A time-varying rolling robust transmission expansion method based on Sinkhorn time-varying budget

Abstract

This invention relates to the field of power system transmission network planning and robust optimization technology, and proposes an hourly rolling robust transmission extension method with Sinkhorn time-varying budgets. This method acquires target transmission network data and hourly source-load data to construct a basic model; it constructs the current source-load state distribution and historical source-load experience distribution according to rolling time periods, calculates the Sinkhorn distance between them and maps it to source-load risk coefficients, thereby determining the time-varying deviation coefficients and uncertain budgets on the generation and load sides, forming a time-varying uncertainty set; then, through alternating iterations of the robust transmission extension master problem and sub-problems, it obtains the worst-case source-load deviation scenario and candidate line construction schemes, and inherits existing lines to subsequent time periods. This method can adaptively adjust robust conservatism, avoid redundant investment, and improve planning economy, time continuity, and resistance to uncertainty.

Description

Technical Field

[0001] This invention relates to the field of power system transmission network planning and robust optimization technology, and in particular to a time-by-time rolling robust transmission extension method that uses Sinkhorn distance to characterize source-load state offset and generates time-varying deviation coefficients and time-varying uncertain budgets accordingly. Background Technology

[0002] Transmission network expansion planning is used to determine whether to build or expand candidate transmission lines within a given planning period to meet the needs of load growth, renewable energy integration, and system safety. With the increasing proportion of renewable energy sources such as wind and solar power, the volatility of power generation has increased, and load demand has become more pronounced in terms of time periods, regions, and randomness. Traditional transmission network expansion planning methods that rely on deterministic source-load forecasts are insufficient to adequately address the risks of line congestion, power curtailment, or load shedding caused by extreme source-load deviations.

[0003] Existing robust transmission network planning methods mostly describe source-load uncertainty by using fixed uncertain budgets, extreme scenario sets, typical scenario sets, or preset wind and solar power output and load samples. Although this can improve the safety of the planning scheme, it is difficult to adaptively adjust the robust conservatism according to the degree of deviation of the current source-load state from the historical experience distribution. At the same time, although some multi-stage or extended planning methods consider time-series planning, they do not integrate the time-varying budget generation mechanism based on distribution distance and the hourly rolling line state inheritance mechanism into the solution process of the robust transmission network extended master problem-subproblem.

[0004] Furthermore, power transmission network planning exhibits a clear temporal sequence. Once a candidate line is completed in a certain period, it should generally continue to be put into operation in subsequent periods, and its investment costs should not be repeatedly included. Static programming methods often only focus on a single target year or a few discrete scenarios, making it difficult to express the impact of hourly changes in source and load states and historical construction results on subsequent decisions. While simple sequential static programming can solve problems in different time periods, it lacks a unified rolling inheritance mechanism, making it prone to local optima or duplicate investment.

[0005] In this invention, the Sinkhorn distance refers to the optimal transmission distance formed by introducing an entropy regularization term on top of the Wasserstein distance. It is characterized by differentiability, high computational efficiency, and suitability for characterizing differences in empirical distributions. If the Sinkhorn distance between the current source load state distribution and the historical source load empirical distribution is used to measure the degree of source load offset, the uncertain budget can be transformed from a fixed, manually defined parameter into a dynamically changing risk response parameter, thereby improving robustness during high-risk periods and reducing conservatism during low-risk periods.

[0006] Therefore, there is an urgent need for a transmission expansion method that addresses the dynamic changes in source load uncertainty. This method should be able to adaptively generate uncertain budgets for different time periods based on the deviation between the current source load distribution and historical experience distribution. These budgets should be embedded into the iterative solution process of the main problem and sub-problems in robust transmission expansion planning. Furthermore, by combining the line state inheritance mechanism in hourly rolling planning, the method can avoid repeated investment in existing candidate lines in subsequent time periods. This would improve the uncertainty resistance of the planning scheme while reducing the redundant construction costs caused by overly conservative planning. Summary of the Invention

[0007] The purpose of this invention is to provide a robust transmission extension method for hourly rolling based on Sinkhorn time-varying budgets, which addresses the problems in existing robust transmission extension planning where uncertain budgets rely on manual fixed settings, are difficult to reflect hourly source-load state shifts, and the difficulty in effectively inheriting candidate line construction results in subsequent rolling periods. To achieve the above objective, the method includes the following steps:

[0008] S1: Obtain node data, existing line data, candidate line data, generation node data, load node data, and hourly source-load data of the target transmission network, construct the basic model of the transmission network, and set candidate line construction variables, line commissioning status variables, and the maximum investment budget for the planning period;

[0009] S2: Establish an hourly rolling planning process according to the order of rolling periods. In each current rolling period, construct the current source load state vector using the nominal value of power generation capacity and the nominal value of load demand. Construct a historical source load sample set based on historical adjacent periods, the same hourly historical period, or typical daily historical period. Construct the current source load state distribution and the historical source load empirical distribution through the current source load state vector and the historical source load sample set.

[0010] S3: Calculate the Sinckhorn distance between the current source load state distribution and the historical source load experience distribution, map the Sinckhorn distance to a source load risk coefficient to characterize the degree of deviation of the current source load state, and determine the time-varying deviation coefficient and time-varying uncertain budget for the current rolling period based on the source load risk coefficient. The time-varying deviation coefficient includes the power generation output down-bias coefficient and the load demand up-bias coefficient, and the time-varying uncertain budget includes the power generation uncertain budget and the load uncertain budget.

[0011] S4: Construct a time-varying uncertainty set based on the time-varying deviation coefficient and the time-varying uncertain budget, and input this time-varying uncertainty set into the robust transmission expansion model. Determine the candidate line construction schemes and line commissioning status for the current rolling period through the robust transmission expansion master problem. Search for the worst source-load deviation scenario that makes the system operating cost most unfavorable within the time-varying uncertainty set through the robust transmission expansion sub-problems. Feed the worst source-load deviation scenario back to the robust transmission expansion master problem for iterative solving of the master problem and sub-problems to obtain the candidate line construction schemes for the current rolling period. At the same time, inherit the candidate lines already constructed in the current rolling period to subsequent rolling periods so that they remain in operation in subsequent periods and are not repeatedly included in the investment cost, until the transmission expansion planning for all rolling periods is completed, and the final robust transmission expansion scheme is obtained.

[0012] This invention is a time-by-time rolling robust transmission network extension method based on Sinkhorn time-varying budgets. The basic transmission network model includes a static network decision layer and system operation constraints under uncertain conditions. Let the rolling time period set be... , The set of existing routes is represented by the set of candidate routes. All routes are collected as follows Candidate routes During the rolling period The construction cost is During the rolling period The construction variables are The operational status is Rolling period The worst-case running cost obtained from the subproblem is Then, the cumulative target of the transmission expansion plan after completing all rolling periods can be expressed as:

[0013] The network decision-making model satisfies the following constraints: planning period investment budget constraint, existing line commissioning constraint, candidate line state inheritance constraint, unique construction constraint, and binary construction constraint.

[0014] in, The maximum investment budget allowed during the planning period. For rolling time period index, Indicates candidate routes During the rolling period Construction, Indicates candidate routes During the rolling period Construction, This indicates no construction. The investment budget constraint ensures that the total expansion investment over the entire time span does not exceed the available budget. This constraint determines whether the model can alleviate congestion and load shedding through line construction. The line construction status constraint includes two parts: existing line commissioning constraints and candidate line status inheritance constraints. These stipulate that at the beginning of the time span, the status of all existing transmission lines should be 1, and the status should remain 1 after the line is completed. The unique construction constraint stipulates that each candidate line can be constructed at most once during the entire planning period to avoid duplicate investment in the same line. The binary constraint ensures the duality of investment decisions and stipulates that line construction decisions can only be selected from the two states of construction and no construction.

[0015] Furthermore, in step S2, for any current scrolling period... During that period Power generation nodes The nominal value of the power generation capacity and the first load nodes The load demand baseline nominal value is normalized to obtain the normalized generation capacity result. and normalized load demand results : ,

[0016] in, , Let them represent the set of generating nodes and the set of load nodes, respectively. , These are used to represent the current scrolling period. The normalized benchmark for nominal generation capacity and nominal load demand. To avoid constants with a denominator of zero, and These are the baseline nominal values ​​for power generation capacity and load demand for the current rolling period, respectively. and These represent the coefficients that represent the changes in nominal generation capacity and load demand over time during the current rolling period. and These represent the nominal values ​​of generation capacity and load demand, respectively, after considering the time-varying nominal values. Through the above normalization process, the generation capacity and load demand are placed on a unified dimensional scale, avoiding the unbalanced impact of nodes of different capacity levels on the Sinkhorn distance calculation. The normalized generation capacity and normalized load demand are concatenated according to node order to form the current source-load state vector for the current rolling period. :

[0017] in, The number of power generation nodes. The number of load nodes is determined, and then adjacent historical periods before the current rolling period, historical periods of the same hour, or historical periods of a typical day are selected as sample sources to obtain the historical source load sample set. :

[0018] Based on the current source load state vector Construct the current source load state distribution Based on historical source load sample sets Constructing historical source load empirical distribution :

[0019] in, For the first A historical source sample, The number of historical source load samples. Represents the current source load state vector Dirac measure at the location, Indicates samples located in the historical source load state Dirac measure at the location.

[0020] Furthermore, in step S3, the current source load state distribution is first defined. Historical source load experience distribution The distance between Wasserstein :

[0021] in, The support set for the source load state vector. For and A set of transportation plans distributed at the periphery; For transportation planning, it is used to represent the probabilistic quality matching relationship between the current source load state distribution and the historical source load experience distribution; Let be the distance cost function between source and load state samples. An entropy regularization term is introduced based on the Wasserstein distance to obtain the optimal transmission distance for the current rolling period. This entropy-regularized optimal transmission distance is then used as the Sinkhorn distance in this invention to characterize the degree of deviation between the current source and load state distribution and the historical source and load empirical distribution. :

[0022] in, Here is the entropy regularization parameter. and They are respectively with and The corresponding reference measure, The product measure of the two. For transportation planning Regarding product measure Relative entropy:

[0023] In the form of discrete historical samples, the Sinkhorn distance can be written as:

[0024] in, For elements in discrete transportation planning, The distance cost between source and load state samples. and These represent the current source load state distribution and the historical source load empirical distribution in discrete sample form, respectively. and The reference measure corresponding to the current source load state distribution is given at the sample points. and The weights; when selecting , At this time, the entropy regularization term is used to suppress excessive sparsity in the transportation plan, allowing the Sinkhorn distance to more smoothly characterize the deviation between the current source load distribution and the historical source load experience distribution. Normalizing the Sinkhorn distance yields the source load risk coefficient for the current rolling period. :

[0025] in, and These are the lower and upper limits of the historical Sinkhorn distance, respectively. To prevent constants with a denominator of zero, the source load risk coefficient is mentioned. The larger the value, the greater the deviation of the current source load state distribution from the historical source load empirical distribution.

[0026] Furthermore, in step S3, the following parameters are determined based on the source-load risk coefficient: the power generation output down-bias coefficient, the load demand up-bias coefficient, the power generation uncertain budget, and the load uncertain budget for the current rolling period:

[0027] Among them, the power output down-biasing coefficient on the power generation side and load-side demand skew coefficient Used to determine the magnitude of source-load deviation, generation-side uncertain budget and load-side uncertain budget Used to limit the number of generating nodes and load nodes that reach the most unfavorable boundary within the same rolling time period. and These are the lower and upper limits of the power output deflection coefficient on the generation side, respectively. and These represent the lower and upper limits of the load-side demand skewness coefficient, respectively. The function is an up-rounding function that ensures the uncertain budgets on the generation side and the load side are integer budgets. and These represent the lower and upper limits of the uncertain budget on the power generation side, respectively. and These represent the lower and upper limits of the uncertain budget on the load side, respectively.

[0028] Furthermore, the maximum deviation between power generation capacity and load demand is generated by the power generation-side output down-biasing coefficient and the load-side demand up-biasing coefficient: ,

[0029] in, For the maximum deviation of power generation capacity, For the maximum deviation of load demand, and These are coefficients representing the maximum deviation between generation capacity and load demand during the current rolling period, respectively, as a function of time. Based on the generation output down-biasing coefficient during the current rolling period. and load-side demand skew coefficient Determine the worst-case deviation form of the power generation capacity. The worst-case deviation from load demand :

[0030] in, and These are binary uncertainties on the generation and load sides, respectively. Based on the generation-side uncertain budget for the current rolling period. and load-side uncertain budget Set budget constraints: ,

[0031] Among them, when At that time, the unit capacity deviates downward to the most unfavorable level; when At that time, load demand deviates upward to the most unfavorable level.

[0032] Further, in step S4, given the candidate line construction scheme and line commissioning status, the worst-case operating cost under the current network structure is taken as the sub-problem objective. The worst-case source-load deviation scenario is then determined under the conditions of satisfying node power balance constraints, DC power flow constraints, reference node phase angle constraints, node phase angle upper and lower limits constraints, line capacity constraints, upper limit constraints of power generation output, load demand constraints, and upper limit constraints of load shedding. The worst-case operating cost obtained from the sub-problem is defined as follows:

[0033] in, For the time-varying uncertain set of the current rolling period, For the unit During the rolling period Power generation output, For load During the rolling period The shear load, For the unit During the rolling period The cost of electricity generation, For load During the rolling period The cost of load shedding penalty For the line During the rolling period The trend For the load during the rolling period The demand, For nodes During the rolling period The voltage phase angle.

[0034] The inner-layer operation problem satisfies the following constraints: node power balance, DC power flow, reference node phase angle, node phase angle upper and lower limits, line capacity, generator output upper limit, load demand, and load shedding upper limit. Specifically, these include: ,

[0035] in, For a set of nodes, For access nodes A collection of generator units, For access nodes The load set, These are the dual variables corresponding to the balance constraint; For the line During the period susceptivity, and The lines are respectively The starting node and the ending node, This is the dual variable corresponding to the power flow constraint; Indicates the reference node, Let be the dual variable corresponding to this equation; For the line Maximum transmission capacity This is the dual variable corresponding to the constraint; Indicates the line Permissible lower bound for reverse current flow This is the dual variable corresponding to the constraint; The upper limit of the node phase angle. This represents the set of nodes excluding the reference node. This is the dual variable corresponding to the constraint; This is the lower limit of the node phase angle. This is the dual variable corresponding to the constraint; Let be the dual variable corresponding to this equation; This is the dual variable corresponding to the constraint; For load During the rolling period Maximum shearable load ratio For uncertain load demand, Let be the dual variable corresponding to this constraint.

[0036] The node power balance constraint ensures power balance at each node, where the sum of generation, inflow power, and load shedding at each node should equal the sum of node load and outflow power. The DC power flow constraint displays the power flow of each line. It is important to note that the power flow depends on the actual state of the line. When a line is in operation, the power flow is determined by the susceptance and the phase angle difference between the two ends. If a line is not physically connected to the grid, its power flow is zero. The above DC power flow relationship is equivalently processed using the Big-M linearization form described later. The reference phase angle constraint fixes the voltage angle of the reference bus to zero to eliminate the degree of freedom caused by the overall phase angle translation in the DC power flow model. The upper and lower limits of line power flow constraints set the upper and lower limits of line power flow, stipulating that the forward power flow of a line must not exceed its upper capacity limit and the reverse power flow of a line must not exceed its capacity boundary. The upper and lower limits of phase angle constraints restrict the voltage angle of each bus, where the phase angle of non-reference nodes must not exceed the given upper limit and must not be lower than the given lower limit to ensure that the DC power flow model is within a reasonable operating range. The non-negativity constraint ensures that both generation and load shedding are non-negative values. Finally, load demand constraints match the demand level with uncertain demand variables, generation capacity upper limit constraints limit generation to within uncertain available generation capacity, and load shedding upper limit constraints limit the amount of load shedding to within the allowable proportion of uncertain load demand.

[0037] To improve the solution efficiency of the robust transmission extended subproblem, given the candidate line construction schemes and line commissioning status, the inner-layer operation minimization problem is replaced with its dual problem, thus transforming the minimax subproblem into a single-layer maximization problem. The objective function of the dual subproblem can be expressed as:

[0038] in, , , , , , and These are all dual variables corresponding to the operational constraints. Through this dual subproblem, the source-load uncertainty parameter that maximizes the operating cost under the current line operation state is searched, and this parameter is taken as the worst-case source-load deviation scenario for the current rolling period.

[0039] The dual subproblem satisfies the dual feasibility constraints corresponding to the original operational problem, including dual constraints corresponding to power generation output variables, dual constraints corresponding to load demand variables, dual constraints corresponding to load shedding variables, dual balance constraints corresponding to line power flow variables, dual balance constraints corresponding to non-reference node phase angle variables, dual balance constraints corresponding to reference node phase angle variables, and corresponding dual variable sign constraints, specifically including: , , ,

[0040] in, For the unit The power balance dual variable of the node, For load The power balance dual variable of the node, , The lines are respectively The starting and ending nodes. The above dual constraints are used to ensure that the dual subproblem and the original inner running problem satisfy a strong duality relationship.

[0041] Furthermore, since the objective function of the dual subproblem contains a product term of uncertain parameters and dual variables, and the uncertain parameters include binary uncertain variables... and Therefore, substituting the time-varying uncertainty set into the dual objective function will produce bilinear terms of binary and continuous dual variables. To transform the subproblem into mixed-integer linear programming, auxiliary variables are introduced and linearization is performed using the Big-M method. Specifically, the part of the subproblem's objective function containing uncertain parameters can be expanded as follows:

[0042] For the product of a binary variable and its continuous dual variable, an auxiliary variable is introduced, and the following Big-M linearization constraint is applied:

[0043] in, To ensure sufficient positive numbers for linearization efficiency, we use 10 in this example. 6 , , and The linearization auxiliary variables are used to represent... , and When the corresponding binary uncertain variable is 0, the corresponding auxiliary variable is 0; when the corresponding binary uncertain variable is 1, the corresponding auxiliary variable is equal to the corresponding continuous dual variable. The Big-M method is also used to linearize the bilinear term of DC power flow generated by the line's operational status and phase angle difference.

[0044] Furthermore, for any current rolling period Based on the worst-case source load deviation scenario obtained from the sub-problems, construct the main problem cut constraints for the current rolling period, and in the current rolling period... The generated worst-case source load deviation scenario set Next, reselect candidate route construction schemes for the current rolling period to minimize the sum of the upper bounds of investment and operating costs for the current rolling period:

[0045] in, Rolling period in the main problem The upper limit of operating costs This represents the current iteration number. For the current rolling period The generated set of worst-case source load deviation scenarios For the scene index in the scene set, and Scenes The power generation output and load shedding.

[0046] For each worst-case source load deviation scenario identified by the subproblem, the main problem replicates a set of operating variables corresponding to that worst-case source load deviation scenario, and ensures that the operating variables satisfy the aforementioned nodal power balance constraints, DC power flow constraints, reference node phase angle constraints, line capacity constraints, node phase angle upper and lower limits constraints, generation output upper limit constraints, load demand constraints, and load shedding upper limit constraints:

[0047] The column constraint generation method is executed within each current scrolling period, including: for any current scrolling period Initialize the current scrolling period worst source load deviation scenario set Upper Realm Lower Boundary Number of iterations and preset convergence threshold Solve the robust transmission extension master problem for the current rolling period to obtain candidate line construction variables, line commissioning state variables, and upper bound variables for operating costs. Update the lower bound for the current rolling period according to the objective function of the master problem. Substitute the line commissioning state variables into the robust transmission extension subproblem for the current rolling period to obtain a new worst-case source-load deviation scenario. Update the upper bound for the current rolling period according to the sum of the investment cost and the operating cost of the subproblem for the current rolling period. Determine whether the upper and lower bounds satisfy the preset convergence conditions.

[0048] in, This is the upper bound of the current rolling period. This is the lower bound of the current rolling period. To preset the convergence threshold, To avoid constants with a denominator of zero, if the preset convergence condition is not met, the new worst-case source load deviation scenario is added to the worst-case source load deviation scenario set for the current rolling period. The running constraints and scene cuts corresponding to the scenario are added to the main problem of the current rolling period, and the main problem-sub-problem alternating iteration continues; if the preset convergence condition is met, the candidate line construction scheme of the current rolling period is output.

[0049] Furthermore, in step S4, for those satisfying Candidate routes This indicates that the candidate route is in the current rolling period. If constructed, then for any subsequent rolling period ,set up: ,in, This applies to any subsequent rolling period. The above settings ensure that existing candidate transmission lines remain operational during subsequent rolling periods and avoid double-counting investment costs for those periods.

[0050] The rolling time period sequence is repeatedly executed, including hourly rolling planning, construction of current source-load state vectors, Sinkhorn distance calculation, generation of source-load risk coefficients, generation of time-varying deviation coefficients and time-varying uncertain budgets, search for worst-case source-load deviation scenarios, iterative solution of main problem and sub-problems, and hourly inheritance of existing candidate lines. Finally, the newly added candidate lines for each rolling time period, the first construction period of each candidate line, the cumulative commissioned grid, and the final robust transmission expansion scheme are obtained.

[0051] Compared with the prior art, the present invention has at least the following beneficial effects:

[0052] This invention utilizes Sinkhorn distance to measure the degree of deviation between the current source load state distribution and the historical source load experience distribution, and maps this degree of deviation to a source load risk coefficient. This reduces the dependence of time-varying uncertain budgets on fixed human experience settings. Furthermore, based on the source load risk coefficient, it generates a generator output down-bias coefficient, a load demand up-bias coefficient, a generator uncertain budget, and a load uncertain budget, enabling the robust transmission expansion model to adaptively adjust its conservatism according to the source load risk level at different times. At the same time, by incorporating the downward deviation of generation capacity, the upward deviation of load demand, and budget constraints into the time-varying uncertainty set, it can more accurately characterize the worst-case source load deviation scenario in transmission expansion planning.

[0053] This invention improves the solution efficiency of the robust transmission extension model by performing dual transformation on the robust operation subproblem and Big-M linearization on the bilinear terms generated by binary uncertain variables and continuous dual variables. This transforms the worst-case source load deviation scenario search problem into a mixed-integer linear programming problem. Furthermore, it employs a column constraint generation method to iteratively solve the robust transmission extension main problem and subproblems. In the main problem, candidate line construction schemes are determined, while in the subproblems, the worst-case source load deviation scenario is searched. The constraints corresponding to the new worst-case source load deviation scenario are iteratively added to the main problem, thereby improving the solution efficiency of the robust transmission extension model.

[0054] The present invention sets up a time-by-time inheritance mechanism for existing candidate lines, so that existing candidate lines can continue to be put into operation in subsequent rolling periods without being repeatedly included in investment costs, which can better conform to the temporal continuity of transmission line construction decisions and engineering realities. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the overall process of a time-by-time rolling robust transmission extension method based on Sinkhorn time-varying budgets according to the present invention.

[0056] Figure 2 This is a schematic diagram illustrating the construction of the source load state vector, historical source load sample set, and empirical distribution in an embodiment of the present invention.

[0057] Figure 3This is a schematic diagram illustrating the mapping of Sinkhorn distance to source load risk coefficients and the generation of time-varying uncertain budgets in an embodiment of the present invention.

[0058] Figure 4 This is a flowchart illustrating the alternating iteration of the robust transmission extension master problem and subproblems in an embodiment of the present invention.

[0059] Figure 5 This is a schematic diagram of the hourly inheritance of candidate lines and the final power transmission expansion planning results in an embodiment of the present invention.

[0060] Figure 6 This is a topology diagram of the Garver-6 node system according to an embodiment of the present invention. Detailed Implementation

[0061] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0062] This embodiment provides a time-by-time rolling robust transmission expansion method based on a Sinkhorn time-varying budget. For example... Figure 1 As shown, the method includes basic data acquisition, establishment of a time-by-time rolling planning process, construction of the current source load state vector and historical source load sample set, Sinckhorn distance calculation, generation of source load risk coefficient, generation of time-varying deviation coefficient and time-varying uncertain budget, alternating iterative solution of the robust transmission extension master problem and subproblems, time-by-time inheritance of existing candidate lines, and output of the final robust transmission extension scheme.

[0063] In this example, the target transmission network includes a set of nodes. , This indicates that the existing route set and the candidate route set are... All routes are collected as follows For any line ,use and They represent the lines respectively. The starting and ending nodes, using Indicates the line susceptance. For candidate lines, the maximum transmission capacity of the line is... ,use Indicates the rolling period Construction costs.

[0064] correspond Figure 1 Step 1 involves acquiring node data, existing line data, candidate line data, generation node data, load node data, and hourly source-load data for the target transmission network. This data forms the basic model of the transmission network, and variables related to candidate line construction, line commissioning status, and the maximum investment budget for the planning period are defined. Let the rolling time period set be... During the rolling period The construction variables are The operational status is , The rolling period is the maximum investment budget allowed during the planning period. The worst-case running cost obtained from the subproblem is The decision-making objectives for the grid structure during the rolling period are:

[0065] The above network structure decision satisfies the constraints of total investment budget during the planning period, existing line commissioning, candidate line status inheritance, unique construction, and binary construction:

[0066] Among them, the investment budget constraint is used to limit the total construction cost of candidate lines during the planning period, that is, to satisfy: historical cumulative investment + current rolling period new investment ≤ planning period maximum investment budget; the existing line commissioning constraint means that the existing transmission lines are in operation in each rolling period; the candidate line status inheritance constraint means that once a candidate line is constructed, it remains in operation in subsequent rolling periods; the unique construction constraint is used to avoid the same candidate line being constructed repeatedly in different rolling periods.

[0067] correspond Figure 1 Step 2 in this example uses K-means clustering to select typical days for the target transmission network from hourly source-load data, and establishes an hourly rolling planning process according to the typical day and hourly order. The hourly rolling planning process uses each typical day and hour as a current rolling period. After solving the robust transmission extension model for the current rolling period, the line construction results are transferred to subsequent rolling periods. In other embodiments, the hourly rolling planning process can also be established according to the natural day-hourly order, the annual hourly period order, or a preset representative period order.

[0068] correspond Figure 1 Step 3 and Figure 2 The current information processing procedure shown applies to any current scrolling period. Read the first number of the time period Power generation nodes The nominal value of the power generation capacity and the first load nodes The nominal load demand baseline value is obtained and normalized to obtain the normalized generation capacity result. and normalized load demand results : ,

[0069] in, , Let them represent the set of generating nodes and the set of load nodes, respectively. , These are used to represent the current scrolling period. The normalized benchmark for nominal generation capacity and nominal load demand. To avoid constants with a denominator of zero, and These are the baseline nominal values ​​for power generation capacity and load demand for the current rolling period, respectively. and These represent the coefficients that represent the changes in nominal generation capacity and load demand over time during the current rolling period. and These represent the nominal generation capacity and nominal load demand, respectively, after considering the time-varying nominal values. The normalized generation capacity and normalized load demand are concatenated according to node order to obtain the current source-load state vector for the current rolling period. :

[0070] in, The number of power generation nodes. The number of load nodes, then corresponding to Figure 2 The historical information processing procedure shown selects at least one of the following as sample sources: adjacent historical periods before the current rolling period, historical periods within the same hour, or historical periods of a typical day, to construct a historical source load sample set. :

[0071] in, For the first A historical source sample, The number of historical source load samples is determined based on the current source load state vector. Construct the current source load state distribution Based on historical source load sample sets Constructing historical source load empirical distribution :

[0072] in, Represents the current source load state vector Dirac measure at the location, Indicates samples located in the historical source load state The Dirac measure at that point. Therefore... Figure 2 The current source load state vector, historical source load sample set, current source load state distribution, and historical source load empirical distribution are all determined.

[0073] correspond Figure 1 Step 4 and Figure 3 The Sinkhorn distance calculation process shown is based on the current source load state distribution. Historical source load experience distribution The Sinkhorn distance between them is mapped to a source load risk coefficient that characterizes the degree of current source load state shift. First, the Wasserstein distance between them is defined. :

[0074] in, The support set for the source load state vector. For and For a set of transportation plans distributed at the periphery, For transportation planning, Let be the distance cost function between source and load state samples.

[0075] An entropy regularization term is introduced based on the Wasserstein distance to obtain the optimal transmission distance for the current rolling period. This entropy-regularized optimal transmission distance is then used as the Sinkhorn distance in this invention to characterize the degree of deviation between the current source load state distribution and the historical source load empirical distribution. :

[0076] in, Here is the entropy regularization parameter. and They are respectively with and The corresponding reference measure, The product measure of the two. For transportation planning Regarding product measure Relative entropy:

[0077] In the form of discrete historical samples, the Sinkhorn distance can be written as:

[0078] in, For elements in discrete transportation planning, The distance cost between source and load state samples. and These represent the current source load state distribution and the historical source load empirical distribution in discrete sample form, respectively. and The reference measure corresponding to the current source load state distribution is given at the sample points. and The weights; when selecting , At that time, the entropy regularization term is used to suppress excessive sparsity in the transportation plan, so that the Sinkhorn distance can more smoothly characterize the degree of deviation between the current source load state distribution and the historical source load experience distribution.

[0079] correspond Figure 1 Step 5 and Figure 3 The distance normalization process in the middle normalizes the Sinkhorn distance to obtain the source load risk coefficient for the current rolling period. :

[0080] in, and These are the lower and upper limits of the historical Sinkhorn distance, respectively. To prevent constants with a denominator of zero, the source load risk coefficient is mentioned. The larger the value, the greater the deviation of the current source load state distribution from the historical source load empirical distribution. Corresponding to... Figure 3 middle" The meaning of "the larger the load, the larger the budget" is that the source load risk coefficient is used to adjust the conservatism of the robust model for the current rolling period.

[0081] correspond Figure 1 Step 6 and Figure 3 The generation and load side time-varying budget generation process is based on the source-load risk coefficient. Determine the following for the current rolling period: Downward bias of generation output, upward bias of load demand, uncertain budget for generation, and uncertain budget for load.

[0082] Among them, the power output down-biasing coefficient on the power generation side and load-side demand skew coefficient Used to determine the magnitude of source-load deviation, generation-side uncertain budget and load-side uncertain budget Used to limit the number of generating nodes and load nodes that reach the most unfavorable boundary within the same rolling time period. and These are the lower and upper limits of the power output deflection coefficient on the generation side, respectively. and These represent the lower and upper limits of the load-side demand skewness coefficient, respectively. The function is rounded up to ensure that the uncertain budgets on the generation side and the load side are integer budgets. These four quantities together constitute the time-varying deviation coefficient and the time-varying uncertain budget for the current rolling period.

[0083] The maximum deviation between power generation capacity and load demand is generated by the power generation side output down-biasing coefficient and the load side demand up-biasing coefficient: ,

[0084] in, For the maximum deviation of power generation capacity, For the maximum deviation of load demand, and These are coefficients representing the maximum deviation between generation capacity and load demand during the current rolling period, respectively, as a function of time. Based on the generation output down-biasing coefficient during the current rolling period. and load-side demand skew coefficient Determine the worst-case deviation form of the power generation capacity. The worst-case deviation from load demand :

[0085] in, and These are binary uncertainties on the generation and load sides, respectively, based on the generation-side uncertain budget for the current rolling period. and load-side uncertain budget Set budget constraints: ,

[0086] Among them, when At that time, the unit capacity deviates downward to the most unfavorable level; when At that time, load demand deviates upward to the most unfavorable level. Therefore, Figure 3 The “output time-varying uncertain budget” is specifically implemented as the time-varying uncertain set of the current rolling period. .

[0087] correspond Figure 1 Steps 7 and 8 in the process, and Figure 4 The illustrated main problem-subproblem alternating solution process addresses the time-varying uncertainty set of the current rolling time period. The robust transmission extended model, with line commissioning status inherited from the preceding rolling period as input, is solved using a column constraint generation method. Given candidate line construction schemes and line commissioning statuses, the worst-case operating cost under the current network structure is taken as the sub-problem objective.

[0088] in, For the time-varying uncertain set of the current rolling period, For the unit During the rolling period Power generation output, For load During the rolling period The shear load, For the line During the period The trend For load During the rolling period The demand, For nodes During the rolling period voltage phase angle, For the unit During the rolling period The cost of electricity generation, For load During the rolling period The cost of load shedding penalty.

[0089] The inner-layer operation problem satisfies the following constraints: node power balance, DC power flow, reference node phase angle, line capacity, node phase angle upper and lower limits, generator output upper limit, load demand, and load shedding upper limit. Specifically, for any node... The node power balance constraint is:

[0090] in, For access nodes A collection of generator units, For access nodes The load set, For the dual variable corresponding to this balance constraint, and The lines are respectively The starting node and the ending node.

[0091] For any line The DC power flow relationship and line capacity constraints are represented in a linearized form:

[0092] in, It is a sufficiently large positive number. When At that time, the line is in operation, and the DC power flow equation is restored; when At that time, the line was not in operation, and its power flow was limited to 0 by capacity constraints.

[0093] The reference node phase angle constraints, node phase angle upper and lower limit constraints, power generation upper limit constraints, load demand constraints, and load shedding upper limit constraints are as follows: ,

[0094] in, For the dual variable corresponding to the phase angle constraint of the reference node, Indicates the reference node, This represents the upper limit of the node voltage phase angle. This is the lower limit of the node phase angle. and These are the dual variables corresponding to the upper and lower limits of the node phase angle constraints, respectively. This represents the set of nodes excluding the reference node. These are the dual variables corresponding to the load demand equality constraints. For the dual variables corresponding to the power generation capacity constraint, For load During the rolling period Maximum shearable load ratio These are the dual variables corresponding to the load shedding upper limit constraint.

[0095] To improve the efficiency of solving subproblems, given candidate line construction schemes and line operation status, the inner-layer operation minimization problem is replaced with its dual problem, thus transforming the minimax subproblem into a single-layer maximization problem. The objective function of the dual subproblem is:

[0096] in, and These are the dual variables corresponding to the upper and lower limits of line capacity constraints.

[0097] The dual subproblem also satisfies the dual feasibility constraints corresponding to the inner runtime problem, including:

[0098] in, For the unit The power balance dual variable of the node, For load The power balance dual variable of the node, , The lines are respectively The starting and ending nodes. Through the above dual transformation, the subproblem can search for the source-load uncertainty parameters that maximize the operating cost under the given line operation state, thus obtaining... Figure 4 The worst-case source-load deviation scenario and the updated upper bound of the objective function are shown in the figure.

[0099] Because the objective function of the dual subproblem contains a product term of uncertain parameters and dual variables, and the uncertain parameters include binary uncertain variables. and Therefore, substituting the time-varying uncertainty set into the objective function of the dual subproblem will produce a bilinear term consisting of binary variables and continuous dual variables. For the product of the binary variables and continuous dual variables, an auxiliary variable is introduced, and the following Big-M linearization constraint is set:

[0100] in, To ensure sufficient positive numbers for linearization efficiency, we use 10 in this example. 6 , , and The linearization auxiliary variables are used to represent... , and When the corresponding binary uncertain variable takes the value 0, the corresponding auxiliary variable is 0; when the corresponding binary uncertain variable takes the value 1, the corresponding auxiliary variable is equal to the corresponding continuous dual variable. Thus, the product of the binary uncertain variable and the continuous dual variable is transformed into a linear constraint, allowing the worst-case source load deviation scenario search problem to be transformed into a mixed-integer linear programming problem to be solved.

[0101] correspond Figure 4 The main problem-solving steps involve constructing cut constraints for the main problem based on the worst-case source load deviation scenario obtained from the subproblems, and then using a column constraint generation method to iteratively solve the main problem and subproblems alternately. For any current rolling period... Based on the worst-case source load deviation scenario obtained from the sub-problems, construct the main problem cut constraints for the current rolling period, and in the current rolling period... The generated worst-case source load deviation scenario set Next, reselect candidate route construction schemes for the current rolling period to minimize the sum of the upper bounds of investment and operating costs for the current rolling period:

[0102] The upper bound of the operating cost in the main problem satisfies:

[0103] in, Rolling period in the main problem The upper limit of operating costs This represents the current iteration number. For the current rolling period The generated set of worst-case source load deviation scenarios For the scene index in the scene set, and Scenes The power generation output and load shedding.

[0104] For each worst-case source-load deviation scenario identified by the subproblem, the main problem replicates a set of operating variables corresponding to that worst-case source-load deviation scenario, ensuring that these operating variables satisfy the aforementioned node power balance constraints, DC power flow constraints, reference node phase angle constraints, line capacity constraints, node phase angle upper and lower limits constraints, generation output upper limit constraints, load demand constraints, and load shedding upper limit constraints. This guarantees that the current candidate line construction scheme meets operational feasibility requirements under all generated worst-case source-load deviation scenarios. As the number of iterations increases, the operating constraints and scenario cuts corresponding to new worst-case source-load deviation scenarios are continuously added to the main problem, and the approximation of the original robust transmission extension model by the main problem gradually tightens.

[0105] correspond Figure 4 The process shown, the column constraint generation method includes the following steps:

[0106] The first step is to... for any current scrolling period Input the time-varying uncertain budget and inherited line state corresponding to the current rolling period, and initialize the worst source load deviation scenario set for the current rolling period. Upper Realm Lower Boundary Number of iterations and preset convergence threshold ;

[0107] The second step is to proceed during the current rolling period. worst source load deviation scenario set Solve the robust transmission extension master problem for the current rolling period to obtain candidate line construction variables. Line commissioning status variables and the upper bound variable of operating costs And update the lower bound according to the objective function of the main problem. ;

[0108] The third step involves substituting the candidate line construction schemes and line commissioning status into the dual subproblem corresponding to the current rolling period, searching for a new worst-case source load deviation scenario within the time-varying uncertainty set of the current rolling period, and updating the upper bound of the current rolling period based on the sum of the investment cost and the subproblem operating cost of the current rolling period. ;

[0109] The fourth step is to determine whether the relative gap between the upper and lower bounds of the current scrolling period meets the preset convergence condition:

[0110] in, To preset the convergence threshold, To avoid constants with a denominator of zero, if the preset convergence condition is not met, the new worst-case source load deviation scenario is added to the worst-case source load deviation scenario set for the current rolling period. The corresponding operational constraints and scenario cuts are added to the main problem of the current rolling period, and the main problem-subproblem alternating iteration continues. If the preset convergence condition is met, the candidate route construction scheme for the current rolling period is output. This process corresponds to... Figure 4 The process is as follows: "Solve the main problem - solve the subproblems - determine the convergence condition - output the candidate route construction plan for the current rolling period".

[0111] correspond Figure 1 Step 9 and Figure 5The time-by-time inheritance process shown inherits the operational status of candidate transmission lines that have been completed in the current rolling period in subsequent rolling periods. Specifically, if a candidate line... During the current rolling period If constructed, then for any subsequent rolling period ,set up: ,

[0112] in, Indicates that candidate lines have been constructed. It will remain operational during subsequent rolling periods. This indicates that the candidate line will not be constructed again in subsequent rolling periods. Through the above-mentioned time-by-time inheritance mechanism, the constructed candidate lines remain in operation in subsequent rolling periods and are not repeatedly included in the investment cost, thus maintaining the temporal continuity of transmission line construction decisions.

[0113] like Figure 5 As shown, during the rolling period New construction lines obtained Afterwards, the cumulative number of operational lines was 100. During the rolling period New construction lines obtained Subsequently, the cumulative set of operational lines was updated to... ; and so on, until the rolling period. Afterwards, the cumulative number of operational lines was 100. The existing candidate lines are inherited in subsequent rolling periods to avoid duplicate investment and to form a record of the initial construction period for each candidate line.

[0114] In this example, the following can be used: Figure 6 The Garver-6 node transmission network shown is used as a case study system. Bus 1 to Bus 6 are treated as node objects, and the transmission lines in the diagram are considered as existing or candidate lines. The set of generating nodes, the set of load nodes, and hourly source-load data are set according to the generation resources and load demands connected to each node. Based on this case study system, according to... Figures 1 to 5 The process shown sequentially executes the construction of the current source-load state vector, Sinkhorn distance calculation, determination of time-varying uncertain budget, robust transmission extension solution, and line inheritance operation to verify the applicability of the method in typical transmission network scenarios.

[0115] The transmission expansion planning for all rolling periods is repeatedly executed in sequence, including constructing the current source-load state vector, constructing the historical source-load sample set, calculating the Sinckhorn distance, generating the source-load risk coefficient, determining the time-varying deviation coefficient and time-varying uncertain budget, searching for the worst-case source-load deviation scenario, iteratively solving the main problem and sub-problems based on the column constraint generation method, and inheriting the constructed candidate lines hourly, until the transmission expansion planning for all rolling periods is completed.

[0116] The final output includes newly added candidate lines for each rolling period, the initial construction period of each candidate line, the cumulative operational grid structure, construction costs, and the final robust transmission expansion scheme. The final robust transmission expansion scheme dynamically adjusts the robust planning conservatism based on the deviation of the hourly source load state distribution from the historical source load experience distribution, and avoids duplicate investment in already constructed candidate lines through an hourly line inheritance mechanism.

[0117] To verify the effectiveness of the method of this invention, a maximum investment budget of 40M€ was set in the Garver-6 node transmission network during the planning period, and the Sinkhorn time-varying uncertain budget method proposed in this invention was compared with the manual fixed uncertain budget method. In the manual fixed uncertain budget method, the generation-side uncertain budget is set to 2, the load-side uncertain budget is set to 2, the generation-side output down-biasing coefficient is set to 0.5, and the load-side demand up-biasing coefficient is set to 0.2, and the above parameters remain unchanged throughout the rolling period. The method of this invention, on the other hand, dynamically generates a source-load risk coefficient based on the Sinkhorn distance between the current source-load state distribution and the historical source-load experience distribution in each rolling period, and adaptively determines the generation-side uncertain budget, load-side uncertain budget, generation-side output down-biasing coefficient, and load-side demand up-biasing coefficient for the current rolling period based on the source-load risk coefficient.

[0118] Table 1: Comparison of Model Indicators Model fixed budget for labor Sinkhorn Time-Variation Budget Number of newly built lines 5 items (2-3, 2-6, 3-6, 4-6, 5-6) 5 items (2-3, 2-6, 3-5, 4-6, 5-6) Total investment of the line 36.492120 M€ 31.085880 M€ Upper bound of average single time period 414.332373 M€ 359.756135 M€ Maximum single-period upper bound 679.842107 M€ 623.382562 M€ Total cost over all time 477347.385313 M€ 414470.153042 M€ Runtime 26.55 seconds 22.85 seconds As shown in Table 1, the Sinkhorn time-varying budget model can adaptively adjust the uncertain budget according to the changes in source and load states. Under the same number of new lines, it can select a more economical and efficient extension corridor, reduce line investment and system operating costs, and thus obtain a transmission extension scheme with better overall economy and robustness.

Claims

1. A time-varying rolling robust transmission expansion method based on Sinckhorn time-varying budgets, characterized in that, The method includes the following steps: S1: Obtain node data, existing line data, candidate line data, generation node data, load node data, and hourly source-load data of the target transmission network, construct the basic model of the transmission network, and set candidate line construction variables, line commissioning status variables, and the maximum investment budget for the planning period; S2: Establish an hourly rolling planning process according to the order of rolling periods. In each current rolling period, construct the current source load state vector using the nominal value of power generation capacity and the nominal value of load demand. Construct a historical source load sample set based on historical adjacent periods, the same hourly historical period, or typical daily historical period. Construct the current source load state distribution and the historical source load empirical distribution through the current source load state vector and the historical source load sample set. S3: Calculate the Sinckhorn distance between the current source load state distribution and the historical source load experience distribution, map the Sinckhorn distance to a source load risk coefficient to characterize the degree of deviation of the current source load state, and determine the time-varying deviation coefficient and time-varying uncertain budget for the current rolling period based on the source load risk coefficient. The time-varying deviation coefficient includes the power generation output down-bias coefficient and the load demand up-bias coefficient, and the time-varying uncertain budget includes the power generation uncertain budget and the load uncertain budget. S4: Construct a time-varying uncertainty set based on the time-varying deviation coefficient and the time-varying uncertain budget, and input this time-varying uncertainty set into the robust transmission expansion model. Determine the candidate line construction schemes and line commissioning status for the current rolling period through the robust transmission expansion master problem. Search for the worst source-load deviation scenario that makes the system operating cost most unfavorable within the time-varying uncertainty set through the robust transmission expansion sub-problems. Feed the worst source-load deviation scenario back to the robust transmission expansion master problem for iterative solving of the master problem and sub-problems to obtain the candidate line construction schemes for the current rolling period. At the same time, inherit the candidate lines already constructed in the current rolling period to subsequent rolling periods so that they remain in operation in subsequent periods and are not repeatedly included in the investment cost, until the transmission expansion planning for all rolling periods is completed, and the final robust transmission expansion scheme is obtained.

2. The hourly rolling robust transmission expansion method with Sinckhorn time-varying budget as described in claim 1, characterized in that, In step S2, constructing the current source load state vector, the historical source load sample set, the current source load state distribution, and the historical source load empirical distribution specifically includes: Step (1) For any current scrolling period To connect each power generation node in the target transmission network The nominal value of the generation capacity and each load node The nominal load demand baseline value is normalized, where the first... Normalization results of each power generation node and the Normalized results of each load node They are respectively: ， in, , Let them represent the set of generating nodes and the set of load nodes, respectively. , These are used to represent the current scrolling period. The normalized benchmark for nominal generation capacity and nominal load demand. To avoid constants with a denominator of zero, and These are the baseline nominal values ​​for power generation capacity and load demand for the current rolling period, respectively. and These represent the coefficients that represent the changes in nominal generation capacity and load demand over time during the current rolling period. and These represent the nominal value of generation capacity and the nominal value of load demand after considering the time variation of nominal values, respectively. The normalization process is used to bring the generation capacity and load demand under a unified dimensional scale, so as to serve as the input for Sinckhorn distance calculation. Step (2) concatenates the normalized generation capacity and normalized load demand according to the node sequence to obtain the current source-load state vector. This ensures that each rolling period corresponds to a vector that can simultaneously characterize the state of the generation side and the state of the load side: in, The number of power generation nodes. This represents the number of load nodes. Step (3) Select at least one of the following as the sample source: the adjacent historical period before the current rolling period, the historical period of the same hour, or the historical period of a typical day, to obtain the historical source load sample set. : in, For the first A historical source sample, This represents the number of historical source payload samples. Step (4) Based on the current source load state vector Construct the current source load state distribution Based on historical source load sample sets Constructing historical source load empirical distribution : ， in, Represents the current source load state vector Dirac measure at the location, Indicates samples located in the historical source load state The Dirac measure at the location, constructing the current source charge state distribution. Historical source load experience distribution Used for subsequent Sinkhorn distance calculations.

3. The hourly rolling robust transmission extension method with Sinckhorn time-varying budget as described in claim 1, characterized in that, In step S3, the Sinckhorn distance is calculated, and the Sinckhorn distance is mapped to a source load risk coefficient that characterizes the degree of current source load state offset. The time-varying deviation coefficient and time-varying uncertainty budget for the current rolling period are determined by the source load risk coefficient. Specifically, this includes: Step (1) Based on the current source load state distribution Historical source load experience distribution Based on the discrete sample representation of the Wasserstein distance between the two, an entropy regularization term is introduced, and the optimal entropy regularized transmission distance between them is calculated as the Sinckhorn distance. : in, For and For a set of transportation plans distributed at the periphery, The distance cost between source and load state samples. and These represent the current source load state distribution and the historical source load empirical distribution in discrete sample form, respectively. The transportation plan is based on the current source load distribution and the historical source load experience distribution. For elements in the aforementioned transportation plan, and The reference measure corresponding to the current source load state distribution is given at the sample points. and The weight, This is the entropy regularization parameter; Step (2) maps the Sinkhorn distance to a source load risk coefficient that characterizes the degree of current source load state shift. : in, and These are the lower and upper limits of the historical Sinkhorn distance, respectively. To prevent constants with a denominator of zero, the source load risk coefficient... The larger the value, the greater the deviation of the current source load state distribution from the historical source load empirical distribution; Step (3) Determine the time-varying deviation coefficient for the current rolling period based on the source-load risk coefficient, wherein the time-varying deviation coefficient includes the power generation output down-bias coefficient. and load-side demand skew coefficient : ， in, and These are the lower and upper limits of the power output deflection coefficient on the generation side, respectively. and These are the lower and upper limits of the load-side demand skewness coefficient, respectively. Step (4) Based on the power generation output down-biasing coefficient and the load demand up-biasing coefficient, generate the maximum deviation of power generation capacity for the current rolling period. Maximum deviation from load demand : ， in, and These are coefficients representing the maximum deviation between the current rolling period's power generation capacity and load demand over time. Step (5) Determine the time-varying uncertain budget for the current rolling period based on the source-load risk coefficient, wherein the time-varying uncertain budget includes the generation-side uncertain budget. and load-side uncertain budget : ， in, The function is an up-rounding function that ensures the uncertain budgets on the generation side and the load side are integer budgets. and These represent the lower and upper limits of the uncertain budget on the power generation side, respectively. and These represent the lower and upper limits of the uncertain budget on the load side, respectively.

4. The hourly rolling robust transmission extension method with Sinckhorn time-varying budget as described in claim 1, characterized in that, The robust transmission extension subproblem in step S4, which searches within the time-varying uncertainty set for the worst-case source-load deviation scenario that minimizes system operating costs, specifically includes: Step (1) Based on the power generation output down-biasing coefficient of the current rolling period and load-side demand skew coefficient Determine the worst-case deviation form of the power generation capacity. The worst-case deviation from load demand : ， in, and These are binary uncertainties on the generation side and the load side, respectively; Step (2) Based on the uncertain budget of the power generation side during the current rolling period and load-side uncertain budget Set budget constraints: ， ， Step (3) Based on the candidate line construction schemes and line commissioning status determined by the robust transmission extension master problem, construct the inner layer DC power flow operation problem for the current rolling period. The inner layer DC power flow operation problem aims to minimize the sum of generation cost and load shedding penalty cost, and satisfies the following constraints: node power balance constraint, DC power flow constraint, reference node phase angle constraint, node phase angle upper and lower limit constraint, line capacity constraint, generation output upper limit constraint, load demand constraint, and load shedding upper limit constraint. Step (4) Within the time-varying uncertainty set, with the objective of maximizing the operating cost of the current rolling period, solve the robust transmission extension subproblem to obtain the worst-case source-load deviation scenario for the current rolling period. The worst-case operating cost obtained from the subproblem is: in, For the time-varying uncertain set of the current rolling period, For the unit During the rolling period Power generation output, For load During the rolling period The shear load, For the unit During the rolling period The cost of electricity generation, For load During the rolling period The cost of load shedding penalty For the line During the rolling period The trend For the load during the rolling period The demand, For nodes During the rolling period The voltage phase angle, the subproblem is transformed into a mixed integer linear programming problem by replacing the inner operation minimization problem with its dual problem and linearizing the product of binary uncertain variables and continuous dual variables.

5. The hourly rolling robust transmission extension method with Sinckhorn time-varying budget as described in claim 1, characterized in that, In step S4, the robust transmission extension main problem-subproblem alternating iteration and the inheritance of candidate lines already constructed in the current rolling period to subsequent rolling periods specifically include: Step (1) Initialize the current scrolling period worst source load deviation scenario set Upper Realm Lower Boundary Number of iterations and preset convergence threshold ; Step (2) in the current rolling period worst source load deviation scenario set Next, we establish the robust transmission extension master problem: in, For the candidate route set, Candidate routes During the rolling period Construction costs, Candidate routes During the rolling period Construction variables, Rolling period in the main problem The upper bound variable of operating cost, and for any scenario Set an upper bound constraint on operating costs: in, and Scenes The power generation output and load shedding are as follows; Step (3) solves the robust transmission extension master problem to obtain candidate line construction variables. Line commissioning status variables and the upper bound variable of operating cost And based on the current rolling period The main problem is updating the lower bound of the objective function. ; Step (4) substitutes the candidate line construction schemes and line commissioning status determined by the robust transmission extension master problem into the robust transmission extension subproblem corresponding to the current rolling period, searches for new worst-case source-load deviation scenarios within the time-varying uncertainty set of the current rolling period, and then, based on the current rolling period... The sum of investment costs and sub-problem operating costs is updated to the upper bound. ; Step (5) Determine whether the convergence condition is met: in, To preset the convergence threshold, To avoid constants with a denominator of zero, if this condition is not met, a new worst-case source load deviation scenario will be added. , and return to step (2) to continue iterating; if satisfied, output the candidate line construction scheme for the current rolling period; Step (6) for satisfying Candidate routes This indicates that the candidate route is in the current rolling period. Constructed; for any subsequent rolling period ,set up: ,in, For any subsequent rolling period, the existing candidate transmission lines will remain in operation and will not be included in the investment cost repeatedly. Step (7) According to the rolling time period set The time period sequence is used to repeat steps (1) to (6) for each rolling time period until the robust transmission expansion planning for all rolling time periods is completed, and finally the newly added candidate lines, the first construction period of each candidate line, the cumulative commissioned grid and the final robust transmission expansion scheme are obtained for each rolling time period.

Images