Power distribution network optimization scheduling acceleration solving method based on affine algorithm

Abstract

The invention discloses a power distribution network optimization scheduling acceleration solving method based on an affine algorithm. The method comprises the following steps: 1) constructing an uncertain factor affine expression; 2) constructing a decision and state variable affine form; 3) establishing a power distribution network affine optimization model; 4) performing linearization processing on the affine optimization model of the power distribution network; 5) deriving an analytic expression of node voltage about the decision variable and an analytic expression of branch power about the decision variable; 6) performing scale reduction on the affine optimization model of the power distribution network, and constructing a power distribution network optimization scheduling model based on an affine algorithm; and 7) solving the power distribution network optimization scheduling model to obtain a power distribution network scheduling scheme. According to the method, the affine optimization calculation efficiency can be greatly improved under the condition of ensuring that the calculation precision is not lost.

Description

Technical Field

[0001] The invention relates to the field of power system uncertainty optimization calculation, and in particular to an accelerated solution method for distribution network optimization dispatching based on an affine algorithm. Background Art

[0002] Environmental problems have seriously hindered the sustainable development of power systems. Integrating distributed resources such as wind power and photovoltaics based on clean energy into distribution networks has become a key means to alleviate environmental problems. Secondly, the rapid development of electric vehicles is gradually realizing low-carbon transportation. However, given the inherent randomness and intermittent characteristics of distributed resources, effectively dealing with these uncertainties has become the core challenge and key to ensuring the safety and economic operation of distribution networks. Affine algorithm is an effective uncertainty interval analysis method and has been widely used to solve uncertainties in power systems. Affine algorithm establishes the connection between uncertain factors and system state quantities and decision quantities by defining affine first-order polynomials and reconstructing optimization models, thereby quantitatively analyzing the transmission trajectory of uncertain factors and their impact on optimal scheduling. However, due to the access of a large number of distributed resources, a large number of variables and constraints are inevitably generated in the affine form definition and model reconstruction stages, which greatly reduces the efficiency of model solution. In view of this situation, an analytical method can be used to characterize state variables with system decision quantities to reduce redundant variables and constraints, and then the affine optimization calculation of the distribution network can be performed to ensure the efficiency of optimal scheduling.

[0003] There are two main ways to construct the correlation between uncertainty parameters and optimization variables based on affine algorithms. One is to use sensitivity analysis methods to obtain the noise element coefficients of state variables related to uncertain resource fluctuations. However, for each fluctuation of uncertain factors, an optimal power flow problem needs to be solved, so it is necessary to solve as many optimization problems as uncertain factors, which undoubtedly greatly increases the computational burden, and this method is no longer applicable. Another way is to use affine similarity operations to reconstruct equality constraints, but this will inevitably generate a large number of new constraints and cannot guarantee the efficiency of generating optimized scheduling results. Summary of the invention

[0004] The object of the present invention is to provide a distribution network optimization scheduling accelerated solution method based on an affine algorithm, comprising the following steps:

[0005] 1) Obtain basic information of distribution network;

[0006] 2) Obtain the interval distribution of uncertain factors based on the boundary information of uncertain factors, inversely deduce the affine center value and noise element coefficient of uncertain factors, and construct the affine expression of uncertain factors;

[0007] 3) Construct affine forms of decision and state variables to characterize the correlation between uncertain factors and optimization variables;

[0008] 4) Establish an affine optimization model for distribution network;

[0009] 5) Introducing auxiliary variables Replacing the absolute value variables in the distribution network affine optimization model, so as to linearize the distribution network affine optimization model;

[0010] 6) Derive the analytical expressions of node voltage and branch power with respect to decision variables;

[0011] 7) Based on the analytical expressions of node voltage and branch power on decision variables, the distribution network affine optimization model is scaled down and a distribution network optimization scheduling model based on affine algorithm is constructed;

[0012] 8) Solve the distribution network optimization dispatching model and obtain the distribution network dispatching plan.

[0013] Furthermore, the basic information of the distribution network includes network topology, distributed power supply parameters, new energy data, load data, and system capacity data.

[0014] Furthermore, the uncertainties include wind power, photovoltaic power and load;

[0015] The affine expression of the uncertainty factor is as follows

[0016]

[0017]

[0018] In the formula, and They are the boundary information of the output of uncertain factors in period t; is the noise element coefficient, which is used to characterize the degree of fluctuation of the uncertainty; u is the set of uncertainty factor types; Affine expression for the uncertainty factor; P 0,t is the affine center value of the uncertain factor, used to represent the certain part of the affine value; u,t =[-1,1] is the noise element coefficient The corresponding noise element is used to characterize the fluctuation.

[0019] Furthermore, the affine form of decision and state variables is as follows:

[0020]

[0021] In the formula, is the affine form of decision and state variables; X 0,t is the affine center value; is the noise element coefficient; εu,t =[-1,1] is the noise element coefficient The corresponding noise element.

[0022] Furthermore, the objective function of the distribution network affine optimization model is as follows:

[0023]

[0024] In the formula, is an affine, continuous and differentiable function consisting of the cost affine center value f0 and the offset cost under uncertainty constitute; X0 and are the affine form, affine center value and noise element coefficient of the variable respectively; and They are the prices for purchasing and selling electricity to the superior power grid respectively. and They are the central values ​​of power purchased and sold to the superior power grid respectively; and are the corresponding noise element coefficients; b m and c m The variable cost and fixed cost coefficients of conventional distributed generators, respectively; and are the central value of the output of conventional distributed generators and the noise element coefficient respectively; M is the set of conventional distributed generators. is the set of optimized time periods. Δt is the duration of each time period in the scheduling cycle; ω is the weight coefficient;

[0025] The constraints of the distribution network affine optimization model include the affine operation constraint equations of the adjustable equipment and the affine operation constraints of the distribution network;

[0026] The adjustable device affine operation constraint equation is as follows:

[0027]

[0028]

[0029] In the formula, and are continuous differentiable affine functions describing the i-th inequality and j-th equality constraints respectively; A represents the comparison operator extended to the affine domain; W and N are the sets of inequality and equality constraints;

[0030] Wherein, the inequality constraint set W includes formula (7)-formula (20), formula (25)-formula (26), and the equality constraint N includes formula (21)-formula (24);

[0031]

[0032]

[0033]

[0034]

[0035] In the formula, and are the upper and lower boundaries of the conventional distributed power output; R U and R D are the maximum upward and downward climbing rates respectively; and are the central value and noise element coefficient of the conventional distributed generator output in period t-1 respectively;

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] In the formula, and are the affine center values ​​of the charging and discharging power of energy storage device k respectively. and are binary variables representing the charging and discharging states of energy storage, respectively. and are the noise element coefficients of the charging and discharging power of the energy storage equipment respectively. and are the maximum and minimum charging power of the energy storage device respectively. and They are the maximum and minimum discharge power of the energy storage device respectively. 0,k,t is the affine center value of the energy storage charge state. is the noise element coefficient of the charge state of the energy storage device. and are the charge and discharge efficiency respectively. and are the upper and lower limits of the state of charge respectively. K is the set of energy storage devices.

[0045]

[0046]

[0047] In the formula, and are the interaction power boundary values ​​respectively. and They are binary variables that represent the status of the distribution network purchasing and selling electricity to the superior power grid.

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] Where p 0,j,t With v 0,j,t are the center value of injected power and the square of voltage amplitude at node j in period t respectively. and are the active and reactive power center values ​​of the branch between node i and node j respectively. and is the corresponding noise element coefficient. Represents the set of downstream branches of node j. ij and x ij are the resistance and reactance values ​​respectively. A collection of network nodes.

[0055] Furthermore, when linearizing the distribution network affine optimization model, the following constraints are added:

[0056]

[0057] In the formula, Represents the noise element coefficient The absolute value when it is positive or negative.

[0058] Further, the steps of deriving the analytical expression of the node voltage with respect to the decision variable include:

[0059] a1) Construct the voltage amplitude v of node i i About the root node voltage v ROOT The relationship is:

[0060]

[0061] In the formula, and are the active and reactive power of the upstream branch of node i respectively; r m and x m are the resistance and reactance values ​​respectively;

[0062] a2) When the injected active and reactive power of any node n generates uncertain fluctuations ΔP n and ΔQ n When , calculate the active and reactive power offset of the upstream branch, that is:

[0063]

[0064] a3) Combine formulas (28)-(29) to calculate the node voltage offset when the interaction power smoothes the fluctuation Right now:

[0065]

[0066] In the formula, the vector ΔP=[ΔP1,ΔP2,…,ΔP n ] and ΔQ=[ΔQ1,ΔQ2,…,ΔQ n ] are the node uncertain active and reactive injection power vectors respectively;

[0067] vector Any element in is the sum of the resistances of the upstream branches shared by node i and all other nodes. Any element in is the sum of the reactances of the upstream branches shared by node i and all other nodes, expressed as follows:

[0068]

[0069] a4) Calculate the voltage offset when the adjustable resource is used to smooth the fluctuation Right now:

[0070]

[0071] In the formula Represents the vector of the influence of fluctuation on the square of node voltage amplitude; when When, the degree of impact when or When, the degree of impact when or When, the impact is the set of branches between the fluctuation node n and the node k connected to the adjustable resource; It is the root node of the branch where node n is located. A set of nodes on the main and branch paths. Represents the set of nodes on all branch roads, It is the set of all nodes on the branch path where node n is located, but does not include the root node of the branch path. is the set of branches between node n and node k. up (n) is the upstream node of node n.

[0072] a5) Construct the total voltage offset Δv i The expression is:

[0073]

[0074] In the formula, K is the set of energy storage devices; and are the allocation coefficient vectors related to the interactive power and the adjustable device j respectively. For a certain injection power fluctuation, Established;

[0075] a6) Add noise elements and separate the uncertain factors from the injected power fluctuation to construct the analytical expression of the node voltage with respect to the decision variable, namely:

[0076]

[0077] In the formula, ε t is the noise element; is the node voltage;

[0078] Among them, the matrix matrix As shown below:

[0079]

[0080]

[0081] In the formula, u k is the index of the uncertainty factor k. The nth element in the kth column of R represents the noise element coefficient of the interactive power / adjustable device output related to the uncertainty factor k at node n. MG and is the influencing factor matrix, which represents the mapping relationship between decision variables and voltage variables.

[0082] Further, the steps of deriving the analytical expression of the branch power with respect to the decision variable include:

[0083] b1) Construct the offset expression of branch power under the influence of uncertain fluctuation, that is:

[0084]

[0085] In the formula, and They are the offset of branch power when only interactive power or adjustable equipment is considered to smooth uncertain fluctuations; and Respectively represent the matrix of the correlation between branch m and each node; if and only if the branch Correlation coefficient otherwise when When when or When when or When It is the set of all branches on the main branch path. represents the set of all branches on the branching path, and Represents the set of all branches on the branch path where node n is located;

[0086] b2) Construct the analytical expression of branch power with respect to decision variables, namely:

[0087]

[0088] In the formula is the active power on branch m during period t. is the noise element coefficient vector of branch power. is the branch power.

[0089] Furthermore, when the distribution network affine optimization model is scaled down, the uncertain branch power and node voltage constraints are updated as follows:

[0090]

[0091]

[0092] Where F is the node-branch association matrix between a node and its parent branch. L is the node-branch association matrix between a node and its child branches. u,t and vu,t are the noise element coefficient vectors of branch power and node voltage respectively.

[0093] Furthermore, the distribution network optimization dispatching model based on the affine algorithm is constructed by formulas (4), (7)-(21), (23), (25)-(27), (37)-(38);

[0094] The distribution network optimization scheduling model is solved by the Cplex solver.

[0095] The technical effect of the present invention is unquestionable. The present invention constructs a strict mapping relationship between the system state quantity and the decision quantity through an analytical method, avoids defining a large number of state variables, and replaces the constraints related to the state variable noise element coefficients to reduce their number, thereby greatly improving the calculation efficiency of affine optimization without losing calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 is the node voltage offset in four cases;

[0097] Figure 2 It is an IEEE33-node distribution network system;

[0098] Figure 3 It is an IEEE69 node distribution network system. DETAILED DESCRIPTION

[0099] The present invention is further described below in conjunction with the embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to the common technical knowledge and customary means in the art, which should all be included in the protection scope of the present invention.

[0100] Embodiment 1:

[0101] See also Figures 1 to 3 , a distribution network optimization dispatching acceleration solution method based on affine algorithm, comprising the following steps:

[0102] 1) Obtain basic information of distribution network;

[0103] 2) Obtain the interval distribution of uncertain factors based on the boundary information of uncertain factors, inversely deduce the affine center value and noise element coefficient of uncertain factors, and construct the affine expression of uncertain factors;

[0104] 3) Construct affine forms of decision and state variables to characterize the correlation between uncertain factors and optimization variables;

[0105] 4) Establish an affine optimization model for distribution network;

[0106] 5) Introducing auxiliary variables Replacing the absolute value variables in the distribution network affine optimization model, so as to linearize the distribution network affine optimization model;

[0107] 6) Derive the analytical expressions of node voltage and branch power with respect to decision variables;

[0108] 7) Based on the analytical expressions of node voltage and branch power on decision variables, the distribution network affine optimization model is scaled down and a distribution network optimization scheduling model based on affine algorithm is constructed;

[0109] 8) Solve the distribution network optimization dispatching model and obtain the distribution network dispatching plan.

[0110] Embodiment 2:

[0111] See also Figures 1 to 3 , a distribution network optimization scheduling acceleration solution method based on affine algorithm, the technical content is the same as Example 1, further, the basic information of the distribution network includes network topology, distributed power supply parameters, new energy data, load data, and system capacity data.

[0112] Embodiment 3:

[0113] See also Figures 1 to 3 , a distribution network optimization dispatching acceleration solution method based on affine algorithm, the technical content is the same as any one of embodiments 1-2, further, the uncertain factors include wind power, photovoltaic and load;

[0114] The affine expression of the uncertainty factor is as follows

[0115]

[0116]

[0117] In the formula, and They are the boundary information of the output of uncertain factors in period t; is the noise element coefficient, which is used to characterize the degree of fluctuation of the uncertainty; u is the set of uncertainty factor types; Affine expression for the uncertain factor; P 0,t is the affine center value of the uncertain factor, used to represent the certain part of the affine value; u,t =[-1,1] is the noise element coefficient The corresponding noise element is used to characterize the fluctuation.

[0118] Embodiment 4:

[0119] See also Figures 1 to 3, a distribution network optimization dispatching acceleration solution method based on affine algorithm, the technical content is the same as any one of embodiments 1-3, further, the decision and state variable affine form is as follows:

[0120]

[0121] In the formula, is the affine form of decision and state variables; X 0,t is the affine center value; is the noise element coefficient; ε u,t =[-1,1] is the noise element coefficient The corresponding noise element.

[0122] Embodiment 5:

[0123] See also Figures 1 to 3 , a distribution network optimization dispatching acceleration solution method based on affine algorithm, the technical content is the same as any one of embodiments 1-4, further, the objective function of the distribution network affine optimization model is as follows:

[0124]

[0125] In the formula, is an affine, continuous and differentiable function consisting of the cost affine center value f0 and the offset cost under uncertainty constitute; X0 and are the affine form, affine center value and noise element coefficient of the variable respectively; and They are the prices for purchasing and selling electricity to the superior power grid respectively. and They are the central values ​​of power purchased and sold to the superior power grid respectively; and are the corresponding noise element coefficients; b m and c m The variable cost and fixed cost coefficients of conventional distributed generators, respectively; and are the central value of the output of conventional distributed generators and the noise element coefficient respectively; M is the set of conventional distributed generators. is the set of optimized time periods. Δt is the duration of each time period in the scheduling cycle; ω is the weight coefficient;

[0126] The constraints of the distribution network affine optimization model include the affine operation constraint equations of the adjustable equipment and the affine operation constraints of the distribution network;

[0127] The adjustable device affine operation constraint equation is as follows:

[0128]

[0129]

[0130] In the formula, and are continuous differentiable affine functions describing the i-th inequality and j-th equality constraints respectively; A represents the comparison operator extended to the affine domain; W and N are the sets of inequality and equality constraints;

[0131] Wherein, the inequality constraint set W includes formula (7)-formula (20), formula (25)-formula (26), and the equality constraint N includes formula (21)-formula (24);

[0132] Affine operating constraints for conventional distributed generators:

[0133]

[0134]

[0135]

[0136]

[0137] In the formula, and are the upper and lower boundaries of the conventional distributed power output; R U and R D are the maximum upward and downward climbing rates respectively; and are the central value and noise element coefficient of the conventional distributed generator output in period t-1 respectively;

[0138] Affine operation constraints of energy storage equipment:

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] In the formula, and are the affine center values ​​of the charging and discharging power of energy storage device k respectively. and are binary variables representing the charging and discharging states of energy storage, respectively. and are the noise element coefficients of the charging and discharging power of the energy storage equipment respectively. and are the maximum and minimum charging power of the energy storage device respectively. and They are the maximum and minimum discharge power of the energy storage device respectively. 0,k,t is the affine center value of the energy storage charge state. is the noise element coefficient of the charge state of the energy storage device. and are the charge and discharge efficiency respectively. and are the upper and lower limits of the state of charge respectively. K is the set of energy storage devices.

[0148] Affine operation constraints of energy storage equipment:

[0149]

[0150]

[0151] In the formula, and are the interaction power boundary values ​​respectively. and They are binary variables that represent the status of the distribution network purchasing and selling electricity to the superior power grid.

[0152] The affine operation constraints of the distribution network are as follows:

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159] Where p 0,j,t With v 0,j,t are the center value of injected power and the square of voltage amplitude at node j in period t respectively. and are the active and reactive power center values ​​of the branch between node i and node j respectively. and is the corresponding noise element coefficient. Represents the set of downstream branches of node j. ij and x ij are the resistance and reactance values ​​respectively. A collection of network nodes.

[0160] Embodiment 6:

[0161] A distribution network optimization dispatching acceleration solution method based on an affine algorithm, the technical content is the same as any one of embodiments 1-5, further, when the distribution network affine optimization model is linearized, the following constraints are added:

[0162]

[0163] In the formula, Represents the noise element coefficient The absolute value when it is positive or negative.

[0164] Embodiment 7:

[0165] A distribution network optimization dispatching acceleration solution method based on an affine algorithm, the technical content is the same as any one of embodiments 1-6, and further, the step of deriving the analytical expression of the node voltage with respect to the decision variable includes:

[0166] a1) Construct the voltage amplitude v of node i i About the root node voltage v ROOT The relationship is:

[0167]

[0168] In the formula, and are the active and reactive power of the upstream branch of node i respectively; r m and x m are the resistance and reactance values ​​respectively;

[0169] a2) When the injected active and reactive power of any node n generates uncertain fluctuations ΔP n and ΔQ n When , calculate the active and reactive power offset of the upstream branch, that is:

[0170]

[0171] a3) Combine formulas (28)-(29) to calculate the node voltage offset when the interaction power smoothes the fluctuation Right now:

[0172]

[0173] In the formula, the vector ΔP=[ΔP1,ΔP2,…,ΔP n ] and ΔQ=[ΔQ1,ΔQ2,…,ΔQ n ] are the node uncertain active and reactive injection power vectors respectively;

[0174] vector Any element in is the sum of the resistances of the upstream branches shared by node i and all other nodes. Any element in is the sum of the reactances of the upstream branches shared by node i and all other nodes, expressed as follows:

[0175]

[0176] a4) Calculate the voltage offset when the adjustable resource is used to smooth the fluctuation Right now:

[0177]

[0178] In the formula Represents the vector of the influence of fluctuation on the square of node voltage amplitude; when When, the impact when or When, the impact when or When, the impact is the set of branches between the fluctuation node n and the node k connected to the adjustable resource; It is the root node of the branch where node n is located. A set of nodes on the main and branch paths. Represents the set of nodes on all branch roads, It is the set of all nodes on the branch path where node n is located, but does not include the root node of the branch path. is the set of branches between node n and node k. up (n) is the upstream node of node n.

[0179] a5) Construct the total voltage offset Δv i The expression is:

[0180]

[0181] In the formula, K is the set of energy storage devices; and are the allocation coefficient vectors related to the interactive power and the adjustable device j respectively. For a certain injection power fluctuation, Established;

[0182] a6) Add noise elements and separate the uncertain factors from the injected power fluctuation to construct the analytical expression of the node voltage with respect to the decision variable, namely:

[0183]

[0184] In the formula, ε t is the noise element; is the node voltage;

[0185] Among them, the matrix matrix As shown below:

[0186]

[0187]

[0188] In the formula, u k is the index of the uncertainty factor k. The nth element in the kth column of R represents the noise element coefficient of the interactive power / adjustable device output related to the uncertainty factor k at node n. MG and is the influencing factor matrix, which represents the mapping relationship between decision variables and voltage variables.

[0189] Embodiment 8:

[0190] A distribution network optimization dispatching accelerated solution method based on an affine algorithm, the technical content is the same as any one of embodiments 1-7, and further, the step of deriving the analytical expression of the branch power with respect to the decision variable includes:

[0191] b1) Construct the offset expression of branch power under the influence of uncertain fluctuation, that is:

[0192]

[0193] In the formula, and They are the offset of branch power when only interactive power or adjustable equipment is considered to smooth uncertain fluctuations; and Respectively represent the matrix of the correlation between branch m and each node; if and only if the branch Correlation coefficient otherwise when When when or When when or When It is the set of all branches on the main branch path. represents the set of all branches on the branching path, and Represents the set of all branches on the branch path where node n is located;

[0194] b2) Construct the analytical expression of branch power with respect to decision variables, namely:

[0195]

[0196] In the formula is the active power on branch m during period t. is the noise element coefficient vector of branch power. is the branch power.

[0197] Embodiment 9:

[0198] A distribution network optimization scheduling acceleration solution method based on an affine algorithm, the technical content is the same as any one of embodiments 1-8, further, when the distribution network affine optimization model is scaled down, the branch power and node voltage constraints of the uncertain part are updated as follows:

[0199]

[0200]

[0201] Where F is the node-branch association matrix between a node and its parent branch. L is the node-branch association matrix between a node and its child branches. u,t and v u,t are the noise element coefficient vectors of branch power and node voltage respectively.

[0202] Embodiment 10:

[0203] A distribution network optimization dispatching acceleration solution method based on an affine algorithm, the technical content is the same as any one of embodiments 1-9, further, the distribution network optimization dispatching model based on the affine algorithm is constructed by formulas (4), (7)-(21), (23), (25)-(27), (37)-(38);

[0204] The distribution network optimization scheduling model is solved by the Cplex solver.

[0205] Embodiment 11:

[0206] An accelerated solution method for optimal dispatching of distribution network based on affine algorithm, the steps are as follows:

[0207] (1) Obtaining basic information of the distribution network

[0208] Obtain basic data of the power system, including network topology, distributed power parameters, new energy data, load data, system capacity data, etc.

[0209] (2) Define the uncertainty factor affine expression

[0210] The interval distribution of uncertain factors is obtained according to the boundary information, and the affine center value of the uncertain factors and the noise element coefficient are inversely deduced, and then the affine expression of the uncertain factors is defined.

[0211]

[0212]

[0213] In the formula and are the boundary information of the uncertain factors in period t respectively. is the noise element coefficient of the uncertainty u. u is the set of uncertain factor types. is an affine expression for the uncertain quantity. 0,t is the affine center value. u,t is the noise element coefficient The corresponding noise element.

[0214] (3) Constructing affine forms of decision and state variables

[0215] Then, the affine form of the decision and state variables is constructed, which contains the noise element coefficients corresponding to each noise element in equation (2) to establish the correlation between the uncertain factors and the optimization variables.

[0216] (4) Establishing the objective function of affine optimization of distribution network

[0217] According to the affine minimization operation, a weight coefficient ω is added to weigh the central value cost and the offset cost caused by the fluctuation of uncertain factors.

[0218]

[0219] in is an affine, continuous and differentiable function consisting of the cost affine center value f0 and the offset cost under uncertainty constitute. X0 and are the affine form, affine center value and noise element coefficient of the variable respectively. and They are the prices for purchasing and selling electricity to the superior power grid respectively. and They are the central values ​​of power purchased and sold to the superior power grid respectively. and are the corresponding noise element coefficients. m and c m Variable cost and fixed cost coefficients of conventional distributed generators, respectively. and are the central value of the output of conventional distributed generators and the noise element coefficient respectively. M is the set of conventional distributed generators. is the set of optimized time periods. Δt is the duration of each time period in the scheduling cycle.

[0220] (5) Establish affine operation constraint equations for each adjustable device

[0221] Considering conventional distributed generators, energy storage devices, and electricity purchased and sold to the superior power grid, the operating constraints of these adjustable resources are reconstructed into affine operating constraints through affine operations.

[0222]

[0223]

[0224] in and are continuously differentiable affine functions describing the i-th inequality and j-th equality constraints, respectively. W and N are the sets of inequality and equality constraints. A represents the comparison operator extended to the affine domain.

[0225] (6) Establishing affine operation constraints for distribution network

[0226] Based on affine comparison operators (inequality operations and similarity operations), distribution network operation constraints are mapped from the real number domain to the affine domain.

[0227]

[0228]

[0229]

[0230]

[0231]

[0232]

[0233] Where p 0,j,t With v 0,i,tare the center value of injected power and the square of voltage amplitude at node j in period t respectively. and are the active and reactive power center values ​​of the branch between node i and node j respectively. and is the corresponding noise element coefficient. Represents the set of downstream branches of node j. ij and x ij are the resistance and reactance values ​​respectively. A collection of network nodes.

[0234] (7) Introducing auxiliary variables to solve nonlinear problems

[0235] The absolute value of the noise element coefficient generated after affine reconstruction transforms the optimization model into a nonlinear problem. In order to reduce the difficulty of solving and improve the efficiency of solving, auxiliary variables are introduced. Replace the absolute value variables in the objective function and constraints, and add the following constraints to linearize the model:

[0236]

[0237] In the formula Represents the noise element coefficient Absolute value when positive / negative.

[0238] (8) Derivation of the analytical expression of node voltage with respect to decision variables

[0239] The influence of uncertainty on the square of the voltage amplitude at node i depends on the positional relationship between node i, adjustable resources (such as energy storage, conventional distributed resources, and interactive power), and power change nodes. Based on the linear superposition idea, the offset Δv of the square of the voltage amplitude at node i is i It can be decomposed into two parts: 1) Voltage offset when the fluctuation is only smoothed by the interaction power 2) Voltage offset when the fluctuation is smoothed only by adjustable resources

[0240] When only the power interaction on the root node is considered, we define is the set of branches on the path from node i to the root node. According to the linearized Distflow model, the square of the voltage amplitude of node i is about the root node voltage v ROOT The relationship can be expressed as follows:

[0241]

[0242] In the formula and are the active and reactive power of the upstream branch of node i respectively.

[0243] If the injected active and reactive power of any node n generates uncertain fluctuations ΔP n and ΔQ n , the calculation method of the active and reactive power offset of the upstream branch is shown in formula (13). By combining formula (13) and (14), the node voltage offset can be obtained by formula (15):

[0244]

[0245]

[0246] Where ΔP=[ΔP1,ΔP2,…,ΔP n ] and ΔQ=[ΔQ1,ΔQ2,…,ΔQ n ] are the node uncertain active and reactive injection power vectors respectively. Any element in is the sum of the resistance / reactance of the upstream branch shared by node i and other nodes, which can be expressed as:

[0247]

[0248] To avoid redundant description, only the effect of active power changes is considered in the following derivation, because the mechanisms affecting active power and reactive power are similar.

[0249] Considering only the node voltage variation under adjustable devices is much more complicated, because adjustable resources at different locations will have different effects on the node voltage offset. Similar to equation (15), It can be expressed as:

[0250]

[0251] In the formula A vector representing the degree of influence of fluctuations on the square of node voltage amplitude.

[0252] First determine The positive and negative properties of is the set of branches between the fluctuating node n and the node k connected to the adjustable resource. According to the position relationship between the reference node i, node k and n, there are five cases. Case 1 is From equations (13) and (14), we can see that in this case like Can get At this time, the fluctuation power flow trajectory is analyzed according to the main branch path or branch path situation of the fluctuation node and the adjustable device node in the radial network (a total of four situations). Figure 1 .

[0253] In the above four cases, It is a negative value, indicating that the increase of the injected power at node n will cause the voltage at node i to shift in the increasing direction. There are also four cases when the injected power at node n increases and causes the voltage at node i to shift in the decreasing direction, and the degree of influence is determined by the total resistance of the intersection branch of the branch upstream of the reference node and the branch between the adjustable device and the fluctuation node, as shown in Table x.

[0254] Table 2 Influence coefficient Calculation method

[0255]

[0256]

[0257] in It is the root node of the branch where node n is located. A set of nodes on the main and branch paths. Represents the set of nodes on all branch roads, It is the set of all nodes on the branch path where node n is located, but does not include the root node of the branch path. is the set of branches between node n and node k. up (n) is the upstream node of node n.

[0258] Furthermore, the total voltage offset can be expressed by introducing the distribution coefficient and combining equations (15) and (17) as follows:

[0259]

[0260] Where K is the set of energy storage devices. and are the allocation coefficient vectors related to the interactive power and the adjustable device j respectively. For a certain injection power fluctuation, Established.

[0261] In fact, -ΔPdiag(α MG )and That is, the noise element coefficient in the affine form of the interactive power and the adjustable device output. According to formula (2), the affine form of the node voltage variable can be further expressed by adding noise elements and separating the uncertain factors from the injected power fluctuation:

[0262]

[0263] in

[0264]

[0265]

[0266] Where u k is the index of the uncertainty factor k. The nth element in the kth column of R represents the noise element coefficient of the interactive power / adjustable device output related to the uncertainty factor k at node n. MG and is the influencing factor matrix, which represents the mapping relationship between decision variables and voltage variables.

[0267] (9) Derive the analytical expression of branch power with respect to decision variables

[0268] Similarly, the offset of branch power under the influence of uncertain fluctuations can also be decomposed into multiple components corresponding to the interactive power and the output of the adjustable device, as shown below:

[0269]

[0270] In the formula and They are respectively the offset of branch power when only interactive power or adjustable equipment is considered to smooth uncertain fluctuations. and They represent the matrices of the correlation between branch m and each node. According to formula (14), if and only if branch Correlation coefficient otherwise

[0271] However, due to the complexity of the location of the adjustable device, it is difficult to determine the correlation coefficient. Similar to the above node voltage analysis, according to the position relationship between the reference branch m, the fluctuation node n and the node k connected to the adjustable device, it can be divided into five cases. Case 1 is It can be deduced when There are four situations, and all of them have All situations are shown in Table 2.

[0272] Table 2 Correlation coefficient Calculation method

[0273]

[0274] in It is the set of all branches on the main branch path. represents the set of all branches on the branching path, and Represents the set of all branches on the branch path where node n is located.

[0275] Referring to formula (19), the affine form of branch power can be further modified as follows:

[0276]

[0277] In the formula is the active power on branch m during period t. is the noise element coefficient vector of branch power.

[0278] (10) Reduce the size of the affine optimization model

[0279] Once the noise element coefficients of the state variables are expressed as the noise element coefficients of the decision variables, the uncertain branch power and node voltage constraints can be redefined as:

[0280]

[0281]

[0282]

[0283] Where F is the node-branch association matrix between a node and its parent branch. L is the node-branch association matrix between a node and its child branches. u,t and v u,t are the noise element coefficient vectors of branch power and node voltage respectively.

[0284] After adopting the derived analytical formula of state variables, the original (N ev +N w +N v +N b )×N bra ×T branch power noise coefficients are completely eliminated. Although the node voltage noise coefficients cannot be completely eliminated due to constraints (10)-(11), their number has been reduced by (N ev +N w +N v +N b )×N b ×T reduced to N b ×T. According to formula (12), the number of auxiliary variables is reduced to (N ev +N w +N v +N b -1)×2×N b ×T. Therefore, the total reduction is [(4×N b -1)×(N ev +N w +N v +N b -1)-3×N b ]×T variables, and the number of constraints is reduced by [(4×N b -1)×(N ev +N w +N v +N b-1)-1]×T. (N ev 、N w 、N v 、N b 、N bra and N b are the number of electric vehicle clusters, wind farms, photovoltaic power stations, distribution network nodes and branches, and T is the number of time periods in an optimization cycle. )

[0285] (11) Solve the affine optimization model of distribution network

[0286] Combining equations (1)-(6), (8), (10)-(12), (22)-(23), we can establish an affine optimization model for the distribution network. The nonlinear constraints of this model are all linearized, and the final model is a mixed integer linear programming model, which can be solved by the Cplex solver.

[0287] Embodiment 12:

[0288] A verification of the distribution network optimization dispatch acceleration solution method based on the affine algorithm described in any one of Embodiments 1-11 is as follows:

[0289] The main steps of the accelerated solution method for distribution network optimization scheduling based on affine algorithm are: 1. Obtain basic information of the power grid and gas network; 2. Define the affine form of uncertain factors, state variables and decision variables; 3. Establish an affine optimization model of the distribution network; 4. Derive the analytical expression of the node voltage with respect to the decision variables; 5. Derive the analytical expression of the branch power with respect to the decision variables; 6. Reduce the scale of the affine optimization model; 7. Solve the affine optimization model of the distribution network.

[0290] Combined with the implementation plan of specific example 1 (IEEE 33-node distribution network system), the advantages of this method are further explained as follows:

[0291] (1) Input basic grid information

[0292] Input IEEE33 node distribution network basic data including: each node active power, reactive power, reference voltage, maximum and minimum voltage, branch resistance and reactance, etc. New energy and load data including: dispatch interval values ​​of wind power, photovoltaic and load in each period. Equipment parameters including: conventional distributed power supply and energy storage equipment parameters.

[0293] (2) Define the affine form of uncertain factors, state variables, and decision variables

[0294] According to the input new energy and load interval values, the central value and noise element coefficient are inversely deduced to construct an affine expression of uncertain factors. Based on this, the affine form of state quantities and decision quantities such as branch power, node voltage, and energy storage device output is constructed.

[0295] (3) Establishing an affine optimization model for distribution network

[0296] Based on affine minimization, similarity and inequality operations, combined with the input basic data, the distribution network affine optimization model and comparison model required for the final solution are established.

[0297] The present invention calculates the operation results of the IEEE 33-node distribution network system through two methods, M1 and M2.

[0298] M1: directly define the affine form of the state variables and construct affine constraints related to the state variables based on similarity operations;

[0299] M2: An acceleration strategy that uses the parsed state variable formula to reduce the size of the optimization model.

[0300] (4) Solving the affine optimization model of the distribution network

[0301] Based on the constructed MILP and cplex commercial solver, the distribution network affine optimization model is solved multiple times to obtain the solution results (the average value is taken after 10 solutions). The solution results are as follows:

[0302] Table 3 Solution results of affine optimization model using different methods under IEEE 33-node system

[0303]

[0304] Table 3 shows that the method of the present invention reduces the model scale (the number of variables and constraints is reduced) while ensuring that the solution accuracy is not lost (the solution cost is the same), thereby greatly improving the calculation efficiency (the solution time saving rate is about 88%).

[0305] Combined with the implementation plan of specific example 2 (IEEE69 node distribution system), the solution efficiency of this method is further explained as follows:

[0306] Table 4 Solution results of affine optimization model using different methods under IEEE69 node system

[0307]

[0308] Table 4 further demonstrates the advantages of the method of the present invention. In a larger distribution system, the solution efficiency is improved more significantly, saving about 96% of the solution time, which greatly improves the usability of the optimization model to meet actual engineering needs.

[0309] In summary, the accuracy and speed of the proposed method can be verified in the simulation results of the two examples.

Claims

1. A distribution network optimization dispatching accelerated solution method based on affine algorithm, characterized in that: The following steps are involved: 1) Obtain basic information of distribution network; 2) Obtain the interval distribution of uncertain factors based on the boundary information of uncertain factors, inversely deduce the affine center value and noise element coefficient of uncertain factors, and construct the affine expression of uncertain factors; 3) Construct affine forms of decision and state variables to characterize the correlation between uncertain factors and optimization variables; 4) Establish an affine optimization model for distribution network; 5) Introducing auxiliary variables Replacing the absolute value variables in the distribution network affine optimization model, so as to linearize the distribution network affine optimization model; 6) Derive the analytical expressions of node voltage and branch power with respect to decision variables; 7) Based on the analytical expressions of node voltage and branch power on decision variables, the distribution network affine optimization model is scaled down and a distribution network optimization scheduling model based on affine algorithm is constructed; 8) Solve the distribution network optimization dispatching model and obtain the distribution network dispatching plan.

2. According to claim 1, a distribution network optimization scheduling acceleration solution method based on affine algorithm is characterized in that: The basic information of the distribution network includes network topology, distributed power supply parameters, new energy data, load data, and system capacity data.

3. The method for accelerating the optimal dispatching of a distribution network based on an affine algorithm according to claim 1 is characterized in that: The uncertainties mentioned include wind power, photovoltaic power and load; The affine expression of the uncertainty factor is as follows In the formula, and P t They are the boundary information of the output of uncertain factors in period t; is the noise element coefficient, which is used to characterize the fluctuation degree of the uncertainty; is a set of uncertain factor types; Affine expression for the uncertainty factor; P 0,t is the affine center value of the uncertain factor, used to represent the certain part of the affine value; u,t =[-1,1] is the noise element coefficient The corresponding noise element is used to characterize the fluctuation.

4. The method for accelerating the optimal dispatching of a distribution network based on an affine algorithm according to claim 1 is characterized in that: The affine form of decision and state variables is as follows: In the formula, is the affine form of decision and state variables; X 0,t is the affine center value; is the noise element coefficient; ε u,t =[-1,1] is the noise element coefficient The corresponding noise element.

5. The method for accelerating the optimal dispatching of a distribution network based on an affine algorithm according to claim 1 is characterized in that: The objective function of the distribution network affine optimization model is as follows: In the formula, is an affine, continuous and differentiable function consisting of the cost affine center value f0 and the offset cost under uncertainty constitute; X0 and are the affine form, affine center value and noise element coefficient of the variable respectively; and They are the prices for purchasing and selling electricity to the superior power grid respectively. and They are the central values ​​of power purchased and sold to the superior power grid respectively; and are the corresponding noise element coefficients; b m and c m The variable cost and fixed cost coefficients of conventional distributed generators, respectively; and are the central value of the output of conventional distributed generators and the noise element coefficient respectively; M is the set of conventional distributed generators. is the set of optimized time periods. Δt is the duration of each time period in the scheduling cycle; ω is the weight coefficient; The constraints of the distribution network affine optimization model include the affine operation constraint equations of the adjustable equipment and the affine operation constraints of the distribution network; The adjustable device affine operation constraint equation is as follows: In the formula, and are continuous differentiable affine functions describing the i-th inequality and j-th equality constraints respectively; A represents the comparison operator extended to the affine domain; W and N are the sets of inequality and equality constraints; Wherein, the inequality constraint set W includes formula (7)-formula (20), formula (25)-formula (26), and the equality constraint N includes formula (21)-formula (24); In the formula, and are the upper and lower boundaries of the conventional distributed power output; R U and R D are the maximum upward and downward climbing rates respectively; and are the central value and noise element coefficient of the conventional distributed generator output in period t-1 respectively; In the formula, and are the affine center values ​​of the charging and discharging power of energy storage device k respectively. and are binary variables representing the charging and discharging states of energy storage, respectively. and are the noise element coefficients of the charging and discharging power of the energy storage equipment respectively. and are the maximum and minimum charging power of the energy storage device respectively. and They are the maximum and minimum discharge power of the energy storage device respectively. 0,k,t is the affine center value of the energy storage charge state. is the noise element coefficient of the charge state of the energy storage device. and are the charge and discharge efficiency respectively. and SoC k are the upper and lower limits of the state of charge respectively. K is the set of energy storage devices. In the formula, and P MG are the interaction power boundary values ​​respectively. and They are binary variables that represent the status of the distribution network purchasing and selling electricity to the superior power grid. Where p 0,j,t With v 0,j,t are the center value of injected power and the square of voltage amplitude at node j in period t respectively. and are the active and reactive power center values ​​of the branch between node i and node j respectively. and is the corresponding noise element coefficient. Represents the set of downstream branches of node j. ij and x ij are the resistance and reactance values ​​respectively. A collection of network nodes.

6. The method for accelerating the optimal dispatching of a distribution network based on an affine algorithm according to claim 1 is characterized in that: When linearizing the distribution network affine optimization model, add the following constraints: In the formula, Represents the noise element coefficient The absolute value when it is positive or negative.

7. The method for accelerating the optimal dispatching of a distribution network based on an affine algorithm according to claim 1 is characterized in that: The steps to derive the analytical expression of node voltage with respect to decision variables include: 1) Construct the voltage amplitude v of node i i About the root node voltage v ROOT The relationship is: In the formula, and are the active and reactive power of the upstream branch of node i respectively; r m and x m are the resistance and reactance values ​​respectively; 2) When the injected active and reactive power of any node n generates uncertain fluctuations ΔP n and ΔQ n When , calculate the active and reactive power offset of the upstream branch, that is: 3) Combine formulas (28)-(29) to calculate the node voltage offset when the interaction power smoothes the fluctuation Right now: In the formula, the vector ΔP=[ΔP1,ΔP2,…,ΔP n ] and ΔQ=[ΔQ1,ΔQ2,…,ΔQ n ] are the node uncertain active and reactive injection power vectors respectively; vector Any element in is the sum of the resistances of the upstream branches shared by node i and all other nodes. Any element in is the sum of the reactances of the upstream branches shared by node i and all other nodes, expressed as follows: 4) Calculate the voltage offset when the adjustable resource is used to smooth the fluctuation Right now: In the formula Represents the vector of the influence of fluctuation on the square of node voltage amplitude; when When, the impact when or When, the impact when or When, the impact is the set of branches between the fluctuation node n and the node k connected to the adjustable resource; It is the root node of the branch where node n is located. A set of nodes on the main and branch paths. Represents the set of nodes on all branch roads, It is the set of all nodes on the branch path where node n is located, but does not include the root node of the branch path. is the set of branches between node n and node k. up (n) is the upstream node of node n. 5) Construct the total voltage offset Δv i The expression is: In the formula, K is the set of energy storage devices; and are the allocation coefficient vectors related to the interactive power and the adjustable device j respectively. For a certain injection power fluctuation, Established; 6) Add noise elements and separate the uncertain factors from the injected power fluctuation to construct the analytical expression of the node voltage with respect to the decision variable, namely: In the formula, ε t is the noise element; is the node voltage; Among them, the matrix matrix As shown below: In the formula, u k is the index of the uncertainty factor k. The nth element in the kth column of R represents the noise element coefficient of the interactive power / adjustable device output related to the uncertainty factor k at node n. MG and is the influencing factor matrix, which represents the mapping relationship between decision variables and voltage variables.

8. The method for accelerating the optimal dispatching of a distribution network based on an affine algorithm according to claim 1 is characterized in that: The steps to derive the analytical expression of branch power with respect to decision variables include: 1) Construct the offset expression of branch power under the influence of uncertain fluctuation, that is: In the formula, and They are the offset of branch power when only interactive power or adjustable equipment is considered to smooth uncertain fluctuations; and Respectively represent the matrix of the correlation between branch m and each node; if and only if the branch Correlation coefficient otherwise when When when or When when or When It is the set of all branches on the main branch path. represents the set of all branches on the branching path, and Represents the set of all branches on the branch path where node n is located; 2) Construct the analytical expression of branch power with respect to decision variables, namely: In the formula, is the active power on branch m during period t. is the noise element coefficient vector of branch power; is the branch power.

9. The method for accelerating the optimal dispatching of a distribution network based on an affine algorithm according to claim 1 is characterized in that: When the distribution network affine optimization model is scaled down, the uncertain branch power and node voltage constraints are updated as follows: Where F is the node-branch association matrix between a node and its parent branch. L is the node-branch association matrix between a node and its child branches. u,t and v u,t are the noise element coefficient vectors of branch power and node voltage respectively.

10. The method for accelerating the optimal dispatching of a distribution network based on an affine algorithm according to claim 1, characterized in that: The distribution network optimization dispatching model based on affine algorithm is constructed by formulas (4), (7)-(21), (23), (25)-(27), (37)-(38); The distribution network optimization scheduling model is solved by the Cplex solver.

Images