Method for judging relaxation property of charge and discharge complementary constraint of energy storage equipment

Abstract

The invention discloses a method for judging the relaxation property of charge and discharge complementary constraint of energy storage equipment, and relates to the technical field of energy storage related optimization problems, and the method comprises the following steps: defining variable vectors and constraint conditions of the energy storage related optimization problems, then establishing the energy storage related optimization problems in a standard form, and defining various subsets of a constraint function index set; determining a mathematical expression of each sub-condition in the criterion of the complementary constraint relaxation property according to the defined energy storage related optimization problem and the index subset of the constraint function; and integrating the mathematical expressions of the sub-conditions to obtain a criterion of the complementary constraint relaxation property. According to the method, by establishing the energy storage related optimization problem in a standard form, a complementary constraint relaxation property judgment method which is not limited to the form of the optimization problem is given, exact conditions and schemes are provided for reducing the problem complexity of the energy storage related optimization problem and improving the problem solving efficiency, and the method has wide application prospects.

Description

Technical Field

[0001] The present invention relates to the technical field of energy storage related optimization problems, and in particular to a method for determining the relaxability of a complementary constraint on charging and discharging energy of an energy storage device. Background Art

[0002] In the current period of energy transformation, renewable energy is gradually replacing traditional fossil energy. This is a transformation that has forced the power system to undergo rapid and drastic changes to adapt to the uncertainty brought about by renewable energy. As an important tool for regulating the balance of electricity supply and demand, the utilization rate of energy storage systems has been significantly improved in this transformation. Energy storage systems can effectively alleviate the impact of intermittency and uncertainty brought about by the transformation of renewable resources.

[0003] Energy storage-related optimization problems refer to optimization problems involving the optimization of energy storage and release power scheduling of energy storage systems. The complementary storage and release constraints of energy storage equipment introduce strong non-convex characteristics to this type of optimization problem, which directly affects the solution efficiency and solvability of the problem, greatly reducing the solution efficiency and solvability of the problem. The existing method improves the solution efficiency of the problem by relaxing the complementary constraints, but there is no general method to judge the relaxability of the complementary constraints. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] Therefore, the technical problem solved by the present invention is: the existing technology has not yet provided a universal judgment method for the relaxability of complementary constraints, and how to establish a standard form of energy storage-related optimization problem and determine the various sub-conditions related to each energy storage according to the characteristics of the energy storage-related optimization problem, and then integrate the various sub-conditions to obtain the criterion for the relaxability of complementary constraints.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions: a method for judging the relaxability of complementary constraints on charging and discharging energies of energy storage equipment, comprising defining variable vectors and constraints of energy storage-related optimization problems, then establishing a standard form of energy storage-related optimization problems and defining various subsets of constraint function index sets; determining the mathematical expressions of each sub-condition in the criterion of the relaxability of complementary constraints according to the defined energy storage-related optimization problems and the index subsets of the constraint functions; and integrating the mathematical expressions of each sub-condition to obtain the criterion of the relaxability of complementary constraints.

[0007] As a preferred solution of the method for determining the relaxable property of the complementary constraint of energy storage device charging and discharging described in the present invention, the energy storage-related optimization problem includes defining the variables of the energy storage-related optimization problem in vector form, which is expressed as:

[0008]

[0009] Among them, P ch Represents the energy storage power vector of the energy storage device, P dc represents the energy storage device's energy release power vector, Y represents the vector of other variables except energy storage power and energy release power, N = {1,2,…,n N} represents the index set of energy storage devices, n N represents the number of energy storage devices, Y = {1,2,…n Y} represents the index set of elements in vector y, n Y represents the number of elements in vector Y, Indicates n N The set of real vectors of dimension , Indicates n Y The set of real vectors of dimension , represents the energy storage power of energy storage device i, represents the energy release power of energy storage device i, y j represents the jth element in the vector Y; the constraints in the energy storage related optimization problem except the variable boundary constraints and complementary constraints are defined in vector form, expressed as:

[0010]

[0011] Among them, g(P ch ,P dc ,y) represents a continuously differentiable constraint function vector, G represents a constraint function vector g(P ch ,P dc ,y) is the index set of the elements in n G Represents the vector g(P ch ,P dc , the number of elements in y), Indicates n G The set of real vectors of dimension g n (P ch ,P dc ,y) represents the vector g(P ch ,P dc ,y); check g(P ch ,P dc ,y) whether the conditions are met, the satisfied conditions are expressed as:

[0012] g n (P ch ,P dc ,y)=g n (P n ,y),

[0013]

[0014] Among them, P n yes The linear combination of i,n Represents vector P n The i-th element in a i,n and b i,n Respectively and The linear combination coefficients of represents the set of real numbers; this condition shows that g n (P ch ,P dc ,y) is also about (P n ,y) function. If the conditions are not met, this method is not applicable.

[0015] As a preferred solution of the method for determining the relativizable property of the complementary constraint of energy storage device charging and discharging described in the present invention, wherein: the establishment of the standard form of energy storage related optimization problem includes establishing the energy storage related optimization problem according to the optimization target of the energy storage related optimization problem, and the optimization target of the energy storage related optimization problem is expressed as:

[0016]

[0017] Among them, F(P ch ,P dc ,y) represents the objective function of the energy storage related optimization problem, The energy storage related optimization problem is represented by (P ch ,P dc ,y) is the variable minimization objective function F(P ch ,P dc ,y); According to the constraints other than variable boundary constraints and complementary constraints in the energy storage related optimization problem, the energy storage related optimization problem is established. The constraints other than variable boundary constraints and complementary constraints in the energy storage related optimization problem are expressed as:

[0018] stg(P ch ,P dc ,y)≥0:λ g

[0019] in, A vector of Lagrange multipliers representing constraints other than variable bounds and complementarity constraints, Represents λ g The nth element in st represents the constraints of the energy storage related optimization problem; according to P in the energy storage related optimization problem ch , P dc And the boundary constraints of y are used to establish energy storage related optimization problems. In energy storage related optimization problems, P ch , P dcAnd the boundary constraints of y are expressed as:

[0020]

[0021] in, Respectively represent 0≤P ch and The Lagrange multiplier vector of , Respectively λ ch , The i-th element in Respectively represent 0≤P dc and The Lagrange multiplier vector of , Respectively λ dc , The i-th element in λ y , Respectively y ≤y and The Lagrange multiplier vector of , Respectively λ y , The jth element in They represent the maximum energy storage power vector and the maximum energy release power vector, y, Represent the lower boundary vector and upper boundary vector of y respectively; energy storage related optimization problem is established according to the complementary constraints of energy storage related optimization problem, and the complementary constraints of energy storage related optimization problem are expressed as:

[0022]

[0023] in, Represents the Hadamard product.

[0024] As a preferred solution of the method for determining the relaxability of the complementary constraint of the energy storage device charge and discharge energy of the present invention, wherein: the various subsets of the constraint function index set defined include the following: ch ,P dc ,y) each element g n (P ch ,P dc ,y) respectively with P ch , P dc , the partial derivative of each element in y determines the subset of G, expressed as:

[0025]

[0026] Among them, k i,m,n For simplified representation, subset Expressions for the subconditions of the criterion used to later determine the relaxability of the complementary constraint.

[0027] As a preferred solution of the method for judging the relaxability of the complementary constraint of the energy storage device charging and discharging according to the present invention, the mathematical expression of each sub-condition includes selecting an arbitrary positive real number α for each energy storage device i∈N i and β i , according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of conditions A-1 and A-2; the expression of condition A-1 is expressed as:

[0028]

[0029] Condition A-2 expression, expressed as:

[0030]

[0031] For each energy storage device i∈N, select an arbitrary constraint function number m∈G, and select A subset of G k+ , and then according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of conditions B-1, B-2 and B-3; the expression of condition B-1 is expressed as:

[0032]

[0033] Condition B-2 expression is expressed as:

[0034]

[0035] Condition B-3 expression, expressed as:

[0036]

[0037] As a preferred solution of the method for judging the relaxability of the complementary constraint of the energy storage device charging and discharging of the energy storage device described in the present invention, the mathematical expression of each sub-condition also includes selecting an arbitrary constraint function sequence number m∈G for each energy storage device i∈N, and selecting according to the corresponding i and m A subset of G k+ , Select A subset of G a+ , select A i - A subset of G a- , Select A subset of G b+ , Select A subset of G b- , select a subset Y′ of Y, and then select for each j∈Y′ A subset of G y+ (j) Select A subset of G y- (j) Select a real number γ that is not 0 j , and then according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of conditions C-1, C-2, C-3 and C-4; the expression of condition C-1, for any n′∈GG k+ , if a i,n′ k i,m,n′ >0, it is expressed as:

[0038]

[0039] If a i,n′ k i,m,n′ <0, it is expressed as:

[0040]

[0041] in, Indicates that (a i,n′ ,b i,n′ ) is a set of constraint function indices with linearly dependent coefficients; the expression of condition C-2, for any n′∈GG k+ , if b i,n′ k i,m,n′ >0, it is expressed as:

[0042]

[0043] If b i,n′ k i,m,n′ <0, it is expressed as:

[0044]

[0045] in, Indicates that (a i,n′ ,b i,n′ ) is a set of constraint function indices with linearly related coefficients; Condition C-3 expression, for any n′∈GG k+ , if ∑c j,n′ >0, it is expressed as:

[0046]

[0047] like It is expressed as:

[0048]

[0049] in, Used to simplify the expression; conditional C-4 expression, expressed as:

[0050]

[0051] As a preferred solution of the method for judging the relativizable property of complementary constraint of energy storage device charging and discharging energy described in the present invention, wherein: the criterion of the relativizable property of complementary constraint includes the conditions A-1, A-2, B-1, B-2, B-3, C-1, C-2, C-3 and C-4 obtained in the criterion of the relativizable property of complementary constraint determined according to the defined energy storage related optimization problem and the index subset of constraint function to form the criterion of the relativizable property of complementary constraint; case 1: condition A-1 or condition A-2 is established; case 2: condition B-1 is established; case 3: condition B-2 is established, and at least one of conditions B-3, C-1, C-2, C-3 and C-4 is established; if any one of cases 1, 2 and 3 is satisfied, then the optimization objective of the energy storage related optimization problem, the constraint conditions except the variable boundary constraint and the complementary constraint, P ch , P dc As well as the boundary constraints of y and the complementary constraints in the complementary constraints It has the property of being relaxable and relaxing the complementary constraint The obtained relaxed problem has the same optimal solution as the original problem; the relaxed problem includes the optimization objective of the energy storage related optimization problem, the constraints in the energy storage related optimization problem except the variable boundary constraints and complementary constraints, and the P ch , P dcand y boundary constraints, and complementary constraints of energy storage related optimization problems; the original problem includes the optimization objectives of energy storage related optimization problems, the constraints in energy storage related optimization problems except for variable boundary constraints and complementary constraints, and P ch , P dc and y’s boundary constraints, and complementary constraints for energy storage related optimization problems.

[0052] Another object of the present invention is to provide a judgment system for the relaxability of complementary constraints on charging and discharging energies of energy storage devices, which can obtain the criterion for the relaxability of complementary constraints by establishing a standard form of energy storage-related optimization problem, thereby solving the problem that there is no universal judgment method for the relaxability of complementary constraints.

[0053] As a preferred solution of the judgment system of the relaxable property of complementary constraint of energy storage device charging and discharging energy described in the present invention, it includes: a definition module, a sub-condition module, and an integration module; the definition module is used to define the variable vector and constraint conditions of the energy storage related optimization problem, and then establish the energy storage related optimization problem in a standard form and define various subsets of the constraint function index set; the sub-condition module is used to determine the mathematical expression of each sub-condition in the criterion of the relaxable property of complementary constraint according to the defined energy storage related optimization problem and the index subset of the constraint function; the integration module is used to integrate the mathematical expressions of each sub-condition to obtain the criterion of the relaxable property of complementary constraint.

[0054] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of a method for determining the relaxability of a charge-discharge energy complementarity constraint of an energy storage device.

[0055] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a method for determining the relaxability of a charge-discharge energy complementarity constraint of an energy storage device.

[0056] Beneficial effects of the present invention: The method for judging the relaxable properties of complementary constraints on charging and discharging energies of energy storage devices provided by the present invention establishes a standard form of energy storage-related optimization problem and determines the various sub-conditions related to each energy storage according to the characteristics of the energy storage-related optimization problem, and then integrates the various sub-conditions to obtain a criterion for the relaxable properties of complementary constraints. It not only provides a method for judging the relaxable properties of complementary constraints that is not limited to the form of the optimization problem, but also provides specific conditions and solutions for reducing the complexity of energy storage-related optimization problems and improving the efficiency of problem solving. The judgment method provided by the present invention can provide multiple types of criteria for the relaxable properties of complementary constraints for various energy storage-related optimization problems, so that researchers can test and analyze the relaxable properties of complementary constraints in more ways and from more angles, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0058] Figure 1 An overall flow chart of a method for determining the relaxability of the charge-discharge energy complementarity constraint of an energy storage device provided in the first embodiment of the present invention.

[0059] Figure 2 A flowchart of a method for determining the relaxability of a charge-discharge energy complementarity constraint of an energy storage device provided in the first embodiment of the present invention.

[0060] Figure 3 A schematic diagram of determining the expressions of Condition A-1 and Condition A-2 of a method for determining the relaxable property of the complementary constraint of charge and discharge energy of an energy storage device provided in the first embodiment of the present invention.

[0061] Figure 4 A schematic diagram of determining the expressions of Conditions B-1, B-2 and B-3 of a method for determining the relaxable property of the complementary constraint of charge and discharge energy of an energy storage device provided in the first embodiment of the present invention.

[0062] Figure 5 A schematic diagram of determining the expressions of Conditions C-1, C-2, C-3 and C-4 of a method for determining the relaxable property of the complementary constraint of charge and discharge energy of an energy storage device provided in the first embodiment of the present invention.

[0063] Figure 6 An overall flow chart of a system for determining the relaxability of the charge-discharge energy complementarity constraint of an energy storage device provided in the third embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0065] Example 1, reference Figure 1-Figure 5 , which is an embodiment of the present invention, provides a method for determining the relaxability of the charge-discharge energy complementarity constraint of an energy storage device, comprising:

[0066] S1: Define the variable vector and constraints of the energy storage related optimization problem, then establish the standard form of the energy storage related optimization problem and define various subsets of the constraint function index set.

[0067] Furthermore, the energy storage related optimization problem includes defining the variables of the energy storage related optimization problem in vector form, which is expressed as:

[0068]

[0069] Among them, P ch Represents the energy storage power vector of the energy storage device, P dc represents the energy storage device's energy release power vector, Y represents the vector of other variables except energy storage power and energy release power, N = {1,2,…,n N} represents the index set of energy storage devices, n N represents the number of energy storage devices, Y = {1,2,…n Y} represents the index set of elements in vector y, n Y represents the number of elements in vector Y, Indicates n N The set of real vectors of dimension , Indicates n Y The set of real vectors of dimension , represents the energy storage power of energy storage device i, represents the energy release power of energy storage device i, y j represents the jth element in the vector Y; the constraints in the energy storage related optimization problem except the variable boundary constraints and complementary constraints are defined in vector form, expressed as:

[0070]

[0071] Among them, g(P ch ,P dc ,y) represents a continuously differentiable constraint function vector, G represents a constraint function vector g(P ch ,P dc ,y) is the index set of the elements in n G Represents the vector g(P ch ,P dc , the number of elements in y), Indicates n G The set of real vectors of dimension g n (P ch ,P dc ,y) represents the vector g(P ch ,P dc ,y); check g(P ch ,P dc ,y) whether the conditions are met, the satisfied conditions are expressed as:

[0072] g n (P ch ,P dc ,y)=g n (P n ,y),

[0073]

[0074] Among them, P n yes The linear combination of i,n Represents vector P n The i-th element in a i,n and b i,n Respectively and The linear combination coefficients of represents the set of real numbers; this condition shows that g n (P ch ,P dc ,y) is also about (P n ,y) function. If the conditions are not met, this method is not applicable.

[0075] It should be noted that establishing a standard form of energy storage related optimization problem includes establishing an energy storage related optimization problem according to the optimization target of the energy storage related optimization problem. The optimization target of the energy storage related optimization problem is expressed as:

[0076]

[0077] Among them, F(P ch ,P dc ,y) represents the objective function of the energy storage related optimization problem, The energy storage related optimization problem is represented by (P ch ,P dc ,y) is the variable minimization objective function F(P ch ,P dc ,y); According to the constraints other than variable boundary constraints and complementary constraints in the energy storage related optimization problem, the energy storage related optimization problem is established. The constraints other than variable boundary constraints and complementary constraints in the energy storage related optimization problem are expressed as:

[0078] stg(P ch ,P dc ,y)≥0:λ g

[0079] in, A vector of Lagrange multipliers representing constraints other than variable bounds and complementarity constraints, Represents λ gThe nth element in st represents the constraints of the energy storage related optimization problem; according to P in the energy storage related optimization problem ch , P dc And the boundary constraints of y are used to establish energy storage related optimization problems. In energy storage related optimization problems, P ch , P dc And the boundary constraints of y are expressed as:

[0080]

[0081] in, Respectively represent 0≤P ch and The Lagrange multiplier vector of , Respectively λ ch , The i-th element in Respectively represent 0≤P dc and The Lagrange multiplier vector of , Respectively λ dc , The i-th element in λ y , Respectively y The Lagrange multiplier vector for ≤y and y≤y, Respectively λ y , The jth element in They represent the maximum energy storage power vector and the maximum energy release power vector, respectively. y , Represent the lower boundary vector and upper boundary vector of y respectively; energy storage related optimization problem is established according to the complementary constraints of energy storage related optimization problem, and the complementary constraints of energy storage related optimization problem are expressed as:

[0082]

[0083] in, Represents the Hadamard product.

[0084] It should also be noted that the various subsets defining the constraint function index set include those based on g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) respectively with P ch , P dc , the partial derivative of each element in y determines the subset of G, expressed as:

[0085]

[0086] Among them, k i,m,n For simplified representation, subset Expressions for the subconditions of the criterion used to later determine the relaxability of the complementary constraint.

[0087] S2: Determine the mathematical expressions of each sub-condition in the criterion of the relaxability of complementary constraints according to the defined energy storage-related optimization problem and the index subset of the constraint function.

[0088] Furthermore, the mathematical expressions of each sub-condition include selecting an arbitrary positive real number α for each energy storage device i∈N i and β i , according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of conditions A-1 and A-2; the expression of condition A-1 is expressed as:

[0089]

[0090] Condition A-2 expression, expressed as:

[0091]

[0092] For each energy storage device i∈N, select an arbitrary constraint function number m∈G, and select A subset of G k+ , and then according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of conditions B-1, B-2 and B-3; the expression of condition B-1 is expressed as:

[0093]

[0094] Condition B-2 expression is expressed as:

[0095]

[0096] Condition B-3 expression, expressed as:

[0097]

[0098] It should be noted that the mathematical expressions of each sub-condition also include selecting an arbitrary constraint function number m∈G for each energy storage device i∈N, and selecting A subset of G k+ , Select A subset of G a+ , Select A subset of G a- , Select A subset of G b+ , Select A subset of G b- , select a subset Y′ of Y, and then select for each j∈Y′ A subset of G y+ (j) Select A subset of G y- (j) Select a real number γ that is not 0 j , and then according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of conditions C-1, C-2, C-3 and C-4; the expression of condition C-1, for any n′∈GG k+ , if a i,n′ k i,m,n′ >0, it is expressed as:

[0099]

[0100] If a i,n′ k i,m,n′ <0, it is expressed as:

[0101]

[0102] in, Indicates that (a i,n′ ,b i,n′ ) is a set of constraint function indices with linearly dependent coefficients; the expression of condition C-2, for any n′∈GG k+ , if b i,n′ k i,m,n′ >0, it is expressed as:

[0103]

[0104] If b i,n′ k i,m,n′ <0, it is expressed as:

[0105]

[0106] in, Indicates that (a i,n′ ,b i,n′ ) is a set of constraint function indices with linearly related coefficients; Condition C-3 expression, for any n′∈GG k+ , if ∑c j,n′ >0, it is expressed as:

[0107]

[0108] like It is expressed as:

[0109]

[0110] in, Used to simplify the expression; conditional C-4 expression, expressed as:

[0111]

[0112] S3: Integrate the mathematical expressions of each sub-condition to obtain the criterion for the relaxability of complementary constraints.

[0113] Furthermore, the criterion of the complementary constraint relaxability property includes the conditions A-1, A-2, B-1, B-2, B-3, C-1, C-2, C-3 and C-4 obtained in the criterion of the complementary constraint relaxability property determined according to the defined energy storage related optimization problem and the index subset of the constraint function to form the criterion of the complementary constraint relaxability property; case 1: condition A-1 or condition A-2 is established; case 2: condition B-1 is established; case 3: condition B-2 is established, and at least one of conditions B-3, C-1, C-2, C-3 and C-4 is established; if any one of cases 1, 2 and 3 is satisfied, the optimization objective of the energy storage related optimization problem, the constraints except the variable boundary constraints and the complementary constraints, P ch , P dc As well as the boundary constraints of y and the complementary constraints in the complementary constraints It has the property of being relaxable and relaxing the complementary constraint The resulting relaxed problem has the same optimal solution as the original problem.

[0114] It should be noted that the relaxation problem includes the optimization objectives of energy storage related optimization problems, the constraints in energy storage related optimization problems except for variable boundary constraints and complementary constraints, and the Pch , P dc and y’s boundary constraints, and complementary constraints for energy storage related optimization problems.

[0115] It should also be noted that the original problem includes the optimization objectives of energy storage related optimization problems, the constraints in energy storage related optimization problems except for variable boundary constraints and complementary constraints, and the P ch , P dc and y’s boundary constraints, and complementary constraints for energy storage related optimization problems.

[0116] Embodiment 2 is an embodiment of the present invention, and provides an application of a method for determining the relaxability of the complementary constraint of charging and discharging energy of an energy storage device to a multi-period AC optimal power flow problem.

[0117] Firstly, the variable vector and constraints of the multi-period AC optimal power flow problem are defined. Then, the multi-period AC optimal power flow problem is established and various subsets of the constraint index set are defined.

[0118] The variables of the multi-period AC optimal power flow problem are defined in vector form, expressed as:

[0119]

[0120] Among them, P ch Represents the energy storage power vector of the energy storage device, P dc represents the energy release power vector of the energy storage device, y represents the vector composed of other variables except the energy storage power and the energy release power, represents the node set, E represents the power transmission line set, represents a set of scheduling periods, represents the energy storage power of the energy storage device at node i in the scheduling period t, represents the energy release power of the energy storage device at node i in scheduling period t, y j represents the jth element in vector y, represents the active power output of the generator at node i in the scheduling period t, represents the reactive power output of the generator at node i in the scheduling period t, represents the active load of node i in scheduling period t, represents the reactive load of node i in the scheduling period t, represents the active power reduction of the wind turbine at node i in the scheduling period t, represents the reactive power of the converter passing through node i in the scheduling period t, e i,t represents the energy state of the energy storage device at node i in scheduling period t, v i,t represents the square of the voltage amplitude of node i in scheduling period t, p ij,trepresents the active power passing through line (i, j) in the scheduling period t, q ij,t represents the reactive power passing through line (i, j) in the dispatch period t, l ij,t Represents the square of the current amplitude passing through line (i, j) in scheduling period t.

[0121] The constraints in the multi-period AC optimal power flow problem except for the variable boundary constraints and the complementary constraints are defined as follows.

[0122] Define the active power balance equation of the node It is expressed as:

[0123]

[0124] Define the reactive power balance equation of the node It is expressed as:

[0125]

[0126] Ohm's Law Defining Power Lines It is expressed as:

[0127]

[0128] Defining the power flow equations for power lines It is expressed as:

[0129]

[0130] Defines the charging power transfer limit through the inverter It is expressed as:

[0131]

[0132] Define power transfer limits for power lines It is expressed as:

[0133]

[0134] Define the discharge power transfer limits through the converter It is expressed as:

[0135]

[0136] Define the down ramp limit for the generator It is expressed as:

[0137]

[0138] Define the ramp-up limit for the generator It is expressed as:

[0139]

[0140] Defining the energy state equation for energy storage It is expressed as:

[0141]

[0142] Define the charging and discharging energy demand equation for energy storage It is expressed as:

[0143]

[0144] Defining the convex envelope of the complementarity constraint It is expressed as:

[0145]

[0146] Then the constraint index set G is expressed as:

[0147]

[0148] The two endpoints of the line (i, j) are the starting node i and the ending node j, j:i→j represents the set of all the ending nodes j connected to the starting node i, and k:k→i represents the set of all the starting nodes k connected to the ending node i. represents the active power output of the wind turbine at node i in the scheduling period t, r ij 、x ij Respectively represent the resistance and reactance of line (i, j), r ki 、x ki denote the resistance and reactance of the line (k,i) respectively, represents the upper limit of the transmission power of line (i, j), represents the transmission power upper limit of the converter at node i, They represent the upper and lower ramp limits of the generator at node i, Δt represents the scheduling cycle interval, They represent the charging efficiency and discharging efficiency of the energy storage device at node i, represents the charging and discharging energy demand of the energy storage device at node i, They represent the upper limit of charging power and the upper limit of discharging power of the energy storage device at node i, respectively. They represent the Lagrange multipliers of the corresponding constraints respectively.

[0149] Then, according to the multi-period AC optimal power flow problem, the optimization objective of the multi-period AC optimal power flow problem is expressed as:

[0150]

[0151] All constraints in the problem are expressed as:

[0152] st constraint I,I∈G

[0153]

[0154] in, represents the complementary constraint of energy storage, v i , e i represent the lower limits of the corresponding variables, represent the upper limits of the corresponding variables,

[0155] denote the Lagrange multipliers of the corresponding upper and lower constraints respectively.

[0156] Select The following subset of G is obtained, expressed as:

[0157]

[0158] Secondly, according to the mathematical expressions of each sub-condition, select α i =1 and β i =1, and we get the expressions of conditions A-1 and A-2 for the multi-period AC optimal power flow problem.

[0159] Condition A-1 is expressed as:

[0160]

[0161] Condition A-2 is expressed as:

[0162]

[0163] Select The expressions of conditions B-1, B-2 and B-3 of the multi-period AC optimal power flow problem are obtained.

[0164] Condition B-1 is expressed as:

[0165]

[0166] Condition B-2 is expressed as:

[0167]

[0168] Condition B-3 is expressed as:

[0169]

[0170] Select Select Select Select Y′={e i,τ ; τ ≥ t}, select Select The expressions of conditions C-1, C-2, C-3 and C-4 of the multi-period AC optimal power flow problem are obtained.

[0171] Condition C-1 is expressed as:

[0172]

[0173] Condition C-2 is expressed as:

[0174]

[0175] Condition C-3 is expressed as:

[0176]

[0177] Condition C-4 is expressed as:

[0178]

[0179] Finally, the following criterion for the relaxability of complementary constraints is formed based on the obtained conditions A-1, A-2, B-1, B-2, B-3, C-1, C-2, C-3 and C-4:

[0180] If any of the following conditions is met, the complementary constraints in the multi-period AC optimal power flow problem constraints are It has the property of being relativizable and relaxing the complementary constraint The resulting relaxed problem has the same optimal solution as the original problem.

[0181] Case 1: Condition A-1 or Condition A-2 is met.

[0182] Case 2: Condition B-1 is met.

[0183] Case 3: Condition B-2 is met, and at least one of conditions B-3, C-1, C-2, C-3, and C-4 is met.

[0184] In summary, after adopting the above scheme, the present invention provides an innovative method for the field of energy storage related optimization problems, which can obtain the criteria for the relaxability of complementary constraints in various types of energy storage related optimization problems, and provides exact conditions and solutions for reducing the complexity of energy storage related optimization problems and improving the efficiency of problem solving. It has broad application prospects in problems such as power operation and dispatching optimization, and integrated energy system operation.

[0185] Example 3, reference Figure 6, as an embodiment of the present invention, provides a system for judging the relaxability of the complementary constraint of charging and discharging energy of energy storage equipment, including a definition module, a sub-condition module, and an integration module.

[0186] The definition module is used to define the variable vector and constraints of the energy storage related optimization problem, and then establish the standard form of the energy storage related optimization problem and define various subsets of the constraint function index set; the sub-condition module is used to determine the mathematical expression of each sub-condition in the criterion of the relaxability of complementary constraints according to the defined energy storage related optimization problem and the index subset of the constraint function; the integration module is used to integrate the mathematical expressions of each sub-condition to obtain the criterion of the relaxability of complementary constraints.

[0187] If the function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0188] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0189] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.

[0190] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc. It should be noted that the above embodiments are only used to illustrate the technical solution of the present invention and are not limited. Although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

[0191] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for determining the relaxability of the complementary constraint of energy storage equipment charging and discharging, characterized in that: include: Define the variable vector and constraints of the energy storage related optimization problem, then establish the energy storage related optimization problem in standard form and define various subsets of the constraint function index set; Determine the mathematical expressions of each sub-condition in the criterion of the relaxability of the complementary constraint according to the defined energy storage related optimization problem and the index subset of the constraint function; By integrating the mathematical expressions of each sub-condition, we can obtain the criterion for the relaxability of complementary constraints.

2. The method for determining the relativizable property of the complementary constraint of charge and discharge energy of an energy storage device according to claim 1, characterized in that: The energy storage related optimization problem includes defining the variables of the energy storage related optimization problem in vector form, which is expressed as: Among them, P ch Represents the energy storage power vector of the energy storage device, P dc represents the energy storage device's energy release power vector, Y represents the vector of other variables except energy storage power and energy release power, N = {1,2,…,n N } represents the index set of energy storage devices, n N represents the number of energy storage devices, Y = {1,2,…n Y } represents the index set of elements in vector y, n Y represents the number of elements in vector Y, Indicates n N The set of real vectors of dimension , Indicates n Y The set of real vectors of dimension , represents the energy storage power of energy storage device i, represents the energy release power of energy storage device i, y j represents the jth element in vector Y; The constraints in energy storage related optimization problems except for variable boundary constraints and complementary constraints are defined in vector form, expressed as: Among them, g(P ch ,P dc ,y) represents a continuously differentiable constraint function vector, G represents a constraint function vector g(P ch ,P dc ,y) is the index set of the elements in n G Represents the vector g(P ch ,P dc , the number of elements in y), Indicates n G The set of real vectors of dimension g n (P ch ,P dc ,y) represents the vector g(P ch ,P dc ,y)'s nth element; Check g(P ch ,P dc ,y) whether the conditions are met, the satisfied conditions are expressed as: g n (P ch ,P dc ,y)=g n (P n ,y), Among them, P n yes The linear combination of i,n Represents vector P n The i-th element in a i,n and b i,n Respectively and The linear combination coefficients of represents the set of real numbers; This condition indicates that g n (P ch ,P dc ,y) is also about (P n ,y) function. If the conditions are not met, this method is not applicable.

3. The method for determining the relativizable property of the complementary charge and discharge energy constraint of the energy storage device according to claim 2, characterized in that: The energy storage related optimization problem of establishing a standard form includes establishing the energy storage related optimization problem according to the optimization target of the energy storage related optimization problem. The optimization target of the energy storage related optimization problem is expressed as: Among them, F(P ch ,P dc ,y) represents the objective function of the energy storage related optimization problem, The energy storage related optimization problem is represented by (P ch ,P dc ,y) is the variable minimization objective function F(P ch ,P dc ,y); According to the constraints other than the variable boundary constraints and complementary constraints in the energy storage related optimization problem, the energy storage related optimization problem is established. The constraints other than the variable boundary constraints and complementary constraints in the energy storage related optimization problem are expressed as follows: s.t.g(P ch ,P dc ,y)≥0:λ g in, A vector of Lagrange multipliers representing constraints other than variable bounds and complementarity constraints, Represents λ g The nth element in , st represents the constraints to which the energy storage related optimization problem is subject; According to the energy storage related optimization problem P ch , P dc And the boundary constraints of y are used to establish energy storage related optimization problems. In energy storage related optimization problems, P ch , P dc And the boundary constraints of y are expressed as: in, Respectively represent 0≤P ch and The Lagrange multiplier vector of , Respectively λ ch , The i-th element in Respectively represent 0≤P dc and The Lagrange multiplier vector of , Respectively λ dc , The i-th element in λ y , Respectively y ≤y and The Lagrange multiplier vector of , Respectively λ y , The jth element in They represent the maximum energy storage power vector and the maximum energy release power vector, respectively. y , Represent the lower boundary vector and upper boundary vector of y respectively; The energy storage related optimization problem is established according to the complementary constraints of the energy storage related optimization problem. The complementary constraints of the energy storage related optimization problem are expressed as: in, Represents the Hadamard product.

4. The method for determining the relativizable property of the complementary constraint of charge and discharge energy of an energy storage device according to claim 3, characterized in that: The various subsets of the defined constraint function index set include: ch ,P dc ,y) each element g n (P ch ,P dc ,y) respectively with P ch , P dc , the partial derivative of each element in y determines the subset of G, expressed as: Among them, k i,m,n For simplified representation, subset Expressions for the subconditions of the criterion used to later determine the relaxability of the complementary constraint.

5. The method for determining the relativizable property of the complementary constraint of charge and discharge energy of an energy storage device according to claim 4, characterized in that: The mathematical expressions of the sub-conditions include selecting an arbitrary positive real number α for each energy storage device i∈N i and β i , according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of conditions A-1 and A-2; Condition A-1 expression, expressed as: Condition A-2 expression, expressed as: For each energy storage device i∈N, select an arbitrary constraint function number m∈G, and select A subset of G k+ , and then according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of condition B-1, condition B-2 and condition B-3; Condition B-1 expression, expressed as: Condition B-2 expression is expressed as: Condition B-3 expression, expressed as:

6. The method for determining the relativizable property of the complementary constraint of charge and discharge energy of an energy storage device according to claim 5, characterized in that: The mathematical expressions of the sub-conditions also include selecting an arbitrary constraint function sequence number m∈G for each energy storage device i∈N, and selecting A subset of G k+ , Select A subset of G a+ , Select A subset of G a- , Select A subset of G b+ , Select A subset of G b- , select a subset Y′ of Y, and then select for each j∈Y′ A subset of G y+ (j) Select A subset of G y- (j) Select a real number γ that is not 0 j , and then according to the objective function F(P ch ,P dc ,y) and g(P ch ,P dc ,y) each element g n (P ch ,P dc ,y) Determine the expressions of Condition C-1, Condition C-2, Condition C-3 and Condition C-4; Condition C-1 expression, for any n′∈GG k+ , if a i,n′ k i,m,n′ >0, it is expressed as: If a i,n′ k i,m,n′ <0, it is expressed as: in, Indicates that (a i,n′ ,b i,n′ ) a set of constraint function indices with linearly dependent coefficients; Condition C-2 expression, for any n′∈GG k+ , if b i,n′ k i,m,n′ >0, it is expressed as: If b i,n′ k i,m,n′ <0, it is expressed as: in, Indicates that (a i,n′ ,b i,n′ ) a set of constraint function indices with linearly dependent coefficients; Condition C-3 expression, for any n′∈GG k+ , if ∑c j,n′ >0, it is expressed as: like It is expressed as: in, Used to simplify representation; Condition C-4 expression, expressed as:

7. The method for determining the relativizable property of the complementary constraint of charge and discharge energy of an energy storage device according to claim 6, characterized in that: The criterion of the complementary constraint relaxability property includes the conditions A-1, A-2, B-1, B-2, B-3, C-1, C-2, C-3 and C-4 obtained in the criterion of the complementary constraint relaxability property determined according to the defined energy storage related optimization problem and the index subset of the constraint function to form the criterion of the complementary constraint relaxability property; Case 1: Condition A-1 or Condition A-2 is met; Case 2: Condition B-1 is met; Case 3: Condition B-2 is met, and at least one of conditions B-3, C-1, C-2, C-3, and C-4 is met; If any of the cases 1, 2, and 3 is satisfied, then the optimization objective of the energy storage optimization problem, the constraints except the variable boundary constraints and the complementary constraints, P ch , P dc As well as the boundary constraints of y and the complementary constraints in the complementary constraints It has the property of being relaxable and relaxing the complementary constraint The obtained relaxed problem has the same optimal solution as the original problem; The relaxation problem includes the optimization objective of energy storage related optimization problems, the constraints other than variable boundary constraints and complementary constraints in energy storage related optimization problems, and the P ch , P dc and y’s boundary constraints, complementary constraints for energy storage related optimization problems; The original problem includes the optimization objectives of energy storage related optimization problems, the constraints in energy storage related optimization problems except for variable boundary constraints and complementary constraints, and the P ch , P dc and y’s boundary constraints, and complementary constraints for energy storage related optimization problems.

8. A system using the method for determining the releasable property of the complementary constraint of charge and discharge energy of an energy storage device as claimed in any one of claims 1 to 7, characterized in that: Includes definition module, sub-condition module, and integration module; The definition module is used to define the variable vector and constraint conditions of the energy storage related optimization problem, and then establish the energy storage related optimization problem in a standard form and define various subsets of the constraint function index set; The sub-condition module is used to determine the mathematical expressions of each sub-condition in the criterion of the relaxability of the complementary constraint according to the defined energy storage-related optimization problem and the index subset of the constraint function; The integration module is used to integrate the mathematical expressions of each sub-condition to obtain the criterion of the relaxability of the complementary constraint.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for determining the relaxability of the charge-discharge energy complementarity constraint of the energy storage device described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for determining the relaxability of the charge-discharge energy complementarity constraint of the energy storage device described in any one of claims 1 to 7 are implemented.

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