A fully distributed direct current optimal power flow method, device, equipment and medium

Abstract

The application provides a fully distributed direct current optimal power flow method, device, equipment and medium, including: according to the distributed economic dispatch model of solving the marginal cost λ i And the node active power injection power P i Of any node i of the system with a consistency algorithm, the node phase distributed calculation equation is established to determine the overload line of the power system; the Lagrange multiplier method model of the centralized direct current optimal power flow model with the minimum generation cost as the target is established, and the optimization equation set of the Lagrange multiplier method model is generated; according to the node phase distributed calculation equation and the optimization equation set, iterative processing is carried out, and the fully distributed direct current optimal power flow model is generated; the iterative processing includes the iterative processing of the node equation, the node corresponding to the non-overload line and the node corresponding to the overload line. In addition, the existing distributed economic dispatch method with direct current optimal power flow as the core cannot realize centralized direct current optimal power flow, thereby affecting the distributed management and control of the power source of the power system.

Description

Technical Field

[0001] This invention relates to the field of power system energy management technology, specifically to a fully distributed DC optimal power flow method, apparatus, equipment, and medium. Background Technology

[0002] DC power flow is a linearized expression of AC power flow and is widely used in economic dispatch due to its high computational efficiency. Driven by policies such as energy conservation, emission reduction, and environmental protection, renewable energy power generation, such as wind and solar power, is being integrated into the power system on a large scale in the form of decentralized, distributed, and microgrids. Factors such as the privacy, security, and efficiency of information among various power source stakeholders have led to a decentralized management structure among traditional power sources and various renewable energy power generation sources in the power system, making it difficult to achieve traditional centralized DC optimal power flow calculations. Therefore, distributed DC optimal power flow calculation methods have become a hot topic and focus of research for experts and scholars both domestically and internationally, resulting in many excellent achievements. Among these, consensus algorithms are widely used in the field of decentralized economic dispatch because they do not require a coordination center. Currently, there are economic dispatch methods based on consensus algorithms for multi-agent and islanded microgrids, consensus algorithms considering generator upper and lower limits and optimal feedback gains, which have been applied to decentralized economic dispatch calculations in microgrids, consensus decentralized economic dispatch algorithms with improved network weights that address issues of transaction privacy, high communication speed, and security, and non-quadratic form functions of renewable energy generation costs have been established, along with a consensus economic dispatch model for maximizing overall social benefits in power generation and consumption.

[0003] However, the aforementioned decentralized economic dispatch method based on DC optimal power flow cannot solve the problem of transmission line overload. In actual use, the transmission lines of the power system energy management system may be overloaded. Since the existing decentralized economic dispatch method based on DC optimal power flow cannot solve the problem of transmission line overload, it cannot achieve centralized DC optimal power flow, thus affecting the decentralized management and control of power sources in the power system.

[0004] In view of the above, this application is hereby submitted. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a fully distributed DC optimal power flow method, apparatus, equipment and medium, which can effectively solve the problem that the existing decentralized economic dispatch method based on DC optimal power flow cannot solve the problem of overload on transmission lines, and therefore cannot achieve centralized DC optimal power flow, thus affecting the decentralized management and control of power sources in the power system.

[0006] This invention discloses a fully distributed DC optimal power flow method, comprising:

[0007] The marginal cost λ of any node i in the system is calculated using a consensus algorithm. i and its node active power injection P i A decentralized economic dispatch model is established, and node phase decentralized calculation equations are set up to determine the overloaded lines of the power system.

[0008] A Lagrange multiplier method model for a centralized DC optimal power flow model with the objective of minimizing power generation cost is established, and the optimal equation set of the Lagrange multiplier method model is generated.

[0009] The fully distributed DC optimal power flow model is generated by iterative processing based on the node phase dispersion calculation equation and the optimization equation set. The iterative processing includes the dispersion iterative processing of the node equation, the iterative processing of the nodes corresponding to non-overloaded lines, and the iterative processing of the nodes corresponding to overloaded lines.

[0010] Preferably, the marginal cost λ of any node i in the system is solved using a consensus algorithm. i and its node active power injection P i The decentralized economic scheduling model establishes a node phase decentralized calculation equation, specifically as follows:

[0011] The marginal cost λ of any node i in the system is calculated using a consensus algorithm. i and its node active power injection P i The decentralized economic scheduling model generates the active power injection of nodes. Among them, the active power injection P at DC power flow node i i Equal to the power flow P of the associated transmission line ij The sum of θ i θ represents the phase of node i. j Represents the phase of node j, x ij Indicates transmission line l ij Reactance at two endpoints i and j;

[0012] Expand and rearrange the active power injection of the node to generate the phase iterative solution equation for node i;

[0013] The phase iterative solution equation is improved to generate the node phase dispersion calculation equation.

[0014] Preferably, the marginal cost λ of any node i in the system is solved using a consensus algorithm. i and its node active power injection P i The decentralized economic scheduling model is Where, λ i (k+1) represents λ i The value of the (k+1)th iteration, N iLet a represent the set of adjacent nodes of node i. ij λ represents the element in the i-th row and j-th column of an adjacency matrix whose row sum is 1. j (k) represents λ j (Marginal cost of node j) The value of the kth iteration, ε i Represents a small positive number, controlling the iteration speed and accuracy, ΔP i (k) represents the active power deviation of node i in the k-th iteration, P i (k+1) represents the active power deviation of node i in the (k+1)th iteration, ΔP j (k) represents the active power deviation of node j in the k-th iteration, P i (k) represents the active power of node i in the k-th iteration, P i (k+1) represents the active power of node i in the (k+1)th iteration. and These are obtained by taking the minimum and maximum values ​​of the active power of the generator at node i, respectively.

[0015] Preferably, the centralized DC optimal power flow model with the objective of minimizing power generation cost is... Where, N G α represents the total number of generators. i ,β i γ i Let P represent the coefficients of the quadratic, linear, and constant terms of the cost function of generator i, respectively. Gi P represents the active power output of generator i. Di θ represents the active load at node i. i θ represents the phase of node i. j Indicates the phase of node j; x ij Indicates line l ij The reactance of (nodes i and j at both ends), N i N represents the total number of nodes directly connected to node i, and N represents the total number of nodes in the system. This represents the minimum active power output of generator i. This represents the maximum active power output of generator i. Indicates line l ij The active power limit (with nodes i and j at both ends).

[0016] Preferably, a Lagrange multiplier method model is established for a centralized DC optimal power flow model with the objective of minimizing power generation costs, and the optimal equation set of the Lagrange multiplier method model is generated, specifically as follows:

[0017] Lagrange multiplier method model for establishing a centralized DC optimal power flow model with the objective of minimizing power generation cost. Where, λ i(i = 1, 2, ..., N) represents the Lagrange multiplier of the active power injection constraint at node i, μ ij Indicates line l ij (With nodes i and j at both ends) The Lagrange multiplier of active power transmission constraints, line l ij (When the two endpoints are i and j) when active transmission exceeds the limit, μ ij >0, otherwise, μ ij =0;

[0018] The Lagrange multiplier method model is subjected to partial derivatives and transformations to generate a system of optimal equations, wherein the system of optimal equations is based on λ. i (i = 1, 2, ..., N), P Gi (i = 1, 2, ..., N) G ), θ i (i = 1, 2, ..., N-1), μ ij (l ij =1, 2, ..., L; i, j∈Π) for a total of N+N G +N-1+L=N G A system of optimization equations with +2N+L-1 unknowns.

[0019] Preferably, an iterative process is performed based on the node phase dispersion calculation equation and the optimization equation set to generate a fully distributed DC optimal power flow model, specifically as follows:

[0020] Based on the node phase dispersion calculation equation, the node equations of the optimization equation set are solved by dispersion iteration to generate the corresponding explicit function.

[0021] Based on the node phase dispersion calculation equation, the corresponding nodes of the non-overloaded line are iteratively processed to generate the iterative equations for the corresponding nodes of the non-overloaded line.

[0022] Based on the node phase dispersion calculation equation, the nodes corresponding to the overloaded line in the optimization equation set are iteratively processed to generate the iterative equations for the nodes corresponding to the overloaded line.

[0023] Distributed iterative processing is performed on the explicit function, the iterative equations of the nodes corresponding to the non-overloaded lines, and the iterative equations of the nodes corresponding to the overloaded lines to solve for the node phases and generate a fully distributed DC optimal power flow model.

[0024] Preferably, the explicit function, the iterative equations for the nodes corresponding to the non-overloaded lines, and the iterative equations for the nodes corresponding to the overloaded lines are subjected to distributed iterative processing, specifically as follows:

[0025] Let variable k = 0, and give initial phase values ​​for N-1-L unknowns;

[0026] Based on the explicit function, the first phase value of the N-1-L unknowns in the first iteration is solved, where the phase value is expressed as λ1(k), λ2(k), ..., λ N-1-L (k) form expression;

[0027] The iterative equations for the corresponding nodes of the non-overloaded lines are solved iteratively, and the iterative results are denoted as λ1(k), λ2(k), ..., λ N-1-L (k) is expressed in the form of unknown quantities;

[0028] The Kaczmarz algorithm is used to iteratively solve the iterative equations for the nodes corresponding to the non-overloaded lines and the nodes corresponding to the overloaded lines, obtaining λ1(k), λ2(k), ..., λ N-1-L The value of (k);

[0029] Let λ1(k), λ2(k), ..., λ N-1-L Substituting the value of (k) into the explicit function generates the second phase value of N-1-L unknowns;

[0030] Calculate the phase error between the first phase value and the second phase value, and repeat the above steps until the phase error reaches the preset convergence condition.

[0031] This invention also discloses a fully distributed DC optimal power flow device, comprising:

[0032] The economic scheduling unit of the consensus algorithm is used to solve for the marginal cost λ of any node i in the system using the consensus algorithm. i and its node active power injection P i A decentralized economic dispatch model is established, and node phase decentralized calculation equations are set up to determine the overloaded lines of the power system.

[0033] The DC optimal power flow model derivation unit is used to establish a Lagrange multiplier method model of a centralized DC optimal power flow model with the goal of minimizing power generation cost, and to generate the optimization equation set of the Lagrange multiplier method model.

[0034] The distributed DC optimal power flow model generation unit is used to perform iterative processing based on the node phase dispersion calculation equations and the optimization equation set to generate a fully distributed DC optimal power flow model. The iterative processing includes decentralized iterative processing of the node equations, iterative processing of nodes corresponding to non-overloaded lines, and iterative processing of nodes corresponding to overloaded lines.

[0035] The present invention also discloses a fully distributed DC optimal power flow device, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor executes the computer program to implement a fully distributed DC optimal power flow method as described above.

[0036] The present invention also discloses a readable storage medium storing a computer program that can be executed by a processor of the device in which the storage medium is located, to implement a fully distributed DC optimal power flow method as described in any of the above claims.

[0037] In summary, this embodiment provides a fully distributed DC optimal power flow method, apparatus, equipment, and medium. First, based on the economic dispatch model of the traditional consensus algorithm, a node phase distributed calculation method is established, and a distributed calculation method for active power flow of transmission lines is given, thereby identifying overloaded lines in the system. Second, a centralized DC optimal power flow Lagrange optimal model is proposed, and the optimal equation is derived. Third, based on this, combined with an improved traditional consensus algorithm, a fully distributed DC optimal power flow model and its solution method are realized. Finally, simulation verification using a real system as an example demonstrates the effectiveness of the proposed method. This solves the problem that existing distributed economic dispatch methods centered on DC optimal power flow cannot address the issue of transmission line overload, thus failing to achieve centralized DC optimal power flow and affecting the decentralized management of power sources in the power system. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating a fully distributed DC optimal power flow method provided in an embodiment of the present invention.

[0039] Figure 2 This is a schematic diagram of an actual power system provided in an embodiment of the present invention.

[0040] Figure 3 This is a schematic diagram of the λ values ​​of each node calculated by formula (1) of a fully distributed DC optimal power flow method provided in an embodiment of the present invention.

[0041] Figure 4 This is a schematic diagram of the active power (per unit value) of each generator calculated by formula (1) of a fully distributed DC optimal power flow method provided in an embodiment of the present invention.

[0042] Figure 5 This is a schematic diagram illustrating the node phase iteration process of an algorithm for a fully distributed DC optimal power flow method provided in an embodiment of the present invention.

[0043] Figure 6(a) illustrates the algorithm for calculating λ and μ at five nodes using a fully distributed DC optimal power flow method provided in this embodiment of the invention.23 A schematic diagram showing the convergence of the first 100 iterations.

[0044] Figure 6(b) illustrates the algorithm for calculating λ and μ at five nodes using a fully distributed DC optimal power flow method provided in this embodiment of the invention. 23 A schematic diagram showing the convergence of the first 300 iterations.

[0045] Figure 6(c) illustrates the algorithm for calculating λ and μ at five nodes using a fully distributed DC optimal power flow method provided in this embodiment of the invention. 23 A schematic diagram showing the convergence of the first 600 iterations.

[0046] Figure 7 This is a schematic diagram of a fully distributed DC optimal power flow device provided in an embodiment of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0049] Please see Figure 1 The first embodiment of the present invention provides a fully distributed DC optimal power flow method, which can be executed by a fully distributed DC optimal power flow device (hereinafter referred to as a distributed device), specifically by one or more processors within the distributed device, to implement the following steps:

[0050] S101, based on the consensus algorithm to solve for the marginal cost λ of any node i in the system. i and its node active power injection P i A decentralized economic dispatch model is established, and node phase decentralized calculation equations are set up to determine the overloaded lines of the power system.

[0051] Specifically, step S101 includes: calculating the marginal cost λ of any node i in the system using a consensus algorithm. iand its node active power injection P i The decentralized economic scheduling model generates the active power injection of nodes. Among them, the active power injection P at DC power flow node i i Equal to the power flow P of the associated transmission line ij The sum of θ i θ represents the phase of node i. j Represents the phase of node j, x ij Indicates transmission line l ij Reactance at two endpoints i and j;

[0052] Expand and rearrange the active power injection of the node to generate the phase iterative solution equation for node i;

[0053] The phase iterative solution equation is improved to generate the node phase dispersion calculation equation.

[0054] In practical applications, power system energy management systems may experience overload on transmission lines. Existing decentralized economic dispatch methods based on optimal DC power flow cannot address the overload problem on transmission lines, thus failing to achieve centralized optimal DC power flow and consequently affecting the decentralized management of power sources in the power system.

[0055] Specifically, in this embodiment, the traditional consensus algorithm is first subjected to economic scheduling to solve for the marginal cost λ of any node i in the system. i and its node active power injection P i The decentralized economic scheduling model is Where, λ i (k+1) represents λ i The value of the (k+1)th iteration, N i Let a represent the set of adjacent nodes of node i. ij λ represents the element in the i-th row and j-th column of an adjacency matrix whose row sum is 1. j (k) represents λ j (Marginal cost of node j) The value of the kth iteration, ε i Represents a small positive number, controlling the iteration speed and accuracy, ΔP i (k) represents the active power deviation of node i in the k-th iteration, P i (k+1) represents the active power deviation of node i in the (k+1)th iteration, ΔP j (k) represents the active power deviation of node j in the k-th iteration, P i (k) represents the active power of node i in the k-th iteration, P i (k+1) represents the active power of node i in the (k+1)th iteration. and These are the minimum and maximum values ​​of the active power of the generator at node i, respectively. Formula (1) is actually a DC optimal power flow calculation without considering line safety constraints. Therefore, according to the DC power flow, the active power injection P at node i is... i Equal to the power flow P of the associated transmission line ij The sum of Where, θ i θ represents the phase of node i. j Represents the phase of node j, x ij Indicates transmission line l ij The reactance at both ends (nodes i and j). Expanding and rearranging equation (2), we can express it as an iterative solution for the phase at node i. Where, θ i (k+1) represents the (k+1)th iteration value of the phase of node i, P i* This represents the nodal injection active power result obtained by formula (1), θ j (k) represents θ j The k-th iteration value; Formula (3) shows that when the active power injection P of each node of the system is obtained according to Formula (1), i* Then, the phase of node i can be solved iteratively by using the phases of its neighboring nodes. According to formula (3), the phase of each node in the system can be solved iteratively. This determines whether the transmission line associated with the phase is overloaded. If there is no overloaded line, the result of formula (1) is the economic dispatch result of the system. If there is an overloaded line, since formula (1) cannot solve the economic dispatch of transmission line overload, it needs to be improved and the calculation continues.

[0056] S102, Establish a Lagrange multiplier method model for a centralized DC optimal power flow model with the goal of minimizing power generation cost, and generate the optimization equation set of the Lagrange multiplier method model;

[0057] Specifically, step S102 includes: establishing a Lagrange multiplier method model for a centralized DC optimal power flow model with the objective of minimizing power generation costs. Where, λ i (i = 1, 2, ..., N) represents the Lagrange multiplier of the active power injection constraint at node i, μ ij Indicates line l ij (With nodes i and j at both ends) The Lagrange multiplier of active power transmission constraints, line l ij (When the two endpoints are i and j) when active transmission exceeds the limit, μ ij >0, otherwise, μ ij =0;

[0058] The Lagrange multiplier method model is subjected to partial derivatives and transformations to generate a system of optimal equations, wherein the system of optimal equations is based on λ. i (i = 1, 2, ..., N), P Gi (i = 1, 2, ..., N) G ), θ i (i = 1, 2, ..., N-1), μ ij (l ij =1, 2, ..., l; ij∈Π) for a total of N+N G +N-1+L=N G A system of optimization equations with +2N+L-1 unknowns.

[0059] Specifically, in this embodiment, the centralized DC optimal power flow model with the objective of minimizing power generation cost is as follows: Where, N G α represents the total number of generators. i ,β i γ i Let P represent the coefficients of the quadratic, linear, and constant terms of the cost function of generator i, respectively. Gi P represents the active power output of generator i. Di θ represents the active load at node i. i θ represents the phase of node i. j Indicates the phase of node j; x ij Indicates line l ij The reactance of (nodes i and j at both ends), N i N represents the total number of nodes directly connected to node i, and N represents the total number of nodes in the system. This represents the minimum active power output of generator i. This represents the maximum active power output of generator i. Indicates line l ij The active power limit (with nodes i and j at both ends).

[0060] In this embodiment, in order to obtain the optimal solution of formula (5), its Lagrange multiplier method model is established. Where, λ i (i = 1, 2, ..., N) represents the Lagrange multiplier of the active power injection constraint at node i, μ ij Indicates line l ij (With nodes i and j at both ends) The Lagrange multiplier of active power transmission constraints, line l ij (When the two endpoints are i and j) when active transmission exceeds the limit, μ ij >0, otherwise, μ ij =0. The condition for the optimal solution of formula (6) is to take the partial derivative with respect to each variable. The result of the partial derivative is shown in formula (7). In formula (7), the second equation is obtained by taking the partial derivative with the node phase as a variable, while the phase of the slack node is a constant, so there are N-1 equations. The second equation in formula (7) is expressed in the form of overloaded line and non-overloaded line. Where L represents the total number of overloaded lines. For simplicity, it is calculated based on a maximum of 2L nodes, meaning that overloaded lines are not connected. If overloaded lines are interconnected, the number of nodes is less than 2L. The complexity of the description increases depending on the connection situation, such as two overloaded lines connected or multiple overloaded lines connected. Regardless of the situation, the number of variables and equations remains consistent with the subsequent correspondence. S represents the set of non-overloaded line nodes (excluding balanced nodes), and Π represents the set of overloaded line nodes (excluding balanced nodes).

[0061] Combining formulas (7) and (8), we establish a system based on λ. i (i = 1, 2, ..., N), P Gi (i = 1, 2, ..., N) G ), θ i (i = 1, 2, ..., N-1), μ ij (l ij =1, 2, ..., L; i, j∈П) for a total of N+N G +N-1+L=N G A system of optimization equations with +2N+L-1 unknowns The total number of equations in formula (9) is N. G +N-2L-1+2L+L+N=N G +2N+L-1, the total number of equations is the same as the total number of unknowns, so it can be solved.

[0062] S103, perform iterative processing based on the node phase dispersion calculation equation and the optimization equation set to generate a fully distributed DC optimal power flow model. The iterative processing includes dispersion iterative processing of the node equations, iterative processing of nodes corresponding to non-overloaded lines, and iterative processing of nodes corresponding to overloaded lines.

[0063] Specifically, step S103 includes: performing a distributed iterative solution process on the node equations of the optimization equation set according to the node phase dispersion calculation equation to generate the corresponding explicit function;

[0064] Based on the node phase dispersion calculation equation, the corresponding nodes of the non-overloaded line are iteratively processed to generate the iterative equations for the corresponding nodes of the non-overloaded line.

[0065] Based on the node phase dispersion calculation equation, the nodes corresponding to the overloaded line in the optimization equation set are iteratively processed to generate the iterative equations for the nodes corresponding to the overloaded line.

[0066] Distributed iterative processing is performed on the explicit function, the iterative equation of the node corresponding to the non-overloaded line, and the iterative equation of the node corresponding to the overloaded line to solve the node phase and generate a fully distributed DC optimal power flow model. Specifically, the variable k = 0 is set, and N-1-L unknown phase initial values ​​are given.

[0067] Based on the explicit function, the first phase value of the N-1-L unknowns in the first iteration is solved, where the phase value is expressed as λ1(k), λ2(k), ..., λ N-1-L (k) form expression;

[0068] The iterative equations for the corresponding nodes of the non-overloaded lines are solved iteratively, and the iterative results are denoted as λ1(k), λ2(k), ..., λ N-1-L (k) is expressed in the form of unknown quantities;

[0069] The Kaczmarz algorithm is used to iteratively solve the iterative equations for the nodes corresponding to the non-overloaded lines and the nodes corresponding to the overloaded lines, obtaining λ1(k), λ2(k), ..., λ N-1-L The value of (k);

[0070] Let λ1(k), λ2(k), ..., λ N-1-L Substituting the value of (k) into the explicit function generates the second phase value of N-1-L unknowns;

[0071] Calculate the phase error between the first phase value and the second phase value, and repeat the above steps until the phase error reaches the preset convergence condition.

[0072] Specifically, in this embodiment, firstly, the node equations are solved using a distributed iterative method. Let the total number of overloaded lines obtained by the power system through formula (4) be L, and let the node pairs corresponding to these L overloaded lines be {(i1, j1), (i2, j2), ..., (i L j L For any pair of nodes (i) s j s Assuming the power flow originates from node i s Flow to node j s It can be obtained from formula (4); according to the first equation in formula (9), the node has the following relationship with the phase at both ends. Among them, (i s j s ) represents the two end nodes corresponding to the s-th overloaded line. and Each represents its phase. This indicates the reactance of the line. This represents the maximum known active power flow allowed for the line. Formula (10) shows that for an overloaded line, the unknown phases at both ends of the line can be represented by any one of them, that is, one of the two unknown phases can be solved. When there are L overloaded lines in the system, then the corresponding 2L unknown phases can be solved by L. Therefore, for the power system with N-1 unknown phases in the second equation of formula (9), there are a total of N-1-L unknown phases. Among them, the slack node is set as node N, and its phase is 0, which is known. These N-1-L unknown phases can be solved by N-1-L equations. Let's assume they are the first N-1-L equations, and their distributed iteration form is: , where, λ1(k), λ2(k),..., λ N-1-L (k) represent λ1, λ2, ..., λ respectively. N-1-L The value of the kth iteration, α i ,β i (i = 1, 2, ..., N-1-L) represent the coefficients of the first and second terms of the quadratic cost function of the generator at node i, respectively. b represents the active load of node i. ij (i = 1, 2, ..., N-1-L) represents the line reactance between node i and its neighboring nodes. Since the last node N is a slack node with a phase of 0, the result of multiplying it is 0, so it is not written out. This represents the k-th iteration value of the phase of N-1-L unknown quantities. For ease of description, the phases of the first N-1-2L nodes and the first node of the L overloaded lines are expressed as unknown quantities, f1~f N This represents the explicit function that can be formed. In order to solve the N-1-L unknown phases as the main iteration and the nodal marginal price as the sub-iteration, the N-1-L unknown phases in formula (12) are expressed as λ1(k), λ2(k), ..., λ N-1-L explicit function of (k) Among them, g1~g N-1-L Let λ1(k), λ2(k), ..., λ be the explicit functions obtained by formula (12). N-1-L (k) is expressed in the form of an unknown quantity.

[0073] Formula (11) only expresses N-1-L of the second equation in Formula (9). The remaining L+1 equations are also functions of the phases of the N-1-L nodal unknowns, and the phases of these N-1-L unknowns can be expressed by formula (12) λ1(k), λ2(k), ..., λ N-1-L (k) expression Among them, h N-L h N-L+1h N This represents the explicit function obtained by formula (12), which is actually expressed as λ1(k), λ2(k), ..., λ N-1-L (k) is expressed in the form of unknowns. From formulas (12) and (13), it can be seen that if λ1(k), λ2(k), ..., λ can be solved... N-1-L (k), then λ N-L (k), λ N-L+1 (k), ..., λ N (k) can be solved for. Alternatively, it can be solved, and this can be used to continue iteratively. Below are given λ1(k), λ2(k), ..., λ N-1-L (k) Distributed iterative solution method: Since this iterative solution belongs to a sub-iteration, it is a step in the main iterative solution of the unknown phase at the corresponding node, and is therefore distinguished from the main iterative expression. Hereinafter, t is used as the iteration marker. Furthermore, in the sub-iteration process, to avoid non-convergence, the Kaczmarz algorithm is used for computation.

[0074] Secondly, the iterative equations for the nodes corresponding to the non-overloaded line are derived. From the third equation in formula (9), a total of N-1-2L iterative equations for the nodes at both ends of the non-overloaded line can be obtained. Compared with the traditional consensus algorithm of formula (1), formula (14) directly gives the adjacency matrix element values. It eliminates the need for setting element values ​​where the row sum of a traditional adjacency matrix is ​​1, while simultaneously providing the numerical value of the node phase.

[0075] Finally, the iterative equations for the nodes corresponding to the overloaded lines are derived. For L overloaded lines, the nodes at both ends satisfy the fourth equation in formula (9), and 2L iterative equations can be established. Let nodes i and j be the nodes at both ends of an overloaded line. Since the overloaded line also has the Lagrange unknown μ, ij It also requires iterative solution, therefore, for node i, the iterative equation is: Where, μ im (t+1) represents the (t+1)th iteration value of the Lagrange unknown of the overloaded line formed by nodes i and m, x im This represents the reactance value of the line. If the line formed by node i and node m is a non-overload line, then this value is 0. λ m (t) represents the t-th iteration value of the marginal price at node m. For node j, the iteration equation is: Where, N j μ represents the total number of neighboring nodes of node j. jm(t+1) represents the (t+1)th iteration value of the Lagrange unknown of the overloaded line formed by node j and node m, x jm This represents the reactance value of the line. If the line formed by node j and node m is a non-overload line, then this value is 0. Combining formulas (14) to (16), it can be seen that the total number of equations is N-2L-1+2L=N-1, and the number of unknowns is N-1-L: λ1(t), λ2(t), ..., λ N-1-L (t) and L μ ij There are N-1 equations (t), and the total number of equations is equal to the total number of unknowns, which can be solved iteratively.

[0076] In this embodiment, the solution process, namely the distributed iterative steps of formulas (12) to (16), is as follows: Step 1, set k = 0, and give initial values ​​for the phases of N-1-L unknowns, generally set as zero vectors; Step 2, according to formula (12), solve for the phase values ​​of the N-1-L unknowns in the first iteration, which are λ1(k), λ2(k), ..., λ N-1-L (k) Form expression; Step 3, according to formula (13), iteratively solve for λ. N-L (k), λ N-L+1 (k), ..., λ N (k), which is actually represented by λ1(k), λ2(k), ..., λ N-1-L (k) is expressed in the form of unknown quantity; Step 4, the Kaczmarz algorithm is used to iteratively solve formulas (14) to (16). The convergence condition is set to the minimum value of the numerical error between two consecutive iterations. If it does not converge, the iteration continues. After convergence, λ1(k), λ2(k), ..., λ N-1-L (k) values; Step 5, set λ1(k), λ2(k), ..., λ N-1-L (k) Substitute the numerical value into formula (12) to obtain N-1-L unknown phase values. The convergence condition is based on the fact that the phase numerical error between the two consecutive phase values ​​reaches a certain small value. If it does not converge, set k = k + 1 and go to step two. If it converges, output the result.

[0077] In this embodiment, the node phase is solved using the method described above. and λ1(k), λ2(k),...,λ N-1-L (k) and λ N-L (k), λ N-L+1 (k), ..., λ N After (k), the active power output of each node generator can be solved by the fifth equation in formula (9).

[0078] In this embodiment, the following is adopted: Figure 2The actual power system shown is simulated using the fully distributed DC optimal power flow method. The generator cost function parameters, generator limits, and load active power (per unit value) are shown in Table 1.

[0079] Table 1:

[0080]

[0081] The transmission line parameters (per unit value) are shown in Table 2.

[0082] Table 2:

[0083]

[0084]

[0085] The algorithm was implemented using Matlab programming and employed nonlinear programming and Matpower software. Figure 2 The system shown performs traditional centralized DC optimal power flow calculations and is compared with the algorithm in the fully distributed DC optimal power flow method.

[0086] According to formula (1) Figure 2 The system shown was subjected to economic dispatch calculations, and the λ values ​​of each node and the active power of the generators (per unit value) were obtained, as shown in Table 3.

[0087] Table 3:

[0088]

[0089] The λ iteration of each node is as follows Figure 3 As shown, the iterative process of generator active power is as follows: Figure 4 As shown in Table 4, the active power flow (per unit value) of the line is as follows.

[0090] Table 4:

[0091]

[0092] The negative sign indicates the opposite direction. As shown in Table 4, the active power flow of transmission line 2-3 exceeds the limit of 5, as shown in Table 2. Therefore, the algorithm in the fully distributed DC optimal power flow method needs to be used to continue the calculation.

[0093] Based on the overload of line 2-3, L = 1. There are N-1-L = 3 unknown node phases in the system, namely θ1, θ3, and θ4. The phase of node 2 can be expressed by the phase of node 3. At this point, there are N-1-L=3 equations in formula (12), and the phase iteration equations for the unknowns θ1, θ3, and θ4 are functions of λ1, λ2, and λ3; formula (13) has L+1=2 equations, and λ4 and λ5 are functions of λ1, λ2, and λ3. In the system, nodes 1 and 4 are the nodes corresponding to the non-overloaded lines, and are calculated according to formula (14), resulting in 2 equations. Nodes 2 and 3 are the nodes corresponding to the overloaded lines, and are calculated according to formulas (15) to (16), resulting in 2 equations. The λ4 and λ5 involved in these 4 equations can be replaced by their adjacent information, i.e., formula (13), so only λ1, λ2, λ3, and μ are considered. 23 There are 4 unknowns, which can be solved iteratively. Following the solution process described above, let the initial values ​​of the unknown phases be [θ1, θ3, θ4] = [0 0 0], and let the iterative convergence errors of the phases θ1, θ3, and θ4 be λ1, λ2, λ3, and μ. 23 The iterative convergence error is set to 10. -9 The node phase values ​​are shown in Table 5. Figure 5 As shown in the figure, the horizontal axis represents the number of iterations, and the vertical axis represents the phase value of each node. The comparison of the node marginal cost results calculated by the algorithm of the fully distributed DC optimal power flow method, the nonlinear programming method, and the Matpower method is shown in Table 6 and Figure 6.

[0094] Table 6:

[0095]

[0096] The active power of each node generator, i.e., the active power of the node generators calculated by the algorithm of the fully distributed DC optimal power flow method, the nonlinear programming method, and the Matpower method, is compared in Table 7.

[0097] Table 7:

[0098]

[0099] Since the iteration convergence error is set to 10 -9 After 2392 iterations, the convergence was achieved. Figure 6(a) shows the results of the first 100 iterations, Figure 6(b) shows the results of the first 300 iterations, and Figure 6(c) shows the results of the first 600 iterations. Figure 5 The lowest curve is μ 23 The iterative curves, the five curves above are the marginal cost convergence curves of the five nodes in Table 6.

[0100] In summary, given the large-scale integration of high-proportion renewable energy generation into the power system, and the decentralized management of various power sources due to factors such as profit, privacy, and security, it is necessary to study the distributed DC optimal power flow problem. The fully distributed DC optimal power flow method, based on a consensus algorithm, utilizes phase-distributed iterative solutions to obtain the active power flow of transmission lines and determine overload conditions. Furthermore, this method can disperse and obtain information such as marginal cost, generator active power, and phase at each node, and the results are consistent with those calculated by nonlinear programming. This addresses the problem that existing decentralized economic dispatch methods centered on DC optimal power flow cannot solve the problem of transmission line overload, thus failing to achieve centralized DC optimal power flow and consequently affecting the decentralized management of power sources in the power system.

[0101] Please see Figure 7 A second embodiment of the present invention provides a fully distributed DC optimal power flow device, comprising:

[0102] The consensus algorithm's economic scheduling unit 201 is used to solve for the marginal cost λ of any node i in the system using the consensus algorithm. i and its node active power injection P i A decentralized economic dispatch model is established, and node phase decentralized calculation equations are set up to determine the overloaded lines of the power system.

[0103] The DC optimal power flow model derivation unit 202 is used to establish a Lagrange multiplier method model of a centralized DC optimal power flow model with the goal of minimizing power generation cost, and to generate the optimal equation set of the Lagrange multiplier method model.

[0104] The distributed DC optimal power flow model generation unit 203 is used to perform iterative processing based on the node phase dispersion calculation equation and the optimization equation set to generate a fully distributed DC optimal power flow model. The iterative processing includes decentralized iterative processing of the node equations, iterative processing of nodes corresponding to non-overloaded lines, and iterative processing of nodes corresponding to overloaded lines.

[0105] A third embodiment of the present invention provides a fully distributed DC optimal power flow device, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements a fully distributed DC optimal power flow method as described in any of the above embodiments.

[0106] The fourth embodiment of the present invention provides a readable storage medium storing a computer program that can be executed by a processor of the device in which the storage medium is located, to implement a fully distributed DC optimal power flow method as described in any of the above embodiments.

[0107] Exemplary examples show that the computer program described in the third and fourth embodiments of the present invention can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in implementing a fully distributed DC optimal power flow device. For example, the apparatus described in the second embodiment of the present invention.

[0108] The processor referred to can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the fully distributed DC optimal power flow method, connecting various parts of the fully distributed DC optimal power flow method through various interfaces and lines.

[0109] The memory can be used to store the computer program and / or modules. The processor implements various functions of a fully distributed DC optimal power flow method by running or executing the computer program and / or modules stored in the memory and calling the data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, text conversion function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, text message data, etc.). In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital card (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0110] If the implemented module is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0111] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0112] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions that fall within the scope of the present invention are within the scope of protection of the present invention.

Claims

1. A fully distributed DC optimal power flow method, characterized in that, include: Based on the consensus algorithm to solve any node in the system marginal cost and its node active power injection A decentralized economic dispatch model is established, and node phase decentralized calculation equations are constructed to determine overloaded lines in the power system. The formula for the decentralized economic dispatch model is as follows: The equation for calculating the phase dispersion at nodes is as follows: The power flow of the transmission line is This allows for the determination of whether the transmission line associated with the phase is overloaded. express No. The value of the next iteration. Represents a node Set of adjacent nodes This represents the adjacency matrix with a row sum of 1. Line 1 Column elements, express The value of the kth iteration. Representing small positive numbers, controlling the iteration speed and precision. Represents a node No. Active power deviation in the next iteration Represents a node No. Active power deviation in the next iteration Indicates generator The first-order term of the cost function, Indicates generator The quadratic term of the cost function, and They are nodes The generator's active power is obtained by taking its minimum and maximum values. Represents a node No. Active power deviation in the next iteration Represents a node No. Active power in the next iteration Represents a node No. Active power in the next iteration Represents a node Phase 1 The value of the next iteration. Indicates transmission line Reactance, This represents the active power result of node injection obtained by formula (1). express The The value of the next iteration. Represents a node phase, Represents a node The phase; A Lagrange multiplier method model for a centralized DC optimal power flow model with the objective of minimizing power generation costs is established. The optimal equations of this Lagrange multiplier method model are generated, and the formulas for these optimal equations are as follows: , Indicates the line The active power limit, Represents the set of overloaded line nodes. Indicates generator Those who have made contributions Represents a node Active load, Indicates the total number of system nodes. Represents a node Lagrange multipliers with active injection constraints Indicates the total number of overloaded lines. Represents the set of non-overloaded line nodes. Indicates the line Lagrange multipliers with active transmission constraints Indicates the total number of generators; Based on the node phase dispersion calculation equations and the optimization equations, an iterative process is performed to generate a fully distributed DC optimal power flow model. The iterative process includes the dispersion iterative process of the node equations of the optimization equations, the iterative process of the nodes corresponding to non-overloaded lines, and the iterative process of the nodes corresponding to overloaded lines.

2. The fully distributed DC optimal power flow method according to claim 1, characterized in that, Based on the consensus algorithm to solve any node in the system marginal cost and its node active power injection The decentralized economic scheduling model establishes a node phase decentralized calculation equation, specifically as follows: Based on the consensus algorithm to solve any node in the system marginal cost and its node active power injection The decentralized economic scheduling model generates the active power injection of nodes. Among them, DC power flow nodes Active power injection Equal to the power flow of the associated transmission lines sum; Expand and rearrange the active power injection of the nodes to generate nodes. The phase iterative solution equation; The phase iterative solution equation is improved to generate the node phase dispersion calculation equation.

3. The fully distributed DC optimal power flow method according to claim 1, characterized in that, The optimal power flow model for centralized DC transmission with the goal of minimizing power generation costs is as follows: , where represents the generator The coefficient of the constant term in the cost function represents the generator. Minimum work output Indicates generator Maximum active power output.

4. The fully distributed DC optimal power flow method according to claim 3, characterized in that, A Lagrange multiplier method model for a centralized DC optimal power flow model with the objective of minimizing power generation costs is established, and the optimal equation system of the Lagrange multiplier method model is generated, specifically as follows: Lagrange multiplier method model for establishing a centralized DC optimal power flow model with the objective of minimizing power generation cost. Among them, the line Active transmission exceeds the limit ,otherwise, ; The Lagrange multiplier method model is subjected to partial derivatives and transformations to generate a system of optimal equations, wherein the system of optimal equations is based on... , , , common A system of optimization equations with 1 unknown.

5. The fully distributed DC optimal power flow method according to claim 1, characterized in that, Based on the node phase dispersion calculation equations and the optimization equations, an iterative process is performed to generate a fully distributed DC optimal power flow model, specifically: Based on the node phase dispersion calculation equation, the node equations of the optimization equation set are solved by dispersion iteration to generate the corresponding explicit function. Based on the node phase dispersion calculation equation, the corresponding nodes of the non-overloaded line are iteratively processed to generate the iterative equations for the corresponding nodes of the non-overloaded line. Based on the node phase dispersion calculation equation, the nodes corresponding to the overloaded line in the optimization equation set are iteratively processed to generate the iterative equations for the nodes corresponding to the overloaded line. Distributed iterative processing is performed on the explicit function, the iterative equations of the nodes corresponding to the non-overloaded lines, and the iterative equations of the nodes corresponding to the overloaded lines to solve for the node phases and generate a fully distributed DC optimal power flow model.

6. The fully distributed DC optimal power flow method according to claim 5, characterized in that, Distributed iterative processing is performed on the explicit function, the iterative equations for the nodes corresponding to the non-overloaded lines, and the iterative equations for the nodes corresponding to the overloaded lines, specifically as follows: Let variables and given Initial values ​​of the phase of each unknown quantity; Based on the explicit function, the solution for the first iteration is obtained. The first phase value of an unknown quantity, wherein the phase value is... Formal expression; The iterative equations for the corresponding nodes of the non-overloaded lines are solved iteratively, and the iterative results are expressed as follows: Expressed in the form of unknown quantities; The Kaczmarz algorithm is used to iteratively solve the iterative equations for the nodes corresponding to the non-overloaded lines and the nodes corresponding to the overloaded lines, yielding the results. The value; The Substituting the numerical value into the explicit function generates The second phase value of an unknown quantity; Calculate the phase error between the first phase value and the second phase value, and repeat the above steps until the phase error reaches the preset convergence condition.

7. A fully distributed DC optimal power flow device, characterized in that, A method for implementing a fully distributed DC optimal power flow as described in any one of claims 1 to 6 includes: The economic scheduling unit of the consensus algorithm is used to solve the problem of any node in the system using the consensus algorithm. marginal cost and its node active power injection A decentralized economic dispatch model is established, and node phase decentralized calculation equations are set up to determine the overloaded lines of the power system. The DC optimal power flow model derivation unit is used to establish a Lagrange multiplier method model of a centralized DC optimal power flow model with the goal of minimizing power generation cost, and to generate the optimization equation set of the Lagrange multiplier method model. The distributed DC optimal power flow model generation unit is used to perform iterative processing based on the node phase dispersion calculation equation and the optimization equation set to generate a fully distributed DC optimal power flow model. The iterative processing includes decentralized iterative processing of the node equations, iterative processing of nodes corresponding to non-overloaded lines, and iterative processing of nodes corresponding to overloaded lines.

8. A fully distributed DC optimal power flow device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor, when executing the computer program, implements a fully distributed DC optimal power flow method as described in any one of claims 1 to 6.

9. A readable storage medium, characterized in that, The storage medium contains a computer program that can be executed by a processor of the device in which the storage medium resides, to implement a fully distributed DC optimal power flow method as described in any one of claims 1 to 6.

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