Power distribution network reconstruction method based on comprehensive improved balance optimization algorithm

Abstract

The invention relates to a power distribution network reconstruction method based on a comprehensive improved balance optimization algorithm, which belongs to the technical field of intelligent power distribution, and comprises the following steps: establishing a network model, initializing an EO algorithm, defining a fitness function, executing the EO algorithm, reconstructing a network, and obtaining switch state configuration of a power distribution network according to the EO algorithm. Carrying out network reconstruction on the positions of the distributed power generation units and the power generation capacity configuration so as to achieve a preset optimization target; according to the method, the optimization problem of the power distribution network is effectively solved, and the method has a lower error rate and a higher global optimal solution search success rate.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent power distribution, and particularly to a power distribution network reconstruction method based on a comprehensive improved equilibrium optimization algorithm (NIEO) for comprehensively improving power distribution network reconstruction to optimize network performance. Background Art

[0002] With the growing global demand for sustainable development, especially in the energy field, various new technologies and solutions have been rapidly developed and applied to reduce environmental pollution and improve energy efficiency. The power system, as the infrastructure of modern society, particularly needs to reduce its impact on the environment while ensuring the reliability and efficiency of energy supply. Among them, solving the optimal integrated combination optimization problem of distribution network reconfiguration (PDNR) and distributed generation (DGs) is one of the key technologies to improve the efficiency of power distribution networks, reduce energy consumption, and enhance grid stability.

[0003] Traditional power network design often focuses on stable and reliable power supply. However, with the increasing proportion of renewable energy, especially solar and wind energy, the dynamic management and optimal configuration of the power grid have become necessary means to improve network performance. For example, through network reconfiguration, line losses can be effectively reduced, voltage distribution can be optimized, and the reliability and flexibility of the power grid can be improved. However, the reconfiguration of the power system involves complex calculations and decision-making processes, which need to be carried out under the satisfaction of multiple constraints and objectives.

[0004] In recent years, a series of meta-heuristic optimization algorithms have been proposed and applied to the PDNR problem, such as particle swarm optimization (PSO), genetic algorithm (GA), and the newly developed equilibrium optimizer (EO) algorithm. These algorithms have their own advantages, but there are also certain limitations, such as slow convergence speed and easy to fall into local optimum. Summary of the Invention

[0005] In view of the above problems existing in the prior art, the present invention provides a power distribution network reconstruction method based on a comprehensive improved equilibrium optimizer (EO) algorithm, which can effectively solve the optimization problem of the power distribution network and has a lower error rate and a higher success rate of searching for the global optimal solution.

[0006] The technical solution adopted by the present invention includes the following steps:

[0007] Step 1, establish a network model, establish a mathematical model of the power distribution network, including all buses, branches, switches, and related electrical parameters;

[0008] Step 2, initialize the EO algorithm, set the initial parameters of the EO algorithm, including particle parameters, the number, position, and velocity of particles;

[0009] Step 3, define the fitness function, which is used to evaluate the performance of each candidate solution, including power loss, voltage deviation, and system reliability index;

[0010] Step 4, execute the EO algorithm. Based on the current state of the power system and the objective function, iteratively find the optimal solution through the dynamic adjustment of the equilibrium state. In each iteration, update the position and velocity of the particles according to the rules of the equilibrium optimizer, evaluate the fitness of each particle, and update the global optimal and individual optimal solutions according to the fitness;

[0011] Step 5, network reconfiguration. According to the switch state configuration of the distribution network, the location of the distributed generation unit, and the power generation configuration obtained from the EO algorithm, perform network reconfiguration to achieve the predetermined optimization goal.

[0012] Furthermore, the specific steps of Step 1 include:

[0013] Step 1.1, determine the network topology structure. After changing the switch positions in the distribution network, ensure that it still maintains a radial topology structure. The following are the necessary conditions for maintaining the network radial structure at the end of the reconfiguration:

[0014] The number of switches for the branch to maintain a radial structure:

[0015] ∧ = B - N + S

[0016] where B, N, and S are the numbers of branches, buses, and feeders respectively;

[0017] When operating in a radial system, the following conditions need to be met: <1> Each load has its own power supply source; <2> There are no loops (closed loops) in the network; <3> All nodes are within the subgraph;

[0018] The number of S on the radial distribution line satisfies:

[0019] N S = N Bus -1

[0020] Create a bus incidence matrix:

[0021]

[0022] Check whether the network is a radial network:

[0023]

[0024] In the formula, A is the obtained submatrix. When its determinant is ±1, it means that the distribution network operates in a radial topology structure;

[0025] Step 1.2: Select a power flow calculation algorithm. Adopt the model formula of the power summation method based on the backward / forward (B / F) algorithm. The power flow problem of a single source is determined by a two-way recursive equation. Based on this, the line is connected between bus i and bus k, where bus i is closer to the feeder, and the branch impedance is Z s = R s + jX s , and the branch shunt admittance is y s , where the total shunt admittance is between bus i and bus k;

[0026] The power summation algorithm includes the following steps,

[0027] (1) Assume that all bus voltages are 1 p.u., i.e.,

[0028] (2) Calculate the active and reactive power

[0029]

[0030] In the formulas, the superscripts L, inj, and F1 in P and Q represent load, injection, and flow respectively, and represent the total active and total reactive flows through the entire downstream line connected to bus k respectively;

[0031] (3) Calculate the active (P s ) and reactive (Q s ) power flows near bus I (backward scan):

[0032]

[0033] (4) Calculate the voltage magnitude and angle of each bus (forward scan):

[0034]

[0035]

[0036] where

[0037]

[0038] I s flows through the impedance (Z s = R s + jX s ), and the voltage magnitude and angle at the bus are written as:

[0039]

[0040] where

[0041]

[0042] If the voltage angle (d i ) of bus i is not equal to zero, then the voltage angle (d k ) of the k-th bus becomes:

[0043] d k = d i - tan -1 (a1 - a2)

[0044] Use the above formula to determine the voltage magnitude and angle of each bus in the network in a forward iterative manner;

[0045] (5) Compare the received voltage with the values of the previous and next iterations, and calculate the absolute error,

[0046]

[0047] where, n b and iter are the number of branches and the number of iterations. If the calculated value is less than the selected value ∈, the iteration is terminated; otherwise, return to step (2).

[0048] Furthermore, step 2 specifically includes:

[0049] Step 2.1, initialize the population size n and the dimension d;

[0050] Step 2.2, generate an initial concentration vector for each particle i where the initial value of each dimension is randomly generated within the predefined upper and lower bounds [L b , U b :

[0051]

[0052] where, represents the initial concentration vector of the i-th particle, rand(i) returns a uniform random number within the interval [0, 1], L b and U b are the minimum value (C min ) and the maximum value (C max ) of all dimension vectors respectively, and n represents the number of particles in the population;

[0053] Step 2.3, calculate the initial mass of each particle and normalize it

[0054]

[0055] Step 2.4, calculate the equilibrium candidate solution C eq(i) :

[0056]

[0057] Step 2.5, calculate the average value C of the balanced candidate solutions eq(ave) :

[0058] C eq(ave) = sum(C eq(i) ) / n

[0059] Step 2.6, construct the balance pool C eq(pool) , which contains all C eq(i) and C eq(ave) .

[0060] Furthermore, the specific steps of Step 3 are as follows:

[0061] Step 3.1, determine the constraint conditions. In the power system, the change in voltage is required to be maintained within the limit range:

[0062]

[0063] At the same time, the change in bus voltage is maintained within the range of ±10%, and the change in feeder voltage is maintained within the range of ±5%:

[0064]

[0065] Meanwhile, the current-carrying capacity of the cables in the system should not exceed the maximum current limit:

[0066]

[0067] Step 3.2, define the optimization objective function. Considering certain constraint conditions, the basic solution of the power system reconstruction problem is obtained by minimizing the power loss and increasing the bus voltage. The loss in the power system is minimized by maintaining the bus voltage at the expected value in the system. The active power loss in the power system is calculated using the following formula:

[0068] P loss(i,k) = r i,k · |I i,k | 2

[0069] The power loss in the distribution system with a dynamic structure is obtained by the sum of the loss values of the active branches. The total loss on the distribution system is defined by the equation:

[0070]

[0071] where i - k represents the bus number, P k and Q kDenote the active power and reactive power values of the k-th bus, r represents the branch resistance between the i-th bus and the k-th bus, and V k denotes the bus voltage, and N br denotes the number of branches, and S w denotes whether the branch is active. When the branch is active, its value is "1"; otherwise, its value is "0".

[0072] The following equations give the active power loss reduction of the PDN before and after reconfiguration Step 3.3, define the voltage deviation index DV

[0073]

[0074] where V D :

[0075]

[0076] is the voltage magnitude of the i-th bus, and N i is the total number of buses; bus Determine a single objective function:

[0077] where X1 and X2 are weight coefficients, which are selected as 2 / 3 and 1 / 3 respectively;

[0078]

[0079] The objective of the fitness function is to minimize the power loss and voltage deviation after reconstruction, so as to obtain the optimal topology of the distribution network.

[0080] Furthermore, the specific steps of step 4 include:

[0081] Step 4.1, initialize the size n of the population and the initial parameters of each particle;

[0082] where, select the best four particles and their positions defined in the optimization process as candidate solutions of the search algorithm; calculate the arithmetic mean of the selected four particles to represent the balance of the fifth particle, and create a vector of the balance pool, as shown in the following formula:

[0083]

[0084]

[0085] Step 4.2, calculate the fitness value of each particle in the objective function;

[0086] where the fitness function (f) needs to satisfy:

[0087] ​

[0088] Step 4.3, calculate the updated concentration,

[0089] a) Generate a random vector $\vec{r}$ and (taking values between [0, 1])

[0090] b) Define the exponential term function as follows:

[0091]

[0092] where

[0093]

[0094] Finally

[0095]

[0096] Step 4.4, calculate the generation rate parameter:

[0097]

[0098] where

[0099]

[0100] GP takes the value 0.5

[0101] Step 4.5, use the recycling strategy to measure the diversity index of the balance pool,

[0102] a) Calculate the Euclidean distance between particles in the balance pool to measure the diversity index I of the balance pool DV :

[0103]

[0104] where, N eq is the number of particles in the balance pool;

[0105] b) Determine whether to perform exploitation or exploration operations according to the value of the diversity index I DV :

[0106]

[0107] where, C dmax and C dmin are the minimum and maximum values of the variables respectively, rand and ∈ are random numbers, and € is a specific value;

[0108] Step 4.6, use the improved concentration update equation of IEO to further optimize and update the concentration of particles:

[0109] Cnew = C eq + G[λ(1 - F)+(C - C eq )F]

[0110] Where F is the exponential term and G is the generation rate. If the newly generated is better than the previous position, it is replaced;

[0111] Step 4.7: Repeat steps 4.3 - 4.4 until the termination condition is met;

[0112] Step 4.8: Output the optimal solution and execute the network reconfiguration decision.

[0113] The advantages and effects of the present invention are as follows: The present invention proposes a new optimization algorithm. By improving the algorithm structure and search strategy, the quality of the solution and the search efficiency are improved, thus more effectively solving the integrated optimization problem of PDNR and DGs. The algorithm is based on the dynamic balance theory and introduces a multi-strategy control and adaptive adjustment mechanism to adapt to the changes and uncertainties in the operation of the power network, providing a stable and efficient solution. In addition, the new algorithm will take into account the actual operation limitations of the power network, such as voltage levels, line capacities, and system stability, etc., to ensure the feasibility and practicality of the optimized configuration. On this basis, the present invention specifically proposes a comprehensive improved balance optimization algorithm (NIEO), which combines the recycling strategy of IEOA and the improved concentration update mechanism of IEO, and improves the optimization efficiency and effect by better utilizing the search space and expanding the search around the local optimal points, especially performing well in the problems of dynamic network reconfiguration and renewable distributed generation unit configuration.

[0114] In summary, the technical solution of the present invention not only helps to improve the operation efficiency and reliability of the power distribution network, but also can significantly reduce energy consumption and operating costs, which is of great significance for promoting the modernization and sustainable development of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Figure 1 It is a schematic diagram of the 33-bus radial distribution network structure in the present invention;

[0116] Figure 2 It is a flow chart of establishing the objective function in the present invention;

[0117] Figure 3 It is a flow chart of power summation method power flow calculation in the present invention;

[0118] Figure 4 It is a flow chart of the comprehensive improved balancer optimization algorithm in the present invention;

[0119] Figure 5 It is the overall flow chart of the present invention. Detailed implementation manners

[0120] In order to enable those skilled in the art of the present technology to better understand the technical solutions in the present invention, the following clearly and completely describes the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0121] Embodiment

[0122] A power distribution network reconstruction method based on a comprehensive improved equilibrium optimization algorithm (NIEO) of the present invention includes the following steps:

[0123] Step 1: Establish a network model, and establish a mathematical model of the power distribution network, including all buses, branches, switches, and related electrical parameters.

[0124] Step 1.1: Determine the network topology structure, the purpose of which is to keep the radial topology structure after changing the switch positions in the distribution network. The following are the necessary conditions for maintaining the radial structure of the network at the end of reconstruction.

[0125] Number of switches for the branch to maintain the radial structure:

[0126] ∧ = B - N + S

[0127] Where B, N, and S are the numbers of branches, buses, and feeders respectively.

[0128] When operating in a radial system, the following conditions need to be met: <1> Each load has its own power supply source; <2> There are no loops (closed loops) in the network; <3> All nodes are within the subgraph.

[0129] The number of S on the radial distribution line satisfies:

[0130] N S = N Bus - 1

[0131] Create a bus incidence matrix:

[0132]

[0133] Check whether the network is a radial network:

[0134]

[0135] In the formula, A is the obtained submatrix. When its determinant is ±1, it means that the distribution network operates in a radial topology structure.

[0136] Step 1.2: Select an appropriate power flow calculation algorithm. Traditional power flow algorithms such as Newton-Raphson (NR), Gauss-Seidel (GS), and Fast Decoupled (FD) are used for power flow analysis of grid networks. Due to the high R / X or I / V ratio of the distribution network, traditional methods cannot generate solutions with the required accuracy in the power grid system. The present invention adopts a model formula of the power summation method based on the backward / forward algorithm (B / F).

[0137] The power flow problem of a single source can be determined by a two-way recursive equation. Considering that this line is connected between bus i and k, where bus i is closer to the feeder. The branch impedance is Z s = R s + jX s , and the branch shunt admittance is y s , where the total shunt admittance is between bus i and k.

[0138] The power summation algorithm includes the following 5 steps:

[0139] (1) Assume that all bus voltages are 1 p.u., i.e.,

[0140] (2) Calculate the active and reactive power

[0141]

[0142] In the formulas, the superscripts L, inj, and F1 in P and Q represent load, injection, and flow respectively. and represent the total active and total reactive power flows through the entire downstream line connected to bus k respectively.

[0143] (3) Calculate the active (P s ) and reactive (Q s ) power flows near bus I (backward scan):

[0144]

[0145] (4) Calculate the voltage magnitude and angle of each bus (forward scan):

[0146]

[0147] where

[0148]

[0149] I s flows through the impedance (Z s = R s + jXs ), the voltage magnitude and angle at the bus can be written as:

[0150]

[0151] where

[0152]

[0153] If the voltage angle (d i ) of bus i is not equal to zero, then the voltage angle (d k ) of the kth bus becomes:

[0154] d k = d i - tan -1 (a1 - a2)

[0155] Use the above formula to determine the voltage magnitude and angle of each bus in the network in a forward iterative manner.

[0156] (5) Compare the received - end voltage with the values of the previous and next iterations, and calculate the absolute error.

[0157]

[0158] where, n b and iter are the number of branches and the number of iterations. If the calculated value is less than the selected value ∈ (∈ is taken as 10 -6 ) in this invention, then terminate the iteration, otherwise return to step (2).

[0159] Step 2: Initialize the EO algorithm, set the initial parameters of the EO algorithm, including the granularity parameter, the number, position, and velocity of particles, etc.

[0160] Step 2.1: Initialize the population size n and dimension d;

[0161] Step 2.2: Generate an initial concentration vector for each particle i where the initial value of each dimension is randomly generated within the predefined upper and lower bounds [L b , U b :

[0162]

[0163] where, represents the initial concentration vector of the ith particle, and rand(i) returns a uniform random number in the interval [0, 1]. L b and U b are the minimum value (C min ) and maximum value (C max), where n represents the number of particles in the population.

[0164] Step 2.3: Calculate the initial mass of each particle and normalize it.

[0165]

[0166] Step 2.4: Calculate the equilibrium candidate solution C for each particle eq(i) :

[0167]

[0168] Step 2.5: Calculate the average value of the equilibrium candidate solutions C eq(ave) :

[0169] C eq(ave) = sum(C eq(i) ) / n

[0170] Step 2.6: Construct the equilibrium pool C eq(pool) , which contains all C eq(i) and C eq(ave) .

[0171] The above steps ensure that the initialization of the algorithm population satisfies the mass conservation condition and prepares for the subsequent iterative optimization process.

[0172] Step 3: Define the fitness function. Define the fitness function to evaluate the performance of each candidate solution, including power loss, voltage deviation, and system reliability index, etc.

[0173] Step 3.1: Determine the constraint conditions. In the power system, the change in voltage is required to be kept within the limit range:

[0174]

[0175] At the same time, keep the change in bus voltage within the range of ±10%, and the change in feeder voltage within the range of ±5%:

[0176]

[0177] The numerical results of the base value, minimum value, and maximum voltage value of each bus test system can be found in Appendix A.

[0178] Meanwhile, the current-carrying capacity of the cables in the system should not exceed the maximum current limit:

[0179]

[0180] Step 3.2: Define the optimization objective function

[0181] Considering certain constraints, the basic solution of the power system reconfiguration problem can be obtained by minimizing power losses and increasing the bus voltage. The present invention aims to minimize losses by maintaining the expected value of the bus voltage in the system. For this purpose, the active power loss in the power system is calculated using the following formula:

[0182] P loss(i,k) = r i,k ·|I i,k | 2

[0183] The power loss in a distribution system with a dynamic structure is obtained by summing the loss values of the active branches, and the total loss on the distribution system is defined by the equation:

[0184]

[0185] where i - k represents the bus number, P k and Q k represent the active power and reactive power values of the k-th bus, r represents the branch resistance between the i-th bus and the k-th bus, V k represents the bus voltage, N br represents the number of branches, and S w represents whether the branch is active. When the branch is active, its value is "1", otherwise its value is "0".

[0186] The following equation gives the reduction in active power loss before and after reconfiguration of the PDN

[0187]

[0188] Step 3.3: Define the voltage deviation index DV D :

[0189]

[0190] where V i is the voltage magnitude of the i-th bus, and N bus is the total number of buses.

[0191] One of the main advantages of minimizing voltage deviation is to eliminate the poor configurations obtained by PDNR optimization. Thus, the bus voltage and the performance of the power system are improved.

[0192] In the multi-objective optimization method, the weighted summation method (WSA) attempts to transform the multi-objective optimization problem into a single-objective function. The PDN optimization problem can be solved using an equation as the single-objective function. The objective function considering the PDNR problem is used to minimize the active power loss and voltage deviation.

[0193] Combine the above two objectives into a single objective function:

[0194]

[0195] where X1 and X2 are weight coefficients, which are selected as 2 / 3 and 1 / 3 respectively.

[0196] Therefore, the objective of the fitness function is to minimize the reconstructed power loss and voltage deviation, so as to obtain the optimal topology of the distribution network. The whole process needs to meet some constraints, such as voltage magnitude limit, bus current limit and radial network structure, etc.

[0197] Step 4: Execute the EO algorithm. According to the current state of the power system and the objective function, iteratively search for the optimal solution through the dynamic adjustment of the equilibrium state. In each iteration, update the position and velocity of the particles according to the rules of the equilibrium optimizer. Evaluate the fitness of each particle, and update the global optimal and individual optimal solutions according to the fitness.

[0198] Step 4.1: Initialize the size n of the population and the initial parameters of each particle (refer to Step 2).

[0199] Among them, select the best four particles and their concentrations (positions of the particles) defined in the optimization process as the candidate solutions of the search algorithm. Calculate the arithmetic mean of the selected four particles, which represents the balance (solution) of the fifth particle. They are used to create the vector of the balance pool, as shown in the following formula:

[0200]

[0201] Step 4.2: Calculate the fitness value of each particle in the objective function (refer to Step 3).

[0202] Among them, the fitness function (f) needs to satisfy:

[0203]

[0204] Step 4.3: Calculate the updated concentration

[0205] c) Generate a random vector \(\vec{r}\) and (taking values between [0, 1])

[0206]

[0207]

[0208] where

[0209]

[0210] Finally

[0211]

[0212] Step 4.4; Calculate the generation rate parameter

[0213]

[0214] where

[0215]

[0216] GP takes the value of 0.5

[0217] Step 4.5: Measure the diversity index of the balance pool using the recycling strategy:

[0218] a) Calculate the Euclidean distance between particles in the balance pool to measure the diversity index I of the balance pool DV :

[0219]

[0220] where N eq is the number of particles in the balance pool.

[0221] b) Decide whether to perform exploitation or exploration operations according to the value of the diversity index I DV :

[0222]

[0223] where C dmax and C dmin are the minimum and maximum values of the variables respectively, rand and ∈ are random numbers, and € is a specific value.

[0224] Step 4.6: Use the improved concentration update equation of IEO to further optimize and update the concentration of particles:

[0225] C new = C eq + G[λ(1 - F)+(C - C eq )F]

[0226] where F is the exponential term and G is the generation rate. If the newly generated is better than the previous position, then replace it.

[0227] Step 4.7: Repeat Steps 3 - 4 until the termination condition (maximum number of iterations or convergence) is met.

[0228] Step 4.8: Output the best solution and execute the network reconstruction decision.

[0229] The network is reconstructed according to the switch state configuration of the distribution network, the location of distributed generation units and the power generation configuration obtained by the EO algorithm to achieve the predetermined optimization goal.

[0230] Application Examples

[0231] The present invention proposes a comprehensive improved balancer optimization algorithm (NIEO), and verifies the applicability of the method on a 33-node IEEE standard power distribution test system. The specific steps include:

[0232] Step L1: define the objective function;

[0233] Step L1.1: The objective function of the present invention includes two parts:

[0234] (1) Minimize active power loss, the formula is as follows:

[0235]

[0236] Where ik represents the bus number, P k and Q k represents the active power and reactive power value of the kth bus, r represents the branch resistance between the i-th bus and the k-th bus, V k Indicates bus voltage, N br Indicates the number of branches, S w Indicates whether the branch is active. When the branch is active, its value is "1", otherwise its value is "0".

[0237] (2) Minimize the voltage deviation index DVD, the formula is as follows:

[0238]

[0239] Where V i is the voltage amplitude of the ith bus, N bus is the total number of buses.

[0240] Step L1.2: Combine the above two objectives into a single objective function:

[0241]

[0242] Among them, X1 and X2 are weight coefficients, which are selected as 2 / 3 and 1 / 3 respectively.

[0243] Step L2: Define constraints

[0244] (1) Bus voltage limitation:

[0245]

[0246] (2) Feeder voltage limitation:

[0247]

[0248] (3) Branch current limit:

[0249]

[0250] Step L3: Radial structure inspection

[0251] Method 1: To ensure the radiality of the network topology, the following conditions need to be met:

[0252] (1) Number of switches to be opened:

[0253] ∧ = B - N + S

[0254] (2) Node power supply independence: Each load has its own power supply

[0255] (3) The network has no loops

[0256] (4) All nodes are located within the subgraph

[0257] Method 2: Create a bus incidence matrix:

[0258]

[0259] Check whether the network is a radial network:

[0260]

[0261] Where A is the obtained submatrix. When its determinant is ±1, it means that the distribution network operates in a radial topology.

[0262] Step L4: Power flow calculation

[0263] The present invention uses the power summation method based on backward / forward (B / F) to calculate the current flow (as Figure 3 ), including 5 steps:

[0264] (1) Initialize all bus voltages to 1 p.u.

[0265] (2) Calculate the active and reactive powers of the branch impedance

[0266]

[0267] Where the superscripts L, inj, and F1 in P and Q respectively represent load, injection, and flow. And respectively represent the total active and total reactive flows through the entire downstream line connected to bus k.

[0268] (3) Calculate the active and reactive power of each branch through backward scanning

[0269]

[0270] (4) Calculate the voltage magnitude and phase angle of each bus through forward scanning

[0271]

[0272] Among them

[0273]

[0274] I s flows through the impedance (Z s = R s + jX s ), the voltage magnitude and angle at the bus can be written as:

[0275]

[0276] Among them

[0277]

[0278] If the voltage angle (d i ) of bus i is not equal to zero, then the voltage angle (d k ) of the kth bus becomes:

[0279] d k = d i - tan -1 (a1 - a2)

[0280] Use the above formula to determine the voltage magnitude and angle of each bus in the network in a forward iterative manner.

[0281] (5) Iterate until the convergence condition is met

[0282]

[0283] Among them, n b and iter are the number of branches and the number of iterations. If the calculated value is less than the selected value ∈, the iteration is terminated (∈ takes the value of 10 -6 ) in the present invention, otherwise return to step (2).

[0284] Solution of the L5.EO algorithm

[0285] The EO algorithm is a new heuristic optimization algorithm that simulates the equilibrium state of a simple dynamic system. Its iterative process ( Figure 4 ) includes the following steps:

[0286] Step L5.1: Determine the size n of the population and the initial parameters of each particle

[0287] Among them, select the best four particles and their concentrations (particle positions) defined during the optimization process as candidate solutions for the search algorithm. Calculate the arithmetic mean of the selected four particles, which represents the balance (solution) of the fifth particle. They are used to create the vector of the balance pool, as shown in the following formula:

[0288]

[0289] Step L5.2: Calculate the fitness value of each particle in the objective function.

[0290] Among them, the fitness function (f) needs to satisfy:

[0291]

[0292] Step L5.3: Calculate the updated concentration

[0293] e) Generate a random vector $\vec{r}$ and (taking values between [0, 1])

[0294] f) Define the function as follows

[0295]

[0296] Among them

[0297]

[0298] Finally

[0299]

[0300] Step L5.4; Calculate the generation rate parameter

[0301]

[0302] Among them

[0303]

[0304] GP takes the value of 0.5

[0305] Step L5.5: Use the recycling strategy to measure the diversity index of the balance pool:

[0306] a) Calculate the Euclidean distance between particles in the balance pool to measure the diversity index I of the balance pool DV :

[0307]

[0308] Among them, N eq is the number of particles in the equilibrium cell.

[0309] b) According to the diversity index I DV The value of determines whether to perform exploitation or exploration operations:

[0310]

[0311] Among them, C dmax and C dmin are the minimum and maximum values ​​of the variable, rand and ∈ are random numbers, and € is a specific value.

[0312] Step L5.6: Use the improved concentration update equation of IEO to further optimize the concentration of updated particles:

[0313] C new =C eq +G[λ(1-F)+(CC eq )F]

[0314] Among them, F is the exponential term and G is the generation rate. If it is better than the previous position, replace it.

[0315] Step L5.7: Repeat steps L5.3-L5.4 until the termination condition (maximum number of iterations or convergence) is met.

[0316] Step L5.8: Output the best solution and execute network reconfiguration decisions.

[0317] According to the switch state configuration of the distribution network, the location of the distributed generation unit and the power generation configuration obtained by the NIEO algorithm, the network is reconstructed to achieve the predetermined optimization goal. Taking the 33 bus system as an example, considering several different load moments, a simple comparison of the power loss before and after optimization is made, as shown in Table 1.

[0318] The present invention realizes comprehensive improvement and optimization based on the EO algorithm through the above method, makes better use of the search space and expands the search around the local optimal point, improves the optimization efficiency and effect, effectively reduces the active power loss, improves the voltage quality and system reliability, and performs well in dynamic network reconstruction and renewable distributed power generation unit configuration problems.

[0319] The above are only specific embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0320] Table 1

[0321]

Claims

1. A power distribution network reconstruction method based on a comprehensive improved balance optimization algorithm, characterized in that: The steps include: Step 1: Establish a network model, and establish a mathematical model of the power distribution network, including all buses, branches, switches and related electrical parameters; Step 2, E0 algorithm initialization, setting the initial parameters of the E0 algorithm, including particle parameters, the number, position and speed of particles; Step 3, define a fitness function to evaluate the performance of each candidate solution, including power loss, voltage deviation, and system reliability indicators; Step 4: Execute the E0 algorithm to iteratively search for the optimal solution by dynamically adjusting the equilibrium state according to the current state of the power system and the objective function. In each iteration, the position and velocity of the particle are updated according to the rules of the equilibrium optimizer, the fitness of each particle is evaluated, and the global optimal solution and the individual optimal solution are updated according to the fitness. Step 5: Network reconstruction: Reconstruct the network according to the switch state configuration of the distribution network, the location of the distributed generation units and the power generation configuration obtained by the E0 algorithm to achieve the predetermined optimization goal.

2. The method for reconfiguring a power distribution network based on a comprehensive improved balance optimization algorithm according to claim 1, characterized in that: The step 1 specifically includes: Step 1.1, determine the network topology, change the switch position in the distribution network, so that it still maintains the radial topology. The following are the necessary conditions for maintaining the radial structure of the network at the end of the reconstruction: Number of switches in branch-maintained radial structure: ∧=B-N+S Among them, B, N, and S are the number of branches, busbars, and feeders, respectively; When operating in a radial system, the following conditions must be met: <1> Each load has its own supply source; <2> There are no loops (closed loops) in the network; <3> All nodes are within the subgraph; The number of S on the radial distribution line satisfies: N S =N Bus -1 Create a bus incidence matrix: Check if the network is a radial network: Where A is the obtained submatrix, and when its determinant is ±1, it means that the distribution network operates in a radial topology; Step 1.2: Select the power flow calculation algorithm, and use the model formula of the power summation method based on the forward and backward algorithm (B / F). The power flow problem of a single source is determined by a bidirectional recursive equation. Based on this, the line is connected between buses i and k, where bus i is closer to the feeder and the branch impedance is Z s =R s +jX s , the branch shunt admittance is y s , where the total shunt admittance is between buses i and k; The power summing algorithm consists of the following steps, (1) Assume that all bus voltages are 1p.u, that is, (2) Calculate the active power of branch impedance and reactive power The superscripts L, inj, and F1 in P and Q represent load, injection, and flow, respectively. and denote the total active and total reactive flows through the entire downstream line connected to bus k, respectively; (3) Calculate the active power (P) near bus I s ) and reactive power (Q s ) Trend (scan backward): (4) Calculate the voltage amplitude and angle of each bus (forward scan): in I s The current flows through the impedance (Z s =R s +jX s ), the voltage magnitude and angle at the bus are written as: in If the bus voltage angle (d i ) is not equal to zero, then the kth bus voltage angle (d k )become: <h2 style=";text-align:left;direction:ltr">d<h2 style=";text-align:left;direction:ltr"> k <h2 style=";text-align:left;direction:ltr"> =d<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> -tan<h2 style=";text-align:left;direction:ltr"> -1 <h2 style=";text-align:left;direction:ltr"> (a1-a2) Use the above formula to determine the voltage magnitude and angle of each bus in the network in a forward iterative manner; (5) Compare the receiving end voltage with the values ​​of the previous and next iterations, and calculate the absolute error, Among them, n b and iter is the number of branches and iterations. If the calculated value is less than the selected value ∈, the iteration is terminated, otherwise return to step (2).

3. The method for reconfiguring a power distribution network based on a comprehensive improved balance optimization algorithm according to claim 1, characterized in that: The step 2 specifically includes: Step 2.1, initialize the population size n and dimension d; Step 2.2: Generate an initial concentration vector for each particle i The initial value of each dimension is within the predefined upper and lower boundaries [L b , U b ] Randomly generated within: in, represents the initial concentration vector of the ith particle, rand(i) returns a uniform random number in the interval [0, 1], L b and U b are the minimum values ​​of all dimensional vectors (C min ) and the maximum value (C max ), n represents the number of particles in the population; Step 2.3, calculate the initial mass of each particle and normalize it Step 2.4, calculate the equilibrium candidate solution C for each particle eq(i) : Step 2.5, calculate the average C of the equilibrium candidate solution eq(ave) : C eq(ave) =sum(C eq(i) ) / n Step 2.6, build balance pool C eq(pool) , which contains all C eq(i) and C eq(ave) .

4. The method for reconfiguring a power distribution network based on a comprehensive improved balance optimization algorithm according to claim 1, characterized in that: So step 3 specifically includes: Step 3.1, determine the constraints. In the power system, the voltage change is required to remain within the limit value range: At the same time, the bus voltage variation is kept within ±10% and the feeder voltage variation is kept within ±5%: At the same time, the current carrying capacity of the cables in the system should not exceed the maximum current limit: Step 3.2, define the optimization objective function, and obtain the basic solution of the power system reconstruction problem by minimizing the power loss and improving the bus voltage under certain constraints. Minimize the loss by keeping the bus voltage at the expected value in the system, and calculate the active power loss in the power system using the following formula: P loss(i，k) =r i，k ·|I i，k | 2 The power loss in a distribution system with a dynamic structure is obtained by the sum of the loss values ​​of the active branches. The total loss on the distribution system is defined by the equation: Where ik represents the bus number, P k and Q k represents the active power and reactive power value of the kth bus, r represents the branch resistance between the i-th bus and the k-th bus, V k Indicates bus voltage, N br Indicates the number of branches, S w Indicates whether the branch is active. When the branch is active, its value is "1", otherwise its value is "0"; The following equation gives the PDN before reconfiguration: and after reconfiguration Reduced active power loss Step 3.3, define the voltage deviation index DV D : Where V i is the voltage amplitude of the ith bus, N bus is the total number of buses; Determine a single objective function: Among them, X1 and X2 are weight coefficients, which are selected as 2 / 3 and 1 / 3 respectively; The goal of the fitness function is to minimize the power loss and voltage deviation after reconstruction, thereby obtaining the optimal topology of the distribution network.

5. The method for reconfiguring a power distribution network based on a comprehensive improved balance optimization algorithm according to claim 1, characterized in that: The step 4 specifically includes: Step 4.1, initialize the population size n and the initial parameters of each particle; Among them, the best four particles and the positions of the particles defined in the optimization process are selected as candidate solutions of the search algorithm; the arithmetic mean of the selected four particles is calculated to represent the balance of the fifth particle, and the vector of the balance pool is created, as shown in the following formula: Step 4.2, calculate the fitness value of each particle in the objective function; Among them, the fitness function (f) needs to satisfy: Step 4.3, calculate the updated concentration, a) Generate a random vector and (value between [0, 1]) b) Define the exponential function as follows: in at last Step 4.4, calculate the generation rate parameter: in Step 4.5, using the recycling strategy to measure the diversity index of the balance pool, a) Calculate the Euclidean distance between particles in the balancing pool and measure the diversity index I of the balancing pool DV : Among them, N eq is the number of particles in the equilibrium cell; b) According to the diversity index I DV The value of determines whether to perform exploitation or exploration operations: Among them, C dmax and C dmin are the minimum and maximum values ​​of the variable, rand and ∈ are random numbers. is a specific value; Step 4.6, use the improved concentration update equation of IEO to further optimize the concentration of updated particles: C new =C eq +G[λ(1-F)+(C-C eq )F] Among them, F is the exponential term, G is the generation rate, if the new generation If the position is better than the previous one, replace it; Step 4.7, repeat steps 4.3-4.4 until the termination condition is met; Step 4.8: Output the best solution and execute network reconfiguration decisions.

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