A virtual power plant dynamic support capacity quantification and boundary calculation method based on inverse optimization

Abstract

The application discloses a kind of virtual power plant dynamic support capacity quantification and boundary measurement method based on inverse optimization, it is related to power system operation and control field, first, the physical model of virtual power plant multi-time period dynamic optimal power flow based on second-order cone relaxation is constructed;Second, with the minimum of virtual power plant grid connection point limited measurement data residual as the goal, a composite inverse optimization model containing feasible region compactness penalty is constructed;Then, using the asymmetric moving average sequential updating algorithm with attenuation, the equivalent power boundary and virtual energy capacity of the system are accurately inversed from multi-scenario operation data;Finally, the target response time length is explicitly introduced, and the state-dependent dynamic flexibility envelope considering instantaneous energy state constraints is constructed.The application overcomes the limitation of bottom-layer parameter black box, and quantifies the dynamic support potential of virtual power plant under multi-time scale in detail, providing a defense over-limit decision basis for safe dispatch.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control, specifically a method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization. Background Technology

[0002] Driven by the "dual carbon" goal, the penetration rate of massive heterogeneous distributed resources such as photovoltaics, energy storage, and flexible loads on the user side is rapidly increasing. To fully tap the regulation potential of these dispersed resources, virtual power plants (VPS) have emerged as an advanced Internet of Things (IoT) and aggregation technology. By breaking down physical geographical boundaries, VPS aggregates massive distributed resources into a single logical entity, representing its participation in active grid dispatch and electricity market transactions. However, in practical engineering applications, because the underlying devices aggregated by VPS often belong to different stakeholders and communication monitoring blind spots exist, the aggregated power, actual energy capacity, and internal network constraints within these massive distributed flexible resources exhibit significant "non-transparent" characteristics that are not directly observable.

[0003] Currently, when virtual power plants participate in grid dispatch and market bidding, the assessment and control of their active support capabilities face two major technical bottlenecks: First, the underlying resource status is highly variable and the internal parameters are "black boxes," making it difficult to accurately assess the true external support boundaries of virtual power plants through traditional forward modeling. Second, existing capacity quantification methods often deviate from the dynamic temporal characteristics of the underlying physical operation and ignore the dynamic constraints of the system's instantaneous energy state on power output. This makes it easy for virtual power plants to overestimate their capabilities and exceed energy dissipation limits when reporting or executing long-term dispatch instructions, which in turn can lead to market defaults or grid operation risks.

[0004] Prior art 1 (Patent Publication No.: CN112052543A) discloses a guaranteed grid search modeling method based on mixed-integer second-order cone programming. This invention establishes node power balance constraints based on the power flow equations of the power system and performs second-order cone optimization relaxation on the model, thereby improving the speed and accuracy of the guaranteed grid search. However, this method has obvious engineering limitations: it is essentially still within the scope of traditional modeling, and the construction and solution of the model are highly dependent on the precise known parameters of the power grid topology, line impedance, and unit output. In virtual power plants with a high proportion of distributed resources, the actual operating boundaries and aggregate parameters of massive flexible resources are often unknown or opaque. Traditional forward models cannot obtain the real physical operating boundaries without a precise underlying data foundation, making this method ineffective for quantifying the dynamic support capabilities of virtual power plants with unknown underlying parameters.

[0005] Prior art 2 (patent publication number: CN116957295A) discloses a cooperative planning method for the reliability of a distribution area-microgrid based on a mixed integer second-order cone model. This invention treats the microgrid as a special node within the distribution area to establish an equivalent power model. However, in grid-connected operation mode, the equivalent node power is directly calculated statically using the "annual average" of photovoltaic, wind, and load power within the microgrid. The drawback of this method is that it uses a long-term static average, completely obliterating the dynamic fluctuation characteristics of distributed flexibility resources on a short time scale. More importantly, this equivalent model only considers absolute power balance, severely deviating from the instantaneous state-of-charge constraints of key flexibility equipment such as energy storage and the cross-time-series coupling characteristics of "power-energy." When a virtual power plant performs actual intraday or real-time active support tasks, if the constraint of energy dissipation on power output capacity is ignored, the actual support capacity of the system is prone to a precipitous drop due to "energy depletion" or "battery overcharging," triggering the risk of grid dispatch exceeding limits.

[0006] Existing technologies either rely on static forward models with completely known parameters or employ macroscopic average equivalent methods that ignore dynamic characteristics. These approaches fail to achieve deep integration of data and underlying physical mechanisms in virtual power plant environments where underlying parameters are not transparent. Therefore, a dynamic support capability quantification method is needed that can inversely retrieve underlying equivalent parameters from limited macroscopic observation data and closely integrate with the real-time energy state of the equipment. Summary of the Invention

[0007] The purpose of this invention is to address the problems in the prior art by providing a method for quantifying and calculating the dynamic support capacity and boundaries of a virtual power plant based on inverse optimization. This method integrates data-driven approaches with a physical underlying model. By constructing a composite inverse optimization model and a sequential update algorithm, it accurately inverts the equivalent operating parameters of the system from limited grid-connected point observation data. Furthermore, it constructs a state-dependent flexibility envelope, enabling a safe and refined quantitative assessment of the real active support capacity of the virtual power plant across multiple time scales, effectively mitigating the physical limit-breaking risks caused by long-term scheduling.

[0008] To achieve the above objectives, the present invention provides a method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization, comprising the following technical solutions: Step S1: Construct a forward dynamic optimal power flow model for a virtual power plant based on second-order cone relaxation, and establish the physical constraints for the operation of the virtual power plant; Step S2: Introduce inverse optimization theory, construct the objective function by minimizing the residuals of the observed data and the compactness penalty of the feasible region, and establish an inverse optimization model for virtual power plant parameter identification; Step S3: Propose an asymmetric moving average sequential update algorithm with decay to process multi-time period scenario data and solve for the equivalent active power boundary and virtual energy capacity; Step S4: Based on the equivalent parameters identified by inverse optimization, construct a state-dependent flexibility envelope to quantify the dynamic support capability of the virtual power plant under different response durations.

[0009] As a further aspect of the present invention, step S1 is analyzed, wherein: Based on the aggregated energy supply structure and supply and demand equipment of physical nodes under virtual power plant aggregation, a dynamic optimal power flow model of virtual power plant based on second-order cone relaxation is constructed: 1) Objective function The objective function of the optimal forward power flow model is to minimize the total system operating cost. The cost function consists of the fuel cost of conventional generators, the cost of purchasing electricity from the upstream grid, and the grid loss cost, as shown in the following form: in, This represents the total number of time periods within the scheduling cycle. The set of nodes for all generator sets in the system; Indicates the first The generator set is Contributing effort at all times; For the first The power generation cost function of the Taiwanese generator unit adopts a quadratic function form to reflect the increasing marginal cost characteristic. 2) Constraints Auxiliary variables are introduced to convexify the nonlinear power flow equations, constructing mathematical expressions for nodal power balance and branch power flow. This transforms the nonlinear terms in the traditional power flow equations into a convex constraint form that can be handled. The following auxiliary variables are introduced: in, Represents a node At any moment The voltage magnitude is used to eliminate the quadratic term of the voltage magnitude in the power flow equation; in, For point With nodes At any moment Voltage phase angle difference, auxiliary variable Characterized by the cosine component of the inter-node voltage phasor product, corresponding to the conductance-related term of the branch admittance, and auxiliary variables. The sinusoidal component characterizing the voltage phasor product between nodes corresponds to the susceptance-related term of the branch admittance; (1) Nodal power balance equations Used to describe the active and reactive power supply and demand relationship at each node, specifically expressed as follows: in, For nodes The active power output of distributed power sources; The active power includes distributed resource nodes; The active power demand of the node load; right side This represents the set of physical nodes under the virtual power plant aggregation. Represents a node To all its neighboring nodes The sum of transmitted active power ensures a balance between the supply and demand of active power at each node. If a certain node... With nodes If not adjacent It is always 0; The mathematical expression for the reactive power balance equation at a node is as follows: in, , and These correspond to the reactive power output of distributed power sources and energy storage devices, and the reactive power demand of the load, respectively; the right side represents the nodes. The sum of reactive power transmitted to adjacent nodes ensures a balance between reactive power supply and demand at each node. in, , The conductance elements of the nodal admittance matrix are... For susceptance elements, through auxiliary variables , , The active power flow of the branch is represented as a linear combination, eliminating the nonlinear coupling in the original power flow equation; The above equation linearizes the reactive power flow of the branch through auxiliary variables, providing support for the convexity solution of the optimization model; (2) Second-order cone relaxation constraint Based on the algebraic definition of the auxiliary variables above, the two ends of the branch satisfy the following triangular identity coupling relationship: Introduce second-order cone relaxation constraints for auxiliary variables. , With the square of the node voltage term The coupling relationship between them is made convex: Here, the set of branches in the set of physical nodes under the virtual power plant aggregation is defined as follows: The above equation can be further equivalently transformed into the standard second-order cone norm form: (3) Voltage and power constraints Voltage constraints represent each node At any time square of voltage amplitude Limits are set between given upper and lower limits; in, Represents the active power of the node With reactive power The absolute upper and lower limits, while introducing the gradient rate. Constrain the power step amplitude between adjacent time steps to ensure the smoothness of system response and equipment safety; (4) Energy storage system operation constraints in, Indicates the first The equivalent output power of each energy storage node is determined by the discharge power. With charging power The difference determines; The energy changes at the nodes of the energy storage system are described using difference equations, and the cumulative state of charge of the stored energy over time is affected by the charging and discharging power: in, and These represent charge and discharge efficiencies, respectively. in, , It limits the physical extreme values ​​of a single charge and discharge cycle; and The maximum and minimum energy limits of the nodes are restricted; in, This means that the energy state of the energy storage nodes must remain consistent at the beginning and end of the scheduling cycle. (5) Converter capacity constraints .

[0010] As a further aspect of the present invention, step S2 is specifically analyzed, wherein: Step S2 introduces inverse optimization theory, constructing an objective function by minimizing the residuals of the observed data and penalizing the compactness of the feasible region, and establishing an inverse optimization model for virtual power plant parameter identification, specifically including: 1) Definition of inverse optimization variables (1) Observed variables The observed variable is defined as the difference between the power flow at the grid connection point under active support and the normal baseline power flow: Among them, the virtual power plant is defined in Actual active power response at time t Reactive power actual response quantity The total power measured at the grid connection point is respectively Subtract the baseline work when not involved in adjustment get; (2) Decision variables Decision variables are the output terms of the inverse optimization model, and are divided into two categories: static capacity boundary and dynamic trajectory. The static capacity boundary is used to define the physical limits of the active support capacity of a virtual power plant, including the equivalent active power boundary. Equivalent virtual energy capacity and equivalent apparent power capacity ;in, This indicates the maximum active power throughput capacity that the virtual power plant can provide to the outside world, which is determined by the upper and lower limits of the hardware physical limits of the distributed resources inside the virtual power plant and the network topology. This indicates the total amount of energy that can be flexibly utilized within the virtual power plant; and This represents the overall capacity limit of the virtual power plant at the grid connection point; Dynamic running trajectories are used to characterize the temporal evolution of the system within a scheduling cycle, including the fitted power trajectory. With virtual energy state trajectory Fitting power trajectory This represents the active and reactive power output sequence of the virtual power plant generated through reverse reconstruction; virtual energy state trajectory. This represents the time-series evolution path of the equivalent state of charge within the virtual power plant obtained through inversion; 2) Inverse optimization objective function Fitting error based on external characteristics With feasible region compactness penalty It is composed of two linearly superimposed parts: in, This is a weighted least squares fitting term used to quantize the fitted power trajectory. Compared with the actual observed trajectory The deviation between them is penalized using the square of the Euclidean distance; The variance normalization weight is represented by the standard deviation of the measurement noise introduced into the denominator, taking into account that active power and reactive power usually have a difference of order of magnitude in terms of dimensional scale. As a compactness penalty item; This is the global regularization coefficient, used to balance the relationship between fitting accuracy and boundary compactness. and It is a physical dimension alignment factor used to eliminate numerical differences between energy and apparent power and active power; 3) Inverse optimization constraints (1) Power balance constraint The collection of physical nodes under virtual power plant aggregation possesses bidirectional resource adjustment capabilities. Equivalent virtual active power at time It can be decomposed into virtual discharge power With virtual charging power The net difference, and the virtual active power output envelope at any time within the boundary of the equivalent active capacity to be identified. Within; (2) PQ coupling and inverter capacity constraints in, As a fundamental physical prior, the equivalent apparent power capacity to be identified Greater than or equal to the equivalent active capacity limit; This is a standard second-order cone relaxation constraint, indicating that the active and reactive trajectories fitted by inverse optimization are always constrained in the complex plane by a constraint. Within a circular region of radius [radius]; This indicates the lower limit of the power factor and the control dead zone at the actual grid connection point. The proportional coefficient is used to further limit the maximum available reactive power regulation depth; Connecting independent time segments into a dynamically evolving physical process: in, To achieve a comprehensive equivalent charge and discharge efficiency; Among them, virtual energy trajectory Restricted to by Within the determined upper and lower limits, and This represents the maximum allowable depth of discharge and maximum charge limit of the system; the cyclic closed-loop control requires a typical daily or scheduling cycle. The virtual energy state remains consistent throughout; The ratio between equivalent charge / discharge power and capacity is a reverse optimization regularization constraint. Without underlying parameters, the solver will search for meaningless solutions with infinite capacity and minimal power. Introducing parameters... ,exist and Establish a priori physical proportion relationship between them to narrow the solution space of inverse optimization.

[0011] As a further aspect of the present invention, step S3 is specifically analyzed, wherein: Step S3 proposes a decaying asymmetric moving average sequential update algorithm to process multi-time period scenario data and solve for the equivalent active power boundary and virtual energy capacity, specifically including: A sequential update algorithm is used to fuse time-series data from multiple scenarios, and an asymmetric moving average mechanism with decay is introduced to ensure smooth parameter convergence while endowing the model with adaptive identification capabilities for different operating states. in, Indicates the first The nth iteration, i.e., the input of the nth iteration The set of variable estimates after inverse optimization of typical daily scene data represents the set of values ​​that the inverse optimization model seeks to optimize the global objective function. Minimize the optimal solution set, where, and Represents the active power and energy estimates obtained under a specific single-day scenario; Introducing iteration-based The attenuation mechanism The initial base update rate, This is the decay coefficient, which increases with the number of training rounds. The increase in base update rate Gradually decrease the value to suppress parameter oscillations in the later stages of convergence of the algorithm; Based on the parameters identified in the new round Smoothing values ​​with historical values Based on the relative sizes between them, an asymmetric weight update strategy is constructed. The capacity identified from a single observation is greater than the historical smoothing value, which satisfies the condition. When this occurs, it indicates that the virtual power plant is currently experiencing a heavy load or extreme usage scenario, and a coefficient greater than 1 is used. Accelerate updates, and through To prevent overshoot; when the single recognition capacity is small, it meets the requirements. In this case, an update coefficient less than 1 is used. Slow down the update rate to maintain the system's long-term memory of extreme operating conditions on high-load days; in, This indicates the identification results from the previous round; This represents the original identification result of this round, using the calculated adaptive weights. The identification results from the previous round are weighted and fused with the original identification results from the current round to finally output a globally stable identification result with generalization ability. ; Extraction length is A sliding observation window is used, and the average relative rate of change of parameters within the window is calculated. The convergence criterion is as follows: in, As a preset convergence threshold, this criterion requires the parameter to be continuous. Within a cycle The average oscillation amplitude is lower than If the result is converged, then the inverse optimization result is considered to have converged.

[0012] As a further aspect of the present invention, step S4 is specifically analyzed, wherein: Step S4 proposes equivalent parameters based on inverse optimization identification to construct a state-dependent flexibility envelope, quantifying the dynamic support capability of the virtual power plant under different response durations, specifically including: 1) Definition of dynamic flexibility for state-dependent PE Because the inverse optimization process processed several days' worth of runtime data, For mathematical expectation operators, from The virtual energy state trajectory of the next iteration Extract a baseline energy evolution trajectory with universality and generalization ability. ; Indicates virtual power plants in The time-based flexibility is defined as a closed interval, which is determined by the maximum sustained discharge power. With maximum continuous charging power Common definition; 2) Dynamic power envelope calculation A dynamic power envelope calculation formula that takes into account both hardware and energy constraints, presented in the form of a nonlinear piecewise function: in, This indicates that the virtual power plant can continuously absorb active power. The theoretical upper limit of hours is controlled by the minimum value of two physical quantities: the static hardware rated equivalent power limit. and dynamic energy margin converted power ; This indicates that the virtual power plant can continuously generate active power. The theoretical upper limit of hours is limited by the minimum values ​​of two physical quantities, namely the hardware discharge limit. and dynamic discharge energy margin converted power It determines the direction of energy flow. Take the negative sign.

[0013] The beneficial effects of this invention are as follows: A second-order cone relaxation dynamic optimal power flow model is constructed based on the physical operation characteristics of the virtual power plant to provide underlying physical constraints. Addressing the black-box constraint of non-transparent underlying equipment parameters, a composite inverse optimization model is constructed with the goal of minimizing the residuals of grid connection point observation data. This model can accurately inversely derive the equivalent physical boundaries within the system without fully understanding the specific physical parameters of the massive underlying equipment. An iterative solution is performed using a sequential update algorithm with a decaying asymmetric moving average mechanism. This effectively filters out high-frequency noise from measurements while adaptively identifying the heavy or light load state of the grid, endowing the model with efficient generalization ability and noise robustness in complex source-load scenarios. Based on the equivalent parameters derived through inverse derivation, a state-dependent flexible envelope that explicitly incorporates the target response time is constructed. This comprehensively considers the dynamic constraints of instantaneous energy state on power capacity, transforming complex underlying operational constraints into intuitive dynamic safety boundaries. It accurately quantifies the power drop effect caused by energy dissipation in long-term support tasks, thereby effectively avoiding the risk of exceeding limits due to energy depletion or overcharging in actual scheduling, and improving the safety and reliability of the virtual power plant's multi-timescale active support regulation. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of multi-scenario temporal load clustering features in Embodiment 2 of the present invention; Figure 2 This is a convergence evolution curve of the equivalent physical parameters of the inverse optimization model in Embodiment 2 of the present invention with the number of iterations; Figure 3 This is a schematic diagram of the dynamic flexibility envelope and running trajectory of the state-dependent PE in Embodiment 2 of the present invention; Figure 4 This is a comparison chart showing the sensitivity analysis of different response durations to the dynamic flexibility envelope in Embodiment 2 of the present invention. Detailed Implementation

[0015] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0016] Example 1 A method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization is provided, including: Step S1: Construct a forward dynamic optimal power flow model for a virtual power plant based on second-order cone relaxation, and establish the physical constraints for the operation of the virtual power plant; Step S2: Introduce inverse optimization theory, construct the objective function by minimizing the residuals of the observed data and the compactness penalty of the feasible region, and establish an inverse optimization model for virtual power plant parameter identification; Step S3: Propose an asymmetric moving average sequential update algorithm with decay to process multi-time period scenario data and solve for the equivalent active power boundary and virtual energy capacity; Step S4: Based on the equivalent parameters identified by inverse optimization, construct a state-dependent flexibility envelope to quantify the dynamic support capability of the virtual power plant under different response durations.

[0017] As a method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization according to the present invention, step S1 is analyzed, wherein: Based on the aggregated energy supply structure and supply and demand equipment of physical nodes under virtual power plant aggregation, a dynamic optimal power flow model of virtual power plant based on second-order cone relaxation is constructed: 1) Objective function The objective function of the optimal forward power flow model is to minimize the total system operating cost. The cost function consists of the fuel cost of conventional generators, the cost of purchasing electricity from the upstream grid, and the grid loss cost, as shown in the following form: in, This represents the total number of time periods within the scheduling cycle. The set of nodes for all generator sets in the system; Indicates the first The generator set is Contributing effort at all times; For the first The power generation cost function of the Taiwanese generator unit adopts a quadratic function form to reflect the increasing marginal cost characteristic. 2) Constraints Auxiliary variables are introduced to convexify the nonlinear power flow equations, constructing mathematical expressions for nodal power balance and branch power flow. This transforms the nonlinear terms in the traditional power flow equations into a convex constraint form that can be handled. The following auxiliary variables are introduced: in, Represents a node At any moment The voltage magnitude is used to eliminate the quadratic term of the voltage magnitude in the power flow equation; in, For point With nodes At any moment Voltage phase angle difference, auxiliary variable Characterized by the cosine component of the inter-node voltage phasor product, corresponding to the conductance-related term of the branch admittance, and auxiliary variables. The sinusoidal component characterizing the voltage phasor product between nodes corresponds to the susceptance-related term of the branch admittance; (1) Nodal power balance equations Used to describe the active and reactive power supply and demand relationship at each node, specifically expressed as follows: in, For nodes The active power output of distributed power sources; The active power includes distributed resource nodes; The active power demand of the node load; right side This represents the set of physical nodes under the virtual power plant aggregation. Represents a node To all its neighboring nodes The sum of transmitted active power ensures a balance between the supply and demand of active power at each node. If a certain node... With nodes If not adjacent It is always 0; The mathematical expression for the reactive power balance equation at a node is as follows: in, , and These correspond to the reactive power output of distributed power sources and energy storage devices, and the reactive power demand of the load, respectively; the right side represents the nodes. The sum of reactive power transmitted to adjacent nodes ensures a balance between reactive power supply and demand at each node. in, , The conductance elements of the nodal admittance matrix are... For susceptance elements, through auxiliary variables , , The active power flow of the branch is represented as a linear combination, eliminating the nonlinear coupling in the original power flow equation; The above equation linearizes the reactive power flow of the branch through auxiliary variables, providing support for the convexity solution of the optimization model; (2) Second-order cone relaxation constraint Based on the algebraic definition of the auxiliary variables above, the two ends of the branch satisfy the following triangular identity coupling relationship: Introduce second-order cone relaxation constraints for auxiliary variables. , With the square of the node voltage term The coupling relationship between them is made convex: Here, the set of branches in the set of physical nodes under the virtual power plant aggregation is defined as follows: The above equation can be further equivalently transformed into the standard second-order cone norm form: (3) Voltage and power constraints Voltage constraints represent each node At any time square of voltage amplitude Limits are set between given upper and lower limits; in, Represents the active power of the node With reactive power The absolute upper and lower limits, while introducing the gradient rate. Constrain the power step amplitude between adjacent time steps to ensure the smoothness of system response and equipment safety; (4) Energy storage system operation constraints in, Indicates the first The equivalent output power of each energy storage node is determined by the discharge power. With charging power The difference determines; The energy changes at the nodes of the energy storage system are described using difference equations, and the cumulative state of charge of the stored energy over time is affected by the charging and discharging power: in, and These represent charge and discharge efficiencies, respectively. in, , It limits the physical extreme values ​​of a single charge and discharge cycle; and The maximum and minimum energy limits of the nodes are restricted; in, This means that the energy state of the energy storage nodes must remain consistent at the beginning and end of the scheduling cycle. (5) Converter capacity constraints .

[0018] As a preferred embodiment of the virtual power plant dynamic support capacity quantification and boundary calculation method based on inverse optimization of the present invention, step S2 is specifically analyzed, wherein: Step S2 introduces inverse optimization theory, constructing an objective function by minimizing the residuals of the observed data and penalizing the compactness of the feasible region, and establishing an inverse optimization model for virtual power plant parameter identification, specifically including: 1) Definition of inverse optimization variables (1) Observed variables The observed variable is defined as the difference between the power flow at the grid connection point under active support and the normal baseline power flow: Among them, the virtual power plant is defined in Actual active power response at time t Reactive power actual response quantity The total power measured at the grid connection point is respectively Subtract the baseline work when not involved in adjustment get; (2) Decision variables Decision variables are the output terms of the inverse optimization model, and are divided into two categories: static capacity boundary and dynamic trajectory. The static capacity boundary is used to define the physical limits of the active support capacity of a virtual power plant, including the equivalent active power boundary. Equivalent virtual energy capacity and equivalent apparent power capacity ;in, This indicates the maximum active power throughput capacity that the virtual power plant can provide to the outside world, which is determined by the upper and lower limits of the hardware physical limits of the distributed resources inside the virtual power plant and the network topology. This indicates the total amount of energy that can be flexibly utilized within the virtual power plant; and This represents the overall capacity limit of the virtual power plant at the grid connection point; Dynamic running trajectories are used to characterize the temporal evolution of the system within a scheduling cycle, including the fitted power trajectory. With virtual energy state trajectory Fitting power trajectory This represents the active and reactive power output sequence of the virtual power plant generated through reverse reconstruction; virtual energy state trajectory. This represents the time-series evolution path of the equivalent state of charge within the virtual power plant obtained through inversion; 2) Inverse optimization objective function Fitting error based on external characteristics With feasible region compactness penalty It is composed of two linearly superimposed parts: in, This is a weighted least squares fitting term used to quantize the fitted power trajectory. Compared with the actual observed trajectory The deviation between them is penalized using the square of the Euclidean distance; The variance normalization weight is represented by the standard deviation of the measurement noise introduced into the denominator, taking into account that active power and reactive power usually have a difference of order of magnitude in terms of dimensional scale. As a compactness penalty item; This is the global regularization coefficient, used to balance the relationship between fitting accuracy and boundary compactness. and It is a physical dimension alignment factor used to eliminate numerical differences between energy and apparent power and active power; 3) Inverse optimization constraints (1) Power balance constraint The collection of physical nodes under virtual power plant aggregation possesses bidirectional resource adjustment capabilities. Equivalent virtual active power at time It can be decomposed into virtual discharge power With virtual charging power The net difference, and the virtual active power output envelope at any time within the boundary of the equivalent active capacity to be identified. Within; (2) PQ coupling and inverter capacity constraints in, As a fundamental physical prior, the equivalent apparent power capacity to be identified Greater than or equal to the equivalent active capacity limit; This is a standard second-order cone relaxation constraint, indicating that the active and reactive trajectories fitted by inverse optimization are always constrained in the complex plane by a constraint. Within a circular region of radius [radius]; This indicates the lower limit of the power factor and the control dead zone at the actual grid connection point. The proportional coefficient is used to further limit the maximum available reactive power regulation depth; Connecting independent time segments into a dynamically evolving physical process: in, To achieve a comprehensive equivalent charge and discharge efficiency; Among them, virtual energy trajectory Restricted to by Within the determined upper and lower limits, and This represents the maximum allowable depth of discharge and maximum charge limit of the system; the cyclic closed-loop control requires a typical daily or scheduling cycle. The virtual energy state remains consistent throughout; The ratio between equivalent charge / discharge power and capacity is a reverse optimization regularization constraint. Without underlying parameters, the solver will search for meaningless solutions with infinite capacity and minimal power. Introducing parameters... ,exist and Establish a priori physical proportion relationship between them to narrow the solution space of inverse optimization.

[0019] As a preferred embodiment of the virtual power plant dynamic support capacity quantification and boundary calculation method based on inverse optimization of the present invention, step S3 is specifically analyzed, wherein: Step S3 proposes a decaying asymmetric moving average sequential update algorithm to process multi-time period scenario data and solve for the equivalent active power boundary and virtual energy capacity, specifically including: A sequential update algorithm is used to fuse time-series data from multiple scenarios, and an asymmetric moving average mechanism with decay is introduced to ensure smooth parameter convergence while endowing the model with adaptive identification capabilities for different operating states. in, Indicates the first The nth iteration, i.e., the input of the nth iteration The set of variable estimates after inverse optimization of typical daily scene data represents the set of values ​​that the inverse optimization model seeks to optimize the global objective function. Minimize the optimal solution set, where, and Represents the active power and energy estimates obtained under a specific single-day scenario; Introducing iteration-based The attenuation mechanism The initial base update rate, This is the decay coefficient, which increases with the number of training rounds. The increase in base update rate Gradually decrease the value to suppress parameter oscillations in the later stages of convergence of the algorithm; Based on the parameters identified in the new round Smoothing values ​​with historical values Based on the relative sizes between them, an asymmetric weight update strategy is constructed. The capacity identified from a single observation is greater than the historical smoothing value, which satisfies the condition. When this occurs, it indicates that the virtual power plant is currently experiencing a heavy load or extreme usage scenario, and a coefficient greater than 1 is used. Accelerate updates, and through To prevent overshoot; when the single recognition capacity is small, it meets the requirements. In this case, an update coefficient less than 1 is used. Slow down the update rate to maintain the system's long-term memory of extreme operating conditions on high-load days; in, This indicates the identification results from the previous round; This represents the original identification result of this round, using the calculated adaptive weights. The identification results from the previous round are weighted and fused with the original identification results from the current round to finally output a globally stable identification result with generalization ability. ; Extraction length is A sliding observation window is used, and the average relative rate of change of parameters within the window is calculated. The convergence criterion is as follows: in, As a preset convergence threshold, this criterion requires the parameter to be continuous. Within a cycle The average oscillation amplitude is lower than If the result is converged, then the inverse optimization result is considered to have converged.

[0020] As a preferred embodiment of the virtual power plant dynamic support capacity quantification and boundary calculation method based on inverse optimization of the present invention, step S4 is specifically analyzed, wherein: Step S4 proposes equivalent parameters based on inverse optimization identification to construct a state-dependent flexibility envelope, quantifying the dynamic support capability of the virtual power plant under different response durations, specifically including: 1) Definition of dynamic flexibility for state-dependent PE Because the inverse optimization process processed several days' worth of runtime data, For mathematical expectation operators, from The virtual energy state trajectory of the next iteration Extract a baseline energy evolution trajectory with universality and generalization ability. ; Indicates virtual power plants in The time-based flexibility is defined as a closed interval, which is determined by the maximum sustained discharge power. With maximum continuous charging power Common definition; 2) Dynamic power envelope calculation A dynamic power envelope calculation formula that takes into account both hardware and energy constraints, presented in the form of a nonlinear piecewise function: in, This indicates that the virtual power plant can continuously absorb active power. The theoretical upper limit of hours is controlled by the minimum value of two physical quantities: the static hardware rated equivalent power limit. and dynamic energy margin converted power ; This indicates that the virtual power plant can continuously generate active power. The theoretical upper limit of hours is limited by the minimum values ​​of two physical quantities, namely the hardware discharge limit. and dynamic discharge energy margin converted power It determines the direction of energy flow. Take the negative sign.

[0021] Example 2 Reference Figure 1-4 As an embodiment of the present invention, a method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization is provided. To verify the beneficial effects of the present invention, a comparative experiment is conducted for scientific demonstration.

[0022] The simulation example uses a standard IEEE 33-node distribution network system as the underlying physical topology for verification. Distributed energy storage systems are configured at nodes 3, 6, 15, and 18 as flexibility resources, and a high-proportion distributed photovoltaic cluster is simultaneously connected at node 15. To verify the effectiveness of the invention, the entire IEEE 33-node distribution network containing distributed resources is equivalently aggregated into a virtual power plant, representing its participation in the active support and control of the power grid. The relevant algorithm parameters and inverse optimization model settings are configured in the model, as shown in Table 1.

[0023] Table 1 Inverse Optimization Algorithm and System Parameter Settings First, a time-series clustering algorithm is used to reduce the dimensionality of the historical load and renewable energy output data for 20 consecutive days, such as... Figure 1 As shown, three typical scenarios—heavy load days, medium load days, and low load days—are extracted. These serve as the input driving data for subsequent sequential update algorithms, covering a variety of situations from voltage over-limit edge conditions caused by high penetration rates to normal operating conditions.

[0024] Figure 2The convergence evolution of the equivalent physical parameters of the inverse optimization model with each iteration is presented. The algorithm exhibits extremely high computational efficiency during the global optimization process, with a total global iterative training time of only 88.32s and an average single iteration time as low as 0.3397s, and meets the convergence criterion at the 260th iteration. Under continuous optimization of the compactness penalty term, the system's equivalent active power boundary robustly converges to 0.5863 MW, and the equivalent energy capacity boundary converges to 2.2852 MWh.

[0025] Figure 3 Shows the setting response time = The spatial relationship between the state-dependent PE dynamic flexibility envelope and its trajectory in a 1-hour scenario. From Figure 3 As can be seen, the flexibility envelope exhibits a contracted hexagonal structure in terms of geometric topology, intuitively reflecting the absolute constraint of instantaneous energy state on power output. For example, during late-night hours, when energy storage is close to full charge, the maximum allowable charging power is severely compressed, and the system exhibits strong asymmetric flexibility (extremely high discharge potential while almost depleted charging potential). This confirms that blindly issuing absolute high-power charging commands can easily lead to the risk of overcharging and exceeding limits in underlying devices.

[0026] Figure 4 It shows the response time of different targets. A comparative sensitivity analysis of the dynamic flexibility envelope. With... With the continuous increase in [data / capabilities], the active support capability of virtual power plants exhibits a distinct two-stage characteristic (i.e., a transition from a hardware-constrained physical constraint-dominated region to a dynamic energy-constrained region). When entering long-term scheduling scenarios (such as...) After 2.0 hours, the system's maximum available output exhibits an inversely proportional, nonlinear, sharp drop, with available power decreasing by as much as 50.8%, and the envelope area shrinking dramatically. This effectively quantifies the power drop effect caused by energy dissipation.

[0027] This invention is beneficial for improving the scientific rigor and safety of virtual power plant control decisions in complex active support scenarios. The proposed method for quantifying the dynamic support capabilities of virtual power plants based on inverse optimization overcomes the engineering drawbacks of traditional forward modeling, which heavily relies on opaque underlying parameters. It identifies and accurately quantifies the dynamic constraints of instantaneous energy states on support power during long-term scheduling, generating a safe operating boundary that combines underlying physical accuracy with upper-level anti-overrun scheduling capabilities.

[0028] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

[0029] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0030] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization, characterized in that, include: Step S1: Construct a forward dynamic optimal power flow model for a virtual power plant based on second-order cone relaxation, and establish the physical constraints for the operation of the virtual power plant; Step S2: Introduce inverse optimization theory, construct the objective function by minimizing the residuals of the observed data and the compactness penalty of the feasible region, and establish an inverse optimization model for virtual power plant parameter identification; Step S3: Use a sequential update algorithm to process multi-time period scenario data and solve for the equivalent active power boundary and virtual energy capacity; wherein, the sequential update algorithm adopts an asymmetric moving average mechanism with decay, which dynamically adjusts the parameter update weight according to the relationship between the parameter value identified in the current iteration and the historical smooth value. Step S4: Based on the equivalent parameters identified by inverse optimization, construct a state-dependent flexibility envelope to quantify the dynamic support capability of the virtual power plant under different response durations. In step S2, the inverse optimization model for identifying virtual power plant parameters is constructed, specifically including: 1) Definition of inverse optimization variables (1) Observed variables The observed variable is defined as the difference between the power flow at the grid connection point under active support and the normal baseline power flow: ； ； Among them, the virtual power plant is defined in Actual active power response at time t Reactive power actual response quantity The total power measured at the grid connection point is respectively Subtract the baseline work when not involved in adjustment get; (2) Decision variables Decision variables are the output terms of the inverse optimization model, and are divided into two categories: static capacity boundary and dynamic trajectory. The static capacity boundary is used to define the physical limits of the active support capacity of a virtual power plant, including the equivalent active power boundary. Equivalent virtual energy capacity and equivalent apparent power capacity ;in, This indicates the maximum active power throughput capacity that the virtual power plant can provide to the outside world, which is determined by the upper and lower limits of the hardware physical limits of the distributed resources inside the virtual power plant and the network topology. This indicates the total amount of energy that can be flexibly utilized within the virtual power plant; and This represents the overall capacity limit of the virtual power plant at the grid connection point; Dynamic running trajectories are used to characterize the temporal evolution of the system within a scheduling cycle, including the fitted power trajectory. With virtual energy state trajectory Fitting power trajectory This represents the active and reactive power output sequence of the virtual power plant generated through reverse reconstruction; virtual energy state trajectory. This represents the time-series evolution path of the equivalent state of charge within the virtual power plant obtained through inversion; 2) Inverse optimization objective function Fitting error based on external characteristics With feasible region compactness penalty It is composed of two linearly superimposed parts: ； ； ； in, This is a weighted least squares fitting term used to quantize the fitted power trajectory. Compared with the actual observed trajectory The deviation between them is penalized using the square of the Euclidean distance; The variance normalization weight is represented by the standard deviation of the measurement noise introduced into the denominator, taking into account that active power and reactive power usually have a difference of order of magnitude in terms of dimensional scale. As a compactness penalty item; This is the global regularization coefficient, used to balance the relationship between fitting accuracy and boundary compactness. and It is a physical dimension alignment factor used to eliminate numerical differences between energy and apparent power and active power.

2. The method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization according to claim 1, characterized in that, In step S1, the forward dynamic optimal power flow model of the virtual power plant based on second-order cone relaxation is constructed as follows: 1) Objective function The objective function of the optimal forward power flow model is to minimize the total system operating cost. The cost function consists of the fuel cost of conventional generators, the cost of purchasing electricity from the upstream grid, and the grid loss cost, as shown in the following form: ； in, This represents the total number of time periods within the scheduling cycle. The set of nodes for all generator sets in the system; Indicates the first The generator set is Contributing effort at all times; For the first The power generation cost function of the Taiwanese generator unit adopts a quadratic function form to reflect the increasing marginal cost characteristic. 2) Constraints Auxiliary variables are introduced to convexify the nonlinear power flow equations, constructing mathematical expressions for nodal power balance and branch power flow. This transforms the nonlinear terms in the traditional power flow equations into a convex constraint form that can be handled. The following auxiliary variables are introduced: ； in, Represents a node At any moment The voltage magnitude is used to eliminate the quadratic term of the voltage magnitude in the power flow equation; ； ； in, For point With nodes At any moment Voltage phase angle difference, auxiliary variable Characterized by the cosine component of the inter-node voltage phasor product, corresponding to the conductance-related term of the branch admittance, and auxiliary variables. The sinusoidal component characterizing the voltage phasor product between nodes corresponds to the susceptance-related term of the branch admittance; (1) Nodal power balance equations Used to describe the active and reactive power supply and demand relationship at each node, specifically expressed as follows: ； in, For nodes The active power output of distributed power sources; The active power includes distributed resource nodes; The active power demand of the node load; right side This represents the set of physical nodes under the virtual power plant aggregation. Represents a node To all its neighboring nodes The sum of transmitted active power ensures a balance between the supply and demand of active power at each node. If a certain node... With nodes If not adjacent It is always 0; The mathematical expression for the reactive power balance equation at a node is as follows: ； in, , and These correspond to the reactive power output of distributed power sources and energy storage devices, and the reactive power demand of the load, respectively; the right side represents the nodes. The sum of reactive power transmitted to adjacent nodes ensures a balance between reactive power supply and demand at each node. ； in, , The conductance elements of the nodal admittance matrix are... For susceptance elements, through auxiliary variables , , The active power flow of the branch is represented as a linear combination, eliminating the nonlinear coupling in the original power flow equation; ； The above equation linearizes the reactive power flow of the branch through auxiliary variables, providing support for the convexity solution of the optimization model; (2) Second-order cone relaxation constraint Based on the algebraic definition of the auxiliary variables above, the two ends of the branch satisfy the following triangular identity coupling relationship: ； Introduce second-order cone relaxation constraints for auxiliary variables. , With the square of the node voltage term The coupling relationship between them is made convex: ； Here, the set of branches in the set of physical nodes under the virtual power plant aggregation is defined as follows: The above equation can be further equivalently transformed into the standard second-order cone norm form: ； (3) Voltage and power constraints ； Voltage constraints represent each node At any time voltage amplitude square Limits are set between given upper and lower limits; ； ； ； in, Represents the active power of the node With reactive power The absolute upper and lower limits, while introducing the gradient rate. Constrain the power step amplitude between adjacent time steps to ensure the smoothness of system response and equipment safety; (4) Energy storage system operation constraints ； in, Indicates the first The equivalent output power of each energy storage node is determined by the discharge power. With charging power The difference determines; The energy changes at the nodes of the energy storage system are described using difference equations, and the cumulative state of charge of the stored energy over time is affected by the charging and discharging power: ； in, and These represent charge and discharge efficiencies, respectively. ； ； ； in, , It limits the physical extreme values ​​of a single charge and discharge cycle; and The maximum and minimum energy limits of the nodes are restricted; ； in, This means that the energy state of the energy storage nodes must remain consistent at the beginning and end of the scheduling cycle. (5) Converter capacity constraints 。 3. The method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization according to claim 2, characterized in that, In step S2, constructing the inverse optimization model for virtual power plant parameter identification also includes: 3) Inverse optimization constraints (1) Power balance constraint ； ； The collection of physical nodes under virtual power plant aggregation possesses bidirectional adjustment resources. Equivalent virtual active power at time It can be decomposed into virtual discharge power With virtual charging power The net difference, and the virtual active power output envelope at any time within the boundary of the equivalent active capacity to be identified. Within; (2) PQ coupling and inverter capacity constraints ； ； ； in, As a fundamental physical prior, the equivalent apparent power capacity to be identified Greater than or equal to the equivalent active capacity limit; This is a standard second-order cone relaxation constraint, indicating that the active and reactive trajectories fitted by inverse optimization are always constrained in the complex plane by a constraint. Within a circular region of radius [radius]; This indicates the lower limit of the power factor and the control dead zone at the actual grid connection point. The proportional coefficient is used to further limit the maximum available reactive power regulation depth; Connecting independent time segments into a dynamically evolving physical process: ； in, To achieve a comprehensive equivalent charge and discharge efficiency; ； ； Among them, virtual energy trajectory Restricted to by Within the determined upper and lower limits, and This represents the maximum allowable depth of discharge and maximum charge limit of the system; the cyclic closed-loop control requires a typical daily or scheduling cycle. The virtual energy state remains consistent throughout; ； The ratio between equivalent charge / discharge power and capacity is a reverse optimization regularization constraint. Without underlying parameters, the solver will search for meaningless solutions with infinite capacity and minimal power. Introducing parameters... ,exist and Establish a priori physical proportion relationship between them to narrow the solution space of inverse optimization.

4. The method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization according to claim 3, characterized in that, The sequential update algorithm constructed in step S3 specifically includes: A sequential update algorithm is used to fuse time-series data from multiple scenarios, and an asymmetric moving average mechanism with decay is introduced to ensure smooth parameter convergence while endowing the model with adaptive identification capabilities for different operating states. ； in, Indicates the first The nth iteration, i.e., the input of the nth iteration The set of variable estimates after inverse optimization of typical daily scene data represents the set of values ​​that the inverse optimization model seeks to optimize the global objective function. Minimize the optimal solution set, where, and Represents the active power and energy estimates obtained under a specific single-day scenario; ； ； Introducing iteration-based The attenuation mechanism The initial base update rate, This is the decay coefficient, which increases with the number of training rounds. The increase in base update rate Gradually decrease the value to suppress parameter oscillations in the later stages of convergence of the algorithm; Based on the parameters identified in the new round Smoothing values ​​with historical values Based on the relative sizes between them, an asymmetric weight update strategy is constructed. The capacity identified from a single observation is greater than the historical smoothing value, which satisfies the condition. When this occurs, it indicates that the virtual power plant is currently experiencing a heavy load or extreme usage scenario, and a coefficient greater than 1 is used. Accelerate updates, and through To prevent overshoot; when the single recognition capacity is small, it meets the requirements. In this case, an update coefficient less than 1 is used. Slow down the update rate to maintain the system's long-term memory of extreme operating conditions on high-load days; ； ； in, This indicates the identification results from the previous round; This represents the original identification result of this round, using the calculated adaptive weights. The identification results from the previous round are weighted and fused with the original identification results from the current round to finally output a globally stable identification result with generalization ability. ; Extraction length is A sliding observation window is used, and the average relative rate of change of parameters within the window is calculated. The convergence criterion is as follows: ； ； in, As a preset convergence threshold, this criterion requires the parameter to be continuous. Within a cycle The average oscillation amplitude is lower than If the result is converged, then the inverse optimization result is considered to have converged.

5. The method for quantifying and calculating the dynamic support capacity and boundary of a virtual power plant based on inverse optimization according to claim 4, characterized in that, Step S4, which constructs a state-dependent flexibility envelope, specifically includes: 1) Definition of dynamic flexibility for state-dependent PE ； ； Because the inverse optimization process processed several days' worth of runtime data, For mathematical expectation operators, from The virtual energy state trajectory of the next iteration Extract a baseline energy evolution trajectory with universality and generalization ability. ; Indicates virtual power plants in The time-based flexibility is defined as a closed interval, which is determined by the maximum sustained discharge power. With maximum continuous charging power Common definition; 2) Dynamic power envelope calculation A dynamic power envelope calculation formula that takes into account both hardware and energy constraints, presented in the form of a nonlinear piecewise function: ； in, This indicates that the virtual power plant can continuously absorb active power. The theoretical upper limit of hours is controlled by the minimum value of two physical quantities: the static hardware rated equivalent power limit. and dynamic energy margin converted power ; This indicates that the virtual power plant can continuously generate active power. The theoretical upper limit of hours is limited by the minimum values ​​of two physical quantities, namely the hardware discharge limit. and dynamic discharge energy margin converted power It determines the direction of energy flow. Take the negative sign.

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