A multi-objective optimization method for distribution network with distributed generation considering carbon emissions

Abstract

A multi-objective optimization method for a distribution network containing distributed power sources taking into account carbon emissions, comprising the following steps: 1) constructing a multi-objective optimization model for the distribution network; 2) using a hierarchical analysis method to determine the weights of each objective function in the above-mentioned multi-objective optimization model; 3) using an improved beetle whisker particle swarm algorithm to improve the global search capability and local search accuracy of the algorithm for solving the above-mentioned multi-objective optimization model. By integrating a multi-objective optimization model and an improved hierarchical analysis method, the present invention not only optimizes economic indicators, but also takes carbon emission costs into consideration for the first time, thereby achieving the dual economic and environmental benefits of distribution network planning. The improved beetle whisker particle swarm algorithm used further improves the search efficiency and solution accuracy, ensuring the robustness and rapid convergence of the algorithm when dealing with high-dimensional complex problems. The method effectively reduces network losses and carbon emissions, improves voltage distribution, and provides technical support for the green transformation and sustainable development of power systems.

Description

Technical Field

[0001] The present invention relates to the field of power system energy optimization, and in particular to a multi-objective optimization method for a distribution network containing distributed power sources taking carbon emissions into consideration. Background Art

[0002] As an indispensable part of the power system, the distribution network bears the important responsibility of transmitting the main grid power to the end users. The development and application of distributed power sources have technical problems such as harmonic pollution and abnormal increase of short-circuit current. The access of distributed power sources, especially their installation location and capacity, has an important impact on the power flow distribution, network loss, voltage distribution and carbon emissions of the distribution network. The optimal configuration of distributed power sources involves the optimal location and capacity, which is a large-scale nonlinear combination optimization problem. In recent years, many scholars have studied the optimal configuration of distributed power sources from different angles. Some studies have established a planning model with the lowest active network loss cost and user power purchase cost, and used improved algorithms to solve the model, but these studies may ignore the influence of environmental factors. Some studies have also proposed new system voltage enhancement indicators, but they have not fully considered economic and environmental factors. In addition, some studies have tried to combine the beetle whisker algorithm with the particle swarm algorithm to solve the economic load distribution problem of the power system, and found that its optimization effect is better than the traditional algorithm. Summary of the invention

[0003] In response to the challenge of optimizing the configuration of distributed power sources in the power system, this paper proposes a distribution network optimization dispatching method that comprehensively considers carbon emissions and economic efficiency. This paper designs an incentive strategy that combines carbon emission trading and green certificate trading, aiming to stimulate market players to actively participate in environmental rights and interests trading, thereby improving the carbon emission reduction efficiency of the overall power system and the absorption capacity of new energy.

[0004] The multi-objective optimization method of a distribution network containing distributed generation considering carbon emissions described in the present invention aims to optimize the configuration of distributed generation (DG) in the distribution network to achieve the dual goals of economy and environmental protection. It includes the following steps:

[0005] Step 1: Construct a DG optimization configuration model. First, establish a DG optimization configuration model. The objective function is the annual investment and operation cost, user electricity purchase cost, active network loss and annual carbon emissions. The power balance constraint, voltage constraint, distribution line limit transmission power, DG device capacity, DG active power output constraint and reactive power constraint are used as constraints. These constraints ensure the stability of the network after DG is connected to the distribution network, and then plan a suitable optimization configuration plan.

[0006] Its objective function is:

[0007] 1) DG investment cost

[0008]

[0009] Where: x i Whether to install DG on the node; N d is the number of nodes where DG is installed; r is the fixed annual interest rate, which is 0.07; T is the planning period; C Di The investment cost of installing DG at node i; C ri is the DG operating cost; P DGi Indicates the capacity of the DG installed on node i.

[0010] 2) User electricity purchase cost

[0011] f2=(P w -P ∑DG -(P loss -P′ loss ))T max C e

[0012] Where: P w is the total capacity of the system; P ∑DG is the total active output of DG; P loss and P' loss are respectively the active power loss before and after connecting to DG; T max is the annual maximum load utilization hours; C e The unit electricity price.

[0013] 3) Network loss costs

[0014] The objective function is constructed based on the minimum active network loss of the system

[0015]

[0016] Where: P loss is the active network loss of the distribution network; N b is the number of branches; G k is the conductance of the kth branch between nodes i and j; U i is the voltage amplitude of node i; U j is the voltage amplitude at node j; δ ij is the voltage phase angle difference between nodes i and j.

[0017] The system's active network loss is converted into economic indicators as shown in the formula.

[0018] f3=P loss T max C e

[0019] Where: T max is the annual maximum load utilization hours; C e The unit electricity price.

[0020] 4) Carbon emission fees

[0021] In order to achieve the best energy-saving and emission-reduction effect of the system after planning, the present invention constructs the objective function with the lowest annual carbon emission cost of the system, as shown below.

[0022] f4=C C (P loss +P load -P ∑DG )T max

[0023] Where: C C Penalty fee per unit of carbon emissions; P load is the total load; when generating electricity with traditional fossil energy, 0.344t of coal is needed to produce 1MW·h, and burning 1t of coal produces 2620kg of CO2. The national penalty for carbon emissions is 9.75 yuan / t.

[0024] The constraints are:

[0025] 1) Node power balance constraints

[0026]

[0027] Where: P Gi , Q Gi are the active and reactive power injected at node i, U i , U j are the voltage amplitudes at nodes i and j respectively, G ij , B ij are the conductance and susceptance between nodes i and j, respectively, θ ij is the phase angle difference between nodes i and j.

[0028] 2) Node voltage constraints

[0029] U imin ≤U i ≤U imax

[0030] Where: U imin , U imax are the upper and lower limits of the voltage at node i respectively.

[0031] 3) Transmission line maximum transmission power constraints

[0032] P ij <P ij,max

[0033] Where: P ij is the transmission power of the line between nodes i and j, P ij,max It is the maximum rated power allowed to be transmitted on the line.

[0034] 4) DG access capacity constraints

[0035] P DG <μ∑P load

[0036] Where: μ is 0.25; ∑P load is the total system load capacity.

[0037] Step 2: Determine the weight coefficient of the multi-objective function. Comprehensively consider the four objective functions of DG investment cost, user power purchase cost, network loss cost and carbon emission cost. Since the value range of each objective function is different, in order to make the objective functions at the same level and better weigh the weights between them, each sub-objective is dimensionless to improve the efficiency and accuracy of the optimization process. The present invention adopts the extreme standard method in the linear dimensionless method.

[0038]

[0039] Where: i = 1, 2…m; j = 1, 2…n; y ij is the data after target extreme differentiation; x ij is the value of evaluation strategy i and index j; max{x ij} and min{x ij} are x ij The maximum and minimum values ​​of .

[0040] Regarding the improved analytic hierarchy process, Saaty proposed the analytic hierarchy process (AHP) in 1970. This method uses the 9-scale method to construct the judgment matrix. However, when there are many indicator factors, the scaling method has a large amount of calculation and the differences are unclear. In addition, due to the inconsistent focus of decision makers and the deviation of expert experience, the calculation results of the final weights will have certain ambiguity and range, and the probability of failing the consistency test will increase. Therefore, improvements are made to the above two points: the 5-scale method (0, 0.25, 0.5, 0.75, 1) is used to compare each indicator to obtain a comparison matrix; then mathematical knowledge is used to convert the comparison matrix into a consistency judgment matrix, thereby avoiding the subsequent consistency test. The steps for obtaining subjective weights using the improved analytic hierarchy process are as follows:

[0041] The 5-scale method is used to compare the importance of each indicator factor to obtain the comparison matrix A = {a ij} n×n , where n is the number of indicators, and the definitions of different scale values ​​are as follows:

[0042]

[0043] 1) Construct an indirect judgment matrix B from the comparison matrix A = {b ij} n×n , first, define as shown in the formula:

[0044]

[0045] Where: r i is the sum of each row of matrix A; r max and r min r i The maximum and minimum values ​​of m The base point for comparison scale.

[0046] The matrix B is obtained through the mathematical transformation shown in the following formula.

[0047]

[0048] Obviously, the matrix B satisfies: ii =1, b ij =1 / b ji .

[0049] 2) Use the logarithmic method to further transform the matrix B within the error tolerance range, so that the judgment matrix C = {c ij} n×n Satisfy the consistency test, as shown in the formula:

[0050]

[0051] For any i, j, s = 1, 2…n, it can be proved by the formula that the judgment matrix C satisfies consistency.

[0052]

[0053] 3) Through the calculation of traditional hierarchical analysis method, as shown in the formula, the subjective weight α of each indicator is obtained: i .

[0054]

[0055] Normalize the multiple targets

[0056] After each sub-goal is dimensionless, the hierarchical analysis method is used to subjectively weight each objective function, thereby determining the weight of each sub-goal and unifying multiple sub-objective functions into:

[0057]

[0058] Where: i is the weight coefficient; f is the dimensionless objective function.

[0059] Step 3: Use the improved beetle beard particle swarm algorithm to solve

[0060] Particle swarm optimization algorithm is an optimization algorithm that simulates bird predation behavior. The mathematical expressions for updating particle velocity v and position x are shown as follows:

[0061] v i (t+1)=v i (t)+c1r1(t)[p i,best -x i (t)]

[0062] +c2r2(t)[g best -x i (t)]

[0063] x i (t+1)=x i (t)+v i (t+1)

[0064] Where: c1 and c2 are both non-negative learning parameters; r1 and r2 are random numbers between (0,1) to ensure population diversity; t is the number of iterations; p i,best is the individual fitness value recorded for the i-th particle; g best The extreme fitness value recorded for the particle population.

[0065] Although the particle swarm optimization algorithm has advantages in convergence speed, it lacks dynamic adjustment of particle speed and is easy to fall into local optimum. In addition, the convergence accuracy is low in the late convergence stage and it is difficult to converge. To address the above problems, the beetle whisker search algorithm is used to provide autonomous optimization capability for particle speed adjustment.

[0066] In 2017, Jiang and Li were inspired by the foraging and mate-seeking behaviors of longhorn beetles and proposed a new bionic optimization algorithm - the longhorn beetle whisker search algorithm. The algorithm has low complexity and is easy to implement. It can achieve the optimization purpose without clarifying the specific form and gradient information of the objective function to be optimized. Its bionic principle is: in the process of looking for food, the longhorn beetle does not know the specific location of the food. It captures the concentration of odor in the surrounding environment through the left and right antennae on its head. If the longhorn beetle detects that the concentration perceived by the left antennae is higher, it will move to the left; otherwise, it will move to the right. Through this simple principle, the longhorn beetle can eventually find food effectively. By combining the longhorn beetle whisker algorithm and the particle swarm algorithm, and using the local search capability of the longhorn beetle whisker algorithm and the global search capability of the particle swarm algorithm at the same time, a better optimization solution can be found. The disadvantage is that the longhorn beetle cannot dynamically balance the global search and the local search when searching for the best, and it is not easy to jump out of the local optimal solution in the late convergence period. Therefore, three improvements are made to the longhorn beetle whisker algorithm. Therefore, the present invention applies three different methods to the longhorn beetle whisker particle swarm algorithm, which are as follows:

[0067] 1) Logistic chaotic mapping.

[0068] According to the randomness, ergodicity and regularity of chaotic mapping, the population is initialized with a chaotic sequence so that the individuals of the population are evenly distributed in the entire area, and the population diversity is improved without changing the randomness of the population, thereby improving the quality of the solution. Among them, the Logistic chaotic mapping shows stronger global ergodicity than other chaotic mappings, so the present invention adopts the Logistic chaotic mapping.

[0069] First, the population positions and velocities are randomly generated and mapped to (0,1).

[0070]

[0071] Where: x max and x min are the maximum and minimum values ​​of the position respectively; v max and v min are the maximum and minimum speed respectively.

[0072] Then, x ci and v ci Substitute into the Logistic chaotic map to get x ci+1 、v ci+1 .

[0073]

[0074] Wherein: μ∈(0,4), when 3.5669<μ<4, it enters a chaotic state, and when μ is closer to 4, the generated sequence distribution is more uniform, and in the present invention, μ is taken as 4.

[0075] Finally, the chaotic value is transformed into the search space of the population using the following formula, generating the initial values ​​of the new population position and velocity as x' ci 、v' ci .

[0076]

[0077] 2) Dynamic inertia weight.

[0078] The coefficient of the position inherited by the longhorn beetle from the previous generation is 1, and it is easy to fall into a rigid state when the position is updated, which makes the longhorn beetle unable to dynamically balance the global search and local search when searching for the best, thereby reducing the selection diversity of the search space. By adjusting the weight size, the global search and local search of the longhorn beetle algorithm can be balanced. In the initial stage of iteration, choosing a larger weight can make the previous generation of longhorn beetles have a greater impact on the current longhorn beetle, thereby avoiding premature convergence and enhancing the global search ability. In the later stage of iteration, gradually reduce the weight to reduce the connection with the previous generation of longhorn beetles, improve the local search ability of longhorn beetles, and help longhorn beetles converge quickly near the optimal value.

[0079] In the i-th iteration, the dynamic inertia weight w is determined as follows:

[0080] w=w max -(i / i max ) 3 ×(w max -w min )

[0081] Where: i max is the maximum number of iterations; in the invention, w is taken max =0.9; w min =0.4.

[0082] After the dynamic inertia weight is introduced, the position update formula of the longhorn beetle becomes:

[0083] x i =w·x i-1 +δ i asign(f l -f r )

[0084] 3) Levi flight trajectory optimization strategy.

[0085] Lévy flight is a random walk strategy that is often used to describe the position movement of animals in nature. This strategy has a heavy-tailed distribution and can move long and short distances. Long-distance movement can speed up the algorithm's optimization speed, while short-distance movement helps the algorithm to perform a more refined search. When the algorithm is locally developed in the later stage, it helps the algorithm to jump out of the local optimal solution. The introduction of the Lévy flight mechanism can speed up the algorithm's optimization speed and avoid falling into the local optimum. The expression of the Lévy flight movement mode L is shown in formula (31):

[0086]

[0087] Where: μ, v are standard normal distributions that obey N(0,1), Φ is The normal distribution of Γ is the standard Gamma function; in the present invention, λ=1.5.

[0088] The Levy flight mechanism L is introduced to optimize the position update method of the longhorn beetle. When the longhorn beetle self-learns, it adjusts according to the improved movement strategy. The position update method is shown as follows:

[0089] x i =w·x i-1 +L·δ i asign(f l -f r )

[0090] In terms of optimization and scheduling technology, the present invention innovatively proposes an improved beetle whisker particle swarm algorithm and applies it to the optimization and scheduling of distribution networks. Faced with complex distribution network optimization problems involving multiple variables and multiple constraints, the algorithm can effectively explore the global optimal solution in a vast search space and fully tap the potential optimization potential and optimal operation strategy of the system. At the same time, in view of the time-varying characteristics, uncertainty factors and multi-objective optimization requirements in the distribution network, the algorithm significantly improves the robustness and adaptability of the system through its flexible iterative search strategy. Overall, thanks to its global search capability, excellent adaptability and efficient computing performance, the improved beetle whisker particle swarm algorithm has become a key technical means to deal with the complexity and uncertainty in distribution network optimization problems.

[0091] Compared with the prior art, the present invention has the following advantages:

[0092] 1. The present invention establishes a model based on four indicators: DG annual investment cost, electricity purchase cost, network loss cost, and carbon emission cost. After normalization, the improved hierarchical analysis method is used to determine the target weights, and then the problem is converted into a single-objective problem for solution. Through example verification, the DG optimization configuration model established by the present invention can reduce the user's electricity purchase cost, effectively reduce the system network loss, and at the same time reduce the carbon emission cost, improve the overall voltage distribution of the system, and has a positive effect on the DG access to the distribution network.

[0093] 2. The improved analytic hierarchy process proposed in the present invention aims to solve the problems of unclear differences and large amount of calculation when using the 9-scale method when there are many indicator factors. At the same time, it can also reduce the ambiguity and range of weight calculation results caused by expert experience deviation and different emphasis of decision makers, and avoid later consistency tests. Specifically, the improved method uses the 5-scale method to compare each indicator factor to reduce the computational complexity caused by the number of scales. Then, within a certain error tolerance range, the comparison matrix is ​​converted into a consistency judgment matrix. This method can not only reduce the calculation time, but also improve the reliability of the judgment matrix and reduce the uncertainty of weight calculation.

[0094] 3. An improved particle swarm algorithm for beetle whiskers is proposed, which introduces Logistic chaotic mapping, dynamic inertia weight and Levy flight mechanism. Through simulation examples and comparison with the optimization results of standard particle swarm algorithm and beetle whisker particle swarm algorithm, it is verified that the improved particle swarm algorithm for beetle whiskers has good adaptability, better optimization results than other algorithms, faster convergence speed, higher robustness, and can maintain stable search performance when dealing with complex problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 This is a schematic diagram of the process of the improved particle swarm algorithm proposed in the present invention.

[0096] Figure 2 This is the IEEE33 distribution system diagram used in the example analysis.

[0097] Figure 3 is the voltage amplitude of each node of IEEE33 in the example analysis.

[0098] Figure 4 This is the convergence curve of the improved beetle whisker particle swarm algorithm proposed in the present invention. DETAILED DESCRIPTION

[0099] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The specific embodiments described here are only used to explain the technical solution of the present invention and are not limited to the present invention.

[0100] Step 1: Build a DG optimization configuration model, as follows:

[0101] Objective Function

[0102] 1) DG investment cost

[0103]

[0104] Where: x i Whether to install DG on the node; N d is the number of nodes where DG is installed; r is the fixed annual interest rate, which is 0.07; T is the planning period; C Di The investment cost of installing DG at node i; C ri is the DG operating cost; P DGi Indicates the capacity of the DG installed on node i.

[0105] 2) User electricity purchase cost

[0106] f2=(P w -P ∑DG -(P loss -P′ loss ))T max Ce

[0107] Where: P w is the total capacity of the system; P ∑DG is the total active output of DG; P loss and P' loss are respectively the active power loss before and after connecting to DG; T max is the annual maximum load utilization hours; C e The unit electricity price.

[0108] 3) Network loss costs

[0109] The objective function is constructed based on the minimum active network loss of the system

[0110]

[0111] Where: P loss is the active network loss of the distribution network; N b is the number of branches; G k is the conductance of the kth branch between nodes i and j; U i is the voltage amplitude of node i; U j is the voltage amplitude at node j; δ ij is the voltage phase angle difference between nodes i and j.

[0112] The system's active network loss is converted into economic indicators as shown in the formula.

[0113] f3=P loss T max C e

[0114] Where: T max is the annual maximum load utilization hours; C e The unit electricity price.

[0115] 4) Carbon emission fees

[0116] In order to achieve the best energy-saving and emission-reduction effect of the system after planning, the present invention constructs the objective function with the lowest annual carbon emission cost of the system, as shown in the formula.

[0117] f4=C C (P loss +P load -P ∑DG )T max

[0118] Where: C C Penalty fee per unit of carbon emissions; P loadis the total load. When using traditional fossil energy to generate electricity, 0.344 t of coal is needed to produce 1 MW·h. Burning 1 t of coal produces 2620 kg of CO2. The national penalty for carbon emissions is 9.75 yuan / t

[15] .

[0119] Constraints

[0120] 1) Node power balance constraints

[0121]

[0122] Where: P Gi , Q Gi are the active and reactive power injected at node i, U i , U j are the voltage amplitudes at nodes i and j respectively, G ij , B ij are the conductance and susceptance between nodes i and j, respectively, θ ij is the phase angle difference between nodes i and j.

[0123] 2) Node voltage constraints

[0124] U imin ≤U i ≤U imax

[0125] Where: U imin , U imax are the upper and lower limits of the voltage at node i respectively.

[0126] 3) Transmission line maximum transmission power constraints

[0127] P ij <P ij,max

[0128] Where: P ij is the transmission power of the line between nodes i and j, P ij,max It is the maximum rated power allowed to be transmitted on the line.

[0129] 4) DG access capacity constraints

[0130] P DG <μ∑P load

[0131] Where: μ is 0.25; ∑P load is the total system load capacity.

[0132] These constraints ensure the stability of the network after DG is connected to the distribution network, and then plan the appropriate optimization configuration plan.

[0133] Step 2: Determination of weight coefficients of multi-objective functions

[0134] Dimensionless:

[0135] Taking into account the four objective functions of DG investment cost, user electricity purchase cost, network loss cost and carbon emission cost, the objective functions in the domain have different value ranges. In order to make the objective functions at the same order of magnitude and better weigh the weights between them, each sub-goal is dimensionless to improve the efficiency and accuracy of the optimization process. The present invention adopts the extreme difference standard method in the linear dimensionless method, as shown in the formula.

[0136]

[0137] Where: i = 1, 2…m; j = 1, 2…n; y ij is the data after target extreme differentiation; x ij is the value of evaluation strategy i and indicator j;

[0138] Saaty proposed the Analytic Hierarchy Process (AHP) in 1970. This method uses the 9-scale method to construct a judgment matrix. However, when there are many indicator factors, the scaling method has a large amount of calculation and the differences are unclear. In addition, due to the inconsistent focus of decision makers and the deviation of expert experience, the calculation results of the final weights will have certain ambiguity and range, and the probability of failing the consistency test will increase. Therefore, improvements are made to the above two points: the 5-scale method (0, 0.25, 0.5, 0.75, 1) is used to compare each indicator to obtain a comparison matrix; then mathematical knowledge is used to convert the comparison matrix into a consistency judgment matrix, thereby avoiding the subsequent consistency test. The steps for obtaining subjective weights using the improved analytic hierarchy process are as follows:

[0139] 1) Use the 5-scale method to compare the importance of each indicator factor to obtain the comparison matrix A = {a ij}n×n, where n is the number of indicators, and the definitions of different scale values ​​are as follows:

[0140]

[0141] 2) Construct an indirect judgment matrix B from the comparison matrix A = {b ij}n×n, first, define it as follows:

[0142]

[0143] Where: r i is the sum of each row of matrix A; r max and r min r i The maximum and minimum values ​​of mThe base point for comparison scale.

[0144] The matrix B is obtained through the mathematical transformation shown in the following formula.

[0145]

[0146] Obviously, the matrix B satisfies: ii =1, b ij =1 / b ji .

[0147] 3) Use the logarithmic method to further transform the matrix B within the error tolerance range, so that the judgment matrix C = {c ij}n×n satisfies the consistency check, as shown in the formula:

[0148]

[0149] For any i, j, s = 1, 2…n, it can be proved by the formula that the judgment matrix C satisfies consistency.

[0150]

[0151] 4) Through the calculation of traditional hierarchical analysis method, as shown in the formula, the subjective weight α of each indicator is obtained i .

[0152]

[0153] Multi-objective normalization:

[0154] After each sub-goal is dimensionless, the hierarchical analysis method is used to subjectively weight each objective function, thereby determining the weight of each sub-goal and unifying multiple sub-objective functions into:

[0155]

[0156] Where: i is the weight coefficient; f is the dimensionless objective function.

[0157] See also Figure 1 , which is a flow chart of the improved beetle whisker particle swarm algorithm proposed in the present invention.

[0158] Step 3: Use the improved beetle beard particle swarm algorithm to solve the DG optimization configuration as follows:

[0159] 1) Input the distribution network structure parameters into the database, including node information, branch impedance, and load data; initialize the parameters, set the population size, dimension, maximum number of iterations, speed, and location.

[0160] 2) Initialize the population position X according to the Logistic chaos map i=(x i1 ,x i2 ,...,x iDdim ) and speed V i =(v i1 ,v i2 ,...,v iDdim ), and use the fitness function to calculate the individual optimal value p best , where the maximum value is the global optimal value g best .

[0161] 3) Enter iteration:

[0162] ① Set the acceleration coefficient c1 = c2 = 1.5, calculate w according to the formula, regard the initial position of each particle as the center of mass position of the beetle, and regard the initial velocity of the particle as the velocity of the beetle. Call the initial structural parameters of the distribution network in the database and re-establish the structural parameters according to the position of the beetle, perform power flow calculation, and then use the formula to calculate the fitness value f of the left and right antennae of the beetle respectively l 、f r ;

[0163] ② Use the improved update strategy, that is, update the current position of the longhorn beetle according to the formula, and update the particle speed according to the formula.

[0164] ③ The particle speed is processed out of bounds, and then the particle position is updated according to the formula and processed out of bounds. Finally, the fitness value f of the new particle position is x With p best For comparison, if f x <p best , then update p best , f x Assign to p best , otherwise unchanged;

[0165] ④Compare the global optimal value with the individual optimal value. If p best <g best Then p best Assign to g best , otherwise unchanged.

[0166] 4) Whether to terminate the iteration, if so, return the optimal value g best and the corresponding position; if not, update the step size of the longicorn and its decreasing factor, and return to the iteration phase.

[0167] See also Figure 2 and Figure 3 and Figure 4 , Figure 2 This is the IEE33 node power distribution system diagram. Figure 3 is the voltage amplitude of each node of IEEE33, Figure 4 The convergence curves of the improved beetle whisker particle swarm algorithm of the present invention are compared with those of other algorithms.

[0168] Step 4: Perform case analysis, as follows:

[0169] The proposed model is simulated and analyzed using the IEEE 33-node standard distribution system. The total network load of the distribution network is 3715kW+j2300kvar, its benchmark capacity is 10MVA, node 1 is set as the power node, the head end benchmark voltage is 12.66kV, and the power factor is 0.9. Annual maximum utilization hours T max =3200h; unit electricity price C e = 0.5 yuan / kWh; DG unit installation cost C Di = 1600 yuan / kW; operation and maintenance cost C ri =500 yuan / kW; the annual operating time of the system is 8760 hours.

[0170] Algorithm parameter settings: population size is 200; maximum number of iterations is 210; spatial dimension D dim is 30; the initial step size is 10; the step size decrease factor δ e is 0.95; the acceleration coefficient c1=c2=1.5.

[0171] The improved analytic hierarchy process is used to determine the weights of each objective function. The present invention takes weights w1=0.2118, w2=0.2660, w3=0.4047, and w4=0.1177 according to the calculation results.

[0172] The simulation example analysis is as follows:

[0173] According to the above parameters, simulation was carried out using particle swarm optimization, beetle whisker particle swarm optimization and improved beetle whisker particle swarm optimization. The results are shown in the following table.

[0174]

[0175] It can be seen from the table that before connecting to DG, the system's electricity purchase cost, network loss and carbon emission costs were all high. After the DG was optimized by the improved BAS-PSO algorithm proposed in the present invention, the electricity purchase cost was reduced from the original 5.6212 million yuan to 4.2945 million yuan, and the electricity purchase cost was reduced by 23.6% after optimization. The electricity purchase costs of the PSO algorithm and BAS-PSO algorithm were reduced by 21.95% and 22.31% respectively, both of which were less than the optimization results of the improved BAS-PSO algorithm. In terms of network loss, the network loss of the improved BAS-PSO algorithm was reduced from 201.72kW to 70.81kW, a reduction of 64.89%, and the network loss cost was significantly reduced, while the PSO algorithm and BAS-PSO algorithm were reduced by 55.96% and 62.18% respectively, both of which were lower than the optimization results of the improved BAS-PSO algorithm. From the perspective of carbon emission costs, the improved BAS-PSO algorithm has the best optimization results, which are reduced compared with the PSO algorithm and BAS-PSO algorithm. In the above schemes, nodes 9-18 and 30-33 are connected to more DGs and generally have higher capacities, which means that these nodes are suitable for installing DGs and are all located close to the end of the line.

[0176] After the improved BAS-PSO algorithm of the present invention is optimized, the lowest node voltage is 0.9581pu, the average voltage is 0.9742pu, and the voltage of each node in the distribution network has been significantly improved. In the first 18 nodes, the improved BAS-PSO algorithm has always been between the PSO algorithm and the BAS-PSO algorithm for the system node voltage. After the 18th node, the PSO algorithm improves the voltage level the worst. Between the 18th node and the 27th node, the improved BAS-PSO algorithm improves the node voltage to the best extent. After the 27th node, the BAS-PSO algorithm improves the voltage level slightly better than the improved BAS-PSO algorithm, but the overall voltage level is improved. The improved BAS-PSO is the best. In summary, the improved BAS-PSO algorithm has the best improvement in the system voltage.

Claims

1. A multi-objective optimization method for a distribution network containing distributed power sources considering carbon emissions, characterized by: The steps include: Step 1: Construct DG optimization configuration model: Establish DG optimization configuration model, the objective function is annual investment and operation cost, user power purchase cost, active network loss and annual carbon emission, with power balance constraint, voltage constraint, distribution line limit transmission power, DG device capacity, DG active power output constraint and reactive power constraint as constraint conditions; Step 2: Determine the weight coefficient of the multi-objective function: Comprehensively consider the four objective functions of DG investment cost, user power purchase cost, network loss cost and carbon emission cost. Since the value range of each objective function is different, each sub-objective is dimensionless to improve the efficiency and accuracy of the optimization process: the extreme difference standard method in the linear dimensionless method is used. After each sub-objective is dimensionless, the hierarchical analysis method is used to subjectively weight each objective function, thereby determining the weight of each sub-objective; Step 3: Use the improved beetle whisker particle swarm algorithm to solve the problem: combine the particle swarm algorithm with the beetle whisker algorithm, improve the search and convergence performance through the beetle perception mechanism, and use the local search of the beetle whiskers and the global search of the particle swarm to obtain a better solution; then make three improvements to the beetle whisker algorithm: introduce Logistic chaos mapping to improve population diversity and thus improve the quality of the solution; propose a dynamic inertia weight to improve the local search ability of the beetle, which helps the beetle to converge quickly near the optimal value; introduce the Levy flight mechanism to speed up the algorithm's optimization speed and avoid falling into the local optimum.

2. According to the multi-objective optimization method of the distributed power distribution network considering carbon emissions in claim 1, it is characterized by the analytic hierarchy process described in step 2, the steps are as follows: Comprehensively consider the four objective functions of DG investment cost, user power purchase cost, network loss cost and carbon emission cost. Since the value range of each objective function is different, in order to make the objective functions at the same level and better weigh the weights between them, each sub-objective is dimensionless to improve the efficiency and accuracy of the optimization process. The range standard method in the linear dimensionless method is adopted: Where: i = 1, 2…m; j = 1, 2…n; y ij is the data after target extreme differentiation; x ij is the value of evaluation strategy i and index j; max{xij} and min{xij} are x ij The maximum and minimum values ​​of ; 1) For the improved analytic hierarchy process, the 5-scale method (0, 0.25, 0.5, 0.75, 1) is used to compare the indicators to obtain a comparison matrix; then the comparison matrix is ​​converted into a consistency judgment matrix using mathematical knowledge to avoid the subsequent consistency test; the steps for obtaining the subjective weight using the improved analytic hierarchy process are as follows: The 5-scale method is used to compare the importance of each indicator factor to obtain the comparison matrix A = {a ij } n×n , where: n is the number of indicators, and the definitions of different scale values ​​are as follows: 2) Construct an indirect judgment matrix B from the comparison matrix A = {b ij } n×n , first of all, define it as follows: Where: r i is the sum of each row of matrix A; r max and r min r i The maximum and minimum values ​​of m It is a base point comparison scale; The matrix B is obtained by the mathematical transformation shown in the following formula: Obviously, the matrix B satisfies: ii =1, b ij =1 / b ji ; 3) Use the logarithmic method to further transform the matrix B within the error tolerance range, so that the judgment matrix C = {c ij } n×n Satisfies the consistency check, as shown below: For any i, j, s = 1, 2...n, it can be proved that the judgment matrix C satisfies consistency: 4) Through the calculation of traditional hierarchical analysis method, as shown in the formula, the subjective weight α of each indicator is obtained i ; Then normalize the multiple targets: After each sub-goal is dimensionless, the hierarchical analysis method is used to subjectively weight each objective function, thereby determining the weight of each sub-goal and unifying multiple sub-objective functions into: Where: i is the weight coefficient; f is the dimensionless objective function.

3. According to a multi-objective optimization method for a distributed power distribution network considering carbon emissions according to claim 1, it is characterized in that the particle swarm algorithm described in step 3 is combined with the longicorn beard algorithm to solve the problem, and the steps are as follows: (1) The mathematical expression of the beetle whisker search algorithm is as follows: 1) In n-dimensional space, set the centroid position of the longhorn beetle to x and the position of the longhorn beetle's left whisker to x l , the position of the right whisker of the longicorn is x r , the distance between the two whiskers is d, where x, x l , x lr All are n-dimensional vectors; 2) Initialize the position of the longhorn beetle. Since the direction of the longhorn beetle's center of mass is random, a random n-dimensional unit vector a is used to represent the direction of the longhorn beetle's head: Where: rands(n,1) is a randomly generated n-dimensional vector; 3) Determine the spatial position of the left and right whiskers of the longicorn: Where: x li and x ri are the spatial positions of the left and right whiskers of the longicorn in the i-th iteration; i is the number of iterations; d i is the i-th iteration; 4) Calculate the fitness values ​​of the left and right whiskers of the longhorn beetle and determine the step length factor: Where: f l 、f r are the fitness values ​​of the left and right whiskers of the longicorn beetle respectively; δ i is the step length of the longicorn in the i-th iteration; 5) Update the position of the longhorn beetle: x i =x i-1 +δ i asign(f l -f r ) Where: sign() is the sign function; 6) Update the distance between the two whiskers: d i =θd i-1 Where: θ is the set proportional coefficient, which is 0.95; 7) Determine whether the termination condition is met. If so, terminate the process. If not, repeat steps (2) to (6) until the termination condition is met. (2) Logistic Chaotic Mapping: The population is initialized with a chaotic sequence so that individuals are evenly distributed throughout the region, which improves population diversity and the quality of the solution without changing the randomness of the population. Logistic chaotic mapping is used: First, the population position and velocity are randomly generated and mapped to (0,1): Where: x max and x min are the maximum and minimum values ​​of the position respectively; v max and v min are the maximum and minimum values ​​of the speed respectively; Then, x ci and v ci Substitute into the Logistic chaotic map to get x ci+1 、v ci+1 : Where: μ∈(0,4), when 3.5669<μ<4, it enters a chaotic state. When μ is closer to 4, the generated sequence distribution is more uniform. Take μ as 3.998; Finally, the chaotic value is transformed into the search space of the population using the following formula, generating the initial values ​​of the new population position and velocity as x' ci 、v' ci : (3) Dynamic inertia weight: By adjusting the weight, the global search and local search of the beetle algorithm are balanced; in the initial stage of iteration, a larger weight is selected to make the previous generation of beetles have a greater impact on the current beetle, avoiding premature convergence and enhancing the global search ability; in the later stage of iteration, the weight is gradually reduced to reduce the connection with the previous generation of beetles, improve the local search ability of the beetle, and make the beetle converge quickly near the optimal value; In the i-th iteration, the dynamic inertia weight w is determined as follows: w=w max -(y / y max ) 3 ×(w max -w min ) Where: i max is the maximum number of iterations; take w max =0.9; w min =0.4; After the dynamic inertia weight is introduced, the position update formula of the longhorn beetle becomes: x i =w·x i-1 +δ i asign(f l -f r ) (4) Levi flight trajectory optimization strategy: The expression of Levi flight motion mode L is as follows: Where: μ, v are standard normal distributions that obey N(0,1), Φ is The normal distribution of Γ is the standard Gamma function; λ=1.5; The Levy flight mechanism L is introduced to optimize the position update method of the longhorn beetle. The longhorn beetle adjusts itself according to the improved movement strategy. The position update method is shown in the following formula: x i =w·x i-1 +L·δ i asign(f l -f r )。

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