Radial power distribution network implicit convex optimization method based on characteristic values

Abstract

The invention provides a characteristic value-based implicit convex optimization method for a radial power distribution network. The method comprises the following steps of: constructing a photovoltaic bearing capacity non-convex optimization model of the power distribution network by taking maximum photovoltaic bearing capacity as a target; converting the power distribution network photovoltaic bearing capacity non-convex optimization model into an upper-layer second-order cone programming problem and a plurality of lower-layer single-constraint quadratic programming sub-problems by increasing auxiliary variables; converting the plurality of lower-layer single-constraint quadratic programming sub-problems into corresponding characteristic value optimization sub-problems which can be subjected to parallel calculation; and performing iterative calculation on the upper-layer second-order cone optimization problem and the lower-layer characteristic value optimization sub-problem based on an alternating direction multiplier method to obtain a radial power distribution network implicit convex optimization result. According to the method, the optimization precision and feasibility are improved, and meanwhile, the calculation complexity is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of distribution network optimization operation, and in particular to an eigenvalue-based implicit convex optimization method for radial distribution networks. Background Art

[0002] As the global energy mix shifts toward clean, low-carbon energy, traditional centralized power systems are gradually transitioning to distributed energy systems. In particular, large amounts of renewable energy, such as photovoltaic and wind power, are rapidly being integrated into distribution networks. This trend not only promotes the greening of energy systems but also poses unprecedented challenges to distribution network planning and operation. Traditional distribution networks, primarily powered by a single power source, have relatively simple structures and clear power flow directions, relying on relatively mature optimization technologies. However, the integration of distributed energy resources complicates power flow directions, leading to the emergence of bidirectional power flow. This reverse power flow presents new technical bottlenecks for grid scheduling and control.

[0003] As the proportion of distributed generation (DGs) continues to increase, distribution networks must also cope with voltage fluctuations, dynamic changes in power flow, and other issues. To maintain the stability and reliability of distribution networks in this complex environment, traditional optimization algorithms often relax the problem to a certain extent. These relaxation techniques typically assume that there is no reverse power flow within the system, that the optimization objective can be expressed as an increasing function, and that the voltage fluctuation range is controllable. However, when a large proportion of DGs are present in the system, these assumptions often fail. The failure of these assumptions directly leads to a decrease in the accuracy of the distribution network optimization problem, which may produce unrealistic optimization results and even make the system infeasible in actual operation, increasing the risk of safe operation of the power system. Summary of the Invention

[0004] In view of this, the present invention provides an eigenvalue-based implicit convex optimization method for radial distribution networks to solve the above problems.

[0005] The present invention provides an eigenvalue-based implicit convex optimization method for a radial distribution network, comprising: constructing a non-convex optimization model for the photovoltaic carrying capacity of the distribution network with the goal of maximizing the photovoltaic carrying capacity; converting the non-convex optimization model for the photovoltaic carrying capacity of the distribution network into an upper-layer second-order cone programming problem and a lower-layer quadratic programming subproblem with multiple single constraints by adding auxiliary variables; converting the lower-layer quadratic programming subproblems with multiple single constraints into corresponding eigenvalue optimization subproblems that can be calculated in parallel; and iteratively calculating the upper-layer second-order cone optimization problem and the lower-layer eigenvalue optimization subproblem based on an alternating direction multiplier method to obtain an implicit convex optimization result for the radial distribution network.

[0006] In another implementation of the present invention, the non-convex optimization model of the photovoltaic carrying capacity of the distribution network is simply described as:

[0007]

[0008] Among them, f(x) is the system objective function, x is the system decision variable, N θ is the set of nodes in the system except those connected to the upper power grid, g i and h j are the convex equality and inequality constraints for the safe operation of the system, N eq and N ieq are the number of equality constraints and the number of inequality constraints respectively. The last formula is the only non-convex quadratic equality constraint for node i in the system.

[0009] In another implementation of the present invention, the upper-level second-order cone programming problem is expressed as:

[0010] upper layer:

[0011] In another implementation of the present invention, the quadratic programming subproblem of the lower-level multiple single constraints is expressed as:

[0012] Lower level:

[0013] In another implementation of the present invention, any one of the multiple single-constraint quadratic programming subproblems in the lower layer is expressed as:

[0014]

[0015] Among them, y i The decision variable x for node i i Auxiliary variable, A i is the coefficient of the quadratic term in the objective function, a i is the coefficient of the first-order term in the objective function, B i is the coefficient of the quadratic term in the only non-convex quadratic constraint in node body i, b i is the coefficient of the linear term in the only non-convex quadratic constraint, β i is the constant term in the only non-convex quadratic constraint.

[0016] In another implementation of the present invention, any one of the eigenvalue optimization subproblems is expressed as:

[0017]

[0018] Among them, M0 and M1 are constructed matrices of appropriate dimensions, O is a zero matrix or zero vector of appropriate dimensions, is the estimated value of the Lagrange multiplier of node entity i.

[0019] In another implementation of the present invention, the alternating direction multiplier method is used to iteratively calculate the upper-level second-order cone optimization problem and the lower-level eigenvalue optimization subproblem to obtain the implicit convex optimization result of the radial distribution network, including: for the lower-level eigenvalue optimization subproblem, the eigenvalue of the specific matrix is ​​calculated by estimation and correction to obtain the optimization variable value of the lower layer; for the upper-level second-order cone optimization problem, the ADMM theory is used to interact with the upper-level decision variables, the global residual is calculated, and the upper-level decision variables are corrected until the global residual reaches a credible threshold to obtain the implicit convex optimization result of the radial distribution network.

[0020] Another aspect of the present invention provides an eigenvalue-based implicit convex optimization system for a radial distribution network, which is characterized by comprising: a model construction module: constructing a non-convex optimization model of the photovoltaic carrying capacity of the distribution network with the goal of maximizing the photovoltaic carrying capacity; a model decomposition module: converting the non-convex optimization model of the photovoltaic carrying capacity of the distribution network into an upper-level second-order cone programming problem and a lower-level quadratic programming sub-problem with multiple single constraints by adding auxiliary variables; a sub-problem conversion module: converting the lower-level quadratic programming sub-problems with multiple single constraints into corresponding eigenvalue optimization sub-problems that can be calculated in parallel; a result output module: iteratively calculating the upper-level second-order cone optimization problem and the lower-level eigenvalue optimization sub-problem based on the alternating direction multiplier method to obtain the implicit convex optimization result of the radial distribution network.

[0021] In another aspect of the present invention, an electronic device is provided, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the eigenvalue-based implicit convex optimization method for a radial distribution network are implemented as described in any one of the above items.

[0022] Another aspect of the present invention provides a computer storage medium, characterized in that a computer program is stored on the computer storage medium, and when the computer program is executed by a processor, the steps of the eigenvalue-based implicit convex optimization method for a radial distribution network as described in any one of the above are implemented.

[0023] The eigenvalue-based implicit convex optimization method for radial distribution networks of the present invention avoids the problems of inaccuracy and infeasibility of traditional second-order cone relaxation technology by strategically decomposing the non-convex model into an upper-level second-order cone programming problem and multiple single quadratically constrained programming (QP1QC) sub-problems at the lower level; converts multiple complex sub-problems at the lower level into multiple corresponding eigenvalue optimization sub-problems, greatly simplifying the solution process of the lower-level non-convex sub-problems; by gradually satisfying the non-convex quadratic equality constraints, the accuracy and feasibility of the optimization results in the complex radial distribution network problem are ensured, thereby improving the accuracy of the overall optimization model. At the same time, in the process of coordinated optimization of the upper and lower level problems, the computational complexity is effectively reduced and the solution efficiency of the algorithm is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. By reading the detailed description of the embodiments below, the advantages and benefits of the solutions will become clear to those skilled in the art. The drawings are only for the purpose of illustrating preferred embodiments and are not to be considered as limiting the present invention. In the drawings:

[0025] Figure 1 The figure is a flow chart of an implicit convex optimization method for a radial distribution network based on eigenvalues ​​according to an embodiment of the present invention.

[0026] Figure 2 Schematic diagram of a power flow model of a distribution network according to an embodiment of the present invention.

[0027] Figure 3 This is a schematic diagram of the error results of non-convex equality constraints under the second-order cone relaxation technology of an embodiment of the present invention.

[0028] Figure 4 This is a schematic diagram of the error results of non-convex equality constraints based on the eigenvalue optimization algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and detailedly described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in the embodiments of the present invention should fall within the scope of protection of the embodiments of the present invention.

[0030] Faced with the rapid access of large-scale distributed power sources, the development of new distribution network optimization algorithms that adapt to complex and uncertain environments has become a research hotspot. These new algorithms need to be able to handle bidirectional power flows and multi-dimensional uncertainty, and accurately reflect the actual operating state of the system during the optimization process, thereby ensuring that the optimization results are not only feasible in theory, but also guarantee the safety and stability of the power system in actual operation. Therefore, under this current trend, there is an urgent need to develop a new distribution network optimization algorithm to address the inaccuracy or infeasibility of traditional relaxation techniques, improve system stability and security, and provide technical support for achieving a green and low-carbon energy structure.

[0031] Figure 1 A schematic flow chart of a radial distribution network implicit convex optimization method based on eigenvalues ​​provided by an embodiment of the present invention is shown in FIG. Figure 1 As shown, this embodiment mainly includes:

[0032] S101. Construct a non-convex optimization model for the photovoltaic carrying capacity of the distribution network with the goal of maximizing the photovoltaic carrying capacity.

[0033] S102. By adding auxiliary variables, the non-convex optimization model of the photovoltaic carrying capacity of the distribution network is converted into an upper-level second-order cone programming problem and a lower-level quadratic programming sub-problem with multiple single constraints.

[0034] S103: Convert the lower-level multiple single-constraint quadratic programming subproblems into corresponding parallel-computable eigenvalue optimization subproblems.

[0035] S104. Perform iterative calculations on the upper-level second-order cone optimization problem and the lower-level eigenvalue optimization subproblem based on the alternating direction multiplier method to obtain an implicit convex optimization result of the radial distribution network.

[0036] The eigenvalue-based implicit convex optimization method for radial distribution networks of the present invention avoids the problems of inaccuracy and infeasibility of traditional second-order cone relaxation technology by strategically decomposing the non-convex model into an upper-level second-order cone programming problem and multiple single quadratically constrained programming (QP1QC) sub-problems at the lower level; converts multiple complex sub-problems at the lower level into multiple corresponding eigenvalue optimization sub-problems, greatly simplifying the solution process of the lower-level non-convex sub-problems; by gradually satisfying the non-convex quadratic equality constraints, the accuracy and feasibility of the optimization results in the complex radial distribution network problem are ensured, thereby improving the accuracy of the overall optimization model. At the same time, in the process of coordinated optimization of the upper and lower level problems, the computational complexity is effectively reduced and the solution efficiency of the algorithm is improved.

[0037] In another implementation of the present invention, the non-convex optimization model of the photovoltaic carrying capacity of the distribution network is simply described as:

[0038]

[0039] Among them, f(x) is the system objective function, x is the system decision variable, N θ is the set of nodes in the system except those connected to the upper power grid, g i and h j are the convex equality and inequality constraints for the safe operation of the system, N eq and N ieq are the number of equality constraints and the number of inequality constraints respectively. The last formula is the only non-convex quadratic equality constraint for node i in the system.

[0040] For example, there are many distribution network optimization scenarios, and the objective functions of the optimization models are different, such as system economy, voltage safety, etc., but the operating constraints are similar. The present invention selects the maximum photovoltaic carrying capacity as the goal. The model only considers continuous decision variables, resulting in the optimization problem being continuous, nonlinear, and non-convex, which is representative. In order to meet the needs of subsequent models and algorithms, Figure 2 As shown, the present invention sets the reference positive direction of the radial distribution network flow from the load node to the node connected to the upper grid. In this direction, except for the node connected to the upper grid, all other nodes have a unique parent node, that is, the node connected to the node and pointing in the positive direction of the system. The non-convex optimization model of the distribution network photovoltaic carrying capacity is specifically expressed as:

[0041]

[0042] Where p i,PV represents the photovoltaic active power output of node i, (i, F i ) indicates starting from node i to F i The branch of the node, F i is the parent node of node i, that is, the upper node from node i to the node connected to the power grid, v i represents the square of the voltage at node i, l (t,i) represents the square of the current in branch (t,i), N θ Represents the set of nodes except the nodes connected to the upper power grid, and Respectively represent the branches (i, F i ) of active and reactive power, and Respectively represent the branch (i, F i )'s resistance and reactance, p i and q i denote the injected active power and injected reactive power of node i, s i,P and s i,L They represent the photovoltaic output and load of node i respectively. It is a typical non-convex quadratic constraint, which makes the problem difficult to solve.

[0043] In another implementation of the present invention, the upper-level second-order cone programming problem is expressed as:

[0044] upper layer:

[0045] In another implementation of the present invention, the quadratic programming subproblem of the lower-level multiple single constraints is expressed as:

[0046] Lower level:

[0047] For example, to facilitate the representation of the following algorithms and models, define the variable x i and y i They represent the vectors composed of the original optimization decision variables and auxiliary optimization decision variables of node entity i.

[0048]

[0049] Then the only non-convex quadratic constraint in the original problem model is equivalently expressed as:

[0050]

[0051] It is easy to see that formula (4) can be converted into a second-order cone constraint, which is a convex set, while formula (5) is non-convex. Using the defined decision variable vector, the original problem can be decomposed into two layers:

[0052]

[0053] Among them, X i and Y i Represent the upper convex feasible region and the lower non-convex feasible region of node i, respectively. Thus, the original problem is decomposed into two mutually decoupled layers. To ensure that the decomposed model is meaningful, it is necessary to establish a consensus constraint between the upper and lower layers. That is, the original problem is expressed as:

[0054]

[0055] The consensus constraint above is: Mx i =Ny i , then the augmented Lagrangian form of the above problem is:

[0056]

[0057] Among them, i represents the Lagrange multiplier of the node i variable, and ρ represents the penalty factor of the augmented Lagrange term. Then the upper-level variables, lower-level variables, Lagrange multipliers, and original residuals of the original problem can be updated according to (10)-(13) respectively.

[0058]

[0059] Among them, k represents the number of iterations, r k+1 represents the original residual after the k+1th iteration, Represents the bi-norm of a vector or matrix. Solve for the upper and lower level variables sequentially, update the Lagrange multipliers, and calculate the original residual. Repeat this process until the residual is less than a given threshold or the maximum number of iterations is reached. This yields the values ​​of all optimization variables and the objective function.

[0060] In another implementation of the present invention, any one of the multiple single-constraint quadratic programming subproblems in the lower layer is expressed as:

[0061]

[0062] Among them, y i The decision variable x for node i i Auxiliary variable, A i is the coefficient of the quadratic term in the objective function, a i is the coefficient of the first-order term in the objective function, B i is the coefficient of the quadratic term in the only non-convex quadratic constraint in node body i, b i is the coefficient of the linear term in the only non-convex quadratic constraint, β i is the constant term in the only non-convex quadratic constraint.

[0063] In another implementation of the present invention, any one of the eigenvalue optimization subproblems is expressed as:

[0064]

[0065] Among them, M0 and M1 are matrices of appropriate dimensions, and O is a zero matrix or zero matrix of appropriate dimensions.

[0066] vector, is the estimated value of the Lagrange multiplier of node entity i.

[0067] For example, since the SP2 subproblem shown in Equation (12) has non-convex constraints, it is a typical non-convex problem. It is difficult to solve it directly and the accuracy is low. Therefore, it is converted into an equivalent eigenvalue subproblem. First, rewrite the SP2 subproblem as:

[0068]

[0069] Among them, the objective function is written in the standard quadratic programming form, A i 、B i are 6×6 real matrices with quadratic coefficients of the objective function and constraints, respectively, (·) TRepresents the transpose of a matrix or vector, a i is the linear term coefficient of the objective function.

[0070] The core idea of ​​equivalent transformation is to first give an optimal dual variable λ i The approximate estimated interval of A i +λ i B i Positive definite; then select any value in this interval as the optimal dual variable λ i Finally, the problem (14) is equivalently expressed as a convex eigenvalue optimization problem, and a simple transformation technique is applied to update the solution of the eigenvalue optimization problem. To this end, the following optimization process can be performed to obtain the approximate interval D of the optimal dual variable that meets the conditions: λ :

[0071] λ i,min =arg min{λ i |A i +λ i B i >0,λ i ≥0} (15)

[0072] λ i,max =arg min{-λ i |A i +λ i B i >0,λ i ≥0} (16)

[0073] D λ =(λ i,min ,λ i,max ) (17)

[0074] Theoretically, any value in the interval can be selected as the estimated value, but for simplicity, the midpoint of the interval is usually selected as the estimated value and recorded as Then, the optimal dual variable λ is gradually approached through iterative optimization. i,* , since in interval D λ Any value in A can guarantee i +λ i B i is strictly positive definite and non-singular, so define:

[0075] y(λ i )=-(A i +λ i B i ) -1 a i (18)

[0076] γ(λ i)=g[y(λ i )] (19)

[0077] According to the KKT condition theory, the actual optimal dual variable is to find λ i,* Make γ(λ i,* )=0, theoretically, the optimal dual variable can be obtained by solving γ(λ i )=0, but when A i or B i When the matrix is ​​not symmetric, it is quite difficult to solve the equation. Therefore, γ(λ i )=0 is equivalent to a generalized eigenvalue optimization problem. Define M0 and M1 as:

[0078]

[0079] Then, prove that i,* is the matrix M0+λ i An eigenvalue of M1, that is, there exists a non-zero vector zi such that:

[0080] (M0+λ i,* M1)z i =0 (21)

[0081] For any interval D λ λ in i , we can convert (M0+λ i The determinant of M1) is expressed as:

[0082] det(M0+λ i M1)=(-1) n γ(λ i )det(A i +λ i B i ) 2 (twenty two)

[0083] Here, det(·) represents the determinant of (·). The reasons are as follows:

[0084]

[0085] First, multiply the second line of the above equation by y(λ i ) T Then add it to the first row; then multiply the second column of the above formula by y(λ i ) T Then add it to the first column, and finally expand the simplified determinant row by row to get the following expression:

[0086]

[0087] Because Ai +λ i B i non-singular, its determinant is not zero, then the above determinant is only valid if γ(λ i )=0, which means that λ i That is the optimal dual variable λ i,* , that is, det(M0+λ i,* M1)=0 is strictly true. The above proof shows that we can solve the eigenvalue optimization problem det(M0+λ i M1)=0 to find the optimal λ i,* Next, we will further explain λ i,* is interval D λ The only eigenvalue on , and consider how to gradually approach the optimal value from the estimated value. To achieve this, define: Consider the following eigenvalue problem:

[0088]

[0089] The eigenvalues ​​of formula (25) and (24) have the following one-to-one correspondence: That is, the optimal eigenvalues ​​of (24) and (25) can be given by the following relationship: Studies have shown that γ(λ i ) in interval D λ It can take positive and negative values, as long as y(λ i ) is not a constant, γ(λ i ) is strictly decreasing on this interval. According to the mean value theorem, in the interval D λ There must be a unique optimal value λ on i,* So that γ(λ i,* )=0. When the estimated value Make When , the optimal eigenvalue of formula (21) should be greater than Big, that is Similarly, when When , the optimal eigenvalue of formula (21) should be greater than Small, that is Therefore, it is necessary to follow the transformation method Appropriately increase or decrease the original estimate to approach the optimal dual variable λ i,* After obtaining the optimal value, the corresponding optimization variables can be obtained according to formula (18). Each sub-problem in the lower layer can be calculated in parallel in this way until the optimized values ​​of all sub-problems are obtained, and the lower layer model is solved.

[0090] In another implementation of the present invention, the alternating direction multiplier method is used to iteratively calculate the upper-level second-order cone optimization problem and the lower-level eigenvalue optimization subproblem to obtain the implicit convex optimization result of the radial distribution network, including: for the lower-level eigenvalue optimization subproblem, the eigenvalue of the specific matrix is ​​calculated by estimation and correction to obtain the optimization variable value of the lower layer; for the upper-level second-order cone optimization problem, the ADMM theory is used to interact with the upper-level decision variables, the global residual is calculated, and the upper-level decision variables are corrected until the global residual reaches a credible threshold to obtain the implicit convex optimization result of the radial distribution network.

[0091] In another implementation of the present invention, the proposed algorithm can be described as follows: First, the original problem is decomposed into a tractable centralized SOCP planning problem at the upper level, and then decomposed into multiple relatively independent non-convex QP1QC subproblems at the lower level. These are then equivalently represented as one-to-one eigenvalue subproblems. For the lower-level problem, the eigenvalues ​​of a specific matrix are estimated and corrected to obtain the optimized variable values ​​at the lower level. The ADMM theory is then used to interact with the upper-level decision variables to calculate the global residual and correct the upper-level decision variables until the residual reaches a credible threshold. The algorithm execution process is shown in Table 1.

[0092] Table 1. Flowchart of an implicit convex optimization method for radial distribution networks based on eigenvalues

[0093]

[0094] In another implementation of the present invention, after the method designed by the present invention is implemented, the following example scenario is set: the improved IEEE 33, 69 and 136 node distribution systems are used for example analysis. All numerical results are performed on a computer configured with Intel(R) Core(TM) i7-8700 CPU@3.20GHz and 64GB memory. The upper and lower layer models are solved by the commercial solver GUROBI 12.0.0. Photovoltaic units are installed at different nodes of the three distribution systems with different node sizes, and the maximum capacity of a single unit is 3MW, 3MW and 5MW respectively. The unit location and capacity information are shown in Table 2.

[0095] Table 2 PV unit configuration information

[0096]

[0097] In another implementation of the present invention, using the aforementioned unit configuration and maximizing PV capacity as the objective function, the second-order cone relaxation technique (SOCR) and the eigenvalue-based optimization algorithm (EBHC) were used to evaluate the PV capacity of three improved systems of different sizes. The error between the two optimization results was calculated. The resulting actual PV output and system line losses are shown in Table 3.

[0098] Table 3 System line loss and objective function value

[0099]

[0100] Results show that while significant differences exist between the two methods in terms of objective function values, PV unit output, and system losses, taking the IEEE 69-bus system as an example, the second-order cone relaxation technique only considers the overall objective function while ignoring the actual system requirements. The feasible region after relaxation is not tight. Although the system's PV output reaches its maximum, the system line losses also reach their maximum. Clearly, this solution is infeasible in practice, and excessive line losses do not meet the actual system operating requirements. On the other hand, the optimization results of the EBHC algorithm show that while maximizing the PV load capacity, it also strictly considers the actual system constraints, maintaining the system line losses within an acceptable range. In other words, the EBHC algorithm ensures a reasonable power flow distribution without any relaxation of the original non-convex quadratic equality constraints, resulting in reliable results. Therefore, both the total PV unit output and the system line losses are within reasonable ranges, making the results practical for the system.

[0101] In another embodiment of the present invention, in order to reflect the accuracy of the EBHC algorithm described in the present invention, the following absolute error (26) and relative error (27) calculation methods are defined, and the improved 69-node system is taken as an example with reference to the defined calculation methods, and the branch power flow errors of the system are analyzed and calculated using the traditional second-order cone optimization technology and the EBHC algorithm described in the present invention.

[0102]

[0103] The error results of each branch of the system with respect to the non-convex equality constraint are as follows: Figure 3 and Figure 4 As shown. Figure 3 The results show that in the optimization results of the second-order cone relaxation technology, the non-convex quadratic equality constraints that should have been equal are completely unequal. The errors on both sides of the equations of each branch are large. The errors of most branches exceed 60%, and even exceed 90% on branches numbered 20, 21, 22, 62, and 63, which seriously violates the actual physical constraints and further illustrates the inaccuracy of the second-order cone relaxation technology. Figure 4It can be seen that under the EBHC algorithm proposed in this invention, the same non-convex quadratic equality constraint has almost no error, and the result curves of the variables on both sides of the equation almost completely overlap. After calculating the relative error of each branch, it can be seen that even the relative error of branch 51 with the largest error is only 0.1189%, which can ensure that within 10 -3 That is, the calculation results under this method conform to the actual physical constraints, effectively avoid relaxation errors, and the calculation results are accurate. The optimized solution at this time is the actual feasible solution of the system.

[0104] To further demonstrate the differences between the EBHC algorithm proposed in this paper in systems of different scales, the absolute and relative errors of the IEEE 33-, 69-, and 136-node systems were calculated using the traditional second-order cone optimization technique and the eigenvalue-based optimization algorithm proposed in this paper. The results are shown in Table 4.

[0105] Table 4. System error results of different scales

[0106]

[0107] The results show that in the optimization scenario with photovoltaic carrying capacity as the target, the second-order cone relaxation technique produces unacceptable absolute errors in the three test systems of different scales, and the error increases as the system scale increases. This is because the overall system error is the sum of the errors of each branch. When the system scale increases, the number of branches increases, and the overall error after summation also increases. However, since the relative error is relative to the system, it does not strictly increase with the increase of system scale. Even so, the relative errors in the IEEE 33, 69 and 136 node systems reached 59.56%, 58.10% and 32.5656% respectively, which are unacceptable. In contrast, the relative errors of the EBHC algorithm proposed in this invention are 0.00061%, 0.0249% and 0.00036% respectively, which can ensure that the overall relative error of the system is within 0.001 (within 0.1%), which is within the acceptable range.

[0108] The above actual example analysis can be concluded:

[0109] 1) The original non-convex quadratic equality constraint problem can be equivalently transformed into an upper-level second-order cone optimization problem and multiple eigenvalue optimization sub-problems at the lower level for iterative solution.

[0110] 2) Compared with the second-order cone relaxation technique, the eigenvalue-based optimization algorithm can effectively establish the strict validity of non-convex equality constraints while ensuring the safety and feasibility of the system. The proposed algorithm has smaller error, higher accuracy, and a wider range of applicable scenarios.

[0111] The method of the present invention is suitable for the optimization of large-scale radial distribution networks. This innovative method provides ideas for the accurate solution of radial distribution networks and has strong reference significance and practical application potential for optimization scenarios where classical relaxation techniques are inaccurate.

[0112] Another aspect of the present invention provides an eigenvalue-based implicit convex optimization system for radial distribution networks, characterized by comprising:

[0113] Model construction module: Construct a non-convex optimization model of the photovoltaic carrying capacity of the distribution network with the goal of maximizing the photovoltaic carrying capacity.

[0114] Model decomposition module: By adding auxiliary variables, the non-convex optimization model of the photovoltaic carrying capacity of the distribution network is transformed into an upper-level second-order cone programming problem and a lower-level quadratic programming sub-problem with multiple single constraints.

[0115] Subproblem conversion module: converts the quadratic programming subproblems of the lower layer with multiple single constraints into corresponding eigenvalue optimization subproblems that can be calculated in parallel.

[0116] Result output module: Based on the alternating direction multiplier method, the upper-level second-order cone optimization problem and the lower-level eigenvalue optimization subproblem are iteratively calculated to obtain the implicit convex optimization result of the radial distribution network.

[0117] The eigenvalue-based implicit convex optimization system for radial distribution networks of the present invention avoids the problems of inaccuracy and infeasibility of traditional second-order cone relaxation technology by strategically decomposing the non-convex model into an upper-level second-order cone programming problem and multiple single quadratically constrained programming (QP1QC) sub-problems at the lower level; converts multiple complex sub-problems at the lower level into multiple corresponding eigenvalue optimization sub-problems, greatly simplifying the solution process of the lower-level non-convex sub-problems; by gradually satisfying the non-convex quadratic equality constraints, the accuracy and feasibility of the optimization results in the complex radial distribution network problem are ensured, thereby improving the accuracy of the overall optimization model. At the same time, in the process of coordinated optimization of the upper and lower level problems, the computational complexity is effectively reduced and the solution efficiency of the algorithm is improved.

[0118] In another aspect of the present invention, an electronic device includes a processor, a memory, a communication bus, and a communication interface.

[0119] in:

[0120] The processor, memory and communication interface communicate with each other through a communication bus.

[0121] Communication interface, used to communicate with other electronic devices or servers.

[0122] The processor is used to execute the program, and specifically can execute the steps of any one of the eigenvalue-based implicit convex optimization methods for radial distribution networks in the above embodiments.

[0123] Specifically, the program may include program codes including computer operation instructions.

[0124] The processor may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application. The one or more processors included in the smart device may be processors of the same type, such as one or more CPUs; or different types of processors, such as one or more CPUs and one or more ASICs.

[0125] Memory is used to store programs. The memory may include high-speed RAM memory, and may also include non-volatile memory (non-volatile memory), such as at least one disk storage.

[0126] The program can be specifically configured to cause a processor to execute the steps of any of the eigenvalue-based implicit convex optimization methods for radial distribution networks described in the embodiments. The specific implementation of each step in the program can refer to the corresponding descriptions of the steps and units executed in any of the eigenvalue-based implicit convex optimization methods for radial distribution networks in the aforementioned steps, and will not be repeated here. Those skilled in the art will clearly understand that, for ease and brevity of description, the specific working processes of the devices and modules described above can refer to the corresponding process descriptions in the aforementioned method embodiments.

[0127] The exemplary embodiments of the present application further provide a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable a computer to execute the methods of the various embodiments of the present application.

[0128] The method according to the embodiment of the present invention described above can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD ROM, RAM, floppy disk, hard disk or magneto-optical disk), or as computer code that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded via a network and will be stored in a local recording medium, so that the method described herein can be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor or programmable or dedicated hardware (such as an ASIC or FPGA). It can be understood that a computer, a processor, a microprocessor controller or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, a processor or hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown here, the execution of the code converts the general-purpose computer into a dedicated computer for executing the method shown here.

[0129] Thus far, specific embodiments of the present invention have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve the desired results. Additionally, the processes depicted in the accompanying drawings do not necessarily require the specific order shown, or sequential order, to achieve the desired results.

[0130] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, back, etc.) are only used to explain the relative position relationship between the components in a certain specific order (as shown in the accompanying drawings). If the specific order changes, the directional indication will also change accordingly.

[0131] In the description of the present invention, the terms "first" and "second" are used solely to facilitate description of different components or names and should not be construed as indicating or implying a sequential relationship, relative importance, or implicitly specifying the quantity of the technical features being described. Therefore, features specified as "first" or "second" may explicitly or implicitly include at least one of such features.

[0132] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in this specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0133] It should be noted that although the specific embodiments of the present invention are described in detail in conjunction with the accompanying drawings, this should not be construed as limiting the scope of protection of the present invention. Within the scope described by the claims, various modifications and variations that can be made by those skilled in the art without creative effort still fall within the scope of protection of the present invention.

[0134] The examples of the embodiments of the present invention are intended to briefly illustrate the technical features of the embodiments of the present invention so that those skilled in the art can intuitively understand the technical features of the embodiments of the present invention, and are not intended to improperly limit the embodiments of the present invention.

[0135] Finally, 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A radial distribution network implicit convex optimization method based on eigenvalues, characterized by: include: A non-convex optimization model for photovoltaic carrying capacity of distribution network is constructed with the goal of maximizing photovoltaic carrying capacity. By adding auxiliary variables, the non-convex optimization model of the photovoltaic carrying capacity of the distribution network is transformed into an upper-level second-order cone programming problem and a lower-level quadratic programming sub-problem with multiple single constraints; Convert the quadratic programming subproblems of the multiple single constraints in the lower layer into corresponding eigenvalue optimization subproblems that can be calculated in parallel; Based on the alternating direction multiplier method, the upper-level second-order cone optimization problem and the lower-level eigenvalue optimization subproblem are iteratively calculated to obtain an implicit convex optimization result of the radial distribution network.

2. The method according to claim 1, characterized in that The non-convex optimization model of the photovoltaic carrying capacity of the distribution network is simply described as: Among them, f(x) is the system objective function, x is the system decision variable, N θ is the set of nodes in the system except those connected to the upper power grid, g i and h j are the convex equality and inequality constraints for the safe operation of the system, N eq and N ieq are the number of equality constraints and the number of inequality constraints respectively. The last formula is the only non-convex quadratic equality constraint for node i in the system.

3. The method according to claim 2, characterized in that The upper-level second-order cone programming problem is expressed as: upper layer:

4. The method according to claim 2, characterized in that The quadratic programming subproblem of the lower layer multiple single constraints is expressed as: Lower level:

5. The method according to claim 4, characterized in that Any one of the multiple single-constrained quadratic programming subproblems in the lower layer can be expressed as: Among them, y i The decision variable x for node i i Auxiliary variable, A i is the coefficient of the quadratic term in the objective function, a i is the coefficient of the first-order term in the objective function, B i is the coefficient of the quadratic term in the only non-convex quadratic constraint in node body i, b i is the coefficient of the linear term in the only non-convex quadratic constraint, β i is the constant term in the only non-convex quadratic constraint.

6. The method according to claim 5, characterized in that Any one of the eigenvalue optimization subproblems can be expressed as: Among them, M0 and M1 are constructed matrices of appropriate dimensions, O is a zero matrix or zero vector of appropriate dimensions, is the estimated value of the Lagrange multiplier of node entity i.

7. The method according to claim 1, characterized in that The method of iteratively calculating the upper-level second-order cone optimization problem and the lower-level eigenvalue optimization subproblem based on the alternating direction multiplier method to obtain an implicit convex optimization result of the radial distribution network includes: For the eigenvalue optimization subproblem of the lower layer, the eigenvalue of a specific matrix is ​​calculated by estimation and correction to obtain the optimization variable value of the lower layer; For the upper-level second-order cone optimization problem, the ADMM theory is used to interact with the upper-level decision variables, calculate the global residual, and correct the upper-level decision variables until the global residual reaches a credible threshold, thereby obtaining the implicit convex optimization result of the radial distribution network.

8. A radial distribution network implicit convex optimization system based on eigenvalues, characterized by: include: Model construction module: Construct a non-convex optimization model of the photovoltaic carrying capacity of the distribution network with the goal of maximizing the photovoltaic carrying capacity; Model decomposition module: by adding auxiliary variables, the non-convex optimization model of the photovoltaic carrying capacity of the distribution network is converted into an upper-level second-order cone programming problem and a lower-level quadratic programming sub-problem with multiple single constraints; Sub-problem conversion module: converts the quadratic programming sub-problems of the lower layer with multiple single constraints into corresponding eigenvalue optimization sub-problems that can be calculated in parallel; Result output module: Based on the alternating direction multiplier method, the upper-level second-order cone optimization problem and the lower-level eigenvalue optimization subproblem are iteratively calculated to obtain the implicit convex optimization result of the radial distribution network.

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of an eigenvalue-based implicit-convex optimization method for a radial distribution network are implemented as claimed in any one of claims 1 to 7.

10. A computer storage medium, characterized in that The computer storage medium stores a computer program, which, when executed by a processor, implements the steps of the eigenvalue-based implicit-convex optimization method for a radial distribution network according to any one of claims 1 to 7.

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