A method for solving optimal power flow problem of wind power generator and FACTS device

Abstract

The application discloses a method for solving optimal power flow problems of wind power generators and FACTS devices, which comprises the following steps: establishing a mathematical model of coordinated configuration of the wind power generators and the FACTS devices, a target function, a constraint condition, updating a population with parameters by using a sine-cosine optimization algorithm, obtaining an optimal individual position by using a horizontal and vertical cross algorithm on the updated population, searching for individuals near the optimal individual position by using a pattern search strategy, taking the target function as a fitness function, and performing optimal selection on the optimal individual and the individuals near the optimal individual by using a greedy strategy until the number of iterations is greater than or equal to a preset threshold value, and stopping the optimal selection to obtain a final optimal individual; and solving the optimal power flow problems of the wind power generators and the FACTS devices by using the wind power generator and FACTS device parameters in the final optimal individual. The method has high capability of solving OPF problems.

Description

Technical Field

[0001] This invention belongs to the field of power system distribution network technology, specifically relating to a method for solving the optimal power flow problem of wind turbines and FACTS devices. Background Technology

[0002] Currently, due to increased global emphasis on environmental protection, the growing consumption of fossil fuels, and the imposition of carbon taxes, utilities are turning their attention to renewable energy sources beyond conventional energy. Consequently, renewable energy has received widespread attention from researchers, and more and more renewable energy sources are being encouraged to integrate into the power grid for electricity conversion. At the same time, safety, power quality, efficiency, and stability are key objectives that modern power grids strive for in the face of increasing demand and distributed generation congestion. Flexible AC transmission systems (FACTS) are increasingly widely used in modern power systems to address electricity demand and other issues. Therefore, integrating renewable energy with FACTS devices to solve the optimal power flow (OPF) problem is essential.

[0003] The Operating Power Flow (OPF) problem, as one of the fundamental problems in power system operation and planning, is of great research significance for the reliable and economical operation of power systems. The main objective of the OPF problem is to optimize power generation or fuel costs by adjusting generator dispatching, generator terminal voltage, transformer tap settings, and reactive power compensation, while satisfying constraints such as power flow balance, generator capacity, and network security. The OPF problem is a complex non-convex nonlinear optimization problem. In recent years, many methods have been studied for solving the OPF problem, such as nonlinear programming (NLP), quadratic programming, integer programming, linear programming, and decomposition methods. Although these methods can find the global optimum to some extent, they also have significant drawbacks: the problem can only be solved with linear objective functions and constraints, but linear approximation operations for the OPF problem will lead to large errors in the final optimization results. Therefore, the above techniques are not suitable for solving the OPF problem.

[0004] To overcome the above shortcomings, various heuristic optimization techniques have attracted widespread attention from researchers because they do not require any specific shape or constraints on the objective function, thus effectively solving the OPF problem. Currently, scholars in this research field have proposed a variety of heuristic algorithms, among which the most classic are ant colony optimization and particle swarm optimization. Recent heuristic algorithms include gray wolf optimization, starvation search, Harris eagle algorithm, artificial bee colony algorithm, and swarm predation algorithm. Many of these heuristic algorithms have shown good performance on the OPF problem, including improved and hybrid versions. For example, a new fuzzy adaptive hybrid configuration has been developed, combining a new PSO and DE approach oriented towards joint adaptation to solve the multi-objective OPF problem; the combination of the two minimizes the power generation cost. These algorithms have achieved good results to a certain extent, but their speed and accuracy still need improvement.

[0005] Therefore, there is an urgent need to design a method with high speed and accuracy to solve the OPF problem of wind turbines and FACTS devices. Summary of the Invention

[0006] This invention provides a method for solving the optimal power flow problem of wind turbines and FACTS devices, which has a high ability to solve the OPF problem.

[0007] A method for solving the optimal power flow problem of wind turbines and FACTS devices includes:

[0008] (1) Establish a mathematical model for the coordinated configuration of wind turbine generators and FACTS equipment based on the IEEE 30 bus system; establish an objective function for the optimal power flow problem with the goal of minimizing energy cost;

[0009] (2) Construct a population, which includes multiple individuals. Each individual is composed of multidimensional vector parameters, which are composed of wind turbine and FACTS equipment parameters. Initialize the position of each individual in the population based on the constraints, and initialize the parameters in each individual.

[0010] (3) Use the sine and cosine optimization algorithm to perform a global search on the parameters of the wind turbine and FACTS equipment to update the position of each individual in the population and obtain the updated population. Then, use the horizontal and vertical cross algorithm on the updated population to obtain the optimal individual position.

[0011] (4) Use a pattern search strategy to search for individuals near the optimal individual position. Use the objective function as the fitness function and a greedy strategy to select the optimal individual and its nearby individuals. Iterate steps (3) and (4) until the number of iterations is greater than or equal to the preset threshold, and then stop the selection to obtain the final optimal individual.

[0012] (5) Solve the optimal power flow problem of wind turbines and FACTS devices by using the parameters of wind turbines and FACTS devices in the final optimal individual.

[0013] The mathematical model for the coordinated configuration of wind turbines and FACTS equipment includes a line power flow equation mathematical model for thyristor-controlled series compensators, thyristor-controlled phase shifters, and static var compensators, while the wind turbine model is a random probability mathematical model of wind energy.

[0014] The mathematical model for the power flow equation of the thyristor-controlled series compensator is as follows:

[0015] From bus m to bus n:

[0016]

[0017]

[0018] From bus n to bus m:

[0019]

[0020]

[0021] Among them, P mn P represents the active power between bus m and bus n. nm Q represents the active power between bus n and bus m. mn Q represents the reactive power between bus m and bus n. nm V represents the reactive power between bus n and bus m. m and V n δ represents the voltage values ​​of the m-th and n-th rows of the bus, respectively. m and δ n G represents the phase angle of each bus. mn and B mn These represent the line conductance and susceptance between bus m and bus n, respectively;

[0022] The mathematical model of the line power flow equation for a thyristor-controlled phase shifter is as follows:

[0023]

[0024]

[0025]

[0026]

[0027] Where Φ represents the phase shift angle introduced by the thyristor-controlled phase shifter;

[0028] The mathematical model of the power flow equation for a static var compensator is as follows:

[0029]

[0030] Among them, Q SVC B represents the reactive power provided by the SVC. SVC Indicates the equivalent susceptance in the line;

[0031] The mathematical model for the random probability of wind energy is as follows:

[0032]

[0033]

[0034] Where f w (p w ) represents the probability of wind power output; c and k represent the Weibull scale factor and shape parameter, respectively; v r v out v in p represents the rated wind speed, the turbine cut-out wind speed, and the turbine cut-in wind speed, respectively. wr This indicates the rated output of a single wind turbine.

[0035] The probability f of wind power output power being in a continuous region between zero and rated power w (p w )for:

[0036]

[0037] The objective functions for the optimal power flow problem are established with the goal of minimizing energy costs. These objective functions are the total generation cost objective function, the actual power loss objective function, and the total cost objective function.

[0038] Among them, the total power generation cost target C gen for:

[0039]

[0040] Where, N TG N represents the number of fuel generators. WG C represents the number of wind turbines. Ti C represents the fuel cost of generating electricity for the i-th generator; w,i C represents the direct cost of wind power for the i-th generator; Rw,i C represents the reserve cost of the i-th generator; Pw,i P represents the penalty cost of the i-th generator; TGi P represents the output power of the i-th fuel generator;ws,i P represents the planned power of the i-th wind turbine; wav,i Let represent the wind power probability density function of the i-th wind turbine.

[0041] Actual power loss P loss for:

[0042]

[0043] Among them, G m(ij) δ represents the transfer conductance of the m-th branch path connecting buses i and j, and nl represents the number of transmission lines. i and δ j V represents the angle difference between the voltage amplitudes of the i-th and j-th voltage lines, respectively. i and V j These represent the voltage values ​​of the i-th and j-th bus rows, respectively.

[0044] Total cost target C gross for:

[0045] C gross =C gen +P loss ×n

[0046] Where n is the conversion coefficient.

[0047] The constraints include:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] Among them, P Gi and Q GiP represents the active and reactive power generated by the i-th generator set, respectively; Li and Q Li P represents the active and reactive load demand at load bus i; is and Q is Y represents the active and reactive power injected by TCP at load bus i, respectively; ij θ represents the admittance of the transmission line between the i-th and j-th buses; ij δ represents the admittance phase angle between the i-th and j-th busbars; ij This represents the angle difference in voltage magnitude between the i-th and j-th buses; NB represents the number of buses, NG represents the total number of generator buses, NT represents the number of transformers, NL represents the number of transmission lines, NTCPS represents the number of TCPS, and P... Gi and Q Gi V represents the active and reactive power generated by the i-th generator set; Gi T represents the voltage amplitude of the i-th generator set; t This represents the number of turns in the t-th transformer coil. and S represents the minimum and maximum voltage amplitudes at load bus i. lq and Represented as the apparent power flow and the upper limit of the maximum apparent power flow for the i-th line; and Let represent the minimum and maximum values ​​of the series compensation degree of the m-th TCSC, respectively; and These represent the minimum and maximum values ​​of the phase shift angle for the nth TCPS, respectively. and N represents the minimum and maximum reactive power of the j-th SVC, respectively; TCSC N TCPS and N SVC These represent the number of TCSC, TCPS, and SVC devices in the wind power system, respectively.

[0060] Initialize the position of each individual in the population based on constraints, including:

[0061] The upper and lower bounds of the multidimensional vector parameters of each individual are determined based on the constraints. The position of each individual in the population is initialized based on these bounds, and the objective function value of each individual is calculated. (Throughout the algorithm, selection is based on the objective function value. Therefore, the objective function value is used throughout the entire algorithm; for example, when generating a new generation of the population, the objective function value is calculated for that population.)

[0062] The initialization formula is as follows:

[0063] X eg =LBeg +rand*(UB eg -LB eg ); e=1,2,3,…,E; g=1,2,3,…,G;

[0064] Among them, X eg Let LB be the position of the e-th individual on the g-th dimension in the population. eg UB is the lower bound of the e-th parameter in the g-th dimension. eg is the upper bound of the e-th parameter in the g-th dimension, rand is a uniformly distributed random real number greater than or equal to 0 and less than 1, E is the population size, and G is the dimension, i.e., the number of parameters to be optimized.

[0065] A sine and cosine optimization algorithm is used to perform a global search on the parameters of the wind turbine and FACTS equipment to update the position of each individual in the population, resulting in an updated population. The updated population contains the individual positions. for:

[0066]

[0067]

[0068] in, This represents the position of the e-th individual at iteration t. Let r4 be the individual at the optimal position after t iterations, where r4 is a random parameter between [0,1], T represents the number of iterations, a is a constant, t represents the index of the number of iterations, and r2 and r3 are random factors.

[0069] The optimal individual position is obtained by performing a cross-cutting algorithm on the updated population, including:

[0070] Each individual in the updated population is taken as the first parent individual. Horizontal crossover is performed to generate the first offspring individual. Using the objective function as the fitness function, the second parent individual is selected from the first parent individual and the first offspring individual. Vertical crossover is performed based on the second parent individual to generate the second offspring individual. Then, using the objective function as the fitness function, the third parent individual is selected from the second parent individual and the second offspring individual. The individual with the smallest objective function value among the third parent individuals is selected as the optimal individual, and the position of the optimal individual in the population is obtained.

[0071] A pattern search strategy is used to search for individuals x near the optimal individual location. e for:

[0072] x e =x0+v(h)*L

[0073] Where x0 is the position of the optimal individual, h∈(1,2,…,2G), and L represents the search step size;

[0074] A greedy strategy is used to select the optimal individual and its neighbors, including:

[0075] If f(x) e If f(x0) < f(x0), then L = δL, δ > 1

[0076] Where f(·) is the objective function, and δ is the acceleration factor, representing expanding the search range;

[0077] If f(x) e If f(x0) > f(x0), then L = λL, λ < 1

[0078] Where λ represents the deceleration factor, indicating a narrowing of the search range;

[0079] If the preset threshold for the number of iterations is not reached, continue iterating steps (3) and (4) until the preset threshold is reached, then stop the selection process to obtain the final optimal individual.

[0080] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0081] This invention proposes an improved sine and cosine optimization algorithm based on a cross-sectional mechanism and a pattern search algorithm. The former encourages individual communication, enriches the diversity of the population, and improves the individual's exploration ability. The latter provides a better solution for SCA by directly scanning the neighborhood of the best solution, which not only improves the stability of SCA, but also improves the ability to solve the OPF problem. Attached Figure Description

[0082] Figure 1 A flowchart illustrating a method for solving the optimal power flow problem of wind turbines and FACTS devices, provided for a specific implementation.

[0083] Figure 2 A schematic diagram of the basic circuit structure of the TCSC provided for a specific implementation method;

[0084] Figure 3 A schematic diagram of the basic circuit structure of TCPS provided for a specific implementation method;

[0085] Figure 4 A schematic diagram of the basic circuit structure of the SVC provided for a specific implementation method;

[0086] Figure 5 A detailed flowchart of the CPSCA algorithm provided for specific implementation methods;

[0087] Figure 6 The convergence curves of CPSCA and other improved algorithms obtained through simulation experiments are shown in the case where the total cost of wind power generation is used as the objective function, as provided for a specific implementation method. Detailed Implementation

[0088] The present invention will be explained in detail with reference to the accompanying drawings and specific examples.

[0089] like Figure 1 As shown, this invention provides a method for solving the optimal power flow problem of wind turbines and FACTS devices, with the following specific steps:

[0090] S1: Modeling is performed based on data provided by the IEEE 30 bus system, which combines wind turbines and FACTS devices; such as Figures 2 to 4 As shown, the model includes a FACTS model and a wind turbine model; wherein, the FACTS equipment includes a thyristor-controlled series compensator model (TCSC), a thyristor-controlled phase shifter model (TCPS), and a static var compensator model (SVC); the wind turbine model includes a wind energy stochastic probability model.

[0091] exist Figure 2 In this context, TCSC is a reactor X controlled by a thyristor. L and a fixed series capacitor X C It is composed of parallel lines. The mathematical model of the power flow equation for the TCSC is shown below:

[0092] • From bus m to bus n

[0093]

[0094]

[0095] • From bus n to bus m

[0096]

[0097]

[0098] Among them, P mn and Q mn V represents the active and reactive power between bus m and bus n; m and V n These represent the voltage values ​​of the m-th and n-th bus rows, respectively. δ m and δ n These represent the phase angles of each bus. G mn and B mn These represent the line conductance and susceptance between bus m and bus n, respectively;

[0099] exist Figure 3In China, TCPS (Transient Power Flow System) is an effective technique for continuously regulating steady-state power flow, damping inter-regional oscillations, and improving the transient stability limit of the system; it is an important component of power networks. The mathematical model of the TCPS line power flow equation is shown below:

[0100]

[0101]

[0102]

[0103]

[0104] Where Φ represents the phase shift angle introduced by TCPS;

[0105] exist Figure 4 In power supply systems, SVC (Self-Powered Dynamics) plays a crucial role, improving the power factor of the grid, reducing losses in power transformers and transmission lines, increasing power supply efficiency, and improving the power supply environment. The mathematical model of the SVC line power flow equation is shown below:

[0106]

[0107] Among them, Q SVC B represents the reactive power provided by the SVC. SVC The equivalent susceptance in the line is represented by the following mathematical model for the random probability of wind energy:

[0108]

[0109]

[0110] Where f w (p w ) represents the probability of wind power output; c and k represent the Weibull scale factor and shape parameter, respectively; v r v out v in p represents the rated wind speed, the turbine cut-out wind speed, and the turbine cut-in wind speed, respectively. wr This indicates the rated output of a single wind turbine.

[0111] The probability f of wind power output power being in a continuous region between zero and rated power w (p w )for:

[0112]

[0113] S2: Establish the objective function for the optimal power flow problem with the goal of minimizing energy cost. The objective functions are the total generation cost objective function, the actual power loss objective function, and the total cost objective function.

[0114] Among them, the total power generation cost target C gen for:

[0115]

[0116] Where, N TG N represents the number of fuel generators. WG C represents the number of wind turbines. Ti C represents the fuel cost of generating electricity for the i-th generator; w,i C represents the direct cost of wind power for the i-th generator; Rw,i C represents the reserve cost of the i-th generator; Pw,i P represents the penalty cost of the i-th generator; TGi P represents the output power of the i-th fuel generator; ws,i P represents the planned power of the i-th wind turbine; wav,i Let represent the wind power probability density function of the i-th wind turbine.

[0117] Actual power loss P loss for:

[0118]

[0119] Among them, G m(ij) δ represents the transfer conductance of the m-th branch path connecting buses i and j, and nl represents the number of transmission lines. i and δ j V represents the angle difference between the voltage amplitudes of the i-th and j-th voltage lines, respectively. i and V j These represent the voltage values ​​of the i-th and j-th bus rows, respectively.

[0120] Total cost target C gross for:

[0121] C gross =C gen +P loss ×n (15)

[0122] Where n is 10 3 ×0.10.

[0123] Construct constraints, which include:

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] Among them, P Gi and Q Gi P represents the active and reactive power generated by the i-th generator set, respectively; Li and Q Li P represents the active and reactive load demand at load bus i; is and Q is Y represents the active and reactive power injected by TCP at load bus i, respectively; ij θ represents the admittance of the transmission line between the i-th and j-th buses; ij δ represents the admittance phase angle between the i-th and j-th busbars; ij This represents the angle difference in voltage magnitude between the i-th and j-th buses; NB represents the number of buses, NG represents the total number of generator buses, NT represents the number of transformers, NL represents the number of transmission lines, NTCPS represents the number of TCPS, and P... Gi and Q Gi V represents the active and reactive power generated by the i-th generator set; Gi T represents the voltage amplitude of the i-th generator set; t This represents the number of turns in the t-th transformer coil. and S represents the minimum and maximum voltage amplitudes at load bus i. lq and Represented as the apparent power flow and the upper limit of the maximum apparent power flow for the i-th line; and Let represent the minimum and maximum values ​​of the series compensation degree of the m-th TCSC, respectively; and These represent the minimum and maximum values ​​of the phase shift angle for the nth TCPS, respectively. and N represents the minimum and maximum reactive power of the j-th SVC, respectively; TCSC N TCPS and N SVC These represent the number of TCSC, TCPS, and SVC devices in the wind power system, respectively.

[0136] S3: Using the method for solving the optimal power flow problem of wind turbines and FACTS devices proposed in this invention, namely the CPSCA algorithm, the optimal model parameter vector for solving the optimal power flow problem of wind turbines and FACTS devices is obtained, such as... Figure 5 As shown, the specific steps are as follows:

[0137] S3.1: Construct a population X, which includes multiple individuals. Each individual is composed of multidimensional vector parameters, which are composed of wind turbine and FACTS device parameters.

[0138] Parameter initialization involves determining the maximum number of iterations T and the population size N in the proposed method. Based on constraints, upper bounds UB and lower bounds LB are set for the parameter vectors of the wind turbine generator and FACTS equipment. The population size X is set appropriately to ensure random initialization covers the entire search space; therefore, it is set to 40 in this study. Each individual in the population consists of a D-dimensional vector; D represents the dimension of the optimization problem, i.e., the number of parameters to be optimized.

[0139] S3.2: Randomly initialize the individuals in population X within the upper and lower bounds, using the following initialization formula:

[0140] X eg =LB eg +rand*(UB eg -LB eg ); e=1,2,3,…,E; g=1,2,3,…,G; (27)

[0141] Among them, X eg Let LB be the position of the e-th individual on the g-th dimension of the population. eg UB is the lower bound of the e-th parameter in the g-th dimension. eg is the upper bound of the e-th parameter in the g-th dimension, rand is a uniformly distributed random real number greater than or equal to 0 and less than 1, E is the number of individuals in the population, and G is the dimension, i.e., the number of parameters to be optimized.

[0142] The objective function values ​​of the initialized individuals are calculated. The objective functions are the total power generation cost objective function, the actual power loss objective function, and the total cost objective function.

[0143] S3.3: The Sine-Cosine Optimization Algorithm (SCA) is used to perform a global search on the parameters of the wind turbine and FACTS equipment to update the position of each individual in the population, resulting in the updated population. The updated population contains the individual positions. for:

[0144]

[0145]

[0146] in, This represents the position of the e-th individual at iteration t. Let r4 be the individual at the optimal position after t iterations, where r4 is a random parameter between [0,1], T represents the number of iterations, a is a constant, t represents the index of the number of iterations, and r2 and r3 are random factors.

[0147] r1 determines the area of ​​the search space around the proposed solution; this parameter balances the algorithm's exploratory and exploitative capabilities. r2 controls the distance towards or outward from the endpoint. r3 represents a random weight; when r3 > 1, the algorithm tends to explore more, and when r3 < 1, the algorithm tends to exploit more. r4 is a random parameter between [0,1] used to switch the algorithm between sine and cosine update rules.

[0148] Calculate the objective function value for each individual in the updated population, and set the position of the individual with the smallest current fitness objective function value as the optimal individual. The optimal individual is then updated in subsequent cross-cutting strategies; subsequently, the updated optimal individual is used in pattern search.

[0149] S3.4: To improve the search performance of SCA and avoid the algorithm getting trapped in local optima too early, a crossover strategy is introduced. Each individual in the updated population is designated as the first parent. Horizontal crossover generates the first offspring. Using the objective function as the fitness function, a second parent is selected from the first parent and first offspring. Vertical crossover is then performed based on the second parent to generate the second offspring. Again, using the objective function as the fitness function, a third parent is selected from the second parent and second offspring. The individual with the smallest objective function value among the third parent is selected as the optimal individual, and the optimal individual's position in the population is determined.

[0150] The update process is as follows:

[0151]

[0152] in, and This represents two first-generation individuals (X) in the D dimension. id and Xjd The two first-generation individuals generated after the lateral search operation; ε1 and ε2 represent continuous uniform random numbers between (0,1); C1 and C2 represent random numbers between (-1,1).

[0153] After the horizontal crossover operation is completed, individual competition needs to be conducted in the first parent population X, that is, the second parent population needs to be selected from the first parent population and the first offspring population. The specific operation is as follows:

[0154]

[0155] Where F represents the objective function; MS hc This represents the first generation population generated through a lateral search operation. Although this selection process calculates the objective function value based on different objective functions, it consistently uses the above formula (greedy strategy) to select the second generation of parent individuals.

[0156] The second offspring are generated by vertical crossover based on the second parent individual. for:

[0157]

[0158] in, Indicates the parents in the second-generation individual population. and The i-th offspring individual in the d1-th dimension is obtained through a vertical crossover operation (d1≠d2); ε represents a random number between (0,1);

[0159] After the vertical crossover operation is completed, and the objective function is used as the fitness function, a third parent population is selected from the second parent population and the second offspring population. The individual with the smallest objective function value is selected from the third parent population as the optimal individual. The position of the optimal individual is used as the initial point x0 of the pattern search strategy for a fine local search.

[0160] S3.5: Use a pattern search strategy to search for individuals x near the optimal individual location. e for:

[0161] x e =x0+v(h)*L (34)

[0162] Where x0 is the position of the optimal individual, h∈(1,2,…,2G), and L represents the search step size; a greedy strategy is used to select the optimal individual and its neighboring individuals, including:

[0163] If f(x) e If f(x0) < f(x0), then L = δL, δ > 1

[0164] Where f(·) is the objective function, and δ is the acceleration factor, representing expanding the search range;

[0165] If f(x) e If f(x0) > f(x0), then L = λL, λ < 1

[0166] Where λ represents the deceleration factor, indicating a narrowing of the search range;

[0167] If the preset threshold for the number of iterations has not been reached, continue iterating through steps S3.3 to S3.5 until the preset threshold is reached, at which point the selection process stops and the final optimal individual is obtained.

[0168] This invention provides a method for solving the optimal power flow problem in wind turbines and FACTS devices, namely the CPSCA algorithm. CPSCA first executes the basic strategy of the original SCA optimization algorithm to update the population, and then performs a crossover mechanism operation on the updated population. The detailed process of the crossover in CPSCA is as follows: Assume the current candidate solution set is X, which contains N candidate individuals. First, through lateral crossover, information exchange between two individuals is encouraged, and two new individuals MS are generated through the lateral crossover operation. hc It then competes with other individuals in the parent population to select the best individual. Each individual then performs vertical cross-operations across different dimensions, expanding the search space and driving the exploration trend through learning in these different dimensions.

[0169] Next, a pattern search algorithm is performed after the cross-cutting search method to discover higher-quality candidate solutions. The quality of the population is improved by merging nearby points for optimization. In the implementation, the `patternsearch()` function in Matlab is called directly. Furthermore, the iteration termination condition for pattern search is set to 0.1 times the maximum number of iterations of CPSCA in the experiment, with other parameters set to default values. In addition, since the randomness of CPSCA can lead to the solution set going out of bounds, the SF technique is used during the CPSCA iteration process to extract effective information from infeasible solutions and guide the algorithm towards a globally feasible solution.

[0170] like Figure 6 The image shows the convergence curves of CPSCA compared to recent metaheuristic algorithms, including PSO, HGWOSCA, DE, SaDE, CBA, FPA, MSCA, and SCA, in a case where the total cost of wind power generation is the objective function. CPSCA significantly outperforms the other algorithms, indicating better convergence.

[0171] As shown in Tables 1 to 3, the control parameters of the IEEE 30 test system obtained by CPSCA and the latest metaheuristic algorithms under different objective functions are shown. Based on the objective function values ​​obtained from the control parameters, it can be seen that the objective function value obtained by using the CPSCA algorithm provided by this invention is the minimum.

[0172] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

[0173] Table 1: Comparison of CPSCA algorithm with other algorithms for the total power generation cost target.

[0174]

[0175] Table 2: Comparison of CPSCA algorithm with other algorithms for actual power loss.

[0176]

[0177] Table 3: Comparison of CPSCA algorithm with other algorithms for the total cost objective

[0178]

Claims

1. A method for solving the optimal power flow problem of wind turbines and FACTS devices, characterized in that, include: (1) Establish a mathematical model for the coordinated configuration of wind turbine generators and FACTS equipment based on the IEEE 30 bus system; Establish the objective function for the optimal power flow problem with the goal of minimizing energy cost; (2) Construct a population, which includes multiple individuals. Each individual is composed of multidimensional vector parameters, which are composed of wind turbine and FACTS equipment parameters. Initialize the position of each individual in the population based on the constraints. (3) Use the sine and cosine optimization algorithm to perform a global search on the parameters of the wind turbine and FACTS equipment to update the position of each individual in the population and obtain the updated population. Then, use the horizontal and vertical cross algorithm on the updated population to obtain the optimal individual position. The specific steps of step (3) include: The Sine and Cosine Optimization Algorithm (SCA) is used to perform a global search on the parameters of the wind turbine and FACTS equipment to update the position of each individual in the population, resulting in the updated population. The updated population contains the individual positions. for: ,in, express The first iteration The location of each individual In order to be in The individual at the optimal position in the next iteration. It is a random parameter between [0,1]. Indicates the number of iterations; It is a constant. An index representing the number of iterations. , It is a random factor; The parameter determines the area of ​​the search space surrounding the proposed solution, and can balance the algorithm's exploratory and excavation capabilities. Used to control the distance toward or outward from the endpoint; Represents random weights, when >1 indicates that the algorithm is more inclined to explore, when This indicates that the algorithm is more inclined to be developed; It is a random parameter between [0,1] used by the algorithm to switch between sine and cosine update rules; Calculate the objective function value of each individual in the updated population, and set the position of the individual with the smallest current fitness objective function value as the optimal individual. The optimal individual will be updated in the subsequent cross-cutting strategy. Afterwards, the updated optimal individual will be used in the pattern search. To improve the search performance of SCA and avoid the algorithm getting trapped in local optima too early, a cross-crossing strategy is introduced. Each individual in the updated population is taken as the first parent individual. Cross-crossing is performed horizontally to generate the first offspring individual. The objective function is used as the fitness function to select the second parent individual from the first parent individual and the first offspring individual. Based on the second parent individual, cross-crossing is performed vertically to generate the second offspring individual. The objective function is used as the fitness function again to select the third parent individual from the second parent individual and the second offspring individual. The individual with the smallest objective function value among the third parent individuals is selected as the optimal individual, and the position of the optimal individual in the population is obtained. The update process is as follows: ,in, and This represents two first-generation individuals in the D dimension. and The two first-generation individuals generated after the lateral search operation; and Represents a continuous uniform random number between (0,1); and Represents a random number between (-1, 1); After the lateral crossover operation is completed, individual competition needs to be conducted in the first parent population X, that is, the second parent population needs to be selected from the first parent population and the first offspring population. The specific operation is as follows: , where f represents the objective function; This indicates the first generation population generated through the horizontal search operation. Although the objective function values ​​are calculated based on different objective functions, the above formula is used to select the second generation population of parents. The second offspring are generated by vertical crossover based on the second parent individual. for: ,in, Indicates the parents in the second-generation individual population. and Through the vertical cross operation in the first Wei Shang Di Individual offspring ; Represents a random number between (0, 1); After the vertical crossover operation is completed, and using the objective function as the fitness function, a third generation of individuals is selected from the second and second generation populations. The individual with the smallest objective function value among the third generation is then selected as the optimal individual, and the position of this optimal individual is used as the initial point for the pattern search strategy. , perform a fine local search; (4) use a pattern search strategy to search for individuals near the optimal individual position, use the objective function as the fitness function, use a greedy strategy to select the optimal individual and its nearby individuals, iterate steps (3) and (4) until the number of iterations is greater than or equal to the preset threshold, stop the selection to obtain the final optimal individual; (5) Solve the optimal power flow problem of wind turbines and FACTS devices by using the parameters of wind turbines and FACTS devices in the final optimal individual.

2. The method for solving the optimal power flow problem of wind turbines and FACTS devices according to claim 1, characterized in that, The mathematical model for the coordinated configuration of wind turbines and FACTS equipment includes a line power flow equation mathematical model for thyristor-controlled series compensators, thyristor-controlled phase shifters, and static var compensators, while the wind turbine model is a random probability mathematical model of wind energy. The mathematical model for the power flow equation of the thyristor-controlled series compensator is as follows: From bus m to bus n: , From bus n to bus m: , ,in, For bus m to bus n The active power between For bus n to bus m The active power between For bus m to bus n The reactive power between For bus n to bus m The reactive power between and They represent the first m Rank and First n The voltage value of the busbar. and These represent the phase angles of each bus. and They represent buses respectively. m and bus n The line conductance and susceptance between them; The mathematical model of the line power flow equation for a thyristor-controlled phase shifter is as follows: , , , ,in, This indicates the phase shift angle introduced by a thyristor-controlled phase shifter; The mathematical model of the power flow equation for a static var compensator is as follows: ,in, This indicates the reactive power provided by the SVC. Indicates the equivalent susceptance in the line; The mathematical model for the stochastic probability of wind energy is as follows: , ,in This indicates the probability of wind power output. c and k These represent the Weibull scale factor and shape parameter, respectively. , , These represent the rated wind speed, the turbine cut-out wind speed, and the turbine cut-in wind speed, respectively. This indicates the rated output of a single wind turbine.

3. The method for solving the optimal power flow problem of wind turbines and FACTS devices according to claim 2, characterized in that, The probability that the wind power output power is in a continuous region between zero and rated power for: .

4. The method for solving the optimal power flow problem of wind turbines and FACTS devices according to claim 1, characterized in that, The objective functions for the optimal power flow problem are established with the goal of minimizing energy costs. These objective functions are the total generation cost objective function, the actual power loss objective function, and the total cost objective function. Among them, the total power generation cost target for: in, Indicates the number of fuel generators. Indicates the number of wind turbines. Indicates the first The fuel cost of generating electricity for a single generator; Indicates the first The direct cost of wind power for each generator; Indicates the first The reserve cost of a generator; Indicates the first The penalty cost of each generator; Indicates the first The output power of the fuel generator; Indicates the first The planned power output of each wind turbine; Indicates the first The wind power probability density function of a wind turbine generator; Actual power loss for: ,in, Indicates connection bus and j The m Transfer conductance of branch lines, Indicates the number of transmission lines. and They represent the first The angle difference between the voltage amplitudes of the j-th and j-th lines, They represent the first Rank and First j The voltage value of the busbar; Total cost target for: .

5. The method for solving the optimal power flow problem of wind turbines and FACTS devices according to claim 1, characterized in that, The constraints include: , , , , , , , , , , ,in, and They represent the first The active and reactive power generated by the generator sets; and Indicates the load bus The active and reactive power load demand at the location; and This indicates that TCP is on the load bus. The active power and reactive power injected at the respective locations; Indicates the first Article and Section j Admittance of transmission lines between busbars; Indicates the first Article and Section j Admittance phase angle between the busbars; Indicates the first Article and Section j The angle difference in voltage amplitude between the busbars; Indicates the number of busbars. The total number of generator buses is listed. Indicates the number of transformers. Indicates the number of transmission lines. Indicates the number of TCPS. and Indicates the first i The active and reactive power generated by the generator sets; Indicates the first i Voltage amplitude of the generator set; Indicates the first The number of turns in the coil of a transformer. and Represented as load bus The minimum and maximum voltage amplitudes and Represented as the first The apparent power current and the maximum apparent power current limit of each line; and They represent the first Minimum and maximum values ​​of TCSC series compensation degree; and They represent the first Minimum and maximum values ​​of the phase shift angle of each TCPS; and They represent the first Minimum and maximum reactive power of each SVC; , and These represent the number of TCSC, TCPS, and SVC devices in the wind power system, respectively.

6. The method for solving the optimal power flow problem of wind turbines and FACTS devices according to claim 1 or 5, characterized in that, Initialize the position of each individual in the population based on constraints, including: The upper and lower bounds of the multidimensional vector parameters of each individual are determined based on the constraints. The position of each individual in the population is then initialized based on these upper and lower bounds, using the following initialization formula: in, For the first in the population g The first dimension e The location of each individual For the first e The first g The lower bound of the parameter of dimension, For the first e The first g The upper bound of the parameter of dimension, The numbers are uniformly distributed random real numbers that are greater than or equal to 0 and less than 1. E For the population size, G The dimension is the number of parameters that need to be optimized.

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