Multi-objective power flow voltage optimization method for distribution network considering distributed photovoltaic access

Abstract

The present application relates to a kind of distribution network multi-objective power flow voltage optimization method considering distributed photovoltaic access, on the basis of multi-objective grey wolf algorithm search mechanism, join the disturbance mechanism of balance optimizer algorithm, further expand the search range of multi-objective swarm intelligence algorithm, effectively improve the convergence and distribution of algorithm search result;Compared with the existing swarm intelligence optimization algorithm, the optimization method proposed in the present application can provide better, more flow voltage optimization scheme for decision makers, more can meet the decision needs of decision makers under different target preferences, therefore can meet the scene demand of actual distribution network power flow voltage optimization.

Description

Technical Field

[0001] This invention relates to the field of distribution network technology, and more specifically to a multi-objective power flow voltage optimization method for distribution networks considering distributed photovoltaic access. Background Technology

[0002] The large-scale integration of distributed photovoltaic (PV) power into the distribution network will cause a series of power quality problems, including increased grid losses, power flow fluctuations, high voltage at the end of the distribution network, reverse power flow at the beginning of the distribution network, and three-phase imbalance. These issues pose new challenges to the safe, stable, and economical operation of the distribution system. Therefore, multi-objective power flow voltage optimization for distribution networks considering distributed PV integration has become an urgent need to ensure the power quality and safe and stable operation of the distribution network.

[0003] In practical applications, intelligent optimization algorithms that combine multi-objective Pareto dominance theory are generally used for multi-objective power flow voltage optimization of distribution networks. The main optimization algorithms include multi-objective particle swarm optimization (MOPSO), non-dominant sorting-based genetic algorithm (NSGA-II), multi-objective evolutionary algorithm (MOEA), multi-objective gray wolf pack algorithm (MOGWO), and multi-objective balance optimizer algorithm (MOEO).

[0004] In the application scenario of multi-objective power flow voltage optimization in distribution networks, due to the limitations of swarm update methods and external archive maintenance mechanisms, the solutions obtained by existing swarm intelligent optimization algorithms generally suffer from slow convergence speed, easy getting trapped in local optima, and poor Pareto front distribution performance. Summary of the Invention

[0005] The purpose of this invention is to propose a multi-objective power flow voltage optimization method for distribution networks that considers distributed photovoltaic access, in order to solve the technical problems that existing swarm intelligence optimization algorithms generally have slow convergence speed, are prone to getting trapped in local optima, and have poor Pareto front distribution performance.

[0006] To achieve the above objectives, this invention proposes a multi-objective power flow voltage optimization method for distribution networks considering distributed photovoltaic (PV) integration, the method comprising the following steps:

[0007] Step S1: Collect and process the operating data of each monitoring point in the power distribution network and the nameplate parameters of each power equipment;

[0008] Step S2: Based on the operating data and the nameplate parameters, perform system modeling of the distribution network and establish a multi-objective power flow voltage optimization control model;

[0009] Step S3: Set the initial parameters of the power flow voltage optimization algorithm and perform population initialization to obtain an initial population. Calculate the objective function value of each individual in the initial population and determine whether it meets the constraints. Select individuals from the initial population that are not dominated by other individuals according to the multi-objective Pareto dominance principle and store them in an external file.

[0010] Step S4: Select elite individuals from the external archives, perform group update according to the preset group update algorithm to obtain a new generation group; calculate the objective function value of each individual in the new generation group, and determine whether it meets the constraints.

[0011] Step S5: Based on the multiple Pareto dominance principle, select individuals from the new generation group that are not dominated by other individuals and store them in the external archive, and update the external archive; and ensure that the number of individuals in the external archive never exceeds a preset maximum value through a diversity maintenance mechanism;

[0012] Step S6: Determine whether the preset iteration termination condition is met. If the condition is not met, proceed to step S3 to continue the iteration. If the condition is met, stop the iteration and obtain the final power flow voltage optimization control scheme from the external file.

[0013] Preferably, the operational data includes voltage, current, and power at each monitoring point during different time periods; the power equipment includes distributed photovoltaic systems, power transformers, power lines, and reactive power compensation devices.

[0014] Preferably, step S2 includes:

[0015] With the optimization objectives of minimizing system loss, minimizing average voltage deviation, and minimizing curtailment rate of distributed photovoltaic equipment, and with the on-load tap changer taps, reactive power compensation capacity, and active and reactive power output of distributed photovoltaic equipment at each time period as decision variables, and with power flow balance constraints, system voltage operation constraints, and component current operation constraints as constraints, a multi-objective power flow voltage optimization model for distribution networks considering distributed photovoltaic access scenarios is established.

[0016] Preferably, step S3 includes:

[0017] Based on the Monte Carlo method, an initial population of a certain number of individuals is randomly and equally generated within the upper and lower bound constraints of the decision variables. Each individual in the initial population corresponds to a power flow voltage control strategy.

[0018] After generating the initial group, the power flow and voltage distribution under each power flow voltage control strategy are obtained through power flow calculation, and then the corresponding objective function value is calculated and it is determined whether it meets the preset requirements for safe and stable operation of the power system.

[0019] Based on the Pareto domination mechanism and the individual's objective function value, all individuals in the initial group are compared, and based on the comparison results, all individuals in the initial group that are not dominated by other individuals are stored in the external file.

[0020] Preferably, step S4 includes:

[0021] An adaptive grid-based sorting method is used to divide the target space into a grid consisting of multiple hypercubes. The hypercubes in the grid are selected by a roulette wheel selection method, and then an individual is randomly and equally selected from the selected hypercubes. The fewer individuals that a hypercube contains that are not dominated by other individuals, the higher the probability that the hypercube will be selected.

[0022] Repeat the above steps three times, and select three individuals from the external archives as elite individuals, and name them α individual, β individual and δ individual respectively.

[0023] Update each individual in the group using a preset group update method, as shown below:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] Where k is the current iteration number of the algorithm, and K is the maximum iteration number of the algorithm; X(k) and X(k+1) are the n-dimensional decision variables corresponding to any individual in the k-th and k+1-th generations of the population, respectively. α (k), X β (k), X δ (k) represents the n-dimensional decision variables corresponding to individuals α, β, and δ selected after the k-th selection; C1, C2, C3 are n-dimensional random vectors corresponding to individuals α, β, and δ, respectively, and follow a uniform distribution on the interval [-2, 2]; A1, A2, A3 are n-dimensional random vectors corresponding to individuals α, β, and δ, respectively, and follow a uniform distribution on the interval [-a, a]; a satisfies the relation Its value decreases as the number of iterations increases; λα , λ β , λ δ Let F be an n-dimensional random vector corresponding to individuals α, β, and δ, respectively, and follow a unit uniform distribution; α F β F δ Let n be the n-dimensional random vectors corresponding to individuals α, β, and δ, respectively, satisfying the relation r is an n-dimensional random vector that follows a unit uniform distribution. G is the product of element group operations; α G β G δ Let be the n-dimensional random vectors corresponding to individuals α, β, and δ, respectively, and satisfy the relationship shown in equation (9);

[0032]

[0033]

[0034] GCP = 0.5r1 × (r2 ≥ 0.5) × r

[0035]

[0036]

[0037] GCP = 0.5r1 × (r2 ≥ 0.5) × r

[0038]

[0039]

[0040] GCP = 0.5r1 × (r2 ≥ 0.5) × r

[0041] Where r1 and r2 are both random numbers that follow a uniform unit distribution.

[0042] Preferably, step S5 includes:

[0043] The update principle of the external archive is as follows: each non-dominated individual in the current population is compared with all individuals in the external archive according to the Pareto dominance principle; all dominated individuals in the external archive are deleted, and a new generation of individuals not dominated by any individuals in the external archive are stored in the external archive; the crowding distance of each individual in the external archive is calculated based on a crowding distance calculation mechanism, and a diversity maintenance mechanism is used to prevent the data capacity of the external archive from overflowing; wherein, the crowding distance calculation mechanism is as follows: all individuals in the external archive are sorted according to the size of the objective function value, and individuals with the smallest or largest function value are regarded as extreme individuals, and the rest are regarded as intermediate individuals; the crowding distance of the extreme individuals is set to infinitely large, while the crowding distance of the intermediate individuals is equal to the absolute normalized difference of the objective function values ​​of two adjacent individuals;

[0044] The diversity maintenance mechanism for external files is as follows: when the number of individuals in the external files exceeds the set maximum value, the individual with the smallest crowding distance in the external files is deleted until the number of individuals in the external files equals the preset maximum value.

[0045] The present invention has the following beneficial effects:

[0046] This invention incorporates a perturbation mechanism from a balance optimizer algorithm into the multi-objective gray wolf pack algorithm search mechanism, further expanding the search range of the multi-objective swarm intelligence algorithm and effectively improving the convergence and distribution of the algorithm's search results. Compared with existing swarm intelligence optimization algorithms, the optimization method proposed in this invention can provide decision-makers with higher quality and more diverse power flow voltage optimization schemes, better meeting the decision-making needs of decision-makers under different objective preferences, and thus better meeting the needs of actual power flow voltage optimization scenarios in distribution networks.

[0047] Other features and advantages of the present invention will be set forth in the following detailed description. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0049] Figure 1 This is a flowchart of a multi-objective power flow voltage optimization method for a distribution network considering distributed photovoltaic access, as described in an embodiment of the present invention.

[0050] Figure 2This is a schematic diagram of the topology of an IEEE 33-node power distribution system in a specific example of the present invention.

[0051] Figure 3 This is a schematic diagram of the daily active power output curve of a distributed photovoltaic device in a specific example of the present invention.

[0052] Figure 4 This is a schematic diagram of the daily power variation curve of a load node in a specific example of the present invention.

[0053] Figure 5 This is a schematic diagram of the Pareto front obtained by using the multi-objective gray wolf pack algorithm, the multi-objective equilibrium optimizer algorithm, and the proposed multi-objective swarm intelligent optimization algorithm to optimize an embodiment in a specific example of the present invention. Detailed Implementation

[0054] The various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. Furthermore, numerous specific details are set forth in the following detailed embodiments to better illustrate the invention. Those skilled in the art will understand that the invention can be practiced without certain specific details. In some instances, means well known to those skilled in the art have not been described in detail in order to highlight the spirit of the invention.

[0055] like Figure 1 The diagram shows a flowchart of a multi-objective power flow voltage optimization method for distribution networks considering distributed photovoltaic (PV) access, proposed in an embodiment of the present invention. Combining the multi-objective gray wolf pack algorithm and the selection and update mechanism of the multi-objective balancing optimizer, a novel multi-objective swarm intelligent optimization algorithm is proposed for power flow voltage optimization in scenarios considering distributed PV access. The method in this embodiment mainly includes the following steps S1-S6:

[0056] Step S1: Collect and process the operating data of each monitoring point in the power distribution network and the nameplate parameters of each power equipment;

[0057] Specifically, the operational data includes voltage, current, and power at each monitoring point during different time periods; the power equipment includes distributed photovoltaic systems, power transformers, power lines, and reactive power compensation devices.

[0058] Step S2: Based on the operating data and the nameplate parameters, perform system modeling of the distribution network and establish a multi-objective power flow voltage optimization control model;

[0059] Specifically, the optimization objectives are to minimize system loss, average voltage deviation, and curtailment rate of distributed photovoltaic equipment. The decision variables are the taps of on-load tap changers, the compensation capacity of reactive power compensation devices, and the active and reactive power output of distributed photovoltaic equipment at each time period. The constraints are power flow balance constraints, system voltage operation constraints, and component current operation constraints. A multi-objective power flow voltage optimization model for distribution networks considering distributed photovoltaic access scenarios is established.

[0060] To ensure that the generated power can be effectively utilized within the distribution network and to improve the economic efficiency of distribution network operation, reducing the losses of the distribution system should be one of the optimization objectives. Therefore, in this embodiment of the invention, minimizing the average system loss of the distribution network is taken as one of the optimization objectives in the following form:

[0061]

[0062] Where, N L N represents the total number of power lines in the power system. t P represents the total number of time periods in the model. loss (t) represents the total power grid loss during the t-th time period, L is the set of all power lines in the power system, and G ij (t) and B ij (t) represents the conductance and susceptance between nodes i and j in the nodal admittance matrix during the t-th time period, V i (t) and θ ij (t) represents the effective voltage value at node i and the voltage phase difference between node i and node j in the t-th time period;

[0063] To ensure the safe and stable operation of the power distribution system, the voltage of each node in the power distribution network should be maintained near its rated value. Therefore, in this embodiment of the invention, the optimization objective is to minimize the average voltage deviation of each node in the power distribution network, as shown below:

[0064]

[0065] Among them, V i,base N is the reference voltage at node i. B V represents the total number of nodes. i * (t) represents the per-unit voltage value at node i, where * indicates the per-unit value;

[0066] To improve the utilization rate of distributed photovoltaic (PV) equipment and ensure that as much clean photovoltaic power as possible is supplied to the distribution network, minimizing the average curtailment rate of distributed PV equipment should be considered as one of the optimization objectives. The calculation method for this optimization objective is as follows:

[0067]

[0068] Among them, P PV,i (t) represents the actual active power generated by the i-th distributed photovoltaic device during the t-th time period, P PV,i,max (t) represents the maximum active power that the i-th distributed photovoltaic device can send to the distribution network during the t-th time period, N. PV T represents the total number of distributed photovoltaic (PV) devices. PV Let |T| be the set of time periods during which the maximum active power output of all distributed photovoltaic devices is greater than 0. PV |For set T PV The number of elements contained;

[0069] In scenarios considering distributed photovoltaic (PV) integration, the main methods for optimizing power flow voltage control in distribution systems include adjusting the taps of on-load tap-changing transformers, the compensation capacity of reactive power compensation devices, and the active and reactive power outputs of distributed PV equipment. Therefore, this embodiment of the invention uses the on-load tap-changing transformer ratio K for each time period. Ti (t), reactive power compensation Q of parallel compensation device Ci (t), Active power output of distributed power sources P DGi (t) and reactive power Q DGi (t) is used as the decision variable in the optimization model, and the upper and lower bound constraints for the decision variable are set as shown below:

[0070]

[0071] Where, N G N T N C N DG These are, in order, the total number of generator nodes in the power system, the total number of adjustable taps on on-load tap-changing transformers, the total number of parallel capacitor banks, and the total number of distributed generation nodes;

[0072] The power distribution system must satisfy the following equality constraint so that the total inflow power at each node of the distribution network equals the total outflow power. This constraint is the power flow balance constraint of the power distribution system and is a major component of the equality constraint in the power flow voltage optimization model of the distribution network:

[0073]

[0074] Among them, P Gi (t) and Q Gi P(t) represents the total active power and total reactive power generated by the generator at node i during the t-th time period, respectively. Li (t) and Q Li Q(t) represents the total active power and total reactive power consumed by the load at node i during the t-th time period, respectively. Ci(t) represents the reactive power compensated by the reactive power compensation device at node i during the t-th time period;

[0075] To ensure the safe and stable operation of the power distribution system, this embodiment of the invention stipulates that the voltage at each node of the power distribution network, the total incoming power factor at each node, and the current of each branch should satisfy the following inequality constraints:

[0076]

[0077] Among them, I (i,j) (t) represents the current in branch (i,j) during the t-th time period;

[0078] Furthermore, the multi-objective power flow voltage optimization model can be abstracted into the following form:

[0079]

[0080] Where y is a target vector consisting of m optimization objectives, and x is a decision vector of dimension n. x and These are the lower and upper bounds of the decision vector, respectively, g i (x) is used to define inequality constraints, h j (x) is used to define equality constraints, where p is the number of all inequality constraints and q is the number of all equality constraints;

[0081] Step S3: Set the initial parameters of the power flow voltage optimization algorithm and perform population initialization to obtain an initial population. Calculate the objective function value of each individual in the initial population and determine whether it meets the constraints. Select individuals from the initial population that are not dominated by other individuals according to the multi-objective Pareto dominance principle and store them in an external file.

[0082] Specifically, step S3 includes:

[0083] Based on the Monte Carlo method, an initial population of a certain number of individuals is randomly and equally generated within the upper and lower bound constraints of the decision variables. Each individual in the initial population corresponds to a power flow voltage control strategy.

[0084] After generating the initial group, the power flow and voltage distribution under each power flow voltage control strategy are obtained through power flow calculation, and then the corresponding objective function value is calculated and it is determined whether it meets the preset requirements for safe and stable operation of the power system.

[0085] Based on the Pareto domination mechanism and the individual's objective function value, all individuals in the initial group are compared, and based on the comparison results, all individuals in the initial group that are not dominated by other individuals are stored in the external file.

[0086] Specifically, embodiments of the present invention introduce a multi-objective Pareto domination mechanism, where set X... f Let X be the set of all feasible solutions in the n-dimensional decision space. The Pareto dominance relation is defined as: for x1, x2 ∈ X f If and only if for All have f i (x1)≤f i (x2), and Make f i (x1) <f i (x2), in which case x1 dominates x2, denoted as

[0087] Furthermore, the Pareto optimal solution is defined as: for x * ∈X f If and only if Make When, then x is called * The Pareto optimal solution is also called a non-dominated solution or a non-dominated solution. Furthermore, the set of all Pareto optimal solutions is called the Pareto optimal solution set, which can also be called the non-dominated solution set or the non-dominated solution set. Then, the mapping of the Pareto optimal solution set to the target space is defined as the Pareto front.

[0088] Step S4: Select elite individuals from the external archives, perform group update according to the preset group update algorithm to obtain a new generation group; calculate the objective function value of each individual in the new generation group, and determine whether it meets the constraints.

[0089] Specifically, step S4 includes:

[0090] An adaptive grid-based sorting method is used to divide the target space into a grid consisting of multiple hypercubes. The hypercubes in the grid are selected by a roulette wheel selection method, and then an individual is randomly and equally selected from the selected hypercubes. The fewer individuals that a hypercube contains that are not dominated by other individuals, the higher the probability that the hypercube will be selected.

[0091] Based on the elite individual selection mechanism of the gray wolf pack algorithm, the above steps are repeated 3 times to select 3 individuals from the external files as elite individuals, and they are named α individual, β individual and δ individual respectively.

[0092] After the elite individuals are selected, the decision variables of each individual in the group should be updated based on the position of the elite individuals, so as to gradually bring the search results closer to the optimal results. In order to improve the convergence and distribution of the algorithm search, this embodiment of the invention combines the advantages of the gray wolf pack algorithm and the balanced optimizer algorithm in terms of algorithm search performance, and proposes a pre-set group update method with a hybrid update mechanism as shown below for group update. The update method is as follows:

[0093]

[0094] Where k is the current iteration number of the algorithm, and K is the maximum iteration number of the algorithm; X(k) and X(k+1) are the n-dimensional decision variables corresponding to any individual in the k-th and k+1-th generations of the population, respectively. α (k), X β (k), X δ (k) represents the n-dimensional decision variables corresponding to individuals α, β, and δ selected after the k-th selection; C1, C2, C3 are n-dimensional random vectors corresponding to individuals α, β, and δ, respectively, and follow a uniform distribution on the interval [-2, 2]; A1, A2, A3 are n-dimensional random vectors corresponding to individuals α, β, and δ, respectively, and follow a uniform distribution on the interval [-a, a]; a satisfies the relation Its value decreases as the number of iterations increases; λ α , λ β , λ δ Let F be an n-dimensional random vector corresponding to individuals α, β, and δ, respectively, and follow a unit uniform distribution; α F β F δ Let n be the n-dimensional random vectors corresponding to individuals α, β, and δ, respectively, satisfying the relation r is an n-dimensional random vector that follows a unit uniform distribution. G is the product of element group operations; α G β G δ Let be the n-dimensional random vectors corresponding to individuals α, β, and δ, respectively, and satisfy the relationship shown in equation (9);

[0095]

[0096] Where r1 and r2 are both random numbers that follow a uniform unit distribution;

[0097] Step S5: Based on the multiple Pareto dominance principle, select individuals from the new generation group that are not dominated by other individuals and store them in the external archive, and update the external archive; and ensure that the number of individuals in the external archive never exceeds a preset maximum value through a diversity maintenance mechanism;

[0098] Specifically, the update principle of the external archive is as follows: Each non-dominant individual in the current population is compared with all individuals in the external archive according to the Pareto dominance principle. All dominated individuals in the external archive are deleted, and new generation individuals not dominated by any individuals in the external archive are stored in the external archive. The crowding distance of each individual in the external archive is calculated based on a crowding distance calculation mechanism, and a diversity maintenance mechanism is used to prevent data capacity overflow in the external archive. Specifically, if the external archive is empty, new generation individuals are directly stored in the external archive; if a new generation individual is dominated by individuals in the external archive, the new generation individual is directly discarded; if a new generation individual dominates some individuals in the external archive, all dominated individuals in the original external archive are discarded, and new generation individuals are stored in the external archive; if a new generation individual does not dominate any individuals in the external archive, all individuals in the external archive are retained, and new generation individuals are stored in the external archive.

[0099] Among these methods, the individual density estimation method is crucial to the performance of multi-objective optimization algorithm search result distribution. To improve the breadth and uniformity of multi-objective optimization algorithm search results distribution in the target space, this invention employs a crowding distance-based calculation method for individual density estimation of external files. The calculation mechanism of the crowding distance is as follows: all individuals in the external files are sorted according to the magnitude of the objective function value, and individuals with the minimum or maximum function value are considered extreme individuals, while the remaining individuals are considered intermediate individuals. The crowding distance of the extreme individuals is set to infinity, while the crowding distance of the intermediate individuals is equal to the absolute normalized difference of the objective function values ​​of two adjacent individuals.

[0100] The diversity maintenance mechanism for external files is as follows: when the number of individuals in the external files exceeds the set maximum value, the individual with the smallest crowding distance in the external files is deleted until the number of individuals in the external files equals the preset maximum value;

[0101] Step S6: Determine whether the preset iteration termination condition is met. If the condition is not met, proceed to step S3 to continue the iteration. If the condition is met, stop the iteration and obtain the final power flow voltage optimization control scheme from the external file.

[0102] The following is a specific example illustrating the application process of the method in this embodiment of the invention:

[0103] (1) Collect and process the operation data of each monitoring point in the power distribution network and the nameplate parameters of each power equipment;

[0104] This example uses the IEEE 33-node distribution network system as the case study. The IEEE 33-node system is a typical regional three-phase radial distribution system, consisting of 33 nodes and 32 branches, including one source node and 32 load nodes. The total system voltage is 12.66 kV, the total network load is 3750 kW + j2300 kvar, and the per-unit voltage of the source node is taken as 1.05. Its topology diagram is shown below. Figure 2 As shown in Table 1, the node and branch parameters are as follows. In accordance with the national standard "Q / GDW 480-2010: Technical Regulations for Distributed Power Generation Access to the Power Grid," the total access capacity of distributed power generation in the distribution network cannot exceed 25% of the maximum load within the power supply area of ​​the upstream transformer. Therefore, the access capacity of the photovoltaic equipment at each node is configured to 200kW, and the distributed photovoltaic equipment is scheduled to be installed at nodes 8, 25, and 32. For ease of result analysis, in this example, the daily active power curves of each distributed photovoltaic device are the same, and the daily power variation curves of each load node are also the same. The daily active power curves of the distributed photovoltaic devices and the daily power variation curves of the load nodes are shown in Table 1. Figure 3-4 As shown.

[0105] Table 1 - Node and branch parameters of the IEEE 33-node system

[0106]

[0107] (2) Based on the operating data and nameplate parameters, the distribution network is modeled and a multi-objective power flow voltage optimization control model is established;

[0108] In this example, the distributed photovoltaic (PV) equipment is installed at nodes 8, 25, and 32 and operates at unity power factor. The maximum active power curves for each time period are shown below. Figure 4As shown, the active power generated by the distributed photovoltaic equipment can be continuously adjusted within the range of 0 to the maximum active power at different times. Nodes 2, 4, 7, 8, 14, 23, 24, 25, 29, 30, 31, and 32, with relatively large reactive power deficits, are selected as the installation nodes for reactive power compensation equipment. The reactive power compensation equipment is set to be continuously adjustable, with compensation ranges of 0–60 kvar, 0–80 kvar, 0–100 kvar, -100–100 kvar, 0–80 kvar, 0–50 kvar, 0–200 kvar, -200–200 kvar, 0–70 kvar, 0–100 kvar, 0–70 kvar, and -100–100 kvar, respectively. In accordance with the requirements of the national standard "Q / GDW 480-2010: Technical Regulations for Distributed Power Generation Access to the Grid", the per-unit voltage value at each node is limited to 0.93–1.07 kV. Between PUs, the incoming power factor at each node is not less than 0.9; based on this, with the optimization objectives of minimizing the average system loss of the distribution network, minimizing the average voltage deviation of each node, and minimizing the average curtailment rate of distributed photovoltaics, a three-objective power flow voltage optimization control model for the IEEE 33-node distribution system considering the distributed photovoltaic access scenario is established.

[0109] (3) Set the initial parameters of the power flow voltage optimization algorithm and perform population initialization. Calculate the objective function value of each individual in the initial population and determine whether it meets the constraints. Select non-dominated individuals from the initial population and store them in the external archive according to the multi-objective Pareto dominance principle.

[0110] In this example, the maximum number of iterations for the power flow voltage optimization algorithm is set to 200, and the maximum size of the population and the external archive is also set to 200. Using the Monte Carlo method, 200 initial populations are randomly and equally generated within the upper and lower bounds of the decision variables. Each individual in this population corresponds to a specific power flow voltage control strategy. After the initial populations are generated, power flow calculations are used to obtain the power flow and voltage distribution under each power flow voltage control strategy. The corresponding objective function value is then calculated, and it is determined whether it meets the requirements for the safe and stable operation of the power system. A Pareto dominance mechanism is introduced to compare all individuals in the initial population based on the objective function value. All individuals in the initial population that are not dominated by other individuals, i.e., the non-dominated individuals in the initial population, are stored in the external archive.

[0111] (4) Combining the gray wolf pack algorithm and the selection mechanism of the balance optimizer, elite individuals are selected from the external archives, and a new generation of population is obtained according to the proposed population update method. Then, the objective function value of each individual in the new generation of population is calculated, and it is determined whether the constraint conditions are met.

[0112] In this example, an adaptive grid-based sorting method is used to divide the 3D target space into a grid consisting of 10×10×10 hypercubes. A roulette wheel selection method is used to filter the hypercubes within the grid; the fewer non-dominated individuals a hypercube contains, the higher its probability of being selected. Individuals are then randomly and equally selected from within the hypercubes. This process is repeated three times to select three elite individuals from the external archive, named α, β, and δ individuals, respectively. Finally, the proposed population update mechanism is used to update each individual in the population, as shown below:

[0113]

[0114]

[0115]

[0116]

[0117] Where: k is the current iteration number of the algorithm, K is the maximum iteration number of the algorithm; X(k) and X(k+1) are the n-dimensional decision variables corresponding to any individual in the k-th and k+1-th generations of the population, respectively. α (k), X β (k), X δ (k) represents the n-dimensional decision variables corresponding to the α, β, and δ individuals selected after the k-th selection; C is an n-dimensional random vector, uniformly distributed on the interval [-2, 2]; A is an n-dimensional random vector, uniformly distributed on the interval [-a, a]; a satisfies the relation Its value decreases as the number of iterations increases; λ is an n-dimensional random vector that follows a unit uniform distribution; F is an n-dimensional random vector that satisfies the relation r is an n-dimensional random vector that follows a unit uniform distribution. G is the product of element-wise group operations; G is an n-dimensional random vector satisfying the following relationship

[0118]

[0119]

[0120] Both r1 and r2 are random numbers that follow a uniform unit distribution.

[0121] (5) Select non-dominated individuals from the new generation of groups according to the Pareto domination principle and update the external files. Ensure that the size of the external files does not exceed the preset maximum value through the diversity maintenance mechanism.

[0122] External file updates: If the external file is empty, the new generation of individuals is directly stored in the external file; if the new generation of individuals is dominated by individuals in the external file, the new generation of individuals is directly discarded; if the new generation of individuals dominate some individuals in the external file, all dominated individuals in the original external file are discarded and the new generation of individuals is stored in the external file; if the new generation of individuals does not dominate any of the individuals in the external file, all individuals in the external file are retained and the new generation of individuals is stored in the external file.

[0123] Individual density estimation: This invention uses a crowding distance-based calculation method to estimate the individual density of external archives;

[0124] External file diversity maintenance: When the size of an external file exceeds the set maximum value of 200, delete the individual with the smallest crowding distance in the external file, so that the size of the external file is always within 200.

[0125] (6) Determine whether the iteration termination condition is met. If the condition is not met, proceed to step three to continue. If the condition is met, stop the iteration and obtain the final power flow voltage optimization control scheme from the external archive.

[0126] To verify the superior search performance of the proposed multi-objective optimization algorithm, this example compares the solution results of the multi-objective gray wolf pack algorithm and the multi-objective balanced optimizer algorithm with those of the proposed multi-objective swarm intelligence optimization algorithm. The Pareto front obtained using the above three multi-objective swarm intelligence optimization algorithms is as follows: Figure 5 As shown, by Figure 5 It can be seen that the Pareto front obtained by the multi-objective gray wolf pack algorithm is uniformly distributed near the intermediate solution, but its overall distribution range in the target space is not wide enough. The Pareto front obtained by the multi-objective balancing optimizer algorithm has a too narrow distribution range in the three-dimensional target space, with the objective function values ​​corresponding to the external files all concentrated near the intermediate solution, and the spatial distribution is uneven. The proposed multi-objective optimization algorithm has a stronger search capability for extreme solutions than the multi-objective gray wolf pack algorithm and the multi-objective balancing optimizer algorithm, and the search results can be widely and uniformly distributed in the target space. In summary, the proposed multi-objective swarm intelligent optimization algorithm has significantly improved the distribution performance compared with existing multi-objective algorithms, and therefore can better meet the needs of multi-objective power flow voltage optimization in actual distribution networks.

[0127] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and substitutions will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical applications, or technological improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for multi-objective power flow voltage optimization in distribution networks considering distributed photovoltaic (PV) integration, characterized in that, The method includes the following steps: Step S1: Collect and process the operating data of each monitoring point in the power distribution network and the nameplate parameters of each power equipment; Step S2: Based on the operating data and the nameplate parameters, perform system modeling of the distribution network. The optimization objectives are to minimize system loss, average voltage deviation, and curtailment rate of distributed photovoltaic equipment. The decision variables are the taps of on-load tap changers, the compensation capacity of reactive power compensation devices, and the active and reactive power output of distributed photovoltaic equipment at each time period. The constraints are power flow balance constraints, system voltage operation constraints, and component current operation constraints. A multi-objective power flow voltage optimization model for the distribution network considering the distributed photovoltaic access scenario is established. Step S3: Set the initial parameters of the power flow voltage optimization algorithm and perform population initialization to obtain an initial population. Calculate the objective function value of each individual in the initial population and determine whether it meets the constraints. Select individuals from the initial population that are not dominated by other individuals according to the multi-objective Pareto dominance principle and store them in an external file. Step S4: Select elite individuals from the external archives, perform group update according to the preset group update algorithm to obtain a new generation group; calculate the objective function value of each individual in the new generation group, and determine whether it meets the constraints. Step S5: Based on the multiple Pareto dominance principle, select individuals from the new generation group that are not dominated by other individuals and store them in the external archive, and update the external archive; and ensure that the number of individuals in the external archive never exceeds a preset maximum value through a diversity maintenance mechanism; Step S6: Determine whether the preset iteration termination condition is met. If the condition is not met, proceed to step S3 to continue the iteration. If the condition is met, stop the iteration and obtain the final power flow voltage optimization control scheme from the external file.

2. The multi-objective power flow voltage optimization method for distribution networks considering distributed photovoltaic access according to claim 1, characterized in that, The operational data includes voltage, current, and power at each monitoring point during different time periods; the power equipment includes distributed photovoltaic systems, power transformers, power lines, and reactive power compensation devices.

3. The method for multi-objective power flow voltage optimization of distribution networks considering distributed photovoltaic access according to claim 2, characterized in that, Step S3 includes: Based on the Monte Carlo method, an initial population of a certain number of individuals is randomly and equally generated within the upper and lower bound constraints of the decision variables. Each individual in the initial population corresponds to a power flow voltage control strategy. After generating the initial group, the power flow and voltage distribution under each power flow voltage control strategy are obtained through power flow calculation, and then the corresponding objective function value is calculated and it is determined whether it meets the preset requirements for safe and stable operation of the power system. Based on the Pareto domination mechanism and the individual's objective function value, all individuals in the initial group are compared, and based on the comparison results, all individuals in the initial group that are not dominated by other individuals are stored in the external file.

4. The multi-objective power flow voltage optimization method for distribution networks considering distributed photovoltaic access according to claim 3, characterized in that, Step S4 includes: An adaptive grid-based sorting method is used to divide the target space into a grid consisting of multiple hypercubes. The hypercubes in the grid are selected by a roulette wheel selection method, and then an individual is randomly and equally selected from the selected hypercubes. The fewer individuals that a hypercube contains that are not dominated by other individuals, the higher the probability that the hypercube will be selected. Repeat the above steps three times, and select three individuals from the external archives as elite individuals, and name them α individual, β individual and δ individual respectively. Update each individual in the group using a preset group update method, as shown below: in, k This represents the current iteration number of the algorithm. K This represents the maximum number of iterations for the algorithm. X ( k ), X ( k +1) are respectively the first k generation and first k Any individual in the +1 generation group corresponds to n Dimensional decision variables, X α ( k ), X β ( k ), X δ ( k ) are respectively the first k The α, β, and δ individuals selected subsequently correspond to n 1D decision variables; C1, C2, and C3 represent the decision variables for individuals α, β, and δ, respectively. n A 1-dimensional random vector follows a uniform distribution on the interval [-2, 2]; A1, A2, and A3 are the values ​​corresponding to individuals α, β, and δ, respectively. n A dimensional random vector, following the interval [- a , a Uniform distribution on ]; a Satisfying Relationships Its value decreases as the number of iterations increases; , , These are the corresponding individuals α, β, and δ, respectively. n A dimensional random vector, following a unit uniform distribution; , , These are the corresponding individuals α, β, and δ, respectively. n A dimensional random vector that satisfies the relation , , , To conform to a uniform distribution n 3D random vector, The product of group operations on elements; , , These are the corresponding individuals α, β, and δ, respectively. n A random vector of dimension satisfies the relationship shown in the following equation; in, r 1 and r Both 2 are random numbers that follow a uniform unit distribution.

5. The multi-objective power flow voltage optimization method for distribution networks considering distributed photovoltaic access according to claim 4, characterized in that, Step S5 includes: The update principle of the external archive is as follows: each non-dominated individual in the current population is compared with all individuals in the external archive according to the Pareto dominance principle; all dominated individuals in the external archive are deleted, and a new generation of individuals not dominated by any individuals in the external archive are stored in the external archive; the crowding distance of each individual in the external archive is calculated based on a crowding distance calculation mechanism, and a diversity maintenance mechanism is used to prevent the data capacity of the external archive from overflowing; wherein, the crowding distance calculation mechanism is as follows: all individuals in the external archive are sorted according to the size of the objective function value, and individuals with the smallest or largest function value are regarded as extreme individuals, and the rest are regarded as intermediate individuals; the crowding distance of the extreme individuals is set to infinitely large, while the crowding distance of the intermediate individuals is equal to the absolute normalized difference of the objective function values ​​of two adjacent individuals; The diversity maintenance mechanism for external files is as follows: when the number of individuals in the external files exceeds the set maximum value, the individual with the smallest crowding distance in the external files is deleted until the number of individuals in the external files equals the preset maximum value.

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