm. Background Technology

[0002] Against the backdrop of increasingly severe global climate change and energy security issues, the deep integration of photovoltaic (PV) power generation with distribution networks is profoundly transforming the operational characteristics and optimization requirements of these networks. The randomness and intermittency of PV grid connection lead to voltage exceedances and increased network losses. Furthermore, distributed PV systems are mostly connected as single-phase units in distribution networks, and their varying phase locations exacerbate the imbalance in three-phase distribution networks. These problems affect the safe and stable operation of distribution networks. Existing research has already implemented multi-timescale coordinated control based on the regulation characteristics of different equipment.

[0003] However, the complexity of three-phase unbalanced scenarios requires the optimization model to simultaneously consider voltage suppression and network loss minimization. Traditional single-phase modeling is difficult to adapt to such complex scenarios as three-phase unbalanced distribution networks.

[0004] In addition, the currently used intelligent algorithms have problems such as slow convergence speed and easy getting trapped in local optima, making it difficult to accurately and efficiently solve the reactive power optimization problem of the distribution network.

[0005] Therefore, it is necessary to establish a multi-time-scale reactive power optimization model for distribution networks that considers three-phase imbalance, and to use intelligent algorithms with good solution performance and short computation time to solve the optimization model. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and propose a multi-time-scale reactive power optimization method for unbalanced distribution networks based on an improved Golden Jackal algorithm. By comprehensively improving the basic Golden Jackal optimization algorithm and considering the three-phase imbalance of the photovoltaic distribution network, a day-ahead-intraday optimization model is established. While ensuring three-phase balance, it can effectively reduce voltage bias and power loss, thereby ensuring the economy and stability of the distribution network.

[0007] The technical problem solved by this invention is achieved through the following technical solution: A multi-time-scale reactive power optimization method for unbalanced distribution networks based on the improved Golden Cow algorithm includes the following steps: Step 1 considers three-phase voltage imbalance. Based on the equipment characteristics of the power capacitor CB and the on-load tap-changing transformer OLTC, a day-ahead reactive power-voltage optimization model and its constraints for a three-phase unbalanced distribution network with discrete equipment involved in regulation are established. Step 2 collects day-ahead source-load data, and solves the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with discrete equipment involved in regulation constructed in Step 1 based on the improved Golden Jack optimization algorithm, to obtain the hourly operation scheme of the power capacitor CB and the on-load tap-changing transformer OLTC. Step 3: Based on the constraints of the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with discrete equipment involved in regulation constructed in Step 1, and according to the equipment characteristics of the static var compensator (SVC) and photovoltaic inverter, establish the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment involved in regulation and its constraints. Step 4: Based on the action plan obtained in Step 2, solve the intraday reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment involved in regulation constructed in Step 3 using the improved Golden Jackal optimization algorithm, and obtain the hourly action plan of SVC and photovoltaic inverter in the intraday optimization model.

[0008] Furthermore, the objective function of the daytime reactive power-voltage optimization model for the three-phase unbalanced distribution network involving discrete equipment in step 1 aims to minimize the sum of node voltage offset cost, network loss cost, on-load tap changer (OLTC) operation cost, and power capacitor (CB) operation cost at all 24 time points throughout the day. The node voltage offset cost is obtained by multiplying the voltage offset economic coefficient by the sum of the phase voltage offsets of all nodes; the network loss cost is obtained by multiplying the network loss economic coefficient by the sum of the squares of the phase currents of all branches and the corresponding phase line resistances; and the node voltage offset is defined as the absolute value of the difference between the actual node voltage and the reference value.

[0009] Furthermore, the constraints of the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network in step 1, in which discrete devices participate in regulation, include power balance equations, voltage and current safety constraints, three-phase voltage imbalance constraints, and CB constraints.

[0010] Furthermore, the specific implementation method of the improved golden jackal optimization algorithm in step 2 is as follows: Step 2.0.1 combines low-difference sequence generation and chaotic mapping traversal to enhance and improve population initialization, ensuring the traversal characteristics of the population in space; The first initial population is generated using a low-discrepancy sequence based on prime numbers to ensure uniformity of high-dimensional projection; the second initial population is generated using a nonlinear chaotic parameter to improve the Logistic chaotic mapping and enhance ergodicity; the fitness values ​​of the initial populations generated by the two methods are compared, and individuals with better fitness are selected to form the final initial population. Step 2.0.2 By designing a hyperbolic tangent-power-law hybrid decay model, global exploration and local exploitation can be maintained; A basic decay framework based on the hyperbolic tangent function is established to maintain the escape energy at a high level in the early stage of iteration; a dynamic decay accelerator based on the power law function is created to ensure rapid convergence in the later stage of iteration; the basic decay framework and the dynamic decay accelerator are multiplied to construct the final escape energy. Step 2.0.3 proposes a dynamic weighted leadership mechanism to enhance the guiding role of the best individual and avoid getting trapped in local optima; Based on the fitness of male and female golden jackals and the fitness of the currently updated individual, the position weights of male and female golden jackals are calculated. The positions of male and female golden jackals are then weighted and combined using these weights, and a sign function correction term is introduced to obtain the updated solution. The leadership dynamic weighting mechanism quantifies the leader's contribution through fitness ratio weights, regulates the exploration intensity through dispersion feedback, and injects randomness through Lévy perturbation. This three-order collaborative approach enhances the algorithm's global convergence capability.

[0011] Furthermore, step 2 includes the following steps: Step 2.1: Input data and set parameters for the improved golden jackal optimization algorithm; The input data includes the photovoltaic output, load, branch impedance, reactive power compensation parameters and constraint parameters of the distribution network, and the setting parameters include the number of algorithm populations, the number of iterations and the initial escape energy. Step 2.2 Combines low-difference sequence generation and chaotic mapping traversal to enhance and improve population initialization; Step 2.3 Calculate the objective function value for each population; Step 2.4 Select the male and female golden jackals based on the objective function value; Step 2.5: Adjust the escape energy using a hyperbolic tangent-power-law hybrid decay model; Step 2.6 Update the position according to the leadership dynamic weighting mechanism to obtain the selected optimal solution. The optimal solution is the decision variable that minimizes the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network in which discrete equipment participates in regulation. Step 2.7 Determine if convergence has occurred. If the convergence condition is met, stop the calculation. The convergence condition refers to reaching the maximum number of iterations. If the convergence condition is not met, return to step 2.3. The optimal solution obtained in step 2.8 is the operation scheme of the power capacitor CB and the on-load tap-changing transformer OLTC from 0:00 to 23:00 on the next day.

[0012] Moreover, the objective function of the daily reactive power-voltage optimization model of the three-phase unbalanced distribution network in step 3, which involves continuous equipment regulation, aims to minimize the sum of node voltage offset cost and network loss cost at 96 times throughout the day; its constraints include power balance equation, voltage and current safety constraints, static var compensator (SVC) output power constraints, and photovoltaic inverter reactive power adjustable constraints.

[0013] Furthermore, step 4 includes the following steps: Step 4.1 Perform data input and parameter settings for the improved golden jackal optimization algorithm; The input data includes the photovoltaic output, load, branch impedance, reactive power compensation parameters and constraint parameters of the distribution network, and the setting parameters include the number of algorithm populations, the number of iterations and the initial escape energy. Step 4.2 Combines low-difference sequence generation and chaotic mapping traversal to enhance and improve population initialization; Step 4.3 Calculate the objective function value for each population; Step 4.4 Select the male and female golden jackals based on the objective function value; Step 4.5: Adjust the escape energy using a hyperbolic tangent-power-law hybrid decay model; Step 4.6 Update the position according to the leadership dynamic weighting mechanism to obtain the selected optimal solution. The optimal solution is the decision variable that minimizes the intraday reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment participation in regulation. Step 4.7 Determine if convergence has occurred. If the convergence condition is met, stop the calculation. The convergence condition refers to reaching the maximum number of iterations. If the convergence condition is not met, return to step 4.3. The optimal solution obtained in step 4.8 is the operation scheme of SCV and photovoltaic inverter every 15 minutes of the day.

[0014] The advantages and positive effects of this invention are: This invention first improves the Golden Jackal optimization algorithm by combining low-discrepancy sequence generation and chaotic mapping traversal enhancement to improve population initialization, ensuring the traversal characteristics of the population in space. It then designs a hyperbolic tangent-power-law hybrid decay model to maintain global exploration and enhance local development. A leadership dynamic weighting mechanism is proposed to enhance the guiding role of optimal individuals and avoid getting trapped in local optima. Considering the three-phase voltage imbalance of the distribution network and the discrete characteristics of regulating equipment, a day-ahead reactive power-voltage optimization model is established and solved using the improved Golden Jackal optimization algorithm. Using the equipment action scheme obtained from the day-ahead optimization as the basis for intraday optimization, an intraday reactive power-voltage optimization model for a three-phase unbalanced distribution network considering continuous equipment is established to regulate reactive power and voltage. The improved Golden Jackal optimization algorithm is then used to solve this model, thus completing the second stage of optimization. This invention comprehensively improves the basic Golden Jackal optimization algorithm, considering the three-phase imbalance of the photovoltaic distribution network, and establishes a day-ahead and intraday optimization model. While ensuring three-phase balance, it can effectively reduce voltage bias and power loss, thereby ensuring the economy and stability of the distribution network. Attached Figure Description

[0015] Figure 1This is a flowchart of the multi-time-scale reactive power optimization method for unbalanced distribution networks based on the improved Golden Jackal algorithm of this invention.

[0016] Figure 2 This is a schematic diagram of the improved golden jackal optimization algorithm of the present invention.

[0017] Figure 3 This is a schematic diagram of the power flow of a three-phase distribution network according to the present invention.

[0018] Figure 4 This is an embodiment of the IEEE 33 power distribution system of the present invention.

[0019] Figure 5 This is a diagram showing the three-phase load and photovoltaic characteristics of an embodiment of the present invention.

[0020] Figure 6 The above is an OLTC action diagram showing the optimization results of the embodiments of the present invention.

[0021] Figure 7 The diagram shows the optimized three-phase CB action results of the present invention.

[0022] Figure 8 The diagram shows the per-unit voltage values ​​of the nodes before and after optimization in this embodiment of the invention.

[0023] Figure 9 This is a comparison chart of network loss before and after optimization in an embodiment of the present invention.

[0024] Figure 10 This is a diagram showing the per-unit voltage values ​​of different nodes after optimization within a day according to an embodiment of the present invention.

[0025] Figure 11 This is a diagram of the optimized three-phase network loss within a day according to an embodiment of the present invention.

[0026] Figure 12 This is a diagram showing the maximum absolute value of the three-phase imbalance after optimization within a day in an embodiment of the present invention. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings.

[0028] A multi-time-scale reactive power optimization method for unbalanced distribution networks based on an improved Golden Jackal algorithm, such as... Figure 1 As shown, it includes the following steps: Step 1 considers three-phase voltage imbalance. Based on the equipment characteristics of the power capacitor CB and the on-load tap-changing transformer OLTC, a day-ahead reactive power-voltage optimization model and its constraints for a three-phase unbalanced distribution network with discrete equipment involved in regulation are established.

[0029] In the day-ahead reactive power-voltage optimization model for three-phase unbalanced distribution networks, considering network losses and voltage deviations, as well as the cost of discrete equipment operation, multiplying them by economic coefficients, yields the objective function of the day-ahead reactive power-voltage optimization model for three-phase unbalanced distribution networks involving discrete equipment regulation in step 1: in, , , , These represent the node voltage offset cost, network loss cost, and OLTC and CB operation costs at time t, respectively. in, , These are the voltage offset economic factor and the network loss economic factor, respectively. For the set of all nodes in the distribution network, For three-phase distribution network phases, for time Phase node voltage offset, for time Mutually Current between nodes To take into account the effects of three-phase self-inductance and mutual inductance Mutually Phase line resistance between nodes; Set the node voltage offset to the absolute value of the difference between the actual node voltage and the reference value: in, for time Phase node Voltage value, for time Phase node Voltage reference value.

[0030] Establish a three-phase power flow constraint model, such as Figure 3 The diagram shows the structure of a three-phase distribution network. The day-ahead reactive power-voltage optimization model for a three-phase unbalanced distribution network with discrete equipment involved in regulation includes constraints on the power balance equation, voltage and current security constraints, three-phase voltage imbalance constraints, and CB constraints.

[0031] The power balance equation is as follows: Voltage and current safety constraints are: in, , They are respectively time Branch Road The first segment of active and reactive power, and They are respectively time Phase node and subsequent nodes The active and reactive power of the first segment of the connected branch circuit. To account for the effects of interphase coupling Mutually The resistance of the branch circuit To account for the effects of interphase coupling Mutually The reactance of the branch circuit, and These represent the injection power at the time phase nodes, and They are respectively time Phase node The load power. For a moment Mutually Active power output of the photovoltaic node. yes time Phase node power capacitor banks compensate for reactive power. for Voltage amplitude at time node. and These are the maximum and minimum values ​​of the node voltage amplitude. and This represents the maximum and minimum amplitude of the branch current.

[0032] In three-phase distribution networks, three-phase unbalance is a crucial indicator related to the safe operation of the network. This invention, referencing the IEEE standard definition of three-phase unbalance in distribution networks, defines three-phase voltage unbalance as a constraint on three-phase voltage imbalance: in, This represents the average value of the three-phase voltage amplitude.

[0033] Distribution network reference voltage Represented as: Establish a discrete control device model where CB can be adjusted separately on different phases. The constraints of CB are: The limitation on the number of actions of the CB group can lead to inter-time coupling problems within the scheduling cycle. Therefore, it is added to the objective function in the form of a soft constraint, counting the change of the CB group from time t to t+1 as one time, and defining a binary variable: In step 21, the operating cost of the CB device is: in, For time t The i-th CB gear position, Let CB be a binary variable representing the action. for The adjustable reactive power of the i-th phase CB, since the OLTC is located at the connection point between the distribution network and the upstream power grid, is set to the first-stage voltage of the three-phase distribution network to simplify calculations. Always maintain consistency.

[0034] The OLTC action is similar to CB; the change in the OLTC group from time t to t+1 is counted as one instance, and a binary variable is defined: In step 22, the operating cost of the OLTC device is: in, The initial position, For time t The i-th OLTC gear position, Let OLTC be a binary variable representing actions. At time t+1 The i-th OLTC gear position, Let t be the gear position of the OLTC at time t.

[0035] Step 2 collects day-ahead source-load data, and solves the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with discrete equipment involved in regulation, based on the improved Golden Jackal optimization algorithm, to obtain the hourly operation scheme of the power capacitor CB and the on-load tap-changing transformer OLTC.

[0036] This invention proposes a multi-strategy improved Golden Jackal optimization algorithm. Based on the Golden Jackal optimization algorithm, it combines low-discrepancy sequence generation and chaotic mapping traversal enhancement to improve population initialization, ensuring the traversal characteristics of the population in space (generating an initial population with low-discrepancy sequences based on prime numbers, then using dynamic parameters to improve Logistic chaotic mapping to generate another population, and finally selecting the individuals with better fitness from the two groups to form the initial population). A hyperbolic tangent-power-law hybrid decay model is designed to maintain global exploration and enhance local development (using a hyperbolic tangent function in the early iteration to maintain high escape energy, and adding a power-law term in the later iteration to promote energy exponential decrease). A leadership dynamic weighting mechanism is proposed to enhance the guiding role of the optimal individual and avoid getting trapped in local optima (calculating dynamic weights for male / female Golden Jackals based on fitness differences, adjusting weights based on population dispersion, injecting Lévy perturbations, and using third-order synergy to enhance guidance).

[0037] Using the improved Golden Jackal optimization algorithm, the day-ahead reactive power-voltage optimization model of a three-phase unbalanced distribution network involving discrete equipment regulation, constructed in step 1, is solved to obtain the action schemes of the power capacitors (CB) and on-load tap changers (OLTC) in the day-ahead optimization model. This includes inputting day-ahead source loads, distribution network / equipment parameters, constraints, setting the algorithm population size, maximum iteration count, etc.; generating an initial population according to the improved method, substituting it into the objective function to calculate fitness; selecting male / female Golden Jackals, adjusting escape energy according to the hybrid model, updating the population according to the leadership mechanism, recalculating fitness, and updating the leader; after reaching the maximum iteration count, outputting the optimal individual's corresponding CB and OLTC tap positions for each phase from 0:00 to 23:00 on the following day.

[0038] In the Golden Jackal Optimization Algorithm, golden jackals typically hunt in pairs with a clear division of labor. The male golden jackal leads the tracking and encirclement of prey, guiding group action and representing the current globally optimal solution in the algorithm. The female golden jackal cooperates with the male to ambush or disrupt prey, working together to complete the hunt and representing the suboptimal solution in the algorithm. Together, they guide population renewal. The Golden Jackal Optimization Algorithm includes the following steps: (1) Population initialization: Randomly generate an initial prey population (i.e., candidate solutions): in, Let i be the position of the i-th individual in the j-th dimension. , This represents the boundary of the search space.

[0039] (2) Calculate the fitness value and select the optimal solution (position of the male golden jackal). ) and suboptimal solution (female golden jackal position) ).

[0040] (3) Set escape energy to control the transition of the algorithm from exploration (global exploration) to development (local optimization): Where t is the current iteration number, T is the maximum iteration number, and E decreases from the initial value to 0. A constant set, It is a constant.

[0041] (4) During the exploration phase, prey is searched, simulating the behavior of the golden jackal in its extensive prey-hunting activities: in, , The locations of the male and female golden jackals were updated during the exploration phase. Add random numbers for Lévy to enhance the diversity of the global search: in, , For parameters that follow a normal distribution, This is the scale parameter.

[0042] (5) During the development phase, the golden jackal closes in and surrounds its prey. Where Ym and Yfm are the positions of the male and female golden jackals, respectively, and Prey is the position vector of the prey.

[0043] (6) Final position update, through collaborative decision-making based on the average male and female jackal position balance: in, This is the latest location of the golden jackal.

[0044] like Figure 2 As shown, the specific implementation method of the improved golden jackal optimization algorithm is as follows: Step 2.0.1, while using upper and lower bounds to initialize the population in the Golden Jackal optimization algorithm has the advantage of simplicity, it suffers from the limitation of uneven distribution of Golden Jackal individuals in the solution space. This, to some extent, restricts the maintenance of population diversity and the improvement of optimization efficiency. Therefore, by combining low-discrepancy sequence generation and chaotic mapping traversal enhancement to improve population initialization, the traversal characteristics of the population in the space are ensured, thus improving the population diversity in the Golden Jackal optimization algorithm.

[0045] Step 2.0.1.1 Utilize low-discrepancy sequences of prime bases to ensure high-dimensional projection uniformity: Among them, among them, Initialize the population position for the i-th individual in the j-th dimension using Halton's algorithm. , For the search space boundary, Values ​​for low-difference sequences; Step 2.0.1.2 Improve the Logistic chaotic mapping to enhance ergodicity by setting nonlinear chaotic parameters: in, For nonlinear chaotic parameters, Let z be the solution for the i-th individual in the j-th dimension under the Logistic mapping, and z be the iterative state variable of the chaotic mapping. The constant is T, and the maximum number of iterations is T. Step 2.0.1.3 Compare the fitness values ​​of the initial population generated in Step 2.0.1.1 and Step 2.0.1.2, and select the initial solution with the better fitness.

[0046] Step 2.0.2 The convergence speed of the Golden Jackal optimization algorithm is related to the escape energy, which decreases linearly from 1.5 to 0. However, this is a characteristic of the continuous convergence process of nonlinear algorithms, so the linearly decreasing escape energy cannot fully reflect the actual optimization search process. By designing a hyperbolic tangent-power-law hybrid decay model, we can achieve a gradual decrease in the early stage (maintaining global exploration) and a rapid convergence in the later stage (enhancing local development).

[0047] Step 2.0.2.1 Establish the basic attenuation framework. When t < 0.6T, the tanh function grows slowly, making... Maintaining at a high level: in, The initial maximum energy, Control the steepness of the curve, This is the offset used to determine the start point of the delay decay. To escape the base energy value; Step 2.0.2.2 Create a dynamic decay accelerator to ensure rapid convergence in the later stages: in, For dynamic decay accelerator, The decay is exponential, accelerating exponentially in the later stages, especially when t > 0.6T. The significant deceleration forces the escape energy to converge rapidly to 0; Step 2.0.2.3 Construct the final escape energy: Where E represents the final escape energy; Step 2.0.3 Since the optimal individual's function as a leader is not fully utilized, the Golden Jackal optimization algorithm is prone to getting trapped in local optimization. This invention proposes a dynamic weighted leadership mechanism to enhance the guiding role of the optimal individual and avoid getting trapped in local optima.

[0048] in, The positional weight of the male golden jackal, This represents the fitness value for the male golden jackal's position. The positional weight of the female golden jackal. This represents the fitness value for the female golden jackal's location. This refers to the fitness value of the currently updated golden jackal. For the updated solution, Location of the male golden jackal Location of the female golden jackal The value is constant; the leadership dynamic weighting mechanism quantifies the leader's contribution through fitness ratio weights, regulates the exploration intensity through dispersion feedback, and injects randomness through Levy perturbation. The three-order synergy significantly improves the algorithm's global convergence ability.

[0049] Step 2 includes the following steps: Step 2.1: Input data and set parameters for the improved golden jackal optimization algorithm; The input data includes the photovoltaic output, load, branch impedance, reactive power compensation parameters, and constraint parameters of the distribution network. The set parameters include the number of algorithm populations, the number of iterations, and the initial escape energy. , As an optimization variable; Step 2.2 Combines low-difference sequence generation and chaotic mapping traversal to enhance and improve population initialization; Step 2.3 Calculate the objective function value for each population; Step 2.4 Select the male and female golden jackals based on the objective function value; Step 2.5: Adjust the escape energy using a hyperbolic tangent-power-law hybrid decay model; Step 2.6 Update the position according to the leadership dynamic weighting mechanism to obtain the selected optimal solution. The optimal solution is the decision variable that minimizes the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network in which discrete equipment participates in regulation. Step 2.7 Determine if convergence has occurred. If the convergence condition is met, stop the calculation. The convergence condition refers to reaching the maximum number of iterations. If the convergence condition is not met, return to step 2.3.

[0050] The optimal solution obtained in step 2.8 is the operation scheme of the power capacitor CB and the on-load tap-changing transformer OLTC from 0:00 to 23:00 on the next day.

[0051] The aforementioned "setting escape energy to control the transition of the algorithm from exploration (global exploration) to development (local optimization)" is the principle of the normal Golden Jackal optimization algorithm, where the escape energy is used to determine whether it is a global search or a local optimization. To improve upon this linear decay disadvantage, this invention employs a method based on hyperbolic tangent and power-law functions. Therefore, in this invention, the number of iterations is used to determine whether it is a global search or a local optimization. The final escape energy is also obtained by multiplying the base escape energy by the dynamic decay accelerator.

[0052] Step 3: Based on the constraints of the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with discrete equipment involved in regulation constructed in Step 1, and according to the equipment characteristics of the static var compensator (SVC) and photovoltaic inverter, establish the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment involved in regulation and its constraints.

[0053] The objective function of the intraday reactive power-voltage optimization model for the three-phase unbalanced distribution network with continuous equipment involved in regulation in step 3 is: in, and These represent the node voltage offset cost and network loss cost at time t, respectively.

[0054] The constraints of the intraday reactive power-voltage optimization model for a three-phase unbalanced distribution network with continuous equipment regulation include: power balance equations, voltage and current safety constraints, SVC output power constraints, and reactive power adjustable constraints of photovoltaic inverters.

[0055] The power balance equation is as follows: in, For a moment Mutually The reactive power output of the node SVC, For a moment Mutually The reactive power output of the photovoltaic system at the node can be regulated by the SVC and PV on different phases respectively; Voltage and current safety constraints are: The SVC output power constraint is: in, and These represent the upper and lower limits of reactive power output.

[0056] The reactive power adjustable constraint of the photovoltaic inverter is: in, for Mutually Apparent power of nodal photovoltaics.

[0057] Step 4: Based on the action plan obtained in Step 2, solve the intraday reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment involved in regulation constructed in Step 3 using the improved Golden Jackal optimization algorithm, and obtain the action plan of SVC and photovoltaic inverter every 15 minutes in the intraday optimization model.

[0058] Step 4 includes the following steps: Step 4.1 Perform data input and parameter settings for the improved golden jackal optimization algorithm; The input data includes the photovoltaic output, load, branch impedance, reactive power compensation parameters, and constraint parameters of the distribution network. The set parameters include the number of algorithm populations, the number of iterations, and the initial escape energy. , As an optimization variable; Step 4.2 Combines low-difference sequence generation and chaotic mapping traversal to enhance and improve population initialization; Step 4.3 Calculate the objective function value for each population; Step 4.4 Select the male and female golden jackals based on the objective function value; Step 4.5: Adjust the escape energy using a hyperbolic tangent-power-law hybrid decay model; Step 4.6 Update the position according to the leadership dynamic weighting mechanism to obtain the selected optimal solution. The optimal solution is the decision variable that minimizes the intraday reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment participation in regulation. Step 4.7 Determine if convergence has occurred. If the convergence condition is met, stop the calculation. The convergence condition refers to reaching the maximum number of iterations. If the convergence condition is not met, return to step 4.3.

[0059] The optimal solution obtained in step 4.8 is the operation scheme of SCV and photovoltaic inverter every 15 minutes of the day.

[0060] Based on the above-mentioned unbalanced distribution network multi-timescale reactive power optimization method based on the improved Golden Jackal algorithm, the effectiveness of the present invention is verified by performing calculations on the improved IEEE-33 node system.

[0061] like Figure 4 As shown. The system has a base voltage of 12.66 kV and a base capacity of 10 MVA. To reflect the three-phase imbalance characteristics of the distribution network, the three-phase unbalanced load data used in this invention is obtained by combining the proportional coefficient with the IEEE 33-node basic data. The three-phase load and photovoltaic output characteristics are as follows: Figure 5 As shown.

[0062] Furthermore, the location and capacity of photovoltaic (PV) connections vary across different phases of the distribution network. In phase A, PV systems are connected at positions 6, 17, and 29, with capacities of 5000, 1500, and 5000 kVA, respectively. In phase B, PV systems are connected at positions 12, 17, and 22, with capacities of 1000, 3500, and 1000 kVA, respectively. In phase C, PV systems are connected at positions 6 and 26, each with a capacity of 5000 kVA.

[0063] The SVCs on the three phases are connected at nodes 9, 19, and 27, respectively, with the same adjustable capacity of -100 to 300 kvar. The CBs on the three phases are connected at nodes 17, 20, and 32, respectively, with the same adjustable range and single-group adjustable capacity, with the maximum range being 6. The switching capacity is 100 kvar. The OLTC adjustment range is [0.94-1.06], with an adjustment step of 0.01 pu. Parameters and locations are shown in Table 1, and the optimized operating results are shown in Table 2.

[0064] Table 1 Equipment Parameters and Location

[0065] Table 2 shows the optimized operation results.

[0066] As shown in Table 2, the total network loss of the optimized system was significantly reduced throughout the day. During the entire optimization period, the network loss decreased from 15529.6 kWh to 13775.23 kWh, a reduction of 11.29%, proving that the method proposed in this invention can effectively reduce line losses. The optimized voltage remained stable within a safe range throughout the day, and the voltage deviation decreased from 1156.84 kV to 795.96 kV, a reduction of 31.19%, and was closer to the reference voltage, improving the power quality of the system and contributing to its safe and stable operation.

[0067] Figure 6 The diagram shows the operation of the OLTC. As can be seen from the diagram, due to the limitation on the maximum number of daily operations, the OLTC is mostly in the original position. When the photovoltaic output gradually decreases to no output at all, the OLTC position is raised to increase the voltage at the end node and prevent undervoltage.

[0068] Figure 7 Regarding the operation of three-phase CB1, CB compensates for reactive power by switching capacitor banks. In phase A, CB1 at node 17 did not operate, while the reactive power of CB2 and CB3 at nodes 20 and 32 was affected by the load. In phase B, CB1 at node 17 did not operate, CB2 at node 20 was at a lower setting throughout the day, and CB3 at node 32 was at almost the highest setting throughout the day, compensating the end node.

[0069] Table 3 Comparison of results from different algorithms

[0070] Table 3 shows the optimization results of Particle Swarm Optimization (PSO), Golden Jackal Optimization (GJO), and Improved Golden Jackal Optimization (IGJO). Figure 8 For comparing the voltage at node 16 of phase A under different optimization algorithms, Figure 9 This section compares the A-phase network losses under different optimization algorithms. While the PSO algorithm can partially improve the node voltage deviation problem, the voltage at node 16 is significantly lower during the 21:00-23:00 period, posing a risk of exceeding limits and threatening the safe and stable operation of the distribution network. In contrast, the IGJO algorithm reduces the daily voltage deviation at node 16 by 65.12% and 37.08% compared to the PSO and GJO algorithms, respectively, significantly suppressing the impact of source-load fluctuations on the grid voltage. After optimization, the active power loss of the IGJO algorithm decreases by 2.86% and 35.7% compared to the GJO and PSO algorithms, respectively. The IGJO algorithm not only reduces the operating cost of discrete voltage regulating equipment but also improves the safety and economy of distribution network operation, and its computational efficiency is also superior.

[0071] To further verify the limitations of the proposed method in voltage control, different typical nodes of the three phases were selected for comparison. Node 28 was selected for phase A, which is close to the photovoltaic access point and located at the end of the line. Node 17 was selected for phase B, which is located at the very end of the line and is equipped with photovoltaics. This node exhibited the most severe voltage over-limit and under-voltage issues, reaching 1.077 pu and 0.884 pu, respectively. Node 32 was selected for phase C, the very end of the line, and no voltage exceeding the safe range was observed at this node. The × curve represents the optimized node voltage. Figure 10 As can be seen, the optimized node voltage not only completely eliminates the voltage over-limit and under-voltage conditions, but also fluctuates around the standard value of 1.0 pu most of the time, exhibiting excellent voltage quality.

[0072] Figure 11 The optimized network loss is shown below. After optimization using the method proposed in this invention, the total network loss for each phase is reduced to 1.877 MVA, 0.788 MVA, and 2.180 MVA, respectively. The total system network loss is reduced from 13.618 MVA to 4.864 MVA, a reduction of 67.5%. The above comparison demonstrates that the method proposed in this invention, in addition to ensuring voltage stability and reducing three-phase imbalance, plays a significant role in reducing distribution network losses. The total network loss for each phase refers to the sum of the hourly network losses for each phase over 24 hours.

[0073] Figure 12 To show the absolute values ​​of the maximum imbalance before and after optimization, the curve with circles (○) represents the absolute value of the maximum imbalance before optimization, and the curve with arrows (×) represents the absolute value of the maximum imbalance after optimization. As can be seen from the graph, the average decrease in the absolute value of the maximum imbalance across all nodes exceeds 65%, with most nodes achieving optimization of over 90%. The highest absolute value of the maximum imbalance after optimization is 2.69%, a significant decrease compared to the highest value of 4.85% before optimization. The number of nodes with maximum imbalance approaching 0 has increased significantly, indicating that the system's operating state is more stable after optimization.

[0074] It should be emphasized that the embodiments described in this invention are illustrative rather than limiting. Therefore, this invention includes, but is not limited to, the embodiments described in the specific implementation. Any other implementations derived by those skilled in the art based on the technical solutions of this invention are also within the scope of protection of this invention.

Claims

1. A multi-time-scale reactive power optimization method for unbalanced distribution networks based on an improved Golden Jackal algorithm, characterized by: Includes the following steps: Step 1 considers three-phase voltage imbalance. Based on the equipment characteristics of the power capacitor CB and the on-load tap-changing transformer OLTC, a day-ahead reactive power-voltage optimization model and its constraints for a three-phase unbalanced distribution network with discrete equipment involved in regulation are established. Step 2 collects day-ahead source-load data, and solves the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with discrete equipment involved in regulation constructed in Step 1 based on the improved Golden Jack optimization algorithm, to obtain the hourly operation scheme of the power capacitor CB and the on-load tap-changing transformer OLTC. Step 2.0.1 combines low-difference sequence generation and chaotic mapping traversal to enhance and improve population initialization, ensuring the traversal characteristics of the population in space; The first initial population is generated using a low-discrepancy sequence based on prime numbers to ensure uniformity of high-dimensional projection; the second initial population is generated using a nonlinear chaotic parameter to improve the Logistic chaotic mapping and enhance ergodicity; the fitness values ​​of the initial populations generated by the two methods are compared, and individuals with better fitness are selected to form the final initial population. Step 2.0.2 By designing a hyperbolic tangent-power-law hybrid decay model, global exploration and local exploitation can be maintained; A basic decay framework based on the hyperbolic tangent function is established to maintain the escape energy at a high level in the early stage of iteration; Create a dynamic decay accelerator based on a power-law function to ensure rapid convergence in the later stages of iteration; The final escape energy is constructed by multiplying the basic decay framework with the dynamic decay accelerator. Step 2.0.3 proposes a dynamic weighted leadership mechanism to enhance the guiding role of the best individual and avoid getting trapped in local optima; Calculate the positional weights of male and female golden jackals based on their positional fitness, the positional fitness of female golden jackals, and the fitness of the currently updated individual. The positions of male and female golden jackals are weighted and combined, and a sign function correction term is introduced to obtain the updated solution. The leadership dynamic weighting mechanism quantifies the leader's contribution through fitness ratio weight, regulates the exploration intensity through dispersion feedback, and injects randomness through Lévy perturbation. The three-order synergy improves the global convergence ability of the algorithm. Step 3: Based on the constraints of the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with discrete equipment involved in regulation constructed in Step 1, and according to the equipment characteristics of the static var compensator (SVC) and photovoltaic inverter, establish the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment involved in regulation and its constraints. Step 4: Based on the action plan obtained in Step 2, solve the intraday reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment involved in regulation constructed in Step 3 using the improved Golden Jackal optimization algorithm, and obtain the hourly action plan of SVC and photovoltaic inverter in the intraday optimization model.

2. The method for reactive power optimization of unbalanced distribution networks based on the improved Golden Jackal algorithm according to claim 1, characterized in that: The objective function of the day-ahead reactive power-voltage optimization model for the three-phase unbalanced distribution network involving discrete equipment in step 1 aims to minimize the sum of node voltage offset cost, network loss cost, on-load tap changer (OLTC) operation cost, and power capacitor (CB) operation cost at all 24 time points throughout the day. The node voltage offset cost is obtained by multiplying the voltage offset economic coefficient by the sum of the voltage offsets of all phases at all nodes; the network loss cost is obtained by multiplying the network loss economic coefficient by the sum of the squares of the currents of all phases in all branches and the corresponding line resistances; and the node voltage offset is defined as the absolute value of the difference between the actual voltage of the node and the reference value.

3. The method for reactive power optimization of unbalanced distribution networks based on the improved Golden Jackal algorithm according to claim 2, characterized in that: The constraints of the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network in step 1, in which discrete devices participate in regulation, include power balance equations, voltage and current safety constraints, three-phase voltage imbalance constraints, and CB constraints.

4. The method for reactive power optimization of unbalanced distribution networks based on the improved Golden Jackal algorithm according to claim 1, characterized in that: Step 2 includes the following steps: Step 2.1: Input data and set parameters for the improved golden jackal optimization algorithm; The input data includes the photovoltaic output, load, branch impedance, reactive power compensation parameters and constraint parameters of the distribution network, and the setting parameters include the number of algorithm populations, the number of iterations and the initial escape energy. Step 2.2 Combines low-difference sequence generation and chaotic mapping traversal to enhance and improve population initialization; Step 2.3 Calculate the objective function value for each population; Step 2.4 Select the male and female golden jackals based on the objective function value; Step 2.5: Adjust the escape energy using a hyperbolic tangent-power-law hybrid decay model; Step 2.6 Update the position according to the leadership dynamic weighting mechanism to obtain the selected optimal solution. The optimal solution is the decision variable that minimizes the day-ahead reactive power-voltage optimization model of the three-phase unbalanced distribution network in which discrete equipment participates in regulation. Step 2.7 Determine if convergence has occurred. If the convergence condition is met, stop the calculation. The convergence condition refers to reaching the maximum number of iterations. If the convergence condition is not met, return to step 2.

3. The optimal solution obtained in step 2.8 is the operation scheme of the power capacitor CB and the on-load tap-changing transformer OLTC from 0:00 to 23:00 on the next day.

5. The method for reactive power optimization of unbalanced distribution networks based on the improved Golden Jackal algorithm according to claim 1, characterized in that: The objective function of the daily reactive power-voltage optimization model for the three-phase unbalanced distribution network in step 3, which involves continuous equipment regulation, aims to minimize the sum of node voltage offset cost and network loss cost at 96 times throughout the day. Its constraints include power balance equation, voltage and current safety constraints, static var compensator (SVC) output power constraints, and photovoltaic inverter reactive power adjustable constraints.

6. The method for reactive power optimization of unbalanced distribution networks based on the improved Golden Jackal algorithm according to claim 1, characterized in that: Step 4 includes the following steps: Step 4.1 Perform data input and parameter settings for the improved golden jackal optimization algorithm; The input data includes the photovoltaic output, load, branch impedance, reactive power compensation parameters and constraint parameters of the distribution network, and the setting parameters include the number of algorithm populations, the number of iterations and the initial escape energy. Step 4.2 Combines low-difference sequence generation and chaotic mapping traversal to enhance and improve population initialization; Step 4.3 Calculate the objective function value for each population; Step 4.4 Select the male and female golden jackals based on the objective function value; Step 4.5: Adjust the escape energy using a hyperbolic tangent-power-law hybrid decay model; Step 4.6 Update the position according to the leadership dynamic weighting mechanism to obtain the selected optimal solution. The optimal solution is the decision variable that minimizes the intraday reactive power-voltage optimization model of the three-phase unbalanced distribution network with continuous equipment participation in regulation. Step 4.7 Determine if convergence has occurred. If the convergence condition is met, stop the calculation. The convergence condition refers to reaching the maximum number of iterations. If the convergence condition is not met, return to step 4.

3. The optimal solution obtained in step 4.8 is the operation scheme of SCV and photovoltaic inverter every 15 minutes of the day.

Images