A method and system for optimizing zoned control parameters of OLTC and photovoltaic inverters in multiple scenarios

Abstract

A method and system for optimizing OLTC and photovoltaic inverter zone control parameters in multiple scenarios includes: obtaining the reactive power sensitivity matrix and electrical distance matrix of the distribution network area to be optimized, and dividing the distribution network into optimized zones; calculating the boundary parameters of the photovoltaic inverters and OLTC within the zone based on the reactive power voltage sensitivity and OLTC tap voltage sensitivity of the photovoltaic inverters within the zone; and using a genetic algorithm to solve for the optimized threshold parameters of the OLTC and photovoltaic inverters within the zone based on the boundary parameters of the photovoltaic inverters and OLTC within the zone, combined with a pre-built parameter optimization model; wherein, the parameter optimization model is constructed with the goal of minimizing the comprehensive network loss, OLTC control cost, and voltage deviation. Dividing the inverters into zones enables unified parameter optimization calculations within the zones, reducing the complexity of model solving and solving the problem of real-time parameter optimization in areas lacking communication equipment.

Description

Technical Field

[0001] This invention relates to the field of power distribution network optimization, specifically to a method and system for optimizing the zonal control parameters of multi-scenario OLTC and photovoltaic inverters. Background Technology

[0002] With the increasing prominence of the energy crisis, solar power generation has become an important development trend, and the installed capacity of grid-connected residential photovoltaic (PV) systems has shown a rapid growth trend in recent years. Due to the randomness and volatility of residential PV systems, a high proportion of grid-connected PV systems can bring many problems to the low-voltage distribution network: PV grid connection injects a large amount of active power, increasing grid losses; PV grid connection has a voltage boosting effect, putting line node voltages at risk of exceeding limits. Therefore, simple, fast, and effective voltage control measures are needed. In rural residential PV areas, the number of grid-connected PV nodes is large and their locations are scattered. Coupled with the lack of robust communication equipment, constructing a simple and robust controller parameter optimization method is crucial.

[0003] Photovoltaic inverters can be rapidly and continuously adjusted without the need for additional equipment. Their reactive power control is fast and economical, making them suitable for voltage control applications where distributed photovoltaic power sources are connected to low-voltage distribution networks. Droop control is a classic voltage control method that uses the photovoltaic inverter to absorb reactive power, thus slowing down the rise in node voltage; conversely, it injects reactive power into the photovoltaic inverter to slow down the drop in voltage.

[0004] An on-load tap changer (OLTC) is a typical voltage regulation device that can set different voltage levels through a tap switch. Figure 1 It is a distribution substation containing three low-voltage distribution lines. Communication equipment is installed at the end of each line and at the OLTC controller. The communication equipment of each line uploads the end voltage to the OLTC controller through a remote terminal. The OLTC controller filters out the maximum and minimum voltages and selects the appropriate tap changer action strategy based on the judgment.

[0005] In rural residential photovoltaic areas, a single low-voltage busbar typically connects to multiple low-voltage lines. Some of these lines have heavy loads, while others have high penetration rates, making regulation more difficult. Therefore, the voltage control method using OLTC-PV inverters is necessary.

[0006] Both inverter reactive power control and OLTC voltage control require parameter settings. Inverter parameter settings typically necessitate individual optimization calculations for each photovoltaic (PV) node inverter. In rural areas with high PV grid integration, the low-voltage distribution network structure is complex, with numerous and dispersed PV grid-connected nodes. OLTC parameter settings require real-time collection of voltage information from each node, thus placing a high reliance on communication equipment. Due to the lack of robust communication infrastructure in rural areas, real-time optimization and setting of controller parameters is challenging when PV grid-connection scenarios change. Therefore, there is an urgent need to develop a multi-scenario applicable OLTC-PV inverter zone control parameter optimization method for rural PV grid-connection scenarios with limited communication capabilities. Summary of the Invention

[0007] To address the aforementioned problems in the existing technology, this invention provides a method for optimizing OLTC and photovoltaic inverter zone control parameters applicable to multiple scenarios, including:

[0008] Obtain the reactive power sensitivity matrix and electrical distance matrix of the distribution network area to be optimized, and then optimize the distribution network by partitioning it.

[0009] Calculate the boundary parameters of the photovoltaic inverter and OLTC within the zone based on the reactive voltage sensitivity and OLTC tap voltage sensitivity of the photovoltaic inverter within the zone.

[0010] Based on the boundary parameters of the photovoltaic inverter and OLTC within the partition, the optimized threshold parameters of the OLTC and photovoltaic inverter within the partition are obtained by using a genetic algorithm in conjunction with a pre-built parameter optimization model.

[0011] The parameter optimization model is constructed with the goal of minimizing the overall network power loss, OLTC control cost, and voltage deviation.

[0012] Preferably, the step of obtaining the reactive power sensitivity matrix and electrical distance matrix of the distribution network to be optimized and then optimizing the photovoltaic inverters in the distribution network by partitioning them includes:

[0013] Using the photovoltaic inverters within the region as nodes, the reactive power sensitivity matrix and electrical distance matrix are obtained through power flow calculation based on the node parameters of the distribution network area to be optimized.

[0014] The average reactive power sensitivity of each node in the distribution network area to be optimized to other nodes is calculated based on the reactive power sensitivity matrix.

[0015] Determine whether the average reactive power sensitivity of node i is greater than the average reactive power sensitivity of the nodes connected to it. If it is greater, then node i is taken as the cluster center. Otherwise, continue to determine whether the average reactive power sensitivity of node i+1 is greater than the average reactive power sensitivity of the nodes connected to it, until the center of all clusters in the distribution network area to be optimized is obtained; where i∈I, and I is the set of nodes.

[0016] Based on the principle of minimizing electrical distance, each node and the cluster center node with the smallest electrical distance are grouped into one class to obtain the preliminary partitioning results of clustering;

[0017] Based on the preliminary partitioning results, boundary optimization is performed on the nodes at the intersection of the two partitions to obtain the optimal partitioning result.

[0018] Preferably, the step of performing boundary optimization on the nodes at the intersection of the two partitions based on the preliminary partitioning results to obtain the optimal partitioning result includes:

[0019] The nodes at the boundary of two partitions are transferred from the current partition to the adjacent partition. After the transfer, it is determined whether the squared difference of the average reactive power sensitivity of each node in the adjacent partition decreases.

[0020] If the value is reduced, the result after partitioning is retained and the remaining boundary points are swapped; otherwise, the swap result is not retained and the remaining boundary points are swapped until all boundary points have been swapped.

[0021] Preferably, the boundary parameters of the photovoltaic inverter include:

[0022] The maximum reactive power regulation capacity of the photovoltaic inverter, the maximum reactive power regulation voltage value of the photovoltaic inverter under overvoltage risk, and the maximum reactive power regulation voltage value of the photovoltaic inverter under undervoltage risk;

[0023] The boundary parameters of the OLTC include: the voltage corresponding to the maximum upward adjustment level of the OLTC and the voltage corresponding to the maximum downward adjustment level of the OLTC.

[0024] Preferably, the threshold parameters of the photovoltaic inverter include:

[0025] The voltage threshold at which the photovoltaic inverter begins to absorb reactive power parameters and the voltage threshold at which the inverter begins to release reactive power parameters.

[0026] The OLTC threshold parameters include: the starting voltage parameters corresponding to each gear level when the OLTC is adjusted upwards and the starting voltage parameters corresponding to each gear level when the OLTC is adjusted downwards.

[0027] Preferably, the construction of the parameter optimization model includes:

[0028] The objective function is constructed by minimizing the overall network power loss, OLTC control cost, and voltage deviation.

[0029] Set power flow constraints, curve slope constraints, reactive power capacity constraints, gear operation frequency constraints, equipment parameter control sequence constraints, gear voltage control constraints, and reactive power control constraints for the objective function.

[0030] Preferably, the objective function is as follows:

[0031]

[0032] In the formula: F is the objective function value; f 1m '、f 2m 'and f 3m 'represent the objective function f for each scenario' 1m f 2m and f 3m The normalized value; f 1m Cost of network loss; f 2m The cost of OLTC gear shifting; f 3m For voltage deviation; s 1m s 2m and s 3m p represents the baseline value for each objective function. m The weight of the scene, where m is the scene number;

[0033] Among them, network loss cost f 1m As shown below:

[0034]

[0035] In the formula: C pur,t P represents the electricity purchase price of the power grid company at time t; loss,t Let Δt be the network loss at time t; Δt is the optimization time length.

[0036] OLTC gear shifting f 2m The costs are as follows:

[0037]

[0038] In the formula: C oltc The cost of one gear of OLTC operation includes operating and maintenance costs; Δk i ω represents the change in OLTC gear level during the i-th test; ω represents the total number of tests.

[0039] Voltage deviation f 3m As shown below:

[0040]

[0041] In the formula: U N Rated voltage; U represents the voltage deviation at node i;i (t) represents the voltage of node i at detection time t; n represents the total number of nodes.

[0042] Preferably, the maximum reactive power regulation capacity of the photovoltaic inverter is calculated using the following formula:

[0043]

[0044] In the formula: This is the maximum reactive power regulation capacity of the photovoltaic inverter; It is the rated grid-connected power of the photovoltaic node; S INV,i The photovoltaic inverter capacity of node i; i is the photovoltaic inverter node;

[0045] The maximum reactive power regulation voltage value of the photovoltaic inverter under the overvoltage risk is calculated by the following formula:

[0046]

[0047] In the formula: These are the parameters corresponding to the maximum reactive power regulation of the photovoltaic inverter. It is the voltage-reactive power sensitivity of node j to node i; It is the maximum voltage that occurs at node i;

[0048] Under the aforementioned undervoltage risk, the maximum reactive power regulation voltage value of the photovoltaic inverter is calculated using the following formula:

[0049]

[0050] In the formula: It is the maximum voltage that occurs at node i;

[0051] The voltage corresponding to the maximum upward adjustment setting of the OLTC is calculated using the following formula:

[0052]

[0053] In the formula: Adjust the voltage corresponding to the maximum upward adjustment level for each OLTC; k max This is the maximum upward adjustment setting for the OLTC. The sensitivity of the terminal voltage to the OLTC range; The highest historical voltage at node μ;

[0054] The voltage corresponding to the maximum downward adjustment setting of the OLTC is calculated using the following formula:

[0055]

[0056] In the formula: k min This is the maximum downward adjustment setting for OLTC.

[0057] Based on the same inventive concept, this invention provides a multi-scenario OLTC and photovoltaic inverter zone control parameter optimization system, including: a zone module, a boundary parameter calculation module, and a threshold parameter calculation module;

[0058] The partitioning module obtains the reactive power sensitivity matrix and electrical distance matrix of the low-voltage distribution network in a designated area with photovoltaic grid connection, and then performs optimization partitioning on the distribution network to be optimized.

[0059] The boundary parameter calculation module calculates the boundary parameters of the photovoltaic inverter and OLTC within the partition based on the reactive voltage sensitivity and OLTC tap voltage sensitivity of the photovoltaic inverter within the partition, respectively.

[0060] The threshold parameter calculation module, based on the boundary parameters of the photovoltaic inverter and OLTC within the partition, and combined with the pre-built parameter optimization model, uses a genetic algorithm to solve for the optimized threshold parameters of the OLTC and photovoltaic inverter within the partition.

[0061] The parameter optimization model is constructed with the goal of minimizing the overall network power loss, OLTC control cost, and voltage deviation.

[0062] Preferably, the partitioning module includes:

[0063] The module includes power flow calculation, average value calculation, cluster center selection, preliminary partitioning, and boundary optimization.

[0064] The power flow calculation submodule uses photovoltaic inverters within the region as nodes and obtains the reactive power sensitivity matrix and electrical distance matrix through power flow calculation based on the node parameters of the distribution network area to be optimized.

[0065] The average value calculation submodule calculates the average value of the reactive power sensitivity of each node in the low-voltage distribution network of the specified area to other nodes based on the reactive power sensitivity matrix.

[0066] The cluster center selection submodule determines whether the average reactive power sensitivity of node i is greater than the average reactive power sensitivity of its connected nodes. If it is greater, node i is selected as the cluster center. Otherwise, it continues to determine whether the average reactive power sensitivity of node i+1 is greater than the average reactive power sensitivity of its connected nodes, until the centers of all clusters in the region are obtained. Where i∈I, I is the set of nodes.

[0067] The preliminary partitioning submodule, based on the principle of minimum electrical distance, divides each node and the cluster center node with the minimum electrical distance into one class, thus obtaining the preliminary partitioning result of the clustering;

[0068] The boundary optimization submodule performs boundary optimization on the nodes at the intersection of the two partitions based on the preliminary partitioning results to obtain the optimal partitioning result.

[0069] The parameter optimization model is constructed to minimize the combined network power loss, OLTC control cost, and voltage deviation.

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

[0071] A method for optimizing OLTC and photovoltaic inverter zone control parameters in multiple scenarios includes: obtaining the reactive power sensitivity matrix and electrical distance matrix of the distribution network area to be optimized, and dividing the distribution network into optimized zones; calculating the boundary parameters of the photovoltaic inverters and OLTC within the zone based on the reactive power voltage sensitivity and OLTC tap voltage sensitivity of the photovoltaic inverters within the zone; and using a genetic algorithm to solve for the optimized threshold parameters of the OLTC and photovoltaic inverters within the zone based on the boundary parameters of the photovoltaic inverters and OLTC within the zone, combined with a pre-built parameter optimization model; wherein the parameter optimization model is constructed with the goal of minimizing the comprehensive network loss power, OLTC control cost, and voltage deviation. Dividing the inverters into zones enables unified parameter optimization calculation within the zones, reducing the complexity of model solving and solving the problem of real-time parameter optimization in areas lacking communication equipment. Attached Figure Description

[0072] Figure 1 This is a diagram of a tap changer control model based on remote measurement.

[0073] Figure 2 This is a flowchart illustrating the steps of the multi-scenario OLTC and photovoltaic inverter zone control parameter optimization method of the present invention;

[0074] Figure 3 This is a flowchart of the photovoltaic inverter partitioning process of the present invention;

[0075] Figure 4 This is a control curve diagram for the inverter;

[0076] Figure 5 This is a graph of the OLTC control curve. Detailed Implementation

[0077] To better understand this invention, the following description, in conjunction with the accompanying drawings and examples, will further illustrate the invention.

[0078] Example 1:

[0079] A method for optimizing the zoned control parameters of OLTC and photovoltaic inverters in multiple scenarios, such as Figure 2 As shown, it includes:

[0080] S1: Obtain the reactive power sensitivity matrix and electrical distance matrix of the low-voltage distribution network in the specified area with photovoltaic grid connection, and perform optimization partitioning on the distribution network to be optimized;

[0081] S2: Calculate the boundary parameters of the photovoltaic inverter and OLTC within the zone based on the reactive voltage sensitivity of the photovoltaic inverter and the voltage sensitivity of the OLTC tap within the zone, respectively.

[0082] S3: Based on the boundary parameters of the photovoltaic inverter and OLTC within the partition, the optimized threshold parameters of the OLTC and photovoltaic inverter within the partition are obtained by using a genetic algorithm in conjunction with the pre-built parameter optimization model.

[0083] The parameter optimization model is constructed with the goal of minimizing the overall network power loss, OLTC control cost, and voltage deviation.

[0084] Specifically, the optimization partitioning process in step S1 of this embodiment mainly considers two aspects:

[0085] 1) Factors affecting the inverter droop control coefficient

[0086] The purpose of zoning is to reduce the difficulty of model solving for inverter parameter calculations and settings, while maintaining the stability of inverter control. Therefore, it is necessary to fully integrate the principles of inverter reactive power control and group inverters with similar reactive power control effects into the same zone for unified setting and control. The most common method for inverter reactive power control is droop control. The droop control coefficient has a significant impact on the stability of inverter reactive power control; therefore, the influencing factors of the droop coefficient can be considered an important determining factor for distribution network zoning.

[0087] The expression for the droop control coefficient matrix M is as follows:

[0088]

[0089] Where: m i To control the slope of the curve, i is the inverter node number.

[0090] Stability conditions for inverter reactive power control:

[0091] ρ(MA)<1 (2)

[0092] In the formula: A is the voltage reactive power sensitivity matrix; ρ is the maximum absolute value of the matrix eigenvalues; since the input of A can also be considered as proportional to the reactance of the feeder, that is, longer lines are more likely to have higher sensitivity amplitude and lower critical slope value. Therefore, photovoltaic inverters in low-voltage distribution networks in rural household photovoltaic areas with longer lines will be more sensitive to instability, and a relatively smaller inverter control curve slope should be selected for more stable control. This invention selects the average reactive power sensitivity of all other nodes in the distribution network to the photovoltaic grid-connected node as the basis for clustering partitioning.

[0093] 2) Impact of low-voltage distribution network topology

[0094] Inverter reactive power control and voltage regulation coordinated by OLTC both operate based on the overall power flow of the distribution network. Therefore, when considering distribution network zoning, the network topology must be fully taken into account. This ensures strong coupling between nodes within a zone and weak coupling between nodes outside the zone. Electrical distance is typically used to represent the degree of coupling between two points. This invention selects the electrical distance between nodes as the second criterion for clustering and partitioning.

[0095] Therefore, in this embodiment, the inverter partitioning should first consider the reactive power sensitivity of the nodes, and determine the cluster centers based on the reactive power sensitivity. After the cluster centers are determined, the topological relationships are considered, and electrical distance is used to optimize the partitioning. Specifically, the detailed process of step S1 is as follows:

[0096] S101: Using the photovoltaic inverters in the region as nodes, the reactive power sensitivity matrix and electrical distance matrix are obtained through power flow calculation based on the node parameters of the distribution network area to be optimized.

[0097] In one implementation, input node parameters, perform power flow calculations, and obtain the reactive power sensitivity matrix S. V-Q The electrical distance between nodes is obtained from the electrical distance matrix D, as shown in the following expression:

[0098]

[0099] S102: Calculate the average reactive power sensitivity of each node in the distribution network area to be optimized relative to other nodes based on the aforementioned reactive power sensitivity matrix. The expression is as follows:

[0100]

[0101] S103: Determine whether the average reactive power sensitivity of node i is greater than the average reactive power sensitivity of the nodes connected to it. If it is greater, then node i is taken as the cluster center. Otherwise, continue to determine whether the average reactive power sensitivity of node i+1 is greater than the average reactive power sensitivity of the nodes connected to it, until the center of all clusters in the distribution network area to be optimized is obtained; where i∈I, and I is the set of nodes.

[0102] In one implementation, the number of partitions and cluster center nodes are determined. Let V i Let V be the set of nodes directly connected to node i, for any j∈V i , Then node i is the point with the largest local reactive power sensitivity. The number of nodes with the largest local reactive power sensitivity is the number of partitions, and the point with the largest local reactive power sensitivity is the cluster center.

[0103] S104: Based on the principle of minimum electrical distance, each node and the cluster center node with the minimum electrical distance are grouped into one class to obtain the preliminary partitioning results of clustering;

[0104] In this embodiment, the electrical distance between a node and each cluster center node can be calculated based on the electrical distance matrix. The distance between a node and each cluster center node is compared. Based on the principle of minimizing the electrical distance, each node and the center node with the smallest electrical distance are divided into a class, and the clustering result is obtained. Each cluster is the preliminary partitioning result.

[0105] S105: Based on the preliminary partitioning results, perform boundary optimization on the nodes at the intersection of the two partitions to obtain the optimal partitioning results.

[0106] In one implementation, after the inverter nodes are partitioned, they belong to adjacent partitions c and d respectively. These two boundary nodes are swapped, with node a assigned to partition d. The sum of squares of the average sensitivity differences ΔS between all nodes within the partition is calculated. 2 The expression is as follows:

[0107]

[0108] In the formula: CN 0,i ∩CN 0,j It is the intersection of the lines and nodes on the paths from node 0 to node i and from node 0 to node j. The elements in the i-th row of D represent the electrical distances between node i and each other. n is the number of photovoltaic nodes, m and λ are the number of photovoltaic nodes in the area (m ≠ λ), V is the node voltage, Q is the reactive power, and X is the reactance. Let be the voltage reactive power sensitivity of node j to node i, representing the effect of changes in the reactive power injected at node j on the voltage at node i. The table represents the average voltage sensitivity of each node to changes in injected reactive power at node j, ΔS. 2 Represents the corresponding nodes i and j within the partition. and The difference The sum of the squares of .

[0109] If the result decreases compared to the previous result, the result is retained; otherwise, it is returned. Node b is assigned to partition c. The squared difference in average sensitivity between nodes within the partition is calculated. If the result decreases, the result is retained; otherwise, it is returned. This process is repeated for the remaining pairs of boundary nodes until all boundary nodes are optimized, finally yielding the optimal partitioning result.

[0110] Specifically, in this embodiment, the boundary parameters of the photovoltaic inverter and OLTC within the partition calculated in step S2, and the threshold parameters of the photovoltaic inverter and OLTC within the partition calculated in step 3, are mainly determined based on the inverter-OLTC voltage control strategy, the inverter control equation, and the OLTC speed control equation. The specific determination process is as follows:

[0111] 1) Inverter-OLTC voltage control strategy

[0112] like Figure 4 This is the photovoltaic inverter-transformer OLTC control curve proposed in this invention, with the end node as the reference node. The black curve is the control curve when the photovoltaic inverter is controlled alone, Q PV The corresponding reactive power output value, when the photovoltaic inverter is controlled independently, is when the node voltage is greater than... When the voltage is low, the photovoltaic inverter begins to absorb reactive power from the grid to suppress a continuous rise in voltage; conversely, when the voltage is low... At this time, the inverter releases reactive power to suppress voltage drop. However, due to the inherent characteristics of photovoltaic inverters, when reactive power is insufficient, as the voltage continues to rise, it may exceed the maximum control voltage corresponding to the inverter's reactive power capacity. At that time, the inverter can only operate at its maximum reactive power capacity. Absorption occurs. Similarly, when the node voltage is lower than this... At that time, the inverter can only operate at its maximum reactive power capacity. When reactive power is released, the voltage regulation effect will be less than ideal. Therefore, when the voltage is at... When this happens, first adjust the OLTC setting upwards to control the inverter and bring the node voltage to its ideal control range. Similarly, when the node voltage is at... Within the specified range, first adjust the OLTC setting downwards to bring the voltage within the inverter's ideal control range, and then perform reactive power control on the inverter. The red line area in the diagram represents the voltage range within which the OLTC needs to operate first.

[0113] The control curve of OLTC gear voltage adjustment is as follows Figure 5 As shown in the piecewise function, an OLTC used for voltage regulation in low-voltage distribution networks typically has 9 levels, with a maximum upward adjustment of four levels and a maximum downward adjustment of four levels. When the voltage exceeds... When the voltage rises, the OLTC switches to the appropriate level to suppress the voltage increase. Similarly, when the node voltage drops to a certain level... At that time, the OLTC switches to the lower gear according to the corresponding voltage to suppress the voltage drop.

[0114] 2) Inverter control equations

[0115] The inverter regulates the grid voltage through reactive power control, as shown in the following control method:

[0116]

[0117] In the formula: V i,t Let Q be the voltage of segment i at time t; PV,i,t Let be the reactive power absorbed or released by the photovoltaic inverter at node i at any given time; The voltage is the maximum reactive power absorbed by the inverter when the node voltage increases; The voltage parameter corresponding to the maximum reactive power absorbed by the inverter; The voltage is the maximum reactive power released by the inverter when the node voltage drops. The voltage parameter corresponding to the maximum reactive power released by the inverter; This is the threshold parameter when the inverter starts absorbing reactive power; This is the threshold parameter corresponding to when the inverter begins to release reactive power.

[0118] 3) OLTC gear control equation

[0119] Using the end node as the reference node, different voltage ranges correspond to their respective adjustment levels. The OLTC has a total of 9 levels, four up and four down, with a voltage adjustment range of ±10%. The control equations are as follows:

[0120]

[0121]

[0122] In the formula: This refers to the maximum voltage range corresponding to the highest adjustment level of the OLTC; similarly... This refers to the minimum voltage range corresponding to the maximum downward adjustment setting of the OLTC. and These are the threshold voltage parameters for downward and upward adjustment of the inverter, respectively; and The starting voltage parameters for each gear position of the OLTC are adjusted upwards and downwards respectively: k is the gear position of the OLTC at time t.

[0123] As can be seen, the OLTC photovoltaic inverter requires the setting of multiple parameters during the voltage control process. The boundary parameters included in step S2 and the threshold parameters included in step S3 are shown in Table 1:

[0124] Control parameters of the proposed scheme in Table 1

[0125]

[0126] Specifically, the boundary parameters of the photovoltaic inverter include:

[0127] The maximum reactive power regulation capacity of the photovoltaic inverter, the maximum reactive power regulation voltage value of the photovoltaic inverter under overvoltage risk, and the maximum reactive power regulation voltage value of the photovoltaic inverter under undervoltage risk;

[0128] The boundary parameters of the OLTC include: the voltage corresponding to the maximum upward adjustment of the OLTC, and the parameter corresponding to the maximum downward adjustment of the OLTC.

[0129] The threshold parameters of the photovoltaic inverter include:

[0130] The voltage threshold at which the photovoltaic inverter begins to absorb reactive power parameters and the voltage threshold at which the inverter begins to release reactive power parameters.

[0131] The OLTC threshold parameters include: the starting voltage parameters corresponding to each gear level when the OLTC is adjusted upwards and the starting voltage parameters corresponding to each gear level when the OLTC is adjusted downwards.

[0132] In one implementation, the maximum reactive power regulation capacity of all photovoltaic inverters within each zone is: for:

[0133]

[0134] In the formula: It is the rated grid-connected power of the photovoltaic node; S INV,i is the photovoltaic inverter capacity of node i; i is the photovoltaic inverter node.

[0135] Parameters corresponding to the maximum reactive power regulation of each photovoltaic inverter That is:

[0136]

[0137] In the formula: It is the voltage-reactive power sensitivity of node i to node j; It is the maximum voltage that occurs at node i.

[0138] Similarly, under the risk of undervoltage The solution is the same as equation (13), and its corresponding voltage parameters The algorithm is as follows:

[0139]

[0140] In the formula: It is the maximum voltage that occurs at node i.

[0141] Select the last node μ As a reference node, the voltage corresponding to the maximum upward adjustment level of each OLTC is adjusted. for:

[0142]

[0143] In the formula: k max This is the maximum upward adjustment setting for the OLTC. The sensitivity of the terminal voltage to the OLTC range; This represents the highest historical voltage at node μ.

[0144] Similarly, the parameters corresponding to the maximum downward adjustment of the OLTC are... for:

[0145]

[0146] In the formula: k min This is the maximum downward adjustment setting for OLTC; This represents the highest historical voltage at node μ.

[0147] Because coordinating the design of the inverter and OLTC boundary parameters can ensure that the OLTC speed adjustment combined with the inverter can output sufficient power to achieve voltage control under extreme conditions, the different voltage regulation effects of OLTC speed changes on different nodes have not yet been considered, which may lead to voltage deviations during the regulation process. On the other hand, the inverter power output will also affect the power loss in the network. Based on the determined boundary parameters of OLTC and photovoltaic inverter, the threshold parameter of OLTC will directly affect the speed adjustment rules, thereby affecting the voltage regulation effect. The threshold parameter of photovoltaic inverter will directly affect the active and reactive power values ​​of photovoltaic grid connection, causing changes in the power in the line and ultimately affecting the network loss.

[0148] To minimize network losses and voltage deviations in the grid, it is necessary to determine the threshold parameters of the OLTC and inverters. However, in rural residential photovoltaic areas, the low-voltage distribution network environment is complex. Optimizing the threshold parameters of each inverter individually places high demands on the complexity of the solution model and the amount of computation. On the other hand, photovoltaic scenarios are highly variable and there is a possibility of photovoltaic switching. Due to the lack of robust communication equipment, it is difficult to optimize and set equipment parameters in real time as the scenario changes. Therefore, in this embodiment of the invention, step S3 uses a genetic algorithm to solve for the optimized threshold parameters of the OLTC and photovoltaic inverters within the partition based on the boundary parameters of the photovoltaic inverters and OLTC within the partition, combined with a pre-built parameter optimization model.

[0149] In one implementation, the construction of the parameter optimization model includes:

[0150] The objective function is constructed by minimizing the overall network power loss, OLTC control cost, and voltage deviation.

[0151] Set power flow constraints, curve slope constraints, reactive power capacity constraints, number of gear operation constraints, equipment parameter control sequence constraints, gear voltage control constraints, and reactive power control constraints for the objective function.

[0152] The specific parameter optimization model is as follows:

[0153] (1) Objective function

[0154] The control model of this invention considers the combined network power loss, OLTC control cost, and voltage deviation as the objective function for multiple typical operating scenarios, and the control variables are... For threshold parameters and OLTC threshold parameters and

[0155]

[0156] In the formula: F is the objective function value; f 1m '、f 2m 'and f 3m 'represent the objective function f for each scenario' 1m f 2m and f 3m The normalized value is used to eliminate the influence of different dimensions of the objective functions on the optimization results; f 1m Cost of network loss; f 2m The cost of OLTC gear shifting; f 3m For voltage deviation, s1, s2, and s3 are the reference values ​​for each objective function. Based on these references, each objective function is normalized, taking the network loss (without control), the economic cost of gear control, and the voltage deviation as the reference values. mLet m be the scene number, and ω1, ω2, and ω3 be the weights assigned to each objective function. The specific expressions for each part of the objective function are as follows:

[0157]

[0158] In the formula: C pur,t P represents the electricity purchase price of the power grid company at time t; loss,t C is the network loss at time t; oltc The cost of one gear of OLTC operation includes operating and maintenance costs; U N The rated voltage is Δt, the optimized time length is Δk. i ω represents the change in OLTC gear level during the i-th test; ω represents the total number of tests. U represents the voltage deviation at node i; i (t) represents the voltage at node i at detection time t, U N Where is the rated voltage, and n is the total number of nodes.

[0159] (2) Current constraints

[0160]

[0161]

[0162] In the formula: P i,t Q i,t G represents the active power and reactive power injected at node i, respectively; ij B ij θ ij These represent the conductance, susceptance, and voltage phase angle difference between nodes i and j, respectively; N is the total number of nodes in the system; V i,t V j,t P represents the voltage magnitudes at nodes i and j, respectively; PV,i,t Q PV,i,t For the active and reactive power of photovoltaic power generation, P load,i,t Q load,i,t The active and reactive power of the load.

[0163] (3) Curve slope constraint

[0164] To prevent instability issues during voltage regulation, the following is introduced: Figure 4 Curve slope constraint.

[0165]

[0166] In the formula: This is the sum of the reactive power sensitivity of all photovoltaic access nodes to the reactive power control node. Inverter control parameters; I nLet n be the set of partition nodes, where n is the partition number; This represents the maximum reactive power absorbed by all photovoltaic inverters within node n of partition n; similarly... ΘpV represents the maximum reactive power absorbed within the region; ΘpV represents the aggregate of grid photovoltaics.

[0167] (4) Reactive capacity constraint

[0168]

[0169] In the formula: and These represent the reactive power absorbed and released by the inverter at node i at time t, respectively.

[0170] (5) Gear shifting action count constraint

[0171]

[0172] In the formula: ω is the number of OLTC detections and adjustments per day, N l The maximum number of actions allowed per day for OLTC.

[0173] (6) Equipment parameter control sequence constraints

[0174] The OLTC-inverter voltage control method proposed in this invention addresses the issue of insufficient reactive power from the capacitor, which prevents ideal control. It first activates the OLTC for overall regulation, followed by local regulation using the inverter. To ensure smooth operation of the equipment, two constraints on threshold parameters are required to guarantee that all voltages remain within a controllable range.

[0175]

[0176] (7) Gear Voltage Control Function

[0177] The adjustment direction and level change are obtained according to the voltage of the node at different times. The level change can be used to control the voltage of the first node according to the equipment parameters of OLTC, thereby affecting the node voltage of the entire network.

[0178]

[0179] Δk=k w+1 -k w (32)

[0180] V 1,w = (1 + 0.025Δk)·V 1,w-1 (33)

[0181] In the formula: Δk is the number of gear changes, V 1,w The voltage value of the first node during the ωth detection and adjustment.

[0182] (8) Reactive power control function

[0183]

[0184] In the formula: Q PV,i,t This represents the reactive power compensation of the photovoltaic inverter. When its value is negative, the inverter absorbs reactive power. It also suppresses voltage rise; when its value is positive, the inverter releases reactive power and suppresses voltage drop.

[0185] This invention employs an improved genetic algorithm with an elite retention strategy, adaptive crossover rate, and mutation rate to solve the proposed parameter optimization model.

[0186] Example 2:

[0187] Based on the same inventive concept, this invention also provides a multi-scenario OLTC and photovoltaic inverter zone control parameter optimization system, including: a zone module, a boundary parameter calculation module and a threshold parameter calculation module;

[0188] The partitioning module obtains the reactive power sensitivity matrix and electrical distance matrix of the low-voltage distribution network in a designated area with photovoltaic grid connection, and then performs optimization partitioning on the distribution network to be optimized.

[0189] The boundary parameter calculation module calculates the boundary parameters of the photovoltaic inverter and OLTC in each zone after partitioning based on the reactive voltage sensitivity and OLTC tap voltage sensitivity of each node in each partition.

[0190] The threshold parameter calculation module, based on the boundary parameters of the photovoltaic inverters and OLTCs in each zone, and combined with the pre-built parameter optimization model, uses a genetic algorithm to solve for the optimized threshold parameters of the OLTCs and photovoltaic inverters in each zone.

[0191] The parameter optimization model is constructed with the goal of minimizing the overall network power loss, OLTC control cost, and voltage deviation.

[0192] Preferably, the partitioning module includes:

[0193] The module includes power flow calculation, average value calculation, cluster center selection, preliminary partitioning, and boundary optimization.

[0194] The power flow calculation submodule uses photovoltaic inverters within the region as nodes and obtains the reactive power sensitivity matrix and electrical distance matrix through power flow calculation based on the node parameters of the distribution network area to be optimized.

[0195] The average value calculation submodule calculates the average value of the reactive power sensitivity of each node in the low-voltage distribution network of the specified area to other nodes based on the reactive power sensitivity matrix.

[0196] The cluster center selection submodule determines whether the average reactive power sensitivity of node i is greater than the average reactive power sensitivity of the nodes connected to it. If it is greater than the average reactive power sensitivity of the nodes connected to it, then node i is taken as the cluster center, until the centers of all clusters in the region are obtained; where i∈I, and I is the set of nodes.

[0197] The preliminary partitioning submodule, based on the principle of minimum electrical distance, divides each node and the cluster center node with the minimum electrical distance into one class, thus obtaining the preliminary partitioning result of the clustering;

[0198] The boundary optimization submodule performs boundary optimization on the nodes at the intersection of the two partitions based on the preliminary partitioning results to obtain the optimal partitioning result.

[0199] Preferably, the boundary optimization submodule includes: a judgment unit and an adjustment unit;

[0200] The judgment unit divides the node at the boundary of two partitions from the current partition to the adjacent partition, and judges whether the square of the difference in average reactive sensitivity of each node in the adjacent partition decreases after the division.

[0201] If the adjustment unit is reduced, the result after division is retained and the remaining boundary points are swapped; otherwise, the swap result is not retained and the remaining boundary points are swapped until all boundary points have been swapped.

[0202] Example 3:

[0203] The idea of ​​an OLTC-PV inverter zoning control parameter optimization method applicable to multiple scenarios is as follows: (1) a zoning method based on unified optimization setting of inverter parameters is proposed; (2) a voltage control method for OLTC-PV inverter is proposed; (3) a zoning and control parameter optimization method for OLTC-PV inverter applicable to multiple scenarios is proposed.

[0204] 1) Photovoltaic inverter zoning method

[0205] Droop control is a common control principle in photovoltaic inverters. The control effect of droop control is closely related to the reactive power sensitivity of the nodes. Based on this, this invention, while ensuring the voltage control effect of the nodes, selects reactive power sensitivity and electrical distance as the zoning criteria and proposes a zoning method for photovoltaic inverters. This method systematically organizes the grid-connected nodes in rural household photovoltaic areas with complex structures and lack of distribution patterns, thereby achieving unified optimization calculation of parameters within the zone. This greatly reduces the complexity of model solution and is applicable to most rural photovoltaic grid-connected areas, demonstrating universality.

[0206] 2) Optimization method for zoned control parameters of OLTC-PV inverter applicable to multiple scenarios

[0207] Photovoltaic grid connection scenarios are diverse, with the possibility of switching on and off, requiring real-time optimization and setting of equipment parameters. However, due to the lack of communication equipment in rural low-voltage distribution networks, real-time parameter setting is difficult. This invention proposes a multi-scenario OLTC-PV inverter parameter optimization method. It combines weighted considerations of PV and load conditions at different times and seasons, distribution network losses, voltage deviations, and OLTC switch operation costs under multiple typical daily operating scenarios during PV commissioning and decommissioning to formulate a comprehensive objective function. The optimized control parameters achieve optimal overall performance across multiple scenarios, thus addressing the problem of real-time parameter optimization in rural areas due to the lack of communication equipment.

[0208] This invention proposes a method for optimizing the zonal control parameters of OLTC-photovoltaic inverters applicable to multiple scenarios. The calculation steps are as follows:

[0209] Step 1: Data processing is performed on the low-voltage distribution network in rural areas with photovoltaic grid connection, and the sensitivity matrix and electrical distance matrix are calculated.

[0210] Step 2: Divide the photovoltaic inverter into zones according to the proposed zoning method. The zoning process is as follows: Figure 3 As shown.

[0211] Step 3: Based on the reactive voltage sensitivity and OLTC tap voltage sensitivity, calculate the boundary parameters of the inverter and OLTC according to equations (13)-(17).

[0212] Step 4: Using the proposed parameter optimization model, the genetic algorithm is used to solve the problem according to the formulas (18)-(34) to calculate the threshold parameters of the photovoltaic inverter and the OLTC threshold parameters based on partitioning and considering multiple scenarios.

[0213] Step 5: Apply the parameter optimization results to the inverter and OLTC parameter settings of low-voltage distribution networks with photovoltaic grid connection.

[0214] (1) The partitioning method proposed in this invention takes into account the principle of inverter reactive power control and stability influencing factors; the inverters in the partition have unified parameter settings, which can reduce the complexity of model solution and greatly reduce the computational complexity of optimization model while ensuring control stability.

[0215] (2) The two-stage control method of OLTC and inverter proposed in this invention makes up for the shortcomings of insufficient reactive power during inverter reactive power control, which leads to relatively poor control effect. Combined with the global voltage regulation method of OLTC, the controllable voltage range is improved compared with single photovoltaic inverter control.

[0216] (3) The OLTC-inverter parameter optimization method proposed in this invention, which considers multiple scenarios, yields parameters with a certain degree of robustness. In rural residential photovoltaic areas, when photovoltaic and load conditions change in different seasons and times, or when local photovoltaic installations are cancelled, the equipment parameters should be optimized and set according to the real-time status of the scenario. However, due to the lack of communication equipment in rural areas, it is impossible to upload the operating status information of each node in real time for unified optimization calculation and parameter setting. The method proposed in this invention considers the comprehensive weights of multiple scenarios to establish an objective function, and the obtained parameter results can be used for a long time to ensure the relative stability of the control results.

[0217] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0218] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0219] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0220] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0221] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0222] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of the claims of the present invention pending approval.

Claims

1. A method for optimizing zonal control parameters of multi-scenario OLTC and photovoltaic inverters, characterized in that, include: Obtain the reactive power sensitivity matrix and electrical distance matrix of the distribution network area to be optimized, and then optimize the distribution network by partitioning it. Calculate the boundary parameters of the photovoltaic inverter and OLTC within the zone based on the reactive voltage sensitivity and OLTC tap voltage sensitivity of the photovoltaic inverter within the zone. Based on the boundary parameters of the photovoltaic inverter and OLTC within the partition, the optimized threshold parameters of the OLTC and photovoltaic inverter within the partition are obtained by using a genetic algorithm in conjunction with a pre-built parameter optimization model. The parameter optimization model is constructed with the goal of minimizing the overall network power loss, OLTC control cost, and voltage deviation. The process of obtaining the reactive power sensitivity matrix and electrical distance matrix of the distribution network to be optimized, and then optimizing the photovoltaic inverters in the distribution network by partitioning them, includes: Using the photovoltaic inverters within the region as nodes, the reactive power sensitivity matrix and electrical distance matrix are obtained through power flow calculation based on the node parameters of the distribution network area to be optimized. The average reactive power sensitivity of each node in the distribution network area to be optimized to other nodes is calculated based on the reactive power sensitivity matrix. Determine whether the average reactive power sensitivity of node i is greater than the average reactive power sensitivity of the nodes connected to it. If it is greater, then node i is taken as the cluster center. Otherwise, continue to determine whether the average reactive power sensitivity of node i+1 is greater than the average reactive power sensitivity of the nodes connected to it, until the center of all clusters in the distribution network area to be optimized is obtained; where i∈I, and I is the set of nodes. Based on the principle of minimizing electrical distance, each node and the cluster center node with the smallest electrical distance are grouped into one class to obtain the preliminary partitioning results of clustering; Based on the preliminary partitioning results, boundary optimization is performed on the nodes at the intersection of the two partitions to obtain the optimal partitioning result.

2. The parameter optimization method as described in claim 1, characterized in that, The step of optimizing the boundary of the nodes at the intersection of the two partitions based on the preliminary partitioning results to obtain the optimal partitioning results includes: The nodes at the boundary of two partitions are transferred from the current partition to the adjacent partition. After the transfer, it is determined whether the squared difference of the average reactive power sensitivity of each node in the adjacent partition decreases. If the value is reduced, the result after partitioning is retained and the remaining boundary points are swapped; otherwise, the swap result is not retained and the remaining boundary points are swapped until all boundary points have been swapped.

3. The parameter optimization method as described in claim 1, characterized in that, The boundary parameters of the photovoltaic inverter include: The maximum reactive power regulation capacity of the photovoltaic inverter, the maximum reactive power regulation voltage value of the photovoltaic inverter under overvoltage risk, and the maximum reactive power regulation voltage value of the photovoltaic inverter under undervoltage risk; The boundary parameters of the OLTC include: the voltage corresponding to the maximum upward adjustment level of the OLTC and the voltage corresponding to the maximum downward adjustment level of the OLTC.

4. The parameter optimization method as described in claim 1, characterized in that, The threshold parameters of the photovoltaic inverter include: The voltage threshold at which the photovoltaic inverter begins to absorb reactive power parameters and the voltage threshold at which the inverter begins to release reactive power parameters. The OLTC threshold parameters include: the starting voltage parameters corresponding to each gear level when the OLTC is adjusted upwards and the starting voltage parameters corresponding to each gear level when the OLTC is adjusted downwards.

5. The parameter optimization method as described in claim 1, characterized in that, The construction of the parameter optimization model includes: The objective function is constructed by minimizing the overall network power loss, OLTC control cost, and voltage deviation. Set power flow constraints, curve slope constraints, reactive power capacity constraints, gear operation frequency constraints, equipment parameter control sequence constraints, gear voltage control constraints, and reactive power control constraints for the objective function.

6. The parameter optimization method as described in claim 5, characterized in that, The objective function is shown in the following equation: In the formula: F The objective function value; , and The objective functions for each scenario are as follows. , and The normalized value; Costs related to network loss; The cost of OLTC gear shifting; For voltage deviation; , and These are the baseline values ​​for each objective function; Weight based on the scene m The scene is numbered; ω1, ω2, and ω3 are the weights of each objective function. Among them, network loss cost As shown below: In the formula: Let be the electricity purchase price of the power grid company at time t; Let t be the network loss at time t; To optimize the time length; OLTC gear control The costs are as follows: In the formula: The cost of one gear of OLTC operation, including operating and maintenance costs; For the first i Changes in OLTC gear position during the next test; Total number of tests; Voltage deviation As shown below: In the formula: Rated voltage; For nodes i Voltage deviation; Let be the voltage of node i at detection time t; n is the total number of nodes.

7. The parameter optimization method as described in claim 3, characterized in that, The maximum reactive power regulation capacity of the photovoltaic inverter is calculated using the following formula: In the formula: This is the maximum reactive power regulation capacity of the photovoltaic inverter; It is the rated grid-connected power of the photovoltaic node; It is a node i The capacity of the photovoltaic inverter; i Photovoltaic inverter node; The maximum reactive power regulation voltage value of the photovoltaic inverter under the overvoltage risk is calculated by the following formula: In the formula: These are the parameters corresponding to the maximum reactive power regulation of the photovoltaic inverter. It is a node j For nodes i Voltage-reactive power sensitivity; It is a node i The maximum voltage that occurs; Under the aforementioned undervoltage risk, the maximum reactive power regulation voltage value of the photovoltaic inverter is calculated using the following formula: In the formula: It is a node i The maximum voltage that occurs; For nodes j The maximum reactive power released by the inverter when the voltage drops; The voltage corresponding to the maximum upward adjustment setting of the OLTC is calculated using the following formula: In the formula: Adjust the voltage corresponding to the maximum upward adjustment level for each OLTC; This is the maximum upward adjustment setting for the OLTC. The sensitivity of the terminal voltage to the OLTC range; For nodes The highest voltage in history; The voltage corresponding to the maximum downward adjustment setting of the OLTC is calculated using the following formula: In the formula: This is the maximum downward adjustment setting for OLTC.

8. A multi-scenario OLTC and photovoltaic inverter zone control parameter optimization system, characterized in that, include: Partitioning module, boundary parameter calculation module, and threshold parameter calculation module; The partitioning module obtains the reactive power sensitivity matrix and electrical distance matrix of the low-voltage distribution network in a designated area with photovoltaic grid connection, and then performs optimization partitioning on the distribution network to be optimized. The boundary parameter calculation module calculates the boundary parameters of the photovoltaic inverter and OLTC within the partition based on the reactive voltage sensitivity and OLTC tap voltage sensitivity of the photovoltaic inverter within the partition, respectively. The threshold parameter calculation module, based on the boundary parameters of the photovoltaic inverter and OLTC within the partition, and combined with the pre-built parameter optimization model, uses a genetic algorithm to solve for the optimized threshold parameters of the OLTC and photovoltaic inverter within the partition. The parameter optimization model is constructed with the goal of minimizing the overall network power loss, OLTC control cost, and voltage deviation. The partitioning module includes: The module includes power flow calculation, average value calculation, cluster center selection, preliminary partitioning, and boundary optimization. The power flow calculation submodule uses photovoltaic inverters within the region as nodes and obtains the reactive power sensitivity matrix and electrical distance matrix through power flow calculation based on the node parameters of the distribution network area to be optimized. The average value calculation submodule calculates the average value of the reactive power sensitivity of each node in the low-voltage distribution network of the specified area to other nodes based on the reactive power sensitivity matrix. The cluster center selection submodule determines whether the average reactive power sensitivity of node i is greater than the average reactive power sensitivity of its connected nodes. If it is greater, node i is selected as the cluster center. Otherwise, it continues to determine whether the average reactive power sensitivity of node i+1 is greater than the average reactive power sensitivity of its connected nodes, until the centers of all clusters in the region are obtained. Where i∈I, I is the set of nodes. The preliminary partitioning submodule, based on the principle of minimum electrical distance, divides each node and the cluster center node with the minimum electrical distance into one class, thus obtaining the preliminary partitioning result of the clustering; The boundary optimization submodule performs boundary optimization on the nodes at the intersection of the two partitions based on the preliminary partitioning results to obtain the optimal partitioning result.

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