Active power distribution network multi-time scale collaborative optimization method based on improved whale algorithm

Abstract

The invention discloses an active power distribution network multi-time scale collaborative optimization method based on an improved whale algorithm. The method comprises the following steps: constructing an active power distribution network multi-time active and reactive collaborative optimization model; a standard whale optimization algorithm is improved; the whale optimization algorithm improved in the step 2 is used for solving the multi-time active and reactive collaborative optimization model of the active power distribution network in the step 1, and a model real-time optimization scheme is obtained. According to the active power distribution network multi-time scale collaborative optimization method based on the improved whale algorithm, the problem of voltage out-of-limit caused by high-proportion photovoltaic access to the power distribution network can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of optimal dispatching of active distribution networks, and particularly to a multi-time scale collaborative optimization method for active distribution networks based on an improved whale algorithm. Background Technique

[0002] The large-scale grid connection of distributed power sources causes over-limit and frequent fluctuations of the distribution network voltage, seriously affecting the power supply quality of the system. As the main control means to improve the power quality of the distribution network, reactive power optimization has always received the key attention of scholars at home and abroad. Many scholars pay more attention to the optimization effect of reactive power optimization on the system, while ignoring the strong coupling relationship between active power and reactive power in the distribution network, making the optimization effect have certain one-sidedness and limitations.

[0003] Due to the existence of a large number of structural variables and non-linear constraints in the distribution network, the optimization problem of the distribution network belongs to a typical non-linear mixed integer programming problem. At present, the methods to solve this problem mainly include numerical optimization algorithms and intelligent algorithms. The numerical optimization algorithm will significantly increase the difficulty of solving the model as the dimension of the decision variable increases. While the intelligent algorithm has good robustness and functionality when dealing with complex non-linear optimization problems, but the conventional intelligent algorithm is difficult to balance the optimization accuracy and optimization speed during optimization. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a multi-time scale collaborative optimization method for active distribution networks based on an improved whale algorithm, which solves the problem of over-limit voltage caused by high-proportion photovoltaic access to the distribution network by coordinating compensation resources with different response capabilities.

[0005] To solve the above technical problem, the technical solution adopted by the present invention is:

[0006] A multi-time scale collaborative optimization method for active distribution networks based on an improved whale algorithm includes the following steps:

[0007] Step 1: Construct a multi-time active and reactive power collaborative optimization model for the active distribution network;

[0008] Step 2: Improve the standard whale optimization algorithm;

[0009] Step 3: Use the improved whale optimization algorithm in Step 2 to solve the multi-time active and reactive power collaborative optimization model of the active distribution network in Step 1, and obtain the real-time optimization solution of the model.

[0010] Constructing the multi-time active and reactive power collaborative optimization model for the active distribution network in Step 1 includes:

[0011] In the day-ahead stage, based on the source-load prediction data, determine the action states of the on-load tap changer OLTC and the shunt capacitor bank CB;

[0012] During the intraday stage, the operating states of fixed discrete devices are fixed, and the real-time response capabilities of the static var compensator (SVC), energy storage system (ESS), and photovoltaic inverter are utilized to eliminate the impact caused by short-term fluctuations in photovoltaic power output.

[0013] During the day-ahead stage, based on the source-load prediction data, the operating states of the on-load tap-changing transformer (OLTC) and shunt capacitor bank (CB) are determined, specifically including:

[0014] 1.1. Establish the day-ahead stage objective function, and the day-ahead stage objective function is as follows:

[0015]

[0016] In the formula: f is the day-ahead objective function; w 1 is the network loss weight coefficient; w 2 is the voltage deviation weight coefficient; w 3 is the action cost weight coefficient of discrete devices; f 1 , f 2 and f 3 are the network loss, voltage deviation, and action cost of discrete devices respectively; l ij is the square of the branch current between nodes i and j; r ij is the branch resistance; N is the set of branches; N b is the number of network nodes; v j is the square of the voltage amplitude at node j; v j,N is the square of the rated voltage at node j; are the action costs of OLTC and CB at time t respectively;

[0017] 1.2. Constraints of the day-ahead stage objective function

[0018] (1) Power flow constraint

[0019]

[0020] In the formula: P i , Q i are the active power and reactive power injected into node i respectively; G ij , B ij and δ ij are the branch conductance, susceptance, and phase angle difference between nodes i and j respectively; U i , U j are the voltages at nodes i and j respectively;

[0021] (2) Safe operation constraint in the day-ahead stage

[0022]

[0023] In the formula: vi,max , v i,min are the upper and lower limits of the voltage magnitude at node i; l ij,max is the upper limit of the branch current magnitude between nodes i and j; v i,t is the voltage at node i at time t; l ij,t is the branch current between nodes i and j at time t;

[0024] (3) Constraints related to discrete devices;

[0025] ① Operating constraints of on-load tap-changer (OLTC):

[0026]

[0027] In the formula: is the actual tap position of the OLTC between nodes i and j at time t; and are the upper and lower limits of the tap positions of the OLTC respectively; T ij,t is the tap position of the OLTC at time t; is the regulation step of the OLTC;

[0028] ② Related constraints of shunt capacitor bank (CB):

[0029]

[0030] In the formula: is the switching capacity of the CB at node j at time t; are the upper and lower limits of the number of switching groups of the CB respectively; is the compensation capacity of a unit CB; is the number of switching groups of the CB at time t.

[0031] During the intraday stage, first, fix the setting values of the shunt capacitor CB and the on-load tap-changer OLTC for 24 hours in the day-ahead stage; second, combined with the minute-level photovoltaic and load output data, use photovoltaic inverters, static var compensators (SVCs), and energy storage systems (ESSs) to achieve real-time regulation of the distribution network voltage; specifically including:

[0032] 1.1. Establish the objective function for the intraday stage

[0033] (1) Minimum active power loss

[0034]

[0035] In the formula: Δt is the time interval of the scheduling period;

[0036] (2) Minimum voltage deviation

[0037]

[0038] Where: N b is the number of network nodes; U i,t is the voltage magnitude at node i at time t; is the rated value of the node voltage;

[0039] 1.2. Intra-day stage objective function constraints

[0040] (1) Energy storage device operation constraints

[0041]

[0042] Where: are respectively the lower and upper limits of the charging power of the energy storage device at node j; are respectively the lower and upper limits of the discharging power of the energy storage device at node j; A char is the charging decision variable; A disc is the discharging decision variable; E j,t is the energy stored in the energy storage device at time t; are respectively the charging and discharging efficiencies of the energy storage device; are respectively the upper and lower limits of the energy storage capacity;

[0043] (2) Static var compensator SVC operation constraints

[0044]

[0045] Where: are respectively the upper and lower limits of the reactive power output of the SVC, is the reactive power output of the SVC at time t;

[0046] (3) Photovoltaic inverter output constraints

[0047]

[0048] Where: are respectively the upper and lower limits of the reactive power output of the photovoltaic inverter; is the capacity of the inverter; is the active power output of the photovoltaic inverter at time t; is the reactive power output of the photovoltaic inverter at time.

[0049] In step 2, the standard whale optimization algorithm is improved, including:

[0050] 2.1. Using the Sobol sequence to generate uniformly distributed initial solutions, and the Sobol sequence initialization formula is:

[0051] x 1 = x min + λ(x max - x min) (14);

[0052] where: x max , x min are the upper and lower limits of the particle position respectively; λ is a random number in the interval [0,1] generated by the Sobol sequence; x 1 is the position of the first whale after update, and the same applies to other whales;

[0053] 2.2: Improve the convergence factor to balance and enhance the exploration and local development capabilities of the algorithm;

[0054] Adopt a non-linear convergence factor, as shown in Equation (15):

[0055]

[0056] where: a initial is the initial value of the convergence factor iteration; a final is the termination value of the convergence factor iteration; μ is the non-linear factor; t is the current iteration number; T is the maximum iteration number;

[0057] 2.3: Introduce a differential evolution algorithm combined with Cauchy perturbation to increase the population diversity during the iteration process and help the algorithm jump out of the local optimum, specifically including:

[0058] ① Mutation operation: Scale the difference between two vectors and add it to a third random vector to generate a mutant vector;

[0059]

[0060] where: ν i,G+1 is the generated mutant vector; cauchy(0,1) is the Cauchy operator; and are 3 different random parent individuals;

[0061] ② Crossover operation: To enhance the population diversity and anti-interference ability of the algorithm, cross the mutant vector and the target vector;

[0062]

[0063] where: u i,G+1 is the new vector after crossover; P is the crossover probability; D is the dimension; is the global optimal position in the j-th dimension; is the individual optimal position in the j-th dimension; rand(j) is a random number between [0,1]; ν i,G+1 is the generated mutant vector; x i,G is a random parent individual that has not undergone crossover;

[0064] ③ Selection operation: Compare the trial vector with the target vector according to the greedy criterion, retain the one with the smaller fitness value, and adjust the individual position by learning excellent individuals to improve the global optimization ability of the algorithm. The selection operation is as follows:

[0065]

[0066] In the formula: f(v i,G+1 ) is the fitness of the individual after crossover; f(x i,G ) is the fitness of the non-crossover parent individual.

[0067] In step 3, use the improved whale optimization algorithm to solve the model, including the following steps:

[0068] S3.1. Initialize parameters: population size, spatial dimension, and upper and lower limits of the search space;

[0069] S3.2. Initialize the population position using the Sobol sequence;

[0070] S3.3. Calculate the individual fitness value, find the optimal fitness value and the optimal individual; perform mutation and crossover operations according to the crossover probability;

[0071] S3.4. Update a according to formula (15), and then update A according to formula (11), while updating c and p;

[0072] S3.5. When p < 0.5, if |A| > 1, enter S3.6, if |A| ≤ 1, enter S3.7, when p ≥ 0.5, enter S3.8;

[0073] S3.6. Perform global search, learn excellent individuals according to formula (18), update the positions of poor individuals, and further update the individual positions according to the position formula in formula (11);

[0074] S3.7. Encircle the prey and update the individual position according to formula (12);

[0075] S3.8. Spiral bubble net predation and update the individual position according to formula (13);

[0076] S3.9. Determine whether the iteration termination condition is satisfied. If satisfied, output the global optimal solution and position information, otherwise enter S3.3 and continue to execute.

[0077] The present invention provides an active distribution network multi-time scale collaborative optimization method based on an improved whale algorithm, having the following technical effects:

[0078] 1). At present, many scholars mainly focus on the optimization effect of reactive power on the power quality of the distribution network, while ignoring the strong coupling relationship between active power and reactive power, and it is difficult for the optimization accuracy to meet the requirements of refined operation of the system.

[0079] In view of the above problems, the present invention proposes a multi-time scale active and reactive power collaborative optimization strategy. Based on the output data of the power source and load at different time scales and considering the action characteristics of different regulating devices, an optimization scheme for different operating periods of the system is formulated. Experimental verification shows that the strategy proposed by the present invention can effectively improve the economy and security of the operation of the distribution network and meet the requirements of the system for real-time response.

[0080] 2) In view of the problems of slow convergence speed, poor optimization accuracy and easy entrapment in local optimum of the traditional WOA algorithm, the present invention improves the above problems. First, the Sobol initialization population strategy is introduced, and Sobol low-discrepancy sequences are used to generate particles with uniform distribution and non-repeating positions, so as to improve the coverage rate and distribution uniformity of the initial solution space. Then, aiming at the problem that it is difficult to balance the global search ability and local development ability in the early and late iterations of the standard WOA algorithm, the convergence factor a is improved to accelerate its decay speed in the early stage and accelerate its decay speed in the later stage, so as to balance and improve the exploration and development ability of the algorithm. Finally, in order to enhance the exploration ability of the algorithm in dealing with complex search environments and improve the population diversity in the iterative process, a differential mutation strategy combined with the Cauchy operator is introduced to expand the diversity of solutions in the iterative process and use the larger step size of the Cauchy operator to help the algorithm jump out of the local optimum.

[0081] By improving the standard WOA algorithm in terms of population initialization mechanism, evolution mechanism and control parameters, the problems of slow convergence speed, low population diversity and easy entrapment in local optimum of the original WOA algorithm are effectively solved. Compared with the IMGWO algorithm, the IMPSO algorithm and the WOA algorithm, the IMWOA algorithm of the present invention exhibits better optimization performance, and the optimized system network loss and voltage deviation are lower. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] The present invention will be further described below with reference to the drawings and embodiments:

[0083] Figure 1 It is a schematic diagram of the multi-time scale collaborative optimization method.

[0084] Figure 2 It is a schematic diagram of the particle distribution generated randomly.

[0085] Figure 3 It is a schematic diagram of the particle distribution generated by the Sobol sequence.

[0086] Figure 4 It is a flow chart of the improved whale optimization algorithm.

[0087] Figure 5 It is the improved IEEE 33-node distribution system.

[0088] Figure 6It is a graph of photovoltaic and load prediction data.

[0089] Figure 7 It is a curve graph of algorithm iteration.

[0090] Figure 8 It is a comparison graph of network losses of different algorithms.

[0091] Figure 9 It is a comparison graph of node voltages of different algorithms at 12:00.

[0092] Figure 10 It is a distribution graph of node voltages of two schemes.

[0093] Figure 11(a) is the operation status graph of OLTC.

[0094] Figure 11(b) is the operation status graph of CB1.

[0095] Figure 11(c) is the operation status graph of CB2.

[0096] Figure 12(a) is the operation status graph of SVC1.

[0097] Figure 12(b) is the operation status graph of SVC2.

[0098] Figure 12(c) is the operation status graph of SVC3.

[0099] Figure 13(a) is the operation status graph of inverter 1.

[0100] Figure 13(b) is the operation status graph of inverter 2.

[0101] Figure 13(c) is the operation status graph of inverter 3.

[0102] Figure 14 It is a schematic diagram of energy storage output. Specific implementation manners

[0103] An active distribution network multi-time scale collaborative optimization method based on an improved whale algorithm includes the following steps:

[0104] Step 1: First, construct an active distribution network multi-time active and reactive collaborative optimization model; in the day-ahead stage, based on source-load prediction data, determine the operation states of on-load tap changers (OLTCs) and shunt capacitor banks (CBs) for the next day. In the intra-day stage, fix the operation states of discrete devices, and utilize the real-time response capabilities of static var compensators (SVCs), energy storage systems (ESSs), and photovoltaic inverters to eliminate the influence caused by short-term fluctuations in photovoltaic output.

[0105] Step 2: Then, the following improvements are made to the standard whale optimization algorithm: (1) Use the Sobol sequence to generate uniformly distributed initial solutions; (2) Improve the convergence factor balance and enhance the exploration and local development capabilities of the algorithm; (3) Introduce a differential evolution algorithm combined with Cauchy perturbation to increase the population diversity during the iteration process and help the algorithm jump out of the local optimum.

[0106] Step 3: Finally, use the improved whale optimization algorithm to generate the solution of the model and obtain the real-time optimization scheme of the model.

[0107] The multi-time scale active and reactive power coordinated optimization strategy is as Figure 1 shown. The specific process is as follows: 1 Multi-time scale active and reactive power coordinated optimization model

[0108] By establishing the objective function and relevant constraints, the compensation resource scheduling scheme at different operation stages is obtained.

[0109] 1.1 Objective function for the day-ahead stage

[0110] Taking into account the economy of distribution network operation and power supply reliability, minimizing network loss and voltage deviation is taken as the optimization objective. At the same time, to reduce the impact of the frequent operation of on-load tap changers (OLTC) and shunt capacitor banks (CB) on their service life, the operation costs of discrete devices are considered in the day-ahead optimization stage.

[0111]

[0112] In the formula: f is the day-ahead objective function; w 1 is the network loss weight coefficient; w 2 is the voltage deviation weight coefficient; w 3 is the operation cost weight coefficient of discrete devices; f 1 、f 2 and f 3 are the network loss, voltage deviation and operation cost of discrete devices respectively; l ij,t is the square of the branch current between nodes i and j; r ij is the branch resistance; N is the branch set; N b is the number of network nodes; v j is the square of the voltage amplitude at node j; v j,N is the square of the rated voltage at node j; are the operation costs of OLTC and CB at time t respectively.

[0113] 1.2 Day-ahead constraints

[0114] (1) Power flow constraint

[0115]

[0116] In the formula: P i, Q i are the active power and reactive power injected into node i, respectively; G ij , B ij and δ ij are the branch conductance, susceptance and phase angle difference between nodes i and j, respectively; U i , U j are the voltages at nodes i and j, respectively.

[0117] (2) Security operation constraints in the day-ahead stage

[0118]

[0119] In the formula: v i,max , v i,min are the upper and lower limits of the voltage magnitude at node i, respectively; l ij,max is the upper limit of the branch current magnitude between nodes i and j; v i,t is the voltage at node i at time t; l ij,t is the branch current between nodes i and j at time t.

[0120] (3) Related constraints of discrete devices

[0121] ① Operating constraints of on-load tap-changer (OLTC):

[0122]

[0123] In the formula: is the actual tap position of the OLTC between nodes i and j at time t; and are the upper and lower limits of the tap positions of the OLTC, respectively; T ij,t is the tap position of the OLTC at time t; is the regulation step of the OLTC.

[0124] ② Related constraints of shunt capacitor bank (CB):

[0125]

[0126] In the formula: is the switching capacity of the CB at node j at time t; are the upper and lower limits of the number of switching groups of the CB, respectively; is the compensation capacity of a unit CB; is the number of switching groups of the CB at time t.

[0127] 1.3 Objective function in the intraday stage

[0128] During the intraday stage, first, the setting values of shunt capacitors and on-load tap-changing transformers are fixed within 24 hours in the day-ahead stage. Second, combining the minute-level PV and load output data, the real-time regulation of the distribution network voltage is achieved by using PV inverters, SVCs, and energy storage devices.

[0129] (1) Minimum active power loss

[0130]

[0131] Where: Δt is the time interval of the scheduling period.

[0132] (2) Minimum voltage deviation

[0133]

[0134] Where: N b is the number of network nodes; U i,t is the voltage magnitude at node i at time t; is the rated value of the node voltage.

[0135] 1.4 Intraday constraints

[0136] (1) Energy storage device operation constraints

[0137]

[0138] Where: are the lower and upper limits of the charging power of the energy storage device at node j, respectively; are the lower and upper limits of the discharging power of the energy storage device at node j, respectively; A char is the charging decision variable; A disc is the discharging decision variable; E j,t is the energy stored in the energy storage device at time t; are the charging and discharging efficiencies of the energy storage device, respectively; are the upper and lower limits of the energy storage capacity, respectively.

[0139] (2) Static var compensator (SVC) operation constraints

[0140]

[0141] Where: are the upper and lower limits of the reactive power output of the SVC, respectively; is the reactive power output of the SVC at time t.

[0142] (3) PV inverter output constraints

[0143]

[0144] Where: are the upper and lower limits of the reactive power output of the PV inverter, respectively; is the capacity of the inverter; is the active power output of the PV inverter at time t; is the reactive power output of the PV inverter at time.

[0145] The power flow constraints and safe operation constraints in the intraday stage are the same as those in the day-ahead stage, which will not be elaborated here.

[0146] 2. Model Solving Algorithm

[0147] The Whale Optimization Algorithm (WOA) is a meta-heuristic optimization algorithm that simulates the foraging behavior of whales. The hunting process includes three stages: searching, surrounding, and attacking. Compared with other intelligent algorithms, the Whale Optimization Algorithm (WOA) has fewer parameters and higher stability during the search process. However, the convergence speed of the standard Whale Optimization Algorithm (WOA) is relatively slow, and it is prone to falling into local optima during the iteration process, and the optimization results have certain limitations. The present invention improves the algorithm for the above problems and uses the improved Whale Optimization Algorithm to solve the model.

[0148] 2.1 Standard Whale Optimization Algorithm

[0149] (1) Searching for food: Whales adopt a random walk mechanism during the prey search stage and update their individual positions by sharing position information with each other. This mechanism ensures the good global optimization ability of the algorithm. In the present invention, each whale individual is regarded as an optimization strategy, and the position dimension is equated with the optimization problem dimension. The position update formula is as follows:

[0150]

[0151] where: x(t) and x(t + 1) are the position vectors of the whale before and after update, respectively; x rand is an arbitrary whale position vector; A and C are coefficients; r is a random number between [0, 1]; a is the convergence factor, where a = 2 - 2t / T, T is the maximum number of iterations; D rand is the random distance.

[0152] (2) Shrinking and surrounding the prey

[0153] The algorithm assumes that the solution with the optimal fitness value is the prey position or close to the prey position. When |A| gradually decreases to less than 1, the algorithm enters the stage of surrounding the prey. In this stage, other individuals in the whale group shrink and surround the prey based on the position of the optimal solution and gradually approach the optimal solution.

[0154]

[0155] where: x * (t) is the individual optimal solution in the t-th iteration. D1 is the distance between the optimal solution and the current individual.

[0156] (3) Spiral bubble net attack

[0157] After detecting the prey, the whale simultaneously performs the behaviors of surrounding the prey and attacking. The algorithm selects the behavior based on a random probability p. When p ≥ 0.5, the whale swims upward in a spiral to hunt. When p < 0.5, it contracts to surround the prey based on the position of the optimal solution. The position update formula is as follows:

[0158]

[0159] In the formula: D 2 is the distance between the individual and the optimal solution in the t-th iteration; l is a random number in the interval [-1, 1]; b is the spiral shape coefficient.

[0160] 2.2 Improved whale optimization algorithm

[0161] Aiming at the problems existing in the standard WOA algorithm, the present invention introduces the Sobol sequence to initialize the whale population to improve the distribution of the initial solution. The improved convergence factor a ensures that while balancing and enhancing the exploration and exploitation capabilities, it speeds up the algorithm iteration speed in the early stage and the optimization accuracy in the later stage. Combining with the differential mutation strategy incorporating the Cauchy operator enhances the population diversity and helps the algorithm jump out of the local optimum. In summary, the present invention proposes an improved whale optimization algorithm (IMWOA).

[0162] (1) Initial population strategy based on Sobol sequence

[0163] The distribution of the initial solution largely affects the search efficiency and optimization accuracy of the algorithm. The standard whale optimization algorithm (WOA) initializes the population by using random numbers, resulting in a poor uniformity of the distribution of the initial solution. The Sobol sequence is a low-discrepancy sequence that generates uniformly distributed and non-repeating points in multi-dimensional space. The present invention uses the Sobol sequence to initialize the population to improve the distribution of the initial solution in the solution space. The Sobol sequence initialization formula is:

[0164] x 1 = x min + λ(x max - x min ) (14);

[0165] In the formula: x max , x min are the upper and lower limits of the particle position respectively; λ is a random number generated by the Sobol sequence in the interval [0, 1]; x 1 is the position of the first whale after update, and the same applies to other whales.

[0166] To demonstrate the superiority of the population initialization strategy of the present invention, the distribution of 500 two-dimensional particles generated in the [0,1] interval by the random method and the Sobol sequence method is compared. As can be seen from Figure 2 and Figure 3 , the distribution of the initial population of the present invention is more uniform and has a higher coverage rate in the solution space. The population distributions generated by the random method and the Sobol sequence are shown in Figure 2 and 3 respectively.

[0167] (2) Improvement of the convergence factor

[0168] The convergence factor a determines the global search ability and local development ability of the algorithm. The convergence factor of the standard WOA algorithm shows a linear decay trend with the increase of the number of iterations. The linear decay convergence strategy will result in the algorithm having a strong global search ability in the early stage, but a slow convergence speed, and a fast convergence speed in the later stage, but it is easy to fall into the local optimum. The present invention proposes a non-linear convergence factor as shown in Equation 15:

[0169]

[0170] where: a initial is the initial value of the convergence factor iteration; a final is the termination value of the convergence factor iteration; μ is the non-linear factor; t is the current iteration number; T is the maximum iteration number.

[0171] After the improvement, the decay rate of a is fast first and then slow, which improves the convergence speed in the early stage and the local optimization accuracy in the later stage of the algorithm.

[0172] (3) Population mutation strategy of differential evolution

[0173] To solve the problems of the WOA algorithm, such as the reduction of population diversity with the increase of the algorithm iteration number and the easy fall into the local optimum due to the single population evolution mechanism. The present invention introduces the crossover, mutation and selection operations of the differential evolution algorithm (Differential Evolution, DE) to enrich the evolution mechanism of the algorithm. During the iteration process of the algorithm, the population diversity is improved by generating mutant individuals. At the same time, the Cauchy operator is introduced to help the algorithm jump out of the local optimum and accelerate the search speed of the optimal solution.

[0174] ③ Mutation operation: The difference between two vectors is scaled and added to a third random vector to generate a mutant vector.

[0175]

[0176] where: ν i,G+1 is the generated mutant vector; cauchy(0,1) is the Cauchy operator; and There are 3 different random parent individuals.

[0177] ④ Crossover operation: To enhance the diversity of the algorithm population and its anti-interference ability, the mutation vector and the target vector are crossed.

[0178]

[0179] In the formula: u i,G+1 is the new vector after crossover; P is the crossover probability; D is the dimension; is the global optimal position in the j-th dimension; is the individual optimal position in the j-th dimension; rand(j) is a random number between [0,1]; ν i,G+1 is the generated mutation vector; x i,G is the random parent individual without crossover.

[0180] ③ Selection operation: According to the greedy criterion, the trial vector is compared with the target vector, and the one with the smaller fitness value is retained. The individual position is adjusted by learning excellent individuals to improve the global optimization ability of the algorithm. The selection operation is as follows:

[0181]

[0182] In the formula: f() is the fitness function; f(v i,G+1 ) is the fitness of the individual after crossover; f(x i,G ) is the fitness of the parent individual without crossover.

[0183] The improved algorithm flow is as Figure 4 shown:

[0184] 3 Case verification

[0185] Now, the improved IEEE 33-node system is used for test verification to verify the effectiveness of the strategy proposed in the present invention. Figure 6 is the improved IEEE 33-node distribution system. The base voltage U B = 12.66 kV; the base capacity S B = 100 MVA; the transformer tap setting is 1.025 ± 5 × 2.5%; the allowable range of the node voltage is 0.95 - 1.05 pu; an energy storage device with a capacity of 1000 kW·h is installed at node 17; capacitors with a total capacity of 400 kvar are installed at nodes 22 and 33; PVs with a capacity of 0.4 MW each are connected to nodes 5, 2, and 21; static var compensators with a capacity of 1000 kvar are installed at nodes 5, 25, and 21; the unit operation cost of OLTC and CB is set to 1.2 yuan per time.

[0186] The source-load prediction data in the day-ahead stage is taken from the public data of a certain place, such as Figure 6As shown

[0187] Pre - day voltage optimization control

[0188] To verify the superiority of the IMWOA algorithm proposed in this invention for solving the model, the pre - day optimization model is solved using the IMWOA, IMPSO, and IMGWO algorithms respectively. The convergence curves of the pre - day algorithms and the solution results of different algorithms are as Figure 7 and shown in Table 1

[0189] According to Figure 7 it can be seen that IMPSO and IMGWO converge to the optimal solution after 200 iterations. The method of this invention finds the optimal solution after 60 iterations, with the fastest convergence speed and the smallest fitness value. In addition, except for the method of this invention, the other two methods show serious premature convergence phenomena. For example, IMPSO falls into the local optimum after 15 iterations, and IMGWO falls into the local optimum after 10 iterations. After introducing the Cauchy perturbation strategy in this invention, the ability of the algorithm to jump out of the local optimum is enhanced

[0190] Table 1 Comparison of results of different pre - day algorithms

[0191]

[0192]

[0193] As can be seen from Table 1, compared with before optimization, the network losses after optimization by IMPSO, IMGWO, and IMWOA are reduced by 43.5%, 61.1%, and 62.4% respectively, and the voltage deviations are reduced by 52.96, 73.4%, and 80.7% respectively. The optimization effect of the method of this invention is the most obvious

[0194] In addition, for the discrete device action strategies obtained after algorithm optimization, IMPSO and IMGWO act 15 times and 10 times more than the method of this invention respectively, which seriously affects the service life of the equipment. The comparison of the system network losses and the voltage distribution results at 12:00 after optimization by different algorithms is as Figure 8 and Figure 9 shown

[0195] From Figure 8 and Figure 9 it can be seen that at the peak power consumption time of 12:00 noon, the network loss before optimization reaches 125.04 kW, and the system network losses after optimization by IMPSO, IMGWO, and IMWOA are reduced by 53.34 kW, 84.24 kW, and 81.15 kW respectively. At the same moment, the voltage at node 17, which is the lowest voltage point before optimization, is 0.9126 pu, and after optimization, it is raised by 2.01%, 2.5%, and 3.2% respectively. By comparison, the system safety and economy are better after optimization using the IMWOA algorithm

[0196] 3.2 Intra-day Voltage Control

[0197] To verify the effectiveness of the multi-time scale optimization strategy adopted in the present invention, the time of 12:00, when fluctuations are relatively frequent, is selected for analysis. The network loss results and node voltage distribution of two scenarios, namely, only day-ahead optimization (Scenario 1) and the method of the present invention (Scenario 2), are compared and analyzed. The optimization results are shown in Table 2 and Figure 10 as follows

[0198] Table 2 Comparison of Optimization Results of Two Scenarios

[0199]

[0200] From Figure 10 and Table 2, it can be seen that after the day-ahead stage optimization, voltage violations still exist at some nodes, and there is a relatively large network loss. However, through the refined adjustment in the intra-day stage, the voltage deviation is reduced from 0.165 pu to 0.0057 pu, and the network loss is reduced from 1.246 MW to 0.043 MW. Moreover, the voltages of all nodes are above 0.97 pu. In summary, the multi-time scale voltage optimization strategy adopted in the present invention can effectively reduce the system network loss and solve the problem of voltage violation.

[0201] To verify that the algorithm proposed in the present invention has more advantages in terms of model optimization effect and solution efficiency, the IMWOA, IMPSO, and IMGWO algorithms are respectively used in the present invention to solve the intra-day model. The optimization results of different algorithms are shown in Table 3.

[0202] Table 3 Comparison of Optimization Results of Different Intra-day Algorithms

[0203]

[0204] As can be seen from Table 3, the optimization effect of IMWOA is the best, but the solution time is between IMPSO and IMGWO. This is because IMGWO uses the way of leading wolf guidance for optimization, and the speed is faster in the later stage of iteration. While IMPSO and IMWOA introduce the operation of selecting elite individuals in differential evolution, which also leads to a slower convergence speed of the algorithm in the later stage of iteration. It is verified that the algorithm proposed in the present invention has a high solution efficiency while ensuring good optimization performance.

[0205] As can be seen from Figure 11, after the optimization of the strategy in this paper, the number of actions of the discrete device has been significantly reduced to 16 times, which helps to extend the device life. The device actions are mainly concentrated between 6:00 am and 12:00 noon because the PV output fluctuates greatly during this period and the system needs to adjust through device actions to meet the reactive power demand. After 18:00 at night, the device basically maintains at a higher gear because the light intensity weakens during this period, resulting in a decrease in PV power generation, while the load demand increases, and the problem of low voltage level is more prominent. Therefore, a higher transformer gear setting and more reactive power compensation are required to ensure the stable operation of the power system.

[0206] As can be seen from Figure 12, SVC2 and SVC2 operate more frequently than SVC1 because the former two are farther from the root node and are more vulnerable to voltage fluctuations. In addition, the large change in the end load will cause rapid changes in the voltage and reactive power demand, and SVC needs to be adjusted frequently.

[0207] As can be seen from Figure 13, during the period from 7:00 to 9:00 when the PV fluctuates frequently and the user load increases, in order to maintain the stability of the power grid, the inverter needs to operate frequently to adapt to these changes and perform corresponding compensation actions. After 18:00, the light intensity decreases, the active power output of the PV decreases, the reactive power increases appropriately, and the power factor will increase to a certain extent.

[0208] According to Figure 14 As shown, this paper uses an energy storage device to suppress the fluctuations of PV output to reduce its impact on the optimization effect. During the period with strong light (i.e., from 9:00 to 15:00), the energy storage device mainly performs charging operations, which helps to smooth the output curve of PV power generation and improve the operation economy and safety of the system. During other periods, the energy storage device mainly discharges to improve the power flow distribution of the system and help maintain the voltage.

Claims

1. An active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm is characterized by: The following steps are involved: Step 1: Construct a multi-time active and reactive collaborative optimization model for active distribution network; Step 2: Improve the standard whale optimization algorithm; Step 3: Use the improved whale optimization algorithm in step 2 to solve the multi-time active and reactive collaborative optimization model of the active distribution network in step 1 to obtain the real-time optimization solution of the model.

2. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 1 is characterized in that: In step 1, a multi-time active and reactive coordinated optimization model of active distribution network is constructed, including: In the day-ahead stage, the operating status of the on-load tap changer OLTC and the shunt capacitor bank CB is determined based on the source load forecast data; During the intraday stage, the action state of discrete devices is fixed, and the real-time response capabilities of the static VAR compensator SVC, energy storage system ESS, and photovoltaic inverter are used to eliminate the impact of short-term photovoltaic output fluctuations.

3. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 2 is characterized in that: In the day-ahead stage, based on the source load forecast data, the operating status of the on-load tap changer OLTC and the shunt capacitor bank CB is determined, including: 1.

1. Establish the objective function of the day-ahead stage. The objective function of the day-ahead stage is as follows: Where: f is the day-ahead objective function; w1 is the network loss weight coefficient; w2 is the voltage deviation weight coefficient; w3 is the discrete device action cost weight coefficient; f1, f2 and f3 are the network loss, voltage deviation and discrete device action costs respectively; l ij is the square of the branch current between nodes i and j; r ij is the branch resistance; N is the branch set; N b is the number of network nodes; v j is the square of the voltage amplitude at node j; v j,N is the square of the rated voltage at node j; are the action costs of OLTC and CB at time t respectively; 1.

2. Day-ahead objective function constraints (1) Power flow constraints Where: P i , Q i are the active power and reactive power injected into node i respectively; G ij , B ij and δ ij are the branch conductance, susceptance and phase angle difference between nodes i and j respectively; U i , U j are the voltages at nodes i and j respectively; (2) Safety operation constraints in the day-ahead phase Where: v i,max 、v i,min are the upper and lower limits of the voltage modulus at node i; l ij,max is the upper limit of the branch current modulus between nodes i and j; v i,t is the voltage at node i at time t; l ij,t is the branch current between nodes i and j at time t; (3) Relevant constraints of discrete devices; ① Operation constraints of on-load tap-changing transformer OLTC: Where: is the actual gear position of the OLTC between nodes i and j at time t; and are the upper and lower limits of the OLTC gear respectively; T ij,t is the gear position of OLTC at time t; is the adjustment step size of OLTC; ②Related constraints of parallel capacitor bank CB: Where: is the switching capacity of CB at node j at time t; They are the upper and lower limits of the number of CB switching groups respectively; is the compensation capacity of unit CB; is the number of CB switching groups at time t.

4. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 2 is characterized in that: In the intraday stage, first, fix the gear setting value of the shunt capacitor CB and the on-load tap-changing transformer OLTC within 24 hours in the day-ahead stage; second, combine the minute-level photovoltaic and load output data, and use the photovoltaic inverter, static VAR compensator SVC, and energy storage system ESS to achieve real-time regulation of the distribution network voltage; specifically, include: 1.

1. Establishing the intraday objective function (1) Minimum active network loss Where: Δt is the time interval of the scheduling cycle; (2) Minimum voltage deviation Where: N b is the number of network nodes; U i,t is the voltage modulus at node i at time t; is the node voltage rating; 1.

2. Intraday objective function constraints (1) Energy storage device operation constraints Where: are the lower and upper limits of the charging power of the energy storage device at node j, respectively; are the lower and upper limits of the discharge power of the energy storage device at node j respectively; A char is the charging decision variable; A disc is the discharge decision variable; E j,t is the energy stored in the energy storage device at time t; are the charging and discharging efficiency of the energy storage device respectively; are the upper and lower limits of energy storage capacity respectively; (2) Static Var Compensator (SVC) Operation Constraints Where: They are the upper and lower limits of reactive power output of SVC, is the reactive power output of SVC at time t; (3) PV inverter output constraints Where: They are the upper and lower limits of the reactive output of the photovoltaic inverter respectively; is the capacity of the inverter; is the active output of the photovoltaic inverter at time t; The photovoltaic inverter is outputting reactive power at all times.

5. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 1 is characterized in that: In step 2, the standard whale optimization algorithm is improved, including using the Sobol sequence to generate a uniformly distributed initial solution. The Sobol sequence initialization formula is: x1=x min +λ(x max -x min )(14); Where: x max 、x min are the upper and lower limits of the particle position respectively; λ is a random number in the interval [0,1] generated by the Sobol sequence; x1 is the position of the first whale after the update, and the same applies to other whales.

6. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 5 is characterized by: In step 2, the standard whale optimization algorithm is improved, including improving the convergence factor, balancing and improving the algorithm's exploration and local development capabilities; The nonlinear convergence factor is used, as shown in formula (15): Where: a initial is the initial value of the convergence factor iteration; a final is the iterative termination value of the convergence factor; μ is the nonlinear factor; t is the current number of iterations; T is the maximum number of iterations.

7. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 6 is characterized by: In step 2, the standard whale optimization algorithm is improved, including the introduction of a differential evolution algorithm combined with Cauchy perturbation to increase population diversity during the iteration process and help the algorithm escape from the local optimum.

8. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 7 is characterized by: The differential evolution algorithm combined with Cauchy perturbation is introduced to increase the population diversity in the iteration process and help the algorithm escape from the local optimum, including: ① Mutation operation: differentially scale the two vectors and add them to a third random vector to generate a mutation vector; Where: ν i,G+1 is the generated mutation vector; cauchy(0,1) is the Cauchy operator; and are 3 different random parent individuals; ②Crossover operation: In order to enhance the diversity and anti-interference ability of the algorithm population, the mutation vector and the target vector are crossed; Where: u i,G+1 is the new vector after crossover; P is the crossover probability; D is the dimension; is the global optimal position in the jth dimension; is the optimal position of the individual in the jth dimension; rand(j) is a random number between [0,1]; ν i,G+1 The generated mutation vector; x i,G is a random parent individual without crossover; ③Selection operation: Compare the test vector with the target vector according to the greedy criterion, retain the one with the smaller fitness value, adjust the individual position by learning from excellent individuals, and improve the global optimization ability of the algorithm; the selection operation is as follows: Where: f(v i,G+1 ) is the individual fitness after crossover; f(x i,G ) is the fitness of the parent individual without crossover.

9. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 1 is characterized by: In step 3, the improved whale optimization algorithm is used to solve the model, including the following steps: S3.1, initialization parameters: population size, spatial dimension and upper and lower limits of search space; S3.2, use Sobol sequence to initialize population position; S3.3, calculate individual fitness values, find the optimal fitness value and the optimal individual; perform mutation and crossover operations according to the crossover probability; S3.4, update a according to formula (15), then update A according to formula (11), and update c and p at the same time; S3.5, when p<0.5, if |A|>1, enter S3.6, if |A|≤1, enter S3.7, when p≥0.5, enter S3.8; S3.6, perform global search, learn excellent individuals according to formula (18), update the positions of poor individuals, and further update the individual positions according to the position formula in formula (11); S3.7, surround the prey and update the individual position according to formula (12); S3.8, spiral bubble net predation, update individual positions according to formula (13); S3.9, determine whether the iteration termination condition is met, and output the global optimal solution and position information, otherwise enter S3.3 to continue execution.

10. The active distribution network multi-time scale collaborative optimization method based on the improved whale algorithm according to claim 9 is characterized in that: In S3.4, the position update formula is as follows: Where: x(t) and x(t+1) are the position vectors of the whale before and after the update respectively; x rand is any whale position vector; A and C are coefficients; r is a random number between [0,1]; a is the convergence factor, where a = 2-2t / T, T is the maximum number of iterations; D rand is a random distance.

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