Dc-ac hybrid distribution network distributed convex optimization method and device

Abstract

The application discloses a kind of AC-DC distribution network distributed convex optimization method and device, method includes: the optimization operation model of AC-DC distribution network containing power electronic transformer is established;Second-order cone relaxation technique and successive linear approximation method are used, and the optimization operation model is converted into successive convex approximation programming model;By target cascade analysis method, the successive convex approximation programming model is decomposed into sub-problems, and distributed convex programming model is constructed, and cyclic iteration is solved, and optimal solution is obtained;Operation control center above the optimization solution is used as control instruction, and the operation control of power electronic transformer and each distributed power supply in AC-DC distribution network in distribution network is carried out, active network loss reduction is realized, and the voltage deviation of entire distribution network is inhibited.The device includes: processor and memory.The application improves the operation performance of distribution network by coordinating the active and reactive power flow of distributed power supply and PET, reduces the active loss, and reduces the voltage deviation of the entire network.

Description

Technical Field

[0001] This invention relates to the field of distributed optimization operation of AC / DC distribution networks, and in particular to a distributed convex optimization method and apparatus for AC / DC distribution networks. Background Technology

[0002] With the increasing application of flexible power electronic devices, the operation and optimization of distribution networks are changing. The integration of large-scale distributed power sources has increased the demand for intelligent management. As a feasible solution, the Power Electronic Transformer (PET) has attracted widespread attention due to its ability to flexibly manage network power flow and facilitate plug-and-play distributed energy. PET consists of power electronic devices and a high-frequency transformer, and has functions such as voltage conversion, reactive power compensation, and active power flow control. The power and voltage at PET ports can be flexibly and independently controlled to improve the overall network performance. PET-based AC / DC hybrid distribution networks offer high flexibility and controllability, promoting safe and efficient network operation. Currently, PET research mainly focuses on topology and control strategies, and the following challenges exist in the field of optimized operation control:

[0003] 1) The flexible regulation capability of PET needs to be further explored. Research has been carried out on the optimization operation of distribution networks containing PET, and the benefits of PET in reducing power generation costs, multi-source coordinated dispatch and hierarchical economic optimization have been confirmed. However, how to improve the network voltage distribution has not yet been considered.

[0004] 2) The strong nonlinear loss of PET and the constant impedance-current-power (ZIP) load characteristics of the distribution network have not been fully considered in the existing field of optimized operation and control of AC / DC distribution networks containing PET;

[0005] 3) The traditional centralized operation and control mode is no longer applicable. AC and DC hybrid distribution networks with PET can integrate AC and DC distribution networks on a larger scale. The centralized control mode has problems such as communication bottlenecks, privacy protection and complex control processes, and there is an urgent need to explore distributed operation and control methods.

[0006] Overall, there is currently a lack of a distributed operation control method for AC / DC distribution networks with PET that takes into account PET losses, ZIP load characteristics, and voltage distribution levels. Summary of the Invention

[0007] This invention provides a distributed convex optimization method and apparatus for AC / DC distribution networks. By coordinating the active and reactive power flows of distributed power sources and power purifiers (PETs), this invention improves the operational performance of the distribution network, reducing active power losses while minimizing voltage deviation across the entire network. It employs second-order cone relaxation techniques and successive linear approximation methods to accurately describe the strong nonlinear losses of PETs and ZIP loads. Based on this, it uses a target cascade analysis method to decompose the centralized operation control process, achieving distributed operation control of AC / DC distribution networks containing PETs. ​​Details are described below:

[0008] A distributed convex optimization method for AC / DC distribution networks, the method comprising:

[0009] Establish an optimized operation model for AC / DC distribution networks that include power electronic transformers;

[0010] By employing second-order cone relaxation technique and successive linear approximation method, the optimization operation model is transformed into a successive convex approximation planning model;

[0011] By using the objective cascade analysis method, the successive convex approximation programming model is decomposed into sub-problems, a distributed convex programming model is constructed, and the optimal solution is obtained by iterative solving.

[0012] The operation control center uses the above optimized solution as control commands to control the operation of power electronic transformers in the distribution network and distributed power sources in the AC / DC distribution network, thereby reducing active power losses and suppressing voltage deviations in the entire distribution network.

[0013] The optimized operating model is as follows:

[0014] Construct a function with the objective of minimizing active power loss and voltage deviation, including: active power loss of power electronic transformers, active power loss of AC and DC distribution networks, and voltage deviation of AC and DC distribution networks;

[0015] Establish constraints, including: AC and DC distribution network branch power flow models, ZIP complex models, PET steady-state power flow models, operating voltage amplitude constraints, distributed generation output constraints, and PET port operation constraints.

[0016] Furthermore, by employing second-order cone relaxation techniques and successive linear approximation methods, the optimization operation model is transformed into a successive convex approximation programming model, specifically as follows:

[0017] The AC / DC power flow equations are relaxed by convexity using a second-order cone relaxation technique; the PET model and ZIP load model are linearized by successive linear approximation; and auxiliary variables are introduced to linearize the objective function.

[0018] The objective function is:

[0019]

[0020] Among them, W a and W β The weights of the objective function are denoted by ; ij represents the branch number; Φ b For the set of branches; R ij I is the resistance of branch ij; ij Let g represent the current in branch ij; g represents the PET serial number; G represents the PET set. Ω represents the active power loss of the g-th PET; k represents the node number; n V is a set of nodes; k Let be the voltage amplitude at the k-th node; The upper limit of the desired voltage; The lower limit of the desired voltage; ":" indicates the degree to which the node voltage amplitude deviates from the desired voltage range, i.e., when... season when season v is the reference value for voltage deviation.

[0021] Furthermore, the successive convex approximation programming model is as follows:

[0022]

[0023]

[0024]

[0025] Among them, V i AC,k-1 and V i DC,k-1 These are the initial values ​​of the node voltage amplitudes of the AC and DC distribution networks given in the k-th iteration, respectively. and V represents the square of the current optimized value of the node voltage in the AC and DC distribution networks, respectively. i AC,k-1 and V i DC ,k-1 This iteration satisfies and

[0026] Specifically, the step of performing iterative solving to obtain the optimal solution involves:

[0027] A nested iterative process consisting of an inner loop and an outer loop is proposed to solve the distributed convex programming model. In the inner loop, the AC subproblem and the DC subproblem are solved in parallel. The PET subproblem acts as a coordinator. Each subproblem belongs to the successive convex programming problem. After the inner loop converges through iterative solution, the outer loop updates the penalty coefficient based on the result of the inner loop.

[0028] A distributed convex optimization device for AC / DC distribution networks, the device comprising: a processor and a memory, the memory storing program instructions, the processor calling the program instructions stored in the memory to cause the device to execute method steps.

[0029] The beneficial effects of the technical solution provided by this invention are:

[0030] 1) This invention fully utilizes the active power flow regulation and reactive power compensation capabilities of power electronic transformers. By optimizing the operation and control of the power injected into the AC and DC ports of the power electronic transformers and the output of distributed power sources connected in the distribution network, it greatly improves the operating performance of the distribution network, reduces active power losses, and suppresses the voltage deviation of the entire network.

[0031] 2) This invention solves the operation control problem of AC and DC distribution networks with power electronic transformers when they are integrated over a large area. By accurately describing the operation control model of each unit in the distribution network and using the target cascade analysis method to decompose the centralized operation control mode, distributed operation control of AC and DC distribution networks with power electronic transformers is realized. Attached Figure Description

[0032] Figure 1 This is a flowchart of the distributed operation control process for AC / DC distribution networks that include power electronic transformers.

[0033] Figure 2 This is a topology diagram of an AC / DC distribution network containing power electronic transformers;

[0034] Figure 3 This is a schematic diagram of the voltage distribution at various nodes of an AC distribution network.

[0035] Figure 4 This is a schematic diagram of a distributed convex optimization device for AC / DC power distribution networks containing power electronic transformers. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0037] Example 1

[0038] This invention provides a distributed convex optimization method for AC / DC distribution networks. This method leverages the active power flow regulation and reactive power compensation capabilities of power electronic transformers to construct an operation control model for an AC / DC hybrid distribution network containing power electronic transformers. Then, based on a target cascade analysis method, the operation control center performs distributed operation control on the AC / DC hybrid distribution network containing power electronic transformers, achieving reduced active power losses while suppressing voltage deviations across the entire distribution network. (See also...) Figure 1 The method includes the following steps:

[0039] 101: Establish an optimized operation model for AC / DC distribution networks containing power electronic transformers;

[0040] 102: The second-order cone relaxation technique and successive linear approximation method are used to transform the optimization operation model into a successive convex approximation planning model;

[0041] 103: By using the goal cascade analysis method, the successive convex approximation programming model is decomposed into sub-problems, a distributed convex programming model is constructed, and the optimal solution is obtained by iterative solving.

[0042] 104: The operation control center uses the optimized solution obtained from the above steps as control commands to control each distributed power source and power electronic transformer in the distribution network, thereby reducing active power losses and suppressing voltage deviation of the entire distribution network.

[0043] Specifically, the optimized operation model for the AC / DC distribution network containing power electronic transformers in step 101 is as follows:

[0044] The operation control centers of power electronic transformers, AC distribution networks, and DC distribution networks collect parameters within their respective networks, including: network topology status, line parameters, load levels, and the output range of distributed power sources.

[0045] Based on the collected parameters, a function is constructed with the objective of minimizing active power loss and voltage deviation, including: active power loss of power electronic transformers, active power loss of AC and DC distribution networks, and voltage deviation of AC and DC distribution networks.

[0046] Establish constraints, including: AC and DC distribution network branch power flow models, ZIP complex models, PET steady-state power flow models, operating voltage amplitude constraints, distributed generation output constraints, PET port operation constraints, etc.

[0047] Specifically, step 102, which employs second-order cone relaxation techniques and successive linear approximation methods to transform the optimization operation model into a successive convex approximation planning model, involves the following:

[0048] A second-order cone relaxation technique is used to convex relax the AC / DC power flow equations.

[0049] The PET model and ZIP load model are linearized using a successive linear approximation method.

[0050] Introducing auxiliary variables linearizes the objective function.

[0051] Specifically, step 103 involves using the objective cascade analysis method to decompose the successive convex approximation programming model into sub-problems, constructing a distributed convex programming model, and performing iterative solving as follows:

[0052] The original centralized optimization problem is decomposed into PET subproblems, AC subproblems, and DC subproblems using the objective cascade analysis method.

[0053] The design employs a two-layer iterative solution process, with each operation control center calling existing mature commercial software, such as Cplex, to efficiently solve the model.

[0054] In step 104, the operation control center uses the optimized solution obtained in the above steps as control commands to control each distributed power source and power electronic transformer in the network. Specifically, this involves:

[0055] The optimized solution obtained includes: the active and reactive power output values ​​of the distributed power source, the voltage amplitude at the power electronic transformer port, and the active and reactive power values ​​injected into the power electronic transformer port, etc.

[0056] The operation control center uses the above optimized solution as control commands and sends them to each controller;

[0057] Each controller receives control commands from the operation control center and performs operation control on the power electronic transformers and distributed power sources in the AC / DC distribution network, thereby reducing active power losses and suppressing voltage deviations in the entire distribution network.

[0058] In summary, the embodiments of the present invention optimize the operation control of the AC and DC ports of the power electronic transformer and the output of the distributed power sources connected in the distribution network through steps 101-104, which greatly improves the operation performance of the distribution network, reduces active power losses, and suppresses the voltage deviation of the entire network.

[0059] Example 2

[0060] The scheme in Example 1 will be further described below with specific calculation formulas and examples:

[0061] 201: Establish an optimized operation model for AC / DC distribution networks including power electronic transformers;

[0062] 1. Objective function:

[0063] In this embodiment of the invention, an optimization model is established with the objective function of minimizing the active power loss and voltage deviation of the AC / DC distribution network containing power electronic transformers. The established objective function is shown in Equation (1).

[0064]

[0065] Among them, W a and W β The weights of the objective function are denoted by ; ij represents the branch number; Φ bFor the set of branches; R ij I is the resistance of branch ij; ij Let g represent the current in branch ij; g represents the PET serial number; G represents the PET set. Ω represents the active power loss of the g-th PET; k represents the node number; n V is a set of nodes; k Let be the voltage amplitude at the k-th node; The upper limit of the desired voltage; The lower limit of the desired voltage; ":" indicates the degree to which the node voltage amplitude deviates from the desired voltage range, i.e., when... season when season v is the reference value for voltage deviation.

[0066] 2. AC / DC distribution network power flow model:

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] in, For AC distribution network branch collection; The active power transmitted by AC distribution network branch ij; The reactive power transmitted by AC distribution network branch ij; and These are the resistance and reactance of AC distribution network branch ij, respectively; Let be the current amplitude of branch ij in the AC distribution network; and These are the active power and reactive power output by distributed generation j in the AC distribution network, respectively. and These are the active power and reactive power injected into the PET AC port, respectively. and These are the active and reactive loads of node j in the AC distribution network, respectively. Let J be the voltage amplitude at node j in the AC distribution network. A collection of DC distribution network branches; The active power transmitted by branch ij in the DC distribution network; Let be the resistance of branch ij in the DC distribution network; Let be the current amplitude of branch ij in the DC distribution network; The active power output by distributed generation j in a DC distribution network; Active power injected into the DC port of the PET; For node j in the DC distribution network, the active load is... V represents the voltage amplitude at node j in the DC distribution network. i DC The voltage amplitude at node i in the DC distribution network; This refers to the active power transmitted by the DC distribution network branch jk.

[0075] 3. ZIP load model:

[0076]

[0077]

[0078]

[0079] in, These are the constant resistance, constant current, and constant power active load factors of the AC distribution network, respectively. These are the constant resistance, constant current, and constant power reactive load factors of the AC distribution network, respectively. These are the constant resistance, constant current, and constant power active load factors for DC distribution networks, respectively. and These are the baseline active and reactive loads of node i in the AC distribution network, respectively. V represents the baseline active load at node i in the DC distribution network. i AC V represents the voltage amplitude at node i in the AC distribution network. i DC Let be the voltage amplitude of node i in the DC distribution network.

[0080] 4. PET steady-state power flow model:

[0081] The active power injected into each AC and DC port of the PET and the active power loss of the PET should always meet the power balance.

[0082]

[0083] Where m and n represent the number of AC and DC ports of the PET, respectively; The active power injected into the i-th AC port of the PET; The active power loss of the PET is denoted as . The power loss of the PET includes the active power loss of the converter, the equivalent branch loss of the VSC, and the high-frequency transformer loss. The loss model of each port of the PET can be obtained by curve fitting, which can be specifically expressed as a quadratic function of the port converter arm current.

[0084]

[0085] in, Let a be the active power loss of the i-th port of the PET. c,i ,b c,i ,c c,i The fitting parameters for PET loss; I c,i The current amplitude injected into the i-th port of the PET.

[0086] The total loss of PET is the active power loss of each AC port. and DC port active power loss sum.

[0087]

[0088] Equations (12)-(14) summarize the steady-state model of a multi-port power electronic transformer that takes into account loss characteristics.

[0089] 5. Safety operation constraints:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098] in, V AC and These are the lower and upper limits of the voltage amplitude at AC distribution network nodes, respectively. V DC and These are the lower and upper limits of the voltage amplitude at DC distribution network nodes, respectively. and These are the lower and upper limits of active power output from distributed generation sources in AC distribution networks, respectively. and These are the lower and upper limits of reactive power output from distributed generation sources in AC distribution networks, respectively. and These are the lower and upper limits of active power output from distributed generation sources in DC distribution networks, respectively. and These are the lower and upper limits for reactive power injected into the PET AC port, respectively. The capacity of PET AC port j; and These are the lower and upper limits of the active power injected into the DC port of the PET, respectively. The reactive power injected into the i-th AC port of PET.

[0099] In summary, equations (1)-(22) constitute the optimized operation model of AC / DC distribution network with PET established in the embodiment of the present invention. In this model, the AC / DC distribution network power flow model, ZIP load model and PET steady state model are all nonlinear constraints, which makes the original problem a nonlinear optimization problem, and an accurate and efficient solution method is urgently needed.

[0100] Step 202: Using second-order cone relaxation technique and successive linear approximation method, the original nonlinear optimization operation model is transformed into a successive convex approximation planning model;

[0101] 1. Second-order cone convex relaxation:

[0102] Introducing variables, Substituting these equations into formulas (2)-(4), (6) and (7) yields the following linearized equations.

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] Then, the branch current equations of the AC / DC distribution network are relaxed as follows:

[0109]

[0110]

[0111] In addition, the PET port capacity constraint employs a rotating cone relaxation, as shown below.

[0112]

[0113] After the above transformation, when the ZIP load model is not considered, the nonlinear power flow model of the AC / DC distribution network is transformed into a second-order cone model.

[0114] 2. Successive linear approximation:

[0115] In this embodiment of the invention, a second-order cone relaxation is performed on the power flow equations of AC and DC distribution networks. The square of the branch current is introduced as an optimization variable, so that the nonlinear term of the PET loss equation described by equation (13) only contains the first-order current term. Now, a first-order Taylor expansion is performed on it, as shown below.

[0116]

[0117] in, The initial value of the PET port current is given for the k-th iteration. This represents the square of the current optimized value of the PET port current. This iteration satisfies Equation (31) can be used to transform equation (13) into a successive linear form, as follows:

[0118]

[0119] Similarly, since the square of the node voltage amplitude is introduced as an optimization variable, the ZIP load model described by equations (9)-(11) contains only a first-order term, which can be transformed into the following successive linear model.

[0120]

[0121]

[0122]

[0123] Among them, V i AC,k-1 and V i DC,k-1 These are the initial values ​​of the node voltage amplitudes of the AC and DC distribution networks given in the k-th iteration, respectively. and V represents the square of the current optimized value of the node voltage in the AC and DC distribution networks, respectively. i AC,k-1 and V i DC ,k-1 This iteration satisfies and

[0124] 3. Objective function linearization:

[0125] The active power losses of AC / DC distribution networks and PET active power losses in the objective function have been transformed into a linear form after the above convex relaxation and successive linear approximation processes. Voltage deviation can be introduced as an auxiliary variable. Linearize it.

[0126]

[0127] in, W represents the active power loss of the g-th PET. a The weighting coefficients for the objective of minimizing network loss; W β The weighting coefficient is the target for minimizing voltage deviation.

[0128] At the same time, the following constraints need to be added:

[0129] J k ≥0 (37)

[0130]

[0131]

[0132] in, The upper limit of the desired voltage; This represents the lower limit of the desired voltage.

[0133] After the above processing, the objective function becomes linear, and the constraints are linear, successive linear, and second-order conical in form. Therefore, the original nonlinear problem is transformed into a successive convex approximation programming model. The optimality and computational efficiency of the convex programming model solution are greatly improved, and efficient solutions can be achieved using existing mature commercial software. It is important to note that the initial values ​​of the successive linear approximation equation need to be updated based on the current optimal value in each iteration until the absolute value of the difference between the initial values ​​in two adjacent iterations is less than a given convergence criterion, at which point the iteration terminates. Where ε0 is the convergence threshold, χ i V is the collection of PET port current, AC node voltage, and DC node voltage. i AC V i DC Let be the voltage amplitude of the i-th node in the AC / DC distribution network. The successive convex approximation programming model proposed in this embodiment of the invention ensures the accuracy of the solution through iterative calculation.

[0134] 203: By using the objective cascade analysis method, the original centralized optimization problem is decomposed into subproblems, a distributed convex programming model is constructed, and the problem is solved iteratively.

[0135] 1. PET sub-problem

[0136] The successive convex approximation programming model is decomposed using the objective cascade analysis method. The active and reactive power transmitted at the connection points between the PET and the AC / DC distribution networks are considered as coupling variables and can be decomposed into objective variables. and response variables Thus, the PET subproblem F can be constructed. PET :

[0137]

[0138] Among them, v j w is the vector of penalty function coefficients. j The penalty function weight vector; symbol Ψ represents the Hadamard product, which is calculated by multiplying matrices term by term; pet This is the set of coupling variables related to PET. pet The objective function for the PET subproblem; g pet The inequality constraints for the PET subproblem include formulas (20), (22), and (30); h pet The equality constraints for the PET subproblem include formulas (12), (14), and (32). The objective variable in the PET subproblem... It is a constant, the response variable. It is a variable.

[0139] 2. AC and DC sub-problems

[0140] Constructing the communication subproblem F ac :

[0141]

[0142] f ac The objective function for the communication subproblem; g ac The inequality constraints for the communication subproblems include formulas (15), (17), (18), (28), and (37)-(39); h ac The equality constraints for the communication subproblem include formulas (23)-(25), (33), and (34). The objective variable in the communication subproblem... It is a variable, a response variable. It is a constant.

[0143] Constructing the communication subproblem F dc :

[0144]

[0145] Among them, f dc The objective function for the communication subproblem; g dcThe inequality constraints for the communication subproblems include formulas (16), (19), (29), and (37)-(39); h dc The equality constraints for the communication subproblem include formulas (26), (27), and (35). The objective variable in the communication subproblem... It is a variable, a response variable. It is a constant.

[0146] 3. Iterative solution process

[0147] After the above processing, the original centralized optimization problem is transformed into a distributed optimization problem. This invention proposes a nested iterative process consisting of an inner loop and an outer loop to solve the distributed convex programming model, such as... Figure 3 As shown in the diagram, the AC and DC subproblems are solved in parallel within the inner loop, while the PET subproblem acts as a coordinator. Each subproblem belongs to a successive convex programming problem and is solved iteratively. After the inner loop converges, the outer loop updates the penalty coefficient based on the results of the inner loop.

[0148] The specific process is as follows:

[0149] 1) Given an initial value k for the inner loop index o =0, initial value of outer loop index k I =0, given the initial value of the penalty function coefficient vector. and the initial value of the penalty function weight vector Given initial values ​​for the target variable

[0150] 2) Let k I =k I +1, solve the AC and DC subproblems in parallel, then solve the PET subproblem to obtain the new objective variable.

[0151] 3) Determine if the inner loop meets the convergence condition, i.e., whether the absolute value of the difference between the objective function in two adjacent iterations is less than the convergence criterion. If convergence is achieved, proceed to step 4); otherwise, return to step 2), where... For the kth I The sum of the objective functions of the AC subproblem, DC subproblem, and PET subproblem in the innermost loop, where ε1 is the convergence threshold;

[0152] 4) Determine if the outer loop meets the convergence criterion. and If convergence occurs, stop the computation to obtain the optimal solution; otherwise, let k... o =k o +1,k I=0, and update the penalty function coefficient vector and penalty function weight vector using formulas (43) and (44), and then return to 2).

[0153]

[0154]

[0155] in, For the kth o The difference between the target variable and the response variable in the outermost loop, ε2 and ε3 are the convergence thresholds, (44)

[0156] τ and ρ are constants.

[0157] 204: The operation control center uses the optimized solution obtained from the above steps as control commands to control each distributed power source and power electronic transformer in the distribution network.

[0158] 1. Generate control commands

[0159] The operation control centers of power electronic transformers, AC distribution networks, and DC distribution networks solve optimization problems by calling commercial solvers such as CPLEX, thereby obtaining optimized solutions such as the active and reactive power output of distributed power sources, the voltage amplitude at the power electronic transformer ports, and the active and reactive power injected into the power electronic transformer ports, and then use these optimized solutions as control commands.

[0160] 2. Transmission control commands

[0161] The operation control centers of power electronic transformers, AC distribution networks, and DC distribution networks send the aforementioned control commands to the operation controllers of each distributed power source within the power electronic transformers and AC / DC distribution networks via a communication system.

[0162] 3. Operation Control

[0163] The controllers of each distributed power source in the power electronic transformer and AC / DC distribution network receive control commands from the operation control center of the power electronic transformer, AC distribution network and DC distribution network, and use these commands as control reference values ​​to control the operation of each distributed power source in the power electronic transformer and AC / DC distribution network.

[0164] In summary, the embodiments of the present invention optimize the operation control of the AC and DC ports of the power electronic transformer and the output of the distributed power sources connected in the distribution network through steps 201-204, which greatly improves the operation performance of the distribution network, reduces active power losses, and suppresses the voltage deviation of the entire network.

[0165] Example 3

[0166] The feasibility of the schemes in Examples 1 and 2 is verified below with specific examples, as detailed in the following description:

[0167] Construct a computational example of an AC / DC distribution network containing power electronic transformers, such as Figure 1 As shown, the power electronic transformer in this test system is connected to a 10kV AC distribution network and a 750V DC distribution network, respectively.

[0168] The following four scenarios are set up for comparative analysis:

[0169] Scenario 1: The network contains 2 PETs, and the proposed model is used for optimization;

[0170] Scenario 2: The network contains only PET1, and the proposed model is used for optimization;

[0171] Scenario 3: The network contains only PET2, and the proposed model is used for optimization;

[0172] Scenario 4: Obtain the original power flow distribution without performing optimization calculations.

[0173] The results for the four scenarios are compared below. Table 1 shows the network active power loss under the four scenarios. Figure 2 A comparison of AC network voltage distribution in four scenarios is presented. It can be seen that, compared to scenario 4, the optimized model proposed in scenario 1 effectively reduces network losses. Compared to scenarios 2 and 3, scenario 1 increases the number of PETs, allowing for more flexible adjustment of active / reactive power flow, which helps reduce overall network active power losses. Furthermore, scenario 1 exhibits the smallest voltage deviation among the four scenarios, thus ensuring the safe operation of the network.

[0174] Table 1 Network active power loss in four scenarios

[0175]

[0176] To verify the effectiveness of the distributed optimization method proposed in this invention, the following three models are compared.

[0177] Model 1: The distributed convex programming model proposed in this invention;

[0178] Model 2: Successive convex approximation programming model, solved using a centralized approach;

[0179] Model 3: The original nonlinear optimization model is solved using a centralized approach.

[0180] The results of the three models are shown in Table 2. It can be seen that the results of Model 2 and Model 3 are consistent, indicating the correctness of the proposed successive convex approximation programming model. In addition, the results of Model 1 and Model 2 are also similar, verifying the effectiveness of the distributed convex programming model proposed in this invention.

[0181] Table 2 Network active power loss under the three models

[0182]

[0183] Example 4

[0184] A distributed convex optimization device for AC / DC distribution networks, see [link / reference] Figure 4 The device includes a processor and a memory, the memory storing program instructions, and the processor calling the program instructions stored in the memory to cause the device to perform the following steps:

[0185] Establish an optimized operation model for AC / DC distribution networks that include power electronic transformers;

[0186] By employing second-order cone relaxation technique and successive linear approximation method, the optimization operation model is transformed into a successive convex approximation planning model;

[0187] By using the objective cascade analysis method, the successive convex approximation programming model is decomposed into sub-problems, a distributed convex programming model is constructed, and the optimal solution is obtained by iterative solving.

[0188] The operation control center uses the above optimized solution as control commands to control the operation of power electronic transformers in the distribution network and distributed power sources in the AC / DC distribution network, thereby reducing active power losses and suppressing voltage deviations in the entire distribution network.

[0189] The optimized operating model is as follows:

[0190] Construct a function with the objective of minimizing active power loss and voltage deviation, including: active power loss of power electronic transformers, active power loss of AC and DC distribution networks, and voltage deviation of AC and DC distribution networks;

[0191] Establish constraints, including: AC and DC distribution network branch power flow models, ZIP complex models, PET steady-state power flow models, operating voltage amplitude constraints, distributed generation output constraints, and PET port operation constraints.

[0192] Furthermore, by employing second-order cone relaxation techniques and successive linear approximation methods, the optimization operation model is transformed into a successive convex approximation programming model, specifically as follows:

[0193] The AC / DC power flow equations are relaxed by convexity using a second-order cone relaxation technique; the PET model and ZIP load model are linearized by successive linear approximation; and auxiliary variables are introduced to linearize the objective function.

[0194] The objective function is:

[0195]

[0196] Among them, Wa and W β The weights of the objective function are denoted by ; ij represents the branch number; Φ b For the set of branches; R ij I is the resistance of branch ij; ij Let g represent the current in branch ij; g represents the PET serial number; G represents the PET set. Ω represents the active power loss of the g-th PET; k represents the node number; n V is a set of nodes; k Let be the voltage amplitude at the k-th node; The upper limit of the desired voltage; The lower limit of the desired voltage; ":" indicates the degree to which the node voltage amplitude deviates from the desired voltage range, i.e., when... season when season v is the reference value for voltage deviation.

[0197] Furthermore, the successive convex approximation programming model is as follows:

[0198]

[0199]

[0200]

[0201] Among them, V i AC,k-1 and V i DC,k-1 These are the initial values ​​of the node voltage amplitudes of the AC and DC distribution networks given in the k-th iteration, respectively. and V represents the square of the current optimized value of the node voltage in the AC and DC distribution networks, respectively. i AC,k-1 and V i DC ,k-1 This iteration satisfies and

[0202] Specifically, the process of iteratively solving the problem to obtain the optimal solution involves:

[0203] A nested iterative process consisting of an inner loop and an outer loop is proposed to solve the distributed convex programming model. In the inner loop, the AC subproblem and the DC subproblem are solved in parallel. The PET subproblem acts as a coordinator. Each subproblem belongs to the successive convex programming problem. After the inner loop converges through iterative solution, the outer loop updates the penalty coefficient based on the result of the inner loop.

[0204] It should be noted that the device descriptions in the above embodiments correspond to the method descriptions in the embodiments, and the embodiments of the present invention will not be repeated here.

[0205] The execution entities of the aforementioned processor and memory can be devices with computing functions such as computers, microcontrollers, and single-chip microcomputers. In specific implementations, the embodiments of the present invention do not limit the execution entities and can select them according to the needs of actual applications.

[0206] Data signals are transmitted between the memory and the processor via a bus, which will not be elaborated upon in this embodiment of the invention.

[0207] Unless otherwise specified, the model numbers of the various devices in this embodiment of the invention are not limited, and any device that can perform the above functions is acceptable.

[0208] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0209] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A distributed convex optimization method for AC / DC distribution networks, characterized in that, The method includes: Establish an optimized operation model for AC / DC distribution networks that include power electronic transformers; By employing second-order cone relaxation technique and successive linear approximation method, the optimization operation model is transformed into a successive convex approximation planning model; By using the objective cascade analysis method, the successive convex approximation programming model is decomposed into sub-problems, a distributed convex programming model is constructed, and the optimal solution is obtained by iterative solving. The operation control center uses the above optimal solution as the control command to control the operation of power electronic transformers in the distribution network and distributed power sources in the AC / DC distribution network, thereby reducing active power losses and suppressing voltage deviation of the entire distribution network. The successive convex approximation programming model is as follows: ； ； ； in, and The first The initial values ​​of the node voltage amplitudes of the AC and DC distribution networks are given in the next iteration; and These represent the squares of the current optimized values ​​of the node voltages in the AC and DC distribution networks, respectively. and This iteration satisfies and ; , , These are the constant resistance, constant current, and constant power active load factors of the AC distribution network, respectively. , , These are the constant resistance, constant current, and constant power reactive load factors of the AC distribution network, respectively. , , These are the constant resistance, constant current, and constant power active load factors for DC distribution networks, respectively. and AC distribution network nodes Baseline active and reactive loads; DC distribution network node Baseline active load.

2. The distributed convex optimization method for AC / DC distribution networks according to claim 1, characterized in that, The optimized operation model is as follows: Construct a function with the objective of minimizing active power loss and voltage deviation, including: active power loss of power electronic transformers, active power loss of AC and DC distribution networks, and voltage deviation of AC and DC distribution networks; Establish constraints, including: AC and DC distribution network branch power flow models, ZIP complex models, PET steady-state power flow models, operating voltage amplitude constraints, distributed generation output constraints, and PET port operation constraints.

3. The distributed convex optimization method for AC / DC distribution networks according to claim 1, characterized in that, By employing second-order cone relaxation techniques and successive linear approximation methods, the optimization operation model is transformed into a successive convex approximation programming model, specifically as follows: The AC / DC power flow equations are relaxed by convexity using a second-order cone relaxation technique; the PET model and ZIP load model are linearized by successive linear approximation; and auxiliary variables are introduced to linearize the objective function.

4. The distributed convex optimization method for AC / DC distribution networks according to claim 2, characterized in that, The objective function is: ； in, and These are the weighting coefficients of the objective function; Indicates the branch number; For branch set; branch road The resistance; branch road The current; Indicates the PET serial number; Represents the PET set; For the first The active power loss of each PET unit; Indicates the node number; A set of nodes; For the first Voltage amplitude at each node; The upper limit of the desired voltage; The lower limit of the desired voltage; when hour, ;when hour, ; This is a reference value for voltage deviation.

5. The distributed convex optimization method for AC / DC distribution networks according to claim 1, characterized in that, The specific steps for performing iterative solving to obtain the optimal solution are as follows: A nested iterative process consisting of an inner loop and an outer loop is proposed to solve the distributed convex programming model. In the inner loop, the AC subproblem and the DC subproblem are solved in parallel. The PET subproblem acts as a coordinator. Each subproblem belongs to the successive convex programming problem. After the inner loop converges through iterative solution, the outer loop updates the penalty coefficient based on the result of the inner loop.

6. A distributed convex optimization device for AC / DC distribution networks, characterized in that, The device includes a processor and a memory, the memory storing program instructions, the processor invoking the program instructions stored in the memory to cause the device to perform the method according to any one of claims 1-5.

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