Diode rectifier based multi-terminal dc power collection system optimal topology design method

Abstract

The optimal topology design method of the diode rectifier based multi-terminal direct current (DC) power collection system comprises the following steps: using graph theory indicators and weighted energy entropy to respectively represent the topology connection relationship characteristics and physical state characteristics of the diode rectifier based multi-terminal DC power collection system; based on the DC power flow calculation results, analyzing the mapping relationship between the graph theory characteristics and performance indicators of the diode rectifier based multi-terminal DC power collection system, and establishing a physical agent model of the diode rectifier based multi-terminal DC power collection system; taking the topology connection relationship as the decision variable, taking the economy, operation efficiency and balance of the diode rectifier based multi-terminal DC power collection system as the optimization target, and based on the established physical agent model, using the improved NSGA-III algorithm to solve the Pareto optimal solution set considering the technical and economic indicators; performing transient simulation verification on the obtained Pareto optimal solution set, and selecting the optimal topology design scheme according to the demand and preference. The optimal topology design method can realize the optimization of various economic and technical indicators through optimization design under the condition that the active control capability is limited.

Description

Technical Field

[0001] This invention relates to the field of DC power system design technology, specifically to an optimal topology design method for a diode-rectified multi-terminal DC collection power system. Summary of the Invention

[0002] With the continuous increase in wind power installed capacity, traditional point-to-point high-voltage direct current (HVDC) transmission methods are no longer sufficient to meet the demands of long-distance, large-scale, and multi-node grid connection. Multi-terminal high-voltage direct current (MTDC) networks, due to their high redundancy, flexibility, and economy, have become an important means to ensure the efficient collection, flexible transmission, and distributed consumption of clean energy over large areas. They consist of multiple converter stations and DC lines forming transmission networks with different topologies. Considering the high construction cost of voltage source converters (VSCs), which are widely used in converter stations, and the high operating losses and lack of fault ride-through capability of traditional line commutated converters (LCCs), researchers have recently focused on diode rectifier units (DRUs) with advantages such as small size, low loss, high reliability, and low cost, proposing various compact and lightweight DC transmission technologies based on DRUs. However, traditional topology design methods for AC power systems have certain limitations in multi-terminal DC power systems, and there is an urgent need to explore optimal topology design methods suitable for such new power systems.

[0003] Reference [1]: Di Haotian, Xiang Wang, Yang Mingrui, et al. Parameter design method and operation characteristic analysis of the AC / DC hybrid collection DC transmission system of Shagohuang New Energy [J / OL]. Proceedings of the CSEE, 1-19. A novel hybrid topology based on diodes and half-bridge-full-bridge modular multilevel converters is proposed as the converter station structure, which is connected to the AC / DC collection wind farm. Based on the wind farm operating conditions, three system operation modes and a system parameter optimization method with converter capacity as the key constraint are designed.

[0004] Reference [2]: C. Wang, A. Ali and F. Blaabjerg, "Composition and Control of a New Type of Hybrid Voltage-Source Converter Based on DRUs and FB-MMC for Large-Scale Offshore Wind Power Integration and Transmission," in IEEE Transactions on Power Electronics, vol. 39, no. 5, pp. 5721-5732, May 2024, doi: 10.1109 / TPEL.2024.3363617. A novel hybrid voltage source converter based on diodes and a full-bridge modular multilevel converter is proposed, which is connected to the AC collection wind farm, and the system parameters are optimized based on the variable modulation ratio m to realize power distribution and SM number design.

[0005] Reference [3]: MK Bucher, R. Wiget, G. Andersson and CM Franck, "Multiterminal HVDC Networks—What is the Preferred Topology?," in IEEE Transactions on Power Delivery, vol. 29, no. 1, pp. 406-413, Feb. 2014, doi:10.1109 / TPWRD.2013.2277552. A simulation framework of "Optimal Power Flow (OPF) in steady state + Electromagnetic Transient (EMT) in transient state" was established. By evaluating the performance of four typical topologies in terms of steady-state loss and transient fault current, the correlation between topological characteristics and physical performance was revealed.

[0006] Reference [4]: ​​Chen Ke, Zhang Yingmin, Li Junsong. Research on the influence of DC power grid structure on power flow distribution [J]. Electrical Measurement & Instrumentation, 2020, 57(19):14-20+26.DOI:10.19753 / j.issn1001-1390.2020.19.003. By deeply exploring the internal connection between topology and system operating characteristics, it is proposed to use entropy theory to describe the power flow balance of the system.

[0007] However, the methods described in the aforementioned literature largely focus on system parameter design based on novel converters, with less consideration given to the topology design of DC power systems. Furthermore, they tend to focus on the performance targets of a single topology without systematically evaluating the advantages and disadvantages of different topologies in various technical and economic indicators. In addition, existing DC power flow calculation methods in grid topology design are mainly designed for flexible high-voltage direct current transmission (VSC-HVDC) systems and cannot be directly applied to novel DC systems based on DRUs.

[0008] Therefore, it is urgent to explore optimal topology design methods applicable to diode-rectified multi-terminal DC collection power systems, to make up for the shortcomings of existing methods, and to provide technical reference for the large-scale construction and topology optimization of such systems in the future.

[0010] This invention provides an optimal topology design method for a diode-rectified multi-terminal DC collection power system. Under the condition of limited active control capability, it achieves optimal economic and technical indicators in many aspects through optimized design.

[0011] The technical solution adopted in this invention is as follows: The optimal topology design method for diode-rectified multi-terminal DC collection power systems includes the following steps: Step 1: Use graph theory indices and weighted energy entropy to represent the topological connectivity and physical state characteristics of a diode-rectified multi-terminal DC collection power system, respectively; Step 2: Based on the DC power flow calculation results, analyze the mapping relationship between the graph theory characteristics and performance indicators of the diode-rectified multi-terminal DC collection power system, and establish a physical proxy model of the diode-rectified multi-terminal DC collection power system; Step 3: Using topological connections as decision variables, and taking the economy, operating efficiency, and balance of the diode-rectified multi-terminal DC collection power system as optimization objectives, and based on the physical proxy model established in Step 2, the improved NSGA-III algorithm is used to solve the Pareto optimal solution set considering technical and economic indicators. Step 4: Perform transient simulation verification on the obtained Pareto optimal solution set, and select the optimal topology design scheme according to requirements and preferences.

[0012] Step 1 includes: S1.1: The topology of the diode-rectified multi-terminal DC collection power system is abstracted into an undirected graph, and the following graph theory indices are introduced to quantify the topology: node degree, average path length, clustering coefficient, betweenness centrality, and number of meshes. S1.2: Using weighted energy entropy As a representative indicator of physical state characteristics, the weighted energy entropy Calculate according to the following formula: ; in, The average load factor of the line; For the first The normalized value of the load rate of each line. The weighted energy entropy represents the total number of lines. It is used to comprehensively reflect the system load rate level and distribution balance.

[0013] Step 2 includes the following steps: S2.1: Sample generation, randomly generate multiple feasible network topologies and check connectivity; S2.2: Perform accurate DC power flow calculations for each network topology to obtain output data; S2.3: Perform statistical testing and visualization analysis on the output data in S2.2, and develop a fast performance estimation formula as a physical proxy model.

[0014] In step S2.2, the accurate DC power flow calculation includes the following sub-steps: S2.2.1: System modeling, including: The diode rectifier converter station and its AC source are equivalent to a current source dependent on DC voltage, and its volt-ampere characteristic is characterized by the following formula: (1); In formula (1): This represents the current flowing through the i-th diode; The open-circuit voltage is represented as , The rectification coefficient of a three-phase full-bridge rectifier; This indicates the voltage output after rectification by the diode; Equivalent resistance ,in, Indicates the on-resistance of the diode. This represents the equivalent resistance of the transformer. This indicates the resistance of the AC line.

[0015] Based on the characteristics of load nodes, load nodes j∈L are modeled, where L is the set of load nodes, including constant power loads, as shown in equation (2): Constant power load: (2); In formula (2): This represents the current passing through the j-th load; This represents the power of the j-th load; This represents the voltage of the j-th load.

[0016] Based on the characteristics of connecting nodes, for connecting node k∈C, C is the set of connecting nodes: , This represents the current at the k-th interconnection node.

[0017] S2.2.2: Let the injected current at node i in the DC grid be... The voltage at node i is The conductance of the line between nodes i and j is Based on Kirchhoff's Current Law (KCL), the relationship between the node voltage and the node injected current at each node is as follows: , i=1,2,...,N(3; In equation (3): the left side The current function injected into the node is determined according to the node type; the right side shows the sum of currents flowing out of the node through the connected lines, where... This is the node admittance matrix, determined by the line resistance; when there is a connection between nodes i and j... , Represents the resistance of the line at nodes i and j; This represents the voltage at the j-th node; N represents the number of nodes.

[0018] Construct the equations for all DC nodes in the network, substitute the node types, and obtain the complete set of equations as shown in equation (4): (4); In equation (4): The admittance matrix represents the connection node; Indicates the voltage at the connection node; Indicates the number of the contact node.

[0019] S2.2.3: Solve the DC node equations of the entire network using the piecewise linear iterative method to obtain the results including total losses. The output data includes the average load rate M; the total loss is calculated using the following formula: (10); In formula (10): This indicates the total number of lines. Indicates the loss of a DC line; This indicates converter losses.

[0020] Step 3 includes the following sub-steps: S3.1: The topology optimization problem is described as a multi-objective optimization problem, i.e., min[ ; Where: x is the decision variable, designed as: whether or not to construct a line between nodes. ; Optimization Objective , , These are: economy, operational efficiency, and power flow balance; S3.2: Custom design of the encoding, evaluation, and operator modules in the improved NSGA-III algorithm; S3.3: The customized coding, evaluation, and operator modules are embedded into the NSGA-III multi-objective evolutionary algorithm framework for solving, and finally output the Pareto optimal solution set.

[0021] The customized design in S3.2 includes: S3.2.1: Chromosome coding design, using a length of M = N The binary string of (N-1) / 2 represents the connection status between all possible node pairs: 1 = connected, 0 = not connected; S3.2.2: Fitness assessment and constraint treatment design, performing feasibility verification and objective function calculation for each individual in the population in turn; S3.2.3: Genetic operator design, performing crossover and mutation operations on points and edges, and adding connectivity repair operations.

[0022] In S3.2.2, the feasibility verification includes convergence judgment and security verification; the objective function calculation includes: Economic calculation: Total cost ;in, Indicates the cost of the line. This indicates the cost of the equipment.

[0023] Operating efficiency calculation: The sum of converter loss and DC loss is used to express the efficiency. The calculation is performed quickly based on the loss estimation formula (10) obtained in step 2. Power flow equilibrium calculation: using weighted energy entropy This means that the calculation is performed according to formula (13): (13).

[0024] Step 4 includes the following sub-steps: S4.1: Based on simplified transient checks, the Pareto optimal solution set is filtered; S4.2: Select representative topologies for detailed simulation to verify the safety and stability of the Pareto solution; S4.3: Select the optimal topology design scheme from the Pareto solution set, taking into account engineering requirements and preferences.

[0025] Step 4.1 includes the following steps: S4.1.1: Check the maximum fault current, only check the most severe fault scenario, estimate the most severe fault current, and quickly check whether it exceeds the rated value of any equipment; S4.1.2: Check all transient constraints, including: check voltage sags and ensure they are within acceptable limits; Assess basic stability by: whether the system can recover after a fault, recovery time, whether voltage collapse will occur, whether the diode will be damaged by reverse voltage, and whether the capacitor discharge energy is within a safe range; S4.1.3: Remove all Pareto solutions that fail the check.

[0026] Step 4.2 includes the following steps: S4.2.1: Model Establishment: The cable adopts a frequency-varying distributed parameter model, the diode adopts a detailed semiconductor physical model, the energy storage system adopts a detailed control model, the transformer considers saturation characteristics and leakage reactance; the control system adopts actual control logic; the protection system considers the dynamic characteristics of the circuit breaker. S4.2.2: Perform sensitivity analysis: a. Multi-fault scenario analysis: pole-to-ground faults at different locations, faults at different times, and combined faults.

[0027] b. Protection system coordination: circuit breaker operating time, protection selectivity, and fault isolation strategy.

[0028] c. Comprehensive evaluation of dynamic performance: voltage dynamic response, current surge characteristics, and system recovery process.

[0029] d. Verify that the selected solution can operate safely and stably under any expected operating conditions.

[0030] Step 4.3 includes the following steps: S4.3.1: Considering the limitations of the engineering scenario, hard constraints such as budget limit, loss limit, minimum weighted energy entropy, reliability requirements (such as the N-1 criterion), and voltage allowable range must be met.

[0031] S4.3.2: Considering priority preferences, analyze the weights of economic efficiency, losses, and weighted energy entropy objectives. If a certain objective is preferred, select the objective with the higher weight.

[0032] S4.3.3: Consider the specific requirements related to the scenario, such as whether to consider future expansion, maintenance difficulty, geographical constraints, and technological maturity.

[0033] This invention discloses an optimal topology design method for a diode-rectified multi-terminal DC collection power system, with the following technical advantages: 1) This invention introduces weighted energy entropy into the DC power grid evaluation system and combines it with graph theory structure indicators to serve as a quantitative description of topological characteristics, thereby achieving a joint characterization of "structural robustness" and "operational balance", which enables the optimized design to take into account the intrinsic relationship between physical structure and electrical performance.

[0034] 2) For novel systems based on diode rectifiers, a complete DC power flow calculation method and a new design paradigm are proposed. By using "simple control of diodes + optimal topology", sufficient performance and high reliability are achieved, which is suitable for DC power grid design without communication coordination.

[0035] 3) This invention utilizes a fast-computing physical surrogate model to provide a highly reliable and fast evaluation surrogate model for subsequent optimization models, significantly reducing the evaluation time required for multi-objective optimization and further improving the optimization efficiency of large-scale systems.

[0036] 4) This invention constructs a multi-dimensional comprehensive evaluation and optimization index, with economy, operational efficiency and balance as comprehensive objectives. It systematically reveals the influence of topology on economy, efficiency and internal balance, and obtains the Pareto optimal design scheme set, making the scheme more practical in engineering.

[0037] 5) This invention adds a feasibility verification strategy before multi-objective optimization, and uses DC power flow convergence (to ensure steady-state feasibility) and DRU exceeding limits and energy storage exceeding limits (to ensure equipment safety) as rigid constraints for preliminary screening, which greatly reduces the feasible solution space, avoids a lot of invalid calculations, and improves optimization efficiency.

[0038] 6) A two-stage comprehensive evaluation system based on "steady-state" and "transient" states is proposed. The first stage involves steady-state power flow calculation and multi-objective optimization, while the second stage involves preliminary transient screening and detailed transient analysis, resulting in a more comprehensive evaluation.

[0039] 7) The present invention can be configured or programmed to execute all methods using devices such as computers, and is also applicable to large-scale topologies. Attached Figure Description

[0040] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a general framework diagram of the optimization method proposed in this paper.

[0041] Figure 2 This is a schematic diagram of the two-stage comprehensive evaluation system of "steady state" and "transient state" adopted in this invention.

[0042] Figure 3 This is a schematic diagram of the converter station based on diodes and grid-type energy storage according to the present invention.

[0043] Figure 4 This is a flowchart of the multi-objective optimization method used in this invention.

[0044] Figure 5 This is a logical topology diagram of nodes.

[0045] Figure 6The graph shows the relationship between MN, APL, and total loss.

[0046] Figure 7 This is a three-dimensional relationship diagram of MN-APL-total loss.

[0047] Figure 8(a) shows a schematic diagram before repair (3 connected components); Figure 8(b) is a schematic diagram of the repaired (fully connected graph). Detailed Implementation

[0048] The optimal topology design method for diode-rectified multi-terminal DC collection power systems includes the following steps: Step 1: Use graph theory indices and weighted energy entropy to represent the topological connectivity and physical state characteristics of a diode-rectified multi-terminal DC collection power system, respectively; Step 2: Based on the DC power flow calculation results, analyze the mapping relationship between the graph theory characteristics and performance indicators of the diode-rectified multi-terminal DC collection power system, and establish a physical proxy model of the diode-rectified multi-terminal DC collection power system; Step 3: Using topological connections as decision variables, and taking the economy, operating efficiency, and balance of the diode-rectified multi-terminal DC collection power system as optimization objectives, and based on the physical proxy model established in Step 2, the improved NSGA-III algorithm is used to solve the Pareto optimal solution set considering technical and economic indicators. Step 4: Perform transient simulation verification on the obtained Pareto optimal solution set, and select the optimal topology design scheme according to requirements and preferences.

[0049] In step 1, the topology of the diode-rectified multi-terminal DC collection power system is abstracted into an undirected graph. G =( V,E ),in: V For converter station node set, E For DC cable edge sets, the following metrics are introduced to quantify the topology: 1.1: Graph theory indicators representing basic structural characteristics: Node degree (D): Based on the number of DC cables connected to the DRU converter station; the higher the node degree (D), the greater the fault current; Average path length (APL): The average of the shortest paths between any two converter stations (unit: km); the smaller the average path length (APL), the lower the steady-state loss, but the higher the fault current; Clustering coefficient (CC): actual number of connections between node neighbors / possible number of connections; the higher the clustering coefficient (CC), the more uniform the fault current distribution and the lower the peak value. Betweenness centrality (BC): the frequency with which a node appears on the shortest path to other nodes; the higher the betweenness centrality (BC), the greater the fault current.

[0050] Number of meshes (MN): The number of independent closed loops in the topology of a diode-rectified multi-terminal DC-DC power system, which directly reflects the system redundancy and power flow regulation capability; the larger the number of meshes (MN), the better the system redundancy and the stronger the power flow regulation capability.

[0051] 1.2: Weighted energy entropy representing physical state characteristics: Weighted energy entropy ( ): Comprehensively reflects the system load rate level and distribution balance; weighted energy entropy ( The larger the value, the lower the load factor and the higher the distribution balance.

[0052] Step 2 includes the following steps: Step 2.1: Sample generation, randomly generate hundreds of feasible network topologies and check connectivity; Step 2.2: Perform accurate DC power flow calculations for each network topology to obtain output data; Step 2.3: Perform statistical tests and visualization analysis on the output data in Step 2.2, and develop a fast performance estimation formula as a physical proxy model.

[0053] In step 2.1, the generated network topology considers that each DRU converter station includes an ideal diode rectifier and a grid-type energy storage system, and the energy storage is regarded as an ideal voltage source that can maintain a constant AC voltage at the common coupling point PCC.

[0054] In step 2.2, the accurate DC power flow calculation includes the following steps: 2.2.1: System Modeling: 1) Based on the VI characteristics of diode converter stations, a DRU converter station and its AC source (grid-type energy storage) are equivalently represented as a current source dependent on DC voltage. Modeling is performed for each diode node i∈S, where S is the set of diode nodes; As shown in equation (1): (1); In formula (1): This represents the current flowing through the i-th diode; The open-circuit voltage is represented as , The rectification coefficient of a three-phase full-bridge rectifier; This indicates the voltage output after rectification by the diode; Equivalent resistance ,in, Indicates the on-resistance of the diode. This represents the equivalent resistance of the transformer. This indicates the resistance of the AC line.

[0055] 2) Based on the characteristics of load nodes, load nodes j∈L are modeled, where L is the set of load nodes, including constant power loads, as shown in equation (2): Constant power load: (2); In formula (2): This represents the current passing through the j-th load; This represents the power of the j-th load; This represents the voltage of the j-th load.

[0056] 3) Based on the characteristics of connecting nodes, for connecting node k∈C, C is the set of connecting nodes: , This represents the current at the k-th interconnection node.

[0057] 2.2.2: Constructing the nodal current balance equations: Let the injected current at node i in the DC power grid be... The voltage at node i is The conductance of the line between nodes i and j is Based on Kirchhoff's Current Law (KCL), the relationship between the node voltage and the node injected current at each node is as follows: , i=1,2,...,N(3; In equation (3): the left side The current function injected into the node is determined according to the node type; the right side shows the sum of currents flowing out of the node through the connected lines, where... This is the node admittance matrix, determined by the line resistance; when there is a connection between nodes i and j... , Represents the resistance of the line at nodes i and j; This represents the voltage at the j-th node; N represents the number of nodes.

[0058] Construct the equations for all DC nodes in the network, substitute the node types, and obtain the complete set of equations as shown in equation (4): (4); In equation (4): The admittance matrix represents the connection node; Indicates the voltage at the connection node; Indicates the number of the contact node.

[0059] 2.2.3: Solve the above system of equations: Considering the piecewise continuity and complementary constraint characteristics of diodes, their properties are nonlinear. A piecewise linear iterative method is used to solve this problem. The specific steps include: ①: Initialization: Guessing the initial voltage ; ②: State determination and linearization: First, determine the status: based on the current voltage. Determine the state of each diode node; if The diode is in the conducting state; if If the diode is off, then the diode is in the off state.

[0060] Secondly, linearization is performed: the system is linearized based on the node states. For a conducting diode ; For the turn-off diode ; For constant power loads Linearization is as follows: (5); ③: Constructing a linearized system: Based on the nodal current equation (1) constructed above, solve the linear system: (6); In formula (6): Represents the coefficient matrix; This represents the state variable to be determined, i.e., the voltage value at the next moment; This represents the difference between the power estimated by the voltage in the k-th iteration and the given injected power, i.e., the power imbalance.

[0061] Where, for diode node i∈S: , (7); In equation (7): The coefficient matrix representing diode node i; Represents the admittance matrix; This represents the power imbalance at diode node i.

[0062] For load node j∈L: , (8); In equation (8): The coefficient matrix representing load node j; This represents the initial voltage at load node j.

[0063] ④: Check convergence: like If the state remains unchanged, then it converges. Indicates the voltage value at the next moment; This indicates the voltage value at this moment; Indicates the error threshold, for Possible values: It typically converges within 10-20 iterations to obtain the output data.

[0064] In step 2.2, the input data for accurate DC power flow calculation includes: DC network topology and parameters. The effective value of AC output voltage of each grid-type energy storage unit and equivalent internal resistance Power of each DC load ; The data output after the accurate DC power flow calculation converges includes: node parameters, branch parameters, and system parameters, where the node parameters include DC node voltages. Power injected into each diode converter station Converter firing angle ; Branch parameters include line active power Current ,resistance ; System parameters include total losses Average load factor M; Total losses represent system operating efficiency and are divided into two parts: line losses and converter losses. DC line losses are generated by resistance heating, and the formula is: (9); In equation (9): This indicates the loss in a DC line.

[0065] Converter losses: Since the DRU is an uncontrolled rectifier device, it has no gate drive and switching action, and only includes conduction losses. and reverse recovery loss In practical design, the loss curves provided by the manufacturer can be used to directly obtain the single-module loss under different DC currents. (Conduction + Reverse Recovery) yields the converter loss as follows: .

[0066] The final power flow calculation directly outputs the total loss: (10); In formula (10): This indicates the total number of lines.

[0067] The average load factor M reflects the overall power flow density of the system. Based on the definition of load factor as the ratio of the actual transmission power of the line to the rated capacity, the calculation formula for line load factor is obtained (11): (11); in: Indicates the line load rate; The active power of the line (power flow result); This is the thermal stability limit of the line, i.e., the rated capacity of the line.

[0068] Then the average load factor of the N lines is obtained, as shown in formula (12): (12).

[0069] Weighted energy entropy represents the system's power flow balance. It is calculated based on power flow calculation results, combined with the average load rate M. The specific steps are as follows: a1: Perform a precise DC power flow calculation on the current topology to obtain the active power flow of each line; a2: Obtain the thermal stability limit, i.e., maximum power, for each line. ; a3: Calculate the load rate for each line: ; a4: Obtain the average load rate of N lines: ; a5: To calculate the entropy value, it is normalized: ; in, This represents the normalized value of the average load factor.

[0070] a6: Calculate line load rate entropy ; a7: The line load rate entropy is weighted by the average line load rate to obtain the weighted line load rate entropy, as shown in the following formula (13): (13).

[0071] That is, weighted energy entropy.

[0072] In step 2.3, statistical tests and visualization analysis are performed on the data from step 2.2. Specific steps include: 2.3.1: Visual Exploration: 1) Plot a scatter plot with graph theory features as the horizontal axis and loss and weighted energy entropy performance as the vertical axis; the scatter plot is plotted on the interface with graph theory features as the horizontal axis and loss and weighted energy entropy performance as the vertical axis; 2) Observe the distribution trend of each point to see if there is a clear correlation trend; the observed correlation distribution trend needs to be analyzed in conjunction with the distribution of actual data points. Usually, it can be seen that the vertical axis and the horizontal axis are positively or negatively correlated.

[0073] 3) Fit the trend line using a simple function; the simple function includes linear fitting. Exponential decay fitting function etc., where a and b are undetermined coefficients.

[0074] 2.3.2: Statistical Tests: 1) Calculate the correlation coefficient: Calculate the Pearson correlation coefficient between each horizontal axis feature and the performance value. The formula is as follows: , used to measure the degree of linear correlation; Calculate the Spearman rank correlation coefficient between each horizontal axis feature and the performance value. The formula is as follows: , is used to measure the degree of monotonic correlation.

[0075] 2) Hypothesis testing: A p-value test was performed on the calculated correlation coefficients, with the null hypothesis being that "the two variables are not correlated". If the p-value < 0.01 (or 0.05), it means that the null hypothesis is not valid at the 99% (or 95%) confidence level, and the two variables are correlated, thus verifying the distribution trend observed in 2.3.1.

[0076] 2.3.3: Binning and Threshold Analysis: 1) Data binning and performance analysis: Divide the value range of a feature into several intervals. For example, divide the value range of a graph theory index, such as the number of meshes MN, into several continuous intervals, such as [0,1],[2,3],[4,5],…[0,1],[2,3],[4,5],… Calculate the average performance index of all samples within each interval using the following formulas: (14).

[0077] in, It represents the average value of a certain performance index; Indicates a specific performance indicator; Indicates the number of samples.

[0078] 2) Finding the performance inflection point / threshold: Observe which interval after which the performance index shows a qualitative improvement; or look for the pattern that "all high-performing samples are characterized by being greater than a certain value". Specifically: Plot a line graph of the interval index (or index mean) versus average performance. Observe whether the curve has a clear inflection point (deteriorating performance) or a clear inflection point (deteriorating performance). For example, when the number of meshes increases from 2 to 3, the average loss suddenly decreases by 20%, then MN=3 can be regarded as a performance inflection point. Select the top 10% of the samples from all samples as "superior samples" (e.g., the lowest loss, the highest weighted energy entropy). Statistically analyze the graph theory index distribution of these superior samples and find the minimum index value that all superior samples satisfy. For example, if the number of meshes of all superior samples is ≥3, then MN≥3 can be regarded as a strong constraint.

[0079] Figure 6 Using the number of meshes (MN) as the horizontal axis and the total system loss as the vertical axis, the average performance curve of the bins and the inflection point identification process are shown. Figure 6 In the diagram, each hollow dot represents the average total loss of all topologies within that mesh count range. When MN ≤ 2, the average loss is > 3.5%, indicating poor performance. When MN ≥ 3, the average loss drops below 2.5%, and the downward trend is gradual. Therefore, MN = 3 is identified as the performance inflection point / threshold. Further analysis of the "excellent samples" (the 10% of samples with the lowest loss) reveals that they all satisfy MN ≥ 3, thus confirming that MN ≥ 3 is a necessary condition for achieving high performance.

[0080] 2.3.4: Multivariate Analysis and Interaction Exploration: 1) Draw a 3D scatter plot of multiple characteristic indicators and performance to observe the combined influence of these indicators and whether a "complementary" effect exists. Details are as follows: Select two graph theory indicators defined in step 1 as independent variables, for example: X X =Number of meshes (MN), Y Y =Average Path Length (APL); Performance Metrics Z =Total Loss P total_loss or weighted energy entropy Hs Using the hundreds of samples obtained from the precise DC power flow calculation in step 2.2 (each sample corresponding to a random topology), extract the (X,Y,Z) triples for each sample. Plot a 3D scatter plot: each point represents a topological sample, and the color or size of the point can map to a third feature (such as the clustering coefficient CC) for higher-dimensional exploration. The data distribution can be observed from a rotatable perspective.

[0081] The complementary effect is defined as follows: when both XX and YY are large or both are small, the performance ZZ is significantly better than when only a single feature is large. For example, if the region with lower loss Z corresponds to a larger MN and a smaller APL, then these two features have a complementary effect, with high redundancy and short paths jointly reducing loss.

[0082] Figure 7 Display a 3D scatter plot with the number of meshes (MN) as the X-axis, the average path length (APL, km) as the Y-axis, and the total loss (%) as the Z-axis. Figure 7 Each point in the diagram represents a topological sample.

[0083] Blue dots (●): Samples with higher loss (>3.5%).

[0084] Red circle (○): Samples with low loss (<2.5%).

[0085] Observing the complementary effect: Low-loss regions (red) are concentrated in areas where MN ≥ 3 and APL ≤ 100 km. Samples that individually satisfy MN ≥ 3 but have a high APL (> 140 km) (blue dots in the upper right corner of the figure) actually have higher losses, indicating that APL has a counteracting effect. Samples that individually satisfy APL ≤ 100 km but have a very small MN (≤ 1) (blue dots in the lower left corner) also have high losses. MN and APL have a complementary effect on reducing losses; high redundancy (large MN) needs to be combined with short paths (small APL) to achieve the best results.

[0086] 2) Multiple regression analysis: Establish a multiple linear model of performance and graph theory indicators, such as... The regression coefficients are then calculated by substituting the actual data for each axis into the model described above. .

[0087] Step 3 includes: 3.1: The topology optimization problem is described as a multi-objective optimization problem, i.e., min[ ; Where: x is the decision variable, designed as: whether or not to construct a line between nodes. ; Optimization Objective , , These are: economy, operational efficiency, and power flow balance; Nonlinear constraints include: diode characteristics, power balance, etc. 3.2: Improvements to the encoding, evaluation, and operator modules in the NSGA-III algorithm, with customized designs as follows: a: Chromosome coding design: For N nodes, the design length is M = N. A binary string of (N-1) / 2 represents the connection status between all possible node pairs: 1 = connected, 0 = not connected; b: Fitness assessment and constraint treatment design: Feasibility verification (rigid constraints) and objective function calculation (flexible objective) are performed on each individual in the population in turn. c: Genetic operator design: Perform crossover and mutation on points and edges, and add connectivity repair.

[0088] 3.3: The improved encoding, evaluation, and operator modules are embedded into the NSGA-III multi-objective evolutionary algorithm framework for solving the problem. The specific process includes: The algorithm encodes chromosomes, initializes the population, evaluates individual fitness, uses genetic operators, generates a new generation of population, and automatically performs non-dominated sorting of individuals, reference point association, selection and elite retention, ultimately outputting the Pareto optimal solution set.

[0089] In section 3.2b, the feasibility verification (rigid constraints) includes convergence judgment and security verification: Convergence judgment: The convergence is judged by whether the fast DC power flow calculation is converged. If it is converged, it is a feasible topology; otherwise, it is not feasible. The fast DC power flow calculation differs from the accurate DC power flow calculation in step 2. The calculation speed is greatly improved by simplification. The simplification includes: assuming that most diodes are in the conducting state; and simplifying the rectifier into a linear model, as shown in equation (1).

[0090] Linear systems can be solved directly using sparse Cholesky decomposition. Safety verification: Consider the safety of both DRU and energy storage. Energy storage is verified based on whether its power capacity is within the maximum / minimum range; DRU is verified based on the operating point of each DRU. , Whether the verification is performed within its safe operating area, and any violation will be subject to a severe penalty. In addition, connection constraints are imposed on the DRU, which must be directly connected to at least one energy storage device.

[0091] In section 3.2b, the objective function calculation (flexible objective) includes: economic calculation cost, operational efficiency calculation loss, and power flow balance calculation weighted energy entropy. For economic efficiency, the sum of line cost and equipment cost can be used for quick calculation; The calculation formula is: .

[0092] in, Indicates the cost of the line. This indicates the cost of the equipment.

[0093] For operating efficiency, the sum of converter loss and DC loss is used, and it can be quickly calculated based on the loss estimation formula (10) obtained in step 2. For power flow equilibrium, the weighted energy entropy defined in step 1 is used. This indicates that the weighted energy entropy estimation formula (13) obtained in step 2 can be used for rapid calculation. Among them, the loss estimation formula (10) and the weighted energy entropy estimation formula (13) are the physical proxy models obtained in step 2, which need to be solved through statistical testing and visualization analysis.

[0094] In section 3.2c, The design methods for intersections include: standard single-point intersections, two-point intersections, or uniform intersections; The standard single-point crossover includes: randomly selecting a crossover point, where the part before the point comes from parent generation 1 and the part after the point comes from parent generation 2; The two-point intersection includes: selecting two intersection points and exchanging the segment between the two points; The uniform crossing includes: randomly selecting crossing points to exchange segments.

[0095] Mutation methods include simple bit flipping (0 / 1 flipping), which involves changing 0 to 1 (adding an edge) or 1 to 0 (removing an edge) with a certain probability. The repair method is to check the connected components and treat the current topology as an undirected graph. G =( V,E Use depth-first search (DFS) or union-find to find all connected components. Record the set of nodes contained in each component; Add or remove edges to isolated nodes or multiple connected components to ensure the final topology is connected. Specifically: Figures 8(a) and 8(b) illustrate a topology with three connected components and its repair process. Initial state: Component 1 (nodes A, B, F), Component 2 (C, D, G), Component 3 (E). Select the closest node pair between Component 1 and Component 2: B and C, and add edge BC. Select the closest node pair between Component 2 and Component 3: D and E, and add edge DE. Ultimately, all nodes are connected, and the number of added edges is minimized (2).

[0096] In section 3.3, each solution in the final Pareto optimal solution set represents an optimal trade-off between cost, loss, and weighted energy entropy, and subsequent optimal decisions can be made based on engineering needs and preferences.

[0097] Step 4 includes the following steps: Step 4.1: Based on simplified transient checks, filter the Pareto optimal solution set; Step 4.2: Select 3-5 representative topologies for detailed simulation to verify the safety and stability of the Pareto solution; Step 4.3: Select the optimal solution from the Pareto solutions based on engineering requirements and preferences.

[0098] Step 4.1 includes the following steps: S4.1.1: Check the maximum fault current, checking only the most severe fault scenario, estimating the most severe fault current, and quickly checking whether it exceeds the rated value of any equipment; details are as follows: Only examine the most severe fault scenarios, such as a DC pole short circuit to ground, and estimate the most severe fault current. I fault, max. If I fault,max> I rated, device I If rated and device represent the rated current of any device, then the solution is discarded.

[0099] S4.1.2: Check all transient constraints, including: check voltage sags and ensure they are within acceptable limits; Assess basic stability by: whether the system can recover after a fault, the recovery time, whether voltage collapse will occur, whether the diodes will be damaged by reverse voltage, and whether the capacitor discharge energy is within a safe range; specifically as follows: Voltage sag Δ U sag Is it within acceptable limits, such as not exceeding 30% of the rated voltage? Can the fault be recovered, and what is the recovery time? t recovery Will voltage collapse occur? Will the diode be damaged by reverse voltage? Is the capacitor discharge energy within a safe range?

[0100] S4.1.3: Remove all Pareto solutions that fail the check. Specifically: The most severe fault current can be approximated by the diode's conduction characteristics: ; in, The equivalent resistance at the fault point.

[0101] After passing through S4.1, the number of remaining Pareto solutions is greatly reduced, allowing us to proceed to the next round of detailed simulation.

[0102] Step 4.2 includes the following steps: S4.2.1: Model Establishment: The cable adopts a frequency-varying distributed parameter model, the diode adopts a detailed semiconductor physical model, the energy storage system adopts a detailed control model, the transformer considers saturation characteristics and leakage reactance; the control system adopts actual control logic; the protection system considers the dynamic characteristics of the circuit breaker. S4.2.2: Perform sensitivity analysis: a. Multi-fault scenario analysis: pole-to-ground faults at different locations, faults at different times, and combined faults.

[0103] b. Protection system coordination: circuit breaker operating time, protection selectivity, and fault isolation strategy.

[0104] c. Comprehensive evaluation of dynamic performance: voltage dynamic response, current surge characteristics, and system recovery process.

[0105] d. Verify that the selected solution can operate safely and stably under any expected operating conditions.

[0106] Step 4.3 includes the following steps: S4.3.1: Considering the limitations of the engineering scenario, hard constraints such as budget ceiling, loss ceiling, minimum weighted energy entropy, reliability requirements (e.g., N-1 criterion), and allowable voltage range must be met. Specifically: The following hard constraints must be met: Budget cap ; Loss Limit ; Minimum weighted energy entropy requirement, This reflects the bottom line of equilibrium; Reliability requirements, such as the N-1 criterion: the system should still be able to operate normally after any line or converter is out of service; Permissible voltage range, for example, ±5% of the rated voltage.

[0107] S4.3.2: Considering priority preferences, analyze the weights of economic efficiency, losses, and weighted energy entropy objectives. If a particular objective is preferred, select the one with the higher weight. Specifically: Weights are assigned based on the project objectives. For example: If economy is the priority, then choose cost. The smallest solution.

[0108] If operational efficiency is the priority, then select total loss. The smallest solution.

[0109] If balance is the priority, then weighted energy entropy is chosen. The largest solution.

[0110] In practical engineering, weighted comprehensive scoring is often used: ; in Choose the solution with the highest score.

[0111] S4.3.3: Considering specific scenario-related requirements, should future expansion, maintenance difficulty, geographical constraints, and technological maturity be taken into account? Details are as follows: Future scalability: Reserved ports; Maintenance difficulty: For example, offshore wind farms may want to reduce the amount of equipment on offshore platforms; Geographical constraints: such as avoiding marine protected areas; Technology maturity: such as choosing a circuit breaker type that has already been commercialized.

[0112] In step 4, the optimal topology design scheme is selected, as follows: Example 1: The method described in this invention is applied to a deep-sea power aggregation system comprising 8 distributed wind power cluster access points (nodes 1-8), 3 DRU converter stations (nodes 9-11), and 1 receiving-end MMC converter station (node ​​12). The system's rated DC voltage is ±320kV, and the total planned transmission capacity is 1200MW.

[0113] Step 1: Extract graph theory metrics. The initial randomly generated topological individual A has a mean node degree of 2.5, an average path length APL of 115km, a number of meshes MN of 3, and a weighted energy entropy Hs of 2.12.

[0114] The second step involves constructing a physical surrogate model. After training with 1000 power flow samples, the physical surrogate model achieves a loss prediction residual of less than 0.2%.

[0115] The third step: NSGA-III optimization. After 300 generations of evolution, the Pareto front was obtained. The economic cost of the candidate solution was 3.25 billion yuan, the operating loss was 2.8%, and the weighted energy entropy was 2.85.

[0116] Step 4: Transient Verification. Under the simulated scenario, the wind power surge at node 4 resulted in a peak DC voltage fluctuation of only 6.5% of the rated value.

[0117] Example 1 Node logical topology diagram as follows Figure 5 As shown. Figure 5 The mesh structure of 8 wind turbine nodes + 3 DRUs + 1 MMC in Example 1 is shown. This topology has MN=3 mesh cells, redundant paths, fault current can be diverted, and high weighted energy entropy.

[0118] Figure 6 The MN-total loss relationship diagram shows that: when When the average total loss drops below 2.5%, choosing a topology with MN≥3 is a necessary condition for high performance.

[0119] Figure 7 The MN-APL-total loss 3D plot reveals that the low-loss region (red circle) is concentrated in... and Therefore, the optimal topology ultimately selected should satisfy both of these conditions.

[0120] Comparative Example 1: The scheme employs a traditional radial topology designed based on the "shortest path" principle. In this scheme, each wind power access point is connected to the nearest DRU station via a single branch, and the DRU station is then connected to the receiving end.

[0121] Indicator Comparison: Comparative Example 1 has a mean node degree of only 1.1, a mesh count of 0, and a weighted energy entropy of... Because the energy is highly concentrated in the main line, the value is only 1.25.

[0122] Performance comparison: Under the same wind power sudden change conditions, due to the lack of damping effect of redundant paths, the peak value of DC voltage fluctuation in Comparative Example 1 reaches 4.8% of the rated value. In addition, under DC short circuit fault, the peak value of the current in the main branch is higher than that in Example 1, and under DC short circuit fault, the peak value of the current in the main branch is 42.5% higher than that in Example 1.

[0123]

[0124] Based on the data in Table 1, Embodiment 1, which applies the method described in this invention, demonstrates significant technical advantages across all key dimensions. This is particularly evident in the weighted energy entropy (…). The performance indicators demonstrate that this invention can actively guide the orderly distribution of energy flow within the system by optimizing the topology, thereby reducing the risk of equipment failure at the physical level. While Comparative Example 1 is simpler in design logic, its... The low value reflects the vulnerability of its power flow and its poor robustness under fault conditions.

[0125] If the project budget is tight: hard constraints In RMB 100 million: Comparative Example 1 has a cost of RMB 3.85 billion, which is consistent with the cost of Example 1, while Example 1 has a cost of RMB 4.52 billion, which is inconsistent with the cost of ...

[0126] For high reliability requirements: N-1 criterion and weighted energy entropy Example 1 The condition is satisfied, but Comparative Example 1 only does not satisfy 1.32, so Example 1 must be selected.

[0127] If we consider the overall weights, such as 30% for economy, 30% for efficiency, and 40% for balance, Example 1 has a clear advantage in balance and efficiency. Although the cost is slightly higher, the overall score may be higher.

Claims

1. An optimal topology design method for a diode-rectified multi-terminal DC collection power system, characterized in that... Includes the following steps: Step 1: Use graph theory indices and weighted energy entropy to represent the topological connectivity and physical state characteristics of a diode-rectified multi-terminal DC collection power system, respectively; Step 2: Based on the DC power flow calculation results, analyze the mapping relationship between the graph theory characteristics and performance indicators of the diode-rectified multi-terminal DC collection power system, and establish a physical proxy model of the diode-rectified multi-terminal DC collection power system; Step 3: Using topological connections as decision variables, and taking the economy, operating efficiency, and balance of the diode-rectified multi-terminal DC collection power system as optimization objectives, and based on the physical proxy model established in Step 2, the improved NSGA-III algorithm is used to solve the Pareto optimal solution set considering technical and economic indicators. Step 4: Perform transient simulation verification on the obtained Pareto optimal solution set, and select the optimal topology design scheme according to requirements and preferences.

2. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification as described in claim 1, characterized in that: Step 1 includes: S1.1: The topology of the diode-rectified multi-terminal DC collection power system is abstracted into an undirected graph, and the following graph theory indices are introduced to quantify the topology: node degree, average path length, clustering coefficient, betweenness centrality, and number of meshes. S1.2: Using weighted energy entropy As a representative indicator of physical state characteristics, the weighted energy entropy Calculate according to the following formula: ； in, The average load factor of the line; For the first The normalized value of the load rate of each line. The weighted energy entropy represents the total number of lines. It is used to comprehensively reflect the system load rate level and distribution balance.

3. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification as described in claim 2, characterized in that: Step 2 includes the following steps: S2.1: Sample generation, randomly generate multiple feasible network topologies and check connectivity; S2.2: Perform accurate DC power flow calculations for each network topology to obtain output data; S2.3: Perform statistical testing and visualization analysis on the output data in S2.2, and develop a fast performance estimation formula as a physical proxy model.

4. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification as described in claim 3, characterized in that: In step S2.2, the accurate DC power flow calculation includes the following sub-steps: S2.2.1: System modeling, including: The diode rectifier converter station and its AC source are equivalent to a current source dependent on DC voltage, and its volt-ampere characteristic is characterized by the following formula: （1）； In formula (1): This represents the current flowing through the i-th diode; The open-circuit voltage is represented as , The rectification coefficient of a three-phase full-bridge rectifier; This indicates the voltage output after rectification by the diode; Equivalent resistance ,in, Indicates the on-resistance of the diode. This represents the equivalent resistance of the transformer. Indicates the resistance of the AC line; Based on the characteristics of load nodes, load nodes j∈L are modeled, where L is the set of load nodes, including constant power loads, as shown in equation (2): Constant power load: (2); In formula (2): This represents the current passing through the j-th load; This represents the power of the j-th load; This represents the voltage of the j-th load; Based on the characteristics of connecting nodes, for connecting node k∈C, C is the set of connecting nodes: , This represents the current at the k-th connection node; S2.2.2: Let the injected current at node i in the DC grid be... The voltage at node i is The conductance of the line between nodes i and j is Based on Kirchhoff's Current Law (KCL), the relationship between the node voltage and the node injected current at each node is as follows: , i=1,2,...,N(3); In equation (3): the left side The current function injected into the node is determined according to the node type; the right side shows the sum of currents flowing out of the node through the connected lines, where... This is the node admittance matrix, determined by the line resistance; when there is a connection between nodes i and j... , Represents the resistance of the line at nodes i and j; This represents the voltage at the j-th node; N represents the number of nodes. Construct the equations for all DC nodes in the network, substitute the node types, and obtain the complete set of equations as shown in equation (4): （4）； In equation (4): The admittance matrix represents the connection node; Indicates the voltage at the connection node; Indicates the number of the contact node; S2.2.3: Solve the DC node equations of the entire network using the piecewise linear iterative method to obtain the results including total losses. The output data includes the average load rate M; the total loss is calculated using the following formula: （10）； In formula (10): Indicates the total number of lines; Indicates the loss of a DC line; This indicates converter losses.

5. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification according to claim 4, characterized in that: Step 3 includes the following sub-steps: S3.1: The topology optimization problem is described as a multi-objective optimization problem, i.e., min[ ; Where: x is the decision variable, designed as: whether or not to construct a line between nodes. ; Optimization Objective , , These are: economy, operational efficiency, and power flow balance; S3.2: Custom design of the encoding, evaluation, and operator modules in the improved NSGA-III algorithm; S3.3: The customized coding, evaluation, and operator modules are embedded into the NSGA-III multi-objective evolutionary algorithm framework for solving, and finally output the Pareto optimal solution set.

6. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification as described in claim 5, characterized in that: The customized design in S3.2 includes: S3.2.1: Chromosome coding design, using a length of M = N The binary string of (N-1) / 2 represents the connection status between all possible node pairs: 1 = connected, 0 = not connected; S3.2.2: Fitness assessment and constraint treatment design, performing feasibility verification and objective function calculation for each individual in the population in turn; S3.2.3: Genetic operator design, performing crossover and mutation operations on points and edges, and adding connectivity repair operations; In S3.2.2, the feasibility verification includes convergence judgment and security verification; The objective function calculation includes: Economic calculation: Total cost ;in, Indicates the cost of the line. Indicates equipment cost; Operating efficiency calculation: The sum of converter loss and DC loss is used to express the efficiency. The calculation is performed quickly based on the loss estimation formula (10) obtained in step 2. Power flow equilibrium calculation: using weighted energy entropy This means that the calculation is performed according to formula (13): （13）。 7. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification according to claim 6, characterized in that: Step 4 includes the following sub-steps: S4.1: Based on simplified transient checks, the Pareto optimal solution set is filtered; S4.2: Select representative topologies for detailed simulation to verify the safety and stability of the Pareto solution; S4.3: Select the optimal topology design scheme from the Pareto solution set, taking into account engineering requirements and preferences.

8. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification according to claim 7, characterized in that: Step 4.1 includes the following steps: S4.1.1: Check the maximum fault current, only check the most severe fault scenario, estimate the most severe fault current, and quickly check whether it exceeds the rated value of any equipment; S4.1.2: Check all transient constraints, including: check voltage sags and ensure they are within acceptable limits; Assess basic stability by: whether the system can recover after a fault, recovery time, whether voltage collapse will occur, whether the diode will be damaged by reverse voltage, and whether the capacitor discharge energy is within a safe range; S4.1.3: Remove all Pareto solutions that fail the check.

9. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification according to claim 7, characterized in that: Step 4.2 includes the following steps: S4.2.1: Model Establishment: The cable adopts a frequency-varying distributed parameter model, the diode adopts a detailed semiconductor physical model, the energy storage system adopts a detailed control model, the transformer considers saturation characteristics and leakage reactance; the control system adopts actual control logic; the protection system considers the dynamic characteristics of the circuit breaker. S4.2.2: Perform sensitivity analysis: a. Multi-fault scenario analysis: pole-to-ground faults at different locations, faults at different times, and combined faults; b. Protection system coordination: circuit breaker operating time, protection selectivity, fault isolation strategy; c. Comprehensive dynamic performance evaluation: voltage dynamic response, current surge characteristics, and system recovery process; d. Verify that the selected solution can operate safely and stably under any expected operating conditions.

10. The optimal topology design method for a multi-terminal DC collection power system based on diode rectification according to claim 7, characterized in that: Step 4.3 includes the following steps: S4.3.1: Considering the limitations of the engineering scenario, hard constraints such as budget limit, loss limit, minimum weighted energy entropy, reliability requirements, and allowable voltage range must be met; S4.3.2: Considering priority preferences, analyze the weights of economic efficiency, losses, and weighted energy entropy objectives. If a certain objective is preferred, select the objective with a higher weight. S4.3.3: Consider the specific requirements related to the scenario, such as whether to consider future expansion, maintenance difficulty, geographical constraints, and technological maturity.

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