Power distribution network flexible interconnection device configuration method based on multi-target fuzzy optimization

Abstract

The invention discloses a power distribution network flexible interconnection device configuration method based on multi-target fuzzy optimization, and relates to the technical field of power systems and automatic control. According to the method, a multi-objective function of minimum power-losing load and minimum network loss is established, and deterministic constraints such as alternating-current and direct-current power flow and equipment capacity and uncertainty constraints of voltage and current out-of-limit probability are considered. Multi-target fuzzy optimization is adopted, and an optimal scheme is scientifically decided by constructing an ideal point and Hamming close degree. For a large-scale mixed integer nonlinear programming problem, a mixed solution strategy combining simulated annealing or improved grey wolf algorithm and cone programming is provided, and efficient decoupling optimization of point distribution and constant volume is realized. And finally, the optimal capacity of the device is determined by integrating the requirements of each fault scene, and the reliability and economy of the system are considered.

Description

Technical Field

[0001] This invention relates to the field of power system and automation control technology, specifically to a method for configuring flexible interconnection devices in distribution networks based on multi-objective fuzzy optimization. Background Technology

[0002] With the large-scale integration of distributed generation (DG), electric vehicles, and diverse loads, traditional distribution networks face prominent challenges such as complex operation and control, uncontrollable power flow, and weak fault recovery capabilities. To improve the flexibility and operational efficiency of distribution networks, flexible interconnection devices, such as Standard Operating Procedures (SOPs), a new type of power distribution equipment based on power electronics technology, are increasingly being applied to modern medium- and low-voltage distribution networks. Flexible interconnection devices possess excellent power control capabilities, optimizing power flow distribution during normal network operation and enabling rapid load transfer in case of faults, thereby improving power supply reliability and system operating economy.

[0003] However, the construction and operation costs of flexible interconnection devices are high, and their location and capacity have a significant impact on the performance improvement of the distribution network. Improper configuration can not only waste resources but also fail to effectively utilize their control capabilities. Therefore, how to scientifically and rationally select the location and capacity of flexible interconnection devices has become a key issue in current distribution network planning and operation.

[0004] Current research employs multi-objective optimization methods to model the configuration of flexible interconnected devices, primarily considering objectives such as minimizing network losses and maximizing load recovery rates. However, existing methods often use weighted summation or genetic algorithms for solving these problems, making it difficult to balance multiple objectives. Furthermore, the robustness and adaptability of these models are insufficient when facing real-world operating conditions such as load fluctuations and uncertainties in distributed power generation output. In addition, most studies have not fully considered the rapid response capability of flexible interconnected devices to power outages during fault scenarios, leading to discrepancies between optimization results and actual operational requirements.

[0005] Therefore, there is an urgent need to propose an optimized configuration method for flexible interconnection devices that comprehensively considers the fault recovery capability, operational economy, and the impact of uncertain factors of the distribution network, so as to achieve efficient utilization of flexible interconnection devices in multiple operating scenarios and improve the intelligence and resilience of the distribution network. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a configuration method for flexible interconnection devices in distribution networks based on multi-objective fuzzy optimization. This method is particularly suitable for enabling rapid load transfer, reducing power outage loads, and optimizing power flow distribution through flexible interconnection devices when a distribution network fault occurs. It also comprehensively considers the economic efficiency, reliability, and uncertainty constraints of distribution network operation.

[0007] The technical solution adopted in this invention is as follows:

[0008] The configuration method for flexible interconnection devices in distribution networks based on multi-objective fuzzy optimization includes the following steps:

[0009] Step 1: Establish a multi-objective optimization function: Establish a multi-objective optimization function, and clarify the optimization objectives with minimum power outage load and minimum distribution network loss as the core.

[0010] Step 2: Constructing the ideal solution and fuzzy membership function: Based on the multi-objective optimization function, solve the ideal solution for each objective and construct the fuzzy membership function to provide a quantitative basis for multi-objective fuzzy decision-making;

[0011] Step 3: Constructing the membership function matrix and standard optimal solution: Based on fuzzy membership functions, construct the membership function matrix and standard optimal solution to form a fuzzy evaluation system for multi-objective optimization;

[0012] Step 4: Calculate Hamming proximity and select the optimal solution: Based on the membership function matrix and the standard optimal solution, the flexible interconnection device configuration scheme that is closest to the ideal solution is selected by calculating and comparing the Hamming proximity.

[0013] Step 5: Constructing a constraint model: Based on the optimization objectives set by combining the physical operating characteristics and actual operating requirements of the distribution network, establish a mathematical model that includes deterministic and uncertain constraints to ensure that the configuration scheme meets the requirements of operational safety and probabilistic reliability.

[0014] Step 6: Solving with a hybrid optimization algorithm: Based on the multi-objective fuzzy optimization model and its constraints, a hybrid optimization algorithm is used to solve the model, achieving efficient collaborative optimization of integer variables and continuous variables.

[0015] Furthermore, step 1 includes the following steps:

[0016] Step 1.1, establish the objective function F1(X) for minimum power loss load:

[0017]

[0018] In the formula, F1(X) is the objective function value of the power outage load, representing the total power outage load; X is the set of optimization variables, including the location and capacity of the flexible interconnection device; N nd S represents the total number of load nodes in the distribution network; i is the load node number; k(i) represents the topological connection between node i and the distribution network. If k(i) = 1, then node i has a closed connection branch with the distribution network after fault recovery; otherwise, k(i) = 0, then there is no closed connection branch; (1-k(i)) represents the proportion of nodes that have not had their power restored; S d (i) represents the proportion of loads transferred from node i that are disconnected due to branch overload, with values ​​ranging from [0, 1]; P d(i) represents the original active load of the i-th node;

[0019] Step 1.2, establish the objective function F2(X) for minimizing distribution network losses:

[0020]

[0021] In the formula, F2(X) is the objective function value of the distribution network loss, representing the total active power loss; j is the branch number; I br R(j) is the effective value of the current in the j-th branch; R(j) is the resistance value of the j-th branch.

[0022] Furthermore, in step 2, the process of solving for the ideal solutions to each objective function is as follows:

[0023] For the objective function F1(X) of minimum power outage load, the minimum value is achieved by increasing the capacity of the flexible interconnection device to a sufficiently large value; the maximum value is achieved by setting the capacity of the flexible interconnection device to 0, i.e., not participating in load transfer.

[0024] For the objective function F2(X) to minimize distribution network losses, the minimum value is obtained by optimizing the power flow distribution; the maximum value is the loss value without power flow optimization.

[0025] In step 2, the process of constructing the trapezoidal membership function is as follows:

[0026] Constructing the trapezoidal membership function r ij :

[0027]

[0028] In the formula, r ij Let F be the trapezoidal membership function value, representing the degree of membership of the i-th objective function to the ideal solution under the j-th configuration scheme, with a value range of [0,1]; i is the objective function number, representing the i-th objective function; j is the configuration scheme number, representing the j-th candidate configuration scheme; F i,j (X) represents the actual value of the i-th objective function under the j-th scheme, that is, the calculation result of the objective function under the current configuration scheme; Let be the minimum ideal solution of the i-th objective function under the j-th scheme, that is, the ideal optimal value of the objective function; The maximum ideal solution of the i-th objective function under the j-th scheme is the worst acceptable value of the objective function.

[0029] Using the trapezoidal membership function r ij This indicates the degree to which the i-th objective function approaches the ideal solution under the j-th configuration scheme, and is used to fuzzify the objective function value.

[0030] Furthermore, in step 3, the membership function matrix R is constructed, represented as:

[0031]

[0032] In the formula, R is an n×m membership function matrix, used to represent the fuzzy membership degree of multiple objective functions under multiple configuration schemes; n is the number of objective functions, that is, the number of optimization objectives considered in the optimization problem; m is the number of configuration schemes, that is, the number of candidate flexible interconnection device deployment and capacity combinations.

[0033] Furthermore, in step 3, the standard optimal solution construction process is as follows:

[0034] Based on the membership function matrix R, the membership vector of the k-th scheme is: [r 1k ,r 2k ,...,r nk ] T , represents the membership combination of the k-th configuration scheme under all objective functions, k∈[1,...,m];

[0035] Constructing the standard optimal solution

[0036]

[0037] In the formula, This is the membership function matrix corresponding to the standard optimal solution; The standard optimal solution represents the optimal combination of objective functions in a fuzzy sense, consisting of the maximum membership degree of each objective function; r 11 ∨r 12 ∨…∨r 1n Let g be the maximum membership degree of all solutions under the i-th objective function, that is, the optimal membership degree value among all configuration solutions in the i-th objective function; i Let g1 be the maximum membership degree of the i-th objective function, which is an element constituting the standard optimal solution, representing the ideal membership degree value of the objective function; (g1,…,g n ) T This is the membership vector of the standard optimal solution, where each element represents the ideal membership value of an objective function, forming a column vector;

[0038] The optimal solution is determined by maximizing the membership degree of each objective function, and this optimal solution serves as a benchmark for comparing all configuration solutions.

[0039] Furthermore, in step 4, the Hamming proximity between each configuration scheme and the standard optimal scheme is calculated using the following formula:

[0040]

[0041] In the formula, Let Hamming proximity be the ratio of the k-th optimized solution B(k) to the standard optimal solution. The degree of closeness is indicated by the value; a larger value indicates that the solution is closer to the ideal solution. B(k) represents the k-th candidate optimization scheme. The standard optimal solution is the ideal optimal solution consisting of the maximum membership degree of each objective function, serving as a benchmark for comparing all candidate solutions; n is the number of objective functions, representing the number of optimization objectives considered in the optimization problem; i is the objective function number, i = 1, 2, ..., n; g i The standard optimal membership degree of the i-th objective function, i.e., the standard optimal solution The membership value corresponding to the i-th objective function; r ik ξ represents the membership degree of the i-th objective function under the k-th scheme, indicating the degree of membership of the i-th objective function to the ideal solution in the k-th candidate scheme, with a value range of [0,1]; ξ is a distance parameter used to define different distance measurement methods;

[0042] The greater the similarity, the closer the configuration is to the ideal solution;

[0043] The optimal configuration is selected based on the closest proximity to the target location. The optimal configuration includes the optimal deployment location and capacity configuration.

[0044] Furthermore, in step 5, the deterministic constraints include: AC power flow balance constraints, DC power flow balance constraints, and flexible interconnection device capacity constraints.

[0045] AC power flow balance constraint: In an AC distribution network, the active power P of node i is... o (i) and reactive power Q o (i) Satisfies the following power flow equations:

[0046]

[0047] In the formula, U i U j G represents the voltage magnitudes at nodes i and j; ij B ij Let θ be the conductance and susceptance of branch ij; ij =θ i -θ j , representing the voltage phase angle difference between nodes i and j;

[0048] Node power balance: The injected active power P at node i in (i) and reactive power Q in (i) Satisfies:

[0049]

[0050] In the formula, P d(i), Q d (i) represents the original active and reactive loads of node i; S d (i) represents the proportion of loads transferred from node i that are disconnected due to branch overload, with values ​​ranging from [0, 1]; P ij Q ij For the simplified active and reactive power flow of the branch; N nd This represents the total number of load nodes in the distribution network.

[0051] DC power flow balance constraint: The flexible interconnection device is interconnected through a DC bus, and the voltages of DC side nodes i' and j' are U respectively. dc (i'), U dc (j'), the DC current I of branch i'j' dc (i'j') is:

[0052] I dc (i'j')=g(i'j')×[U dc (i')-U dc (j')];

[0053] In the formula, g(i'j') is the conductance of the DC branch;

[0054] Based on the node current / power balance, we get:

[0055]

[0056] In the formula, P dc (i'j') represents the power of the DC branch i'j'; N dc This represents the total number of DC-side nodes.

[0057] Flexible interconnect device capacity constraint: The capacity of the k'-th flexible interconnect device should meet the following requirements:

[0058]

[0059] In the formula, P vsc (k'), Q vsc (k') and S vsc (k') represents the actual active power, reactive power, and rated capacity of the flexible interconnection device, respectively.

[0060] Furthermore, in step 5, the uncertainty constraints include: node voltage opportunity constraints and branch current / power opportunity constraints;

[0061] Node voltage constraint: The voltage at node i must satisfy:

[0062] P r {U min ≤U(i)≤U max}≥βu ;

[0063] In the formula, P r {} represents the probability of the event occurring; U(i) is the voltage at node i; U min U max These represent the lower and upper limits of the allowable node voltage, respectively; β u The confidence value for the node voltage constraint;

[0064] The branch current / power opportunity constraint is expressed as follows: the transmission power and current of the j-th branch should satisfy:

[0065]

[0066] In the formula, S br (j) represents the actual transmission power of branch j; I is the rated transmission power of path j; br (j) represents the actual transmission current of branch j; β is the rated transmission current of branch j; br This is the confidence value for the branch safety current constraint.

[0067] Furthermore, in step 6, for the optimization of integer variables of the point location, simulated annealing algorithm or Grey Wolf Optimization (GWO) algorithm is used for global search; for the optimization of continuous variables of capacity configuration, cone programming method is used for local optimization; and for the decoupling optimization of integer and continuous variables, the solution efficiency and convergence are improved.

[0068] Furthermore, the method for configuring flexible interconnection devices in distribution networks based on multi-objective fuzzy optimization also includes:

[0069] Step 7: Simulation Verification and Configuration Result Output: Based on the constructed multi-objective fuzzy optimization model, fuzzy evaluation system, constraint model, and solution algorithm, the optimal configuration result is output through simulation verification, thus completing the layout and capacity optimization configuration of the flexible interconnection device in the distribution network.

[0070] Compared with the prior art, the beneficial effects of the present invention are:

[0071] The present invention proposes a method for configuring flexible interconnection devices in distribution networks based on multi-objective fuzzy optimization, which has the following significant advantages compared with the prior art:

[0072] 1. It achieves multi-objective collaborative optimization, resulting in scientific and rational decision-making:

[0073] Traditional optimization methods often employ weighted summation, whose results heavily rely on manually set weight coefficients, leading to strong subjectivity and difficulty in objectively reflecting the balance between objectives. This invention employs a multi-objective fuzzy optimization method. By constructing ideal points and calculating Hamming proximity, it quantitatively evaluates the "satisfaction degree" of multiple objective functions (such as minimum power loss load and minimum network loss) with respect to the ideal solution, ultimately selecting the solution with the highest proximity degree as the optimal solution. This method avoids the subjectivity of weight setting, enabling a more scientific and objective coordination between reliability and economy, achieving true multi-objective collaborative optimization.

[0074] 2. Balancing fault recovery capabilities with operational economy to improve overall system performance:

[0075] This invention considers two core objectives in its model construction: minimizing the power loss load under fault scenarios and minimizing network losses during normal / fault operation. Through the power regulation flexibility of the flexible interconnection device, it prioritizes power supply to critical loads during faults while optimizing power flow distribution to reduce overall losses. This configuration not only effectively addresses sudden faults but also contributes to energy conservation and consumption reduction during daily operation, comprehensively improving the safety, reliability, and economy of the distribution network.

[0076] 3. Effectively handle uncertainties and enhance the robustness of the configuration scheme:

[0077] Load demand and distributed generation output in power distribution networks exhibit significant volatility and uncertainty. This invention introduces the concept of chance-constrained programming, establishing probabilistic constraints on node voltage and branch current / power. By setting confidence levels, it allows for limit exceedances under low-probability events, while ensuring the safe and stable operation of the system in the vast majority of cases. This method is more practically applicable in engineering than deterministic constraints, and the resulting configuration scheme has stronger adaptability and robustness to uncertain disturbances, avoiding cost waste due to excessive conservatism or risks caused by excessive aggressiveness.

[0078] 4. Employing a hybrid optimization algorithm for efficient solution of large-scale complex problems:

[0079] The site selection and capacity determination problem of flexible interconnected devices is a typical large-scale mixed-integer nonlinear programming (MINLP) problem, which is difficult to solve. This invention innovatively proposes a hybrid optimization algorithm: the upper layer uses simulated annealing or an improved Grey Wolf optimization algorithm for global search to optimize discrete variables such as site locations; the lower layer uses cone programming to solve the continuous capacity configuration and operation optimization problem under a given site location. This strategy of decoupling integer and continuous variables fully leverages the global optimization capability of intelligent algorithms and the local solution efficiency of mathematical programming algorithms, significantly improving the convergence speed and solution accuracy of the algorithm, and effectively addressing the optimization needs of complex distribution networks.

[0080] 5. The configuration results are highly universal and can guide engineering practices:

[0081] The configuration process proposed in this invention explicitly states that the final capacity of the flexible interconnection device should be the maximum value of the optimal capacity under all anticipated fault scenarios. This principle ensures that the configured device capacity is sufficient to cope with the most severe fault conditions, thus possessing universality and engineering feasibility. This method not only provides a theoretically optimal solution but also offers clear and direct engineering implementation guidelines, facilitating its widespread application in actual power grid planning.

[0082] In summary, this invention provides a systematic, scientific, and efficient method for configuring flexible interconnection devices, which solves the problems of single objective, neglect of uncertainty, and difficulty in solving existing technologies. It has important application value for promoting the development of flexible power distribution technology and improving the intelligence level of modern power distribution networks. Attached Figure Description

[0083] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0084] Figure 1 This is a schematic diagram of the overall process of the method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to the present invention.

[0085] Figure 2 A schematic diagram of an improved distribution network model for the IEEE 33-node network;

[0086] Figure 3 A schematic diagram showing the average power outage load reduction rate under various deployment schemes;

[0087] Figure 4 A schematic diagram showing the relationship between the average power outage load reduction rate and the capacity of flexible interconnect devices;

[0088] Figure 5 A schematic diagram illustrating capacity optimization for flexible interconnected devices under anticipated fault sets;

[0089] Figure 6 This is a schematic diagram illustrating the convergence of the minimum power loss load to the optimal solution for objective function 1.

[0090] Figure 7 This is a schematic diagram illustrating the convergence of the objective function 2 (minimum distribution network loss) with the optimal solution.

[0091] Figure 8 A schematic diagram illustrating the optimization of converter operation for flexible interconnection devices. Detailed Implementation

[0092] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and 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.

[0093] This embodiment aims to address the shortcomings of existing flexible interconnection device configuration methods in terms of multi-objective balance, uncertainty robustness, and fault response capability, and provides a multi-objective fuzzy optimization-based flexible interconnection device configuration method for distribution networks. This multi-objective fuzzy optimization-based flexible interconnection device configuration method is particularly suitable for achieving rapid load transfer, reducing power outage loads, and optimizing power flow distribution through flexible interconnection devices when a distribution network fault occurs, while comprehensively considering the economic efficiency, reliability, and uncertainty constraints of distribution network operation.

[0094] Specifically, such as Figure 1 As shown, the configuration method for flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization includes the following steps:

[0095] Step 1: Establish the multi-objective optimization function:

[0096] This step aims to clarify the core objectives of the optimization problem and transform complex engineering requirements into quantifiable and computable mathematical expressions, such as improving power supply reliability and operational economy.

[0097] Specifically, a dual-objective optimization function is constructed with the minimum power outage load and the minimum distribution network loss as its core objectives:

[0098] Objective function 1: Establish the objective function F1(X) for minimum power loss load;

[0099] Establish the following objective function:

[0100]

[0101] In the formula, F1(X) is the objective function value of the power outage load, representing the total power outage load; X is the set of optimization variables, including the location and capacity of the flexible interconnection device; N nd S represents the total number of load nodes in the distribution network; i is the load node number; k(i) represents the topological connection between node i and the distribution network. If k(i) = 1, then node i has a closed connection branch with the distribution network after fault recovery; otherwise, k(i) = 0, then there is no closed connection branch; (1-k(i)) represents the proportion of nodes that have not had their power restored; S d(i) represents the proportion of loads transferred from node i that are disconnected due to branch overload, with values ​​ranging from [0, 1]; P d (i) represents the original active load size of the i-th node.

[0102] The objective function 1 aims to minimize the power loss load when a fault occurs in the distribution network, thereby maximizing the restoration of power supply and improving the reliability of the system's power supply.

[0103] Objective function 2: Establish the objective function F2(X) to minimize distribution network losses;

[0104] Establish the following objective function:

[0105]

[0106] In the formula, F2(X) is the objective function value of the distribution network loss, representing the total active power loss; j is the branch number; I br R(j) is the effective value of the current in the j-th branch; R(j) is the resistance value of the j-th branch.

[0107] Objective function 2 aims to reduce the active power loss of the entire distribution network and improve the system's operational economy by optimizing the power flow distribution.

[0108] These two objective functions together form the core evaluation criteria for all subsequent optimization calculations. Any candidate configuration scheme, namely node placement and capacity, will be evaluated for its merits using its corresponding F1(X) and F2(X) values. This ensures that the entire optimization process always revolves around improving the overall system performance, avoiding blind and subjective decision-making.

[0109] Step 2: Construct the ideal solution and fuzzy membership function:

[0110] This step aims to address the problem of inconsistent dimensions and difficulty in direct comparison of different objective functions in multi-objective optimization, and to provide an objective and scientific "satisfaction" metric for the final decision.

[0111] Specifically, this step uses a multi-objective fuzzy optimization method to transform the actual values ​​of each objective function into the degree of satisfaction with the "ideal optimum", i.e., the membership degree, thereby achieving collaborative evaluation of multiple objectives.

[0112] Step 2.1, Solve for the ideal solution:

[0113] First, for each objective function, we solve for its optimal and worst-case values ​​in extreme cases:

[0114] Ideal solution for minimum power loss load F1:

[0115] Minimum value F1 minAssuming the flexible interconnection device has a large enough capacity to transfer load to the maximum extent during a fault, the power loss load reaches the theoretical minimum.

[0116] Maximum value F1 max Assuming that the capacity of the flexible interconnect device is set to 0, i.e. it does not participate in load transfer, the power outage load reaches the worst state.

[0117] The ideal solution for minimum distribution network loss F2:

[0118] Minimum value The lowest network loss is obtained through power flow optimization calculation.

[0119] Maximum value The initial network loss when the system has not undergone any optimization.

[0120] The set of minimum values ​​of all objective functions is the ideal point of a multi-objective optimization problem.

[0121] Step 2.2, construct the trapezoidal membership function:

[0122] To quantify how close each candidate solution is to the ideal solution, a trapezoidal membership function r is introduced. ij This function will calculate the actual value F of the objective function for the i-th scheme under the j-th scheme. i,j (X) is mapped to the interval [0,1], representing its "satisfaction" or "membership".

[0123] Its definition is as follows:

[0124]

[0125] In the formula, r ij Let F be the trapezoidal membership function value, representing the degree of membership of the i-th objective function to the ideal solution under the j-th configuration scheme, with a value range of [0,1]; i is the objective function number, representing the i-th objective function; j is the configuration scheme number, representing the j-th candidate configuration scheme; F i,j (X) represents the actual value of the i-th objective function under the j-th scheme, that is, the calculation result of the objective function under the current configuration scheme; Let be the minimum ideal solution of the i-th objective function under the j-th scheme, that is, the ideal optimal value of the objective function; The maximum ideal solution of the i-th objective function under the j-th scheme is the worst acceptable value of the objective function.

[0126] The calculation of the trapezoidal membership function is explained using two objective functions as examples:

[0127] Objective function number: i = 1 represents the minimum power loss load; ideal optimal value F i min0MW indicates full recovery; worst acceptable value F i max A value of 1.5MW indicates partial power loss. Objective function number: i=2 represents minimum distribution network loss; ideal optimal value F i min 0.2MW represents the optimal power flow; the worst acceptable value F i max The value is 1.0MW, indicating the difference in power flow.

[0128] For a certain configuration scheme j, if the calculated value is: F 1,j (X) = 0.3MW, F 2,j (X) = 0.5MW;

[0129] Therefore, the membership function values ​​r of the two targets can be calculated separately. 1j r 2j Then, the overall satisfaction level of the solution will be assessed.

[0130] The core function of this step is to normalize and fuzzify the objective function. This is achieved through the membership degree r. ij By unifying the physical meanings of targets MW and kW onto the same dimensionless scale, the problem of direct comparison is solved. The traditional hard judgment of "whether the constraints are met" is transformed into a soft evaluation of "how good" to assess satisfaction; even if a target does not reach absolute optimality, as long as it is close to the ideal value, a high membership degree can still be obtained. This step provides a crucial data foundation and mathematical tools for subsequent comprehensive evaluation of the overall performance of each candidate scheme using methods such as Hamming proximity.

[0131] Step 3: Construct the membership function matrix and the standard optimal solution:

[0132] This step aims to construct a unified framework to systematically compare and rank the performance of all candidate solutions across multiple objectives. By establishing a membership function matrix and a standard optimal solution, a scientific and objective evaluation basis is provided for subsequent multi-objective optimization decisions.

[0133] Step 3.1, construct the membership function matrix R:

[0134]

[0135] In the formula, R is an n×m membership function matrix, used to represent the fuzzy membership degree of multiple objective functions under multiple configuration schemes; n is the number of objective functions, that is, the number of optimization objectives considered in the optimization problem; m is the number of configuration schemes, that is, the number of candidate flexible interconnection device deployment and capacity combinations.

[0136] Each element r in the matrix ijThe trapezoidal membership function value represents the membership degree of the j-th configuration scheme on the i-th objective function, i.e., how close the scheme is to the ideal solution.

[0137] Membership vector: For the k-th solution, its membership degree across all objectives can be represented by a vector as follows:

[0138] [r 1k ,r 2k ,...,r nk ] T , k∈[1,...,m].

[0139] The membership function matrix R summarizes the membership degrees of all candidate schemes on all objectives into a complete dataset, forming a comprehensive evaluation view; it provides a quantitative basis for the performance of each scheme, facilitating subsequent analysis and comparison.

[0140] Step 3.2, construct the standard optimal solution:

[0141] Based on the principle of maximum membership, the maximum membership value g of each objective function is extracted from the membership function matrix. i They are then combined into a virtual ideal solution, called the standard optimal solution. Its corresponding membership function matrix is:

[0142]

[0143] In the formula, This is the membership function matrix corresponding to the standard optimal solution; The standard optimal solution represents the optimal combination of objective functions in a fuzzy sense, consisting of the maximum membership degree of each objective function; r 11 ∨r 12 ∨…∨r 1n Let g be the maximum membership degree of all solutions under the i-th objective function, that is, the optimal membership degree value among all configuration solutions in the i-th objective function; i Let g1 be the maximum membership degree of the i-th objective function, which is an element constituting the standard optimal solution, representing the ideal membership degree value of the objective function; (g1,…,g n ) T This is the membership vector of the standard optimal solution, where each element represents the ideal membership value of an objective function, forming a column vector.

[0144] Assumptions: Two objective functions n=2: minimum power outage load and minimum distribution network loss; three configuration schemes m=3; then the membership function matrix is:

[0145]

[0146] The standard optimal solution is:

[0147]

[0148] This indicates that, among all configuration schemes, the optimal membership degree of objective function 1 is 0.9, and the optimal membership degree of objective function 2 is also 0.9.

[0149] Standard Optimal Solution It is a virtual "benchmark" representing the ideal situation where all objectives are achieved at their most satisfactory state. Standard optimal solution. As a fixed reference benchmark, it is used to measure the merits of other candidate solutions; by comparing with By comparing these options, we can quantify the gap between each solution and the ideal state, thereby enabling scientific and optimal decision-making.

[0150] This step involves constructing the membership function matrix R and the standard optimal solution. The following objectives were achieved: covering the performance of all schemes across all objectives; uniformly evaluating the comprehensive performance of each scheme based on the standard optimal scheme; and providing crucial data support for subsequent scheme optimization using methods such as proximity. This fuzzy evaluation system not only solves the problem of difficulty in directly comparing different objectives but also provides a scientific and objective quantitative tool for multi-objective optimization decision-making.

[0151] Step 4: Calculate the Hamming proximity and select the optimal solution:

[0152] This step aims to comprehensively evaluate and rank multiple candidate configuration schemes, make a final decision among conflicting objectives such as minimum power loss load and minimum network loss, and thus select a flexible interconnection device configuration scheme with optimal overall performance.

[0153] Step 4.1, Hamming proximity calculation:

[0154] Based on the membership function matrix R constructed in step three and the standard optimal solution Hamming proximity is used as the evaluation metric. This method calculates the relationship between each candidate solution B(k) and the ideal "benchmark". The degree of similarity is used to quantify their advantages and disadvantages.

[0155] The specific calculation formula is as follows:

[0156]

[0157] In the formula, Let Hamming proximity be the ratio of the k-th optimized solution B(k) to the standard optimal solution. The degree of closeness is indicated by the value; a larger value indicates that the solution is closer to the ideal solution. B(k) represents the k-th candidate optimization scheme. The standard optimal solution is the ideal optimal solution consisting of the maximum membership degree of each objective function, serving as a benchmark for comparing all candidate solutions; n is the number of objective functions, representing the number of optimization objectives considered in the optimization problem; i is the objective function number, i = 1, 2, ..., n; g i The standard optimal membership degree of the i-th objective function, i.e., the standard optimal solution The membership value corresponding to the i-th objective function; r ik ξ is the membership degree of the i-th objective function under the k-th scheme, representing the degree of membership of the i-th objective function to the ideal solution in the k-th candidate scheme, with a value range of [0,1]; ξ is the distance parameter, used to define different distance measurement methods.

[0158] Proximity N H The value range is [0,1]. The larger the value, the closer the overall performance of the scheme is to the ideal state.

[0159] Step 4.2, Select the optimal solution:

[0160] Compare each candidate solution B(k) (k∈1,...,m) with the standard optimal solution. A comparison of Hamming proximity is performed, and the scheme with the highest proximity is selected as the globally optimal configuration scheme.

[0161] This optimal solution determines the optimal location and capacity configuration of the flexible interconnection device.

[0162] Assumptions: Two objective functions n=2: minimum power outage load and minimum distribution network loss; three candidate solutions k=1,2,3; the standard optimal solution is:

[0163] Then: |B(1)|0.8|0.9||0.9-0.8|+|0.95-0.9|=0.1+0.05=0.15|1-0.15 / 2=0.925|;

[0164] |B(2)|0.7|0.85||0.9-0.7|+|0.95-0.85|=0.2+0.1=0.3|1-0.3 / 2=0.85|;

[0165] |B(3)|0.85|0.95||0.9-0.85|+|0.95-0.95|=0.05+0=0.05|1-0.05 / 2=0.975|;

[0166] The conclusion is that scheme |B(3) has the highest similarity of 0.975, and is therefore the optimal scheme.

[0167] Step 4.3, determine the final configuration capacity:

[0168] Considering that the distribution network may face various fault scenarios i ∈φf set It is necessary to ensure that the device capacity can cope with the most severe situations. Therefore, the optimal capacity S is obtained under each failure scenario. vsc (f i After that, the final flexible interconnect device configuration capacity S vsc Take the maximum value of the optimal capacity across all scenarios:

[0169]

[0170] In the formula, The final configuration capacity of the flexible interconnect device, i.e., the rated capacity of the device that should be actually installed, applicable under all anticipated failure scenarios; S vsc (f i ) is the fth i The optimal capacity scheme under the fault scenario represents the solution obtained through multi-objective fuzzy optimization at the f-th fault. i The optimal capacity configuration calculated under a specific fault scenario satisfies objectives such as minimum power loss load and minimum power consumption under that fault. i For the i-th specific fault scenario, it refers to a specific fault event that may occur in the distribution network; φf set Let N be the set of anticipated failures, representing the set of all possible failure scenarios that need to be considered. fset The total number of anticipated failure scenarios, i.e., the set φf set The number of fault scenarios included; ∨ is the maximum value operator.

[0171] Suppose we consider three failure scenarios: failure scenario number f1 corresponds to the optimal capacity S. vsc (f1) = 1.2MW, and the fault scenario number f2 corresponds to the optimal capacity S. vsc (f2) = 1.4MW; the optimal capacity S corresponds to the fault scenario number f3. vsc (f3) = 1.0MW;

[0172] According to the formula: The final configuration capacity of the flexible interconnect device is 1.4MW to meet the power regulation requirements under the most severe fault scenarios.

[0173] This step transforms the process from "fuzzy evaluation of multiple options" to "single optimal solution." Hamming proximity quantifies and averages the performance deviations of each option across all objectives. Compared to the weighted summation method, which relies on subjective weights, this method aims to "maximize the closeness to the ideal solution," making the decision-making process more objective and rational. Ultimately, a unique optimal solution is generated, providing clear and actionable configuration guidance for engineering practice, including specific installation locations and equipment capacity.

[0174] Step 5: Construct the constraint model:

[0175] This step aims to ensure that the obtained optimized solution is physically feasible and safe and reliable. By establishing a complete set of mathematical constraints, the operating rules and actual needs of the power system are integrated into the optimization model, ensuring that the final selected configuration is not only theoretically "optimal" but also meets the requirements for the safe and stable operation of the power grid.

[0176] First, deterministic constraints:

[0177] Step 5.1, AC power flow balance constraints:

[0178] For any node i in the AC network, its outflowing active power P o (i) and reactive power Q o (i) The power flow equations must be accurate:

[0179]

[0180] In the formula, U i U j G represents the voltage magnitudes at nodes i and j; ij B ij Let θ be the conductance and susceptance of branch ij; ij =θ i -θ j , representing the voltage phase angle difference between nodes i and j.

[0181] In practical engineering, since the phase angle difference between the two ends of the line is usually very small, <10°, it can be simplified: cosθ ij ≈1, sinθ ij ≈θ ij And neglecting ground admittance, a simplified formula for calculating branch power flow is obtained:

[0182]

[0183] According to the principle of power conservation, the active and reactive power injected into a node should be equal to the total power flowing out of that node:

[0184]

[0185] In the formula, P d (i), Q d (i) represents the original active and reactive loads of node i; S d (i) represents the proportion of loads transferred from node i that are disconnected due to branch overload, with values ​​ranging from [0, 1]; P ij Q ij For the simplified active and reactive power flow of the branch; N nd This represents the total number of load nodes in the distribution network.

[0186] Step 5.2, DC power flow balance constraint:

[0187] The flexible interconnection devices are connected via a DC bus. For DC-side nodes i' and j', the DC current between them is determined by the voltage difference and conductance.

[0188] I dc (i'j')=g(i'j')×[U dc (i')-U dc (j')];

[0189] In the formula, I dc (i'j') is the DC current of branch i'j'; g(i'j') is the conductance of the DC branch; U dc (i'), U dc (j') represents the voltages at DC-side nodes i' and j', respectively.

[0190] DC nodes must satisfy Kirchhoff's current / power law, meaning the sum of the inflow and outflow current / power is zero:

[0191]

[0192] In the formula, P dc (i'j') represents the power of the DC branch i'j'; N dc This represents the total number of DC-side nodes.

[0193] Step 5.3, Capacity Constraints of Flexible Interconnect Devices:

[0194] At any given time, the actual apparent power output of the k'th flexible interconnect device must not exceed its rated capacity:

[0195]

[0196] In the formula, P vsc (k'), Q vsc (k') and S vsc (k') represents the actual active power, reactive power, and rated capacity of the flexible interconnection device, respectively.

[0197] Second, uncertainty constraints:

[0198] Considering the random fluctuations in load demand and distributed power output, the concept of chance-constrained programming is introduced, which allows the system to exceed limits under low-probability events, but ensures safe operation in most cases.

[0199] Step 5.4, nodal voltage machine constraints:

[0200] The voltage U(i) of all nodes must fall within the allowable range [U min U max The probability within the range is not lower than the preset confidence level β. u :

[0201] P r {U min ≤U(i)≤U max}≥β u ;

[0202] In the formula, P r {·} represents the probability of the event occurring; U(i) is the voltage at node i; U min U max These represent the lower and upper limits of the allowable node voltage, respectively; β u This represents the confidence value for the node voltage constraint.

[0203] Step 5.5, Branch Current / Power Opportunity Constraints:

[0204] The required transmission power S of each branch is... br (j) and I br (j) Not exceeding its safety limit and The probability is not lower than the preset confidence level β. br :

[0205]

[0206] In the formula, S br (j) represents the actual transmission power of branch j; I is the rated transmission power of path j; br (j) represents the actual transmission current of branch j; β is the rated transmission current of branch j; br This is the confidence value for the branch safety current constraint.

[0207] Deterministic constraints define the hard physical rules that the system must satisfy, including AC / DC power flow, node power balance, and equipment capacity. Uncertainty constraints introduce soft constraints that consider stochasticity to quantify operational risks. This step ensures that all candidate solutions pass these constraints before proceeding to subsequent optimization stages, guaranteeing their physical feasibility. Uncertainty constraints enable the model to adapt to real-world fluctuations, avoiding "fragile" solutions resulting from overly idealized approaches, and significantly enhancing the reliability and adaptability of the final configuration in actual operating environments.

[0208] Step 6: Solve using a hybrid optimization algorithm.

[0209] This step aims to efficiently and accurately solve the aforementioned complex large-scale mixed-integer nonlinear programming (MINLP) problem. By decoupling the optimization process of integer variables for site location from continuous variables for capacity configuration / operation, the advantages of different optimization algorithms are fully utilized, significantly improving solution efficiency and convergence, and providing a feasible computational solution for the configuration of flexible interconnection devices in complex power distribution networks.

[0210] The core strategy of this step is: double nesting and variable decoupling;

[0211] This method employs a two-layer optimization framework, decomposing the original problem into two coupled subproblems:

[0212] Upper-level integer variable optimization: responsible for solving the optimal placement scheme of flexible interconnection devices;

[0213] Lower-level continuous variable optimization: Given a distribution scheme, find the optimal operating mode and capacity configuration.

[0214] The solution process uses the Simulated Annealing (SA) algorithm as its upper-level framework. It iteratively generates candidate placement schemes, which are then passed as constraints to the lower-level model. After the lower-level model solves, it returns the optimal result to the upper-level model to calculate the objective function value of the current placement scheme. Through continuous iteration between the upper and lower levels, the solution eventually converges to the global optimum.

[0215] The upper-level optimization uses intelligent algorithms to solve the point placement scheme:

[0216] The upper-level model uses the installation location of the flexible interconnection device as a decision variable and employs a smart optimization algorithm with strong global search capabilities to solve it.

[0217] Simulated Annealing Algorithm (SA): Simulates the solid annealing process. At high temperatures, it allows for a certain probability of accepting poor solutions, thus escaping local optima. As the "temperature" gradually decreases, the algorithm tends to stabilize and eventually converges to the global optimum or near-optimal solution.

[0218] The core formula is:

[0219]

[0220] In the formula, p represents the acceptance probability, indicating that the algorithm accepts a worse new solution x. new The probability, which is between 0 and 1; E(x) is the objective function value, representing the annual comprehensive cost; exp() is the natural exponential function; E(x) new ) represents the "energy" or objective function value of the new state, indicating the newly generated candidate solution x. new The corresponding objective function value; E(x) old ) represents the "energy" or objective function value of the current state, indicating the solution x currently being considered. old The corresponding objective function value; E(x) new )-E(x old The energy difference represents the difference between the objective function value of the new solution and the current solution; k is the Boltzmann constant; and T is the current temperature, a control parameter during the algorithm's operation.

[0221] Assumption: The objective function value of the current solution is E(x) old ) = 10, the objective function value of the new solution is E(x) new =12, Boltzmann constant k = 1, current temperature T = 5;

[0222] The probability of accepting the new solution is:

[0223]

[0224] The calculations above show that even if the new solution is worse, the algorithm still has about a 67% probability of accepting it.

[0225] The application process is as follows: the SOP placement scheme is regarded as the "state" and the objective function value is regarded as the "internal energy". The optimal placement is searched through random perturbation and probability acceptance mechanism.

[0226] Improved Gray Wolf Optimization Algorithm (GWO): Simulates the hierarchy (α, β, δ, ω) and hunting behavior of gray wolves, performing global search through group cooperation. The following improvements are made based on the conventional gray wolf optimization algorithm:

[0227] Nonlinear convergence factor: A nonlinear convergence factor based on sine and cosine control is adopted to slowly cool down the algorithm in the early stage of iteration to expand the search range, and accelerate convergence in the later stage to improve accuracy.

[0228] The specific expression for the nonlinear convergence factor is:

[0229]

[0230] In the formula: a is the convergence factor, a key parameter controlling the search range of the wolf pack; k is the Boltzmann constant; T is the current temperature, a control parameter during the algorithm's operation.

[0231] Adaptive crossover and mutation: The crossover and mutation operations of the genetic algorithm are introduced, and their probabilities are dynamically adjusted through adaptive operators to effectively increase population diversity and prevent premature convergence.

[0232] Random crossover:

[0233]

[0234] In the formula: X i,d Let be the variable value of the i-th wolf in the d-th dimension, representing a component of the wolf pack in the solution space; i is the wolf's index, representing the i-th individual in the wolf pack; d is the dimension index, representing the d-th dimension of the solution space; r c A random number within the interval [0,1] is used to determine whether to perform a crossover operation; p c The crossover probability is a threshold that determines the probability of a crossover operation occurring; r3 is a random number in the interval [0,1] used to randomly perturb the values ​​after the crossover, increasing diversity; X j,d Let be the variable value of the j-th randomly selected wolf in the d-th dimension.

[0235] Mutation operation:

[0236]

[0237]

[0238] In the formula: r m p is a random number within the interval [0,1], used to determine whether to perform a mutation operation; m r1 is the mutation probability, a threshold that determines the probability of mutation occurring; r4 and r5 are random numbers in the interval [0,1], used to control the magnitude and direction of mutation; b1 and b2 are binary switch variables that determine whether mutation increases or decreases; r6, r7, and r8 are random numbers in the interval [0,1], used to independently determine the values ​​of b1 and b2; η is the high-frequency mutation coefficient, a parameter that controls the mutation magnitude, and its value decreases as the number of iterations increases.

[0239] Adaptive operators:

[0240]

[0241] In the formula, These are the upper and lower bounds of the crossover probability; These are the upper and lower bounds of the mutation probability; aff i Let be the fitness value of the i-th wolf, representing the quality of the solution for that individual; affavg is the average fitness value of the population, the average fitness value of all wolves.

[0242] The lower-level optimization uses cone programming to solve for the operation and capacity:

[0243] Given a deployment scheme, the lower-level model aims to minimize system losses and solve for the optimal operating mode and capacity configuration.

[0244] The original power flow model includes nonlinear terms (U i U j cosθ ij This is a non-convex problem, which is difficult to solve efficiently.

[0245] This step employs second-order cone programming, transforming the nonlinear, non-convex power flow constraints into a convex optimization problem solvable under second-order cone constraints through variable substitution and convex relaxation techniques.

[0246] Regarding variable substitution: Introduce a new variable:

[0247]

[0248] In the formula, X k,i (t) represents the square of the voltage amplitude of node i in the k-th transformer area at time t; Y k,ij (t) represents the product of the voltages at nodes i and i in branch ij within the k-th transformer area at time t, which is related to the power factor; Z k,ij (t) represents the product of the voltages of nodes i and k in branch ij within the k-th transformer area at time t, which is related to the reactive power; k is the transformer area number; i and j are the node numbers, representing the i-th and j-th nodes within the transformer area; t is the time point, representing a certain moment within the optimization cycle.

[0249] Transform nonlinear constraints into linear form:

[0250]

[0251] In the formula, P k,i (t) represents the active power injected by node i in the k-th distribution area at time t; δ(i) is the set of adjacent nodes of node i, representing all nodes directly connected to node i; G k,ij and B k,ij G represents the mutual conductance and mutual susceptance of node ij in the k-th transformer area, respectively; k,ii The self-conductance of node i in the k-th transformer area; Q k,i (t) represents the reactive power injected into node k,i at time t; B k,ii The self-susceptance of node i in the k-th transformer area; U k,min,i and U k,maxiLet I be the minimum and maximum voltage values ​​of node i in the k-th transformer area, respectively; k,ij (t) represents the effective current value at time t on branch ij within the k-th transformer area; I k,max,ij Let be the maximum current on branch ij within the k-th transformer zone.

[0252] Formula The nonlinear constraints are transformed into the following rotational constraints through second-order cone programming:

[0253]

[0254] In the formula, P vsc (k'), Q vsc (k') and S vsc (k') represents the actual active power, reactive power, and rated capacity of the flexible interconnection device, respectively; This represents the 2-norm of a matrix.

[0255] Finally, a nonlinear second-order cone-rotation constraint is introduced to ensure that the optimization model remains within the constraint range of the pointed cone. The specific expression is as follows:

[0256] X k,i (t)X k,j (t)≥Y k,ij (t) 2 +Z k,ij (t) 2 ;

[0257] The advantages of the two-layer optimization framework are: SOCP possesses convexity, transformability, robustness, and sparsity, enabling efficient and reliable solutions to large-scale optimization problems. The transformed MISOCP model can be effectively solved using commercial solvers such as CPLEX or MOSEK.

[0258] Step 6 is the core execution step of the entire optimization process, closely dependent on the complete problem definition and decision-making framework established in steps 1 to 5. The two objective functions established in step 1—minimum power outage load F1(X) and minimum distribution network loss F2(X)—are the core basis for the search and evaluation of all optimization algorithms in this step: simulated annealing and gray wolf optimization. In the two-layer optimization framework of this step, the optimization objective of the lower-level model is F2(X), while the comprehensive objective function of the upper-level model is based on the weighted or fuzzy result of F1(X) and F2(X), such as Hamming proximity. Steps 2, 3, and 4 together construct the evaluation system for multi-objective fuzzy optimization, including the ideal solution, membership function, membership matrix, and Hamming proximity. During the solution process in this step, for each point layout scheme generated by the upper-level algorithm, such as SA or GWO, the lower-level SOCP model calculates its corresponding F1(X) and F2(X). These objective function values ​​are then fed into the fuzzy evaluation system established in steps 2, 3, and 4 to calculate the Hamming proximity N of the scheme. H The upper-level algorithm is based on this N. H The "overall satisfaction" of the placement scheme is evaluated based on the value, and a decision is made on whether to accept the scheme or continue the search. The deterministic and uncertain constraints established in step 5 together define the feasible region of the optimization problem. In the solution process of this step, whether the upper-level intelligent algorithm generates candidate schemes or the lower-level SOCP model performs optimization calculations, it is necessary to strictly check whether these schemes satisfy all constraints. Any scheme that does not satisfy the constraints will be directly rejected or modified to ensure that the final output solution is safe and reliable. In particular, the lower-level SOCP solution itself is directly composed of the linearization and second-order cone relaxation constraints in step 5.

[0259] Steps 1 to 5 together complete the "decoupling" and "transformation" of the original complex problem: decoupling the complex engineering problem into two mathematical objectives, transforming the multi-objective decision-making problem into a single-objective evaluation problem based on proximity, and transforming the nonlinear, non-convex power flow constraints into convex constraints solvable by SOCP. Step 6 is the framework for achieving "cooperative" solution: the upper-layer intelligent algorithm is responsible for exploring the discrete deployment space, while the lower-layer SOCP algorithm is responsible for accurately solving the continuous operation and capacity problem under a given deployment. The two work together iteratively through objective function values ​​and constraint information, ultimately converging to the global optimum.

[0260] This step decomposes the complex MINLP problem into more manageable integer programming and continuous convex optimization problems. The upper layer uses SA or an improved GWO for global exploration; the lower layer uses SOCP for accurate and fast local optimization. Intelligent algorithms avoid getting trapped in local optima, while mathematical programming algorithms ensure the speed and accuracy of solving continuous subproblems. For complex distribution network optimization problems, single algorithms often fail; this hybrid strategy effectively overcomes the solution bottleneck, making engineering applications possible. Through two-level iterations, the final distribution and capacity schemes satisfy all physical and operational constraints.

[0261] Furthermore, to verify the effectiveness of the multi-objective fuzzy optimization-based distribution network flexible interconnection device configuration method, this embodiment also includes the following steps:

[0262] Step 7: Simulation Verification and Configuration Result Output: Based on the constructed multi-objective fuzzy optimization model, fuzzy evaluation system, constraint model, and solution algorithm, the optimal configuration result is output through simulation verification, thus completing the layout and capacity optimization configuration of the flexible interconnection device in the distribution network.

[0263] Specifically, establish such as Figure 2 An improved IEEE 33-node distribution network model.

[0264] The base voltage of the distribution network model is 12.66kV, and the total load is 3.715+j2.3MVA. The load of each node and the impedance of each branch are set according to the standard IEEE 33-node distribution network model. The model has 32 AC branches and 3 branch tie lines, namely L33, L34, and L35. During normal operation, the branch tie line switches are all open. Flexible interconnection devices are connected to different feeders of the distribution network. Figure 2 The diagram shows the connection points at both ends: node 25 and node 33. The safe current of the branch is set to 150A, which means the maximum transmission power of the branch is 150×12.66×1.732 / 1000=3.29MVA.

[0265] Establish a set of anticipated faults Ω for L2-L32 branch faults. fset Ω fset The number of faults is 31. The average load reduction rate under the anticipated fault set is analyzed. The uncertainty constraints of the distribution network node voltage and branch safety current are assumed to follow a normal distribution. The analysis is performed for different confidence values ​​β. u and β br The following is the site layout plan.

[0266] The optimization of the flexible interconnection device layout can be achieved by scanning the anticipated fault set to obtain the average power outage load reduction rate of each node. This project selects 7 layout schemes for analysis, and the corresponding layout points for the 7 layout schemes are (node ​​18, node 33), (node ​​18, node 25), (node ​​18, node 26), (node ​​18, node 30), (node ​​23, node 26), (node ​​23, node 33), and (node ​​18, node 23).

[0267] The average power outage load reduction rate under each deployment scheme is as follows: Figure 3 As shown, when the number of branch tie line switch operations is 0, the deployment scheme 2 (node ​​18, node 25) results in the most significant reduction in power loss load. The flexible interconnection device can provide a channel for load transfer to different feeders through rapid power control after a fault. When the number of branch tie line switch operations is 1, the optimal access point is deployment scheme 1. This is because when branches L2 to L21 fail, the operation of the branch tie line switch can effectively reduce the power loss load. At this time, deployment scheme 1 can further reduce the power loss load when branches L22 to L32 fail. Furthermore, as the confidence value of the uncertainty constraints on node voltage and branch safe current increases, the average power loss load reduction rate of each deployment scheme further increases.

[0268] If the branch tie line switch operates once, there is a possibility that the switching operation after a fault will increase the load power loss time. Taking all factors into consideration, deployment scheme 2 is temporarily selected as the optimized scheme. After a fault, the load transfer is quickly controlled by the flexible interconnection device, avoiding the switching operation of the branch tie line switch after a fault, and also helping to reduce the complexity of fault operation.

[0269] The relationship between the average power outage load reduction rate of deployment scheme 2 and the capacity of flexible interconnection devices is as follows: Figure 4 As shown, the average power outage load reduction rate further increases with the increase in configured capacity; when the configured capacity exceeds 1.8MW, the average power outage load reduction rate and the capacity of the flexible interconnection device show a weak positive correlation. Therefore, after determining the optimal deployment scheme, the upper limit value for the selection of configured capacity can be provided by analyzing the relationship between the average power outage load reduction rate and the capacity.

[0270] Under the anticipated fault set, the optimized capacity of the flexible interconnect device is as follows: Figure 5 As shown, the Hamming proximity of the multi-objective function varies depending on the branch failure. For failures in branches L5 to L16, L23, and L31, the optimal capacity corresponding to the best Hamming proximity is 1.4MW. If the configured capacity increases beyond 1.4MW, the Hamming proximity does not increase further, meaning the configured capacity deviates from the optimal solution. In this case, an excessively large configured capacity will lead to a decrease in equipment economics. Therefore, the optimal capacity selected for the flexible interconnection device is 1.4MW.

[0271] After determining the optimal capacity of the flexible interconnection device, the degree of convergence between each objective function and the optimal solution can be obtained, such as... Figure 6 and Figure 7 As shown, Figure 6 The degree of convergence between the objective function 1 (minimum power loss load) and the optimal solution is considered. Figure 7 The degree of convergence between the objective function 2 (minimum distribution network loss) and the optimal solution is considered. The closer the objective function value is to the minimum optimal solution, the higher the Hamming fit of the fuzzy decision, indicating that the configured capacity is closer to the optimal solution.

[0272] Under the anticipated fault set, the operating power optimization of flexible interconnected devices is as follows: Figure 8 As shown, when a fault occurs in any branch of the distribution network, the control commands of the flexible interconnection device are adjusted to simultaneously consider the objective functions of minimum power loss load and minimum network loss, providing a reference for the actual operation and control of the distribution network.

[0273] In summary, compared with traditional mechanical hard switches, the configuration method of flexible interconnection devices (SOPs) based on multi-objective fuzzy optimization for distribution networks enables dynamic optimization and coordinated scheduling of power flow in the distribution network through continuous and precise control of port output power, providing an important guarantee for the safe and stable operation of modern distribution networks. However, as a fully controlled power electronic device, the manufacturing and maintenance costs of SOPs are relatively high, and the improvement of grid performance is affected by the location and capacity of SOPs. Therefore, it is necessary to conduct relevant research on the location and capacity determination of SOPs. In order to reduce configuration costs while ensuring stable and reliable system operation, this project mainly optimizes the location and capacity determination of flexible interconnection devices, using correlation coefficients to obtain the optimal placement of flexible interconnection devices. Furthermore, during the capacity optimization configuration of interconnection devices, capacity and transmission power balance constraints are constructed for different ports. By constructing a two-layer optimization model combining flexible interconnection device configuration and optimized operation, and considering the response requirements of the load side during actual operation, the optimal configuration scheme of flexible interconnection devices is obtained.

[0274] The complexity of the model may lead to poor convergence of traditional optimization algorithms, thus a single optimization algorithm cannot adequately solve for the configuration scheme of flexible interconnection devices. Therefore, a hybrid optimization algorithm based on simulated annealing, cone programming, and the proposed Grey Wolf optimization algorithm is proposed to solve this problem. By decoupling the integer and continuous variables in the large-scale mixed-integer nonlinear programming problem, and employing intelligent optimization algorithms and mathematical programming methods respectively, the advantages of different algorithms are fully utilized, improving the speed and convergence of the optimization algorithm for solving large-scale mixed-integer nonlinear programming problems.

[0275] Finally, addressing the issue of the inability to quickly achieve emergency power support and load shifting from heavy to light loads between existing distribution substations, an objective function is established to minimize the power outage load and network loss of the distribution substation under a set of anticipated faults. Constrained by the determinism of AC / DC power flow balance in flexible interconnected distribution substations and the uncertainties of branch safety currents and node voltages caused by load fluctuations and distributed power generation in the distribution substations, fuzzy optimization is used to measure the degree to which the multi-objective function with different dimensions approaches the optimal solution. This leads to an optimized configuration method that, while ensuring economic efficiency, fully leverages the ability of flexible interconnection devices to improve the operational reliability of distribution substations.

[0276] Flexible interconnection of low-voltage distribution substations, along with the rational configuration of flexible interconnection devices, can significantly improve the economic efficiency of power distribution system operation. Its flexible control methods also bring numerous benefits to the entire power distribution system, demonstrating promising application prospects. As power distribution system scenarios become increasingly complex, especially considering their timing characteristics, large-scale mixed-integer nonlinear optimization problems in power distribution systems become more difficult to solve, making the advantages of hybrid optimization algorithms even more apparent.

[0277] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for configuring flexible interconnection devices in distribution networks based on multi-objective fuzzy optimization, characterized in that: Includes the following steps: Step 1: Establish a multi-objective optimization function: Establish a multi-objective optimization function, and clarify the optimization objectives with minimum power outage load and minimum distribution network loss as the core. Step 2: Constructing the ideal solution and fuzzy membership function: Based on the multi-objective optimization function, solve the ideal solution for each objective and construct the fuzzy membership function to provide a quantitative basis for multi-objective fuzzy decision-making; Step 3: Constructing the membership function matrix and standard optimal solution: Based on fuzzy membership functions, construct the membership function matrix and standard optimal solution to form a fuzzy evaluation system for multi-objective optimization; Step 4: Calculate Hamming proximity and select the optimal solution: Based on the membership function matrix and the standard optimal solution, the flexible interconnection device configuration scheme that is closest to the ideal solution is selected by calculating and comparing the Hamming proximity. Step 5: Constructing a constraint model: Based on the optimization objectives set by combining the physical operating characteristics and actual operating requirements of the distribution network, establish a mathematical model that includes deterministic and uncertain constraints to ensure that the configuration scheme meets the requirements of operational safety and probabilistic reliability. Step 6: Solving with a hybrid optimization algorithm: Based on the multi-objective fuzzy optimization model and its constraints, a hybrid optimization algorithm is used to solve the model, achieving efficient collaborative optimization of integer variables and continuous variables.

2. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 1, characterized in that: Step 1 includes the following steps: Step 1.1, establish the objective function F1(X) for minimum power loss load: In the formula, F1(X) is the objective function value of the power outage load, representing the total power outage load; X is the set of optimization variables, including the location and capacity of the flexible interconnection device; N nd S represents the total number of load nodes in the distribution network; i is the load node number; k(i) represents the topological connection between node i and the distribution network. If k(i) = 1, then node i has a closed connection branch with the distribution network after fault recovery; otherwise, k(i) = 0, then there is no closed connection branch; (1-k(i)) represents the proportion of nodes whose power supply has not been restored; S d (i) represents the proportion of loads transferred from node i that are disconnected due to branch overload, with values ​​ranging from [0, 1]; P d (i) represents the original active load of the i-th node; Step 1.2, establish the objective function F2(X) for minimizing distribution network losses: In the formula, F2(X) is the objective function value of the distribution network loss, representing the total active power loss; j is the branch number; I br R(j) is the effective value of the current in the j-th branch; R(j) is the resistance value of the j-th branch.

3. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 2, characterized in that: In step 2, the process of solving for the ideal solutions to each objective function is as follows: For the objective function F1(X) of minimum power outage load, the minimum value is achieved by increasing the capacity of the flexible interconnection device to a sufficiently large value; the maximum value is achieved by setting the capacity of the flexible interconnection device to 0, i.e., not participating in load transfer. For the objective function F2(X) to minimize distribution network losses, the minimum value is obtained by optimizing the power flow distribution; the maximum value is the loss value without power flow optimization. In step 2, the process of constructing the trapezoidal membership function is as follows: Constructing the trapezoidal membership function r ij : In the formula, r ij Let F be the trapezoidal membership function value, representing the degree of membership of the i-th objective function to the ideal solution under the j-th configuration scheme, with a value range of [0,1]; i is the objective function number, representing the i-th objective function; j is the configuration scheme number, representing the j-th candidate configuration scheme; F i,j (X) represents the actual value of the i-th objective function under the j-th scheme, that is, the calculation result of the objective function under the current configuration scheme; Let be the minimum ideal solution of the i-th objective function under the j-th scheme, that is, the ideal optimal value of the objective function; The maximum ideal solution of the i-th objective function under the j-th scheme is the worst acceptable value of the objective function. Using the trapezoidal membership function r ij This indicates the degree to which the i-th objective function approaches the ideal solution under the j-th configuration scheme, and is used to fuzzify the objective function value.

4. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 3, characterized in that: In step 3, the membership function matrix R is constructed, represented as: In the formula, R is an n×m membership function matrix, used to represent the fuzzy membership degree of multiple objective functions under multiple configuration schemes; n is the number of objective functions, that is, the number of optimization objectives considered in the optimization problem; m is the number of configuration schemes, that is, the number of candidate flexible interconnection device deployment and capacity combinations.

5. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 4, characterized in that: In step 3, the standard optimal solution is constructed as follows: Based on the membership function matrix R, the membership vector of the k-th scheme is: [r 1k ,r 2k ,...,r nk ] T , represents the membership combination of the k-th configuration scheme under all objective functions, k∈[1,...,m]; Constructing the standard optimal solution In the formula, This is the membership function matrix corresponding to the standard optimal solution; The standard optimal solution represents the optimal combination of objective functions in a fuzzy sense, which is composed of the maximum membership degree of each objective function. Let g be the maximum membership degree of all solutions under the i-th objective function, that is, the optimal membership degree value among all configuration solutions in the i-th objective function; i Let g1 be the maximum membership degree of the i-th objective function, which is an element constituting the standard optimal solution, representing the ideal membership degree value of the objective function; (g1,…,g n ) T This is the membership vector of the standard optimal solution, where each element represents the ideal membership value of an objective function, forming a column vector; The optimal solution is determined by maximizing the membership degree of each objective function, and this optimal solution serves as a benchmark for comparing all configuration solutions.

6. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 1, characterized in that: In step 4, the Hamming proximity of each configuration scheme to the standard optimal scheme is calculated using the following formula: In the formula, Let Hamming proximity be the ratio of the k-th optimal solution B(k) to the standard optimal solution. The degree of closeness, the larger the value, the closer to the ideal solution; B(k) is the kth candidate optimization scheme; The standard optimal solution is the ideal optimal solution consisting of the maximum membership degree of each objective function, serving as a benchmark for comparing all candidate solutions; n is the number of objective functions, representing the number of optimization objectives considered in the optimization problem; i is the objective function number, i = 1, 2, ..., n; g i The standard optimal membership degree of the i-th objective function, i.e., the standard optimal solution The membership value corresponding to the i-th objective function; r ik ξ represents the membership degree of the i-th objective function under the k-th scheme, indicating the degree of membership of the i-th objective function to the ideal solution in the k-th candidate scheme, with a value range of [0,1]; ξ is a distance parameter used to define different distance measurement methods; The greater the similarity, the closer the configuration is to the ideal solution; The optimal configuration is selected based on the closest proximity to the target location. The optimal configuration includes the optimal deployment location and capacity configuration.

7. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 1, characterized in that: In step 5, the deterministic constraints include: AC power flow balance constraints, DC power flow balance constraints, and flexible interconnection device capacity constraints. AC power flow balance constraint: In an AC distribution network, the active power P of node i is... o (i) and reactive power Q o (i) Satisfies the following power flow equations: In the formula, U i U j G represents the voltage magnitudes at nodes i and j; ij B ij Let θ be the conductance and susceptance of branch ij; ij =θ i -θ j , representing the voltage phase angle difference between nodes i and j; Node power balance: The injected active power P at node i in (i) and reactive power Q in (i) Satisfies: In the formula, P d (i), Q d (i) represents the original active and reactive loads of node i; S d (i) represents the proportion of loads transferred from node i that are disconnected due to branch overload, with values ​​ranging from [0, 1]; P ij Q ij For the simplified active and reactive power flow of the branch; N nd This represents the total number of load nodes in the distribution network. DC power flow balance constraint: The flexible interconnection device is interconnected through a DC bus, and the voltages of DC side nodes i' and j' are U respectively. dc (i'), U dc (j'), the DC current I of branch i'j' dc (i'j') is: I dc (i'j')=g(i'j')×[U dc (i')-U dc (j')]; In the formula, g(i'j') is the conductance of the DC branch; Based on the node current / power balance, we get: In the formula, P dc (i'j') represents the power of the DC branch i'j'; N dc This represents the total number of DC-side nodes. Flexible interconnect device capacity constraint: The capacity of the k'-th flexible interconnect device should meet the following requirements: In the formula, P vsc (k'), Q vsc (k') and S vsc (k') represents the actual active power, reactive power, and rated capacity of the flexible interconnection device, respectively.

8. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 1, characterized in that: In step 5, the uncertainty constraints include: node voltage opportunity constraints and branch current / power opportunity constraints; Node voltage constraint: The voltage at node i must satisfy: P r {IN min ≤U(i)≤U max }≥β u ; In the formula, P r {} represents the probability of the event occurring; U(i) is the voltage at node i; U min U max These represent the lower and upper limits of the allowable node voltage, respectively; β u The confidence value for the node voltage constraint; The branch current / power opportunity constraint is expressed as follows: the transmission power and current of the j-th branch should satisfy: In the formula, S br (j) represents the actual transmission power of branch j; I is the rated transmission power of branch j; br (j) represents the actual transmission current of branch j; β is the rated transmission current of branch j; br This is the confidence value for the branch safety current constraint.

9. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 1, characterized in that: In step 6, for the optimization of integer variables of point location, simulated annealing algorithm or Grey Wolf Optimization (GWO) algorithm is used for global search; for the optimization of continuous variables of capacity configuration, cone programming method is used for local optimization; for the decoupling optimization of integer and continuous variables, the solution efficiency and convergence are improved.

10. The method for configuring flexible interconnection devices in a distribution network based on multi-objective fuzzy optimization according to claim 1, characterized in that: The method for configuring flexible interconnection devices in distribution networks based on multi-objective fuzzy optimization also includes: Step 7: Simulation Verification and Configuration Result Output: Based on the constructed multi-objective fuzzy optimization model, fuzzy evaluation system, constraint model, and solution algorithm, the optimal configuration result is output through simulation verification, thus completing the layout and capacity optimization configuration of the flexible interconnection device in the distribution network.

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