Second-order cone relaxation based multi-objective optimization method and system for power distribution network with energy storage

Abstract

The application provides a kind of based on second-order cone relaxation energy storage power distribution network multi-objective optimization method and system, the method includes: constructing the power flow model of power distribution network, and constructing node power balance constraint, voltage drop constraint, operating boundary constraint;Second-order cone relaxation is used to constrain the alternating current power flow relationship of power flow model, and second-order cone relaxation constraint is obtained;With the minimum network loss as the first goal, the minimum generation cost as the second goal, all constraints and optimization goals are summarized to obtain a second-order cone programming model;According to the adjacency matrix, the loop phase angle consistency constraint about the set of mesh is constructed;The second-order cone programming model is solved, and the solving result is checked according to the loop phase angle consistency constraint, if the check fails, the solving result is adjusted, and the solving is re-performed, until the latest solving result meets the loop phase angle consistency constraint.The application can consider high accuracy, high efficiency and high real-time energy storage optimization.

Description

Technical Field

[0001] This invention relates to the field of energy storage optimization technology, and in particular to a multi-objective optimization method and system for distribution networks containing energy storage based on second-order cone relaxation. Background Technology

[0002] Currently, low-voltage distribution areas generally exhibit a radial topology with local closed-loop or weak-loop structures, forming a hybrid radial-grid configuration. Furthermore, a large number of distributed power sources (such as rooftop photovoltaics and residential small wind power) are connected to user-side energy storage devices, resulting in frequent changes in power flow direction within the distribution area and exhibiting reversible power flow characteristics.

[0003] Traditional control methods face significant bottlenecks: while linearized models can reduce the computational threshold by simplifying power flow equations, they cannot accurately capture the nonlinear coupling relationship between voltage, current, and power; heuristic algorithms (such as genetic algorithms and particle swarm optimization) can handle some nonlinear problems, but they are prone to getting trapped in local optima, and their computational efficiency drops significantly with the expansion of transformer area size, making it difficult to simultaneously achieve control accuracy, solution speed, and global optimality. The AC optimal power flow problem itself is nonconvex, and direct solutions face enormous computational complexity, making it difficult to meet the real-time control requirements of actual transformer areas; second-order cone relaxation (SOCP) technology, as an effective means of handling this type of nonconvex problem, can perform convex relaxation on the AC power flow equations under certain conditions (such as transformer area line impedance parameters meeting a specific range), outputting a "compact solution" with minimal deviation from the actual physical state, and can explicitly incorporate constraints such as voltage amplitude upper and lower limits, line current limits, and network loss control targets. However, for the mesh topology of low-voltage distribution areas, if the phase angle relationship in the loop is not specially processed and only the conventional SOCP relaxation model is relied upon, inconsistencies will occur in the recovery of node phase angles in power flow calculations (such as the difference in node phase angles derived from different paths within the same loop exceeding the physical allowable range), which will cause the final control scheme to deviate from the actual physical laws and fail to guarantee operational safety. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-objective optimization method and system for distribution networks with energy storage based on second-order cone relaxation, aiming to solve the core problems of voltage over-limit risk, power flow distribution calculation distortion, energy storage dispatch response lag, and high overall operating cost in traditional technologies.

[0005] In a first aspect, the present invention provides a multi-objective optimization method for a distribution network with energy storage based on second-order cone relaxation, the method comprising:

[0006] Construct a power flow model for the distribution network, and based on the power flow model, construct node power balance constraints, voltage drop constraints, and operating boundary constraints;

[0007] The AC power flow relationship of the power flow model is constrained by second-order cone relaxation, resulting in second-order cone relaxation constraints;

[0008] With minimizing network loss as the primary objective and minimizing power generation cost as the secondary objective, a second-order cone programming model is obtained by summarizing all constraints and optimization objectives.

[0009] Construct an adjacency matrix and perform a depth search based on the adjacency matrix. Obtain the mesh set based on the depth search results and construct a loop phase angle consistency constraint on the mesh set.

[0010] The second-order cone programming model is solved, and the solution is verified according to the loop phase angle consistency constraint. If the verification fails, the solution is adjusted and solved again until the latest solution satisfies the loop phase angle consistency constraint.

[0011] In some embodiments, the step of constructing a power flow model of the distribution network and constructing node power balance constraints, voltage drop constraints, and operating boundary constraints based on the power flow model includes:

[0012] The node power balance constraints are constructed based on the following formula:

[0013] ;

[0014] ;

[0015] in, Let be the active power generated by node i. Let J be the reactive power generation of node j. , Let represent the active load power and reactive load power of node j, respectively. , These represent the total active power and total reactive power transmitted from node j to all downstream nodes k, respectively. The active power received by node j from all upstream nodes i, minus the branch power. The active power loss on the j-side, This refers to the heat loss caused by the current flowing through the resistor. , These represent the active power loss and reactive power loss of node j, respectively. Let J be the conductance at node j. , Let be the squares of the voltage magnitudes at nodes i and j, respectively. The reactive power received by node j from upstream node i, minus the branch power. Reactive power loss, Let be the susceptance of node i. branch road active power, branch road reactive power, branch road The resistance value, branch road The reactance value, branch road The square of the current amplitude;

[0016] The voltage drop constraint is constructed based on the following formula:

[0017] ;

[0018] Construct the runtime boundary constraints according to the following formula:

[0019] ;

[0020] in, , These are the lower and upper limits of the node voltage, respectively. This is the upper limit of the branch current. , These are the lower and upper limits of active power generation, respectively. , These are the lower and upper limits of the active load power, respectively.

[0021] In some embodiments, the step of constraining the AC power flow relationship of the power flow model using second-order cone relaxation to obtain second-order cone relaxation constraints includes:

[0022] Introducing system inertia Establish a mapping relationship, with the mapping variables as follows:

[0023] ;

[0024] in, Let be the power perturbation at node i, x be the combined characterization of system inertia and PFR response capability, y be the normalized net power perturbation quantization value, and z be the frequency safety constraint benchmark threshold. Let be the active power generated by node i. Let be the reactive power generation of node i. For the first frequency response parameters, For PFR capacity, For delivery time, For the dead zone threshold of the power flow response, Where D is the load damping coefficient and D is the load damping constant. This is the sum of the active power of all nodes;

[0025] Multiple sampling groups The sample data were fitted using the weighted least squares method: ,in All are fitting coefficients;

[0026] Construct a second-order cone relaxation based on the linear fitting formula:

[0027] ;

[0028] ;

[0029] in, This represents the Euclidean norm.

[0030] In some embodiments, the step of taking minimizing network loss as the first objective and minimizing power generation cost as the second objective, and summing up all constraints and optimization objectives to obtain the second-order cone programming model includes:

[0031] The first objective is constructed based on the following formula:

[0032] ;

[0033] The second objective is constructed based on the following formula:

[0034] ;

[0035] in, For branch road collection, For a set of nodes, , , All are engine cost coefficients.

[0036] In some embodiments, the steps of constructing an adjacency matrix, performing a depth search based on the adjacency matrix, and obtaining a set of meshes based on the depth search results include:

[0037] Using graph theory methods to analyze the network topology, we define the set of branches directly connected to nodes as follows: Construct an adjacency matrix The matrix dimension is the same as the number of nodes N:

[0038] ;

[0039] Using the adjacency matrix, we start the search from a single node and record the search path. If we encounter an ancestor node that has already been visited during the search, a closed path is formed, which is the mesh. We then define the set of edges for each mesh.

[0040] ;

[0041] in, Let c be the set of edges of the mesh.

[0042] In some embodiments, the step of constructing loop phase angle consistency constraints for the mesh set includes:

[0043] The following formula is used to construct loop phase angle consistency constraints:

[0044] ;

[0045] in, , Let i and j be the phase angles of nodes i and j, respectively.

[0046] In some embodiments, the step of solving the second-order cone programming model and verifying the solution result according to the loop phase angle consistency constraint includes:

[0047] In second-order cone relaxation optimization, the optimization variable , , , ,and It did not directly participate in the optimization. After the optimization was completed, the phase angle was restored using existing variables, and it was verified whether it met the loop phase angle consistency constraint.

[0048] Phase angle recovery is performed using the following formula:

[0049] ;

[0050] in, , Branch roads The real and imaginary parts of admittance.

[0051] Secondly, this invention provides a multi-objective optimization system for a distribution network with energy storage based on second-order cone relaxation, the system comprising:

[0052] The power flow model construction module is used to construct the power flow model of the distribution network and construct node power balance constraints, voltage drop constraints, and operating boundary constraints based on the power flow model.

[0053] The constraint construction module is used to constrain the AC power flow relationship of the power flow model using second-order cone relaxation, resulting in second-order cone relaxation constraints.

[0054] The optimization module is used to minimize network loss as the primary objective and minimize power generation cost as the secondary objective, and to summarize all constraints and optimization objectives to obtain a second-order cone programming model.

[0055] The adjacency matrix construction module is used to construct an adjacency matrix, perform a depth search based on the adjacency matrix, obtain a set of meshes based on the depth search results, and construct a loop phase angle consistency constraint on the set of meshes.

[0056] The verification module is used to solve the second-order cone programming model and verify the solution results according to the loop phase angle consistency constraint. If the verification fails, the solution results are adjusted and the solution is solved again until the latest solution results satisfy the loop phase angle consistency constraint.

[0057] Thirdly, the present invention provides a storage medium that stores one or more programs, which, when executed by a processor, implement the above-described multi-objective optimization method for distribution networks with energy storage based on second-order cone relaxation.

[0058] Fourthly, the present invention provides an electronic device, the electronic device comprising a memory and a processor, wherein:

[0059] The memory is used to store computer programs;

[0060] When the processor executes the computer program stored in the memory, it implements the above-mentioned multi-objective optimization method for distribution networks with energy storage based on second-order cone relaxation.

[0061] Compared with the prior art, the present invention has the following advantages:

[0062] 1. This invention introduces second-order cone relaxation technology into the multi-objective optimization and control model of micro-energy storage in low-voltage power distribution areas. Based on this, it innovatively constructs loop phase angle consistency constraints and a shortest mesh selection mechanism, thereby achieving convex processing of phase angle consistency under mesh topology. Traditional methods, when dealing with non-convex power flow relationships, either sacrifice computational accuracy (e.g., linearization methods) or suffer from excessively low solution efficiency (e.g., mixed integer methods). This is especially true when there are ring network structures and a large number of energy storage devices connected, which can easily lead to power flow calculation distortion and scheduling delays. The breakthrough of this invention lies in maintaining the accuracy of physical constraints while ensuring the speed and globality of the solution through convex optimization, avoiding the contradiction between accuracy, efficiency, and real-time performance that existing methods struggle to balance.

[0063] 2. This invention addresses the voltage and power balance problem in low-voltage distribution areas by employing a second-order cone relaxation method to achieve convexity. Specifically, this involves constructing second-order cone constraints on the non-convex product relationships between the square of node voltage, the square of branch current, and active and reactive power. This ensures that the optimization problem maintains physical accuracy while possessing solvability and global optimality. Furthermore, this invention further utilizes branch voltage drop relationships and loop phase angle consistency constraints to ensure the correctness and consistency of electrical constraints in both radial and ring network operation modes. In addition, this invention embeds the energy dynamic constraints and power injection relationships of micro-energy storage into the node balance equations, directly coupling energy storage operation with the network physical layer, thereby achieving unified optimization of voltage control and energy storage scheduling. Attached Figure Description

[0064] Figure 1 This is a flowchart of a multi-objective optimization method for distribution networks with energy storage based on second-order cone relaxation, proposed in an embodiment of the present invention.

[0065] Figure 2 This is a schematic diagram of the structure of a multi-objective optimization system for a distribution network with energy storage based on second-order cone relaxation, as proposed in an embodiment of the present invention.

[0066] The following detailed description, in conjunction with the accompanying drawings, will further illustrate the present invention. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by those skilled in the art. The terms "comprising" and similar expressions used herein mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, but does not exclude other elements or objects.

[0068] like Figure 1 As shown, an embodiment of the present invention proposes a multi-objective optimization method for distribution networks with energy storage based on second-order cone relaxation. The method includes steps S101 to S105, wherein:

[0069] Step S101: Construct a power flow model of the distribution network, and construct node power balance constraints, voltage drop constraints, and operating boundary constraints based on the power flow model;

[0070] It should be noted that the power flow model includes input parameters such as node set, voltage phasor, voltage amplitude square, voltage phase angle, node active power generation, reactive power generation, complex power, node active load power, reactive load power, impedance, current phasor, current amplitude square, branch active power, and branch reactive power.

[0071] In addition, in some embodiments, node power balance constraints are established for the power flow model. Node power balance is a fundamental law of power system operation. If the active or reactive power of a node is unbalanced, it will lead to grid frequency fluctuations (active power imbalance) or voltage collapse (reactive power imbalance). Therefore, it is necessary to construct strict power balance equations for each node to ensure real-time matching of power supply and demand.

[0072] The node power balance constraints are constructed based on the following formula:

[0073] ;

[0074] ;

[0075] in, Let be the active power generated by node i. Let J be the reactive power generation of node j. , Let represent the active load power and reactive load power of node j, respectively. , These represent the total active power and total reactive power transmitted from node j to all downstream nodes k, respectively. The active power received by node j from all upstream nodes i, minus the branch power. The active power loss on the j-side, This refers to the heat loss caused by the current flowing through the resistor. , These represent the active power loss and reactive power loss of node j, respectively. Let J be the conductance at node j. , Let be the squares of the voltage magnitudes at nodes i and j, respectively. The reactive power received by node j from upstream node i, minus the branch power. Reactive power loss, Let be the susceptance of node i. branch road active power, branch road reactive power, branch road The resistance value, branch road The reactance value, branch road The square of the current amplitude.

[0076] also, This represents the net active power injection of node j. When the value is positive, the node is an "active power surplus node" (such as a generator node), which needs to transmit active power to other nodes. When the value is negative, the node is an "active power deficit node" (such as a load node), which needs to receive active power from other nodes. This represents the net reactive power injection at node j. A positive value indicates "reactive power surplus" (such as generator overexcitation or capacitor commissioning), while a negative value indicates "reactive power deficit" (such as load demand or reactor commissioning). The above constraints explicitly consider branch losses and node losses to avoid deviations between the model and actual operation due to neglecting losses, thus ensuring the physical accuracy of power balance.

[0077] Furthermore, in some embodiments, for power flow models, when current flows through a branch impedance, a voltage drop occurs across the impedance, causing a difference between the voltage at the end node and the voltage at the beginning node of the branch (i.e., voltage drop). Excessive voltage drop may cause the end load voltage to fall below the allowable lower limit, affecting the normal operation of electrical equipment (e.g., reduced motor speed, reduced lighting brightness); excessive voltage rise may damage equipment insulation. Therefore, voltage drop constraints need to be constructed for each branch to characterize the coupling relationship between voltage and power flow.

[0078] The voltage drop constraint is constructed based on the following formula:

[0079] ;

[0080] Furthermore, in some embodiments, the operational boundary constraints are constructed according to the following formula:

[0081] ;

[0082] in, , These are the lower and upper limits of the node voltage, respectively. This is the upper limit of the branch current. , These are the lower and upper limits of active power generation, respectively. , These are the lower and upper limits of the active load power, respectively.

[0083] Step S102: Use second-order cone relaxation to constrain the AC power flow relationship of the power flow model to obtain second-order cone relaxation constraints;

[0084] It should be noted that in this step, system inertia is first introduced. Establish a mapping relationship, with the mapping variables as follows:

[0085] ;

[0086] in, Let be the power perturbation at node i, x be the combined characterization of system inertia and PFR response capability, y be the normalized net power perturbation quantization value, and z be the frequency safety constraint benchmark threshold. Let be the active power generated by node i. Let be the reactive power generation of node i. For the first frequency response parameters, For PFR capacity, For delivery time, For the dead zone threshold of the power flow response, Where D is the load damping coefficient and D is the load damping constant. This is the sum of the active power of all nodes;

[0087] Multiple sampling groups The sample data were fitted using the weighted least squares method: ,in All are fitting coefficients;

[0088] Construct a second-order cone relaxation based on the linear fitting formula:

[0089] ;

[0090] ;

[0091] in, This represents the Euclidean norm.

[0092] In summary, traditional methods for optimizing AC power flow under frequency constraints either employ approximation techniques such as piecewise linearization, which introduces a large number of auxiliary variables, leading to a significant increase in model complexity and a substantial decrease in solution efficiency; or they rely on case-specific parameter tuning, resulting in poor adaptability and difficulty in guaranteeing global approximation accuracy. This is particularly problematic in scenarios with low inertia due to high penetration of new energy sources or in situations with fluctuating parameters, where excessive approximation deviations can easily occur, affecting the effectiveness of frequency security constraints and failing to reliably guarantee grid frequency stability after large disturbances. This invention, however, innovatively introduces system inertia and PFR (Power Flow Rate)... The comprehensive characterization variable x of response capability, the normalized net power disturbance quantification value y, and the frequency safety constraint benchmark threshold z transform the highly nonlinear frequency minimum point constraint relationship into a fittable mapping model. Then, the weighted least squares method is used to linearly fit multiple sets of sample data covering the actual system parameter range to obtain an accurate linear approximation. Subsequently, a standard second-order cone relaxation constraint is constructed based on this linear expression. This achieves tight relaxation of the non-convex relationship of AC power flow through convexification processing, fully preserving the core physical coupling relationship between voltage, current, and power, without introducing a large number of auxiliary variables, thus avoiding the high complexity and cumbersome parameter tuning defects of traditional methods. It can maintain extremely high fitting accuracy in different scenarios such as conventional systems and low-inertia systems, ensuring the accuracy of frequency safety constraints. The constructed second-order cone programming model can be efficiently solved by commercial solvers to meet real-time control requirements, and can accurately capture the frequency minimum point safety requirements under large disturbances, effectively avoiding the risk of frequency exceeding limits. It balances optimization accuracy, solution efficiency, and engineering practicality, and is applicable to various distribution network optimization scenarios including energy storage and new energy sources.

[0093] Step S103: With minimizing network loss as the primary objective and minimizing power generation cost as the secondary objective, summarize all constraints and optimization objectives to obtain the second-order cone programming model;

[0094] It should be noted that in this step, the first objective is constructed based on the following formula:

[0095] ;

[0096] The second objective is constructed based on the following formula:

[0097] ;

[0098] in, For branch road collection, For a set of nodes, , , All are engine cost coefficients.

[0099] Step S104: Construct an adjacency matrix and perform a depth search based on the adjacency matrix. Obtain the mesh set based on the depth search results and construct a loop phase angle consistency constraint on the mesh set.

[0100] In some embodiments, the mesh extraction process is as follows:

[0101] (1) Analyze the network topology using graph theory, defining the set of branches directly connected to nodes i and j as follows: Constructing an adjacency matrix The matrix dimension is the same as the number of nodes N.

[0102] ;

[0103] Since nodes are not connected to themselves, the diagonal elements of the adjacency matrix are all 0. Considering that most nodes in a power network are only directly connected to a few nodes, the adjacency matrix exhibits sparse characteristics. Therefore, a sparse matrix storage method is adopted to reduce the consumption of computing resources.

[0104] (2) Perform a depth-first search on the graph:

[0105] Using an adjacency matrix, a search is performed starting from a given node, recording the search path. If an already visited ancestor node is encountered during the search, a closed path is formed; this is a candidate cycle, or mesh, thus obtaining a batch of candidate cycles. The edge set of a mesh is defined as follows:

[0106] ;

[0107] in, Let c be the set of edges of the mesh.

[0108] (3) Each branch may belong to multiple loops. To avoid redundancy, retain the loop with the fewest branches and remove other long loops that contain that branch. After processing, the final mesh set C is obtained.

[0109] The final mesh set It is necessary to cover all closed loops, with each mesh being an independent constraint unit that will serve as the core input for loop phase angle consistency constraints, ensuring that phase angle constraints can cover the closed-loop structure of the entire power grid.

[0110] Furthermore, in some embodiments, the voltage phase angle reflects the phase relationship of the voltage, and the phase angle difference between nodes... The range of values ​​is To avoid phase ambiguity, the direction and magnitude of active power transmission are directly determined. In a closed-loop network, if the phase angle does not meet the consistency constraint, circulating current will be generated, leading to branch overload, increased network loss, and even equipment failure.

[0111] For a set of meshes, loop phase angle consistency constraints are constructed according to the following formula:

[0112] ;

[0113] in, , Let i and j be the phase angles of nodes i and j, respectively.

[0114] Step S105: Solve the second-order cone programming model and verify the solution result according to the loop phase angle consistency constraint. If the verification fails, adjust the solution result and solve it again until the latest solution result satisfies the loop phase angle consistency constraint.

[0115] It should be noted that the solution results include the voltage at node i. Branch Road Trend Phase angle distribution .

[0116] Furthermore, in some embodiments, in second-order cone relaxation optimization, the optimization variable , , , ,and It did not directly participate in the optimization. After the optimization was completed, the phase angle was restored using existing variables, and it was verified whether it met the loop phase angle consistency constraint.

[0117] First, the elements of the admittance matrix are defined as follows: and Branch roads The real and imaginary parts of admittance, admittance ,therefore:

[0118] , ;

[0119] The admittance matrix reflects the conductivity of a branch. Based on the power-phase relationship of branch power flow, ,and .Will Substitute, separate the real and imaginary parts, and then combine. The phase angle recovery formula can be derived, where, branch road Complex power, branch road The conjugate current, branch road The current, branch road The current.

[0120] After optimization, the phase angle is restored according to the following formula:

[0121] .

[0122] Furthermore, regarding consistency verification: Select a node as a reference point, such as the busbar of a substation, and define its angle as 0 degrees. This will restore... Calculate the sum of phase angles from the reference point to the final return point along each branch of the mesh. If it is not 0 (allowing for small errors, such as...), then... Because numerical calculations have precision biases, it is necessary to calculate the deviation of the phase angle sum for loops that do not meet the constraints. Then, following the principle of uniform distribution, that is, adjusting the same angle for each branch, the deviation is distributed among all branches of the loop. After adjustment, the optimization solution is re-executed until the phase angles meet the consistency constraints.

[0123] In summary, based on the above-described multi-objective optimization method for distribution networks with energy storage based on second-order cone relaxation, this invention has the following advantages:

[0124] 1. This invention introduces second-order cone relaxation technology into the multi-objective optimization and control model of micro-energy storage in low-voltage power distribution areas. Based on this, it innovatively constructs loop phase angle consistency constraints and a shortest mesh selection mechanism, thereby achieving convex processing of phase angle consistency under mesh topology. Traditional methods, when dealing with non-convex power flow relationships, either sacrifice computational accuracy (e.g., linearization methods) or suffer from excessively low solution efficiency (e.g., mixed integer methods). This is especially true when there are ring network structures and a large number of energy storage devices connected, which can easily lead to power flow calculation distortion and scheduling delays. The breakthrough of this invention lies in maintaining the accuracy of physical constraints while ensuring the speed and globality of the solution through convex optimization, avoiding the contradiction between accuracy, efficiency, and real-time performance that existing methods struggle to balance.

[0125] 2. This invention addresses the voltage and power balance problem in low-voltage distribution areas by employing a second-order cone relaxation method to achieve convexity. Specifically, this involves constructing second-order cone constraints on the non-convex product relationships between the square of node voltage, the square of branch current, and active and reactive power. This ensures that the optimization problem maintains physical accuracy while possessing solvability and global optimality. Furthermore, this invention further utilizes branch voltage drop relationships and loop phase angle consistency constraints to ensure the correctness and consistency of electrical constraints in both radial and ring network operation modes. In addition, this invention embeds the energy dynamic constraints and power injection relationships of micro-energy storage into the node balance equations, directly coupling energy storage operation with the network physical layer, thereby achieving unified optimization of voltage control and energy storage scheduling.

[0126] like Figure 2 As shown, one embodiment of the present invention proposes a multi-objective optimization system for a distribution network with energy storage based on second-order cone relaxation. The system includes:

[0127] The power flow model construction module 10 is used to construct the power flow model of the distribution network and construct node power balance constraints, voltage drop constraints, and operating boundary constraints based on the power flow model.

[0128] The constraint construction module 20 is used to constrain the AC power flow relationship of the power flow model using second-order cone relaxation, so as to obtain second-order cone relaxation constraints.

[0129] Optimization module 30 is used to summarize all constraints and optimization objectives with the first objective of minimizing network loss and the second objective of minimizing power generation cost, and obtain a second-order cone programming model.

[0130] The adjacency matrix construction module 40 is used to construct an adjacency matrix, perform a depth search based on the adjacency matrix, obtain a set of meshes based on the depth search results, and construct a loop phase angle consistency constraint on the set of meshes.

[0131] The verification module 50 is used to solve the second-order cone programming model and verify the solution results according to the loop phase angle consistency constraint. If the verification fails, the solution results are adjusted and the solution is solved again until the latest solution results satisfy the loop phase angle consistency constraint.

[0132] In another aspect, the present invention also proposes a storage medium on which one or more programs are stored, which, when executed by a processor, implement the above-described multi-objective optimization method for distribution networks with energy storage based on second-order cone relaxation.

[0133] In another aspect, the present invention also proposes an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to realize the above-mentioned multi-objective optimization method for distribution networks with energy storage based on second-order cone relaxation.

[0134] Those skilled in the art will understand that the logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can mean any means that can contain stored, communicated, propagated, or transmitted programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0135] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0136] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0137] While embodiments of the present invention have been described in detail above, it will be apparent to those skilled in the art that various modifications and variations can be made to these embodiments. However, it should be understood that such modifications and variations fall within the scope and spirit of the invention as set forth in the claims. Furthermore, the invention described herein may have other embodiments and can be implemented or carried out in various ways.

Claims

1. A second-order cone relaxation based multi-objective optimization method for energy storage integrated power distribution networks, characterized in that, The method comprises: a power flow model of the power distribution network is constructed, and node power balance constraints, voltage drop constraints, and operation boundary constraints are constructed according to the power flow model; second-order cone relaxation is used to constrain the alternating current power flow relationship of the power flow model, to obtain second-order cone relaxation constraints; a second-order cone programming model is obtained by taking minimization of network loss as a first target, taking minimization of generation cost as a second target, and collecting all constraints and optimization targets; an adjacency matrix is constructed, and a depth search is performed according to the adjacency matrix, a mesh set is obtained according to a depth search result, and loop phase angle consistency constraints about the mesh set are constructed; the loop phase angle consistency constraints are constructed according to the following formula: ； wherein , are the phase angles of nodes i, j, respectively. the second-order cone programming model is solved, and the solving result is checked according to the loop phase angle consistency constraints; if the checking fails, the solving result is adjusted, and the solving is performed again, until the latest solving result satisfies the loop phase angle consistency constraints; In the second order cone relaxation optimization, the optimization variables , , , , and are not directly involved in the optimization, and after the optimization is completed, the phase angles are restored by the existing variables, and it is verified whether they meet the loop phase angle consistency constraint. the phase angle is recovered according to the following formula: ； wherein , are the real and imaginary parts of the branch admittance, respectively.

2. The second-order cone relaxation based multi-objective optimization method for energy storage integrated power distribution network according to claim 1, wherein, the step of constructing the power flow model of the power distribution network, and constructing the node power balance constraints, the voltage drop constraints, and the operation boundary constraints according to the power flow model comprises: the node power balance constraints are constructed according to the following formula: ； ； wherein, Pj is the active power generated at node j, Qj is the reactive power generated at node j, , Pj and Qj are the active and reactive load powers at node j, respectively, , Pjk and Qjk are the total active and reactive power transmitted by node j to all downstream nodes k, respectively, Pji is the active power received by node j from all upstream nodes i, minus the active power loss in branch Pji is the active power received by node j from all upstream nodes i, minus the active power loss in branch Pji is the active power received by node j from all upstream nodes i, minus the active power loss in branch , Pji and Qji are the active and reactive power loss in branch Gj is the conductance of node j, , Vj2 and Vi2 are the voltage magnitude squared of node j and i, respectively, Qji is the reactive power received by node j from upstream node i, minus the reactive power loss in branch Qji is the reactive power received by node j from upstream node i, minus the reactive power loss in branch Bj is the susceptance of node i, Pji is the active power in branch Pji is the active power in branch Qji is the reactive power in branch Rji is the resistance of branch Xji is the reactance of branch Xji is the reactance of branch Xji is the reactance of branch Xji is the reactance of branch Iji2 is the current magnitude squared of branch Iji2 is the current magnitude squared of branch the voltage drop constraints are constructed according to the following formula: ； the operation boundary constraints are constructed according to the following formula: ； wherein , are lower and upper square limits of the node voltage, respectively, is an upper square limit of the branch current, , are lower and upper limits of the active generation power, respectively, , are lower and upper limits of the reactive load power, respectively.

3. The second-order cone relaxation based multi-objective optimization method for energy storage integrated power distribution network according to claim 2, characterized in that, the step of using the second-order cone relaxation to constrain the alternating current power flow relationship of the power flow model, to obtain the second-order cone relaxation constraints comprises: Introducing system inertia Constructing mapping relationship, mapping variables are: ； wherein, is the power disturbance of node i, x is a comprehensive representation of system inertia and PFR response capability, y is a normalized net power disturbance quantization value, and z is a frequency safety constraint reference threshold, is the active power generation of node i, is the reactive power generation of node i, is a primary frequency response parameter, is a PFR capacity, is a delivery time, is a power flow response dead zone threshold, is a load damping coefficient, and D is a load damping constant, is the sum of active load power of all nodes; Sampling multiple groups The sample data is fitted using a weighted least squares method: wherein are fitting coefficients; the second-order cone relaxation is constructed according to a linear fitting formula: ； ； wherein denotes the Euclidean norm.

4. The second-order cone relaxation based multi-objective optimization method for energy storage integrated power distribution network according to claim 3, characterized in that, the step of obtaining the second-order cone programming model by taking the minimization of network loss as the first target, taking the minimization of generation cost as the second target, and collecting all constraints and optimization targets comprises: the first target is constructed according to the following formula: ； the second target is constructed according to the following formula: ； wherein is a set of branches, is a set of nodes, , , are engine cost coefficients.

5. The second-order cone relaxation based multi-objective optimization method for energy storage integrated power distribution network according to claim 4, wherein, the step of constructing the adjacency matrix, performing the depth search according to the adjacency matrix, and obtaining the mesh set according to the depth search result comprises: Topology of the network is analyzed by graph theory method, and the branch set directly connected with the node is defined as , the adjacency matrix is constructed, and the matrix dimension is consistent with the node number N: ； a closed path is formed if an ancestor node that has been visited is encountered in the search process, that is, a mesh is obtained, and an edge set of the mesh is defined: ； wherein, is the set of edges of mesh c.

6. A second-order cone relaxation based multi-objective optimization system for energy storage integrated distribution network, for implementing the second-order cone relaxation based multi-objective optimization method for energy storage integrated distribution network according to any one of claims 1-5, characterized in that, the system comprises: a power flow model construction module, configured to construct a power flow model of a power distribution network, and construct node power balance constraints, voltage drop constraints, and operation boundary constraints according to the power flow model; a constraint construction module, configured to use second-order cone relaxation to constrain an alternating current power flow relationship of the power flow model, to obtain second-order cone relaxation constraints; an optimization module, configured to obtain a second-order cone programming model by taking minimization of network loss as a first target, taking minimization of generation cost as a second target, and collecting all constraints and optimization targets; an adjacency matrix construction module, configured to construct an adjacency matrix, perform a depth search according to the adjacency matrix, obtain a mesh set according to a depth search result, and construct loop phase angle consistency constraints about the mesh set; a checking module, configured to solve the second-order cone programming model, and check the solving result according to the loop phase angle consistency constraints; if the checking fails, the solving result is adjusted, and the solving is performed again, until the latest solving result satisfies the loop phase angle consistency constraints.

7. A storage medium, characterized by The storage medium stores one or more programs, which are executed by the processor to implement the second-order cone relaxation based multi-objective optimization method for power distribution networks with energy storage according to any one of claims 1-5.

8. An electronic device, comprising: The electronic device comprises a memory and a processor, wherein: The memory is configured to store a computer program; The processor is configured to execute the computer program stored in the memory to implement the second-order cone relaxation based multi-objective optimization method for power distribution networks with energy storage according to any one of claims 1-5.

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