Two-layer coordinated reactive power control strategy for power systems considering source and load uncertainties

Abstract

The present invention relates to a double-layer collaborative reactive control strategy for a power system considering source-load uncertainty, which comprises the following steps: step S1: establishing a distribution network reactive optimization model; step S2: clustering distributed photovoltaic output and load historical data and constructing a probability distribution uncertainty set of a typical scenario; step S3: adopting a distributed blue-rod optimization method to establish a two-stage distributed blue-rod reactive optimization model for a distribution network; step S4: solving the two-stage distributed blue-rod reactive optimization model for each region using a column and constraint generation (column-and-constraint generation, C&CG) algorithm; step S5: constructing a distributed reactive optimization solution framework for a distribution network; step S6: adopting an adaptive super-relaxation penalty parameter alternating direction multiplier method (alternating direction method of multipliers, ADMM) to carry out global coordinated update solution. The present invention can significantly reduce electric energy loss and improve the economy and stability of the power system.

Description

Technical Field

[0001] The present invention relates to the field of reactive power optimization control of power systems, and in particular to a double-layer coordinated reactive power control strategy for power systems that takes source and load uncertainties into consideration. Background Art

[0002] With the widespread deployment of distributed resources such as photovoltaic power generation, wind power and energy storage facilities, the complexity and uncertainty of the system have increased significantly. The access of these distributed resources not only changes the operation mode of the power grid, but also poses new challenges to the stability, security and economy of the power system. Especially in terms of reactive power control, traditional centralized optimization strategies lack sufficient flexibility and adaptability, making it difficult to effectively cope with the high uncertainty and dynamic changes of sources (such as photovoltaic and wind power output) and loads, which directly affects the reliability and power quality of the power grid. In addition, due to the volatility and intermittent nature of the output of distributed resources, the load demand of the power grid at different times and under different conditions is complex and changeable. Traditional methods often simplify models or assume stable load forecasts for design, which often leads to inaccurate or inefficient control strategies when faced with actual operating conditions.

[0003] Therefore, developing a reactive power optimization method that can respond to and accurately handle large-scale distributed resources and load fluctuations in real time has become an important topic in power system research.

[0004] This method should be able to comprehensively consider the actual operating status, resource distribution and load change characteristics of the power grid, and achieve real-time, dynamic and precise control of the grid's reactive power through advanced mathematical models and algorithms, thereby improving the economic operation efficiency and system safety and stability of the power grid. Summary of the Invention

[0005] In order to overcome the shortcomings of the existing technology, the purpose of the present invention is to provide a two-layer collaborative reactive power control strategy for the power system that takes into account the uncertainty of sources and loads, which can effectively improve the stability and economy of the power system, especially when large-scale distributed resources are widely accessed.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A two-layer coordinated reactive power control strategy for a power system considering source and load uncertainty is characterized by comprising the following steps:

[0008] Step S1: Establish a distribution network reactive power optimization model. The model aims to reduce the total loss of the distribution network and includes distributed photovoltaic output constraints, energy storage system (ESS) model constraints, distribution network power flow constraints, on-load tap changer (OLTC) model constraints, capacitor bank (CB) model constraints, and static var compensator (SVC) model constraints.

[0009] Step S2: Use the K-means clustering algorithm to cluster the historical data into scenarios, and construct a probability uncertainty set based on the KL divergence;

[0010] Step S3: adopt the distributed blue rod optimization method to establish a two-stage distributed blue rod reactive power optimization model for the distribution network;

[0011] Step S4: using the column-and-constraint generation (C&CG) algorithm to solve the two-stage distributed blue reactive power optimization model for each region;

[0012] Step S5: Building a distributed reactive power optimization solution framework for the distribution network based on the alternating direction method of multipliers (ADMM) on the basis of the distributed reactive power optimization model of the distribution network;

[0013] Step S6: Adopt the adaptive over-relaxation penalty parameter ADMM algorithm to perform global coordinated update solution.

[0014] In step S1, the distribution network reactive power optimization objective function F is established as:

[0015]

[0016] Where: I ij,t is the current value on the distribution network line ij during period t; r ij is the resistance value of the distribution network line ij; T is the total number of time periods for the reactive power optimization operation of the distribution network; Ω L is the set of load nodes in the distribution network.

[0017] The constraints of the objective function are:

[0018] (1) Distributed photovoltaic output constraints:

[0019]

[0020] Where: and are the active and reactive outputs of distributed photovoltaic at node j in period t, is the upper limit of distributed photovoltaic active output at node j in period t, is the capacity of distributed photovoltaic at node j;

[0021] (2) ESS model constraints:

[0022]

[0023]

[0024] Where: and They represent the charging and discharging status of the ESS at node j in period t, and are both 0-1 variables. and are the active power of node j at time period t when the distribution network charges the ESS and when the ESS discharges the distribution network, and are the maximum and minimum active power when the distribution network at node j charges the ESS, and are the maximum and minimum active power when ESS at node j discharges to the distribution network, B j,t is the state of charge of the ESS at node j in time period t, and are the charging rate and discharging rate of ESS at node j, △t is the optimized operation time interval, is the capacity of ESS at node j, and are the maximum and minimum charges of ESS at node j respectively;

[0025] (3) Distribution network flow constraints:

[0026]

[0027] Where: P j,t and Q j,t are the active and reactive injection powers at node j in period t, P ij,t and Q ij,t are the active power and reactive power flowing from node i into distribution network line ij during period t, respectively, x ij is the reactance value of the distribution network line ij, and are the active and reactive power required for the normal operation of the load at node j in period t, V i,t is the square of the voltage amplitude at node i during time period t, V i max and Vi min V i,t The maximum and minimum values ​​of l ij,t is the square of the current amplitude on the distribution network line ij during time period t, is the square of the maximum current the line can withstand, and are the active and reactive power of the distribution gateway respectively, is the reactive power compensated by CB to the distribution network at node j in period t, is the reactive power compensated by SVC to the distribution network at node j in period t, and They are the maximum and minimum active power of the power distribution gateway port, and They are the maximum and minimum reactive power values ​​of the power distribution network gateway respectively;

[0028] (4) OLTC model constraints: By introducing an auxiliary node o, the OLTC branch of the distribution network is decomposed into two parts, io and oj. The OLTC operation constraints are obtained as follows:

[0029] V o,t =V i,t -2(r ij P ij,t +x ij Q ij,t )+[(r ij ) 2 +(x ij ) 2 ]l ij,t (13)

[0030]

[0031] Where: V o,t is the square of the voltage value at the auxiliary node o during time period t; ij,n,t It is a binary auxiliary variable used to convert the transformer gear into a binary number. ij,t is the gear position of OLTC on distribution network line ij during time period t, K ij is the number of OLTC gears on the distribution network line ij, △k ij is the transformation ratio increment of each gear of OLTC on the distribution network line ij, is the minimum value of the OLTC ratio on the distribution network line ij, M is a sufficiently large number, m ij,t 、x ij,n,t and y ij,n,t Intermediate variables introduced for linearization of OLTC operation constraints;

[0032] (5) CB model constraints:

[0033]

[0034] Where: is the number of CB switching groups at node j in time period t, is the CB unit reactive compensation power at node j, and are the number of switching groups added and reduced at node j in period t, C CB,max N is the upper limit of the number of times CB can act within a complete optimization period T, CB,max The maximum number of switching groups of CB;

[0035] (6) SVC model constraints:

[0036]

[0037] Where: and are the maximum and minimum values ​​of the SVC reactive compensation power at node j, respectively.

[0038] In step S2, the K-means algorithm is used to cluster the distributed photovoltaic output and load historical data collected for Z days to obtain N s Typical scenario curves of distributed photovoltaic output and load and initial scenario probability distribution p 0 .

[0039] The uncertainty set Ω is constructed based on the KL divergence for the typical scenario of distributed photovoltaic output and load. n :

[0040]

[0041] Where: p s is the probability under the typical scenario s; is the initial probability of the typical scene s obtained by clustering; ζ represents the difference between the probability distribution of the typical scene p and the initial probability distribution of the typical scene p 0 The smaller the KL divergence value between them, the more similar the two distributions are, and the closer they are to the optimal solution of the traditional random optimization model.

[0042] In step S3, the discrete variables OLTC gear position, CB switching group number, and ESS charging and discharging operation status are used as the first-stage decision variables x of distributed blue-rod optimization, and other continuous variables are used as the second-stage decision variables y. A two-stage distributed blue-rod reactive power optimization model in vector form is established as follows:

[0043]

[0044] stAx≥b,x∈{0,1} (21)

[0045]

[0046] In the formula: a, A, b, J, R, w, E, f, Q, q, c, d, G, u s is the corresponding coefficient matrix in the reactive power optimization model constraint conditions; Equation (20) is the objective function of the distribution network reactive power optimization model: Equation (1); Equation (21) is the constraint related to the decision variables of the first stage: Equation (4), Equation (14), Equation (17); The first constraint of Equation (22) is the coupling constraint of the decision variables of the first and second stages: Equation (5), Equation (15)-(16); The second constraint of Equation (22) is the constraint of the decision variables of the second stage: Equation (6)-(8), Equation (11)-(13), Equation (18); The third constraint of Equation (22) is the second-order cone constraint: Equation (3), Equation (10); The fourth constraint of Equation (22) is the power balance constraint of distributed photovoltaic output and node load: Equation (2), Equation (9); Ω x is the set of decision variables in the first stage; Ω y is the set of decision variables in the second stage.

[0047] In step S4, the distributed robust reactive power optimization problem of the distribution network is divided into a master problem (MP) and a subproblem (SP) for iterative solution using the C&CG algorithm. When the optimal solution of the MP and SP is less than a given convergence error ε, the algorithm converges and outputs the optimal solution.

[0048] (1) MP is optimized and solved under the drive of the initial scene probability obtained by scene clustering, providing the value of the first-stage decision variable x for SP * and provides a lower bound L for the two-stage distributed blue stick reactive power optimization model B MP is:

[0049]

[0050] stAx≥b,x∈{0,1} (26)

[0051]

[0052] Where: subscript m is the number of iterations of the C&CG algorithm.

[0053] (2) SP is the first-stage decision variable x provided by MP * Find the worst scenario probability distribution And provide an upper bound U for the two-stage distributed blue stick reactive power optimization model B The SP is:

[0054]

[0055] Where: h s Represents the decision variable y under scenario s s,m The minimum cost after conversion is h for all scenes s. s The maximum value after summation.

[0056] In step S5, a distributed reactive power optimization solution framework for the distribution network is constructed based on the ADMM algorithm on the basis of the distributed reactive power optimization model of the distribution network. The distributed reactive power optimization solution framework for the distribution network is established as follows:

[0057]

[0058] stAx a ≥b,x a ∈{0,1} (33)

[0059]

[0060] Where: x a is the decision variable of the first stage of the robust reactive power optimization of the distribution network in area a; a,s is the decision variable of the second stage of the distributed reactive power optimization of the distribution network under scenario s in area a; a,s is the probability value of scene s in area a; u a,s is the constraint value of the uncertainty variable under scenario s in area a; Y a,s,ij Y is the coupling branch variable of the distribution network coupling line ij under scenario s in area a; b,s,ij is the coupling branch variable of the distribution network coupling line ij in scenario s in area b adjacent to area a.

[0061] In step S6, the adaptive over-relaxation penalty parameter ADMM algorithm is used to solve the following steps:

[0062] (1) Initialization. Set the number of iterations of the outer layer distributed reactive power optimization k = 0; the global variables of the coupling branch Dual variables of coupled branches Coupling branch variables Given the initial penalty parameter ρ for each region 0 The value of and convergence accuracy κ = 10 -4 The upper bound of the inner layer blue stick reactive power optimization U B =+∞, lower bound L B = -∞, number of iterations m = 1, convergence error ε = 10 -6 .

[0063] (2) Solve the reactive power optimization model of each region. Establish the augmented Lagrangian objective function of each region as follows:

[0064]

[0065] Y a,s ={U a,s,i ,U a,s,j ,P a,s,ij ,Q a,s,ij ,I a,s,ij} (36)

[0066] Where: is the vector of penalty parameters related to each coupling branch in region a at the kth iteration; for The square of the weighted norm, that is

[0067]

[0068] (3) Inter-region information exchange and update. Each region exchanges coupling variable information through the coupling branch and updates the global variables of each region using equations (38)-(39). and dual variables Right now

[0069]

[0070] Where: is the penalty parameter value related to the coupling branch ij in region a at the kth iteration; is the auxiliary penalty parameter value related to the coupling branch ij in region a at the kth iteration, which is used to make Updated in super slack.

[0071] (4) Algorithm convergence judgment. The present invention constructs the convergence criterion based on the original residual and dual residual of the ADMM algorithm as follows:

[0072]

[0073] Where: is the original residual of region a under scene s at the kth iteration; is the dual residual of region a in scene s at the kth iteration. k ≤10 -4 When , the algorithm converges and outputs the optimal control strategy for distributed reactive power of the distribution network; otherwise, continue with step (5).

[0074] (5) Variable update and return: Update the values ​​of the penalty parameter and the auxiliary penalty parameter according to equations (43)-(44), update k=k+1, and return to step (2).

[0075]

[0076] Where: η and μ2 are the adaptive adjustment coefficients of the penalty parameter and the auxiliary penalty parameter respectively; γ and μ1 are the update criterion coefficients of the penalty parameter and the auxiliary penalty parameter respectively.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] 1. This paper provides a two-stage distributed robust reactive power optimization model for distribution networks. This model considers fluctuations in distributed photovoltaic output and load by constructing a probabilistic uncertainty set based on KL divergence. This not only optimizes the conservatism of the solution but also enhances its reliability. This approach can more effectively handle uncertainties in actual operation and improve the system's adaptability to uncertainties.

[0079] 2. This invention provides a two-layer collaborative reactive power control strategy. The outer layer uses the ADMM algorithm with an adaptive over-relaxation penalty parameter for global update iterative solution, while the inner layer uses the C&CG algorithm to solve the distributed robust reactive power optimization model for each region. This layered solution strategy significantly improves computational efficiency. It also optimizes the solution quality through refined regional control, reduces network losses, and improves the economy and stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 It is a schematic diagram of the steps of the present invention;

[0081] Figure 2 It is an improved 69-node case system;

[0082] Figure 3 It is a typical scenario curve;

[0083] Figure 4 is the objective function convergence curve;

[0084] Figure 5 is the error convergence curve. DETAILED DESCRIPTION

[0085] The technical solutions of the present invention will be more clearly and completely explained below through description of preferred embodiments of the present invention in conjunction with the accompanying drawings.

[0086] like Figure 1 As shown, the present invention is:

[0087] Step S1: Establish a distribution network reactive power optimization model. The model aims to reduce the total loss of the distribution network and includes distributed photovoltaic output constraints, energy storage system (ESS) model constraints, distribution network power flow constraints, on-load tap changer (OLTC) model constraints, capacitor bank (CB) model constraints, and static var compensator (SVC) model constraints.

[0088] Step S2: Use the K-means clustering algorithm to cluster the historical data into scenarios, and construct a probability uncertainty set based on the KL divergence;

[0089] Step S3: adopt the distributed blue rod optimization method to establish a two-stage distributed blue rod reactive power optimization model for the distribution network;

[0090] Step S4: using the column-and-constraint generation (C&CG) algorithm to solve the two-stage distributed blue reactive power optimization model for each region;

[0091] Step S5: Building a distributed reactive power optimization solution framework for the distribution network based on the alternating direction method of multipliers (ADMM) on the basis of the distributed reactive power optimization model of the distribution network;

[0092] Step S6: Adopt the adaptive over-relaxation penalty parameter ADMM algorithm to perform global coordinated update solution.

[0093] During operation of the present invention, step S1: establishing a basic model for reactive power optimization of the distribution network is the basis for all subsequent optimization steps.

[0094] Step S2: Data processing is to process the input data and construct the probability model for the model established in step S1, providing necessary data support and probability framework for subsequent optimization.

[0095] Step S3: Based on the results of step S2, the reactive power optimization model is further developed using a distributed robust optimization method. Here, "distributed robust optimization" is an optimization method that can take input uncertainty into account, and is used to enhance the robustness of the system in the face of uncertainty.

[0096] Step S4: The column and constraint generation algorithm is used to solve the model developed in step S3, which solves the problems caused by the theoretical model and data processing constructed in the first three steps.

[0097] Step S5: Based on the distributed reactive power optimization model, the alternating direction multiplier method (ADMM) is used to establish a distributed reactive power optimization solution framework for the distribution network. This step further enhances the algorithm's distributed processing capabilities in the system optimization solution, making the optimization solution more efficient and practical.

[0098] Step S6: The final stage of the optimization calculation, used to fine-tune and optimize the results of step S5 to ensure the achievement of the global optimal solution and the stability of the system.

[0099] The details are as follows:

[0100] The present invention provides a distribution network reactive power optimization model, and establishes a distribution network reactive power optimization objective function F as follows:

[0101]

[0102] Where: I ij,t is the current value on the distribution network line ij during period t; r ij is the resistance value of the distribution network line ij; T is the total number of time periods for the reactive power optimization operation of the distribution network; Ω L is the set of load nodes in the distribution network.

[0103] The constraints of the objective function are:

[0104] (1) Distributed photovoltaic output constraints:

[0105]

[0106] Where: and are the active and reactive outputs of distributed photovoltaic at node j in period t, is the upper limit of distributed photovoltaic active output at node j in period t, is the capacity of distributed photovoltaic at node j;

[0107] (2) ESS model constraints:

[0108]

[0109]

[0110] Where: and They represent the charging and discharging status of the ESS at node j in period t, and are both 0-1 variables. and are the active power of node j at time period t when the distribution network charges the ESS and when the ESS discharges the distribution network, and are the maximum and minimum active power when the distribution network at node j charges the ESS, and are the maximum and minimum active power when ESS at node j discharges to the distribution network, B j,t is the state of charge of the ESS at node j in time period t, and are the charging rate and discharging rate of ESS at node j, △t is the optimized operation time interval, is the capacity of ESS at node j, and are the maximum and minimum charges of ESS at node j respectively;

[0111] (3) Distribution network flow constraints:

[0112]

[0113] Where: P j,t and Q j,t are the active and reactive injection powers at node j in period t, P ij,t and Q ij,t are the active power and reactive power flowing from node i into distribution network line ij during period t, respectively, x ij is the reactance value of the distribution network line ij, and are the active and reactive power required for the normal operation of the load at node j in period t, V i,t is the square of the voltage amplitude at node i during time period t, V i max and V i min V i,t The maximum and minimum values ​​of l ij,t is the square of the current amplitude on the distribution network line ij during time period t, is the square of the maximum current the line can withstand, and are the active and reactive power of the distribution gateway respectively, is the reactive power compensated by CB to the distribution network at node j in period t, is the reactive power compensated by SVC to the distribution network at node j in period t, and They are the maximum and minimum active power of the power distribution gateway port, and They are the maximum and minimum reactive power values ​​of the power distribution network gateway respectively;

[0114] (4) OLTC model constraints: By introducing an auxiliary node o, the OLTC branch of the distribution network is decomposed into two parts, io and oj. The OLTC operation constraints are obtained as follows:

[0115] V o,t =V i,t -2(r ij P ij,t +x ij Q ij,t )+[(r ij ) 2 +(x ij ) 2 ]l ij,t (13)

[0116]

[0117] Where: V o,t is the square of the voltage value at the auxiliary node o during time period t; ij,n,t It is a binary auxiliary variable used to convert the transformer gear into a binary number. ij,t is the gear position of OLTC on distribution network line ij during time period t, K ij is the number of OLTC gears on the distribution network line ij, △k ij is the transformation ratio increment of each gear of OLTC on the distribution network line ij, is the minimum value of the OLTC ratio on the distribution network line ij, M is a sufficiently large number (i.e., large enough to ensure the validity of the constraint), m ij,t 、x ij,n,t and y ij,n,t Intermediate variables introduced for linearization of OLTC operation constraints;

[0118] (5) CB model constraints:

[0119]

[0120] Where: is the number of CB switching groups at node j in time period t, is the CB unit reactive compensation power at node j, and are the number of switching groups added and reduced at node j in period t, C CB,max N is the upper limit of the number of times CB can act within a complete optimization period T, CB,max The maximum number of switching groups of CB;

[0121] (6) SVC model constraints:

[0122]

[0123] Where: and are the maximum and minimum values ​​of the SVC reactive compensation power at node j, respectively.

[0124] The present invention uses K-means algorithm to cluster the distributed photovoltaic output and load historical data collected for Z days to obtain N s Typical scenario curves of distributed photovoltaic output and load and initial scenario probability distribution p 0 Based on KL divergence, the uncertainty set Ω is constructed for typical scenarios of distributed photovoltaic output and load. n :

[0125]

[0126] Where: p s is the probability under the typical scenario s; is the initial probability of the typical scene s obtained by clustering; ζ represents the difference between the probability distribution of the typical scene p and the initial probability distribution of the typical scene p 0 The smaller the KL divergence value between them, the more similar the two distributions are, and the closer they are to the optimal solution of the traditional random optimization model.

[0127] The present invention uses the discrete variables OLTC gear position, CB switching group number and ESS charging and discharging operation status as the first stage decision variables x of distributed blue-robin optimization, and other continuous variables as the second stage decision variables y. A two-stage distributed blue-robin reactive power optimization model in vector form is established as follows:

[0128]

[0129] stAx≥b,x∈{0,1} (21)

[0130]

[0131] In the formula: a, A, b, J, R, w, E, f, Q, q, c, d, G, u s is the corresponding coefficient matrix in the reactive power optimization model constraint conditions; Equation (20) is the objective function of the distribution network reactive power optimization model: Equation (1); Equation (21) is the constraint related to the decision variables of the first stage: Equation (4), Equation (14), Equation (17); The first constraint of Equation (22) is the coupling constraint of the decision variables of the first and second stages: Equation (5), Equation (15)-(16); The second constraint of Equation (22) is the constraint of the decision variables of the second stage: Equation (6)-(8), Equation (11)-(13), Equation (18); The third constraint of Equation (22) is the second-order cone constraint: Equation (3), Equation (10); The fourth constraint of Equation (22) is the power balance constraint of distributed photovoltaic output and node load: Equation (2), Equation (9); Ω xis the set of decision variables in the first stage; Ω y is the set of decision variables in the second stage.

[0132] and are the active and reactive outputs of distributed photovoltaic at node j in period t, P j,t and Q j,t are the active and reactive injection powers at node j in period t, P ij,t and Q ij,t are the active power and reactive power flowing from node i into distribution network line ij during period t, respectively. ij,t is the square of the current amplitude on the distribution network line ij during period t, V j,t is the square of the voltage value at auxiliary node j during time period t, and are the active and reactive power of the distribution gateway respectively, and are the active power of node j at time period t when the distribution network charges the energy storage and when the energy storage discharges to the distribution network, respectively. j,t is the state of charge of the energy storage at node j during time period t, m ij,t 、x ij,n,t and y ij,n,t The intermediate variables introduced for linearization of the operation constraints of the on-load tap-changing transformer are is the reactive power compensated to the distribution network by the capacitor bank at node j in period t, is the reactive power compensated by SVC to the distribution network at node j in time period t.

[0133] The C&CG algorithm splits the distributed reactive power optimization problem of the distribution network into a master problem (MP) and a subproblem (SP), which are then solved iteratively. The algorithm converges and outputs the optimal solution when the optimal solutions of MP and SP are less than a given convergence error, ε.

[0134] (1) MP is optimized and solved under the drive of the initial scene probability obtained by scene clustering, providing the value of the first-stage decision variable x for SP * and provides a lower bound L for the two-stage distributed blue stick reactive power optimization model B MP is:

[0135]

[0136] stAx≥b,x∈{0,1} (26)

[0137]

[0138] Where: subscript m is the number of iterations of the C&CG algorithm.

[0139] (2) SP is the first-stage decision variable x provided by MP * Find the worst scenario probability distribution And provide an upper bound U for the two-stage distributed blue stick reactive power optimization model B The SP is:

[0140]

[0141] Where: h s Represents the decision variable y under scenario s s,m The minimum cost obtained after conversion is h for all scenes s. s The maximum value after summation.

[0142] The present invention builds a distributed reactive power optimization solution framework for distribution network based on the ADMM algorithm on the basis of the distributed reactive power optimization model of distribution network, and establishes the distributed reactive power optimization solution framework for distribution network as follows:

[0143]

[0144] stAx a ≥b,x a ∈{0,1} (33)

[0145]

[0146] Where: x a is the decision variable of the first stage of the robust reactive power optimization of the distribution network in area a; a,s is the decision variable of the second stage of the distributed reactive power optimization of the distribution network under scenario s in area a; a,s is the probability value of scene s in area a; u a,s is the constraint value of the uncertainty variable under scenario s in area a; Y a,s,ij Y is the coupling branch variable of the distribution network coupling line ij under scenario s in area a; b,s,ij is the coupling branch variable of the distribution network coupling line ij in scenario s in area b adjacent to area a.

[0147] The solution framework established in step S5 is a distributed reactive power optimization solution framework based on the alternating direction method of multipliers (ADMM). The main purpose of this framework is to address reactive power optimization problems in large-scale power systems, especially in the presence of many different regions or nodes, and to optimize system performance and efficiency through distributed computing.

[0148] The solution steps using the adaptive super-relaxation penalty parameter ADMM algorithm are as follows:

[0149] (1) Initialization. Set the number of iterations of the outer layer distributed reactive power optimization k = 0; the global variables of the coupling branch Dual variables of coupled branches Coupling branch variables Given the initial penalty parameter ρ for each region 0 The value of and convergence accuracy κ = 10 -4 The upper bound of the inner layer blue stick reactive power optimization U B =+∞, lower bound L B = -∞, number of iterations m = 1, convergence error ε = 10 -6 .

[0150] (2) Solve the reactive power optimization model of each region. Establish the augmented Lagrangian objective function of each region as follows:

[0151]

[0152] Y a,s ={U a,s,i ,U a,s,j ,P a,s,ij ,Q a,s,ij ,I a,s,ij} (36)

[0153] Where: x a is the decision variable of the first stage of the robust reactive power optimization of the distribution network in region a, y a,s is the decision variable of the second stage of the distributed blue reactive power optimization of the distribution network in scenario s in area a, Y a,s is the variable of the coupled branch of the distribution network in scenario s in area a, is the coupled branch global variable, is the dual variable of the coupling branch, p a,s is the probability value of scene s in area a, U a,s,i Indicates the branch voltage, P a,s,ij represents the active power on branch ij, Q a,s,ij Represents the reactive power on branch ij, I a,s,ij The current in branch ij.

[0154] is the vector of penalty parameters related to each coupling branch in region a at the kth iteration; for The square of the weighted norm, that is

[0155]

[0156] (3) Inter-region information exchange and update. Each region exchanges coupling variable information through the coupling branch and updates the global variables of each region using equations (38)-(39). and dual variables Right now

[0157]

[0158] Where: is the penalty parameter value related to the coupling branch ij in region a at the kth iteration; is the auxiliary penalty parameter value related to the coupling branch ij in region a at the kth iteration, which is used to make Updated in super slack.

[0159] (4) Algorithm convergence judgment. The present invention constructs the convergence criterion based on the original residual and dual residual of the ADMM algorithm as follows:

[0160]

[0161] Where: is the original residual of region a under scene s at the kth iteration; is the dual residual of region a in scene s at the kth iteration. k ≤10 -4 When , the algorithm converges and outputs the optimal control strategy for distributed reactive power of the distribution network; otherwise, continue with step (5).

[0162] (5) Variable update and return: Update the values ​​of the penalty parameter and the auxiliary penalty parameter according to equations (43)-(44), update k=k+1, and return to step (2).

[0163]

[0164] Where: η and μ2 are the adaptive adjustment coefficients of the penalty parameter and the auxiliary penalty parameter respectively; γ and μ1 are the update criterion coefficients of the penalty parameter and the auxiliary penalty parameter respectively.

[0165] The global coordination in step S6 is an optimization step that uses the alternating direction method of multipliers (ADMM) with adaptive over-relaxation penalty parameters to ensure that the local solutions of each region or node in the power system can be integrated into a consistent and optimal solution for the entire system.

[0166] This paper introduces an adaptive over-relaxation penalty parameter into the ADMM, enabling faster convergence in a distributed computing environment and mitigating performance issues caused by improper parameter selection. By adaptively adjusting the penalty parameter, the ADMM demonstrates greater efficiency and stability when solving large-scale distributed optimization problems, effectively improving the operational stability and economic efficiency of power grids.

[0167] like Figure 2As shown, the present invention has carried out a case simulation analysis on the improved 69-node system. The reference voltage of the distribution network is 12.66kV, and the reference capacity is 10MVA. The voltage range of the distribution network nodes is set to 0.95pu~1.05pu, the maximum current that the distribution network line can withstand is set to 1pu, the active range of the distribution network gateway is 0~0.5pu, the reactive range of the distribution network is 0~0.3pu, and the reactive optimization operation period of the distribution network is T=24, ζ=1. The initial values ​​of the penalty parameters are all 0.6, and the initial values ​​of the auxiliary penalty parameters are all 1; the adaptive adjustment coefficient η=1.01, μ2=1.5; the update criterion coefficient γ=0.99, μ1=5. The parameter settings of each device in the system are shown in Table 1. The present invention uses the K-means algorithm to cluster the distributed photovoltaic output and load historical data of Z=3650 days, and obtains a representative typical scenario curve as shown in Figure 3 shown.

[0168] Table 1 Distribution network equipment parameter settings

[0169]

[0170]

[0171] In order to verify the effectiveness and efficiency of the adaptive over-relaxation penalty parameter ADMM used in solving the two-layer collaborative reactive power optimization model of the distribution network, the present invention conducted a comparative analysis of different improved distributed algorithms based on ADMM: Algorithm 1: traditional consistent ADMM; Algorithm 2: accelerated ADMM (A2DM2); Algorithm 3: adaptive over-relaxation penalty parameter ADMM. Figure 4 and Figure 5 The objective function convergence curve and error convergence curve of the double-layer coordinated reactive power optimization model of the distribution network proposed by the present invention are solved by each algorithm respectively. Figure 4 and Figure 5 As can be seen from the figure, within a finite number of algorithm iterations, all three improved ADMM-based algorithms can effectively solve the proposed two-layer collaborative reactive power optimization model, obtaining optimal solutions that are consistent with the centralized approach. The adaptive penalty parameter adjustment strategy in Algorithm 3 optimizes the amplitude of the objective function's oscillation convergence during the ADMM algorithm solution by dynamically adjusting the penalty parameter and employing a super-relaxation technique to accelerate the update of global variables, thereby accelerating the convergence of the distributed algorithm.

Claims

1. A two-layer coordinated reactive power control strategy for power systems considering source and load uncertainty, characterized by: It includes the following steps: Step S1: Establish a reactive power optimization model for the distribution network; Step S2: Use the K-means clustering algorithm to cluster the historical data into scenarios, and construct a probability uncertainty set based on the KL divergence; Step S3: adopt the distributed blue rod optimization method to establish a two-stage distributed blue rod reactive power optimization model for the distribution network; Step S4: using the C&CG algorithm to solve the two-stage blue rod reactive power optimization model of each region; Step S5: Based on the distributed reactive power optimization model of the distribution network, a distributed reactive power optimization solution framework for the distribution network is constructed; Step S6: Adopting the adaptive over-relaxation penalty parameter ADMM algorithm to perform global coordinated update solution; Step S6 includes the following: (1) Initialization; set the number of iterations of the outer layer distributed reactive power optimization k = 0; the global variables of the coupling branch Dual variables of coupled branches Coupling branch variables Given the initial penalty parameter ρ for each region 0 The value of and convergence accuracy κ = 10 -4 ; The upper bound of the inner layer blue stick reactive power optimization U B =+∞, lower bound L B = -∞, number of iterations m = 1, convergence error ε = 10 -6 ; (2) Solve the reactive power optimization model of each region and establish the augmented Lagrangian objective function of each region as follows: Y a,s ={U a,s,i ,U a,s,j ,P a,s,ij ,Q a,s,ij ,I a,s,ij } (36) Where: x a is the decision variable of the first stage of the robust reactive power optimization of the distribution network in region a, y a,s is the decision variable of the second stage of the distributed blue reactive power optimization of the distribution network in scenario s in area a, Y a,s is the variable of the coupled branch of the distribution network in scenario s in area a, is the coupled branch global variable, is the dual variable of the coupling branch, p a,s is the probability value of scene s in area a, U a,s,i Indicates the branch voltage, P a,s,ij represents the active power on branch ij, Q a,s,ij Represents the reactive power on branch ij, I a,s,ij represents the current on branch ij; is the vector of penalty parameters related to each coupling branch in region a at the kth iteration; for The square of the weighted norm, that is (3) Inter-region information exchange and update: Each region exchanges coupling variable information through the coupling branch, and uses equations (38)-(39) to update the global variables of each region. and dual variables Right now Where: is the penalty parameter value related to the coupling branch ij in region a at the kth iteration; is the auxiliary penalty parameter value related to the coupling branch ij in region a at the kth iteration, which is used to make Update in a super slack way; (4) Algorithm convergence judgment: The convergence criterion is constructed based on the original residual and dual residual of the ADMM algorithm: Where: is the original residual of region a under scene s at the kth iteration; is the dual residual of region a in scene s at the kth iteration; when κ k ≤10 -4 When , the algorithm converges and the optimal control strategy for distributed reactive power of distribution network is output; otherwise, continue with step (5); (5) Variable update and return: Update the values ​​of the penalty parameter and the auxiliary penalty parameter according to equations (43)-(44), update k=k+1, and return to step (2); Where: η and μ2 are the adaptive adjustment coefficients of the penalty parameter and the auxiliary penalty parameter respectively; γ and μ1 are the update criterion coefficients of the penalty parameter and the auxiliary penalty parameter respectively.

2. The two-layer coordinated reactive power control strategy for power systems considering source and load uncertainty according to claim 1 is characterized by: In step S1, the objective function F of the distribution network reactive power optimization model is: Where: I ij,t is the current value on the distribution network line ij during period t; r ij is the resistance value of the distribution network line ij; T is the total number of time periods for the reactive power optimization operation of the distribution network; Ω L is the set of load nodes in the distribution network.

3. The two-layer coordinated reactive power control strategy for power systems considering source and load uncertainty according to claim 2 is characterized by: The distribution network reactive power optimization model includes distributed photovoltaic output constraints, energy storage model constraints, distribution network flow constraints, on-load tap-changing transformer model constraints, switching capacitor bank model constraints and static VAR compensator model constraints.

4. The two-layer coordinated reactive power control strategy for power systems considering source and load uncertainty according to claim 3 is characterized by: The distributed photovoltaic output constraint is as follows: Where: and are the active and reactive outputs of distributed photovoltaic at node j in period t, is the upper limit of distributed photovoltaic active output at node j in period t, is the capacity of distributed photovoltaic at node j; The energy storage model constraints are as follows: Where: and They represent the charging and discharging operating states of the energy storage at node j during time period t, and are the active power of the distribution network charging the energy storage and the active power of the energy storage discharging the energy storage to the distribution network at node j in period t, and are the maximum and minimum active power when the distribution network charges the energy storage at node j, and are the maximum and minimum active power when the energy storage at node j discharges to the distribution network, B j,t is the state of charge of the energy storage at node j during time period t, B j,t-1 is the state of charge of the energy storage at node j in time period t-1, and are the charging rate and discharging rate of energy storage at node j, respectively, Δt is the optimized operation time interval, is the energy storage capacity at node j, and are the maximum and minimum energy storage charges at node j respectively; The distribution network flow constraint is as follows: Where: P j,t and Q j,t are the active and reactive injection powers at node j in period t, P ij,t and Q ij,t are the active power and reactive power flowing from node i into distribution network line ij during period t, respectively, x ij is the reactance value of the distribution network line ij, and are the active and reactive power required for the normal operation of the load at node j in period t, V i,t is the square of the voltage amplitude at node i during time period t, V i max and V i min V i,t The maximum and minimum values ​​of l ij,t is the square of the current amplitude on the distribution network line ij during time period t, is the square of the maximum current the line can withstand, and are the active and reactive power of the distribution gateway respectively, is the reactive power compensated to the distribution network by the capacitor bank at node j in period t, is the reactive power compensated by SVC to the distribution network at node j in period t, and They are the maximum and minimum active power of the power distribution gateway port, and They are the maximum and minimum reactive power values ​​of the power distribution network gateway respectively; The on-load tap-changing transformer model is constrained as follows: V o,t =V i,t -2(r ij P ij,t +x ij Q ij,t )+[(r ij ) 2 +(x ij ) 2 ]l ij,t (13) Where: V o,t is the square of the voltage value at the auxiliary node o during time period t; ij,n,t is a binary auxiliary variable, N ij,t is the gear position of the on-load tap-changing transformer on the distribution network line ij during time period t, K ij is the number of gears of the on-load tap-changing transformer on the distribution network line ij, Δk ij is the transformation ratio increment of each gear of the on-load tap-changing transformer on the distribution network line ij, is the minimum value of the on-load tap-changing transformer ratio on the distribution network line ij, M is a sufficiently large number, m ij,t 、x ij,n,t and y ij,n,t Intermediate variables introduced for linearization of operating constraints of on-load tap-changing transformers; The switching capacitor bank model constraint is as follows: Where: is the number of switched capacitor banks at node j in period t, is the unit reactive compensation power of the switched capacitor bank at node j, and are the number of switched capacitor groups added and reduced at node j in period t, C CB,max N is the upper limit of the number of times the capacitor bank can be switched within a complete optimization period T. CB,max The maximum number of switched capacitor groups; The static VAR compensator model constraint is as follows: Where: and are the maximum and minimum values ​​of the reactive compensation power of the static VAR compensator at node j respectively.

5. The two-layer coordinated reactive power control strategy for power systems considering source and load uncertainty according to claim 1 is characterized by: In step S2, the K-means algorithm is used to cluster the distributed photovoltaic output and load historical data collected for Z days to obtain N s Typical scenario curves of distributed photovoltaic output and load and initial scenario probability distribution p 0 .

6. The two-layer coordinated reactive power control strategy for power systems considering source and load uncertainty according to claim 5 is characterized by: Construct uncertainty set Ω based on KL divergence for typical scenarios of distributed photovoltaic output and load n : Where: p s is the probability under the typical scenario s; is the initial probability of the typical scene s obtained by clustering; ζ represents the difference between the probability distribution of the typical scene p and the initial probability distribution of the typical scene p 0 The KL divergence value between .

7. The power system double-layer coordinated reactive power control strategy considering source and load uncertainty according to claim 1 is characterized by: In step S3, the discrete variables on-load tap-changing transformer gear position, the number of switched capacitor groups, and the energy storage charging and discharging operation status are used as the first-stage decision variables x of the distributed blue-rod optimization, and other continuous variables are used as the second-stage decision variables y. A two-stage distributed blue-rod reactive power optimization model in vector form is established as follows: stAx≥b,x∈{0,1} (21) In the formula: a, A, b, J, R, w, E, f, Q, q, c, d, G, u s is the corresponding coefficient matrix in the constraints of the reactive power optimization model; Formula (20) is the objective function of the reactive power optimization model of the distribution network; Formula (21) is the constraint related to the decision variables in the first stage; The first constraint in formula (22) is the coupling constraint of the decision variables in the first and second stages; The second constraint in formula (22) is the decision variable constraint of the second stage; The third constraint in formula (22) is a second-order cone constraint; The fourth constraint of formula (22) is the power balance constraint between distributed photovoltaic output and node load; Ω x is the set of decision variables in the first stage; Ω y is the set of decision variables in the second stage; In step S4, the distributed robust reactive power optimization problem of the distribution network is divided into a main problem MP and a subproblem SP by the C&CG algorithm and solved iteratively; when the optimal solution of MP and SP is less than the given convergence error ε, the algorithm converges and outputs the optimal solution.

8. The two-layer coordinated reactive power control strategy for power systems considering source and load uncertainty according to claim 7 is characterized by: Step S4 includes: (1) MP is optimized and solved under the drive of the initial scenario probability obtained by scenario clustering, providing the value of the first stage decision variable x for SP * and provides a lower bound L for the two-stage distributed blue stick reactive power optimization model B ; MP is: stAx≥b,x∈{0,1} (26) Where: subscript m is the number of iterations of the C&CG algorithm; (2) SP is the first-stage decision variable x provided by MP * Find the worst scenario probability distribution And provide an upper bound U for the two-stage distributed blue stick reactive power optimization model B ; SP is: Where: h s Represents the decision variable y under scenario s s,m The minimum cost obtained after conversion is h for all scenes s. s The maximum value after summation.

9. The two-layer coordinated reactive power control strategy for power systems considering source and load uncertainty according to claim 8 is characterized by: In step S5, a distributed reactive power optimization solution framework for the distribution network is constructed based on the ADMM algorithm on the basis of the distributed reactive power optimization model of the distribution network. The distributed reactive power optimization solution framework for the distribution network is established as follows: s.t.Ax a ≥b,x a ∈{0,1} (33) Where: x a is the decision variable of the first stage of the reactive power optimization of the distribution network in area a; u a,s is the constraint value of the uncertainty variable under scenario s in area a; Y a,s,ij Y is the coupling branch variable of the distribution network coupling line ij under scenario s in area a; b,s,ij is the coupling branch variable of the distribution network coupling line ij in scenario s in area b adjacent to area a.

Images