Power system planning method based on time sequence aggregation and constraint relaxation

Abstract

The invention discloses an electric power system planning method based on time sequence aggregation and constraint relaxation, and belongs to the field of electric power planning, and the method comprises the steps: determining a first constraint condition according to time sequence operation data, and constructing a full time sequence planning model in combination with a preset objective function; obtaining time sequence aggregation data by clustering the time sequence operation data; determining a second constraint condition based on the time sequence aggregation data, and constructing a time sequence aggregation planning model in combination with a preset objective function; solving the time sequence aggregation planning model to obtain a first planning scheme; substituting the first planning scheme into the full-time-sequence planning model to obtain a model upper bound value; constructing a constraint relaxation planning model according to a preset objective function and the post-relaxation constraint condition; solving the constraint relaxation planning model to obtain a model lower bound value; according to the cost relative deviation of the model upper bound value and the model lower bound value, judging whether the preset target function is converged; and during convergence, determining a final planning scheme. The method can solve the problems that the power system planning model is low in solving efficiency and the solving deviation cannot be determined.

Description

Technical Field

[0001] This invention relates to the field of power planning technology, and in particular to a power system planning method based on time series aggregation and constraint relaxation. Background Technology

[0003] While current static time series aggregation methods simplify computation by reducing the number of scenarios, they suffer from a rigid, fixed number of scenarios, making it impossible to dynamically adjust the clustering scenario size based on solution accuracy. Furthermore, existing methods lack systematic relaxation strategies for core constraints such as power balance and renewable energy output, leading to excessively large gaps between upper and lower bounds and convergence difficulties in complex scenarios. This ultimately results in an imbalance between the economic efficiency and safety of the planning scheme, making it difficult to simultaneously meet the dual requirements of solution efficiency and accuracy. Therefore, current power system planning methods are ill-suited to addressing the problems of low computational efficiency and low accuracy caused by large datasets. Summary of the Invention

[0004] This invention provides a power system planning method based on time series aggregation and constraint relaxation, which can solve the problems of low efficiency and low accuracy in existing power system planning technologies.

[0005] To address the aforementioned technical problems, this invention provides a power system planning method based on time series aggregation and constraint relaxation, comprising:

[0006] Acquire time-series operation data of the power system; wherein, the time-series operation data includes node load, wind turbine output power and photovoltaic unit output power at several time points;

[0007] The first constraint is determined based on the time-series running data, and a full-time-series planning model is constructed according to the preset objective function and the first constraint.

[0008] Cluster analysis is performed on the time-series running data to obtain the time-series aggregated data and the number of clusters;

[0009] The second constraint is determined based on the time-series aggregated data, and a time-series aggregated planning model is constructed according to the preset objective function and the second constraint.

[0010] Solve the time-series aggregation programming model to obtain the first programming scheme;

[0011] Substituting the first planning scheme into the full-time-series planning model, the total cost of the first planning scheme is obtained;

[0012] The second constraint condition is relaxed to obtain the relaxed constraint condition.

[0013] Based on the preset objective function and the relaxed constraints, a constraint relaxation programming model is constructed.

[0014] Solve the constrained relaxation programming model to obtain the second programming scheme and the total cost of the second programming scheme;

[0015] Determine whether the preset objective function converges based on the total cost of the first planning scheme, the total cost of the second planning scheme, and the preset convergence gap;

[0016] When the preset objective function converges, a final planning scheme is determined based on the first planning scheme and the second planning scheme; wherein, the final planning scheme includes the installed capacity of each unit and each energy storage device in the power system, as well as the line capacity of each line in the power system.

[0017] As a preferred embodiment, the preset objective function is:

[0018]

[0019] In the formula, C plan The total cost of the planned scheme is represented by g; g is the unit number, b is the energy storage device number, and l is the line number; N g N represents the number of generating units. b N represents the number of energy storage devices. l N represents the number of lines. T α represents the total duration of the time-series data execution. g α is the annualized investment cost per unit capacity of unit g; b α represents the annualized investment cost per unit capacity of energy storage device b. l The annualized investment cost per unit capacity of line l; O g The installed capacity of unit g; O b For energy storage device b, the installed capacity is O. l β represents the line capacity of line l; g The variable generation cost for g generating units; N i This represents the number of unit types after aggregation. The startup cost of the i-th type of polymerization unit; P represents the shutdown cost of the i-th type of polymerization unit; g,t Let g be the output power of unit g at time t; Let be the operating capacity of the i-th type of aggregation unit at time t; Let be the shutdown capacity of the i-th type of aggregation unit at time t.

[0020] As a preferred embodiment, determining the first constraint based on the time-series runtime data includes:

[0021] Obtain pre-built constraints;

[0022] A first time constraint range is constructed based on the time coverage range of the time-series running data;

[0023] The first constraint condition is constructed based on the pre-constructed constraint condition and the first time constraint range;

[0024] The pre-constructed constraints include upper and lower limits of equipment output and ramping constraints, node power balance constraints, new energy penetration rate constraints, unit combination constraints, new energy output constraints, and energy storage equipment operation constraints.

[0025] The upper and lower limits of the equipment output and the ramping constraint are as follows:

[0026]

[0027] In the formula, κ u P represents the ramp rate of equipment u. u,t and P u,t+1 These represent the output power of device u at time t and time t+1, respectively; O u Let u be the capacity of the device; device u includes a generator set and an energy storage device; the node power balance constraint is:

[0028]

[0029] In the formula, and These represent the charging power and discharging power of the energy storage device, respectively; P ls,t and P le,t These represent the feed-out power and feed-in power of the node, respectively; Ψ n,g Ψ represents the unit g connected to node n; n,b Ψ represents the energy storage device b connected to node n. n,ls Ψ represents the feeder line ls connected to node n; n,le D represents the feed line le connected to node n; n,t This represents the load of node n at time t; This represents the load shedding at node n at time t;

[0030] The constraint on the penetration rate of new energy sources is:

[0031]

[0032] In the formula, w and pv are the numbers of the wind turbine and photovoltaic unit, respectively; ξ is the minimum proportion of renewable energy generation; N n This represents the total number of nodes.

[0033] The unit combination constraint is:

[0034]

[0035] In the formula, Ψ i,g Unit g; r belongs to the i-th type of aggregation unit. i,min Minimum output rate of the i-th type of polymer unit; T i on T represents the minimum start-up time for the i-th type of polymer unit; i off This represents the shortest shutdown time for the i-th type of polymer unit; Let be the online capacity of the i-th type of aggregation unit at time t;

[0036] The constraint on the output of the new energy source is:

[0037]

[0038] In the formula, χ is the maximum wind and solar curtailment rate; Let w be the wind curtailment power of wind turbine w at time t; Let PV be the curtailment power of the photovoltaic unit at time t; For the predicted per-unit output of wind turbines and photovoltaic units;

[0039] The operating constraints of the energy storage device are:

[0040]

[0041] In the formula, SOC b,t The state of charge of energy storage device b; η b The charging and discharging efficiency of energy storage device B; B b The energy storage duration of energy storage device b; SOC b,min This represents the minimum allowable power capacity of energy storage device b.

[0042] As a preferred embodiment, the step of performing cluster analysis on the time-series runtime data to obtain the time-series aggregated data and the number of clusters includes:

[0043] The k-means clustering method was used to perform cluster analysis on the time-series operating data to obtain several aggregated units and the number of clusters;

[0044] For each aggregation unit, determine the cluster center and the number of scenarios corresponding to the aggregation unit;

[0045] The data point with the closest Euclidean distance to the cluster center is used as the representative data of the scene.

[0046] The weight of the data representing each scenario is determined based on the number of scenarios.

[0047] The time-series aggregated data is determined based on the representative scenario data of each aggregation unit and the corresponding weights of the representative data of each scenario.

[0048] As a preferred embodiment, determining the second constraint based on the time-series aggregated data includes:

[0049] A second time constraint range is constructed based on the time coverage range of the time-series aggregated data;

[0050] The second constraint is constructed based on the pre-constructed constraint and the second time constraint range.

[0051] As a preferred embodiment, the step of performing constraint relaxation processing on the second constraint condition to obtain the relaxed constraint condition includes:

[0052] Based on the preset constraint range, the temporal constraints in the pre-constructed constraint conditions are relaxed to form the processed constraint conditions.

[0053] By combining the processed constraints and the pre-constructed constraints, relaxed constraints are formed.

[0054] The post-processing constraints are as follows:

[0055]

[0056] In the formula, n represents the node number, k represents the aggregation unit number, and t represents the time point; D n,k,t This represents the load power of node n at time t under unit k. This represents the minimum load power of node n at time t among all data points under unit k in the aggregation process. This represents the maximum load power of node n at time t among all data points under unit k; Let represent the predicted per-unit output of the photovoltaic unit at node n under the condition of the polymer unit k at time t. This represents the minimum predicted per-unit output of the photovoltaic unit at time t among all data points under the k-th aggregation unit at node n. This represents the minimum predicted per-unit output of the photovoltaic unit at time t among all data points under the k-th aggregation unit at node n; This represents the actual photovoltaic output of node n at time t under the k-th polymer unit. This represents the power of light discarded by the nth node at time t under the kth scene. This represents the installed capacity of the photovoltaic unit at node n; This represents the predicted per-unit output of the wind turbine at node n at time t under the conditions of the aggregation unit k. Let represent the minimum predicted per-unit output of the wind turbine at node n under the condition of the aggregation unit k at time t. This represents the maximum predicted per-unit output of the wind turbine at node n at time t under the k-th aggregation unit. This represents the actual wind power output of node n at time t under the k-th aggregation unit. This represents the wind curtailment power of the nth node at time t under the kth scenario. This represents the installed capacity of the wind turbine unit at node n.

[0057] As a preferred embodiment, the step of determining whether the preset objective function has converged based on the total cost of the first planning scheme, the total cost of the second planning scheme, and the preset convergence gap includes:

[0058] Calculate the relative cost deviation based on the total cost of the first planning scheme and the total cost of the second planning scheme;

[0059] Compare the relative cost deviation with the size of the preset convergence gap;

[0060] When the relative cost deviation is less than the preset convergence gap, the preset objective function is determined to have converged.

[0061] When the relative cost deviation is greater than or equal to the preset convergence gap, it is determined that the preset objective function has not converged.

[0062] The relative cost deviation is calculated using the following formula:

[0063]

[0064] In the formula, gap represents the relative cost deviation; X1 represents the total cost of the first planning scheme; and X2 represents the total cost of the second planning scheme.

[0065] As a preferred embodiment, when the preset objective function converges, determining the final planning scheme based on the first planning scheme and the second planning scheme includes:

[0066] In the first planning scheme, the first installed capacity of each unit and each energy storage device in the power system, as well as the first line capacity of each line in the power system, are determined.

[0067] The second planning scheme determines the second installed capacity of each unit and each energy storage device in the power system, as well as the second line capacity of each line in the power system;

[0068] The average value of each of the first installed capacity and each of the second installed capacity is calculated to obtain the installed capacity of each unit and each energy storage device in the power system;

[0069] The line capacity of each line in the power system is obtained by averaging the capacity of each of the first lines and the capacity of each of the second lines.

[0070] Based on the installed capacity of each generating unit and energy storage device in the power system, as well as the line capacity of each line in the power system, a final planning scheme is formed.

[0071] As a preferred embodiment, after determining that the preset objective function has not converged when the cost difference is greater than or equal to the preset convergence gap, the method further includes:

[0072] The number of clusters is increased cyclically, and cluster analysis is performed on the time-series running data based on the updated number of clusters to obtain updated time-series aggregated data. Based on the updated time-series aggregated data, the full-time-series planning model and the constraint relaxation planning model are solved respectively to obtain updated first planning scheme and updated second planning scheme. This process continues until the preset objective function converges. Finally, the planning scheme is obtained based on the updated first planning scheme and updated second planning scheme.

[0073] As a preferred embodiment, after determining the final planning scheme based on the first planning scheme and the second planning scheme when the preset objective function converges, the process includes:

[0074] Based on the installed capacity of each generating unit and each energy storage device in the final planning scheme, the planning and adjustment of each generating unit and each energy storage device of the power system are carried out.

[0075] Based on the line capacity of each line in the final planning scheme, the planning of each line in the power system is adjusted.

[0076] Compared with the prior art, the embodiments of the present invention have the following beneficial effects:

[0077] This invention provides a power system planning method based on time series aggregation and constraint relaxation. The method involves: acquiring time-series operational data of the power system; determining a first constraint based on the time-series operational data and constructing a full-time-series planning model according to a preset objective function and the first constraint; performing cluster analysis on the time-series operational data to obtain time-series aggregated data and the number of clusters; determining a second constraint based on the time-series aggregated data and constructing a time-series aggregated planning model according to the preset objective function and the second constraint; solving the time-series aggregated planning model to obtain a first planning scheme; substituting the first planning scheme into the full-time-series planning model to obtain the total cost of the first planning scheme; performing constraint relaxation on the second constraint to obtain relaxed constraint conditions; constructing a constraint relaxation planning model according to the preset objective function and the relaxed constraint conditions; solving the constraint relaxation planning model to obtain a second planning scheme and the total cost of the second planning scheme; determining whether the preset objective function has converged based on the total cost of the first planning scheme, the total cost of the second planning scheme, and a preset convergence gap; and determining the final planning scheme based on the first and second planning schemes when the preset objective function has converged. This invention effectively reduces the amount of data computation in the model by aggregating time series data, thereby improving planning efficiency. Based on time series aggregation and constraint relaxation, upper and lower bounds of the model are formed respectively, avoiding difficulties in model convergence and effectively improving planning efficiency and accuracy. Attached Figure Description

[0078] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0079] Figure 1 This is a flowchart illustrating an embodiment of the power system planning method based on time series aggregation and constraint relaxation provided by the present invention.

[0080] Figure 2 This is a flowchart illustrating another embodiment of the power system planning method based on time series aggregation and constraint relaxation provided by the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0082] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0083] In the description of the embodiments of this application, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0084] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0085] In the description of the embodiments in this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.

[0086] In the description of the embodiments of this application, the term "multiple" refers to two or more (including two), similarly, "multiple sets" refers to two or more (including two sets), and "multiple pieces" refers to two or more (including two pieces).

[0087] In the description of the embodiments of this application, unless otherwise expressly specified and limited, technical terms such as "installation," "connection," "joining," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.

[0088] See Figure 1To address the problems of low efficiency and low accuracy in existing power system planning technologies, an embodiment of the present invention provides a power system planning method based on time series aggregation and constraint relaxation. This method includes steps 1001 to 1011, each step of which is detailed below:

[0089] Step 1001: Obtain the time-series operation data of the power system; wherein, the time-series operation data includes the node load, wind turbine output power and photovoltaic unit output power corresponding to several time points.

[0090] In this embodiment of the invention, time-series operation data of the power system are collected, including node load, wind turbine output power and photovoltaic unit output power, to construct an initial time-series dataset.

[0091] The initial time series dataset can be represented as:

[0092]

[0093] In the formula, X col This is the initial time series dataset; This represents the time series data of the output power of the node load within the time series [1, T0]. This represents the time-series data of the wind turbine's output power within the time series [1, T0]. This represents the time series data of the output power of the photovoltaic unit within the time series [1, T0].

[0094] Specifically, the time series data of the output power of the node load within the time series [1, T0] can be represented as:

[0095]

[0096] In the formula, Let be the output power of the node load at time t, and T be the transpose of the matrix.

[0097] The time series data of the output power of the wind turbine generator within the time series [1, T0] can be expressed as:

[0098]

[0099] In the formula, Let be the output power of the wind turbine at time t, and T be the transpose of the matrix.

[0100] The output power time series data of the photovoltaic unit within the time series [1, T0] can be expressed as:

[0101]

[0102] In the formula, Let T be the output power of the photovoltaic unit at time t, and T be the transpose of the matrix.

[0103] Step 1002: Determine the first constraint based on the time-series running data, and construct a full-time-series planning model according to the preset objective function and the first constraint.

[0104] In this embodiment of the invention, a full-time-series planning model with multi-factor collaboration and embedded hourly-level resolution production and operation simulation is first constructed. For example, an 8760-hour power system planning model is embedded. The model takes the overall economic optimization of the planning scheme as the objective function and includes model constraints such as upper and lower limits of equipment output and ramp-up constraints, node power balance constraints, new energy penetration rate constraints, unit combination constraints, new energy output constraints, and energy storage equipment operation constraints.

[0105] As a preferred embodiment, the preset objective function is:

[0106]

[0107] In the formula, C plan The total cost of the planned scheme is represented by g; g is the unit number, b is the energy storage device number, and l is the line number; N g The number of generating units includes the number of thermal power units, wind power units, and photovoltaic units; N b N represents the number of energy storage devices. l N represents the number of lines. T α represents the total duration of the time-series data execution. g α is the annualized investment cost per unit capacity of unit g; b α represents the annualized investment cost per unit capacity of energy storage device b. l The annualized investment cost per unit capacity of line l; O g The installed capacity of unit g; O b For energy storage device b, the installed capacity is O. l β represents the line capacity of line l; g The variable generation cost for g generating units; N i This represents the number of unit types after aggregation. The startup cost of the i-th type of polymerization unit; P represents the shutdown cost of the i-th type of polymerization unit; g,t Let g be the output power of unit g at time t; Let be the operating capacity of the i-th type of aggregation unit at time t; Let be the shutdown capacity of the i-th type of aggregation unit at time t.

[0108] As a preferred embodiment, determining the first constraint based on the time-series runtime data includes:

[0109] Obtain pre-built constraints;

[0110] A first time constraint range is constructed based on the time coverage range of the time-series running data;

[0111] The first constraint condition is constructed based on the pre-constructed constraint condition and the first time constraint range;

[0112] The pre-constructed constraints include upper and lower limits of equipment output and ramping constraints, node power balance constraints, new energy penetration rate constraints, unit combination constraints, new energy output constraints, and energy storage equipment operation constraints.

[0113] The upper and lower limits of the equipment output and the ramping constraint are as follows:

[0114]

[0115] In the formula, κ u P represents the ramp rate of equipment u. u,t and P u,t+1 These represent the output power of device u at time t and time t+1, respectively; O u Let u be the capacity of the device; device u includes a generator set and an energy storage device; the node power balance constraint is:

[0116]

[0117] In the formula, and These represent the charging power and discharging power of the energy storage device, respectively; P ls,t and P le,t These represent the feed-out power and feed-in power of the node, respectively; Ψ n,g Ψ represents the unit g connected to node n; n,b Ψ represents the energy storage device b connected to node n. n,ls Ψ represents the feeder line ls connected to node n; n,le D represents the feed line le connected to node n; n,t This represents the load of node n at time t; This represents the load shedding at node n at time t;

[0118] The constraint on the penetration rate of new energy sources is:

[0119]

[0120] In the formula, w and pv are the numbers of the wind turbine and photovoltaic unit, respectively; ξ is the minimum proportion of renewable energy generation; N n This represents the total number of nodes.

[0121] The unit combination constraint is:

[0122]

[0123] In the formula, Ψ i,g Unit g; r belongs to the i-th type of aggregation unit. i,min Minimum output rate of the i-th type of polymer unit; T i on T represents the minimum start-up time for the i-th type of polymer unit; i off This represents the shortest shutdown time for the i-th type of polymer unit; Let be the online capacity of the i-th type of aggregation unit at time t;

[0124] The constraint on the output of the new energy source is:

[0125]

[0126] In the formula, χ is the maximum wind and solar curtailment rate; Let w be the wind curtailment power of wind turbine w at time t; Let PV be the curtailment power of the photovoltaic unit at time t; For the predicted per-unit output of wind turbines and photovoltaic units;

[0127] The operating constraints of the energy storage device are:

[0128]

[0129] In the formula, SOC b,t The state of charge of energy storage device b; η b The charging and discharging efficiency of energy storage device B; B b The energy storage duration of energy storage device b; SOC b,min This represents the minimum allowable power capacity of energy storage device b.

[0130] In this embodiment of the invention, the first constraint condition of the full-time-series programming model includes two aspects: pre-constructed constraint conditions and a first time constraint range. The first time constraint range is the time coverage range of the time-series running data. For example, if the earliest time corresponding to the time-series running data is time 'a' and the latest time is time 'b', then the first time constraint range is [a, b]. Based on the above-mentioned pre-constructed objective function and the first constraint condition, a full-time-series programming model is formed. The model aims at optimizing overall economic efficiency and solves for parameters such as the installed capacity, line capacity, and power of various types of generating units, energy storage devices, and lines.

[0131] In this embodiment of the invention, the full-time-series planning model can be simplified as follows:

[0132] min cost Inv +cost oper

[0133]

[0134] In the formula, u represents the optimal planning scheme for the power system, including the installed capacity of various types of generating units, energy storage, and transmission lines, etc., and v t These are time-related decision variables, including the output of each unit, line power, etc., and cost. Inv Cost represents the system's investment cost. oper This represents the system's operating cost.

[0135] The first row of constraints is f(u,v) t )=b t This represents a time-related constraint that must remain constant within the embedded hourly-level power system planning model, such as a power balance constraint; the second row represents the constraint g(u,v). t )≤c represents an inequality constraint that the system must satisfy at all times, such as an upper limit constraint on output; the third row constraint h(v t ,v t-1 )≤d indicates that the system's state change at each moment needs to satisfy the constraints of the previous moment, that is, constraints with temporal coupling, such as unit ramp-up constraints, energy storage charging state constraints, etc.

[0136] Step 1003: Perform cluster analysis on the time-series running data to obtain the time-series aggregated data and the number of clusters.

[0137] In this embodiment of the invention, after the original time-series running data is collected, data preprocessing operations such as normalization are performed on the time-series running data, and cluster analysis is performed on the preprocessed data to obtain time-series aggregated data.

[0138] As a preferred embodiment, cluster analysis is performed on the time-series runtime data to obtain the time-series aggregated data and the number of clusters, including:

[0139] The k-means clustering method was used to perform cluster analysis on the time-series operating data to obtain several aggregated units and the number of clusters;

[0140] For each aggregation unit, determine the cluster center and the number of scenarios corresponding to the aggregation unit;

[0141] The data point with the closest Euclidean distance to the cluster center is used as the representative data of the scene.

[0142] The weight of the data representing each scenario is determined based on the number of scenarios.

[0143] The time-series aggregated data is determined based on the representative scenario data of each aggregation unit and the corresponding weights of the representative data of each scenario.

[0144] In this embodiment of the invention, cluster analysis is performed on the time-series runtime data. First, the k-means clustering algorithm is used to perform clustering processing, resulting in multiple cluster categories. Each cluster category contains time-series data corresponding to multiple scenarios. The number of scenarios in each cluster category is used as the weight of that cluster category. The data point with the closest Euclidean distance to the cluster center in each cluster category is determined as the representative scenario data corresponding to that category. Finally, the representative scenario data and their corresponding weights are used as the time-series aggregated data. Using the time-series aggregated data to solve the model effectively speeds up the model solving process compared to using the original time-series runtime data.

[0145] Step 1004: Determine the second constraint based on the time series aggregated data, and construct a time series aggregated planning model according to the preset objective function and the second constraint.

[0146] As a preferred embodiment, determining the second constraint based on the time-series aggregated data includes:

[0147] A second time constraint range is constructed based on the time coverage range of the time-series aggregated data;

[0148] The second constraint is constructed based on the pre-constructed constraint and the second time constraint range.

[0149] In this embodiment of the invention, the second constraint condition of the time-series aggregation programming model includes two aspects: a pre-constructed constraint condition and a second time constraint range. The second time constraint range is the time coverage range of the time-series aggregated data. For example, if the earliest time corresponding to the time-series running data is time c and the latest time is time d, then the first time constraint range is [c, d]. The time-series aggregation programming model is formed by the above-mentioned pre-constructed objective function and the second constraint condition.

[0150] In this embodiment of the invention, the time-series aggregation planning model can be expressed as:

[0151]

[0152]

[0153] In the formula, v represents the operating cost of scenario k. k,t This represents the power of the generator unit or line at time t in scenario k. Compared to the power planning model with 8760 hours of embedded data, the power planning model based on time series aggregation only embeds K scenarios, significantly reducing the decision variables and constraints of the model, thus shortening the model solution time.

[0154] Step 1005: Solve the time series aggregation planning model to obtain the first planning scheme.

[0155] In this embodiment of the invention, by solving the time-series aggregation planning model constructed using time-series aggregation data, a first planning scheme for thermal power units, hydropower units, photovoltaic units, wind power units, energy storage equipment, and transmission lines can be obtained. The first planning scheme includes the installed capacity of each unit and energy storage equipment and the line capacity of each line.

[0156] Step 1006: Substitute the first planning scheme into the full-time-series planning model to obtain the total cost of the first planning scheme.

[0157] In this embodiment of the invention, the installed capacity and line capacity in the first planning scheme are substituted into the full-time planning model as known parameters to perform an operation simulation under the given planning scheme. The construction cost and operating cost of the first planning scheme can be obtained, and the total cost of the first planning scheme can be calculated. This cost is the upper bound of the original planning problem.

[0158] Step 1007: Perform constraint relaxation processing on the second constraint condition to obtain the relaxed constraint condition.

[0159] In this embodiment of the invention, the upper bound of the original planning problem is obtained by solving the time-series aggregated programming model to obtain the first planning scheme, and then substituting it into the full-time-series programming model for simulation. The lower bound of the original planning problem can be obtained by solving a constraint-relaxed programming model constructed from the relaxed constraints.

[0160] As a preferred embodiment, the second constraint condition is subjected to constraint relaxation processing to obtain the relaxed constraint condition, including:

[0161] Based on the preset constraint range, the temporal constraints in the pre-constructed constraint conditions are relaxed to form the processed constraint conditions.

[0162] By combining the processed constraints and the pre-constructed constraints, relaxed constraints are formed.

[0163] The post-processing constraints are as follows:

[0164]

[0165] In the formula, n represents the node number, k represents the aggregation unit number, and t represents the time point; D n,k,t This represents the load power of node n at time t under unit k. This represents the minimum load power of node n at time t among all data points under unit k in the aggregation process. This represents the maximum load power of node n at time t among all data points under unit k; Let represent the predicted per-unit output of the photovoltaic unit at node n under the condition of the polymer unit k at time t. These are decision variables; the system needs to optimize ω to minimize the total cost. This represents the minimum predicted per-unit output of the photovoltaic unit at time t among all data points under the k-th aggregation unit at node n. This represents the minimum predicted per-unit output of the photovoltaic unit at time t among all data points under the k-th aggregation unit at node n; This represents the actual photovoltaic output of node n at time t under the k-th polymer unit. This represents the power of light discarded by the nth node at time t under the kth scene. This represents the installed capacity of the photovoltaic unit at node n; This represents the predicted per-unit output of the wind turbine at node n at time t under the conditions of the aggregation unit k. This represents the minimum prediction of the wind turbine at node n at time t under the aggregation unit k.

[0166] per unit output value This represents the maximum predicted per-unit output of the wind turbine at node n at time t under the k-th aggregation unit. This represents the actual wind power output of node n at time t under the k-th aggregation unit. This represents the wind curtailment power of the nth node at time t under the kth scenario. This represents the installed capacity of the wind turbine unit at node n.

[0167] In this embodiment of the invention, the pre-constructed constraints are subjected to constraint relaxation processing, specifically the temporal constraints. The temporal constraints are the time-related constraints f(u,v) in the pre-constructed constraints. t )=b t Other non-time-series constraints remain unchanged. Constraint relaxation is specifically achieved by setting a preset range to control the maximum and minimum values ​​of all data points in each category at each time point.

[0168] Step 1008: Construct a constraint relaxation programming model based on the preset objective function and the relaxed constraints.

[0169] In this embodiment of the invention, after the constraint relaxation process is completed on the pre-constructed constraint conditions, a new constraint relaxation programming model is constructed by combining the second time constraint range of the second constraint conditions and the preset objective function. The lower bound of the original programming problem can be obtained by solving the constraint relaxation programming model.

[0170] Step 1009: Solve the constraint relaxation programming model to obtain the second programming scheme and the total cost of the second programming scheme.

[0171] In this embodiment of the invention, solving the constraint relaxation programming model based on time-series aggregated data and constraint relaxation can effectively reduce the amount of data to be computed, thereby improving the solution speed of the model. Solving this constraint relaxation programming model yields a second programming scheme and its total cost. The total cost of the second programming scheme is the lower bound of the original programming problem.

[0172] Step 1010: Determine whether the preset objective function has converged based on the total cost of the first planning scheme, the total cost of the second planning scheme, and the preset convergence gap.

[0173] In this embodiment of the invention, by solving the above model, the upper and lower bounds of the original planning problem can be obtained. By comparing them with the preset convergence gap, it can be determined whether the objective function has converged, and thus whether it is necessary to continue iteratively solving.

[0174] As a preferred embodiment, determining whether the preset objective function has converged based on the total cost of the first planning scheme, the total cost of the second planning scheme, and the preset convergence gap includes:

[0175] Determining whether the preset objective function converges based on the total cost of the first planning scheme, the total cost of the second planning scheme, and the preset convergence gap includes:

[0176] Calculate the relative cost deviation based on the total cost of the first planning scheme and the total cost of the second planning scheme;

[0177] Compare the relative cost deviation with the size of the preset convergence gap;

[0178] When the relative cost deviation is less than the preset convergence gap, the preset objective function is determined to have converged.

[0179] When the relative cost deviation is greater than or equal to the preset convergence gap, it is determined that the preset objective function has not converged.

[0180] The relative cost deviation is calculated using the following formula:

[0181]

[0182] In the formula, gap represents the relative cost deviation; X1 represents the total cost of the first planning scheme; and X2 represents the total cost of the second planning scheme.

[0183] In this embodiment of the invention, calculating the relative cost deviation between the total cost of the first planning scheme and the total cost of the second planning scheme is equivalent to calculating the relative deviation between the upper and lower bounds of the original planning problem. Comparing this relative cost deviation with a preset convergence gap is equivalent to comparing the relative deviations of the upper and lower bounds with a specified convergence gap. When the relative cost deviation is less than the preset convergence gap, it is equivalent to the relative deviations of the upper and lower bounds being less than the specified convergence gap. At this point, it can be determined that the objective function has converged, and the final planning scheme can be determined based on the first and second planning schemes. However, when the relative cost deviation is greater than or equal to the preset convergence gap, it is determined that the objective function has not converged, and iterative solutions need to be performed on the full-time-series planning model and the constraint relaxation planning model to obtain the final planning scheme.

[0184] Step 1011: When the preset objective function converges, the final planning scheme is determined according to the first planning scheme and the second planning scheme; wherein, the final planning scheme includes the installed capacity of each unit and each energy storage device in the power system, and the line capacity of each line in the power system.

[0185] As a preferred embodiment, when the preset objective function converges, the final planning scheme is determined based on the first planning scheme and the second planning scheme, including:

[0186] In the first planning scheme, the first installed capacity of each unit and each energy storage device in the power system, as well as the first line capacity of each line in the power system, are determined.

[0187] The second planning scheme determines the second installed capacity of each unit and each energy storage device in the power system, as well as the second line capacity of each line in the power system;

[0188] The average value of each of the first installed capacity and each of the second installed capacity is calculated to obtain the installed capacity of each unit and each energy storage device in the power system;

[0189] The line capacity of each line in the power system is obtained by averaging the capacity of each of the first lines and the capacity of each of the second lines.

[0190] Based on the installed capacity of each generating unit and energy storage device in the power system, as well as the line capacity of each line in the power system, a final planning scheme is formed.

[0191] In this embodiment of the invention, when the objective function is determined to converge, the final planning scheme is obtained by averaging the first and second planning schemes. Specifically, for each generating unit and each energy storage device in the power system, the corresponding first installed capacity is obtained in the first planning scheme, and the corresponding second installed capacity is obtained in the second planning scheme. The installed capacity corresponding to the first and second installed capacities is obtained by averaging the first and second installed capacities to obtain the corresponding installed capacity of each generating unit and each energy storage device in the power system. For each line in the power system, the corresponding first line capacity is obtained in the first planning scheme, and the corresponding second line capacity is obtained in the second planning scheme. The line capacity corresponding to the first and second line capacities is obtained by averaging the first and second line capacities to obtain the corresponding line capacity of each line in the power system.

[0192] As a preferred embodiment, after determining that the preset objective function has not converged when the cost difference is greater than or equal to the preset convergence gap, the method further includes:

[0193] The number of clusters is increased cyclically, and cluster analysis is performed on the time-series running data based on the updated number of clusters to obtain updated time-series aggregated data. Based on the updated time-series aggregated data, the full-time-series planning model and the constraint relaxation planning model are solved respectively to obtain updated first planning scheme and updated second planning scheme. This process continues until the preset objective function converges. Finally, the planning scheme is obtained based on the updated first planning scheme and updated second planning scheme.

[0194] In this embodiment of the invention, when the objective function is determined not to have converged, it is necessary to increase the number of clusters, re-cluster the collected time-series running data to obtain updated time-series aggregated data, and solve the full-time-series programming model and the constraint relaxation programming model based on the updated time-series aggregated data to obtain updated first and second planning schemes. The difference between the total cost corresponding to the updated first and second planning schemes is calculated and compared with the preset convergence gap until the objective function converges. The final planning scheme is determined according to the first and second planning schemes corresponding to the convergence of the objective function.

[0195] As a preferred embodiment, when the preset objective function converges, after determining the final planning scheme based on the first planning scheme and the second planning scheme, the following steps are taken:

[0196] Based on the installed capacity of each generating unit and each energy storage device in the final planning scheme, the planning and adjustment of each generating unit and each energy storage device of the power system are carried out.

[0197] Based on the line capacity of each line in the final planning scheme, the planning of each line in the power system is adjusted.

[0198] In this embodiment of the invention, after the final planning scheme of the power system is determined, the power system's generating units and energy storage devices are planned and adjusted according to the installed capacity in the final planning scheme, and the power system's lines are planned and adjusted according to the line capacity in the final planning scheme.

[0199] See Figure 2 This is a flowchart illustrating another embodiment of the power system planning method based on time series aggregation and constraint relaxation provided by the present invention. First, considering economic, environmental, and safety indicators, a full-time-series planning model with an embedded 8760 hours is established. Time series aggregation is performed on the collected time-series operational data to form time-series aggregated data. An iterative solution model is then established based on this aggregated data. The upper bound of this iterative solution model is obtained through a two-stage solution: First, a time-series aggregated planning model is constructed based on the aggregated time series data. Solving this model yields the installed capacity planning result, including installed capacity and line capacity. This installed capacity planning result is then used as known parameters and substituted into the full-time-series planning model for operational simulation. The total cost obtained is the upper bound of the planning problem. The lower bound of the model is obtained by solving the constraint-relaxed planning model. Based on the obtained upper and lower bounds, the gap between them is calculated, and it is determined whether this gap satisfies the convergence condition, i.e., it is less than the specified convergence gap ε. If the convergence condition is not met, the number of aggregation scenarios for time series aggregation is increased, and the model is iterated until the requirement is met. If the convergence condition is met, the model solution is considered complete. The optimal planning value and installed capacity result are obtained based on the first planning result obtained from the upper bound of the calculation model and the second planning result obtained from the lower bound of the calculation model.

[0200] Implementing the above embodiments has the following effects:

[0201] This invention provides a power system planning method based on time series aggregation and constraint relaxation. The method involves: acquiring time-series operational data of the power system; determining a first constraint based on the time-series operational data and constructing a full-time-series planning model according to a preset objective function and the first constraint; performing cluster analysis on the time-series operational data to obtain time-series aggregated data and the number of clusters; determining a second constraint based on the time-series aggregated data and constructing a time-series aggregated planning model according to the preset objective function and the second constraint; solving the time-series aggregated planning model to obtain a first planning scheme; substituting the first planning scheme into the full-time-series planning model to obtain the total cost of the first planning scheme; performing constraint relaxation on the second constraint to obtain relaxed constraint conditions; constructing a constraint relaxation planning model according to the preset objective function and the relaxed constraint conditions; solving the constraint relaxation planning model to obtain a second planning scheme and the total cost of the second planning scheme; determining whether the preset objective function has converged based on the total cost of the first planning scheme, the total cost of the second planning scheme, and a preset convergence gap; and determining the final planning scheme based on the first and second planning schemes when the preset objective function has converged. This invention effectively reduces the amount of data computation in the model by aggregating time series data, thereby improving planning efficiency. Based on time series aggregation and constraint relaxation, upper and lower bounds of the model are formed respectively, avoiding difficulties in model convergence and effectively improving planning efficiency and accuracy.

[0202] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A power system planning method based on time series aggregation and constraint relaxation, characterized in that, include: Acquire time-series operation data of the power system; wherein, the time-series operation data includes node load, wind turbine output power and photovoltaic unit output power at several time points; The first constraint is determined based on the time-series running data, and a full-time-series planning model is constructed according to the preset objective function and the first constraint. Cluster analysis is performed on the time-series running data to obtain the time-series aggregated data and the number of clusters; The second constraint is determined based on the time-series aggregated data, and a time-series aggregated planning model is constructed according to the preset objective function and the second constraint. Solve the time-series aggregation programming model to obtain the first programming scheme; Substituting the first planning scheme into the full-time-series planning model, the total cost of the first planning scheme is obtained; The second constraint condition is relaxed to obtain the relaxed constraint condition. Based on the preset objective function and the relaxed constraints, a constraint relaxation programming model is constructed. Solve the constrained relaxation programming model to obtain the second programming scheme and the total cost of the second programming scheme; Determine whether the preset objective function converges based on the total cost of the first planning scheme, the total cost of the second planning scheme, and the preset convergence gap; When the preset objective function converges, a final planning scheme is determined based on the first planning scheme and the second planning scheme; wherein, the final planning scheme includes the installed capacity of each unit and each energy storage device in the power system, as well as the line capacity of each line in the power system.

2. The power system planning method based on time series aggregation and constraint relaxation according to claim 1, characterized in that, The preset objective function is: In the formula, C plan The total cost of the planned scheme is represented by g; g is the unit number, b is the energy storage device number, and l is the line number; N g N represents the number of generating units. b N represents the number of energy storage devices. l N represents the number of lines. T α represents the total duration of the time-series data execution. g Let α be the annualized investment cost per unit capacity of unit g; b α represents the annualized investment cost per unit capacity of energy storage device b. l The annualized investment cost per unit capacity of line l; O g The installed capacity of unit g; O b For energy storage device b, the installed capacity is O. l Let L be the line capacity of line l; β g The variable generation cost for g generating units; N i This represents the number of unit types after aggregation. The startup cost of the i-th type of polymerization unit; P represents the shutdown cost of the i-th type of polymerization unit; g,t Let g be the output power of unit g at time t; Let be the operating capacity of the i-th type of aggregation unit at time t; Let be the shutdown capacity of the i-th type of aggregation unit at time t.

3. The power system planning method based on time series aggregation and constraint relaxation according to claim 2, characterized in that, Determining the first constraint based on the time-series runtime data includes: Obtain pre-built constraints; A first time constraint range is constructed based on the time coverage range of the time-series running data; The first constraint condition is constructed based on the pre-constructed constraint condition and the first time constraint range; The pre-constructed constraints include upper and lower limits of equipment output and ramping constraints, node power balance constraints, new energy penetration rate constraints, unit combination constraints, new energy output constraints, and energy storage equipment operation constraints. The upper and lower limits of the equipment output and the ramping constraint are as follows: In the formula, κ u P represents the ramp rate of equipment u. u,t and P u,t+1 These represent the output power of device u at time t and time t+1, respectively; O u Let u be the capacity of the device; device u includes a generator set and an energy storage device; the node power balance constraint is: In the formula, and These represent the charging power and discharging power of the energy storage device, respectively; P ls,t and P le,t These represent the feed-out power and feed-in power of the node, respectively; Ψ n,g Ψ represents the unit g connected to node n; n,b Ψ represents the energy storage device b connected to node n. n,ls Ψ represents the feeder line ls connected to node n; n,le D represents the feed line le connected to node n; n,t This represents the load of node n at time t; This represents the load shedding at node n at time t; The constraint on the penetration rate of new energy sources is: In the formula, w and pv are the numbers of the wind turbine and photovoltaic unit, respectively; ξ is the minimum proportion of renewable energy generation; N n This represents the total number of nodes; The unit combination constraint is: In the formula, Ψ i,g Unit g; r belongs to the i-th type of aggregation unit. i,min The minimum output rate of the aggregation unit belonging to the i-th type; This represents the minimum start-up time for the i-th type of polymer unit; This represents the shortest shutdown time for the i-th type of polymer unit; Let be the online capacity of the i-th type of aggregation unit at time t; The constraint on the output of the new energy source is: In the formula, χ is the maximum wind and solar curtailment rate; Let w be the wind curtailment power of wind turbine w at time t; Let PV be the curtailment power of the photovoltaic unit at time t; For the predicted per-unit output of wind turbines and photovoltaic units; The operating constraints of the energy storage device are: In the formula, SOC b,t The state of charge of energy storage device b; η b The charging and discharging efficiency of energy storage device B; B b The energy storage duration of energy storage device b; SOC b,min This represents the minimum allowable power capacity of energy storage device b.

4. The power system planning method based on time series aggregation and constraint relaxation according to claim 3, characterized in that, The cluster analysis of the time-series runtime data to obtain the time-series aggregated data and the number of clusters includes: The k-means clustering method was used to perform cluster analysis on the time-series operating data to obtain several aggregated units and the number of clusters; For each aggregation unit, determine the cluster center and the number of scenarios corresponding to the aggregation unit; The data point with the closest Euclidean distance to the cluster center is used as the representative data of the scene. The weight of the data representing each scenario is determined based on the number of scenarios. The time-series aggregated data is determined based on the representative scenario data of each aggregation unit and the corresponding weights of the representative data of each scenario.

5. The power system planning method based on time series aggregation and constraint relaxation according to claim 4, characterized in that, The determination of the second constraint based on the time-series aggregated data includes: A second time constraint range is constructed based on the time coverage range of the time-series aggregated data; The second constraint is constructed based on the pre-constructed constraint and the second time constraint range.

6. The power system planning method based on time series aggregation and constraint relaxation according to claim 5, characterized in that, The process of relaxing the second constraint to obtain the relaxed constraint includes: Based on the preset constraint range, the temporal constraints in the pre-constructed constraint conditions are relaxed to form the processed constraint conditions. By combining the processed constraints and the pre-constructed constraints, relaxed constraints are formed. The post-processing constraints are as follows: In the formula, n represents the node number, k represents the aggregation unit number, and t represents the time point; D n,k,t This represents the load power of node n at time t under unit k. This represents the minimum load power of node n at time t among all data points under unit k in the aggregation process. This represents the maximum load power of node n at time t among all data points under unit k; Let represent the predicted per-unit output of the photovoltaic unit at node n under the condition of the polymer unit k at time t. This represents the minimum predicted per-unit output of the photovoltaic unit at time t among all data points under the k-th aggregation unit at node n. This represents the minimum predicted per-unit output of the photovoltaic unit at time t among all data points under the k-th aggregation unit at node n; This represents the actual photovoltaic output of node n at time t under the k-th polymer unit. This represents the power of light discarded by the nth node at time t under the kth scene. This represents the installed capacity of the photovoltaic unit at node n; This represents the predicted per-unit output of the wind turbine at node n at time t under the conditions of the aggregation unit k. Let represent the minimum predicted per-unit output of the wind turbine at node n under the condition of the aggregation unit k at time t. This represents the maximum predicted per-unit output of the wind turbine at node n at time t under the k-th aggregation unit. This represents the actual wind power output of node n at time t under the k-th aggregation unit. This represents the wind curtailment power of the nth node at time t under the kth scenario. This represents the installed capacity of the wind turbine unit at node n.

7. The power system planning method based on time series aggregation and constraint relaxation according to claim 1, characterized in that, The step of determining whether the preset objective function has converged based on the total cost of the first planning scheme, the total cost of the second planning scheme, and the preset convergence gap includes: Calculate the relative cost deviation based on the total cost of the first planning scheme and the total cost of the second planning scheme; Compare the relative cost deviation with the size of the preset convergence gap; When the relative cost deviation is less than the preset convergence gap, the preset objective function is determined to have converged. When the relative cost deviation is greater than or equal to the preset convergence gap, it is determined that the preset objective function has not converged. The relative cost deviation is calculated using the following formula: In the formula, gap represents the relative cost deviation; X1 represents the total cost of the first planning scheme; and X2 represents the total cost of the second planning scheme.

8. The power system planning method based on time series aggregation and constraint relaxation according to claim 7, characterized in that, When the preset objective function converges, determining the final planning scheme based on the first planning scheme and the second planning scheme includes: In the first planning scheme, the first installed capacity of each unit and each energy storage device in the power system, as well as the first line capacity of each line in the power system, are determined. The second planning scheme determines the second installed capacity of each unit and each energy storage device in the power system, as well as the second line capacity of each line in the power system; The average value of each of the first installed capacity and each of the second installed capacity is calculated to obtain the installed capacity of each unit and each energy storage device in the power system; The line capacity of each line in the power system is obtained by averaging the capacity of each of the first lines and the capacity of each of the second lines. Based on the installed capacity of each generating unit and energy storage device in the power system, as well as the line capacity of each line in the power system, a final planning scheme is formed.

9. The power system planning method based on time series aggregation and constraint relaxation according to claim 7, characterized in that, After determining that the preset objective function has not converged when the cost difference is greater than or equal to the preset convergence gap, the method further includes: The number of clusters is increased cyclically, and cluster analysis is performed on the time-series running data based on the updated number of clusters to obtain updated time-series aggregated data. Based on the updated time-series aggregated data, the full-time-series planning model and the constraint relaxation planning model are solved respectively to obtain updated first planning scheme and updated second planning scheme. This process continues until the preset objective function converges. Finally, the planning scheme is obtained based on the updated first planning scheme and updated second planning scheme.

10. The power system planning method based on time series aggregation and constraint relaxation according to claim 1, characterized in that, When the preset objective function converges, after determining the final planning scheme based on the first planning scheme and the second planning scheme, the process includes: Based on the installed capacity of each generating unit and each energy storage device in the final planning scheme, the planning and adjustment of each generating unit and each energy storage device of the power system are carried out. Based on the line capacity of each line in the final planning scheme, the planning of each line in the power system is adjusted.

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