Power distribution system voltage / reactive power optimization method and device based on alternating direction multiplier method
By decomposing the voltage/reactive power optimization model of the power distribution system into two optimization modules based on the ADMM method and combining the penalty parameter adjustment, the problem of the inability to quickly converge to the global optimum in the existing technology is solved, and fast and efficient voltage/reactive power optimization is achieved.
Patent Information
- Application Number
- CN202211719739.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-12-30
- Publication Date
- 2026-02-03
- Estimated Expiration
- 2042-12-30
AI Technical Summary
Existing voltage/reactive power optimization methods for power distribution systems cannot guarantee a globally optimal solution within a finite time, and existing methods cannot effectively solve mixed-integer nonlinear nonconvex optimization problems.
The voltage/reactive power optimization model is decomposed into two optimization modules using the alternating direction multiplier method (ADMM). Combined with the response penalty parameter adjustment method, the solution is iteratively solved to ensure convergence and the quality of the optimization results.
It enables rapid convergence to the global optimum in most power distribution systems with discrete/integer devices, improving the efficiency and accuracy of voltage/reactive power optimization.
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Figure CN115986749B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of voltage / reactive power optimization in power distribution systems, and more specifically, to a method and apparatus for voltage / reactive power optimization in power distribution systems based on the alternating direction multiplier method. Background Technology
[0002] In power distribution systems, on-load tap changers (OLTCs) and controlled capacitor banks (SCBs) are typically used to regulate voltage levels and improve reactive power flow. OLTCs are voltage regulators connecting the main substation and distribution lines, while controlled capacitor banks are distributed on the load side for local compensation. The goal of voltage / reactive power optimization is to reduce distribution line losses and maintain voltage distribution within a reasonable range under a series of physical and operational constraints. These constraints include permissible limits for voltage and power flow, power balance, and the operating curves of controllable equipment. The voltage / reactive power optimization problem mixes continuous and discrete variables. The voltage magnitude and phase angle at each node in the system are continuous variables, while the on-load tap changer ratio and capacitor bank switching are discrete variables. Furthermore, the voltage / reactive power optimization model is based on the optimal power flow model and inherently possesses nonlinearity and nonconvexity. Therefore, the voltage / reactive power optimization model is a mixed-integer nonlinear nonconvex optimization problem (MINLP). Nonconvexity implies the possibility of multiple local solutions; for such problems, there is currently no method that can guarantee global optimum within a finite time.
[0003] Currently, there are three main methods for solving the voltage / reactive power optimization problem: (1) relaxing / approximating the power flow model of the distribution network; (2) convexifying the optimization space of the voltage / reactive power problem; and (3) using heuristic or intelligent optimization methods. Although some of these methods guarantee the convergence of the improved voltage / reactive power optimization model, none of them can guarantee that the result is the global optimal solution of the initial general voltage / reactive power optimization model. Summary of the Invention
[0004] The technical problem to be solved by this invention is to provide a voltage / reactive power optimization method and device for power distribution systems based on the Alternating Multiplier Method (ADMM). This method can decompose the generalized voltage / reactive power optimization model into two optimization modules and solve them iteratively in a cascaded manner until convergence. It considers OLTCs and SCBs and is applicable to most voltage / reactive power controllable devices with discrete / integer devices. Furthermore, it embeds a response-based penalty parameter adjustment method into the ADMM method to ensure convergence while maintaining the quality of the optimization results.
[0005] The technical solution adopted by this invention to solve its technical problem is: to construct a voltage / reactive power optimization method for power distribution systems based on the alternating direction multiplier method, including the following steps:
[0006] Step 1: Establish mathematical models of the power distribution system components to obtain the voltage / reactive power optimization model of the power distribution system;
[0007] Step 2: Based on the mathematical model of the power distribution system components established in Step 1, and the voltage / reactive power optimization model of the power distribution system formed, a generalized voltage / reactive power optimization model of the power distribution system is formed.
[0008] Step 3: Based on the generalized distribution system voltage / reactive power optimization model established in Step 2, the ADMM-based optimization method is used to iteratively solve the problem and obtain the results of the ADMM-based distribution system voltage / reactive power optimization method.
[0009] According to the above scheme, the first step includes:
[0010] (1) Establish mathematical models of power distribution system components: including mathematical models of OLTCs, SCBs, and power flow of distribution lines;
[0011] (2) Form a voltage / reactive power optimization model for the power distribution system, including the objective function and constraints for voltage / reactive power optimization.
[0012] According to the above scheme, in the first step, for a power distribution system with N nodes and radial or mesh power distribution lines L, the π-type equivalent circuit model is based on the series impedance z. l and total charging current b l cp Composition, used to model arbitrary two-port devices, including transformers and power distribution lines;
[0013] The OLTC modeling method is as follows: A transformer k is installed on the power distribution line l between nodes i and j. Transformer k is equipped with an on-load tap changer. On the secondary side of the transformer, there is a virtual node m and a virtual variable V. s To correlate the voltage and power flow relationships between OLTCs and their associated distribution lines, assuming an ideal transformer with no power loss between its terminal nodes i and m, the voltage ratio between the secondary side m and the primary side i is equal to the transformer turns ratio t, and the voltage angles of the two nodes are the same, therefore, the secondary voltage is calculated as follows:
[0014]
[0015] in,
[0016]
[0017] In the formula: V i t is the vector representing the voltage magnitude at node i; k The tap ratio of the current discrete OLTCs for the k-th transformer is defined as 90% to 110% of the rated voltage level, with an incremental variation of 5 / 8%.t k For t k The minimum discrete value; For OLTCs, the tap position is indicated.
[0018] Furthermore, the power conservation of an ideal transformer satisfies the following constraints:
[0019] θ m =θ i ,P im =P mj Q im =Q mj
[0020] The SCBs modeling method is as follows: mathematically, it is described as a pure capacitor power injection source, and the actual injected capacitor reactive power is calculated as follows:
[0021]
[0022] in,
[0023]
[0024] In the formula: Let i be the total reactive power injected into the capacitor bank at node i. and These are the minimum and maximum values, respectively. This refers to the k-th capacitor bank connected to the capacitor susceptance. for The minimum discrete value;
[0025] The power flow modeling method for distribution lines is as follows: This is achieved through the active power flow P between nodes i and j of the distribution line l. ij and the trend of no power Q ij The calculation is as follows:
[0026]
[0027] Where: g l Let b be the conductance of line l; l Let L be the susceptance of line l, and L be the set of all lines.
[0028] The active power loss of distribution line l is calculated as follows:
[0029]
[0030] If line l is configured with OLTC, then variable V will be... i Replace with in
[0031] According to the above scheme, the method for forming the voltage / reactive power optimization model of the power distribution system is as follows:
[0032] Forming the objective function: The main objective of voltage / reactive power optimization in the power distribution system is to minimize the active power loss of the distribution lines and maintain an appropriate node voltage distribution;
[0033]
[0034] Adding a minimum load term to the objective function results in:
[0035]
[0036] Constraints are established: in addition to the limitations of OLTCs and SCBs, operational and safety constraints are also considered;
[0037] First, establish node power balance constraints:
[0038]
[0039] To avoid confusion, DGs are not considered. Indicates that i is a node in set N excluding the slack node; the specified slack node is a substation node; when the load node's power demand... Modeling it as a voltage-sensitive function, without considering fixed values, is...
[0040]
[0041] in, V represents the active and reactive power demand of node i at rated voltage and frequency, respectively. n k is the system rated voltage. p ,k q For a predefined voltage index;
[0042] In addition, operational and safety limitations are imposed on voltage magnitude, phase angle, and maximum transmission capacity of distribution lines, as follows:
[0043]
[0044] According to the above scheme, in step two:
[0045] Let h represent the "coupling constraints" between two sets of integer variables x and z and continuous variables. The vector of these coupling constraints is...
[0046]
[0047] The generalized voltage / reactive power optimization problem for power distribution systems is as follows:
[0048]
[0049] Satisfying h(x,z)=0:λ
[0050] in, Let x represent the feasible region formed by the constraints containing x in the first step, and Let z be the feasible region formed by the z-constraint, and let z be the dual variable. These are the Lagrange multiplier vectors associated with the coupling constraints.
[0051] According to the above scheme, the third step further includes:
[0052] (1) Construct the Lagrangian function of the generalized power distribution system voltage / reactive power optimization model. The Lagrangian function is:
[0053] L(x,z,λ)=f(x)+λ T h(x,z)
[0054] In the formula, λ is the Lagrange multiplier vector of the coupling constraint, i.e. the dual variable, x represents the vector of continuous variables, and z represents the vector of integer / 0-1 variables;
[0055] Furthermore, the coupling constraint vector h(x,z) is used as a consistently positive penalty term to punish deviations from the optimal solution:
[0056]
[0057] In the formula, For a predefined penalty parameter, and Let be the square 2-norm of a vector;
[0058] Updating the augmented Lagrange function using the scaled Lagrange multipliers η = λ / ρ is equivalently rewritten as:
[0059]
[0060] To develop an ADMM-based voltage / reactive power optimization method for distribution systems, the generalized voltage / reactive power optimization problem for distribution systems is decomposed into two subproblems: the first subproblem solves for continuous variable x, while treating integer or 0-1 variable z as a constant; the second subproblem is the opposite. The augmented Lagrangian function is used as the objective function for both the first and second subproblems, ensuring that the solver satisfies coupling constraints to achieve optimality.
[0061] (2) Construct the first subproblem. The first subproblem uses the continuous variable x as the decision variable, while treating the integer / 0-1 variables of z and the η multiplier as constants, forming a nonlinear optimization problem (NLP). The mature interior-point method is directly called to solve it. This indicates that the variable is considered given and not optimized;
[0062]
[0063] The constraints defined in the first step are satisfied;
[0064] (3) Construct a second subproblem, which optimizes the relaxation of the repeating terms of the integer / 0-1 variable z, treats the continuous variable x and the η multiplier as constants, and the integer / 0-1 variable z is relaxed between their upper and lower limits; when the optimization process terminates, the assigned z is rounded to the nearest integer value.
[0065]
[0066] satisfy:
[0067]
[0068] (4) Gauss-Seidel iterative solution: The Gauss-Seidel method is used to continuously execute the two optimization subproblems after decomposition, exchange the results, and update the joint dual variables, as shown in the following equation, where the superscript k indicates the iteration number. The iterative process continues until a feasible and sufficiently optimal solution is found:
[0069]
[0070] (5) Convergence condition test: Through preliminary feasibility test, a necessary and sufficient condition for the proposed ADMM-voltage / reactive power optimization method is obtained:
[0071]
[0072] This means that when the iteration process ends and k→∞, the coupling constraint must be satisfied to ensure the feasibility of the result;
[0073] Furthermore, the second convergence criterion observes the stationarity of the results for the second subproblem, ensuring that no better results are obtained.
[0074]
[0075] Therefore, the iterative process of the overall solution steps continues until a sufficiently optimal feasible result is assigned, and the following stopping criterion is used for verification:
[0076] Feasibility Remaining Verification:
[0077] ||r k+1 ||2=||η k+1 -η k ||2≤∈1
[0078] Stationarity residual test:
[0079] ||sk+1 ||2=||(z k+1 -z k )||2≤∈2
[0080] Where ∈1 and ∈2 are predefined thresholds, generally with a tolerance of less than 1×10. -6 .
[0081] According to the above scheme, the third step also includes setting up a device switching priority mechanism:
[0082] Two scaling factors, α and β, are used as priority vectors to control the influence weights of each term in the resulting multi-objective function.
[0083]
[0084] According to the above scheme, the third step also includes: using a responsive update of ρ so that the ADMM solution can achieve convergence while maintaining the quality of the results;
[0085] The ρ update principle is shown in the following formula:
[0086]
[0087] In the formula, ν and μ are adjustable constants, which are usually set as: ν = 2, μ = 10.
[0088] The present invention also provides a voltage / reactive power optimization device for a power distribution system based on the alternating direction multiplier method, comprising:
[0089] The mathematical model building module is used to build mathematical models of power distribution system components and obtain the voltage / reactive power optimization model of the power distribution system.
[0090] The voltage / reactive power optimization model building module is used to build a generalized voltage / reactive power optimization model for the distribution system based on the mathematical models of the distribution system components and the voltage / reactive power optimization model of the distribution system.
[0091] The solution module is used to iteratively solve the voltage / reactive power optimization model of the established generalized distribution system using the ADMM-based optimization method, and obtain the results of the ADMM-based distribution system voltage / reactive power optimization method.
[0092] The present invention also provides an electronic device, comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;
[0093] The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the method.
[0094] The voltage / reactive power optimization method for power distribution systems based on the alternating direction multiplier method of the present invention has the following beneficial effects:
[0095] 1. Compared with existing heuristic-based non-convex mixed-integer nonlinear optimization methods (branch and bound method) and mixed-integer second-order cone programming models based on the Disflow model, the voltage / reactive power optimization method for distribution systems based on ADMM of this invention can achieve better convergence speed and global optimal solution.
[0096] 2. Compared with the commonly used ADMM method, the ADMM of this invention adopts a response mechanism in the penalty parameter setting to adjust the penalty parameter and ensure the convergence of the solution. Attached Figure Description
[0097] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:
[0098] Figure 1 This is a π-equivalent circuit model diagram of the power distribution system voltage / reactive power optimization method based on the alternating direction multiplier method of this invention;
[0099] Figure 2 This is a power distribution line model diagram of a transformer equipped with on-load tap changers (OLTCs) based on the voltage / reactive power optimization method for power distribution systems based on the alternating direction multiplier method of this invention.
[0100] Figure 3 This is a diagram of the controllable capacitor bank (SCBs) model of the power distribution system voltage / reactive power optimization method based on the alternating direction multiplier method of this invention;
[0101] Figure 4 This is a complete ADMM-distribution system voltage / reactive power optimization iterative process diagram based on the alternating direction multiplier method of the present invention. Detailed Implementation
[0102] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0103] This invention presents a voltage / reactive power optimization method for distribution systems based on the alternating direction multiplier method. To solve the mixed-integer nonlinear voltage / reactive power optimization problem in distribution systems, a novel generalized decomposable voltage / reactive power optimization model is first established, including on-load tap changers (OLTCs) and controllable capacitor banks (SCBs). Then, according to the ADMM algorithm, the generalized voltage / reactive power optimization model is decomposed into two optimization modules, which are iteratively solved in a cascaded manner until convergence. Compared with existing heuristic-based nonconvex mixed-integer nonlinear optimization methods (branch and bound methods) and mixed-integer second-order cone programming models based on the Disflow model, this invention achieves better convergence speed and a better global optimum.
[0104] Example 1
[0105] This invention provides a voltage / reactive power optimization method for power distribution systems based on the alternating direction multiplier method, which specifically includes the following steps:
[0106] Step 1: Establish mathematical models of power distribution system components to form a voltage / reactive power optimization model for the power distribution system.
[0107] (1) Establish mathematical models of power distribution system components
[0108] like Figure 1 The figure illustrates the π-type equivalent circuit model used between nodes or terminals i and j. For a power distribution system with N nodes and radial or mesh distribution lines L, the π-type equivalent circuit model consists of series impedance z. l and total charging capacity It is used to model any two-port device (such as transformers, power distribution lines, etc.).
[0109] OLTC modeling: such as Figure 2 The diagram illustrates a power distribution line l between nodes i and j, equipped with a transformer k, which in turn is equipped with a tap changer. On the secondary side of the transformer, there is a virtual node m and a virtual variable V. s This is used to correlate the voltage and power flow relationships between OLTCs and their associated distribution lines. An ideal transformer is assumed to have no power losses between its terminal nodes i and m. The voltage ratio between the secondary side m and the primary side i is equal to the transformer turns ratio t, and the voltage angles at the two nodes are the same. Therefore, the secondary voltage can be calculated as:
[0110]
[0111] in,
[0112]
[0113] In the formula: V i t is the vector representing the voltage magnitude at node i;k The tap ratio of the current discrete OLTCs for the k-th transformer is defined as 90% to 110% of the rated voltage level, with an incremental variation of 5 / 8%. t k For t k The minimum discrete value; For OLTCs, the tap position is indicated.
[0114] Furthermore, the power conservation of an ideal transformer requires the following constraints to be satisfied:
[0115] θ m =θ i ,P im =P mj Q im =Q mj .
[0116] SCBs modeling: Mathematically described as a pure capacitive power injection source, such as Figure 3 The controllable capacitor bank model is shown below. The actual injected capacitor reactive power calculation is as follows:
[0117]
[0118] in,
[0119]
[0120] In the formula: Let i be the total reactive power injected into the capacitor bank at node i. and These are the minimum and maximum values, respectively. This refers to the k-th capacitor bank connected to the capacitor susceptance. for The smallest discrete value.
[0121] Power flow modeling of distribution lines: This involves analyzing the active power flow P between nodes i and j of a distribution line. ij and the trend of no power Q ij It can be calculated as:
[0122]
[0123] Where: g l Let b be the conductance of line l; l Let be the susceptance of line l.
[0124] The active power loss of distribution line l is calculated as follows:
[0125]
[0126] If line l is configured with OLTC, then only variable V needs to be changed. i Replace with in
[0127] (2) Forming a voltage / reactive power optimization model for the power distribution system
[0128] Distribution system voltage / reactive power optimization aims to reduce distribution line losses and maintain appropriate voltage distribution based on a range of physical and operational constraints, typically controlling OLTCs and SCBs. Therefore, the tap positions of OLTCs and SCBs (u...) t and u c These are control variables; they are integers or 0-1 variables. On the other hand, besides other relevant variables (V... s and Q c In addition, the voltage magnitude and phase angle of nodes in the power distribution system are also state variables, which are continuous variables.
[0129] Define variables: Let z represent a vector of integer / 0-1 variables, where,
[0130]
[0131] and,
[0132]
[0133] x represents a vector of continuous variables, where,
[0134]
[0135] and,
[0136] V = [V1,...,V] N ],θ=[θ1,...,θ N ]
[0137]
[0138] Therefore, the mathematical model for voltage / reactive power optimization is established as follows:
[0139] Forming the objective function: The main objective of voltage / reactive power optimization in power distribution systems is to minimize active power losses in power distribution lines and maintain appropriate node voltage distribution.
[0140]
[0141] In addition, to achieve the voltage reduction and energy-saving technology, a load minimization term was added to the objective function, namely:
[0142]
[0143] Establishing constraints: In addition to the limitations of OLTCs and SCBs, operational and safety constraints also need to be considered.
[0144] First, establish node power balance constraints:
[0145]
[0146] In this invention, DGs are not considered to prevent confusion; symbols This indicates that i can be a node in set N other than the slack node. The slack node is typically a substation node. When the load node's power demand... Modeling it as a voltage-sensitive function, rather than considering a fixed value, is as follows:
[0147]
[0148] in, These represent the active and reactive power demands of node i at rated voltage and frequency, respectively. n k is the system rated voltage. p ,k q This is a predefined voltage index.
[0149] In addition, operational and safety limitations are imposed on voltage magnitude, phase angle, and maximum transmission capacity of distribution lines, as follows:
[0150]
[0151] Step 2: Based on Step 1, develop a generalized voltage / reactive power optimization model for the power distribution system.
[0152] Let h represent the "coupling constraints" between two sets of integer variables x and z and continuous variables. The vector of these coupling constraints is:
[0153]
[0154] Therefore, the generalized voltage / reactive power optimization problem of power distribution systems can be rewritten in the following general form:
[0155]
[0156] Satisfying h(x,z)=0:λ
[0157] in Let x represent the feasible region formed by the constraints containing x in the first step, and It is the feasible region formed by the z-constraint. Dual variable It is a Lagrange multiplier vector related to coupling constraints.
[0158] Step 3: Based on the generalized power distribution system voltage / reactive power optimization model established in Step 2, the ADMM-based optimization method is used to iteratively solve the problem;
[0159] ADMM is a proven and efficient classical method for solving large-scale optimization problems with decomposable structures and coupling constraints. The algorithm decomposes a large-scale problem into a series of subproblems, each optimizing its own variables and yielding an optimization result, while simultaneously considering the variables of other problems (i.e., coupling constraints) as constant entities. Furthermore, the coupling constraints are transformed into penalized objective function terms for each subproblem, forcing the solver to satisfy these constraints.
[0160] (1) Constructing the Lagrangian function of the generalized voltage / reactive power optimization model of the power distribution system
[0161] Considering that the Lagrangian function of the generalized power distribution system voltage / reactive power optimization model is:
[0162] L(x,z,λ)=f(x)+λ T h(x,z)
[0163] In the formula, λ is the Lagrange multiplier vector of the coupling constraint (i.e., the dual variable).
[0164] Furthermore, the coupling constraint vector h(x,z) is used as a consistently positive penalty term to punish deviations from the optimal solution:
[0165]
[0166] In the formula, It is a predefined penalty parameter, and It is the square 2-norm of a vector.
[0167] Updating the augmented Lagrange function using the scaled Lagrange multipliers η = λ / ρ can be equivalently rewritten as:
[0168]
[0169] To develop an ADMM-based method for optimizing voltage / reactive power in distribution systems, the generalized voltage / reactive power optimization problem is decomposed into two subproblems. The first subproblem solves for the continuous variable x, while treating the integer or 0-1 variable z as a constant; the second subproblem follows the same principle. The augmented Lagrangian function is used as the objective function for these subproblems, requiring the solver to satisfy coupling constraints to reach optimality.
[0170] (2) Construct the first subproblem
[0171] The first subproblem uses the continuous variable x as the decision variable, while treating the integer / 0-1 variables of z and the η multiplier as constants, forming a nonlinear optimization problem (NLP). This problem can be solved directly using the mature interior-point method. This indicates that the variable is considered given and not optimized.
[0172]
[0173] Satisfy the constraints defined in the first step
[0174] (3) Construct the second subproblem
[0175] Similarly, the second subproblem optimizes by relaxing the repeating terms of the integer / 0-1 variable z, while treating the continuous variable x and the η multiplier as constants. The integer / 0-1 variable z is relaxed between its upper and lower bounds. When the optimization process terminates, the assigned z is rounded to the nearest integer value.
[0176]
[0177] satisfy:
[0178]
[0179] (4) Gauss-Seidel iterative solution
[0180] This invention employs the Gauss-Seidel method to continuously execute the two decomposed subproblems, exchange the results, and update the joint dual variables, as shown in the following equation. The superscript k indicates the iteration number. The iterative process continues until a feasible and sufficiently optimal solution is found.
[0181]
[0182] (5) Convergence condition test
[0183] Through preliminary feasibility testing, a necessary and sufficient condition for the proposed ADMM-voltage / reactive power optimization method was obtained:
[0184]
[0185] This means that when the iteration process ends and k→∞, the coupling constraint must be satisfied to ensure the feasibility of the result.
[0186] Furthermore, the second convergence criterion observes the stationarity of the results for the second subproblem, ensuring that no better results are obtained.
[0187]
[0188] Therefore, the iterative process of the overall solution steps continues until a sufficiently optimal feasible result is assigned. The following stopping criterion is used for verification:
[0189] Feasibility Remaining Verification:
[0190] ||r k+1 ||2=||η k+1 -η k ||2≤∈1
[0191] Stationarity residual test:
[0192] ||s k+1 ||2=||(z k+1 -z k )||2≤∈2
[0193] Where ∈1 and 2 are predefined thresholds, and their tolerance is generally less than 1×10. -6 .
[0194] Therefore, the complete iterative process for voltage / reactive power optimization of the distribution system based on ADMM is as shown in Algorithm 1. Figure 4 As shown.
[0195] The fourth step is to set up a priority mechanism for implementing device switching in order to avoid conflicts in the objective functions between the two subproblems.
[0196] The two subproblems established in the second step have multi-objective function terms and need to be optimized simultaneously, which may lead to solution conflicts and delay the convergence process. Therefore, in order to achieve smoother convergence, this invention introduces a device priority switching method, which helps to switch the priority order (i.e., the priority between OLTCs and SCBs) to prevent device cancellation during the optimization process.
[0197] This invention uses two proportional coefficients, α and β, as priority vectors to control the influence weights of each item in the obtained multi-objective function.
[0198]
[0199] Fifth, in order to ensure convergence and solution quality, a response-based penalty parameter ρ adjustment method was designed.
[0200] The convergence of the ADMM solution method established in the second step is related to the penalty parameter ρ. When the value of ρ is fixed, the ADMM solution method will get stuck in the infeasible region and fail to converge. Therefore, this invention adopts a responsive update of ρ, enabling the ADMM solution to achieve convergence while maintaining the quality of the results.
[0201] The ρ update principle is shown in the following formula:
[0202]
[0203] In the formula, ν and μ are adjustable constants, which are usually set as: ν = 2, μ = 10.
[0204] Step 6: Based on the data from the test system and case studies, output the results of the ADMM-based power distribution system voltage / reactive power optimization method of this invention.
[0205] Example 2
[0206] The present invention also provides a voltage / reactive power optimization device for a power distribution system based on the alternating direction multiplier method, comprising:
[0207] The mathematical model building module is used to build mathematical models of power distribution system components and obtain the voltage / reactive power optimization model of the power distribution system.
[0208] The voltage / reactive power optimization model building module is used to build a generalized voltage / reactive power optimization model for the distribution system based on the mathematical models of the distribution system components and the voltage / reactive power optimization model of the distribution system.
[0209] The solution module is used to iteratively solve the voltage / reactive power optimization model of the established generalized distribution system using the ADMM-based optimization method, and obtain the results of the ADMM-based distribution system voltage / reactive power optimization method.
[0210] Example 3
[0211] The present invention also provides an electronic device, comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;
[0212] The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the method.
[0213] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0214] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0215] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0216] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0217] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.
Claims
1. A voltage / reactive power optimization method for a power distribution system based on the alternating direction multiplier method, characterized in that, Includes the following steps: Step 1: Establish mathematical models of the power distribution system components to obtain the voltage / reactive power optimization model of the power distribution system; Step 2: Based on the mathematical model of the power distribution system components established in Step 1, and the voltage / reactive power optimization model of the power distribution system formed, a generalized voltage / reactive power optimization model of the power distribution system is formed. Step 3: Based on the generalized distribution system voltage / reactive power optimization model established in Step 2, the ADMM-based optimization method is used to iteratively solve the problem and obtain the results of the ADMM-based distribution system voltage / reactive power optimization method. The third step further includes: (1) Construct the Lagrangian function of the generalized power distribution system voltage / reactive power optimization model. The Lagrangian function is: L(x,z,λ)=f(x)+λ T h(x,z) In the formula, λ is the Lagrange multiplier vector of the coupling constraint, i.e. the dual variable, x represents the vector of continuous variables, and z represents the vector of integer / 0-1 variables; Furthermore, the coupling constraint vector h(x,z) is used as a consistently positive penalty term to punish deviations from the optimal solution: In the formula, For a predefined penalty parameter, and Let be the square 2-norm of a vector; Updating the augmented Lagrange function using the scaled Lagrange multipliers η = λ / ρ is equivalently rewritten as: To develop an ADMM-based voltage / reactive power optimization method for distribution systems, the generalized voltage / reactive power optimization problem for distribution systems is decomposed into two subproblems: the first subproblem solves for continuous variable x, while treating integer or 0-1 variable z as a constant; the second subproblem is the opposite. The augmented Lagrangian function is used as the objective function for both the first and second subproblems, ensuring that the solver satisfies coupling constraints to achieve optimality. (2) Construct the first subproblem. The first subproblem uses the continuous variable x as the decision variable, while treating the integer / 0-1 variables of z and the η multiplier as constants, forming a nonlinear optimization problem (NLP). The mature interior-point method is directly called to solve it. This indicates that the variable is considered given and not optimized; The constraints defined in the first step are satisfied; (3) Construct a second subproblem, which optimizes the relaxation of the repeating terms of the integer / 0-1 variable z, treats the continuous variable x and the η multiplier as constants, and the integer / 0-1 variable z is relaxed between their upper and lower limits; when the optimization process terminates, the assigned z is rounded to the nearest integer value. satisfy:
2. The power distribution system voltage / reactive power optimization method based on the alternating direction multiplier method according to claim 1, characterized in that, The first step of the procedure includes: (1) Establish mathematical models of power distribution system components: including mathematical models of OLTCs, SCBs, and power flow of distribution lines; (2) Form a voltage / reactive power optimization model for the power distribution system, including the objective function and constraints for voltage / reactive power optimization.
3. The power distribution system voltage / reactive power optimization method based on the alternating direction multiplier method according to claim 2, characterized in that, In the first step of the procedure, for a power distribution system with N nodes and radial or mesh-like power distribution lines L, the π-type equivalent circuit model is formed by the series impedance z. l and total charging capacity Composition, used to model arbitrary two-port devices, including transformers and power distribution lines; The OLTC modeling method is as follows: A transformer k is installed on the power distribution line l between nodes i and j. Transformer k is equipped with an on-load tap changer. On the secondary side of the transformer, there is a virtual node m and a virtual variable V. s To correlate the voltage and power flow relationships between OLTCs and their associated distribution lines, assuming an ideal transformer with no power loss between its terminal nodes i and m, the voltage ratio between the secondary side m and the primary side i is equal to the transformer turns ratio t, and the voltage angles of the two nodes are the same, therefore, the secondary voltage is calculated as follows: in, In the formula: V i t is the vector representing the voltage magnitude at node i; k The tap ratio of the current discrete OLTCs for the k-th transformer is defined as 90% to 110% of the rated voltage level, with an incremental variation of 5 / 8%. t k For t k The minimum discrete value; For OLTCs, the tap position is indicated. Furthermore, the power conservation of an ideal transformer satisfies the following constraints: θ m =θ i ,P im =P mj ,Q im =Q mj The SCBs modeling method is as follows: mathematically, it is described as a pure capacitor power injection source, and the actual injected capacitor reactive power is calculated as follows: in, In the formula: Let i be the total reactive power injected into the capacitor bank at node i. and These are the minimum and maximum values, respectively. This refers to the k-th capacitor bank connected to the capacitor susceptance. for The minimum discrete value; The power flow modeling method for distribution lines is as follows: This is achieved through the active power flow P between nodes i and j of the distribution line l. ij and the trend of no power Q ij The calculation is as follows: Where: g l Let b be the conductance of line l; l Let L be the susceptance of line l, and L be the set of all lines. The active power loss of distribution line l is calculated as follows: If line l is configured with OLTC, then variable V will be... i Replace with in 4. The power distribution system voltage / reactive power optimization method based on the alternating direction multiplier method according to claim 3, characterized in that, The method for forming a voltage / reactive power optimization model for a power distribution system is as follows: Forming the objective function: The main objective of voltage / reactive power optimization in the power distribution system is to minimize the active power loss of the distribution lines and maintain an appropriate node voltage distribution; Adding a minimum load term to the objective function results in: Constraints are established: in addition to the limitations of OLTCs and SCBs, operational and safety constraints are also considered; First, establish node power balance constraints: To avoid confusion, DGs are not considered. Indicates that i is a node in set N excluding the slack node; the specified slack node is a substation node; when the load node's power demand... Modeling it as a voltage-sensitive function, without considering fixed values, is... Among them, P i n , V represents the active and reactive power demand of node i at rated voltage and frequency, respectively. n k is the system rated voltage. p ,k q For a predefined voltage index; In addition, operational and safety limitations are imposed on voltage magnitude, phase angle, and maximum transmission capacity of distribution lines, as follows:
5. The power distribution system voltage / reactive power optimization method based on the alternating direction multiplier method according to claim 4, characterized in that, In the second step of the above steps: Let h represent the "coupling constraints" between two sets of integer variables x and z and continuous variables. The vector of these coupling constraints is... The generalized voltage / reactive power optimization problem for power distribution systems is as follows: Satisfying h(x,z)=0:λ Where χ represents the feasible region formed by the constraints containing x in the first step, and Let z be the feasible region formed by the z-constraint, and let z be the dual variable. These are the Lagrange multiplier vectors associated with the coupling constraints.
6. The power distribution system voltage / reactive power optimization method based on the alternating direction multiplier method according to claim 1, characterized in that, The third step further includes: (4) Gauss-Seidel iterative solution: The Gauss-Seidel method is used to continuously execute the two optimization subproblems after decomposition, exchange the results, and update the joint dual variables, as shown in the following equation, where the superscript k indicates the iteration number. The iterative process continues until a feasible and sufficiently optimal solution is found: (5) Convergence condition test: Through preliminary feasibility test, a necessary and sufficient condition for the proposed ADMM-voltage / reactive power optimization method is obtained: This means that when the iteration process ends and k→∞, the coupling constraint must be satisfied to ensure the feasibility of the result; Furthermore, the second convergence criterion observes the stationarity of the results for the second subproblem, ensuring that no better results are obtained. Therefore, the iterative process of the overall solution steps continues until a sufficiently optimal feasible result is assigned, and the following stopping criterion is used for verification: Feasibility Remaining Verification: ||r k+1 ||2=||h k+1 -or k ||2≤∈1 Stationarity residual test: ||s k+1 ||2=||(z k+1 -z k )||2≤∈2 Where ∈1 and ∈2 are predefined thresholds, generally with a tolerance of less than 1×10. -6 .
7. The voltage / reactive power optimization method for power distribution systems based on the alternating direction multiplier method according to claim 3, characterized in that, The third step also includes setting up a device switching priority mechanism: Two scaling factors, α and β, are used as priority vectors to control the influence weights of each term in the resulting multi-objective function.
8. The power distribution system voltage / reactive power optimization method based on the alternating direction multiplier method according to claim 1, characterized in that, The third step also includes: updating ρ in a responsive manner so that the ADMM solution converges while maintaining the quality of the results; The ρ update principle is shown in the following formula: In the formula, ν and μ are adjustable constants, which are usually set as: ν = 2, μ = 10.
9. A voltage / reactive power optimization device for a power distribution system based on the alternating direction multiplier method, characterized in that, include: The mathematical model building module is used to build mathematical models of power distribution system components and obtain the voltage / reactive power optimization model of the power distribution system. The voltage / reactive power optimization model building module is used to build a generalized voltage / reactive power optimization model for the distribution system based on the mathematical models of the distribution system components and the voltage / reactive power optimization model of the distribution system. The solution module is used to iteratively solve the voltage / reactive power optimization model of the established generalized distribution system using the ADMM-based optimization method, and obtain the results of the ADMM-based distribution system voltage / reactive power optimization method. The solution methods of the solver module include: (1) Construct the Lagrangian function of the generalized power distribution system voltage / reactive power optimization model. The Lagrangian function is: L(x,z,λ)=f(x)+λ T h(x,z) In the formula, λ is the Lagrange multiplier vector of the coupling constraint, i.e., the dual variable, x represents the vector of continuous variables, and z represents the vector of integer variables. Furthermore, the coupling constraint vector h(x,z) is used as a consistently positive penalty term to punish deviations from the optimal solution: In the formula, For a predefined penalty parameter, and Let be the square 2-norm of a vector; Updating the augmented Lagrange function using the scaled Lagrange multipliers η = λ / ρ is equivalently rewritten as: To develop an ADMM-based voltage / reactive power optimization method for distribution systems, the generalized voltage / reactive power optimization problem for distribution systems is decomposed into two subproblems: the first subproblem solves for continuous variable x, while treating integer or 0-1 variable z as a constant; the second subproblem is the opposite. The augmented Lagrangian function is used as the objective function for both the first and second subproblems, ensuring that the solver satisfies coupling constraints to achieve optimality. (2) Construct the first subproblem. The first subproblem uses the continuous variable x as the decision variable, while treating the integer / 0-1 variables of z and the η multiplier as constants, forming a nonlinear optimization problem (NLP). The mature interior-point method is directly called to solve it. This indicates that the variable is considered given and not optimized; The constraints defined in the first step are satisfied; (3) Construct a second subproblem, which optimizes the relaxation of the repeating terms of the integer / 0-1 variable z, treats the continuous variable x and the η multiplier as constants, and the integer / 0-1 variable z is relaxed between their upper and lower limits; when the optimization process terminates, the assigned z is rounded to the nearest integer value. satisfy:
10. An electronic device, characterized in that, include: The processor, communication interface, memory, and communication bus are connected, with the processor, communication interface, and memory communicating with each other via the communication bus. The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the method according to any one of claims 1 to 8.