Decentralized reactive power optimization method for AC / DC hybrid power station based on Nash equilibrium

Abstract

The present invention relates to the field of power grid optimization, and provides a decentralized reactive power optimization method for an AC / DC hybrid substation based on Nash equilibrium, which includes the following steps: S1, dividing the AC / DC hybrid distribution substation into multiple independently optimized regions; S2, constructing the objective function and related constraints of each region to form a decentralized voltage-reactive power optimization model; S3, using the Nash equilibrium algorithm to independently solve the decentralized voltage-reactive power optimization model for each region to obtain the optimal solution for each region; S4, according to the Nash equilibrium solution of the reactive power optimization model obtained in S3, allocating the reactive output of distributed energy and reactive power in the AC / DC hybrid distribution substation to minimize the active power loss in the AC / DC hybrid distribution substation. The present invention improves the utilization efficiency of distributed renewable energy and reactive power sources such as capacitors by optimizing the reactive power share within the distribution substation, and reliably protects the privacy and security of users in each region.

Description

Technical Field

[0001] The present application relates to the field of power grid optimization, and specifically to a decentralized reactive power optimization method for AC / DC hybrid substations based on Nash equilibrium. Background Art

[0002] In current low-voltage distribution substations, due to the rapid increase in the penetration rate of new DC loads, distributed energy (such as wind power, photovoltaics, etc.) and energy storage equipment, the degree of power electronics and AC / DC hybridization in low-voltage distribution networks is increasing. Hybrid distribution substations with flexible AC / DC interconnection have the advantages of both AC and DC distribution lines; on the other hand, due to the large capacity and high proportion of distributed energy access, the randomness and volatility of its output aggravate the power loss in the operation of distribution substations, limiting the transformation of new distribution networks with renewable energy as the main body to a safe, controllable, flexible and efficient development trend.

[0003] In existing technologies, integrating AC / DC hybrid distribution substations into a low-voltage active distribution network is one of the primary solutions for improving the efficiency of distributed energy. This approach involves interconnecting the AC substation terminals via DC lines and intelligent soft openpoints (SOPs), allowing photovoltaic (PV), flexible DC loads, and reactive power sources to be connected to the DC lines. This interconnection leverages the advantages of distributed PV output. In recent years, research on flexible AC / DC hybrid distribution substations has focused on control schemes for AC / DC voltage and power flows, as well as substation operation strategies. Control schemes emphasize the instantaneous operating conditions of system voltage and frequency, while operation strategies primarily target optimal hourly operation of distributed energy resources.

[0004] Since voltage and reactive power optimization is a major issue in distribution systems, it aims to determine the optimal allocation ratio of various reactive power sources, such as distributed energy resources and reactive power compensators, to optimize specific objective functions while satisfying network constraints. To minimize power losses in hybrid substation networks, voltage and reactive power optimization methods are often employed. Currently, the most common approach is a fully cooperative centralized optimization method, which optimizes and coordinates the overall performance indicators of the AC / DC hybrid substation, such as minimizing the total operating cost of the existing distribution substation system. It is important to note that while the global optimality is achieved through a fully cooperative centralized model, it may not meet the optimization requirements for a specific AC or substation line. Centralized approaches require the collection of all data from the entire substation line at the control center for model solving, which carries a high communication and computational burden. Furthermore, user loads on AC / DC distribution lines may be managed by different operators, and their privacy cannot be protected through centralized approaches. Therefore, optimization methods that can effectively address these decentralized issues should be considered. In summary, it is necessary to adopt a decentralized voltage and reactive power optimization method for AC / DC hybrid substations to achieve good optimization results. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this paper proposes a decentralized reactive power optimization method for AC / DC hybrid substations based on Nash equilibrium. This method coordinates the distribution ratio of reactive power within multiple AC / DC hybrid low-voltage distribution substations. This decentralized coordinated voltage-reactive power optimization method effectively reduces network power losses while protecting the privacy of AC / DC line participants, providing support for the development of novel AC / DC distribution networks.

[0006] To achieve the above objectives, the solution adopted by the present invention is a decentralized reactive power optimization method for AC / DC hybrid substations based on Nash equilibrium, which includes the following steps:

[0007] S1. Divide the AC / DC hybrid distribution station area into N independently optimized areas;

[0008] S2. Construct the objective function and related constraints of each region to form a decentralized voltage and reactive power optimization model;

[0009] S21, minimizing the active power loss of each line in the divided area as the objective function of each area;

[0010] Objective function of the communication area:

[0011] Objective function in the DC region:

[0012] Where i is the area number of the AC / DC hybrid distribution station, and the numbers of the AC area and DC area are uniformly sorted, i = 1, 2, ..., N; A i Indicates that area i is the communication area, D i Indicates that region i is a DC region; represents the objective function when region i is the communication region, represents the objective function when region i is a DC region, P i ls is the active power loss in area i;

[0013] S22. Determine the optimization constraints of the communication area;

[0014] When region i is an AC region, that is, The optimization constraints for region i are:

[0015]

[0016] P i ls =r i l i =P i Ι-P i Ⅱ (7)

[0017]

[0018] Where k is the node number of the line belonging to area i. The node numbers are uniformly sorted in the AC / DC hybrid distribution substation area. K is the set of node numbers in area i, k∈K. and is the active and reactive power load at node k; and The active and reactive power output of distributed energy accessed by node k; represents the reactive output of reactive power sources such as capacitors connected to node k; and are the active power and reactive power of node k in the front-end line flowing to the AC region; and is the active power and reactive power flowing from node k in the AC area to the back-end line; Used to identify whether node k is a sending node or a receiving node. When node k is a sending node is 1 when node k is a receiving node is -1; v k is the square value of the voltage at node k; r i and x i is the resistance and reactance of the line in area i; P i Ι and is the active and reactive power input to the head end of the line in area i; l i is the square value of the line current in region i; ||||2 represents the 2-norm of the matrix, P i Ⅱ and is the active and reactive power output at the end of the line in area i; P i ls and is the active and reactive power loss of the line in area i; v k and are the lower and upper limits of the square value of the voltage at node k; is the upper limit of the square value of the line current in area i; m k 、n k 、 α k , β k are all predefined parameters that limit the reactive output of distributed energy resources connected to node k; is the upper limit of the active output of the distributed energy connected to node k; and The lower and upper limits of reactive power output of reactive power sources such as capacitors connected to k;

[0019] S23, determining optimization constraints for the DC region;

[0020] When region i is a DC region, that is, The optimization constraints for region i are:

[0021]

[0022] P i ls =r i l i =P i Ι -P i Ⅱ (18)

[0023]

[0024] in, is the active power of node k in the front-end line flowing to the DC region; is the active power flowing from node k in the DC region to the back-end line;

[0025] S3. Use the Nash equilibrium algorithm to independently solve the decentralized voltage-reactive power optimization model for each region to obtain the optimal solution for each region;

[0026] S4. According to the Nash equilibrium solution of the reactive power optimization model obtained in step S3, the reactive power output of the distributed energy in the AC / DC hybrid power distribution area is calculated. and reactive power output of reactive power source Distribution is carried out to minimize the active power loss in the AC / DC hybrid distribution station area.

[0027] Preferably, step S1 is specifically as follows:

[0028] The AC / DC hybrid distribution substation is divided into independent areas that need to be optimized, including AC areas and DC areas. Among them: each AC substation line with the head end connected to the distribution network bus and the end connected to the SOP is divided into an independent AC area; each DC line with both ends connected to the SOP is divided into an independent DC area; the number of areas obtained after division is N, where N is a positive integer.

[0029] Preferably, step S3 specifically includes the following steps:

[0030] S31, describing the decentralized voltage-reactive power optimization model in step S2 using a boundary information distribution method;

[0031] S32, based on the boundary variables received in each area The Nash equilibrium algorithm is used to independently solve the decentralized voltage and reactive power optimization model of each region to obtain the independent variables and and new boundary variables and And update the boundary variables received by other regions based on the new boundary variables obtained in each region in, is the boundary variable of other regions received by the communication region i, is the boundary variable of other regions received by DC region i, is the independent variable of the optimization constraint in the optimization model of AC region i, is the independent variable of the optimization constraint in the DC region i optimization model, It is the boundary variable sent by the communication area i to other areas, is the boundary variable sent by DC region i to other regions;

[0032] S33, determine whether the objective function solved in step S32 meets the set iteration stop criteria: if it does, it means that each region can achieve the optimal objective function according to the Nash equilibrium solution, and the iteration stops; if it does not, return to step S32, and update the boundary variables received by each region according to the updated boundary variables received by each region. Continue to solve for the variables.

[0033] Preferably, step S31 uses a boundary information allocation method to describe the decentralized voltage-reactive power optimization model in step S2, specifically:

[0034] (a) When region i is an AC region, that is, The decentralized voltage-reactive power optimization model of region i is:

[0035]

[0036] Wherein, formula (22) is the objective function of the optimization model of communication area i; formula (23) represents all non-equality constraints in the optimization constraints of the optimization model of communication area i; formula (24) represents all equality constraints in the optimization constraints of the optimization model of communication area i; The independent variables of the optimization constraints in the optimization model for communication region i, including the l i 、P i ls 、 These 7 variables; The boundary variables sent by communication area i to other areas, including the nodes in communication area i v k These 4 variables; is the boundary variable of other regions received by the communication region i, is a known value, based on the boundary variables of other regions Can get the communication area i P i Ι and The “boundary variables of other regions” here include boundary variables sent by other DC regions and other AC regions;

[0037] (b) When region i is a DC region, that is, The decentralized voltage-reactive power optimization model of DC region i is:

[0038]

[0039] Wherein, formula (25) is the objective function of the optimization model of DC region i; formula (26) represents all non-equality constraints in the optimization constraints of the optimization model of DC region i; formula (27) represents all equality constraints in the optimization constraints of the optimization model of DC region i; is the independent variable of the optimization constraint in the DC region i optimization model, including the DC region i l i 、P i ls These 4 variables; is the boundary variable sent by DC region i to other regions, including the nodes in DC region i and v k These two variables; is the boundary variable of other regions received by DC region i, is a known value, based on the boundary variables of other regions It can be obtained in DC region i and P i Ι .

[0040] Preferably, the iteration stopping criterion in step S33 is:

[0041]

[0042] Where, e represents the e-th iteration; are the values ​​of the objective function in the communication region obtained at the e-th iteration and the (e-1)-th iteration respectively; are the values ​​of the objective function in the DC region obtained at the e-th iteration and the (e-1)-th iteration respectively; It is a pre-set judgment threshold. When all regions meet the iteration stopping criteria after the e-th iteration, it is considered that the set iteration stopping criteria are met.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1. The AC / DC hybrid distribution station area is divided into independent optimization areas, and a voltage and reactive power optimization model is established for each area. By solving the voltage and reactive power optimization model for each area in the AC / DC hybrid distribution station area, the distributed power and reactive power share within the distribution station area are optimized, thereby improving the utilization efficiency of distributed power and reactive power sources such as capacitors.

[0045] 2. A decentralized optimization solution method based on the Nash equilibrium criterion is used to solve the voltage and reactive power optimization model of each area in the AC / DC hybrid substation. Only the regional boundary variable data can be shared, which can reduce the communication and computing burden while ensuring the privacy of participating customers.

[0046] 3. Through reactive power optimization, the active power loss of the AC / DC hybrid substation network is effectively reduced, and the efficiency of substation operation is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of the process of the decentralized reactive power optimization method of AC / DC hybrid substation based on Nash equilibrium of the present invention;

[0048] Figure 2 A detailed flow chart of the present invention for solving the decentralized voltage and reactive power optimization model for AC / DC hybrid substations;

[0049] Figure 3 A topological diagram of the AC / DC hybrid substation area divided into independent optimization areas in an embodiment of the present invention;

[0050] Figure 4 The comparison results of reactive power share utilization in each region before and after the decentralized voltage-reactive power optimization method is adopted in the embodiment of the present invention;

[0051] Figure 5 The comparison results of active power loss calculation in each region before and after the decentralized voltage and reactive power optimization method is adopted in the embodiment of the present invention;

[0052] Figure 6 It is the calculation result of the stopping standard of the objective function iteration after each optimization solution of a certain communication area in the embodiment of the present invention. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention.

[0054] The embodiment of the present invention provides a decentralized voltage and reactive power optimization method based on Nash equilibrium in AC / DC hybrid substations, which is mainly used to coordinate the distribution ratio of related reactive power sources in multiple AC / DC hybrid low-voltage distribution substations. Figure 1 As shown, the specific steps include:

[0055] S1. Divide the AC / DC hybrid distribution station area into multiple independently optimized areas.

[0056] Within the AC / DC hybrid distribution substation, separate regions requiring optimization are identified, including AC and DC regions. Each AC substation line connected to the distribution network busbar at its head end and to the SOP at its tail end is divided into an independent AC region; each DC line connected to the SOP at both ends is divided into an independent DC region. The specific number of regions N obtained after division is determined by the actual structure of the AC / DC hybrid distribution substation, and N is a positive integer.

[0057] S2. Construct the objective function and related constraints of each region to form a decentralized voltage and reactive power optimization model.

[0058] In the power grid, active power loss can be achieved by changing the line voltage, and the line voltage can be achieved by changing the reactive output. Therefore, voltage and reactive power optimization can reduce active power loss and achieve optimization of the power grid.

[0059] For an AC / DC hybrid power distribution substation consisting of multiple independent areas, if the active power loss of each area is minimized, then the active power loss of the AC / DC hybrid power distribution substation area is minimized. Therefore, an objective function and related constraints are constructed for each area to form a voltage and reactive power optimization model. The specific steps include:

[0060] S21. Minimizing the active power loss of each line in the divided area is used as the objective function of each area.

[0061] Objective function of the communication area:

[0062] Objective function in the DC region:

[0063] Where i is the area number of the AC / DC hybrid distribution station, and the numbers of the AC area and DC area are uniformly sorted, i = 1, 2, ..., N; A i Indicates that area i is the communication area, D i Indicates that region i is a DC region; represents the objective function when region i is the communication region, f Di represents the objective function when region i is a DC region, P i ls is the active power loss in area i.

[0064] S22. Determine the optimization constraints of the communication area.

[0065] When region i is an AC region, that is, The optimization constraints for region i are:

[0066]

[0067] P i ls =r i l i =P i Ι -P i Ⅱ (7)

[0068]

[0069] Where k is the node number of the line belonging to area i. The node numbers are uniformly sorted in the AC / DC hybrid distribution substation area. K is the set of node numbers in area i, k∈K. and is the active and reactive power load at node k; and The active and reactive power output of distributed energy accessed by node k; represents the reactive output of reactive power sources such as capacitors connected to node k; and are the active power and reactive power of node k in the front-end line flowing to the AC region; and is the active power and reactive power flowing from node k in the AC area to the back-end line; Used to identify whether node k is a sending node or a receiving node. When node k is a sending node is 1 when node k is a receiving node is -1; v k is the square value of the voltage at node k; r i and x i is the resistance and reactance of the line in area i; P i Ι and is the active and reactive power input to the head end of the line in area i; l i is the square value of the line current in region i; ||||2 represents the 2-norm of the matrix, P i Ⅱ and is the active and reactive power output at the end of the line in area i; P i ls and is the active and reactive power loss of the line in area i; v k and are the lower and upper limits of the square value of the voltage at node k; is the upper limit of the square value of the line current in area i; m k 、n k 、 α k , β k are all predefined parameters that limit the reactive output of distributed energy resources connected to node k; is the upper limit of the active output of the distributed energy connected to node k; and The lower and upper limits of the reactive output of the reactive power source such as the capacitor connected to k.

[0070] It can be seen that in the optimization constraints of the AC area, formulas (3)-(8) are obtained based on the circuit power flow calculation principle, and formulas (9)-(14) are set according to the circuit operation safety requirements or distributed energy operation requirements.

[0071] S23. Determine the optimization constraints of the DC region.

[0072] When region i is a DC region, that is, The optimization constraints for region i are:

[0073]

[0074] P i ls =r i l i =P i Ι -P i Ⅱ (18)

[0075]

[0076] in, is the active power of node k in the front-end line flowing to the DC region; is the active power flowing from node k in the DC region to the back-end line.

[0077] It can be seen that in the optimization constraints of the DC area, formulas (15)-(18) are obtained based on the circuit power flow calculation principle, and formulas (19)-(21) are set according to the circuit operation safety requirements or distributed energy operation requirements.

[0078] S3. Use the Nash equilibrium algorithm to independently solve the decentralized voltage and reactive power optimization model of each region and obtain the optimal solution for each region, such as Figure 2 As shown, the specific steps include:

[0079] S31. Use the partitioning and assignment of boundary information (PABI) method to describe the decentralized voltage and reactive power optimization model in step 2:

[0080] (a) When region i is an AC region, that is, The decentralized voltage-reactive power optimization model of region i is:

[0081]

[0082] Wherein, formula (22) is the objective function of the optimization model of communication area i; formula (23) represents all non-equality constraints in the optimization constraints of the optimization model of communication area i; formula (24) represents all equality constraints in the optimization constraints of the optimization model of communication area i; The independent variables of the optimization constraints in the optimization model for communication region i, including the l i 、P i ls 、 These 7 variables; The boundary variables sent by communication area i to other areas, including the nodes in communication area i v k These 4 variables; is the boundary variable of other regions received by the communication region i, is a known value, based on the boundary variables of other regions Can get the communication area i P i Ι and The "boundary variables of other regions" here include boundary variables sent from other DC regions and other AC regions.

[0083] (b) When region i is a DC region, that is, The decentralized voltage-reactive power optimization model of DC region i is:

[0084]

[0085] Wherein, formula (25) is the objective function of the optimization model of DC region i; formula (26) represents all non-equality constraints in the optimization constraints of the optimization model of DC region i; formula (27) represents all equality constraints in the optimization constraints of the optimization model of DC region i; is the independent variable of the optimization constraint in the DC region i optimization model, including the DC region i l i 、P i ls These 4 variables; is the boundary variable sent by DC region i to other regions, including the nodes in DC region i and v k These two variables; is the boundary variable of other regions received by DC region i, is a known value, based on the boundary variables of other regions It can be obtained in DC region i and P i Ι .

[0086] S32, based on the boundary variables received in each area The Nash equilibrium algorithm is used to independently solve the decentralized voltage and reactive power optimization model of each region to obtain the independent variables and and new boundary variables and And update the boundary variables received by other regions based on the new boundary variables obtained in each region At initialization, each region initially receives the bounds variable The initial value can be set to 0 or the circuit rated value, and the reactive output of reactive power sources such as distributed power sources and capacitors at each node is set to 0.

[0087] S33, determine whether the objective function solved in step S32 meets the set iteration stop criteria: if it does, it means that each region can achieve the optimal objective function according to the Nash equilibrium solution, and the iteration stops; if it does not, return to step S32, and update the boundary variables received by each region according to the updated boundary variables received by each region. Continue to solve for the variables.

[0088] In this embodiment, the iteration stopping criteria are:

[0089]

[0090] Where, e represents the e-th iteration; are the values ​​of the objective function in the communication region obtained at the e-th iteration and the (e-1)-th iteration respectively; are the values ​​of the objective function in the DC region obtained at the e-th iteration and the (e-1)-th iteration respectively; is a pre-set judgment threshold. When all regions meet the iteration stopping criteria after the e-th iteration, it is considered that the set iteration stopping criteria are met.

[0091] S4. According to the Nash equilibrium solution of the reactive power optimization model obtained in step S3, the reactive power output of the distributed energy in the AC / DC hybrid power distribution area is calculated. and reactive power output of reactive power source Distribute and optimize the AC / DC hybrid distribution station area to minimize the active power loss in the AC / DC hybrid distribution station area.

[0092] This embodiment provides a specific application example to illustrate the whole process of using the method of the present invention to perform decentralized voltage and reactive power optimization based on Nash equilibrium in AC / DC hybrid substations. The object of this embodiment is to connect multiple AC distribution line terminals with DC lines through flexible interconnection devices SOP to form an AC / DC hybrid substation. The independent optimization areas of the AC / DC hybrid substation are divided as follows: Figure 3 The load, renewable energy output and reactive power capacity of each node are shown in the following table.

[0093]

[0094]

[0095] In the table, node k Reactive power capacity is

[0096] Specifically, the method of this embodiment includes the following steps:

[0097] S1. The AC / DC hybrid distribution station area is divided into multiple independently optimized areas:

[0098] Each AC line connected to the distribution network bus at the head end and the SOP at the end is divided into independent optimization areas, namely A1, A2, and A3; the DC line connected to the SOP at both ends is also divided into independent optimization areas, namely D1 and D2; Figure 3 shown.

[0099] S2. Construct the objective function and related constraints of each region to form a decentralized voltage and reactive power optimization model.

[0100] Considering the loss of network active power, determine the voltage and reactive power optimization model of each independent AC and DC area. Specifically, construct the objective function of each area A1, A2, A3, D1, and D2: Minimize the network active power loss Add constraints to form a voltage-reactive power optimization model. The node voltage lower limit in the AC region is 399V and the upper limit is 361V. The node voltage lower limit in the DC region is 393.75V and the upper limit is 356.25V. The line current upper limit in the AC region is 300A, and the line current upper limit in the DC region is 500A.

[0101] S3. Use the Nash equilibrium algorithm to independently solve the decentralized voltage and reactive power optimization model for each region to obtain the optimal solution for each region. Specifically, the following steps are included:

[0102] The PABI method is used to describe the decentralized voltage and reactive power optimization model in the AC and DC areas, and the model for the AC area is determined: Model in the DC region:

[0103] Initialize the boundary variables exchanged between AC and DC areas, and replace the boundary variables received by the area at the beginning with The initial quantities are all set to the voltage rated values, and the reactive output of reactive power sources such as distributed power sources and capacitors at each node is set to 0; then the voltage and reactive power optimization models of areas A1, A2, A3, D1, and D2 are solved independently, and the independent variables and boundary variables of each area obtained by solving the model are updated. Then, the boundary variables are exchanged between areas to complete the first iteration.

[0104] After each iteration, it is determined whether the objective function after solution meets the set iteration stopping criteria. The judgment threshold set in this embodiment is If the stopping criteria are met, the Nash equilibrium solution is obtained for each region, the objective function is optimized, and the iteration stops; if the criteria are not met, the iteration continues. As an example, Figure 6 It is the calculation result of the stopping criterion of the objective function iteration after each optimization solution of a certain communication area in the embodiment.

[0105] S4. After the iteration, the Nash equilibrium solution of the reactive power optimization model obtained in step 3 is and Optimize the allocation of reactive output and reactive power share of distributed power sources in AC / DC hybrid substations. Figure 4 The figures are the comparison results of reactive power utilization in each region before and after the decentralized voltage-reactive power optimization method is adopted in the embodiment. After the optimization is completed by the method of the present invention, the total network loss power of regions A1, A2, A3, D1, and D2 is reduced by 59.4% compared with that before the optimization, and the average reactive power utilization of the entire hybrid substation area is increased by 26.4%. Figure 5 1 is a comparison result of active power loss calculation in each region before and after adopting the decentralized voltage and reactive power optimization method in the embodiment.

[0106] The decentralized voltage and reactive power optimization method of the AC / DC hybrid substation based on Nash equilibrium applied in the embodiment of the present invention solves the voltage and reactive power optimization model of each area in the AC / DC hybrid substation, optimizes the allocation of distributed power sources and reactive power shares in the substation, improves the utilization efficiency of distributed power sources and reactive power sources such as capacitors, effectively reduces the active power loss of the AC / DC hybrid substation network, and improves the efficiency of substation operation; and because only regional boundary variable data is shared, it can reduce the communication and computing burden while ensuring the privacy information of participating customers.

[0107] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A decentralized reactive power optimization method for AC / DC hybrid substations based on Nash equilibrium, characterized in that: It includes the following steps: S1. Divide the AC / DC hybrid distribution station area into N independently optimized areas; S2. Construct the objective function and related constraints of each region to form a decentralized voltage and reactive power optimization model; S21, minimizing the active power loss of each line in the divided area as the objective function of each area; Objective function of the communication area: Objective function in the DC region: Where i is the area number of the AC / DC hybrid distribution station, and the numbers of the AC area and the DC area are arranged in the same order, i = 1, 2, ..., N; A i Indicates that area i is the communication area, D i Indicates that region i is a DC region; represents the objective function when region i is the communication region, represents the objective function when region i is a DC region, P i ls is the active power loss in area i; S22. Determine the optimization constraints of the communication area; When region i is an AC region, that is, The optimization constraints for region i are: P i ls =r i l i =P i Ι -P i Ⅱ (7) Where k is the node number of the line belonging to area i. The node numbers are uniformly sorted in the AC / DC hybrid distribution substation area. K is the set of node numbers in area i, k∈K. and is the active and reactive power load at node k; and The active and reactive power output of distributed energy accessed by node k; represents the reactive power output of the reactive power source connected to node k; and are the active power and reactive power of node k in the front-end line flowing to the AC area; and is the active power and reactive power flowing from node k in the AC area to the back-end line; Used to identify whether node k is a sending node or a receiving node. When node k is a sending node is 1 when node k is a receiving node is -1; v k is the square value of the voltage at node k; r i and x i is the resistance and reactance of the line in area i; P i Ι and is the active and reactive power input to the head end of the line in area i; l i is the square value of the line current in region i; ||||2 represents the 2-norm of the matrix, P i Ⅱ and is the active and reactive power output at the end of the line in area i; P i ls and is the active and reactive power loss of the line in area i; v k and are the lower and upper limits of the square value of the voltage at node k; is the upper limit of the square value of the line current in area i; m k 、n k 、 α k , β k are all predefined parameters that limit the reactive output of distributed energy resources connected to node k; is the upper limit of the active output of the distributed energy connected to node k; and is the lower and upper limits of reactive power output of the reactive power source connected to k; S23, determining optimization constraints for the DC region; When region i is a DC region, that is, The optimization constraints for region i are: P i ls =r i l i =P i Ι -P i Ⅱ (18) in, is the active power of node k in the front-end line flowing to the DC region; is the active power flowing from node k in the DC region to the back-end line; S3. Use the Nash equilibrium algorithm to independently solve the decentralized voltage-reactive power optimization model for each region to obtain the optimal solution for each region; The specific steps include: S31, describing the decentralized voltage-reactive power optimization model in step S2 using a boundary information distribution method; S32, based on the boundary variables received in each area The Nash equilibrium algorithm is used to independently solve the decentralized voltage and reactive power optimization model of each region to obtain the independent variables and and new boundary variables and And update the boundary variables received by other regions based on the new boundary variables obtained in each region in, is the boundary variable of other regions received by the communication region i, is the boundary variable of other regions received by DC region i, is the independent variable of the optimization constraint in the optimization model of AC region i, is the independent variable of the optimization constraint in the DC region i optimization model, It is the boundary variable sent by the communication area i to other areas, is the boundary variable sent by DC region i to other regions; S33, determine whether the objective function solved in step S32 meets the set iteration stop criteria: if it does, it means that each region can achieve the optimal objective function according to the Nash equilibrium solution, and the iteration stops; if it does not, return to step S32, and update the boundary variables received by each region according to the updated boundary variables received by each region. Continue to solve for the variables; S4. According to the Nash equilibrium solution of the reactive power optimization model obtained in step S3, the reactive power output of the distributed energy in the AC / DC hybrid power distribution area is calculated. and reactive power output of reactive power source Distribution is carried out to minimize the active power loss in the AC / DC hybrid distribution station area.

2. The method for decentralized reactive power optimization in an AC / DC hybrid area based on Nash equilibrium according to claim 1 is characterized in that: Step S1 is specifically as follows: The AC / DC hybrid distribution substation is divided into independent areas that need to be optimized, including AC areas and DC areas. Among them: each AC substation line with the head end connected to the distribution network bus and the end connected to the SOP is divided into an independent AC area; each DC line with both ends connected to the SOP is divided into an independent DC area; the number of areas obtained after division is N, where N is a positive integer.

3. The method for decentralized reactive power optimization in an AC / DC hybrid area based on Nash equilibrium according to claim 1 is characterized in that: Step S31 uses the boundary information allocation method to describe the decentralized voltage and reactive power optimization model in step S2, specifically: (a) When region i is an AC region, that is, The decentralized voltage-reactive power optimization model of region i is: Wherein, formula (22) is the objective function of the optimization model of communication area i; formula (23) represents all non-equality constraints in the optimization constraints of the optimization model of communication area i; formula (24) represents all equality constraints in the optimization constraints of the optimization model of communication area i; The independent variables of the optimization constraints in the optimization model for communication region i, including the l i 、P i ls 、 These 7 variables; The boundary variables sent by communication area i to other areas, including the nodes in communication area i v k These 4 variables; is the boundary variable of other regions received by the communication region i, is a known value, based on the boundary variables of other regions Can get the communication area i P i Ι and (b) When region i is a DC region, that is, The decentralized voltage-reactive power optimization model of DC region i is: Wherein, formula (25) is the objective function of the optimization model of DC region i; formula (26) represents all non-equality constraints in the optimization constraints of the optimization model of DC region i; formula (27) represents all equality constraints in the optimization constraints of the optimization model of DC region i; is the independent variable of the optimization constraint in the DC region i optimization model, including the DC region i l i 、P i ls These 4 variables; is the boundary variable sent by DC region i to other regions, including the nodes in DC region i and v k These two variables; is the boundary variable of other regions received by DC region i, is a known value, based on the boundary variables of other regions It can be obtained in DC region i and P i Ι .

4. The method for decentralized reactive power optimization in an AC / DC hybrid substation area based on Nash equilibrium according to claim 1 is characterized in that: The iteration stopping criteria in step S33 are: Where, e represents the e-th iteration; are the values ​​of the objective function in the communication region obtained at the e-th iteration and the (e-1)-th iteration respectively; are the values ​​of the objective function in the DC region obtained at the e-th iteration and the (e-1)-th iteration respectively; It is a pre-set judgment threshold. When all regions meet the iteration stopping criteria after the e-th iteration, it is considered that the set iteration stopping criteria are met.

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