A power distribution network multi-objective distributed optimization scheduling method based on ADMM algorithm

Abstract

The application discloses a kind of distribution network multi-objective distributed optimization scheduling method based on ADMM algorithm, belong to distribution network optimization control field, consider three indexes of distribution network overall operation cost, multi-zone load rate difference and photovoltaic accommodation rate comprehensively, each index is weighted using entropy weight method, to realize the effect of distributed optimization, using ADMM algorithm, overall optimization model is split into upper and lower two layers and is studied.Minimize distribution network power purchase cost and multi-zone load rate difference as target in upper layer, minimize local energy storage operation cost and light abandonment in lower layer as target.A small amount of information is exchanged between upper and lower two layers, and each is optimized, and the optimal output of distributed photovoltaic and energy storage is obtained by iteration until the algorithm converges.The application has the advantages of scientific and reasonable method, strong applicability, good effect and the like.

Description

Technical Field

[0001] This invention belongs to the field of distribution network optimization control, and in particular relates to a multi-objective distributed optimization scheduling strategy for distribution networks based on the ADMM algorithm. Background Technology

[0002] Under the conditions of energy conservation and emission reduction in power grids, distributed photovoltaic (PV) applications are the most widespread. The rapid increase in the number and capacity of distributed PV installations has led to increasingly prominent problems in distribution networks, such as voltage exceeding limits, high operating costs, large load factor differences, and low PV utilization. Many scholars have focused on optimizing distribution networks for single objectives, such as cost, network loss, or PV absorption rate. However, for today's distribution networks, a single optimization objective is often insufficient to achieve optimal overall results. To comprehensively consider distribution network optimization under multiple indicators, multi-objective optimization methods are adopted. However, with the increasing integration of renewable energy, distributed power sources, energy storage systems, and flexible loads into the distribution network, traditional centralized optimization scheduling places increasingly stringent demands on computer memory capacity and processors. A failure of the central management system can lead to overall optimization scheduling failure. Therefore, distributed optimization has rapidly developed. By appropriately dividing complex optimization objectives, each part is optimized independently and exchanges limited information to achieve the effect of centralized optimization. Compared to centralized optimization, it has shorter computation time, smaller memory footprint, less communication overhead, and higher reliability, and is currently widely researched and applied in the industry. Summary of the Invention

[0003] For distribution networks with a high proportion of distributed photovoltaic (PV) access, the purpose of this invention is to propose a multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm. The overall objective function considers three indicators: system operating economy, PV utilization rate, and load rate differences among multiple transformer areas. The objective weights of each indicator are obtained using the entropy weight method. The ADMM algorithm is used to solve the problem. By processing the overall multi-objective optimization problem into upper and lower layers, the sub-problems at each layer are solved separately, and a small amount of information is exchanged between them. This aims to achieve a comprehensive optimal effect for multiple objectives and improve the solution speed.

[0004] A multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm includes the following steps, which are performed sequentially:

[0005] Step 1: Construct a hierarchical optimization scheduling model for the distribution network.

[0006] The objective functions of the model include the total cost model, the load factor difference model for multiple transformer areas, the photovoltaic grid integration model, the multi-objective optimization model, and the weights of multi-objective indicators; and the constraints of the model are established, including network security operation constraints, photovoltaic power circle constraints, and energy storage operation constraints.

[0007] Step 2: Distributed solution based on ADMM algorithm:

[0008] Construct the augmented Lagrangian function corresponding to the objective function; decompose the augmented Lagrangian function into two layers according to variables. The upper layer optimizes with the objective of minimizing the overall operating cost of the distribution network and the load rate difference among multiple transformer areas; retain the results obtained from the upper layer optimization iteration and pass the necessary information to the lower layer; the lower layer accepts the optimization results from the upper layer and optimizes with the objective of minimizing the local energy storage operating cost and the amount of curtailed solar power; retain the results obtained from the lower layer optimization iteration and pass the necessary information to the upper layer.

[0009] Step 3: Multi-objective distributed optimization scheduling of the distribution network based on iterative results:

[0010] Through continuous iteration between upper and lower level problems and continuous transmission of results, until the accuracy requirements of convergence error are met, the optimal output of each node photovoltaic and energy storage unit is finally obtained.

[0011] The total cost model for step one is as follows:

[0012] The total cost of a distribution network includes the electricity purchase cost from the upstream power grid and the operating cost of energy storage, as expressed below:

[0013] (1)

[0014] (2)

[0015] In the formula: To optimize the dispatch cycle of the distribution network, a 24-hour period is adopted. This is the energy storage operating cost coefficient; This represents the set of node numbers connected to the energy storage battery. Represents the set of all node numbers; Let be the operating cost of all energy storage at time t; , These are the discharge power and charging power of the energy storage battery connected at node j at time t, respectively. These represent the active power and reactive power flowing out at node j at time t, respectively. Let t be the active power loss within the network. These represent the prices at time t for the distribution network to purchase a unit of active and reactive energy from the upstream power grid, excluding the price of reactive energy. Set to 0;

[0016] The load rate difference model for multiple distribution areas is as follows:

[0017] The distribution network contains multiple transformers with different parameters and load capacities. A load rate difference index is established between these transformer areas to limit the load rate differences between them. The expression is as follows:

[0018] (3)

[0019] In the formula: This refers to the number of transformers in the system. Let be the power load of the j-th transformer at time t; Let be the rated power of the j-th transformer;

[0020] Photovoltaic power consumption model:

[0021] To improve the grid absorption capacity of distributed photovoltaic (PV) systems, a method is proposed that minimizes the square of the difference between the theoretical injected power and the actual absorbed power. The expression is as follows:

[0022] (4)

[0023] In the formula: This refers to the set of all nodes connected to photovoltaic systems in the distribution network. The theoretical photovoltaic power injection for the k-th node at time t; Let be the actual photovoltaic power absorbed by the k-th node at time t;

[0024] Multi-objective optimization model:

[0025] (5)

[0026] (6)

[0027] In the formula: These are the weight coefficients for each objective, all of which are real numbers greater than or equal to 0 and obtained by the entropy weight method; These are the magnitude correction coefficients for each target, to ensure that all target values ​​are on the same order of magnitude.

[0028] In step one, the weight values ​​of each indicator in the multi-objective indicator weights are selected using the entropy weight method. The weights are determined by the information contained in the dataset, the dataset is standardized, and the entropy weight of each indicator is calculated based on the information in the normalized dataset. Then, the entropy weight of each indicator is corrected to obtain the entropy weight redundancy, and finally, the objective weight values ​​of each indicator are obtained.

[0029] The network security operation constraints of the constraints in step one include branch power flow constraints, node voltage constraints, and node power constraints.

[0030] The photovoltaic power circle constraint under the constraints of step one

[0031] (16)

[0032] (17)

[0033] (18)

[0034] In the formula: Let be the apparent power of the i-th photovoltaic unit at time t; For the i-th photovoltaic unit in

[0035] Predicted power at time t; Let be the rated apparent power of the i-th photovoltaic unit; These are the actual active power and reactive power of the i-th photovoltaic unit at time t, respectively.

[0036] The energy storage operation constraints in step one include energy storage SOC constraints, energy storage capacity constraints, and energy storage power circle constraints.

[0037] Step two involves constructing the augmented Lagrangian function corresponding to the objective function based on the ADMM algorithm optimization model:

[0038] (30)

[0039] In the formula: , These are the Lagrange multipliers corresponding to the active and reactive power equality constraints of node i at time t, respectively. The penalty coefficient for augmenting the equality constraints corresponding to the Lagrange function; Let be the reactive power of the i-th energy storage battery at time t; , Let be the charging power and discharging power of the i-th energy storage battery at time t, respectively. , These are the actual active power and reactive power of the i-th photovoltaic unit at time t, respectively; , These represent the active power and reactive power flowing out of node i at time t, respectively. , Let be the active power and reactive power of the load at node i at time t, respectively.

[0040] The overall objective function is decomposed into two layers for separate solutions. In the lower layer model, the active and reactive power outputs of the photovoltaic units and the energy storage units are the optimization variables, along with the grid electricity price. , The results obtained from the upper-level optimization iteration All quantities are known. The objective is to minimize the local operating cost of energy storage and maximize the photovoltaic absorption capacity. The objective function for the lower-level optimization is:

[0041] (31)

[0042] The active distribution network dispatch center then obtains the results from the lower-level optimization iterations. The optimization aims to minimize the overall power purchase cost of the distribution network and the load rate differences among multiple distribution areas. The objective function of the upper-level optimization is:

[0043] (32)

[0044] In the formula: , They represent the first , The next iteration.

[0045] Step three iterates between the upper and lower level subproblems while continuously adjusting the Lagrange multipliers. , The algorithm is updated to gradually converge, allowing us to obtain the optimal output of each photovoltaic and energy storage unit. The Lagrange multipliers are the dual variables. , The update formula is:

[0046] (33)

[0047] Through the above design scheme, the present invention can bring the following beneficial effects: For distribution networks with a high proportion of distributed photovoltaic access, the present invention proposes a multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm, which achieves the comprehensive optimal effect of multiple objectives, improves the overall solution speed, and enhances the privacy and security of data among various stakeholders while achieving distributed optimization effects. Attached Figure Description

[0048] Figure 1 This invention presents a hierarchical optimization framework diagram for a multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm.

[0049] Figure 2 This is a flowchart illustrating the algorithm solution for a multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm, as described in this invention.

[0050] Figure 3 The topology diagram of a 33-node example is shown in the specific implementation diagram of the multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm of the present invention.

[0051] Figure 4The diagram shows the convergence effect of the original residual and the dual residual in a specific implementation of a multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm of the present invention.

[0052] Figure 5 This diagram illustrates the optimization process of the normalized objective function in the multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm of this invention.

[0053] Figure 6 This is a specific implementation of the ADMM algorithm-based multi-objective distributed optimization scheduling method for distribution networks, without employing a multi-objective optimization method. The diagram shows the maximum and minimum voltage values ​​of each node over 24 hours.

[0054] Figure 7 This is a specific implementation of the multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm of the present invention, showing the maximum and minimum values ​​of the 24-hour voltage of each node after adopting the multi-objective optimization method;

[0055] Figure 8 The voltage change curves of nodes 3 and 18 over 24 hours are shown in the specific implementation diagram of the multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm of the present invention. Detailed Implementation

[0056] The present invention will be further described in detail below with reference to specific embodiments. The following examples are used to illustrate the present invention, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0057] This invention discloses a multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm. The method includes: first, establishing a hierarchical optimization scheduling model for the distribution network including distributed photovoltaic and energy storage, and determining the objective function and constraints; then, performing distributed solution based on the ADMM algorithm, establishing an ADMM-based optimization model, solving for the required parameters based on the constructed model, and then comparing and analyzing the parameters obtained from different schemes. The specific steps are as follows:

[0058] Step 1: Construct a hierarchical optimization scheduling model for the distribution network:

[0059] (1) Objective function:

[0060] The objective function established in this invention mainly includes the following aspects.

[0061] 1) Total Cost Model

[0062] The total cost of a power distribution network mainly includes two parts: the cost of purchasing electricity from the upstream power grid and the operating cost of energy storage, as shown in the following expression:

[0063] (1)

[0064] (2)

[0065] In the formula: To optimize the dispatch cycle of the distribution network, a 24-hour period is adopted. This is the energy storage operating cost coefficient; This represents the set of node numbers connected to the energy storage battery. Represents the set of all node numbers; Let be the operating cost of all energy storage at time t; , These are the discharge power and charging power of the energy storage battery connected at node j at time t, respectively. , These represent the active power and reactive power flowing out at node j at time t, respectively. Let t be the active power loss within the network. These represent the prices at time t for the distribution network to purchase a unit of active and reactive energy from the upstream power grid, excluding the price of reactive energy. Set it to 0.

[0066] 2) Multi-zone load rate difference model

[0067] When a distribution network in a region contains multiple transformers, their load capacities differ due to variations in their parameters. To avoid a significant impact on the distribution network caused by concentrated access to a single transformer area, this invention establishes a load rate difference index for multiple transformer areas to limit the load rate differences between transformer areas. The expression is as follows:

[0068] (3)

[0069] In the formula: This refers to the number of transformers in the system. Let be the power load of the j-th transformer at time t; Let be the rated power of the j-th transformer.

[0070] 3) Photovoltaic consumption model

[0071] Due to the intermittent and fluctuating characteristics of distributed photovoltaic (PV) power, its integration into the grid presents certain challenges. To maximize the integration of distributed PV and avoid resource waste, a method is constructed that minimizes the square of the difference between the theoretical injected power and the actual absorbed power of distributed PV, thereby improving its integration capacity. The expression is as follows:

[0072] (4)

[0073] In the formula: This refers to the set of all nodes connected to photovoltaic systems in the distribution network. The theoretical photovoltaic power injection for the k-th node at time t; Let be the actual photovoltaic power absorbed by the k-th node at time t.

[0074] 4) Multi-objective optimization model

[0075] (5)

[0076] (6)

[0077] In the formula: These are the weight coefficients for each objective, all of which are real numbers greater than or equal to 0 and obtained by the entropy weight method; These are the magnitude correction coefficients for each target, to ensure that all target values ​​are on the same order of magnitude.

[0078] 5) Weighting of multi-objective indicators

[0079] In this invention, the weight values ​​of each indicator are selected using the entropy weight method. The entropy weight method is an objective method for selecting weights. It determines the weights based on the information contained in the dataset. First, the dataset is standardized. Then, the entropy weight value of each indicator is calculated based on the normalized dataset information. Next, the entropy weight values ​​of each indicator are corrected to obtain the entropy weight redundancy. Finally, a relatively objective weight value for each indicator is obtained. The detailed calculation steps are as follows:

[0080] ① Dataset normalization processing

[0081] Forwarding of datasets:

[0082] (7)

[0083] Dataset standardization:

[0084] (8)

[0085] Where: n is the number of datasets; For the i-th sample in the j-th indicator of the unstandardized dataset; For the i-th sample in the j-th metric of the standardized dataset;

[0086] ② Proportion of each element in the dataset

[0087] (9)

[0088] in: This represents the proportion of the i-th sample in the j-th metric of the standardized dataset.

[0089] ③ Information entropy values ​​of each indicator

[0090] (10)

[0091] in: Let j be the information entropy value of the j-th indicator;

[0092] ④ Redundancy values ​​of each indicator

[0093] (11)

[0094] in: This represents the information redundancy value of the j-th indicator;

[0095] ⑤ Information redundancy value normalization

[0096] (12)

[0097] Where: m is the number of evaluation indicators; Let be the weight value of the j-th indicator;

[0098] 2) Constraints

[0099] 1) Network security operation constraints

[0100] ① Branch flow constraints

[0101] (13)

[0102] In the formula: For the node n The set of downstream nodes and their connected nodes; These are the distribution network branches mn exist t Active and reactive power at the head end at any given time; These are the distribution network branches mn Resistance and reactance; For nodes m exist t Voltage amplitude at any given moment; For distribution network branches mn exist t The amplitude of the current at any given moment; They are nodes n exist t The active and reactive power of the load connected at any given time; They are nodes n exist t The active and reactive power of the distributed power source connected at any given time;

[0103] ② Node voltage constraints

[0104] (14)

[0105] In the formula: These are the upper and lower limits of the allowable voltage amplitude at each node;

[0106] ③ Node power constraints

[0107] (15)

[0108] In the formula: , These represent the active power and reactive power flowing out of node i at time t, respectively. , Let be the active power and reactive power of the load at node i at time t, respectively. , These represent the active power and reactive power of the photovoltaic cell connected to node i at time t, respectively. , These represent the active power and reactive power of the energy storage battery connected to node i at time t, respectively.

[0109] 2) Photovoltaic power circle constraint

[0110] (16)

[0111] (17)

[0112] (18)

[0113] In the formula: Let be the apparent power of the i-th photovoltaic unit at time t; Let be the predicted power of the i-th photovoltaic unit at time t; Let be the rated apparent power of the i-th photovoltaic unit; , These are the actual active power and reactive power of the i-th photovoltaic unit at time t, respectively;

[0114] 3) Energy storage operation constraints

[0115] ① Energy storage SOC constraint

[0116] (19)

[0117] (20)

[0118] (twenty one)

[0119] In the formula: This represents the remaining charge level of the i-th energy storage battery at time t; This represents the rated capacity of the i-th energy storage battery; , These are the i-th energy storage batteries. The amount of charging and discharging power at all times; , These are the upper and lower limits of the SOC value of the i-th energy storage battery, respectively; This indicates the monitoring interval for the energy storage battery, which is set to 1 hour in this case. , These are the rated charge and discharge efficiencies of the energy storage battery under standard operating conditions;

[0120] ② Energy storage capacity constraints

[0121] (twenty two)

[0122] (twenty three)

[0123] In the formula: Let be the charge of the i-th energy storage battery at time t; These are the upper and lower limits of the capacity of the i-th energy storage battery, respectively;

[0124] ③ Energy storage power circular constraint

[0125] (twenty four)

[0126] (25)

[0127] (26)

[0128] (27)

[0129] (28)

[0130] (29)

[0131] In the formula: , These are the active power and reactive power of the i-th energy storage battery at time t, respectively. The rated apparent power of the i-th energy storage battery; , Let be the charging power and discharging power of the i-th energy storage battery at time t, respectively. The rated active power of the i-th energy storage battery;

[0132] Step 2, Distributed solution based on ADMM algorithm:

[0133] (1) Optimization model based on ADMM algorithm

[0134] Based on the solution steps of the ADMM algorithm, the augmented Lagrangian function of the objective function is first constructed: (30)

[0135] In the formula: , These are the Lagrange multipliers corresponding to the active and reactive power equality constraints of node i at time t, respectively. The penalty coefficient for augmenting the equality constraints corresponding to the Lagrange function;

[0136] Due to the complexity of the problem, to improve the solution speed of the model, the overall objective function is split into two layers for separate solutions. In the lower layer model, the active and reactive power outputs of the photovoltaic units and the energy storage units are the optimization variables, along with the grid electricity price. , The results obtained from the upper-level optimization iteration , , , All quantities are known. The objective is to minimize the local operating cost of energy storage and maximize the photovoltaic (PV) absorption capacity. The objective function for the lower-level optimization is:

[0137] (31)

[0138] The active distribution network dispatch center then obtains the results from the lower-level optimization iterations. , , , , The optimization aims to minimize the overall power purchase cost of the distribution network and the load rate differences among multiple distribution areas. The objective function of the upper-level optimization is:

[0139] (32)

[0140] In the formula: They represent the first The iteration continues, iterating between the upper and lower level subproblems while continuously adjusting the Lagrange multipliers. The algorithm is updated until it gradually converges, allowing us to obtain the optimal output of each photovoltaic and energy storage unit. The Lagrange multipliers are the dual variables. The update formula is:

[0141] (33)

[0142] The solution process based on the ADMM algorithm is as follows:

[0143] 1) Import the time-of-use electricity price, branch impedance information, node load information, and typical daily photovoltaic time-series output prediction data of the distribution network into MATLAB;

[0144] 2) Determine the weight values ​​corresponding to each indicator based on the entropy weight method;

[0145] 3) Construct the augmented Lagrangian function corresponding to the objective function;

[0146] 4) The augmented Lagrange function is split into two layers according to the variables. The upper layer is optimized with the goal of minimizing the overall operating cost of the distribution network and the difference in load rate among multiple distribution areas.

[0147] 5) Retain the results obtained from the upper-level optimization iteration and pass the necessary information to the lower level;

[0148] 6) The lower layer accepts the optimization results from the upper layer and optimizes itself with the goal of minimizing the local energy storage operating cost and the amount of curtailed solar power;

[0149] 7) Retain the results obtained from the lower-level optimization iterations and pass the necessary information to the upper level;

[0150] 8) Through continuous iteration between the upper and lower level problems and continuous transmission of results, until the accuracy requirements of convergence error are met, the optimal output of each node photovoltaic and energy storage unit is finally obtained.

[0151] The algorithm's solution process is as follows: Figure 2 As shown.

[0152] Example 1, Case Analysis:

[0153] To verify the feasibility and effectiveness of the method proposed in this invention, simulation analysis was performed on the IEEE 33 standard example system of a radial distribution network. The program was written using MATLAB R2020b, and the commercial solver Cplex was selected for solving.

[0154] In this example, the power base capacity is set to 1MVA and the base voltage is set to 12.66kV. Node 1 (root node) is set as the system's balancing node. Except for the root node, all other nodes are connected to photovoltaic and energy storage. Each node is connected to 10 photovoltaic and 10 energy storage devices, and the types of photovoltaic and energy storage power sources are all the same. Detailed parameters are shown in Table 1. Figure 3 The distribution network topology diagram for this example is shown. The total load for 24 hours is 67.1177MW + 41.5533MVAr, and the maximum load is 3.715MW + 2.3MVAr. The allowable voltage upper and lower limits for each node are 0.95pu~1.05pu. Now, multi-objective distributed optimization is performed on this 33-node example system.

[0155]

[0156] 1) Convergence Analysis

[0157] When using the ADMM algorithm to solve the multi-objective optimization model of the distribution network proposed in this invention, the iteration step size is set in the example. According to the entropy weight method, the weight values ​​of each index can be obtained as shown in Table 2. After 150 iterations of the objective function, both the original residual and the dual residual satisfy the convergence condition. The program convergence effect is as follows: Figure 4 As shown, Figure 5 The convergence process of the objective function demonstrates that the multi-objective optimization algorithm proposed in this invention can gradually bring the objective function to the optimal value during the iteration process, thus verifying the effectiveness of the algorithm.

[0158] Table 2 Weight values ​​of each indicator

[0159]

[0160] (2) Results Analysis

[0161] To verify the practicality of the multi-objective optimization model proposed in this invention, five schemes are proposed for verification and analysis: Scheme 1 takes minimizing system operating cost as the optimization objective; Scheme 2 takes maximizing photovoltaic absorption as the optimization objective; Scheme 3 takes minimizing the difference in load rate among multiple transformer areas as the optimization objective; Scheme 4 is a multi-objective optimization that simultaneously considers two indicators: system operating cost and the difference in load rate among multiple transformer areas; Scheme 5 is a multi-objective optimization that comprehensively considers three indicators: system operating cost, photovoltaic absorption, and the difference in load rate among multiple transformer areas.

[0162] 1) Node voltage analysis

[0163] Analysis of 24-hour raw data without employing the multi-objective distributed optimization method proposed in this invention yields the maximum and minimum values ​​of voltage at each node, as follows: Figure 6 As shown, approximately half of the node voltages do not meet the requirements.

[0164] Under the multi-objective optimization method of Scheme 5, the maximum and minimum voltage values ​​of each node over 24 hours are as follows: Figure 7 As shown, the voltage values ​​of each node are all between 0.95 and 1.05, which meets the normal voltage requirements and can ensure good voltage quality of the distribution network.

[0165] To further analyze the voltage values, node 3, which is close to the root node, and node 18, which is far from the root node, were selected to observe their voltage changes. Figure 8 The figure shows the voltage change curves of node 3 and node 18 over 24 hours. As can be seen from the figure, node 18 is farther from the root node, so its voltage change range is larger, while node 3 is closer to the root node, so its voltage change range is smaller, but the voltage values ​​remain within the normal range.

[0166] 2) Analysis of each indicator

[0167] The results for each indicator under different schemes are shown in Table 3. Because the objective functions of different schemes differ, i.e., the focus of the optimization objective differs, the optimization results often vary significantly. The following is an analysis of each optimization scheme:

[0168] Option 1 has the lowest total system cost, with all photovoltaic power being absorbed. The increased photovoltaic output leads to a greater injection power at each node, resulting in the highest relative difference in load rates among multiple photovoltaic areas.

[0169] Option 2 only considers the minimum difference in load rate among multiple distribution areas, which reduces the injected power of each node and the photovoltaic output cannot be fully absorbed, resulting in a significant reduction in the photovoltaic absorption rate. At the same time, the reduction in photovoltaic output reduces the revenue of the distribution network from selling electricity under this situation, ultimately leading to the highest overall operating cost of the distribution network.

[0170] Option 3 aims to maximize the amount of photovoltaic power absorbed, resulting in higher revenue from selling electricity, but at the same time, it increases the difference in load factor between different photovoltaic units.

[0171] Scheme 4 has an objective function that includes both system operating cost and load rate differences between multiple stations. The load rate differences between stations are significantly reduced, the total system cost increases slightly, and the amount of wasted light increases.

[0172] Scheme 5, a multi-objective optimization, improves the photovoltaic absorption rate while reducing the total system cost compared to Scheme 4. The load factor difference between each distribution station is slightly increased. Although it is not superior to the results of individual single-objective optimization, it can comprehensively balance the three objectives, demonstrating the comprehensiveness and superiority of multi-objective optimization.

[0173] Table 3 Comparison of results under various optimization schemes

[0174]

[0175] In summary, this invention proposes a distributed optimization method for distribution networks with high proportion of distributed photovoltaic (PV) access, considering multiple objectives. The objective function comprehensively considers three indicators: total system cost, load rate differences among multiple distribution areas, and PV absorption. The ADMM algorithm is used for distributed solution to obtain the optimal output of distributed PV and energy storage units.

[0176] In the future, with the rapid increase in the number and capacity of distributed photovoltaic (PV) grid connections, problems such as voltage exceeding limits, high operating costs, large load rate differences, and low PV utilization in the distribution network will become increasingly prominent. However, adopting a multi-objective distributed optimization scheduling strategy for the distribution network based on the ADMM algorithm can achieve optimal results for multi-objective comprehensive indicators, improve solution speed, and protect data privacy.

[0177] The embodiments of the present invention are not exhaustive and do not constitute a limitation on the scope of protection of the claims. Those skilled in the art, upon learning from the embodiments of the present invention, can conceive of other substantially equivalent alternatives without inventive effort, all of which are within the scope of protection of the present invention.

Claims

1. A multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm, characterized by: The steps are as follows, and they are performed in sequence: Step 1: Construct a hierarchical optimization scheduling model for the distribution network: The objective functions of the model include the total cost model, the load factor difference model for multiple transformer areas, the photovoltaic grid integration model, the multi-objective optimization model, and the weights of multi-objective indicators; and the constraints of the model are established, including network security operation constraints, photovoltaic power circle constraints, and energy storage operation constraints. Step 2: Distributed solution based on ADMM algorithm: Construct the augmented Lagrangian function corresponding to the objective function; decompose the augmented Lagrangian function into two layers according to variables. The upper layer optimizes with the objective of minimizing the overall operating cost of the distribution network and the load rate difference among multiple transformer areas; retain the results obtained from the upper layer optimization iteration and pass the necessary information to the lower layer; the lower layer accepts the optimization results from the upper layer and optimizes with the objective of minimizing the local energy storage operating cost and the amount of curtailed solar power; retain the results obtained from the lower layer optimization iteration and pass the necessary information to the upper layer. Step 3: Multi-objective distributed optimization scheduling of the distribution network based on iterative results: Through continuous iteration between upper and lower level problems and continuous transmission of results, until the accuracy requirements of convergence error are met, the optimal output of photovoltaic and energy storage units at each node is finally obtained. Step two involves constructing the augmented Lagrangian function corresponding to the objective function based on the ADMM algorithm optimization model: （30） In the formula: To optimize the dispatch cycle of the distribution network, a 24-hour period is adopted. This is the energy storage operating cost coefficient; This represents the set of node numbers connected to the energy storage battery. Represents the set of all node numbers; , These are the Lagrange multipliers corresponding to the active and reactive power equality constraints of node i at time t, respectively. The penalty coefficient for augmenting the equality constraints corresponding to the Lagrange function; Let be the reactive power of the i-th energy storage battery at time t; , Let be the charging power and discharging power of the i-th energy storage battery at time t, respectively. and These are the charging power and discharging power of the j-th energy storage battery at time t, respectively. , These are the actual active power and reactive power of the i-th photovoltaic unit at time t, respectively; , These represent the active power and reactive power flowing out of node i at time t, respectively. , Let be the active power and reactive power of the load at node i at time t, respectively. These are the weight coefficients for each objective, all of which are real numbers greater than or equal to 0 and obtained by the entropy weight method; These are the prices at which the distribution network purchases a unit of active and reactive energy from the upstream power grid at time t, respectively, excluding the price of reactive energy. These are the magnitude correction coefficients for each target, to ensure that all target values ​​are on the same order of magnitude; Let be the power load of the j-th transformer at time t; Let be the rated power of the j-th transformer; The theoretical photovoltaic power injection for the k-th node at time t; Let be the actual photovoltaic power absorbed by the k-th node at time t; The overall objective function is decomposed into two layers for separate solutions. In the lower layer model, the active and reactive power outputs of the photovoltaic units and the energy storage units are the optimization variables, along with the grid electricity price. , And obtained from the upper-level optimization iteration All quantities are known. The objective is to minimize the local operating cost of energy storage and maximize the photovoltaic absorption capacity. The objective function for the lower-level optimization is: (31) The active distribution network dispatch center then obtains the results from the lower-level optimization iterations. The optimization aims to minimize the overall power purchase cost of the distribution network and the load rate differences among multiple distribution areas. The objective function of the upper-level optimization is: （32） In the formula: , They represent the first , The next iteration.

2. The method for multi-objective distributed optimization scheduling of distribution networks based on the ADMM algorithm according to claim 1, characterized in that: The total cost model for step one is as follows: The total cost of a distribution network includes the electricity purchase cost from the upstream power grid and the operating cost of energy storage, as expressed below: (1) (2) In the formula: To optimize the dispatch cycle of the distribution network, a 24-hour period is adopted. This is the energy storage operating cost coefficient; This represents the set of node numbers connected to the energy storage battery. Represents the set of all node numbers; Let be the operating cost of all energy storage at time t; , These are the discharge power and charging power of the energy storage battery connected at node j at time t, respectively. , These represent the active power and reactive power flowing out at node j at time t, respectively. Let t be the active power loss within the network. These represent the prices at time t for the distribution network to purchase a unit of active and reactive energy from the upstream power grid, excluding the price of reactive energy. Set to 0; The load rate difference model for multiple distribution areas is as follows: The distribution network contains multiple transformers with different parameters and load capacities. A load rate difference index is established between these transformer areas to limit the load rate differences between them. The expression is as follows: (3) In the formula: This refers to the number of transformers in the system. Let be the power load of the j-th transformer at time t; Let be the rated power of the j-th transformer; Photovoltaic power consumption model: To improve the grid absorption capacity of distributed photovoltaic (PV) systems, a method is proposed that minimizes the square of the difference between the theoretical injected power and the actual absorbed power. The expression is as follows: (4) In the formula: This refers to the set of all nodes connected to photovoltaic systems in the distribution network. The theoretical photovoltaic power injection for the k-th node at time t; Let be the actual photovoltaic power absorbed by the k-th node at time t; Multi-objective optimization model: (5) (6) In the formula: These are the weight coefficients for each objective, all of which are real numbers greater than or equal to 0 and obtained by the entropy weight method; These are the magnitude correction coefficients for each target, to ensure that all target values ​​are on the same order of magnitude.

3. The method for multi-objective distributed optimization scheduling of distribution networks based on the ADMM algorithm according to claim 1, characterized in that: In step one, the weight values ​​of each indicator in the multi-objective indicator weights are selected using the entropy weight method. The weights are determined by the information contained in the dataset, the dataset is standardized, and the entropy weight of each indicator is calculated based on the information in the normalized dataset. Then, the entropy weight of each indicator is corrected to obtain the entropy weight redundancy, and finally, the objective weight values ​​of each indicator are obtained.

4. The method for multi-objective distributed optimization scheduling of distribution networks based on the ADMM algorithm according to claim 1, characterized in that: The network security operation constraints of the constraints in step one include branch power flow constraints, node voltage constraints, and node power constraints.

5. A multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm according to claim 1, characterized in that: The photovoltaic power circle constraint under the constraints of step one (16) (17) (18) In the formula: Let be the apparent power of the i-th photovoltaic unit at time t; Let be the predicted power of the i-th photovoltaic unit at time t; Let be the rated apparent power of the i-th photovoltaic unit; , These are the actual active power and reactive power of the i-th photovoltaic unit at time t, respectively.

6. The method for multi-objective distributed optimization scheduling of distribution networks based on the ADMM algorithm according to claim 1, characterized in that: The energy storage operation constraints in step one include energy storage SOC constraints, energy storage capacity constraints, and energy storage power circle constraints.

7. A multi-objective distributed optimization scheduling method for distribution networks based on the ADMM algorithm according to claim 1, characterized in that: Step three iterates between the upper and lower level subproblems while continuously adjusting the Lagrange multipliers. , The algorithm is updated to gradually converge, allowing us to obtain the optimal output of each photovoltaic and energy storage unit. The Lagrange multipliers are the dual variables. , The update formula is: (33)。

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