Virtual power plant feasible region representation method and system considering space-time coupling constraints
By splitting the feasible region of a virtual power plant into temporally coupled and decoupled feasible regions, and using a progressive vertex enumeration algorithm for projection calculation, the accuracy and efficiency problems of virtual power plant feasible region representation under high-dimensional temporally coupled constraints are solved, and a more efficient virtual power plant aggregate feasible region representation is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI JIAOTONG UNIV
- Filing Date
- 2025-09-17
- Publication Date
- 2026-06-19
AI Technical Summary
Existing virtual power plant feasible domain characterization techniques cannot accurately and efficiently characterize the aggregated feasible domain of virtual power plants under high-dimensional time coupling constraints, resulting in limited flexibility and economic benefits in the market and dispatch.
The feasible region of the virtual power plant is split into a time-coupled feasible region and a time-decoupled feasible region. An incremental vertex enumeration algorithm is used to project and calculate the aggregated power and key variables. The dimensionality is reduced by the principle of energy consistency. Finally, the intersection is taken to obtain the accurate aggregated feasible region of the virtual power plant.
Without compromising model accuracy, computational complexity is significantly reduced, enabling accurate characterization of the high-dimensional temporal coupling and network topology constraints of virtual power plants, thereby improving market and scheduling flexibility and economic efficiency.
Smart Images
Figure CN121146429B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of virtual power plant technology, and more specifically to a method and system for characterizing the feasible domain of a virtual power plant that considers spatiotemporal coupling constraints. Background Technology
[0002] With the development of new energy technologies, distributed energy resources (DERs) such as wind power, photovoltaics, energy storage and flexible loads are being connected to the power grid on a large scale. Their heterogeneity, dispersion and uncertainty pose severe challenges to power system dispatch and market transactions.
[0003] Virtual Power Plants (VPPs) aggregate massive amounts of DERs into a unified, dispatchable entity through clustering technology, significantly reducing management complexity and enabling them to participate in the energy market as a whole, providing electricity and ancillary services such as frequency regulation and backup, thereby improving system flexibility and economy.
[0004] In order to make effective market trading strategies and operational scheduling decisions, VPP operators must accurately describe the overall operational capability boundaries of the aggregated DERs, that is, to achieve Feasible Region Characterization (FRC).
[0005] Since the operating characteristics of common DERs such as wind power, photovoltaics, and flexible loads can usually be described by linear constraints, theoretically, the aggregate feasible region of a VPP can be represented as a high-dimensional convex polyhedron in multidimensional space. In general, existing FRC methods are mainly divided into two categories: The first category is based on exact solutions, such as using algorithms like Progressive Vertex Enumeration (PVE) to accurately solve for all vertices of the convex polyhedron, theoretically obtaining the most accurate feasible region representation. The second category is based on approximate solutions, which approximate the original feasible region by solving for the parameters of a pre-defined normalized shape template (such as a hypercube, fixed convex polyhedron, chino polyhedron, virtual generator-virtual battery model, hyperellipsoid, etc.).
[0006] For the first type of method, with the widespread application of energy storage-type DERs in VPPs, the temporal coupling characteristics of their charge and discharge states significantly increase the spatial dimensionality and complexity of the feasible region. The computation time of the PVE algorithm is mainly determined by the Quickhull algorithm for generating the convex hull, and the computational complexity of this algorithm increases exponentially with the spatial dimensionality of the feasible region. Industry consensus holds that PVE is only suitable for low-dimensional (e.g., 6 dimensions and below) feasible region calculations and cannot effectively handle the problem of solving for out-of-feasibility characteristics of VPPs, such as energy storage, which exhibits operational coupling characteristics throughout a complete charge-discharge cycle (the charge-discharge cycle of electrochemical energy storage is typically 24 hours).
[0007] For the second type of method, although it effectively avoids the computational complexity caused by high-dimensional temporal coupling by using a pre-defined shape template, and can handle the difficult problem of solving the out-of-domain characteristics of VPPs containing energy storage, its core problem lies in the fact that pre-setting the shape of the feasible domain introduces huge approximation errors. The pre-defined simplified geometry (such as hypercubes, ellipsoids, etc.) is difficult to accurately match the complex boundaries of the actual VPP feasible domain (usually an irregular high-dimensional polyhedron). In addition, the VPP feasible domain often contains both temporal coupling constraints and network topology constraints (such as line capacity, node voltage limits, etc.), making its accurate representation problem essentially an NP-hard problem, further increasing the difficulty of accurate representation.
[0008] In summary, existing VPP feasible region characterization techniques face a core contradiction: on the one hand, precise methods (PVE) cannot be extended to real-world scenarios with energy storage and high-dimensional temporal coupling. On the other hand, while approximate methods are computationally feasible, their insufficient accuracy leads to overly conservative characterization results (significantly underestimating the feasible region or distorting its shape). This conservatism directly reduces the flexibility potential of VPP in the market and scheduling, limiting its full realization of economic benefits and system support capabilities.
[0009] Therefore, how to accurately and efficiently characterize the feasible domain of virtual power plant aggregation under high-dimensional time coupling constraints has become a key technical bottleneck that urgently needs to be overcome in this field. Summary of the Invention
[0010] The main objective of this invention is to provide a method and system for characterizing the feasible region of a virtual power plant considering spatiotemporal coupling constraints, aiming to solve the problem of how to accurately and efficiently characterize the aggregated feasible region of a virtual power plant under high-dimensional temporal coupling constraints.
[0011] The technical solution proposed in this invention is as follows:
[0012] A method for representing the feasible region of a virtual power plant considering spatiotemporal coupling constraints, applied to a virtual power plant feasible region representation system considering spatiotemporal coupling constraints; the method includes:
[0013] The original feasible region of the virtual power plant is split into a time-coupled feasible region and a time-decoupled feasible region. The time-coupled feasible region contains only time-coupled variables and time-coupled constraints, while the time-decoupled feasible region is the union of multiple low-dimensional decoupled feasible regions.
[0014] Based on the principle of energy consistency, the dimensionality of time-coupled variables is reduced, and time-coupled variables are extracted as key variables for the low-dimensional decoupling feasible domain.
[0015] An incremental vertex enumeration algorithm is used to project and calculate the aggregate power and key variables to obtain an external characteristic representation of the low-dimensional decoupling feasible domain that takes into account the key variables.
[0016] The intersection of the time-decoupled feasible region calculated by projection and the time-coupled feasible region is used to obtain the virtual power plant aggregated feasible region.
[0017] Preferably, the step of splitting the original feasible region of the virtual power plant into a time-coupled feasible region and a time-decoupled feasible region includes:
[0018] The original high-dimensional feasible region Projected onto the low-dimensional feasible region ,in, and They are represented as follows:
[0019] (1),
[0020] (2),
[0021] In the formula, For decision variables without time coupling constraints, These are decision variables with time coupling constraints; For the aggregated active power of the virtual power plant, The reactive power of the virtual power plant; , , , , , , , , , and It is a coefficient matrix and Let be the parameter matrix of the equivalent feasible region to be solved.
[0022] Preferably, the time coupling feasible region for:
[0023] (3),
[0024] The feasible region of time decoupling for:
[0025] (4),
[0026] In the formula, satisfying .
[0027] Preferably, the step of splitting the original feasible region of the virtual power plant into a time-coupled feasible region and a time-decoupled feasible region further includes:
[0028] Determine the energy state of energy storage :
[0029] (5),
[0030] In the formula, The charging efficiency represents the energy storage capacity. Represents the discharge efficiency of energy storage; The charging power representing energy storage, Represents the discharge power of energy storage; Represents the capacity of energy storage; Represents a time interval;
[0031] Introduce independent dummy variables into formula (5) To replace the coupled variables in the decoupled feasible region, so as to decouple the entire time domain time in the feasible region. Described as:
[0032] (6),
[0033] In the formula, Represents virtual energy storage variables over T time periods The set, , and The meaning is defined by formula (5); It can be represented as the union of T low-dimensional feasible regions:
[0034] (7).
[0035] Preferably, the step of projecting the aggregate power and key variables using a progressive vertex enumeration algorithm to obtain an external characteristic representation of the low-dimensional decoupling feasible domain considering the key variables includes:
[0036] Expand the projection variable to [ , , ], to describe the projection problem as projection arrive ,in, Described as:
[0037] (8),
[0038] In the formula, The time coupling variable between energy storage and the gas turbine is expressed as: ; Representing the output of the gas turbine, the time-coupled constraint of the gas turbine is represented as a ramp constraint: ; This indicates the lower limit of the gas turbine's gradeability. This indicates the upper limit of the gas turbine's ramp rate; and They are The coefficient matrix.
[0039] Preferably, the projection variable is expanded to [ , , ], to describe the projection problem as projection arrive And then it includes:
[0040] The constraints described in formulas (9) and (10) are applied to the energy storage and gas turbine respectively to ensure that different energy storage units and gas turbine units have common energy characteristics:
[0041] (9),
[0042] (10)
[0043] In the formula, This represents the aggregate of energy storage within a virtual power plant; This represents the collection of gas turbines within a virtual power plant. Representing the k An energy storage in t The state of charge at any given moment; Representing the l A gas turbine in t Output power at any given moment; Representing the l A gas turbine in t The upper limit of output power at any given time; Indicates energy storage Consistent variables, Indicates gas turbine Consistency variables.
[0044] Preferably, the constraint described in formulas (9) and (10) is applied to the energy storage and gas turbine respectively to ensure that different energy storage units and gas turbine units have common energy characteristics, and then the process further includes:
[0045] The new key projection variable is represented as: In the formula, Represents virtual energy storage Consistent variables;
[0046] Projecting the new key variables The expression is as follows:
[0047] (11),
[0048] In the formula, The dimension of the projected variables at each time step is 5, and the solution is obtained precisely using an asymptotic vertex enumeration algorithm. coefficient matrix and ; This represents the active power of the virtual power plant at the common coupling node. This represents the reactive power of the virtual power plant at the common coupling node.
[0049] Preferably, the step of taking the intersection of the time-decoupling feasible region and the time-coupling feasible region after projection calculation to obtain the virtual power plant aggregated feasible region includes:
[0050] Will and The union of the sets is used to recover the time coupling constraints, thus obtaining the equivalent feasible region that takes into account the key variables. :
[0051] (12)
[0052] In the formula, The upper limit of the output power of the gas turbine at time t represents the uniformity variable. Represents a set of times. ; t represents the time index; This represents the energy state of the energy storage consistency variable at the initial time 0. This represents the energy state of the energy storage consistency variable at the end time T; express The set value, express The set value.
[0053] This invention also proposes a virtual power plant feasible region characterization system that considers spatiotemporal coupling constraints, and applies a virtual power plant feasible region characterization method that considers spatiotemporal coupling constraints.
[0054] The above technical solution can achieve the following beneficial effects:
[0055] This invention proposes a feasible domain representation method for virtual power plants considering spatiotemporal coupling constraints. It presents a full-time-domain feasible domain characterization scheme for virtual power plants based on considering both temporal coupling and network topology constraints. This feasible domain characterization method can decouple the original high-dimensional temporally coupled operating domain into multiple low-dimensional temporally decoupled operating domains without reducing model accuracy, significantly reducing the computational complexity of the convex hull algorithm. Compared to existing feasible domain characterization methods capable of solving the full-time-domain feasible domain, the proposed method can adapt to the full-time-domain modeling needs of virtual power plants with different types of temporally coupled devices, such as distributed energy storage and micro gas turbines. Furthermore, the proposed method can adapt to the full-time-domain modeling needs of virtual power plants with network topology constraints, and the characterized equivalent operating domain can more accurately restore the temporal coupling characteristics and network topology constraints of the original operating domain. In other words, this scheme can accurately and efficiently characterize the aggregated feasible domain of virtual power plants. Attached Figure Description
[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.
[0057] Figure 1 This is a flowchart illustrating the first embodiment of a virtual power plant feasible domain characterization method considering spatiotemporal coupling constraints proposed in this invention.
[0058] Figure 2 The virtual power plant test system used in the eighth embodiment of the virtual power plant feasible domain characterization method considering spatiotemporal coupling constraints proposed in this invention adopts the IEEE 33-node topology. Detailed Implementation
[0059] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.
[0060] This invention proposes a method and system for characterizing the feasible domain of a virtual power plant that considers spatiotemporal coupling constraints.
[0061] As attached Figure 1As shown, in the first embodiment of the virtual power plant feasible region characterization method considering spatiotemporal coupling constraints proposed in this invention, this virtual power plant feasible region characterization method considering spatiotemporal coupling constraints is applied to a virtual power plant feasible region characterization system considering spatiotemporal coupling constraints; this embodiment includes the following steps:
[0062] Step S110: Split the original feasible region of the virtual power plant into a time-coupled feasible region and a time-decoupled feasible region. The time-coupled feasible region contains only time-coupled variables and time-coupled constraints, and the time-decoupled feasible region is the union of multiple low-dimensional decoupled feasible regions.
[0063] Specifically, to address the issue of high time dimension, the original feasible domain of the virtual power plant is first split into a time-coupled feasible domain and a time-decoupled feasible domain.
[0064] Step S120: Based on the principle of energy consistency, reduce the dimensionality of time-coupled variables, and extract time-coupled variables as key variables for the low-dimensional decoupling feasible domain.
[0065] Step S130: The progressive vertex enumeration algorithm (PVE algorithm) is used to project the aggregate power and key variables to obtain the external characteristic representation of the low-dimensional decoupling feasible domain considering the key variables.
[0066] Step S140: Take the intersection of the time decoupling feasible region and the time coupling feasible region after projection calculation to obtain the virtual power plant aggregated feasible region.
[0067] This invention proposes a feasible domain representation method for virtual power plants considering spatiotemporal coupling constraints; it presents a full-time-domain feasible domain characterization scheme for virtual power plants based on considering temporal coupling constraints and network topology constraints; this feasible domain characterization method can decouple the original high-dimensional temporally coupled operating domain into multiple low-dimensional temporally decoupled operating domains without reducing model accuracy, significantly reducing the computational complexity of the convex hull algorithm; compared with existing feasible domain characterization methods that can solve the full-time-domain feasible domain, the feasible domain characterization method proposed in this application can adapt to the full-time-domain modeling needs of virtual power plants with different types of temporally coupled devices, such as distributed energy storage, micro gas turbines, etc.; compared with existing feasible domain characterization methods that can solve the full-time-domain feasible domain, the feasible domain characterization method proposed in this application can adapt to the full-time-domain modeling needs of virtual power plants with network topology constraints, and the characterized equivalent operating domain can more accurately restore the temporal coupling characteristics and network topology constraints of the original operating domain; that is, this scheme can accurately and efficiently characterize the aggregated feasible domain of virtual power plants.
[0068] Specifically, for the problem of solving the aggregate feasible region of a virtual power plant with energy storage temporal coupling constraints and network topology constraints, this invention proposes a full-time-domain virtual power plant feasible region solution method embedding a reversible decoupled projection mechanism. First, a reversible decoupled projection mechanism is proposed to reduce the spatial dimension of the feasible region, slicing the original feasible region into a union of multiple low-dimensional feasible regions without disrupting the temporal coupling structure. Second, a projection format based on the energy consistency principle is used to perform parallel projection on the aggregate external characteristics of the sliced low-dimensional feasible regions. Third, the temporal coupling constraints between the sliced feasible regions are restored, reconstructing the temporal coupling characteristics of the feasible region.
[0069] In the second embodiment of the virtual power plant feasible domain characterization method considering spatiotemporal coupling constraints proposed in this invention, based on the first embodiment, step S110 includes the following steps before:
[0070] Step S210: Transform the original high-dimensional feasible region Projected onto the low-dimensional feasible region ,in, and They are represented as follows:
[0071] (1),
[0072] (2),
[0073] In the formula, For decision variables without time coupling constraints, These are decision variables with time coupling constraints; For the aggregated active power of the virtual power plant, The reactive power of the virtual power plant; , , , , , , , , , and It is a coefficient matrix and Let be the parameter matrix of the equivalent feasible region to be solved.
[0074] Specifically, and This represents the network topology constraints within the feasible domain; the existence of network constraints creates spatial coupling relationships between the operational domains of various distributed resources. The overall operational domain of the virtual power plant is no longer a simple summation of the individual operational domains of each distributed resource.
[0075] Specifically, the feasible region representation of the virtual power plant is essentially a projection calculation of the original feasible region. By eliminating excessive information in the original high-dimensional feasible region, a low-dimensional feasible region containing only boundary variables is formed.
[0076] In the third embodiment of the virtual power plant feasible region characterization method considering spatiotemporal coupling constraints proposed in this invention, based on the second embodiment, the time-coupled feasible region... for:
[0077] (3),
[0078] The feasible region of time decoupling for:
[0079] (4),
[0080] In the formula, satisfying .
[0081] Specifically, firstly Constraints and variables with temporal coupling are identified and decoupled, such as... As shown, Representing time-coupled variables, constraints that have a time-coupled relationship and contain only time-coupled variables are described as follows: Therefore, we split the original feasible region into a time-decoupled feasible region. Feasible region with time coupling Through this splitting, it becomes possible to... The time coupling characteristic is no longer present, so the feasible region can be computed in parallel at each time step.
[0082] In the fourth embodiment of the virtual power plant feasible domain characterization method considering spatiotemporal coupling constraints proposed in this invention, based on the third embodiment, step S110 is followed by the following steps:
[0083] Step S410: Determine the energy state of the stored energy :
[0084] (5),
[0085] In the formula, The charging efficiency represents the energy storage capacity. Represents the discharge efficiency of energy storage; The charging power representing energy storage, Represents the discharge power of energy storage; Represents the capacity of energy storage; This represents a time interval, typically 1 hour.
[0086] Specifically, The resulting feasible region is very simple and can be directly connected to... The original feasible region is obtained by intersecting the calculated feasible regions. However, this split will invalidate the power-energy coupling relationship of energy storage in formula (5). To solve this problem, the following steps are performed.
[0087] Step S420: Introduce independent dummy variables into formula (5) To replace the coupling variables in the decoupled feasible region, the introduction of this dummy variable ensures that the feasible regions at each time step are independent after decoupling. This thus decouples the feasible region across the entire time domain. Described as:
[0088] (6),
[0089] In the formula, Represents virtual energy storage variables over T time periods The set, , and The meaning is defined by formula (5); It can be represented as the union of T low-dimensional feasible regions:
[0090] (7).
[0091] In the fifth embodiment of the virtual power plant feasible domain characterization method considering spatiotemporal coupling constraints proposed in this invention, based on the fourth embodiment, step S130 includes the following steps:
[0092] Step S510: Expand the projection variable to [ , , ], to describe the projection problem as projection arrive ,in, Described as:
[0093] (8),
[0094] In the formula, The time coupling variable between energy storage and the gas turbine is expressed as: ; Representing the output of the gas turbine, the time-coupled constraint of the gas turbine is represented as a ramp constraint: ; This indicates the lower limit of the gas turbine's gradeability. This indicates the upper limit of the gas turbine's ramp rate; and They are The coefficient matrix.
[0095] Specifically, Each time step in the problem can be solved independently, simplifying the original problem. However, traditional methods for calculating the feasible region only project the aggregate power, such as... Projected to The resulting feasible region only contains aggregate power variables and cannot be compared with... The time-coupling variables in the data intersect. To address this issue, a method considering the key variable (the time-coupling variable between energy storage and the gas turbine) is proposed. The projection of ) adds a projection dimension, but this operation does not affect [ , The feasible domain of ].
[0096] In the sixth embodiment of the virtual power plant feasible domain characterization method considering spatiotemporal coupling constraints proposed in this invention, based on the fifth embodiment, step S510 is followed by the following steps:
[0097] Step S610: Apply the constraints described in formulas (9) and (10) to the energy storage and gas turbine respectively to ensure that different energy storage units and gas turbine units have common energy characteristics:
[0098] (9),
[0099] (10)
[0100] In the formula, This represents the aggregate of energy storage within a virtual power plant; This represents the collection of gas turbines within a virtual power plant. Representing the k An energy storage in t The state of charge at any given moment; Representing the l A gas turbine in t Output power at any given moment; Representing the l A gas turbine in t The upper limit of output power at any given time; Indicates energy storage Consistent variables, Indicates gas turbine Consistency variables.
[0101] Specifically, regarding the above constraints, the high-dimensionality problem of the projected variables still exists if the energy consistency constraint is not applied. To reduce the projection difficulty, the consistency constraint is introduced to reduce the number of projected variables, but this reduces the feasible region to some extent. However, since the constraint is introduced on the basis of the original feasible region, the feasible region after applying this constraint is an inner approximation of the original feasible region, which can guarantee the feasibility of the operating domain.
[0102] Specifically, due to All constraints are linear, therefore the PVE algorithm can be used to solve them precisely. and However, without additional constraints, The variables included in the projection variables encompass all time-coupled variables of all gas turbines and energy storage in the virtual power plant. The dimensionality of the projected variables remains high, therefore step S610 above is performed.
[0103] Specifically, by applying constraint equations (9) and (10), energy storage and gas turbines with the same time step have the same energy characteristics, thereby reducing the number of key variables to three.
[0104] In the seventh embodiment of the virtual power plant feasible domain characterization method considering spatiotemporal coupling constraints proposed in this invention, based on the sixth embodiment, step S610 is followed by the following steps:
[0105] Step S710: Represent the new key projection variable as follows: In the formula, Represents virtual energy storage Consistent variables;
[0106] Step S720: Projecting the new key variables The expression is as follows:
[0107] (11),
[0108] In the formula, The dimension of the projected variables at each time step is 5, and the solution is obtained precisely using an asymptotic vertex enumeration algorithm. coefficient matrix and ; This represents the active power of the virtual power plant at the common coupling node. This represents the reactive power of the virtual power plant at the common coupling node.
[0109] In the eighth embodiment of the virtual power plant feasible domain characterization method considering spatiotemporal coupling constraints proposed in this invention, based on the seventh embodiment, step S140 includes the following steps:
[0110] Step S810: ... and The union of the sets is used to recover the time coupling constraints, thus obtaining the equivalent feasible region that takes into account the key variables. :
[0111] (12)
[0112] In the formula, The upper limit of the output power of the gas turbine at time t represents the uniformity variable. Represents a set of times. ; t represents the time index; This represents the energy state of the energy storage consistency variable at the initial time 0. This represents the energy state of the energy storage consistency variable at the end time T; express The set value, express The set value.
[0113] Specifically, since increasing the dimension of the projection variable does not affect [ , The feasible region of ], therefore middle[ , The feasible domain and middle[ , The feasible domains of ] are completely equivalent.
[0114] In the eighth embodiment of this invention, the accuracy of the proposed scheme in characterizing the virtual power plant operating domain was verified on an improved IEEE 33-node test system, with time scales selected as T=6, T=12, and T=24, respectively. The virtual power plant system includes 3 distributed photovoltaic units, 6 distributed wind power units, 10 gas turbines, and 10 distributed energy storage units.
[0115] In the virtual power plant system, photovoltaic units are connected to nodes 4, 5, and 7 respectively; distributed wind power is integrated at nodes 11, 15, 19, 24, 28, and 32; gas turbine units and static var compensator units are connected to nodes 3, 5, 9, 12, 14, 16, 19, 21, 26, and 29 respectively; and energy storage is deployed at nodes 5, 7, 11, 14, 19, 21, 26, 28, 30, 31, and 33.
[0116] The daily power load forecast data for the virtual power plant comes from publicly available datasets from the EU and neighboring regions. The virtual power plant test system adopts an IEEE 33-node topology, as shown in the attached diagram. Figure 2 As shown. All algorithms were developed using MATLAB R2023a and the commercial optimization solver GUROBI, and executed on a PC platform with 16GB RAM and an Intel Core i7-12700H CPU (2.70GHz).
[0117] To verify the accuracy of the proposed scheme for virtual power plants, this application compares and analyzes the widely used FRC method (M1) based on virtual energy storage and the FRC method (M2) based on PVE with the proposed scheme (M3).
[0118] Select the average objective function error and average optimal solution error As a comparative analysis metric, the above methods were used to perform aggregate analysis on the operating domains at T=6, T=12, and T=24, respectively. The computational efficiency and accuracy results of the three methods are summarized in Table 1.
[0119] Specifically, both M1 and M3 can achieve internal approximation of the feasible region, ensuring that all solutions within their equivalent feasible region are feasible. However, compared to M3, the average error of the objective function of M1 across the three time scales is calculated as (-0.2154-0.1799-0.1435) / 3=0.1796 and (-1.8451e-4-6.5043e-4-4.6456e-4) / 3=4.3317e-4, representing a reduction of three orders of magnitude in error.
[0120] Furthermore, the average error of the optimal solution M3 across the three time scales is (0.5528+0.7081+0.7089) / 3=0.6566 and (0.0309+0.0813+0.0628) / 3=0.0583, which is an order of magnitude smaller than that of M1. Although M2 exhibits a relatively small FR error, it does not take into account the time coupling constraint, leading to its... If the value is positive, an infeasible point will appear.
[0121]
[0122] Table 1 - Verification Table of Computational Efficiency and Accuracy
[0123] This invention also proposes a virtual power plant feasible region characterization system that considers spatiotemporal coupling constraints, and applies a virtual power plant feasible region characterization method that considers spatiotemporal coupling constraints.
[0124] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.
[0125] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.
Claims
1. A method for representing the feasible region of a virtual power plant considering spatiotemporal coupling constraints, characterized in that, A method applied to a virtual power plant feasible domain characterization system considering spatiotemporal coupling constraints; the method includes: The original feasible region of the virtual power plant is split into a time-coupled feasible region and a time-decoupled feasible region. The time-coupled feasible region contains only time-coupled variables and time-coupled constraints, while the time-decoupled feasible region is the union of multiple low-dimensional decoupled feasible regions. Based on the principle of energy consistency, the dimensionality of time-coupled variables is reduced, and time-coupled variables are extracted as key variables for the low-dimensional decoupling feasible domain. An incremental vertex enumeration algorithm is used to project and calculate the aggregate power and key variables to obtain an external characteristic representation of the low-dimensional decoupling feasible domain that takes into account the key variables. The intersection of the time-decoupled feasible region calculated by projection and the time-coupled feasible region is used to obtain the virtual power plant aggregated feasible region. The process of splitting the original feasible region of the virtual power plant into a time-coupled feasible region and a time-decoupled feasible region includes the following: The original high-dimensional feasible region is projected to a low-dimensional feasible region where, and are expressed as: （1）， （2）， In the formula, For decision variables without time coupling constraints, These are decision variables with time coupling constraints; For the aggregated active power of the virtual power plant, The reactive power of the virtual power plant; , , , , , , , , , and It is a coefficient matrix; and Let be the parameter matrix of the equivalent feasible region to be solved; The time coupling feasible region for: （3）， The time decoupled feasible region Is: （4）， In the formula, the following are satisfied ; The process of splitting the original feasible region of the virtual power plant into a time-coupled feasible region and a time-decoupled feasible region further includes: Determining state of charge of energy storage : （5）， In the formula, The charging efficiency represents the energy storage capacity. Represents the discharge efficiency of energy storage; The charging power representing energy storage, Represents the discharge power of energy storage; Represents the capacity of energy storage; Represents a time interval; Introduce independent dummy variables into formula (5) To replace the coupled variables in the decoupled feasible region, so as to decouple the entire time domain time in the feasible region. Described as: （6）， In the formula, Represents virtual energy storage variables over T time periods The set, , and The meaning is defined by formula (5); It can be represented as the union of T low-dimensional feasible regions: （7）。 2. The virtual power plant feasible region representation method considering space-time coupling constraints according to claim 1, characterized in that, The method employs a progressive vertex enumeration algorithm to project and calculate the aggregate power and key variables, thereby obtaining an external characteristic representation of the low-dimensional decoupling feasible domain considering the key variables. This includes: Expand the projection variable to [ , , ], to describe the projection problem as projection arrive ,in, Described as: （8）， In the formula, The time coupling variable between energy storage and the gas turbine is expressed as: ; Representing the output of the gas turbine, the time-coupled constraint of the gas turbine is represented as a ramp constraint: ; This indicates the lower limit of the gas turbine's gradeability. This indicates the upper limit of the gas turbine's ramp rate; and They are The coefficient matrix.
3. The method for representing the feasible region of a virtual power plant considering spatiotemporal coupling constraints according to claim 2, characterized in that, The expansion of the projection variable to [ , , ], to describe the projection problem as projection arrive And then it includes: The constraints described in formulas (9) and (10) are applied to the energy storage and gas turbine respectively to ensure that different energy storage units and gas turbine units have common energy characteristics: （9）， （10）， In the formula, This represents the aggregate of energy storage within a virtual power plant; This represents the collection of gas turbines within a virtual power plant. Representing the k An energy storage in t The state of charge at any given moment; Representing the l A gas turbine in t Output power at any given moment; Representing the l A gas turbine in t The upper limit of output power at any given time; Indicates energy storage Consistent variables, Indicates gas turbine Consistency variables.
4. The virtual power plant feasible region representation method considering space-time coupling constraints according to claim 3, characterized in that, The constraints described in formulas (9) and (10) are applied to the energy storage and gas turbine respectively to ensure that different energy storage units and gas turbine units have common energy characteristics, and then the following is also included: The new key projection variable is represented as: In the formula, Represents virtual energy storage Consistent variables; Projecting the new key variable is expressed as: （11）， In the formula, The dimension of the projected variables at each time step is 5, and the solution is obtained precisely using an asymptotic vertex enumeration algorithm. coefficient matrix and ; This represents the active power of the virtual power plant at the common coupling node. This represents the reactive power of the virtual power plant at the common coupling node.
5. The virtual power plant feasible region representation method considering space-time coupling constraints according to claim 4, characterized in that, The step of taking the intersection of the time-decoupled feasible region and the time-coupled feasible region after projection calculation to obtain the virtual power plant aggregated feasible region includes: Take with the union to recover the time coupling constraints to get the equivalent feasible region taking into account the key variables : （12）， In the formula, The upper limit of the output power of the gas turbine at time t represents the uniformity variable. Represents a time set, ; t represents the time index; This represents the energy state of the energy storage consistency variable at the initial time 0. This represents the energy state of the energy storage consistency variable at the end time T; express The set value, express The set value; This represents the energy state of the energy storage consistency variable at time t-1. This represents the energy state of the energy storage consistency variable at time t.