Reliability index-based radial power distribution system multi-objective optimization configuration method and system

Abstract

The invention discloses a radial power distribution system multi-objective optimization configuration method and system based on a reliability index. Establishing a group of objective functions (a system total power loss objective function, a system average interruption frequency index, a system average interruption duration index and average unsupplied power energy) to evaluate the optimal terminal configuration of the power distribution system; on the basis of a radiation extension structure of the power distribution system, a constraint condition of multi-objective optimization is constructed; according to the objective function and the constraint condition, solving the objective optimization problem by adopting an enhanced constraint method, and generating a Pareto optimal solution; then, the configuration obtained by applying a backward-forward scanning load flow algorithm to all configuration results is evaluated to verify whether the obtained solution is non-dominated and feasible, and a Pareto optimal solution set is updated; and finally, sorting the obtained solutions according to the preference of a decision maker by adopting a multi-attribute decision program and an ideal solution similarity sorting technical method to obtain an optimal configuration scheme. According to the intelligent terminal configuration obtained through the method, the topological structure and the switch configuration of the power distribution network can be optimized in a collaborative mode, and the reliability, the economical efficiency and the power loss control capacity of the system are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimal configuration of distribution networks, and mainly relates to a multi-objective optimal configuration method and system for a radial distribution system based on reliability indexes. Background Art

[0002] In the process of optimizing and improving the reliability of distribution systems, the configuration of intelligent terminals plays a crucial role. Intelligent terminal devices, such as intelligent switches, sensors, and circuit breakers, can monitor key parameters such as current and voltage in real time, and adjust the switch states through automatic control to achieve dynamic reconfiguration of the distribution network. This reconfiguration not only helps to minimize power losses, but also significantly improves the power supply reliability of the system through rapid fault detection and location, optimized protection measures, and predictive maintenance.

[0003] However, there are several key problems in existing intelligent terminal configuration methods: First, most methods only focus on the optimization of a single objective, such as only considering minimizing power losses or maximizing power supply reliability, and it is difficult to achieve a good balance among multiple performance indexes; Second, existing configuration methods often ignore the radial topological characteristics of distribution systems, resulting in the optimization results may not meet the actual operation requirements; In addition, when configuring intelligent terminals, there is a lack of an effective verification mechanism to ensure the feasibility of the optimization results, especially the feasibility verification when considering load flow constraints.

[0004] Although intelligent terminals support multi-objective optimization algorithms and can theoretically achieve a trade-off among power losses, system reliability, and operating costs, existing optimization methods often use simple weighted sum methods to handle multi-objective problems. This method is difficult to fully reflect the preferences of decision-makers and cannot guarantee that the obtained solution is a true Pareto optimal solution. Although integrating the real-time data provided by intelligent terminals can assist in decision-making, how to effectively use this data to guide the reconfiguration optimization of distribution systems is still an urgent problem to be solved. Facing these technical problems, the industry urgently needs an intelligent terminal configuration method that can simultaneously consider multiple objectives, make full use of radial topological characteristics, have a reliable verification mechanism, and can effectively integrate the preferences of decision-makers. Summary of the Invention

[0005] In view of the problems existing in the prior art, such as the difficulty in achieving the balance of multiple performance indicators in single-objective optimization, the neglect of the radial topological characteristics of the distribution system, the lack of a verification mechanism for the feasibility of optimization results, and the difficulty in effectively integrating the preferences of decision-makers in multi-objective optimization methods, a multi-objective optimal configuration method and system for a radial distribution system based on reliability indicators are proposed. First, based on reliability indicators, a set of objective functions including the objective function of the total power loss of the system, the system average interruption frequency index, the system average interruption duration index, and the average unsupplied energy are established to evaluate the optimal terminal configuration of the distribution system. Then, based on the radial topological structure of the distribution system, the constraint conditions for multi-objective optimization are constructed. According to the objective functions and constraint conditions, the augmented constraint method is used to solve the objective optimization problem to generate Pareto optimal solutions. Then, the configurations obtained by applying the backward-forward sweep load flow algorithm to all configuration results are evaluated to verify whether the obtained solutions are non-dominated and feasible, and the Pareto optimal solution set is updated. Finally, a multi-attribute decision-making procedure and the similarity ranking technique method with the ideal solution are used to rank the obtained solutions according to the preferences of the decision-makers to obtain the optimal configuration plan. The intelligent terminal configuration obtained by the method of the present invention can coordinately optimize the topological structure and switch configuration of the distribution network, and improve the reliability, economy, and power loss control ability of the system.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a multi-objective optimal configuration method for a radial distribution system based on reliability indicators, including the following steps:

[0007] S1: Define a multi-objective optimization problem, and based on reliability indicators, establish a set of objective functions, where the objective functions include the objective function of the total power loss of the system, the system average interruption frequency index, the system average interruption duration index, and the average unsupplied energy;

[0008] S2: Based on the radial topological structure of the distribution system, construct the constraint conditions for multi-objective optimization, and then use the augmented constraint method (AUGMECON) to generate Pareto optimal solutions by solving sub-problems;

[0009] S3: Apply the backward-forward sweep load flow algorithm to all configuration results to verify the feasibility and non-dominance of the solutions obtained in step S2;

[0010] S4: Based on the verification results of step S3, update the Pareto optimal solution set, eliminate infeasible solutions and dominated solutions, and present the updated optimal solution set to the decision-maker; for networks with a total number of nodes not exceeding 50 nodes, compare the feasible solutions and non-dominated solutions with the complete Pareto front; for networks with a total number of nodes exceeding 50 nodes, compare them with the optimal Pareto front;

[0011] S5: Apply the multi-attribute decision-making method to sort the obtained solutions. Adopt the similarity ranking technique method with the ideal solution, calculate the proximity to the ideal solution according to the value of the similarity index, introduce the weight combination number to obtain the average similarity index, and finally select the configuration scheme according to the decision-maker's preference.

[0012] As an improvement of the present invention, the system average interruption frequency index in the objective function of step S1 represents the average number of interruptions per year of the system, specifically:

[0013]

[0014] In the formula, λ i is the failure rate of N i affected customers, and M is the total number of customers served;

[0015] The system average interruption duration index represents the average power outage duration per year, specifically:

[0016]

[0017] In the formula, U i is the interruption duration caused by the failure;

[0018] The average unsupplied energy directly reflects the impact of power interruption on the user's energy supply, specifically:

[0019]

[0020] In the formula, is the active load not supplied during the occurrence of failure i.

[0021] As another improvement of the present invention, the constraint conditions in step S2 are specifically:

[0022]

[0023] Among them, P b represents the active power flow on branch b, represents the active power fed into the substation at bus i, represents the active power demand at bus i, Q b represents the reactive power flow on branch b, represents the reactive power fed into the substation at bus i, represents the active power demand at bus i, represents the set of branches with node i as the end point ("to"), represents the set of branches with node i as the starting point ("from");

[0024] It also includes that the apparent power flowing through the active branch should be less than its rated apparent power limit, specifically:

[0025]

[0026] Among them, S b represents the rated apparent power limit of branch b, x b is a binary variable indicating whether branch b exists, and B represents the set of all branches in the system.

[0027] As another improvement of the present invention, the step S2 uses the enhanced constraint method to solve the target optimization problem, which specifically includes the following steps:

[0028] S21: Preprocessing for the minimization problem of the objective function. To uniformly handle the maximization form of the objective, the objective function to be minimized is multiplied by -1 for conversion:

[0029]

[0030] In the formula, is the decision variable vector, S is the feasible region of the problem, is the i-th objective function.

[0031] S22: Apply the ε-constraint method to transform the multi-objective problem. Select one objective function p as the main objective function, and transform other objective functions into constraint conditions:

[0032]

[0033] Among them, e i is the lower constraint value of the i-th objective function.

[0034] S23: Continuously optimize the multi-objective function using the lexicographic optimization method. This process first optimizes a single objective function, and after obtaining the optimal solution, adds the optimal value of this objective function as an equality constraint to the optimization problem to maintain the optimality of this objective; then continue to optimize the next objective function and repeat this process.

[0035] S24: To obtain a more complete Pareto front, perform grid division on the constraint condition e i , use q i grid points to divide the value range of the i-th objective function into q i-1 intervals; by changing the upper constraint e i corresponding to these grid points, different optimal solutions can be obtained; the choice of the number of grid points q i needs to be balanced between the computational burden and the accuracy of the solution.

[0036] As another improvement of the present invention, in the comparison stage of step S4, the feasible solutions and non-dominated solutions are compared with the reference Pareto front. For a distribution network with a total number of nodes not exceeding 50 nodes, the reference Pareto front is the true Pareto front, and the complete Pareto front is obtained by exhaustive search calculation for all distribution network configurations; for a distribution network with a total number of nodes exceeding 50 nodes, the reference Pareto front is the optimal Pareto front.

[0037] As another improvement of the present invention, in step S5, a similarity ranking technique with respect to the ideal solution is used to rank the optimal solutions. This technique determines the final ranking by considering the distances from the solutions to both the ideal solution and the negative ideal solution. In the similarity ranking technique with respect to the ideal solution, according to the similarity index value, the proximity to the ideal solution is calculated, and the weight combination number N W is introduced to obtain the average similarity index Specifically:

[0038]

[0039] where the weight combination number N W represents the average of the similarity indices of the reference solution i, and the average similarity index represents the average of the similarity indices for the i-th solution obtained for all N W weight combinations.

[0040] To achieve the above object, the technical solution adopted by the present invention is also: a multi-objective optimal configuration system for a radial distribution system based on reliability indices, including a processor and a memory. The memory stores executable code thereon, and when the executable code is executed by the processor, the processor executes the method as described above.

[0041] Compared with the prior art, the present invention has the following beneficial effects: The present invention discloses a multi-objective optimal configuration method and system for a radial distribution system based on reliability indices. The proposed intelligent terminal configuration in the distribution system reconstruction can synergistically optimize the topological structure and switch configuration of the distribution network, improving the reliability, economy, and power loss control ability of the system; when a fault occurs in the distribution network, the switch states can be quickly adjusted through automatic control to isolate the fault area and prevent the fault from spreading to other areas, ensuring the stability and power supply reliability of the system. Through this configuration, the distribution system can improve reliability while optimizing the power flow and reducing system losses, thereby achieving more efficient and stable operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is the flowchart of the steps of the method of the present invention;

[0043] Figure 2 It is a schematic diagram of the IEEE-33 node system in the test example of the present invention. Specific implementation manners

[0044] The following further clarifies the present invention in conjunction with the accompanying drawings and specific implementation manners. It should be understood that the following specific implementation manners are only used to illustrate the present invention and not to limit the scope of the present invention.

[0045] Embodiment 1

[0046] A multi-objective optimal configuration method for a radial distribution system based on reliability indexes, as Figure 1 shown, includes the following steps:

[0047] Step S1: Establish a set of objective functions to evaluate the optimal terminal configuration of the distribution system.

[0048] The distribution network will operate in the reference configuration for most of the time. Selecting a less efficient reference configuration will result in a reduction in the overall reliability of the system at the end of the reliability-related operating period (such as one year). These are the bases for the reliability indexes used in formulating standards, and the method of the present invention also takes these into account. Therefore, on this basis, the following modeling assumptions are introduced:

[0049] 1) The reliability evaluation period of the network is one year.

[0050] 2) The active power demand of each node represents the annual average value.

[0051] 3) Only consider the faults at the network branches by allocating the failure rate to all branches. All other components of the system operator are considered to be completely reliable because reconfiguration during a fault will not cause any change in their behavior.

[0052] 4) The users affected by a specific branch fault are the users located downstream of the fault branch.

[0053] When the method of the present invention deals with the power flow problem, the original non-linear problem is simplified to a linear problem. Existing research has shown that under normal operating conditions, the voltage angle is very small, and the voltage amplitude is close to the nominal voltage level of the system, usually in the range of [0.9 p.u., 1 p.u.]. In addition, these assumptions are natural under the concept of the smart grid, where sufficient monitoring and control further strengthen these quality constraints.

[0054] Therefore, the total power loss of the system is given by the following formula:

[0055]

[0056] Using the concept of the type 2 special ordered set (SOS2) to linearize the squares of the active and reactive powers flowing through the branches, the expression of the loss is linearized.

[0057] The reliability indices include:

[0058] System Average Interruption Frequency Index (SAIFI): It is a reliability index commonly used by power companies, representing the average number of interruptions per year. The calculation method is to weight the number of interruptions by assuming the number of customers as the weight and perform a weighted average:

[0059]

[0060] In the formula, λ i is the failure rate of N i affected customers, and M is the total number of customers served.

[0061] To obtain the parameters required for the model, the following assumptions were adopted: A failure rate was specified or assumed for the line with the highest impedance (maximum value) and the line with the lowest impedance (minimum value). Then, the failure rates of the remaining lines were determined by linear interpolation.

[0062] System Average Interruption Duration Index (SAIDI): It is a commonly used reliability index, representing the average power outage duration per year. It is calculated as the weighted average of the interruption durations, assuming the number of customers as the weight:

[0063]

[0064] In the formula, U i is the interruption duration caused by the fault.

[0065] Average Energy Not Supplied (AENS): Although SAIFI and SAIDI focus on the interruptions experienced by customers, they do not provide any direct information related to the impact of the interruptions on the energy supply. Some feeders may not supply power to a large number of individual users but may transmit a large amount of energy. Therefore, the index providing this information is defined as follows:

[0066]

[0067] In the formula, is the active load not supplied during the occurrence of fault i.

[0068] Step S2: Based on the radial topology of the distribution system, construct the constraints for multi-objective optimization.

[0069] To ensure the radial topology of the distribution system, the radiality condition must satisfy two conditions: 1) No loops should be formed (tree topology); 2) Each bus of the system should be connected to the substation.

[0070] The connectivity is ensured by the power balance equation:

[0071]

[0072] To account for transfer nodes (i.e., nodes with no production or consumption), a simple way to avoid complex constraints is to consider a very small consumption value (e.g., 10 -3 p.u.).

[0073] Active and reactive power flows through branches: Active and reactive power balance is enforced at each node through the following constraints:

[0074]

[0075] The first two equations enforce active and reactive power balance at each node respectively. The third equation states that the apparent power flowing through an active branch should be less than its rated apparent power limit.

[0076] The following two equations represent linear expressions of the square of the active power flowing through SOS2:

[0077]

[0078] Similarly, the following equation represents a linear expression of the reactive power flow:

[0079]

[0080] The variables and are both continuous positive values. The definition of SOS2 also stipulates that there cannot be more than two adjacent values greater than zero.

[0081] This can be achieved by constructing a set of linear mixed-integer programming constraints, although modern solvers have incorporated such variables into the variable types they support. The accuracy of this approximation depends on the sampling of the non-linear function, i.e., the number of samples and the sampling interval.

[0082] Step S3: According to the above multi-objective optimization problem and its constraints, the augmented constraint method (AUGMECON) is used to solve it to generate Pareto optimal solutions.

[0083] AUGMECON is a variant of the "ε-constraint method" and retains the advantages of the "ε-constraint method". In addition, it solves three major problems related to the application of the ε-constraint method: 1) calculating the range of the objective function using the lexicographic optimization method; 2) proving the efficiency of the returned solution; 3) achieving computational operability using various acceleration techniques.

[0084] Without loss of generality, a multi-objective problem of maximizing an objective function is considered. To account for minimizing the objective function, the corresponding objective function is multiplied by -1:

[0085]

[0086] In the formula, is the decision variable vector, and S is the feasible region of the problem.

[0087] The application of the ε - constraint method is to select one objective function p as the objective function of the new problem, while the other objective functions are regarded as constraint conditions.

[0088] The transformed problem is as follows:

[0089]

[0090] For AUGMECON, the payoff table is calculated using the lexicographic optimization method, that is, continuously optimizing the objective function and adding the optimal value of the previous objective function as an equality constraint to maintain the optimal solution. This technique ensures that the solutions obtained by individual optimization are Pareto - optimal solutions.

[0091] Then, use q i grid points to divide the range of p - 1 objective functions into q i - 1 intervals. These q i grid points are used to change the right - hand side value of the i - th objective function.

[0092] The number of sub - problems to be solved is The accuracy of the efficient set approximation depends on the number of grid points used, but the increase in the number of grid points will necessarily lead to a significant increase in computational complexity. Therefore, in practical applications, it is necessary to carefully select an appropriate number of grid points according to the scale of the specific problem and the limitations of computing resources to find an appropriate balance between the accuracy of the solution and computational efficiency.

[0093] Step S4: Apply the backward - forward scanning method to all configuration results to verify whether the above solution is feasible and update the Pareto - optimal solution set.

[0094] The multi - objective problems solved by AUGMECON do not consider the complete load - flow constraints to reduce the computational burden. This brings corresponding challenges. First, in terms of violating distribution system constraints (such as voltage magnitude and angle), several solutions may be infeasible in practice. In addition, from the perspective of the AUGMECON optimization method, several non - dominant solutions may become dominant solutions after the load - flow calculation is completed.

[0095] Since all configurations have a radial topology, the backward - forward scanning method is applied. According to the load - flow results, the objectives involving network physical quantities (such as AENS and SAIDI) are calculated in an exact manner (without using any approximations), so that the solution set obtained by AUGMECON can be analyzed by eliminating all infeasible or dominated solutions resulting from the load - flow calculation.

[0096] Subsequently, the feasible solutions and non-dominated solutions are compared with the reference Pareto front. For relatively small networks, the reference Pareto front can be the complete Pareto front (calculated by exhaustive search of all distribution network configurations), and for large networks, the reference Pareto front can be the most well-known Pareto front (by applying other optimization methods). This stage aims to evaluate whether the solutions regarded as non-dominated truly belong to the reference Pareto front.

[0097] Step S5: Provide the optimal solution set to the decision maker, apply multi-attribute decision-making methods to rank the obtained solutions, and select the final configuration result according to the decision maker's preferences.

[0098] The solutions of multi-objective mathematical programming (MMP) include a set of efficient solutions. Therefore, the decision maker should intervene according to their own preferences and decide on a single solution to be implemented. The decision maker can make a decision based on experience instead of using a systematic method. However, when dealing with a very large set of relatively optimal solutions, a method for ranking and presenting a narrower subset will be very useful for selection. This falls within the category of multi-attribute decision-making (MADM) problems, and the method of the present invention implements the similarity ranking to the ideal solution (TOPSIS) technique.

[0099] Assume that the solutions of the above p-object MMP consist of m Pareto-optimal alternative solutions. The TOPSIS method evaluates the following decision matrix:

[0100]

[0101] Each row in the above formula represents an alternative solution, and each column is related to a goal (minimization or maximization). Generally, each goal is expressed in a different unit.

[0102] Therefore, the next step of the TOPSIS method is to convert the decision matrix into a dimensionless attribute matrix so that the attributes can be compared. The normalization process is performed by dividing each element by the norm of the vector (column) of each criterion.

[0103] The elements of the normalized matrix are given by the following formula:

[0104]

[0105] At this time, the decision maker will provide a set of weights ω = {ω 1 , …, ω j , … ω p}, to represent the relative importance of each goal (criterion). By multiplying each column of the matrix with elements r ij by the weight ω j, a weighted normalization matrix with elements v can be created ij can be created.

[0106] Next, the ideal solution vector (A + ) and the negative ideal solution vector (A - ) must be specified:

[0107]

[0108] In the above formula, J is the set of objectives (criteria) to be maximized, and J′ is the set of objectives to be minimized. These artificial alternatives represent the most desirable (ideal) solution and the least desirable (negative ideal) solution. Then, each alternative is separated from the ideal solution (S i + ) and the negative ideal solution (S i - ) by a separation metric measured by the n-dimensional Euclidean distance:

[0109]

[0110] The last step in applying the TOPSIS method is to calculate the relative closeness to the ideal solution. The alternatives are ranked according to the similarity index in descending order, and the similarity index is calculated as follows:

[0111]

[0112] The value corresponding to the ideal solution is equal to 1.

[0113] Finally, sensitivity analysis is usually applied to design problems to obtain information about the change of a specific parameter (e.g., the rating of a device) by changing a certain input: the smaller the change in the parameter, the more robust the result. The results of the multi-attribute decision-making method are examined according to the change of the relevant parameter (i.e., the weight of the considered objective).

[0114] In this embodiment, the decision maker selects the weights of the objectives according to the given objectives; the change of the weights affects the ranking of the solutions, and the results can be applied to the situation where the priorities of the distribution operators change.

[0115] The TOPSIS ranking is based on the value of the similarity index . In this embodiment, the number of weight combinations N W is introduced, which represents the average value of the similarity indices of the reference solution i.

[0116] In addition, the average similarity index is introduced, which represents the average value of the similarity indices for the i-th solution obtained for all N W weight combinations, i.e., using to represent the similarity index at weight combination j Value:

[0117]

[0118] The value of the average similarity index can well reflect the performance of the solutions obtained by considering different weight combinations.

[0119] Test case

[0120] To verify the effectiveness of the method of the present invention, the IEEE-33 node distribution system is selected as the test system. As Figure 2 shown, the system contains 33 distribution nodes, where node 1 is the power supply node and the remaining 32 nodes are load nodes. The system contains a total of 37 branches, of which 32 branches are normal working branches (represented by solid lines) and 5 branches are tie branches (represented by dashed lines). Switches are installed on all branches, and the reconfiguration of the network topology can be controlled by opening and closing the switches.

[0121] In this test case, steps S1 to S5 are applied to optimize the configuration of the IEEE-33 node system. Through the solution of the AUGMECON method, a series of Pareto optimal solutions are obtained, as shown in Table 1. Table 1 lists 14 different configuration schemes, and each scheme includes the numerical values of three evaluation indexes: active power loss, system average interruption frequency index (SAIFI), and average unsupplied energy (AENS). It can be seen from Table 1 that as the active power loss increases, the reliability indexes (SAIFI and AENS) of the system generally show an improving trend, which reflects the trade-off relationship between the system performance indexes.

[0122] Table 1

[0123] Scheme Active power loss / kW SAIFI / times / year AENS / kWh / user / year 1 139.5012 1.1045 0.4436 2 139.9780 1.0365 0.4120 3 141.9158 1.0195 0.4060 4 142.4863 1.0165 0.4056 5 146.5320 1.0046 0.3996 6 146.2856 1.0032 0.3997 7 146.6258 1.0021 0.4000 8 148.5932 0.9986 0.3993 9 150.4621 1.0005 0.3982 10 150.3654 0.9991 0.3984 11 150.9863 0.9910 0.3952 12 152.3690 0.9871 0.3948 13 156.6192 0.9847 0.3940 14 161.5920 0.9841 0.3936

[0124] To verify the accuracy of the method of the present invention, we also analyzed the IEEE-33 node system by the complete exhaustive search method, and the obtained Pareto optimal solutions are shown in Table 2. By comparing the results of Table 1 and Table 2, it can be found that the Pareto optimal solutions obtained by the method of the present invention are very close to the results obtained by the complete analysis, which proves that the method has high accuracy in solving multi-objective optimization problems. For example, in both methods, the same minimum active power loss value of 139.5012 kW is obtained for Scheme 1, and the other performance indexes are also basically consistent.

[0125] Table 2

[0126] Scheme Active power loss / kW SAIFI / times / year AENS / kWh / user / year 1 139.5012 1.1045 0.4436 2 139.9781 1.0365 0.4120 3 140.7060 1.0318 0.4118 4 141.9165 1.0170 0.4056 5 142.4292 1.0162 0.4054 6 144.5780 1.0158 0.4054 7 146.2891 1.0040 0.4000 8 146.5135 1.0030 0.3998 9 146.6660 1.0020 0.4000 10 148.6080 0.9982 0.3991 11 150.2031 1.0003 0.3984 12 150.2483 0.9992 0.3982 13 150.9774 0.9910 0.3952 14 152.6000 0.9871 0.3943 15 156.1000 0.9847 0.3936 16 161.5801 0.9841 0.3934

[0127] In summary, this case discloses a multi-objective optimization configuration method and system for a radial distribution system based on reliability indices. According to the actual distribution system topology, a multi-objective optimization problem is established, which is to minimize the active power loss and maximize the reliability index of the reference users. Secondly, the dictionary optimization is adopted to efficiently implement the ε-constraint method to solve the multi-objective optimization problem. Then, after generating the Pareto efficient solution set, the obtained configuration is evaluated using the backward / forward sweep load flow algorithm to verify whether the obtained solutions are non-dominated and feasible. Finally, considering that the Pareto front generated by the ε-constraint method does not contain the decision maker's preferences, the present invention adopts a multi-attribute decision-making procedure, namely the technique for order preference by similarity to an ideal solution (TOPSIS) method, to rank the obtained solutions according to the decision maker's preferences, thus facilitating the final selection.

[0128] It should be noted that the above content only illustrates the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. For those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements all fall within the protection scope of the claims of the present invention.

Claims

1. A multi-objective optimization configuration method for radial power distribution system based on reliability index, characterized in that: The steps include: S1: define a multi-objective optimization problem, and establish a set of objective functions based on reliability indicators, wherein the objective functions include a system total power loss objective function, a system average interruption frequency index, a system average interruption duration index, and an average unpowered energy; S2: Based on the radial topology of the distribution system, the constraints of multi-objective optimization are constructed, and the enhanced constraint method is applied to generate the Pareto optimal solution by solving sub-problems; S3: Apply the backward-forward scanning load flow algorithm to all configuration results to verify the feasibility and non-dominance of the solution obtained in step S2; S4: Based on the verification result of step S3, the Pareto optimal solution set is updated, the infeasible solution and the dominated solution are eliminated, and the updated optimal solution set is presented to the decision maker; for networks with a total number of nodes not exceeding 50 nodes, the feasible solution and the non-dominated solution are compared with the complete Pareto frontier; for networks with a total number of nodes exceeding 50 nodes, they are compared with the optimal Pareto frontier; S5: Apply the multi-attribute decision-making method to sort the obtained solutions, adopt the similarity sorting technology method with the ideal solution, calculate the closeness to the ideal solution according to the value of the similarity index, introduce the number of weight combinations to obtain the average similarity index, and finally select the configuration plan according to the decision maker's preference.

2. The multi-objective optimization configuration method for radial power distribution system based on reliability index according to claim 1, characterized in that: The system average interruption frequency index in the objective function of step S1 represents the average number of interruptions per year of the system, specifically: In the formula, λ i YesN i The failure rate of affected customers, M is the total number of customers served; The system average interruption duration index represents the average power outage duration per year, specifically: Where U i The duration of the outage caused by the fault; The average unpowered energy reflects the impact of power outages on user energy supply, specifically: Where P i d is the active load not supplied during the fault i.

3. The multi-objective optimization configuration method for radial power distribution system based on reliability index according to claim 1, characterized in that: The constraints in step S2 are specifically: Among them, P b represents the active power flow on branch b, P i f represents the active power fed into the substation at bus i, P i D represents the active power demand at bus i, Q b represents the reactive power flow on branch b, represents the reactive power fed into the substation at bus i, represents the active power demand at bus i, represents the set of branches ending at node i ("to"), represents the set of branches starting from node i ("to"); it also includes that the apparent power flowing through the active branch should be less than its rated apparent power limit, specifically: Among them, S b represents the rated apparent power limit of branch b, x b is a binary variable, indicating whether branch b exists, and B represents the set of all branches in the system.

4. The multi-objective optimization configuration method for radial power distribution system based on reliability index according to claim 1, characterized in that: The step S2 adopts the enhanced constraint method to solve the target optimization problem, which specifically includes the following steps: S21. Preprocessing for the objective function minimization problem: multiply the objective function to be minimized by -1 to convert it: In the formula, is the decision variable vector, S is the feasible region of the problem, is the i-th objective function; S22. Apply the ε-constraint method to transform the multi-objective problem: select an objective function p as the main objective function, and transform other objective functions into constraints: Among them, e i is the lower limit of the constraint of the i-th objective function; S23, using a dictionary optimization method to continuously optimize multiple objective functions: optimize a single objective function, and after obtaining the optimal solution, add the optimal value of the objective function as an equality constraint to the optimization problem, and then continue to optimize the next objective function, and repeat this process until all objective functions are optimized; S24, for constraint condition e i To perform mesh division, use q i The grid points divide the value range of the i-th objective function into q i-1 interval, change the upper limit of the constraint e corresponding to the grid point i , and obtain different optimal solutions.

5. The multi-objective optimization configuration method for radial power distribution system based on reliability index according to claim 1, characterized in that: In the comparison phase of step S4, the feasible solutions and non-dominated solutions are compared with the reference Pareto frontier. For a distribution network with a total number of nodes not exceeding 50 nodes, the reference Pareto frontier is the real Pareto frontier, and the complete Pareto frontier is calculated by exhaustively searching all distribution network configurations. For distribution networks with a total number of nodes exceeding 50 nodes, the reference Pareto frontier is the optimal Pareto frontier.

6. The multi-objective optimization configuration method for radial power distribution system based on reliability index according to claim 1, characterized in that: In step S5, the optimal solutions are sorted by using a similarity sorting technique with the ideal solution. In the similarity sorting technique with the ideal solution, the similarity index The value of , calculates the closeness to the ideal solution, and introduces the number of weight combinations N W Get the average similarity index Specifically: Among them, the number of weight combinations N W Represents the average value of the similarity index of reference solution i, the average similarity index For all N W The average value of the similarity index for the i-th solution obtained by combining the weights.

7. A multi-objective optimization configuration system for radial power distribution system based on reliability indexes implementing the method as claimed in claim 1, characterized in that: The invention comprises a processor and a memory, wherein the memory stores executable codes, and when the executable codes are executed by the processor, the processor executes the method according to any one of claims 1 to 6.

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