Power distribution network reactive power optimization method and equipment based on full-pure embedding method and sparrow algorithm

Abstract

The invention discloses a power distribution network reactive power optimization method and device based on a full-pure embedding method and a sparrow algorithm, and the method comprises the steps: building a power distribution network reactive power voltage optimization model considering a distributed power supply by taking the minimum operation cost of a power distribution network and the minimum fluctuation of a comprehensive load curve as targets; deriving all-pure embedded power flow models of different node types of the power distribution network, and constructing a recursive solving equation to solve power series coefficients in a Maclaurin expansion of the all-pure embedded models; a sparrow algorithm is improved by using a chaos-sine-cosine algorithm-Leve flight strategy, reactive voltage optimization solution of the power distribution network is considered in combination with a full-pure embedded power flow algorithm, and an optimal compromise scheme is obtained for a generated Pareto solution set through an information entropy-TOPSIS method. According to the method, the problems that the difficulty of stably and efficiently solving the multi-target optimization operation problem of reactive compensation equipment and flexible resources in a power system containing a distributed power supply is relatively high, the algorithm applicability is poor, and the solving efficiency is low are solved.

Description

Technical Field

[0001] The invention belongs to the field of electric power systems, and in particular relates to a distribution network reactive power optimization method and equipment based on a holomorphic embedding method and a sparrow algorithm. Background Art

[0002] In order to actively respond to the "dual carbon" strategic goals, realize the transformation of energy supply and demand, and accelerate the construction of a new power system, the penetration rate of distributed power sources in the distribution network has been continuously improved, making the distribution network transform from a single power source to multiple power sources and two-way flow of power. Furthermore, the intermittent and random nature of distributed power sources has brought challenges to the reactive power optimization problem of the distribution network. How to fully dispatch the reactive compensation equipment and flexible resources of the distribution network to smooth voltage fluctuations, reduce operating costs, improve the power supply quality of the distribution network, and assist the stable and rapid transformation of the power system has great research value.

[0003] Power flow analysis is the basis for optimizing the operation of power systems. Traditional power flow algorithms for distribution networks include the Newton method and the forward-backward method. The forward-backward method cannot handle weak ring network structures well in new power systems and has certain applicability deficiencies. The Newton method has the problem of initial value dependence, which leads to poor convergence performance in distribution networks with flexible and changeable scenarios. In addition, the Jacobi matrix needs to be updated repeatedly during the iterative solution process of this method, which has a large amount of calculation and low efficiency. Once the initial value is not selected appropriately, the number of iterations will increase sharply, the Jacobi matrix will be singular, and the power flow calculation will not converge or will converge to a low voltage solution. At the same time, when a low voltage solution appears in the power flow calculation, a clear signal cannot be issued during the optimization process, which further affects the optimization process and causes the optimization result to obtain an inoperable solution.

[0004] For optimization algorithms, in view of the complex and changeable optimization scenarios of new power systems and the increasingly serious non-convex phenomenon of solution space, the optimization problem of the operating status of reactive compensation equipment and energy storage in the distribution network of distributed power sources is a multi-objective, multi-constrained and multi-dimensional problem. Although traditional optimization algorithms are simple and easy to implement, their applicability is getting worse and worse, and it is impossible to obtain acceptable solutions in a short time. Therefore, a large number of heuristic swarm intelligence optimization algorithms have been proposed one after another, such as particle swarm optimization (PSO) algorithm and ant colony optimization (Ant Colony Optimization) algorithm. The common point of these algorithms is that the algorithm is simple to implement and has good optimization performance. However, the optimization mechanism of the heuristic swarm intelligence optimization algorithm has a certain degree of sporadicity. When the search in the solution space is not comprehensive enough, it is easy to be premature and fall into the local optimum. Therefore, it is necessary to introduce optimization algorithms with higher performance and higher applicability in new power systems.

[0005] The Chinese patent with publication number CN116960998A discloses a power grid dispatching method and device based on an improved sparrow search algorithm, which establishes the output constraints of distributed power sources in the power grid system and the objective function of optimizing operation, collects the output data of photovoltaic arrays, load power consumption and wind turbines predicted by the power grid system; initializes the energy storage output and initial state of the battery according to the output data, sets the parameters of the sparrow search algorithm, initializes the position and optimal solution set of each sparrow, and uses the total cost and wind and solar abandonment rate as the fitness of the sparrow; calculates the fuzzy matrix between the dominance relationship and the optimal solution set in the sparrow population, and determines the sparrow population according to the dominance relationship, and probabilistically selects the optimal solution according to the fuzzy matrix to update the position of the population; outputs the optimal solution when the number of iterations is reached to optimize the output of the battery and the micro gas turbine. The sparrow search algorithm described in the invention requires a large number of iterative updates and calculations of the dominance relationship and fuzzy matrix in the sparrow population, which increases the computational complexity and time consumption of the solution process. Especially in the multi-objective optimization process, the search space is very large, which may make the algorithm difficult to schedule in real time in practical applications. Summary of the invention

[0006] The present invention provides a distribution network reactive power optimization method and device based on the holomorphic embedding method and the sparrow algorithm, aiming to solve the problems of high difficulty, poor algorithm applicability and low solution efficiency in robustly and efficiently solving multi-objective optimization operation problems of reactive compensation equipment and flexibility resources in a power system containing distributed power sources.

[0007] In order to solve the above technical problems, the present invention provides a distribution network reactive power optimization method based on the holomorphic embedding method and the sparrow algorithm, comprising the following steps:

[0008] Firstly, with the goal of minimizing the operating cost of the distribution network and minimizing the fluctuation of the comprehensive load curve, the energy storage system, switchable capacitor group, wind power and photovoltaic power generation on the low-voltage side of the distribution network are taken as optimization variables to establish a distribution network reactive voltage optimization model considering distributed power sources.

[0009] Using a non-initial value-dependent non-iterative recursive holomorphic embedded power flow algorithm, the holomorphic embedded power flow model for different node types in the distribution network is derived. Matrix changes are used to construct a recursive solution equation to solve the power series coefficients in the Maclaurin expansion of the holomorphic embedded model.

[0010] The sparrow algorithm is improved by using chaos-sine-cosine algorithm-Levy flight strategy. Combined with the holomorphic embedded power flow algorithm, the reactive voltage optimization solution of the distribution network considering distributed power sources is solved. The best compromise solution is obtained for the Pareto solution set generated by the sparrow algorithm through the information entropy-TOPSIS method.

[0011] Preferably, the objective function in the reactive power voltage optimization model of the distribution network of the distributed power source with the goal of minimizing the distribution network operation cost is specifically:

[0012] min f1=C ess +C MT +C LA +C loss

[0013] Where min f1 is the distribution network operation cost objective function; C ess is the power call cost of the energy storage system; C MT is the micro-turbine dispatching cost; C LA is the cost of load participating in distribution network dispatching in each period; C loss It is the electricity loss cost of the distribution network in each period.

[0014] The objective function with the goal of minimizing the fluctuation of the comprehensive load curve is as follows:

[0015]

[0016] Where, min f2 is the comprehensive load curve fluctuation objective function; w1 and w2 are the weight coefficients of the two evaluation indicators; and are the maximum and minimum values ​​of the daily load power of the distribution network respectively; is the average daily load of the distribution network; P g (t) is the value of the daily load of the distribution network at time t; P g (t+1) is the value of the daily load of the distribution network at time t+1.

[0017] Preferably, the constraints of the reactive voltage optimization model of the distribution network of the distributed power source specifically include: distributed generation power constraints, voltage constraints, branch power constraints, total power conservation constraints, energy storage device constraints, reactive compensation equipment constraints, and micro-gas unit climbing constraints.

[0018] The distributed generation power constraint is expressed as:

[0019]

[0020] Where P DG (t) is the active power generated by the distributed generation in the distribution network at time t; They are the upper and lower limits of the distributed generation active power respectively.

[0021]

[0022] In the formula, k fore is the prediction error coefficient of wind and solar power output, k foreThe closer it is to 0, the higher the prediction accuracy; It is the day-ahead forecast value of distributed generation output.

[0023] The voltage constraint is expressed as:

[0024]

[0025] Where U i is the voltage amplitude of node i; are the upper and lower limits of the voltage amplitude at node i respectively.

[0026] The branch power constraint is expressed as:

[0027]

[0028] Where P L is the power delivered by the Lth branch in the distribution network; They are the upper and lower limits of the transmission power of the Lth branch respectively.

[0029] The total power conservation constraint is expressed as:

[0030] P TG，t =P cl，t -P DG.t +P LA，t +P ESS，t

[0031] Where P TG，t is the active power output of the conventional unit at time t; P cl，t is the active power of the uncontrollable load at time t; P DG，t is the active output of the distributed generation at time t; P LA，t , P ESS，t are the active power of load and energy storage at time t, respectively. ESS，t A positive value indicates that the energy storage absorbs active power, and a negative value indicates that the energy storage emits active power.

[0032] The energy storage device constraint is expressed as:

[0033]

[0034]

[0035] In the formula, is the upper power limit of the energy storage device; η charge , η discharge are the charging and discharging efficiency of the energy storage device, respectively; E are the upper limits of charge and discharge efficiency respectively; ESS，t and E ESS，t+1are the amount of electricity stored in the energy storage device at time t and time t+1 respectively; Δt is a time period; and They are the upper and lower limits of the capacity of the energy storage device respectively.

[0036] The reactive power compensation equipment constraint is expressed as:

[0037]

[0038] In the formula, Q CB.j.t is the reactive power compensation of capacitor bank j in period t; Q CB is the reactive power compensation of a single capacitor bank; b j.t is the number of capacitor bank j switched on and off in period t; is the maximum number of switched capacitor groups j.

[0039] The ramp constraint of the micro-turbine unit is expressed as:

[0040]

[0041] In the formula, R u，k , R d，k are the upper and lower limits of the ramp amplitude of micro-turbine unit k respectively; Δt is a time period; They represent the power generation power of micro-turbine unit k at time t and time t+1 respectively.

[0042] Preferably, the holomorphic embedded power flow model of different node types in the distribution network is specifically:

[0043]

[0044]

[0045] SL: V i (α)=1+α(V i sp -1)

[0046] Where PQ, PV, and SL represent load nodes, generation nodes, and balance nodes, respectively; α is the full pure embedding factor. When α = 0, the physical meaning of the above full pure embedding power flow model indicates that the power system is in a no-load state, there is no power flow in the power system, and the node-to-ground admittance is not considered. At this time, all node voltages are equal to the balance node voltage of 1, and the reactive power is 0; N is the total number of nodes in the power system, i and k represent the node numbers; Y ik，tr and Y i，shunt Respectively represent the line admittance matrix between node i and node k and the ground admittance matrix of node i; V k (α), V i(α) denotes the voltage holomorphic embedding function of nodes i and k respectively; the upper horizontal line denotes conjugation; S i is the complex power of node i; P i is the active power of node i; j is the imaginary unit; Q i (α) is the reactive power holomorphic function of node i; V i sp is the target voltage of node i.

[0047] Preferably, for a 3-node power system, the recursive solution equation Ax=b constructed by using matrix changes is specifically:

[0048]

[0049]

[0050] In the formula, the matrix on the left is A, which represents the processed node admittance matrix; the middle matrix is ​​the matrix x of the quantity to be solved; the matrix on the right side of the equation is the matrix b of the known quantity; G is Y ik，tr The real part of ik，tr The imaginary part of G and B; the subscripts are node numbers; n represents the nth order; V v.re [n], V v.im [n] represents the real and imaginary parts of the n-th order power series coefficient of the voltage V(α) at ​​node v, v = 1, 2, 3; Q2[n] is the n-th order power series coefficient of the reactive power Q(α) at ​​node 2; δ ni is a pulse function. When n=i, δ ni =1; when n≠i, δ ni =0; V i sp is the target voltage of node i; Im and Re are the imaginary and real parts; R[n-1] is a known polynomial with a power series order less than n; is the conjugate of the complex power of node 3; W i (α) is V i The reciprocal of (α), It is also a holomorphic function; W i (α) The conjugate of the coefficient of the n-1th order power series.

[0051] Preferably, the sparrow algorithm is improved by using chaos-sine-cosine algorithm-Levy flight strategy, and the reactive voltage optimization solution of the distribution network considering distributed power sources is solved by combining the full pure embedded power flow algorithm. The Pareto solution set generated by the sparrow algorithm is obtained by the information entropy-TOPSIS method. Specifically, the optimal compromise solution is as follows:

[0052] S1: Input distribution network parameters, predicted output of wind power generation and photovoltaic power generation, and typical daily load data.

[0053] S2: Set the parameters of the sparrow algorithm, including population size, maximum number of iterations, ratio of explorers to warners, warning value, objective function dimension, external population size, describe the optimization variables and set upper and lower limit constraints.

[0054] S3: Initialize the population, set boundary constraints, initialize the population's historical best fitness, and initialize the external population.

[0055] S4: Update the population size and the status of each sparrow and the power status of the distribution network nodes.

[0056] S5: Determine whether the preset maximum number of iterations has been reached. If so, output the Pareto solution set of the output of the energy storage and reactive power compensation equipment, and obtain the best compromise solution through the information entropy-TOPSIS method.

[0057] S6: If it is not reached, the full pure embedded power flow algorithm is used to calculate the distribution network power flow under the corresponding state of each sparrow to obtain the voltage values ​​of all nodes, the apparent power S of the PQ node, and the active power P of the PV node.

[0058] S7: Calculate the objective function corresponding to each sparrow according to the flow state and record it in the external population according to the dominance relationship.

[0059] S8: Compare the fitness value of each sparrow, select the better sparrow as the explorer, randomly select the early warning, update the positions of followers, early warnings and explorers, and perform constraint control.

[0060] S9: Calculate the updated non-dominated solution relationship of the sparrow population, calculate the crowding degree, add the non-dominated solution to the external population, and remove some solutions of the external population, increase the number of iterations by 1, and return to step S5 to determine the maximum number of iterations.

[0061] Preferably, when the population is initialized in step S3, the initial positions of sparrows are randomly generated in the search space based on the Sin chaos initialization strategy, and the Sin chaos initialization position formula is specifically:

[0062]

[0063] Where, X i+1，j is the position of the sparrow at (i+1, j), the horizontal axis is the sparrow number, and the vertical axis is the dimension identifier of the decision variable; X i，j is the position of the sparrow at (i, j); N and M represent the number of sparrows and the dimension of the decision variable respectively.

[0064] Preferably, when updating the positions of the follower, the warning device and the explorer in step S8, a nonlinear adjustment factor s is introduced based on the sine-cosine algorithm concept, and the position update method is specifically as follows:

[0065]

[0066]

[0067] Where M iter is the maximum number of iterations; m is the current number of iterations; is the position of the sparrow at (i, j) at the m+1th iteration; is the position of the sparrow at (i, j) at the mth iteration; is the sparrow position with the best fitness at the m+1th iteration; R2 represents the warning value; ST represents the safety value; r1 is the control step size parameter, which is generally a random number in [0, 2π]; r2 is the weight factor, which controls the weight of the current optimal solution on the searcher's position update, and its value is generally a random number in [0, 2].

[0068] Based on the Levy flight strategy, the follower iterative position is updated. The position update formula is as follows:

[0069]

[0070] In the formula, is the position of the sparrow at (i, j) at the m+1th iteration; Q represents a random number that obeys the standard overall distribution; is the position of the sparrow with the worst fitness; is the position of the sparrow at (i, j) at the mth iteration; is the position of the sparrow with the best fitness after the new iteration; Levy(B) is the Levy flight model with parameter B.

[0071] Preferably, the best compromise solution obtained by using the information entropy-TOPSIS method in step S5 is specifically:

[0072] Construct the sparrow population-fitness matrix C based on the Pareto solution set generated by the sparrow algorithm:

[0073]

[0074] In the formula, C ij is the fitness of the jth target of the ith sparrow; N′ is the number of individuals in the sparrow population; i=1, 2, ..., N′, j=1, 2.

[0075] Take the inverse of the target value of C to obtain the isotropic matrix Y, normalize the isotropic matrix Y to obtain the matrix Z, calculate the information entropy of each target, and calculate the objective weight of each target based on the information entropy. The objective weight of the jth target is expressed as:

[0076]

[0077] In the formula, w i is the weight of the jth target; E j is the information entropy of the jth target; M′ is the total number of targets.

[0078] Calculate the weighting matrix based on the objective weights:

[0079] R=(Ri j )=w j p ij

[0080] Where R is the weighting matrix; p i，j is the z corresponding to the i-th sparrow under target j i，j The proportion of all sparrows under this target; w j is the weight of the j-th target.

[0081] The positive ideal solution and the negative ideal solution are calculated according to the weighted matrix, and the Euclidean space distance between the evaluation index and the positive and negative ideal solutions is calculated according to the positive and negative ideal solutions.

[0082] The relative closeness of each individual to the ideal solution is calculated based on the Euclidean space distance, and the individual with the largest closeness is selected as the optimal compromise solution.

[0083] On the other hand, the present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the reactive power optimization method for a distribution network based on a holomorphic embedding method and a sparrow algorithm as described in any embodiment of the present invention when executing the computer program.

[0084] Compared with the prior art, the present invention has the following technical effects:

[0085] The method of the present invention aims to minimize the operating cost and load fluctuation by constructing a reactive voltage optimization model of the distribution network considering distributed power sources. Based on the non-initial value dependent, non-iterative recursive holomorphic embedded power flow theory, a distribution network holomorphic embedded power flow model is constructed according to different node types, and the coefficients of the power series of the Taylor expansion of the holomorphic function are further derived to recursively solve the equation, and finally the calculation of the distribution network power flow is realized. On the basis of the sparrow algorithm, the sparrow algorithm is improved by introducing a strategy combining chaos-sine cosine algorithm-Levy flight, which enhances the global optimization ability and convergence speed and avoids the trap of local optimal solution. Finally, the information entropy-TOPSIS method is used to post-process the Pareto solution set generated by the sparrow algorithm, comprehensively consider the multi-objective optimization objectives, and select the optimal compromise solution from it, so as to ensure that the reactive optimization of the distribution network can achieve the optimal balance between system economy and stability while ensuring the quality of power, and has strong real-time and adaptability, which is suitable for the optimization and scheduling of intelligent distribution networks with large-scale access to renewable energy and energy storage systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is an overall flow chart of the reactive power optimization method of distribution network based on the holomorphic embedding method and the sparrow algorithm described in the present invention. DETAILED DESCRIPTION

[0087] In order to make the objectives, technical solutions and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in combination with specific embodiments of the present application and with reference to the accompanying drawings.

[0088] Embodiment 1

[0089] This embodiment provides a method for optimizing reactive power of a distribution network based on a holomorphic embedding method and a sparrow algorithm. Figure 1 As shown, the following steps are included:

[0090] Firstly, with the goal of minimizing the operating cost of the distribution network and minimizing the fluctuation of the comprehensive load curve, the energy storage system, switchable capacitor group (reactive compensation equipment), wind power and photovoltaic power generation on the low-voltage side of the distribution network are taken as optimization variables to establish a distribution network reactive voltage optimization model considering distributed power sources.

[0091] Using a non-initial value-dependent non-iterative recursive holomorphic embedded power flow algorithm, the holomorphic embedded power flow model for different node types in the distribution network is derived. Matrix changes are used to construct a recursive solution equation to solve the power series coefficients in the Maclaurin expansion of the holomorphic embedded model.

[0092] The sparrow algorithm is improved by using chaos-sine-cosine algorithm-Levy flight strategy. Combined with the holomorphic embedded power flow algorithm, the reactive voltage optimization solution of the distribution network considering distributed power sources is solved. The best compromise solution is obtained for the Pareto solution set generated by the sparrow algorithm through the information entropy-TOPSIS method.

[0093] As a preferred implementation of this embodiment, starting from the safety and economy of the distribution network, the objective function is to minimize the fluctuation of the distribution network operation cost and the comprehensive load curve. The objective function of the reactive power voltage optimization model of the distribution network of the distributed power source with the goal of minimizing the distribution network operation cost is specifically:

[0094] min f1=C ess +C MT +C LA +C loss

[0095] C MT =C fuel +C op +C en

[0096] C LA =|U I，t |×P I，t ×e I

[0097] Where min f1 is the distribution network operation cost objective function; C ess is the power call cost of the energy storage system; C MT is the micro-turbine dispatching cost; C LA is the cost of load participating in distribution network dispatching in each period; C loss is the power loss cost of the distribution network in each period; C fuel is the fuel cost; C op is the operation and maintenance cost; C en C is the environmental cost; LA is the cost of load participating in distribution network dispatching in each period; C loss U is the power loss cost of the distribution network in each period; I，t is the response status of user I at time t; P I，t is the response power of user I at time t; e I The incentive price (yuan / MW) for user I to participate in scheduling in a unit time period.

[0098] The objective function with the goal of minimizing the fluctuation of the comprehensive load curve is as follows:

[0099]

[0100] Wherein, min f2 is the comprehensive load curve fluctuation objective function; w1 and w2 are weight coefficients of two evaluation indicators, w1 and w2 can be determined according to the actual application, and in this embodiment, w1=0.25 and w2=0.75; and are the maximum and minimum values ​​of the daily load power of the distribution network respectively; is the average daily load of the distribution network; P g (t) is the value of the daily load of the distribution network at time t; P g (t+1) is the value of the daily load of the distribution network at time t+1.

[0101] As a preferred implementation mode of this embodiment, the constraint conditions of the reactive voltage optimization model of the distribution network of the distributed power source specifically include: distributed generation power constraint, voltage constraint, branch power constraint, total power conservation constraint, energy storage device constraint, reactive compensation equipment constraint, and micro-gas turbine group climbing constraint.

[0102] Specifically, the voltage and power constraints are considered from the perspective of the safety of the power system, ensuring the safety of equipment while ensuring the quality of power supply; the energy storage device constraints can ensure that the charging and discharging power of the energy storage does not exceed the limit to avoid equipment loss; the ramp constraints of the micro-gas unit limit the continuity between the previous moment and the next moment, because its power change has strong coupling between the previous moment and the next moment; the reactive compensation device constraints restrict the number of switchable capacitor groups. The above constraints are used to ensure the reliability and power supply quality of the distribution network.

[0103] The distributed generation power constraint is expressed as:

[0104]

[0105] Where P DG (t) is the active power generated by the distributed generation in the distribution network at time t; They are the upper and lower limits of the distributed generation active power respectively.

[0106]

[0107] In the formula, k fore is the prediction error coefficient of wind and solar power output, k fore The closer it is to 0, the higher the prediction accuracy; It is the day-ahead forecast value of distributed generation output.

[0108] The voltage constraint is expressed as:

[0109]

[0110] Where U i is the voltage amplitude of node i; are the upper and lower limits of the voltage amplitude at node i respectively.

[0111] The branch power constraint is expressed as:

[0112]

[0113] Where P L is the power delivered by the Lth branch in the distribution network; They are the upper and lower limits of the transmission power of the Lth branch respectively.

[0114] The total power conservation constraint is expressed as:

[0115] P TG，t =P cl，t -P DG.t +P LA，t +P ESS，t

[0116] Where P TG，t is the active power output of the conventional unit at time t; P cl，t is the active power of the uncontrollable load at time t; P DG，t is the active output of the distributed generation at time t; P LA，t , P ESS，t are the active power of load and energy storage at time t, respectively. ESS，t A positive value indicates that the energy storage absorbs active power, and a negative value indicates that the energy storage emits active power.

[0117] The energy storage device constraint is expressed as:

[0118]

[0119]

[0120] In the formula, is the upper power limit of the energy storage device; η charge , η discharge are the charging and discharging efficiency of the energy storage device, respectively; E are the upper limits of charge and discharge efficiency respectively; ESS，t and E ESS，t+1 are the amount of electricity stored in the energy storage device at time t and time t+1 respectively; Δt is a time period; and They are the upper and lower limits of the capacity of the energy storage device respectively.

[0121] The reactive power compensation equipment constraint is expressed as:

[0122]

[0123] In the formula, Q CB.j.tis the reactive power compensation of capacitor bank j in period t; Q CB is the reactive power compensation of a single capacitor bank; b j.t is the number of capacitor bank j switched on and off in period t; is the maximum number of switched capacitor groups j.

[0124] The ramp constraint of the micro-turbine unit is expressed as:

[0125]

[0126] In the formula, R u，k , R d，k are the upper and lower limits of the ramp amplitude of micro-turbine unit k respectively; Δt is a time period; They represent the power generation power of micro-turbine unit k at time t and time t+1 respectively.

[0127] As a preferred implementation of this embodiment, the holomorphic embedded power flow model of different node types in the distribution network is specifically:

[0128]

[0129]

[0130] SL: V i (α)=1+α(V i sp -1)

[0131] Where PQ, PV, and SL represent load nodes, generation nodes, and balance nodes, respectively; α is the full pure embedding factor. When α = 0, the physical meaning of the above full pure embedding power flow model indicates that the power system is in a no-load state, there is no power flow in the power system, and the node-to-ground admittance is not considered. At this time, all node voltages are equal to the balance node voltage of 1, and the reactive power is 0; N is the total number of nodes in the power system, i and k represent the node numbers; Y ik，tr and Y i，shunt Respectively represent the line admittance matrix between node i and node k and the ground admittance matrix of node i; V k (α), V i (α) represents the voltage holomorphic embedding function of nodes i and k respectively; the upper horizontal line represents conjugation; S i is the complex power of node i; P i is the active power of node i; j is the imaginary unit; Q i (α) is the reactive power holomorphic function of node i; V i sp is the target voltage of node i.

[0132] As a preferred implementation of this embodiment, taking a 3-node system as an example, including 1 balancing node, several PQ nodes and PV nodes, the recursive solution equation Ax=b constructed by matrix change is specifically:

[0133]

[0134]

[0135] In the formula, the matrix on the left is A, which represents the processed node admittance matrix, which is constant in the process of recursively solving the power series coefficients of the Maclaurin expansion of the holomorphic function; the middle matrix is ​​the matrix x of the quantity to be solved; the matrix on the right side of the equation is the matrix b of the known quantity; G is Y ik，tr The real part of ik，tr The imaginary part of G and B; the subscripts are node numbers; n represents the nth order; V v.re [n], V v.im [n] represents the real and imaginary parts of the n-th order power series coefficient of the voltage V(α) at ​​node v, v = 1, 2, 3; Q2[n] is the n-th order power series coefficient of the reactive power Q(α) at ​​node 2; δ ni is a pulse function. When n=i, δ ni =1; when n≠i, δ ni =0; V i sp is the target voltage of node i; Im and Re are the imaginary and real parts; R[n-1] is a known polynomial with a power series order less than n; is the conjugate of the complex power of node 3; W i (α) is V i The reciprocal of (α), It is also a holomorphic function; W i (α) The conjugate of the coefficient of the n-1th power series. R[n-1] is expressed as:

[0136]

[0137] Where j is an imaginary unit; Q i [k] is the k-th order power series coefficient of reactive power at node i; W i (α) The conjugate of the coefficient of the nk-th order power series.

[0138] As a preferred implementation of this embodiment, the sparrow algorithm is improved by using chaos-sine-cosine algorithm-Levy flight strategy, and combined with the full pure embedded power flow algorithm, the reactive voltage optimization solution of the distribution network considering distributed power sources is solved. The Pareto solution set generated by the sparrow algorithm is obtained by the information entropy-TOPSIS method to obtain the best compromise solution, which is as follows:

[0139] S1: Input distribution network parameters, predicted output of wind power generation and photovoltaic power generation, and typical daily load data.

[0140] S2: Set the parameters of the sparrow algorithm including: population size, maximum number of iterations, ratio of explorers to early warning detectors, early warning value, objective function dimension, external population size, describe the optimization variables and impose upper and lower limit constraints (i.e., the objective function and constraints of the sparrow algorithm brought into the reactive power voltage optimization model of the distribution network).

[0141] S3: Initialize the population, set boundary constraints, initialize the population's historical best fitness, and initialize the external population.

[0142] S4: Update the population size and the status of each sparrow and the power status of the distribution network nodes.

[0143] S5: Determine whether the preset maximum number of iterations has been reached. If so, output the Pareto solution set of the output of the energy storage and reactive power compensation equipment, and obtain the best compromise solution through the information entropy-TOPSIS method.

[0144] S6: If it is not reached, the full pure embedded power flow algorithm is used to calculate the distribution network power flow under the corresponding state of each sparrow to obtain the voltage values ​​of all nodes, the apparent power S of the PQ node, and the active power P of the PV node.

[0145] S7: Calculate the objective function corresponding to each sparrow according to the flow state and record it in the external population according to the dominance relationship.

[0146] S8: Compare the fitness value of each sparrow, select the better sparrow as the explorer, randomly select the early warning, update the positions of followers, early warnings and explorers, and perform constraint control.

[0147] S9: Calculate the updated non-dominated solution relationship of the sparrow population, calculate the crowding degree, add the non-dominated solution to the external population, and remove some solutions of the external population, increase the number of iterations by 1, and return to step S5 to determine the maximum number of iterations.

[0148] As a preferred implementation of this embodiment, when initializing the population (i.e. generating the population initial solution) in step S3, the initial positions of sparrows are randomly generated in the search space based on the Sin chaos initialization strategy, so as to ensure that a full search can be performed in the solution space during the optimization process, improve the population search diversity of the algorithm, and avoid prematureness. The Sin chaos initialization position formula is specifically:

[0149]

[0150] Where, X i+1，jis the position of the sparrow at (i+1, j), the horizontal axis is the sparrow number, and the vertical axis is the dimension identifier of the decision variable; X i，j is the position of the sparrow at (i, j); N and M represent the number of sparrows and the dimension of the decision variable respectively.

[0151] As a preferred implementation of this embodiment, as the number of iterations increases, the search space of the explorer in the sparrow population will gradually decrease, resulting in the early search to the local optimum. Therefore, to solve this problem, when updating the positions of the followers, early warning and explorers in step S8, based on the sine-cosine algorithm idea, a nonlinear adjustment factor s is introduced to increase the search step length as much as possible in the early stage of the sparrow search to increase the global search capability, and reduce the search step length in the later stage of the search to enhance the search capability of the local search space. The specific position update method is:

[0152]

[0153]

[0154] Where M iter is the maximum number of iterations; m is the current number of iterations; is the position of the sparrow at (i, j) at the m+1th iteration; is the position of the sparrow at (i, j) at the mth iteration; is the sparrow position with the best fitness at the m+1th iteration; R2 represents the warning value; ST represents the safety value; r1 is the control step size parameter, which is generally a random number in [0, 2π]; r2 is the weight factor, which controls the weight of the current optimal solution on the searcher's position update, and its value is generally a random number in [0, 2].

[0155] Levy flight is a model based on random walks, which is widely used in optimization, search and exploration problems. The key is to use Levy distribution to generate random steps, which have heavy-tail characteristics and allow large displacements in a short time, thereby improving search efficiency. Based on the Levy flight strategy, the follower iteration position is updated. The Levy flight mechanism simultaneously corrects the sparrow's direction and search step. The specific position update formula is:

[0156]

[0157] In the formula, is the position of the sparrow at (i, j) at the m+1th iteration; Q represents a random number that obeys the standard overall distribution; is the position of the sparrow with the worst fitness; is the position of the sparrow at (i, j) at the mth iteration; is the position of the sparrow with the best fitness after the new iteration; Levy(B) is the Levy flight model with parameter B, and its calculation formula is as follows:

[0158]

[0159] In the formula, r3 and r4 are random numbers in the range of [0, 1], the value of ξ can be 1.5, and the calculation method of σ is:

[0160]

[0161] Wherein, Γ(x)=(x-1).

[0162] As a preferred implementation of this embodiment, the best compromise solution obtained by using the information entropy-TOPSIS method in step S5 is specifically:

[0163] Construct the sparrow population-fitness matrix C based on the Pareto solution set generated by the sparrow algorithm:

[0164]

[0165] In the formula, C ij is the fitness of the jth target of the ith sparrow; N′ is the number of individuals in the sparrow population; i=1, 2, ..., N′, j=1, 2.

[0166] The target value of C is taken inversely to obtain the homophasing matrix Y, and the homophasing matrix Y is normalized to obtain the matrix Z. The information entropy of each target is calculated, and the information entropy is expressed as:

[0167]

[0168]

[0169] In the formula, E j is the information entropy of the jth target; N′ is the number of individuals in the sparrow population; p i，j is the z corresponding to the i-th sparrow under target j i，j The proportion of all sparrows under this target; i，j is the normalized value corresponding to the jth target of the ith sparrow in the normalized matrix Z; M′ is the total number of targets.

[0170] And calculate the objective weight of each target. The objective weight of the jth target is expressed as:

[0171]

[0172] In the formula, w i is the weight of the jth target; E j is the information entropy of the jth target; M′ is the total number of targets.

[0173] Calculate the weighting matrix based on the objective weights:

[0174] R=(R ij )=w j p ij

[0175] Where R is the weighting matrix; p i，j is the z corresponding to the i-th sparrow under target j i，j The proportion of all sparrows under this target; w j is the weight of the j-th target.

[0176] Compute positive and negative ideal solutions based on the weighting matrix:

[0177] R + ={max j R ij |i=1,2,...,N′}

[0178] R - ={min j R ij |i=1,2,...,N′}

[0179] Calculate the Euclidean space distance between the evaluation index and the positive and negative ideal solutions:

[0180]

[0181]

[0182] In the formula, is the Euclidean space distance between the ith individual and the ideal solution; is the positive ideal solution of the jth objective in the matrix R; is the Euclidean space distance between the i-th individual and the negative ideal solution; The negative ideal solution of the jth objective in the matrix R; R i，j is the value of the jth target for the ith individual in the matrix R.

[0183] The relative closeness of each individual to the ideal solution is calculated based on the Euclidean space distance, specifically:

[0184]

[0185] In the formula, C i is the relative proximity of the i-th individual;

[0186] The individual with the largest relative proximity is selected as the optimal compromise.

[0187] Embodiment 2

[0188] This embodiment provides an electronic device, which includes: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the distribution network reactive power optimization method based on the holomorphic embedding method and the sparrow algorithm as described in any embodiment of the present invention is implemented.

[0189] In the embodiments of the present application, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. Among them, A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c can be represented by: a, b, c, a and b, a and c, b and c, or a and b and c, where a, b, c can be single or multiple.

[0190] Those of ordinary skill in the art will appreciate that the various units and algorithm steps described in the embodiments disclosed herein can be implemented in a combination of electronic hardware, computer software, and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0191] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0192] In several embodiments provided in the present application, if any function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory; hereinafter referred to as: ROM), random access memory (Random Access Memory; hereinafter referred to as: RAM), disk or optical disk, and other media that can store program codes.

[0193] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm, characterized in that: The following steps are involved: Firstly, with the goal of minimizing the operating cost of the distribution network and minimizing the fluctuation of the comprehensive load curve, the energy storage system, switchable capacitor bank, wind power and photovoltaic power generation on the low-voltage side of the distribution network are taken as optimization variables to establish a distribution network reactive voltage optimization model considering distributed power sources. Using a non-initial value-dependent, non-iterative, recursive holomorphic embedded power flow algorithm, the holomorphic embedded power flow model for different node types in the distribution network is derived. Using matrix changes, a recursive solution equation is constructed to solve the power series coefficients in the Maclaurin expansion of the holomorphic embedded model. The sparrow algorithm is improved by using chaos-sine-cosine algorithm-Levy flight strategy. Combined with the holomorphic embedded power flow algorithm, the reactive voltage optimization solution of the distribution network considering distributed power sources is solved. The best compromise solution is obtained for the Pareto solution set generated by the sparrow algorithm through the information entropy-TOPSIS method.

2. The reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm according to claim 1 is characterized in that: The objective function of the reactive power voltage optimization model of the distributed power distribution network with the goal of minimizing the distribution network operation cost is specifically: minf1=C ess +C MT +C LA +C Loss Where minf1 is the distribution network operation cost objective function; C ess is the power call cost of the energy storage system; C MT is the micro-turbine dispatching cost; C LA is the cost of load participating in distribution network dispatching in each period; C loss The cost of power loss in the distribution network at each time period; The objective function with the goal of minimizing the fluctuation of the comprehensive load curve is as follows: Where minf2 is the comprehensive load curve fluctuation objective function; w1 and w2 are the weight coefficients of the two evaluation indicators; and are the maximum and minimum values ​​of the daily load power of the distribution network respectively; is the average daily load of the distribution network; P g (t) is the value of the daily load of the distribution network at time t; P g (t+1) is the value of the daily load of the distribution network at time t+1.

3. The reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm according to claim 1 is characterized in that: The constraints of the reactive power voltage optimization model of the distribution network of the distributed power source specifically include: distributed generation power constraints, voltage constraints, branch power constraints, total power conservation constraints, energy storage device constraints, reactive power compensation equipment constraints, and micro-combustion unit climbing constraints; The distributed generation power constraint is expressed as: Where P DG (t) is the active power generated by the distributed generation in the distribution network at time t; are the upper and lower limits of the active power of distributed generation, respectively; In the formula, k fore is the prediction error coefficient of wind and solar power output, k fore The closer it is to 0, the higher the prediction accuracy; is the day-ahead forecast value of distributed generation output; The voltage constraint is expressed as: Where U i is the voltage amplitude of node i; are the upper and lower limits of the voltage amplitude of node i respectively; The branch power constraint is expressed as: Where P L is the power delivered by the Lth branch in the distribution network; are the upper and lower limits of the transmission power of the Lth branch respectively; The total power conservation constraint is expressed as: P TG,t =P cl,t -P DG.t +P LA,t +P ESS,t Where P TG,t is the active power output of the conventional unit at time t; P cl,t is the active power of the uncontrollable load at time t; P DG,t is the active output of the distributed generation at time t; P LA,t , P ESS,t are the active power of load and energy storage at time t, respectively. ESS,t A positive value indicates that the energy storage absorbs active power, and a negative value indicates that the energy storage emits active power; The energy storage device constraint is expressed as: In the formula, is the upper power limit of the energy storage device; η charge , η discharge are the charging and discharging efficiency of the energy storage device, respectively; E are the upper limits of charge and discharge efficiency respectively; ESS,t and E ESS,t+1 are the amount of electricity stored in the energy storage device at time t and time t+1 respectively; Δt is a time period; and are the upper and lower limits of the capacity of the energy storage device respectively; The reactive power compensation equipment constraint is expressed as: In the formula, Q CB.j.t is the reactive power compensation of capacitor bank j during period t; Q CB is the reactive power compensation of a single capacitor bank; b j.t is the number of capacitor bank j switched on and off in period t; is the maximum number of switched groups of capacitor group j; The ramp constraint of the micro-turbine unit is expressed as: In the formula, R u,k , R d,k are the upper and lower limits of the ramp amplitude of micro-turbine unit k respectively; Δt is a time period; They represent the power generation power of micro-turbine unit k at time t and time t+1 respectively.

4. The reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm according to claim 1 is characterized in that: The holomorphic embedded power flow model for different node types in the distribution network is specifically: SL:V i (α)=1+α(V i sp -1) Where PQ, PV, and SL represent load nodes, generation nodes, and balance nodes, respectively; α is the full pure embedding factor. When α = 0, the physical meaning of the above full pure embedding power flow model indicates that the power system is in a no-load state, there is no power flow in the power system, and the node-to-ground admittance is not considered. At this time, all node voltages are equal to the balance node voltage of 1, and the reactive power is 0; N is the total number of nodes in the power system, i and k represent the node numbers; Y ik,tr and Y i,shunt Respectively represent the line admittance matrix between node i and node k and the ground admittance matrix of node i; V k (α), V i (α) denotes the voltage holomorphic embedding function of nodes i and k respectively; the upper horizontal line denotes conjugation; S i is the complex power of node i; P i is the active power of node i; j is the imaginary unit; Q i (α) is the reactive power holomorphic function of node i; V i sp is the target voltage of node i.

5. The reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm according to claim 4 is characterized in that: For a 3-node power system, the recursive solution equation Ax=b constructed using matrix transformation is specifically: In the formula, the matrix on the left is A, which represents the processed node admittance matrix; the middle matrix is ​​the matrix x of the quantity to be solved; the matrix on the right side of the equation is the matrix b of the known quantity; G is Y ik,tr The real part of ik,tr The imaginary part of G and B; the subscripts are node numbers; n represents the nth order; V v.re [n], V v.im [n] represents the real and imaginary parts of the n-th order power series coefficient of the voltage V(α) at ​​node v, v = 1, 2, 3; Q2[n] is the n-th order power series coefficient of the reactive power Q(α) at ​​node 2; δ ni is a pulse function. When n=i, δ ni =1; When n≠i, δ ni =0; V i sp is the target voltage of node i; Im and Re are the imaginary and real parts; R[n-1] is a known polynomial with a power series order less than n; is the conjugate of the complex power of node 3; W i (α) is V i The reciprocal of (α), It is also a holomorphic function; W i (α) The conjugate of the coefficient of the n-1th order power series.

6. The reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm according to claim 1 is characterized in that: The sparrow algorithm is improved by using chaos-sine-cosine algorithm-Levy flight strategy, and combined with the full pure embedded power flow algorithm, the reactive voltage optimization solution of the distribution network considering distributed power sources is solved. The Pareto solution set generated by the sparrow algorithm is obtained by the information entropy-TOPSIS method to obtain the best compromise solution. Specifically: S1: Input distribution network parameters, wind power generation, photovoltaic power generation forecast output, and typical daily load data; S2: Set the parameters of the sparrow algorithm, including population size, maximum number of iterations, ratio of explorers to alarmists, alarm value, objective function dimension, external population size, describe the optimization variables and set upper and lower limit constraints; S3: Initialize the population, set boundary constraints, initialize the historical best fitness of the population, and initialize the external population; S4: Update the population size and the status of each sparrow and the power status of the distribution network nodes; S5: Determine whether the preset maximum number of iterations has been reached. If so, output the Pareto solution set of the output of the energy storage and reactive power compensation equipment, and obtain the best compromise solution through the information entropy-TOPSIS method; S6: If it is not reached, the distribution network power flow under the corresponding state of each sparrow is calculated using the full pure embedded power flow algorithm to obtain the voltage values ​​of all nodes, the apparent power S of the PQ node, and the active power P of the PV node; S7: Calculate the objective function corresponding to each sparrow according to the tidal current state and record it in the external population according to the dominance relationship; S8: Compare the fitness value of each sparrow, select the better sparrow as the explorer, randomly select the early warning, update the positions of the followers, early warnings and explorers, and perform constraint control; S9: Calculate the updated non-dominated solution relationship of the sparrow population, calculate the crowding degree, add the non-dominated solution to the external population, and remove some solutions of the external population, increase the number of iterations by 1, and return to step S5 to determine the maximum number of iterations.

7. The reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm according to claim 6 is characterized in that: When the population is initialized in step S3, the initial positions of sparrows are randomly generated in the search space based on the Sin chaos initialization strategy. The Sin chaos initialization position formula is specifically: Where, X i+1,j is the position of the sparrow at (i+1,j), the horizontal axis is the sparrow number, and the vertical axis is the dimension identifier of the decision variable; X i,j is the position of the sparrow at (i, j); N and M represent the number of sparrows and the dimension of the decision variable respectively.

8. The reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm according to claim 6 is characterized in that: When updating the positions of the follower, the warning device, and the explorer in step S8, a nonlinear adjustment factor s is introduced based on the sine-cosine algorithm concept, and the position update method is specifically as follows: Where M iter is the maximum number of iterations; m is the current iteration number; is the position of the sparrow at (i, j) at the m+1th iteration; is the position of the sparrow at (i, j) at the mth iteration; is the sparrow position with the best fitness at the m+1th iteration; R2 represents the warning value; ST represents the safety value; r1 is the control step size parameter, which is generally a random number in [0,2π]; r2 is the weight factor, which controls the weight of the current optimal solution on the searcher's position update, and is generally a random number in [0,2]; Based on the Levy flight strategy, the follower iterative position is updated. The position update formula is as follows: In the formula, is the position of the sparrow at (i, j) at the m+1th iteration; Q represents a random number that follows the standard overall distribution; is the position of the sparrow with the worst fitness; is the position of the sparrow at (i, j) at the mth iteration; is the position of the sparrow with the best fitness after the new iteration; Levy(B) is the Levy flight model with parameter B.

9. The reactive power optimization method for distribution network based on the holomorphic embedding method and the sparrow algorithm according to claim 6 is characterized in that: The best compromise solution obtained by using the information entropy-TOPSIS method in step S5 is specifically: Construct the sparrow population-fitness matrix C based on the Pareto solution set generated by the sparrow algorithm: In the formula, C ij is the fitness of the jth target of the i-th sparrow; N ′ is the number of individuals in the sparrow population; i=1,2,…,N ′ , j = 1, 2; Take the inverse of the target value of C to obtain the isotropic matrix Y, normalize the isotropic matrix Y to obtain the matrix Z, calculate the information entropy of each target, and calculate the objective weight of each target based on the information entropy. The objective weight of the jth target is expressed as: In the formula, w i is the weight of the jth target; E j is the information entropy of the jth target; M ′ is the total number of targets; Calculate the weighting matrix based on the objective weights: R=(R ij )=w j p ij Where R is the weighting matrix; p i,j is the z corresponding to the i-th sparrow under target j i,j The proportion of all sparrows under this target; w j is the weight of the jth target; Calculate the positive ideal solution and the negative ideal solution according to the weighted matrix, and calculate the Euclidean space distance between the evaluation index and the positive and negative ideal solutions according to the positive and negative ideal solutions; The relative closeness of each individual to the ideal solution is calculated based on the Euclidean space distance, and the individual with the largest closeness is selected as the optimal compromise solution.

10. An electronic device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the reactive power optimization method for a distribution network based on a holomorphic embedding method and a sparrow algorithm as described in any one of claims 1 to 9 when executing the computer program.

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