Privacy-preserving elastic node and distribution network decentralized optimization strategy

Abstract

The application discloses a privacy-considered distributed optimization operation strategy of elastic nodes and distribution networks, and a smart load is formed by connecting an electric power spring and a non-key load in series in a distribution network.The steps of the distributed optimization operation strategy are as follows: A, determining an elastic node power regulation model according to the structure and control method of the electric power spring; B, constructing a distributed optimization operation model of the elastic nodes and the distribution networks in cooperation and considering privacy protection based on the minimum total operation cost as an optimization operation target; and C, solving the distributed optimization operation model in step B by using an improved generalized Benders decomposition method.The distributed optimization operation strategy makes the distribution network operator and the elastic node operator only need to interact a small amount of information such as node power, feasible cut and optimal cut, and thus the privacy of the elastic node is protected; in addition, the convergence of the distributed optimization operation model is improved by improving the generalized Benders algorithm.

Description

Technical Field

[0001] This invention relates to the field of distribution network optimization operation technology, specifically a flexible node and distributed optimization operation strategy for distribution networks that takes privacy protection into account. Background Technology

[0002] The increasing frequency of natural disasters and man-made attacks poses a significant threat to power distribution networks. The large-scale integration of various uncontrollable distributed energy sources also places higher demands on the safe operation capabilities of power distribution networks. Power distribution networks must not only ensure the reliability of routine operations but also maximize their resilience against extreme disturbances, quickly recovering to normal operation and enhancing their inherent flexibility. Therefore, establishing a reliable distributed optimization operation model for resilient nodes and the power distribution network is essential for optimizing the network's operational status. Traditional distributed optimization operation models require calculations of node power, but due to privacy concerns for resilient nodes and power distribution network operators, some power parameters may be unavailable. Therefore, there is an urgent need for a convenient method that optimizes the power interaction between the power distribution network and resilient nodes without requiring internal power and load shedding information within the power distribution network and resilient nodes. Summary of the Invention

[0003] The purpose of this invention is to address the problems existing in the parameter estimation of distribution transformers in existing distribution networks by providing a flexible node and distributed optimization operation strategy for distribution networks that takes privacy protection into account.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A distributed optimization operation strategy for resilient nodes and distribution networks that considers privacy protection is characterized by: connecting power springs in series with non-critical loads in the distribution network to form smart loads. The steps of this distributed optimization operation strategy are as follows:

[0006] A. Determine the power regulation model of the elastic node based on the structure and control method of the electric spring;

[0007] B. Based on minimizing total operating cost as the optimization objective, a decentralized optimization operation model considering privacy protection and distribution network coordination is constructed.

[0008] C. Solve the distributed optimization operation model in step B using the improved generalized Benders decomposition method.

[0009] Based on the structure and control method of electric springs, this paper analyzes the characteristics related to elastic nodes and power regulation: An electric spring (ES) is a power electronic device used in power systems. Its power consumption varies with power generation, effectively mitigating the intermittency and instability of renewable energy generation such as solar and wind power. Although an ES is also a reactive power generator, it differs significantly from traditional reactive power compensation devices. Static var compensators (SVCs) and static var generators (SVGs) are typical reactive power compensation devices, providing strong technical support for the long-term stable operation of power systems. While they can all smooth voltage fluctuations through reactive power compensation, they are based on existing operating modes, i.e., first determining the power load demand and then providing the corresponding power generation. However, the ES overturns the traditional power system operating mode, allowing the energy consumption of the load in the grid to vary with the changes in renewable energy generation. This effectively overcomes the unpredictability of renewable energy generation and represents a completely new control approach. ES can be widely distributed at any node in the power grid. As long as there are non-critical loads with a wide voltage range (such as electric heaters), ES can be connected in series with them to form a smart load to ensure the stability of the voltage of critical loads.

[0010] The flexible node power regulation model in step A includes a non-critical load constraint model and a power spring constraint model. The non-critical load constraint model includes the NCL power equation of equation (1), the ZIP load model of NCL active power of equation (2), the ZIP load model of NCL reactive power of equation (3), and the NCL voltage limit of equation (4).

[0011]

[0012]

[0013]

[0014]

[0015] In equations (1)-(4): Let NCL be the active power of node m at time t; Let NCL be the reactive power of node m at time t; Let be the NCL voltage at node m at time t; Inject the NCL current at node m at time t; Let be the rated active power of the NCL at node m at time t; Let a be the rated reactive power of the NCL at node m at time t; p,NCL b p,NCL and cp,NCL ZIP factor for NCL active power; a q,NCL ,b q,NCL and c q,NCL ZIP factor for NCL reactive power; and These are the upper and lower limits of the NCL voltage value;

[0016] The power spring constraint model includes the smart load power constraint in equation (5), the power consumption equation of ES in equation (6), the SOC calculation equation in equation (7), the SOC constraint in equation (8), and the ES capacity constraint in equation (9):

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] In equations (5)-(9): Let be the active power consumption of the ES at node m at time t; Let be the reactive power consumption of node m at time t; Let be the voltage at node m at time t; The battery charging power at node m at time t; Let be the battery discharge power at node m at time t; Let η be the state of charge of the battery at node m at time t; ch For battery charging coefficient, η dis C is the battery discharge coefficient; Δt is the optimization time step; BS Battery capacity; SOC min and SOC max These are the upper and lower limits of SOC; S m,ES It refers to the ES capacity.

[0023] The total operating cost in step B includes the cost of the elastic node and the distribution network cost. The decentralized optimization operation model that considers privacy protection for the coordination of elastic nodes and distribution network requires each elastic node operator to calculate the feasible cut, the optimal cut, and the power of the interacting nodes and provide the feasible cut, the optimal cut, and the power of the interacting nodes to the distribution network operator, and does not need to provide the internal power of the elastic node and the load shedding information.

[0024] The cost of the elastic node includes load shedding cost, operating cost, and reduction cost. The objective function for the elastic node cost is specifically expressed as follows:

[0025]

[0026]

[0027]

[0028]

[0029] In equations (10)-(13): C m,EN C represents the operating cost of EN at node m; m,NCL The load shedding cost of NCL at node m; For DG, the cost reduction at node m; C m,ES The cost of running ES on node m; For NCL load reduction at node m; For the power reduction of DG at node m; The battery charging power at node m at time t; c is the battery discharge power at node m at time t; com The unit cost of NCL load reduction, c DG The unit cost of DG power reduction, c ch Unit cost of charging the battery, c dis Δt represents the unit cost of battery discharge; Δt represents the optimization time step; and T represents the optimization cycle.

[0030] The constraints of the elastic node cost objective function include DG constraints and EN power balance equations; wherein the DG constraints include the DG power balance equation of equation (14) and the DG capacity limit of equation (15):

[0031]

[0032]

[0033] In equations (14)-(15): Let be the active power of the DG at node m at time t; Let be the reactive power of the DG at node m at time t; Let be the maximum power of the DG at node m at time t; Let m be the capacity of the DG converter at node m;

[0034] The EN power balance equations include the active power balance equation at node m at time t (16) and the reactive power balance equation at node m at time t (17):

[0035]

[0036]

[0037] In equations (16)-(17): Let be the active power of the DG at node m at time t; Let NCL be the active power of node m at time t; Let be the active power consumption of the ES at node m at time t; Let CL be the active power consumption of node m at time t; The active power injection at node m at time t; Let be the reactive power of the DG at node m at time t; Let NCL be the reactive power of node m at time t; Let be the reactive power consumption of node m at time t; Let CL be the reactive power consumption of node m at time t; This represents the reactive power injection at node m at time t.

[0038] The aforementioned distribution network cost includes distribution network operation cost, power exchange cost between the distribution network and the upstream power grid, distributed generation reduction cost, and cost of minimizing traditional load shedding. The specific objective function for distribution network cost is as follows:

[0039] min C DN =C Grid +C DG +C LS (18)

[0040]

[0041]

[0042]

[0043] In equations (18)-(21): C DN For DN operating costs; C Grid The cost of power exchange between DN and the upstream power grid; C DG To cut costs for DG; C LS This reduces the cost of shirking traditional loads. The power purchased at time t Let be the electricity sold at time t; The active power reduction of the i-th DG at time t; For the i-th load reduction at time t; c b For the unit cost of purchasing electricity, c s For the unit cost of selling electricity, c DG The unit cost reduction of DG active power, c LS Δt is the unit cost of load reduction; Δt is the optimization time step; T is the optimization cycle; Ω is the set of nodes.

[0044] The constraints that the distribution network cost objective function needs to satisfy include power flow equation constraints, DG constraints, load shedding constraints, SVC constraints, and safe operation constraints; among which, the power flow equation constraints include the linearized Distflow power flow equation model of equations (22)-(26) and the active power exchange of the slack node in equation (27):

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] In equations (22)-(27): Let be the active power of branch ij at time t; Inject active power into node j at time t; Let be the active power of branch jk at time t; Let be the reactive power of branch ij at time t; Inject reactive power into node j at time t; Let be the reactive power of branch jk at time t; u(j) be the set of nodes ending at node j; v(j) be the set of nodes starting at node j. Inject active power into the DG of node j at time t; Let be the load active power of node j at time t; The active power reduction of the load at node j at time t; For the SVC reactive power injection at node j at time t; Inject reactive power into the DG of node j at time t; Let be the reactive power of the load at node j at time t; The reactive power reduction of the load at node j at time t; V is the voltage at node j at time t; i t Let r be the voltage at node i at time t; ij x is the resistance of branch ij; ij V is the reactance of branch ij; N This refers to the rated node voltage of the distribution network. Let be the active power of the balancing node at time t; Let t be the power purchased by the distribution network from the upper-level power grid at time t; The power sold to the upper-level power grid at time t;

[0052] DG constraints include the DG active power equation in equation (28) and the DG capacity constraint in equation (29); load reduction constraints include the load reduction expressed in equation (30) being less than the load at that node and equation (31) ensuring that the power factor of the load is constant; SVC constraints include the SVC reactive power constraint in equation (32).

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] In equations (28)-(32): Inject active power into the DG of node j at time t; Let be the active power reduced by the DG at node j at time t; Let be the maximum active power output of the DG at node j at time t; The square of the active power injected into the DG at node j at time t; S is the square of the reactive power injected into the DG at node j at time t; j,DG Let be the DG converter capacity of node j; The active power reduction of the load at node j at time t; Let be the load active power of node j at time t; The reactive power reduction of node j at time t; p fj The load power factor; Let be the SVC reactive power of node j at time t; The lower limit of the SVC reactive power at node j. This represents the upper limit of the SVC reactive power of node j;

[0059] Safe operation constraints:

[0060]

[0061]

[0062] In equations (33)-(34): V i t Let V be the node voltage of node i at time t. min The lower limit of the node voltage, V maxThis represents the upper limit of the node voltage; Let be the active power of branch ij at time t; S represents the reactive power of branch ij at time t; ij Let be the capacity of branch ij.

[0063] Because the distributed optimization model in step B contains both complex constraints (integer constraints, nonlinear constraints, and linear constraints), it is difficult to solve directly. Therefore, an improved generalized Benders decomposition method is used to solve it. This method decouples the variables, dividing the original problem into a main problem (containing only variables with complex constraints) and subproblems (containing only variables with linear constraints). The main problem of the algorithm is for the distributed networks operator (DNO), and the subproblems are for the elastic node operator (ENO). The subproblem is a standard linear programming problem. Benders iteratively introduces constraints (determined by obtaining new vertices or epipolar lines through solving subproblems) to increase the lower bound of the original problem (ensuring that the upper bound does not increase), eventually approximating the optimal solution.

[0064] The improved generalized Benders decomposition method in step C for solving the distributed optimization operation model in step B divides the distributed optimization operation model in step B into a main problem for distribution network operators and a sub-problem for resilient node operators. The main problem obtains the distribution network load shedding, reactive power of distributed sources in inelastic nodes, and output of static var compensators by solving the distribution network cost objective function. The sub-problem obtains the charging and discharging power of the electric springs at the resilient nodes, the active power reduced by the electric springs, and the reactive power generated by the electric springs by solving the resilient node cost objective function.

[0065] The compact form of the distributed optimization operation model in step C is as follows:

[0066]

[0067] st f1(x)≤0 (36)

[0068] f2(y m )≤0 (37)

[0069] g1(y m )=0 (38)

[0070] g2(x,y m )=0 (39)

[0071] in

[0072]

[0073]

[0074] x is the set of variables in DN; y m The set of variables for EN; a and b m x and y in the objective function are respectively m The coefficients; Π is the set of elastic nodes; Equation (35) represents the objective function of total operating cost, a T x and Equation (36) is the compact form of the distribution network cost objective function and the flexible node cost objective function under the total operating cost objective function, respectively; Equation (37) is the compact form of the distribution network cost objective function constraint; Equation (38) is the compact form of the NCL voltage limit, SOC constraint, ES capacity constraint and DG capacity limit in the flexible node power regulation model; Equation (39) is the compact form of the NCL power equation, the NCL active power ZIP load model, the NCL reactive power ZIP load model, the smart load power constraint, the ES power consumption equation, the SOC calculation equation and DG power balance equation in the flexible node cost objective function constraint; Equation (39) is the compact form of the EN power balance equation in the flexible node cost objective function constraint.

[0075] The algorithm model for the sub-problem is as follows:

[0076] SP:

[0077] st f2(y m )≤0 (41)

[0078] g1(y m )=0 (42)

[0079] g2(x (k) ,y m )=0 (43)

[0080] Based on the scheduling variable in the (k-1)th iteration and the fixed variables in the k-th iteration State variables and It can be obtained by solving the non-critical load constraint model in the resilient node power regulation model; the scheduling variables and calculated state variables in the (k-1)th iteration can be used It means that g1(y) m ) and g2(x,ym ) for around x (k) and Linearization result obtained using the first-order Taylor formula:

[0081]

[0082]

[0083] exist and Based on this, equations (42) and (43) are approximately expressed as equations (46) and (47), respectively:

[0084] g1'(y m )=0 (46)

[0085] g2'(x (k) ,y m )=0 (47)

[0086] Where g1' and g2' are approximate forms of g1 and g2, respectively; x (k) Let x be the value of the variable x in the k-th iteration;

[0087] If the subproblem is feasible, the optimal solution is expressed as: The optimal cut can be expressed as:

[0088]

[0089] If the subproblem is infeasible, then a feasibility problem is conceived to generate feasible cuts, i.e.,

[0090]

[0091] st f2(y m )≤0 (50)

[0092] g1'(y m )=0 (51)

[0093]

[0094] The generated feasible cut is represented as:

[0095]

[0096] Based on the optimal or feasible cuts obtained from the subproblems, the algorithm model for the main problem can be represented as follows:

[0097]

[0098] st f1(x)≤0 (55)

[0099]

[0100]

[0101] Among them O m,SP and O m,FP These are auxiliary variables for generating the optimal cut and the feasible cut, respectively; and These are slack variables; and These are the Lagrange multipliers of equations (47) and (52) in the optimization problems of optimal cut and feasible cut, respectively.

[0102] The steps in step C for solving the distributed optimization model in step B using the improved generalized Benders decomposition method are as follows:

[0103] C1. For the distribution network, the main problem is solved according to formula (54)-formula (57), and the obtained boundary variables are returned to the operators of each elastic node.

[0104] C2. Calculate the state variables based on the results of step C1. For the elastic node operator, perform linear approximation processing on the sub-problem according to formula (44)-formula (47).

[0105] C3. Solve the subproblem to determine its feasibility. If it is feasible, return the optimal cut to the main problem according to formula (48); otherwise, return the feasible cut to the subproblem according to formula (49)-formula (53).

[0106] C4. Repeat steps C1-C3 until the objective function of the main problem yields the same solution twice in a row, thus obtaining the optimal objective and the optimal value, and then stop the iteration.

[0107] In this invention, the symbols have the following meanings: ES represents electric spring, SVC represents static var compensator, SVG represents static var generator, NCL represents non-critical load, CL represents critical load, EN represents resilient node, DG represents distributed generation, and DN represents distribution network.

[0108] The present invention has the following advantages over the prior art:

[0109] The distributed optimization operation strategy of this invention, based on the elastic nodes constructed from electric springs, can fully utilize the controllability of non-critical loads and improve the flexible operation range of elastic nodes. The proposed distributed optimization operation strategy requires only a small amount of information, such as node power, feasible cut, and optimal cut, between distribution network operators and elastic node operators, thus protecting the privacy of elastic nodes. In addition, by improving the generalized Benders algorithm, the problem that the traditional generalized Benders algorithm cannot handle the non-convex nonlinear model of elastic nodes is solved, thereby improving the convergence of the distributed optimization operation model. Attached Figure Description

[0110] Appendix Figure 1 This is a flowchart of the privacy-protected flexible node and distributed optimization operation strategy for distribution networks of the present invention;

[0111] Appendix Figure 2 This is a diagram showing the installation position of the electric spring used in this invention;

[0112] Appendix Figure 3 This is a flowchart of the improved generalized Benders decomposition method used in this invention;

[0113] Appendix Figure 4 This is a topology diagram of an improved 33-node AC distribution network system used in an embodiment of the present invention;

[0114] Appendix Figure 5 This paper compares the iteration count-cost curves of the distributed optimization operation strategy and the centralized optimization algorithm of this invention. Detailed Implementation

[0115] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0116] like Figure 1-3 As shown: A distributed optimization operation strategy for resilient nodes and distribution networks that considers privacy protection connects power springs in series with non-critical loads in the distribution network to form smart loads. The steps of this distributed optimization operation strategy are as follows:

[0117] A. Based on the structure and control method of the electric spring, determine the power regulation model of the elastic node.

[0118] The flexible node power regulation model includes a non-critical load constraint model and a power spring constraint model. The non-critical load constraint model includes the NCL power equation (1), the NCL active power ZIP load model (2), the NCL reactive power ZIP load model (3), and the NCL voltage limit (4).

[0119]

[0120]

[0121]

[0122]

[0123] In equations (1)-(4): Let NCL be the active power of node m at time t; Let NCL be the reactive power of node m at time t; Let be the NCL voltage at node m at time t; Inject the NCL current at node m at time t; Let be the rated active power of the NCL at node m at time t; Let a be the rated reactive power of the NCL at node m at time t; p,NCL b p,NCL and c p,NCL ZIP factor for NCL active power; a q,NCL ,b q,NCL and c q,NCL ZIP factor for NCL reactive power; and These are the upper and lower limits of the NCL voltage value;

[0124] The power spring constraint model includes the smart load power constraint in equation (5), the power consumption equation of ES in equation (6), the SOC calculation equation in equation (7), the SOC constraint in equation (8), and the ES capacity constraint in equation (9):

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] In equations (5)-(9): Let be the active power consumption of the ES at node m at time t; Let be the reactive power consumption of node m at time t; Let be the voltage at node m at time t; The battery charging power at node m at time t; Let be the battery discharge power at node m at time t; Let η be the state of charge of the battery at node m at time t; ch For battery charging coefficient, η dis C is the battery discharge coefficient; Δt is the optimization time step; BS Battery capacity; SOC min and SOC max These are the upper and lower limits of SOC; S m,ES It refers to the ES capacity.

[0131] B. Based on minimizing total operating cost as the optimization objective, a decentralized optimization operation model is constructed that considers privacy protection, elastic nodes, and distribution network coordination.

[0132] The total operating cost includes the cost of elastic nodes and the cost of the distribution network. The decentralized optimization operation model for elastic nodes and distribution network collaboration, which considers privacy protection, requires each elastic node operator to calculate feasible cuts, optimal cuts and interactive node power and provide feasible cuts, optimal cuts and interactive node power to the distribution network operator, without providing the internal power and load shedding information of the elastic nodes.

[0133] Furthermore, the cost of elastic nodes includes load shedding costs, operating costs, and reduction costs. The objective function for elastic node costs is specifically expressed as follows:

[0134]

[0135]

[0136]

[0137]

[0138] In equations (10)-(13): C m,EN C represents the operating cost of EN at node m; m,NCL The load shedding cost of NCL at node m; For DG, the cost reduction at node m; C m,ES The cost of running ES on node m; For NCL load reduction at node m; For the power reduction of DG at node m; The battery charging power at node m at time t; c is the battery discharge power at node m at time t; com The unit cost of NCL load reduction, c DG The unit cost of DG power reduction, c ch Unit cost of charging the battery, c dis Δt represents the unit cost of battery discharge; Δt represents the optimization time step; and T represents the optimization cycle time.

[0139] The constraints of the above-mentioned elastic node cost objective function include DG constraints and EN power balance equations; wherein the DG constraints include the DG power balance equation of equation (14) and the DG capacity limit of equation (15):

[0140]

[0141]

[0142] In equations (14)-(15): Let be the active power of the DG at node m at time t; Let be the reactive power of the DG at node m at time t; Let be the maximum power of the DG at node m at time t; Let m be the capacity of the DG converter at node m;

[0143] The EN power balance equations include the active power balance equation at node m at time t (16) and the reactive power balance equation at node m at time t (17):

[0144]

[0145]

[0146] In equations (16)-(17): Let be the active power of the DG at node m at time t; Let NCL be the active power of node m at time t; Let be the active power consumption of the ES at node m at time t; Let CL be the active power consumption of node m at time t; The active power injection at node m at time t; Let be the reactive power of the DG at node m at time t; Let NCL be the reactive power of node m at time t; Let be the reactive power consumption of node m at time t; Let CL be the reactive power consumption of node m at time t; This represents the reactive power injection at node m at time t.

[0147] Furthermore, distribution network costs include distribution network operating costs, power exchange costs between the distribution network and the upstream grid, distributed generation reduction costs, and the cost of shedding traditional loads. The specific objective function for distribution network costs is as follows:

[0148] min C DN =C Grid +C DG +C LS (18)

[0149]

[0150]

[0151]

[0152] In equations (18)-(21): C DN For DN operating costs; C Grid The cost of power exchange between DN and the upstream power grid; C DG To cut costs for DG; C LS This reduces the cost of shirking traditional loads. The power purchased at time t Let be the electricity sold at time t; The active power reduction of the i-th DG at time t; For the i-th load reduction at time t; c b For the unit cost of purchasing electricity, c s For the unit cost of selling electricity, c DG The unit cost reduction of DG active power, c LS Δt is the unit cost of load reduction; Δt is the optimization time step; T is the optimization cycle; Ω is the node set.

[0153] The constraints that the distribution network cost objective function needs to satisfy include power flow equation constraints, DG constraints, load shedding constraints, SVC constraints, and safe operation constraints; among which, power flow equation constraints include the linearized Distflow power flow equation model of equations (22)-(26) and the active power exchange of the slack node in equation (27):

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160] In equations (22)-(27): Let be the active power of branch ij at time t; Inject active power into node j at time t; Let be the active power of branch jk at time t; Let be the reactive power of branch ij at time t; Inject reactive power into node j at time t; Let be the reactive power of branch jk at time t; u(j) be the set of nodes ending at node j; v(j) be the set of nodes starting at node j. Inject active power into the DG of node j at time t; Let be the load active power of node j at time t; The active power reduction of the load at node j at time t; For the SVC reactive power injection at node j at time t; Inject reactive power into the DG of node j at time t; Let be the reactive power of the load at node j at time t; The reactive power reduction of the load at node j at time t; Let be the voltage at node j at time t; Let r be the voltage at node i at time t; ij x is the resistance of branch ij; ij V is the reactance of branch ij; N This refers to the rated node voltage of the distribution network. Let be the active power of the balancing node at time t; Let t be the power purchased by the distribution network from the upper-level power grid at time t; The power sold to the upper-level power grid at time t;

[0161] DG constraints include the DG active power equation in equation (28) and the DG capacity constraint in equation (29); load reduction constraints include the load reduction expressed in equation (30) being less than the load at that node and equation (31) ensuring that the power factor of the load is constant; SVC constraints include the SVC reactive power constraint in equation (32).

[0162]

[0163]

[0164]

[0165]

[0166]

[0167] In equations (28)-(32): Inject active power into the DG of node j at time t; Let be the active power reduced by the DG at node j at time t; Let be the maximum active power output of the DG at node j at time t; The square of the active power injected into the DG at node j at time t; S is the square of the reactive power injected into the DG at node j at time t; j,DG Let be the DG converter capacity of node j; The active power reduction of the load at node j at time t; Let be the load active power of node j at time t; The reactive power reduction of node j at time t; p fj The load power factor; Let be the SVC reactive power of node j at time t; The lower limit of the SVC reactive power at node j. This represents the upper limit of the SVC reactive power of node j;

[0168] Safe operation constraints:

[0169]

[0170]

[0171] In equations (33)-(34): Let V be the node voltage of node i at time t. min The lower limit of the node voltage, V max This represents the upper limit of the node voltage; Let be the active power of branch ij at time t; S represents the reactive power of branch ij at time t; ij Let be the capacity of branch ij.

[0172] C. Solve the distributed optimization operation model in step B using the improved generalized Benders decomposition method.

[0173] The improved generalized Benders decomposition method for solving the distributed optimization operation model in step B is to divide the distributed optimization operation model in step B into a main problem for distribution network operators and a sub-problem for resilient node operators. The main problem obtains the distribution network load shedding, reactive power of distributed sources in inelastic nodes, and output of static var compensators by solving the distribution network cost objective function. The sub-problem obtains the charging and discharging power of the electric springs at the resilient nodes, the active power reduced by the electric springs, and the reactive power generated by the electric springs by solving the resilient node cost objective function.

[0174] The steps for solving the distributed optimization model in step B using the improved generalized Benders decomposition method are as follows:

[0175] C1. For the distribution network, the main problem is solved according to the main problem algorithm model of formula (54)-formula (57), and the obtained boundary variables are returned to each elastic node operator;

[0176] C2. Calculate the state variables based on the results of step C1. For the elastic node operator, perform linear approximation processing on the sub-problem according to formula (44)-formula (47).

[0177] C3. Solve the subproblem to determine its feasibility. If it is feasible, return the optimal cut to the main problem according to formula (48); otherwise, return the feasible cut to the subproblem according to formula (49)-formula (53).

[0178] C4. Repeat steps C1-C3 until the objective function of the main problem yields the same solution twice in a row, thus obtaining the optimal objective and the optimal value, and then stop the iteration.

[0179] The compact form of the distributed optimization operation model in step C is as follows:

[0180]

[0181] st f1(x)≤0 (36)

[0182] f2(y m )≤0 (37)

[0183] g1(y m )=0 (38)

[0184] g2(x,y m )=0 (39)

[0185] in

[0186]

[0187]

[0188] x is the set of variables in DN; y m The set of variables for EN; a and b m x and y in the objective function are respectively m The coefficients; Π is the set of elastic nodes; Equation (35) represents the objective function of total operating cost, a T x and Equation (18) and (10) are compact forms of objective functions respectively; Equation (36) is a compact form of Equation (22)-(34); Equation (37) is a compact form of (4), (8), (9) and (15); Equation (38) is a compact form of Equation (1)-(3), (5)-(7) and (14); Equation (39) is a compact form of Equation (16) and (17);

[0189] The algorithm model for the sub-problem is as follows:

[0190] SP:

[0191] st f2(y m )≤0 (41)

[0192] g1(y m )=0 (42)

[0193] g2(x (k) ,y m )=0 (43)

[0194] Based on the scheduling variable in the (k-1)th iteration and the fixed variables in the k-th iteration State variables and It can be obtained by solving equations (1), (2), (3), and (4); the scheduling variables and calculated state variables in the (k-1)th iteration can be used It means that g1(y) m ) and g2(x,y m ) for around x (k) and Linearization result obtained using the first-order Taylor formula:

[0195]

[0196]

[0197] exist and Based on this, equations (42) and (43) are approximately expressed as equations (46) and (47), respectively:

[0198] g1'(y m )=0 (46)

[0199] g2'(x (k) ,y m )=0 (47)

[0200] Where g1' and g2' are approximate forms of g1 and g2, respectively; x (k) Let x be the value of the variable x in the k-th iteration;

[0201] If the subproblem is feasible, the optimal solution is expressed as: The optimal cut can be expressed as:

[0202]

[0203] If the subproblem is infeasible, then a feasibility problem is conceived to generate feasible cuts, i.e.,

[0204]

[0205] st f2(y m )≤0 (50)

[0206] g1'(y m )=0 (51)

[0207]

[0208] The generated feasible cut is represented as:

[0209]

[0210] Based on the optimal or feasible cuts obtained from the subproblems, the algorithm model for the main problem can be represented as follows:

[0211]

[0212] stf1(x)≤0 (55)

[0213]

[0214]

[0215] Among them O m,SP and O m,FP These are auxiliary variables for generating the optimal cut and the feasible cut, respectively; and These are slack variables; and These are the Lagrange multipliers of equations (47) and (52) in the optimization problems of optimal cut and feasible cut, respectively.

[0216] Example

[0217] To better illustrate the advantages of the technical solution of this invention, this embodiment adopts an improved 33-node AC distribution network system, the distribution network topology of which is as follows: Figure 4 As shown in Table 1, this distribution network includes three wind turbines, three photovoltaic units, and seven electric springs. Relevant parameters are shown in Table 1. ZIP load parameters for critical loads (CL), non-critical loads (NL), and other loads (OL) are shown in Table 2.

[0218] In equations (5)-(9): Let be the active power consumption of the ES at node m at time t; Let be the reactive power consumption of node m at time t; Let be the voltage at node m at time t; The battery charging power at node m at time t; Let be the battery discharge power at node m at time t; Let η be the state of charge of the battery at node m at time t; ch For battery charging coefficient, η dis C is the battery discharge coefficient; Δt is the optimization time step; BS Battery capacity; SOC min and SOC max These are the upper and lower limits of SOC; S m,ES It refers to the ES capacity.

[0219] Table 1 Technical parameters of wind turbines, photovoltaic units, and electric springs

[0220]

[0221]

[0222] Table 2 ZIP Load Parameters for NL, CL, and OL

[0223] NL 1.81 -2.31 1.5 5.55 -11.96 7.41 CL 0.27 0.04 0.69 1.43 -2.24 1.82 OL 0.21 0.24 0.55 0.54 -0.09 0.55

[0224] The following three scenarios will be used for comparative analysis:

[0225] Scenario 1: The test system has no electric spring configuration and the reactive power regulation of DG is not considered;

[0226] Scenario 2: The test system considers the reactive power regulation of DG, without the configuration of a power spring;

[0227] Scenario 3: The test system considers the configuration of DG reactive power regulation and electric springs.

[0228] The optimized results of the distribution network operation cost and resilient node operation cost under different scenarios are shown in Table 3.

[0229] Table 3 Data on distribution networks and resilient nodes under different scenarios

[0230]

[0231] As shown in Table 3, compared to Scenario 1, Scenario 2 reduces distribution network operating costs by 892,700 yuan and resilient node operating costs by 90,000 yuan; compared to Scenario 2, Scenario 3 reduces distribution network operating costs by 3,251,100 yuan and resilient node operating costs by 86,700 yuan. Therefore, considering the reactive power regulation capability of distributed generation (DG) and the configuration of power springs can effectively improve the economic efficiency of distribution network operation.

[0232] By solving the distribution network optimization operation model using both the centralized optimization algorithm and the method proposed in this patent, we can obtain Table 4 and... Figure 5 The results are shown in Table 4. As can be seen, although the computation time required by the distributed optimization strategy proposed in this patent may be slightly higher than that of the centralized optimization method, the proposed method enhances the data privacy of individual decision-makers and reduces the communication burden. For a comparison of the number of iterations in the two algorithms, please refer to [link to relevant documentation]. Figure 5 .from Figure 5 As can be seen, the distributed optimization strategy proposed in this patent converges faster than the centralized optimization algorithm.

[0233] Table 4 Comparison of the method proposed in this patent with centralized optimization algorithms

[0234] Centralized optimization algorithm 35.6 3682.47 The method proposed in this patent 124.7 3680.26

[0235] The above embodiments are merely illustrative of the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solutions based on the technical concept proposed in this invention shall fall within the scope of protection of this invention. Technologies not covered in this invention can be implemented using existing technologies.

Claims

1. A distributed optimization operation strategy for resilient nodes and distribution networks that considers privacy protection, characterized in that: The steps of this distributed optimization operation strategy, which connects an electric spring in series with a non-critical load in the distribution network to form a smart load, are as follows: A. Determine the power regulation model of the elastic node based on the structure and control method of the electric spring; B. Based on minimizing total operating cost as the optimization objective, a decentralized optimization operation model considering privacy protection and distribution network coordination is constructed. C. Solve the distributed optimization operation model in step B using the improved generalized Benders decomposition method; The flexible node power regulation model in step A includes a non-critical load constraint model and a power spring constraint model. The non-critical load constraint model includes the NCL power equation of equation (1), the ZIP load model of NCL active power of equation (2), the ZIP load model of NCL reactive power of equation (3), and the NCL voltage limit of equation (4). （1） （2） （3） （4） In equations (1)-(4): for time The NCL active power of the node; for time NCL reactive power of the node; for time NCL voltage at the node; for time NCL injection current at the node; for time The rated active power of the node's NCL; for time The rated reactive power of the node's NCL; ZIP factor for NCL active power; ZIP factor for NCL reactive power; and These are the upper and lower limits of the NCL voltage value; The power spring constraint model includes the smart load power constraint in equation (5), the power consumption equation of ES in equation (6), the SOC calculation equation in equation (7), the SOC constraint in equation (8), and the ES capacity constraint in equation (9): （5） （6） （7） （8） （9） In equations (5)-(9): for time The active power consumption of the node's ES; for time The reactive power consumption of the node's ES; for time The voltage at the node; for time The battery charging power of the node; for time The battery discharge power of the node; for time The state of charge of the node's battery; For battery charging coefficient, This refers to the battery discharge coefficient. To optimize the time step; Battery capacity; and These are the upper and lower limits of SOC; It is the ES capacity; The total operating cost in step B includes the cost of the elastic node and the cost of the distribution network. The decentralized optimization operation model that considers privacy protection for the collaboration between the elastic node and the distribution network requires each elastic node operator to calculate the feasible cut, the optimal cut, and the power of the interactive node and provide the feasible cut, the optimal cut, and the power of the interactive node to the distribution network operator, and does not need to provide the internal power and load shedding information of the elastic node. The cost of the elastic node includes load shedding cost, operating cost, and reduction cost. The objective function for the elastic node cost is specifically expressed as follows: （10） （11） （12） （13） In equations (10)-(13): For EN in The operating cost of a node; For NCL in The cost of load shedding at nodes; For DG in Cost reduction for nodes; For ES in The operating cost of a node; For NCL in Node load reduction; For DG in Node power reduction; for time The battery charging power of the node; for time The battery discharge power of the node; Unit cost reduction for NCL load For DG power reduction unit cost, Unit cost of charging batteries The unit cost of battery discharge; To optimize the time step; To optimize the operating cycle.

2. The privacy-protected resilient node and distributed network optimization operation strategy according to claim 1, characterized in that: The constraints of the elastic node cost objective function include DG constraints and EN power balance equations; wherein the DG constraints include the DG power balance equation of equation (14) and the DG capacity limit of equation (15): （14） （15） In equations (14)-(15): for time The active power of the DG at the node; for time The reactive power of the node's DG; for time Maximum DG power of the node; for The capacity of the DG converter at the node; The EN power balance equation includes equation (16). time The active power balance equation of the node, equation (17) time Nodal reactive power balance equation: （16） （17） In equations (16)-(17): for time The active power of the DG at the node; for time The NCL active power of the node; for time The active power consumption of the node's ES; for time CL active power consumption of the node; for time Active power injection at nodes; for time The reactive power of the node's DG; for time NCL reactive power of the node; for time The reactive power consumption of the node's ES; for time CL reactive power consumption of the node; for time Reactive power injection at nodes.

3. The privacy-protected resilient node and distributed network optimization operation strategy according to claim 1, characterized in that: The aforementioned distribution network cost includes distribution network operation cost, power exchange cost between the distribution network and the upstream power grid, distributed generation reduction cost, and cost of minimizing traditional load shedding. The specific objective function for distribution network cost is as follows: （18） （19） （20） （21） In equations (18)-(21): For DN operating costs; This refers to the cost of power exchange between the DN and the upstream power grid. To cut costs for DG; This reduces the cost of shirking traditional loads. for Power purchase capacity at any time for Electricity sales capacity at any given time; for Time of the first The active power of each DG is reduced; for Time of the first One load reduction; For the unit cost of purchasing electricity, For the unit cost of selling electricity, The unit cost reduction for DG active power The unit cost of load reduction; To optimize the time step; To optimize the operating cycle; It is a set of nodes.

4. The privacy-protected resilient node and distributed network optimization operation strategy according to claim 3, characterized in that: The constraints that the distribution network cost objective function needs to satisfy include power flow equation constraints, DG constraints, load shedding constraints, SVC constraints, and safe operation constraints; among which, the power flow equation constraints include the linearized Distflow power flow equation model of equations (22)-(26) and the active power exchange of the slack node in equation (27): （22） （23） （24） （25） （26） （27） In equations (22)-(27): for Time Branch The active power; for Time Node Injecting active power; for Time Branch The active power; for Time Branch reactive power; for Time Node Inject reactive power; for Time Branch reactive power; For nodes The set of terminal nodes; For the node The set of nodes at the beginning; for Time Node The active power injected by the DG; for Time Node The active power of the load; for Time Node The load reduces active power; for Time Node SVC reactive power injection; for Time Node DG injected reactive power; for Time Node The reactive power of the load; for Time Node Reduce reactive power from the load; for Time Node Voltage; for Time Node Voltage; branch road The resistance; branch road The reactance; This refers to the rated node voltage of the distribution network. for Constantly balance the active power of nodes; for The power purchased by the distribution network from the upper-level power grid at all times; for It continuously sells power to the upstream power grid; DG constraints include the DG active power equation in equation (28) and the DG capacity constraint in equation (29); load reduction constraints include the load reduction expressed in equation (30) being less than the load at that node and equation (31) ensuring that the power factor of the load is constant; SVC constraints include the SVC reactive power constraint in equation (32). （28） （29） （30） （31） （32） In equations (28)-(32): for Time Node The active power injected by the DG; for Time Node The active power reduced by DG; for Time Node The maximum active power output of the DG; for Time Node The square of the active power injected by the DG; for Time Node The square of the reactive power injected by DG; For nodes The capacity of the DG converter; for Time Node The load reduces active power; for Time Node The active power of the load; for Time Node Reduce reactive power from the load; The load power factor; for Time Node SVC reactive power; For nodes The lower limit of SVC reactive power For nodes The upper limit of SVC reactive power; Safe operation constraints: （33） （34） In equations (33)-(34): for time Node voltage, The lower limit of the node voltage. This represents the upper limit of the node voltage; for Time Branch The active power; for Time Branch reactive power; branch road The capacity.

5. The privacy-protected resilient node and distributed network optimization operation strategy according to claim 1, characterized in that: The improved generalized Benders decomposition method in step C for solving the distributed optimization operation model in step B divides the distributed optimization operation model in step B into a main problem for distribution network operators and a sub-problem for resilient node operators. The main problem obtains the distribution network load shedding, reactive power of distributed sources in inelastic nodes, and output of static var compensators by solving the distribution network cost objective function. The sub-problem obtains the charging and discharging power of the electric springs at the resilient nodes, the active power reduced by the electric springs, and the reactive power generated by the electric springs by solving the resilient node cost objective function.

6. The privacy-protected resilient node and distributed network optimization operation strategy according to claim 5, characterized in that: The compact form of the distributed optimization operation model in step C is as follows: （35） s.t. (36) （37） （38） （39） in For the set of variables of DN; y m The set of variables for EN; a and b m x and y in the objective function are respectively m The coefficient; It is a set of elastic nodes; Equation (35) represents the objective function for total operating cost. and Equation (36) is the compact form of the distribution network cost objective function and the flexible node cost objective function under the total operating cost objective function, respectively; Equation (37) is the compact form of the distribution network cost objective function constraint; Equation (38) is the compact form of the NCL voltage limit, SOC constraint, ES capacity constraint and DG capacity limit in the flexible node power regulation model; Equation (39) is the compact form of the NCL power equation, the ZIP load model of NCL active power, the ZIP load model of NCL reactive power, the smart load power constraint, the power consumption equation of ES, the SOC calculation equation and DG power balance equation in the flexible node cost objective function constraint; Equation (39) is the compact form of the EN power balance equation in the flexible node cost objective function constraint. The algorithm model for the sub-problem is as follows: SP: (40) s.t. (41) （42） （43） Based on the scheduling variable in the (k-1)th iteration , and the fixed variable in the k-th iteration State variables , , and It can be obtained by solving the non-critical load constraint model in the resilient node power regulation model; the scheduling variables and calculated state variables in the (k-1)th iteration can be used express, and To surround and Linearization result obtained using the first-order Taylor formula: （44） （45） exist and Based on the condition that = 0, equations (42) and (43) are approximately expressed as equations (46) and (47), respectively: （46） （47） in and They are and Approximate form of x; (k) Let x be the value of the variable x in the k-th iteration; If the subproblem is feasible, the optimal solution is represented as y(k)m, and the optimal cut can be represented as: （48） If the subproblem is infeasible, then a feasibility problem is conceived to generate feasible cuts, i.e., （49） s.t. (50) （51） （52） The generated feasible cut is represented as: （53） Based on the optimal or feasible cuts obtained from the subproblems, the algorithm model for the main problem can be represented as follows: （54） s.t. (55) （56） （57） in and These are auxiliary variables for generating the optimal cut and the feasible cut, respectively; and These are slack variables; and These are the Lagrange multipliers of equations (47) and (52) in the optimization problems of optimal cut and feasible cut, respectively.

7. The privacy-protected resilient node and distributed network optimization operation strategy according to claim 6, characterized in that: The steps in step C for solving the distributed optimization model in step B using the improved generalized Benders decomposition method are as follows: C1. For the distribution network, the main problem is solved according to formula (54)-formula (57), and the obtained boundary variables are returned to each elastic node operator. C2. Calculate the state variables based on the results of step C1. For the elastic node operator, perform linear approximation processing on the sub-problems according to formula (44)-formula (47). C3. Solve the subproblem to determine its feasibility. If it is feasible, return the optimal cut to the main problem according to formula (48); otherwise, return the feasible cut to the subproblem according to formula (49)-formula (53). C4. Repeat steps C1-C3 until the objective function of the main problem yields the same solution twice in a row, then obtain the optimal objective and the optimal solution, and stop the iteration.

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