Distributed resource flexibility quantification method and system based on feasible region and economy

Abstract

The application discloses a kind of based on feasible region and economy distributed resource flexibility quantification method and system, belong to power grid flexibility evaluation or quantification field, method includes: S1 constructs real aggregation flexibility feasible region, constructs initial convex polyhedral feasible region inside real aggregation flexibility feasible region, and gradually approaches real boundary from inside to outside using vertex search method;S2 constructs the optimization scheduling model of aggregation merchant distributed resource, to obtain the marginal price based on aggregation merchant and distribution network coupling node with the minimum total scheduling cost of each distributed resource of aggregation merchant as target;S3 calculates the area change rate of aggregation flexibility feasible region and the change rate of marginal price, constructs the comprehensive importance function of vertex, using feasible region vertex sparsification process strategy, the boundary of feasible region is simplified.The application realizes the accurate quantification of aggregation distributed resource flexibility under the condition of considering time sequence coupling characteristics and resource uncertainty.

Description

Technical Field

[0001] This invention belongs to the field of power grid flexibility assessment or quantification, and relates to the field of distributed resource flexibility quantification. Specifically, it is a method and system for quantifying distributed resource flexibility based on feasible domain and economics. Background Technology

[0002] As the penetration rate of renewable energy in distribution networks continues to increase, the inherent uncertainty and volatility of renewable energy pose new challenges to the safe and stable operation of power systems, making the demand for power system flexibility unprecedentedly urgent. The flexibility of distributed resources refers to the ability of distributed generation resources and distributed adjustable loads to proactively adjust their generation or consumption behavior after receiving external signals (such as electricity price changes or dispatch commands), specifically manifested as increasing, decreasing, or delaying power generation and consumption. Due to their small individual capacity and dispersed distribution, flexible resources on the distribution network side are difficult to participate in system-level dispatch independently. Aggregators, acting as intermediaries between the distribution network and distributed resources, can aggregate various resources, enabling them to participate in dispatch as a whole. In this context, how to quantitatively assess the overall flexibility of distributed resources within aggregators and accurately reflect their economic value is of great significance for improving the resource allocation efficiency of the distribution network and optimizing the safety and economy of system operation.

[0003] To quantitatively characterize flexibility, the academic community has proposed various quantification methods, which can be mainly divided into quantification methods based on flexibility indices and quantification methods based on feasible regions. Quantification methods based on flexibility indices typically quantify flexibility as indicators such as adjustable power margin, voltage margin, and load reduction capacity of distributed resources at a certain moment or time period, or quantify flexibility from the perspective of resource response capabilities such as ramp rate and response delay. However, this method often directly sums the flexibility indices of internal nodes when calculating regional flexibility. While it can preserve the temporal attribute of flexibility to some extent, it has a weak ability to quantify the spatial distribution of flexibility, making it difficult to comprehensively characterize the spatial characteristics of distribution network flexibility. Quantification methods based on feasible regions generally describe the safe operating boundary of the system under various constraints in a geometric way, that is, the range of injected power changes that the system can withstand under the constraint conditions. This method, while considering network space characteristics and accurately representing the overall flexibility adjustment space of the system when characterizing the feasible region, has certain advantages over index-based methods. However, when considering source-load prediction errors, it faces the problem of relying on robust worst-case scenarios or large-scale random sampling, which can easily lead to overly conservative boundaries or the curse of model dimensionality. When considering temporal coupling characteristics, it also faces the problems of model complexity, high computational dimensionality, and high solution costs. Therefore, how to propose a concise and efficient method for constructing and solving the feasible region of aggregated distributed resource flexibility, while ensuring accuracy, and taking into account uncertainty and adapting to temporal coupling characteristics, still requires further in-depth research.

[0004] Furthermore, current research on feasible regions focuses more on analyzing their physical capabilities, lacking research that analyzes and characterizes the economic characteristics within the feasible region from the overall perspective of aggregators. This makes it difficult to smoothly translate the physical potential for flexibility into economic signals for market transactions and scheduling, thus restricting the resource allocation efficiency of the distribution network. Therefore, further research is needed on methods for analyzing and characterizing the economic characteristics of feasible regions for aggregated distributed resources. Summary of the Invention

[0005] To address the aforementioned issues, a distributed resource flexibility quantification method based on feasible domain and economics is proposed. This method considers temporal coupling characteristics and source load prediction errors, and combines the characterization of the feasible domain of aggregated distributed resources with economic characteristic analysis to achieve a scientific and reasonable quantification of flexibility.

[0006] The technical solution adopted in this invention is as follows: A method for quantifying the flexibility of distributed resources based on feasible domain and economics includes the following steps: S1 constructs the real aggregate flexibility feasible region, performs deterministic equivalent transformation of chance constraints through the inverse cumulative distribution function, and then constructs an initial convex polyhedral feasible region inside the real aggregate flexibility feasible region. The vertex search method is used to gradually approximate the real boundary from the inside to the outside to achieve an approximate characterization of the aggregate flexibility feasible region. S2 constructs an optimal scheduling model for distributed resources of aggregators, with the goal of minimizing the total scheduling cost of each distributed resource by the aggregator, and obtains the marginal electricity price based on the coupling nodes of the aggregator and the distribution network according to duality theory and KKT conditions. S3 calculates the rate of change of the area of ​​the feasible region and the rate of change of the marginal electricity price associated with each vertex, constructs the comprehensive importance function of the vertex, and simplifies the boundary of the feasible region.

[0007] Furthermore, the construction of the real aggregation flexibility feasible region mentioned in step S1 specifically means: the real aggregation flexibility feasible region is a region with boundary depth constraints at each time period, covering the entire scheduling cycle of 2 T The specific expression for the 3D time-series trajectory polyhedron is as follows: (1) In the formula, P PCC = [ , …, T and Q PCC = [ , …, ]T represents the active and reactive power vectors of the coupled nodes, respectively; T Representing time points; A*, B*, and βThe coefficient matrix and vector, jointly determined by all network and resource constraints, are used to characterize the boundaries of the flexibility of the coupled node PCC under multi-time-period association. Furthermore, the constraints on the feasible region of true aggregation flexibility include: (1) Power flow constraints for linearization of distribution network: (2) In the formula, i and j Branch roads ij Sending node number and receiving node number; and They are respectively t Time is determined by nodes i Calculated branches ij Active power and reactive power; r ij and x ij Branch roads ij Resistance and reactance; and They are respectively t Time Node i and j The voltage; and These are the sets of all nodes and branches in the network, respectively. (2) Node power balance constraints: (3) (4) In the formula, and They are respectively t Time Node i Active and reactive power are injected into the upper part; and They are respectively t Time Node i The actual active and reactive power output of photovoltaic panels; , and , They are respectively t Time Node i The actual active and reactive power consumed by energy storage and scalable flexible loads; The demand for photovoltaic power output and reducible flexible load consists of a forecast baseline value and a random forecast error, with the forecast error following a normal distribution with a mean of zero. t The time expression is: (5) (6) In the formula, , They are respectively t Time Node i The above forecasts photovoltaic output and demand for scalable flexible loads; , These are the active power reductions from photovoltaic and reduceable flexible loads, respectively. , These are the standard deviations of the prediction errors of the two variables; (3) Opportunity constraints on the upper and lower limits of node voltage: (7) (8) In the formula, P (·) represents the probability measure function; and These are the upper and lower limits of the system's allowed voltage operation, respectively; , This describes the risk thresholds for system voltage exceeding upper and lower limits under uncertain conditions; (4) Line capacity opportunity constraints based on polygonal approximation linearization: (9) In the formula, branch road ij Maximum allowed capacity; α c , β c and γ c These represent the coefficients after linearization; c The numbering of the edges of the inner approximation polygon; This is a threshold used to describe the risk of system line capacity exceeding limits under conditions of uncertainty; (5) Constraints of photovoltaic systems: (10) (11) (12) In the formula, for t Nodes for time prediction i Maximum output power of photovoltaic panels; For nodes i The maximum power factor angle of the photovoltaic inverter; Equation (12) is the linearized expression of Equation (11); (6) Reduceable flexible load constraints: Reducible flexible loads provide flexibility by directly reducing power during operation, enabling rapid and flexible dispatch responses, including non-critical loads such as building lighting and garage ventilation systems; (13) (14) (15) In the formula, and They are respectively t Time Node i The maximum acceptable reduction in active and reactive loads for reducible flexible loads; and They are respectively t Time Node i The reduction in active and reactive power of the flexible load can be reduced. For nodes i The power factor of the flexible load that can be reduced; (7) Constraints of energy storage systems including time-series coupling characteristics: Energy storage systems offer flexibility through their inter-period charge and discharge behavior. Their state is constrained not only by charge and discharge power boundaries but also by time-coupled states of charge, as expressed in the following constraint expression: (16) (17) (18) (19) (20) In the formula, and They are respectively t and t -1 time node i The actual electricity generated by the energy storage system; and These are the charging and discharging efficiencies of the energy storage system; and They are respectively t Time Node i The active power of the energy storage system during charging and discharging; For time intervals; and Maximum charge and discharge power limits for energy storage systems; This represents the maximum capacity of the energy storage system. and These are the upper and lower limits of the state of charge of the energy storage system. and These are the reactive power and power factor angle of the energy storage system, respectively.

[0008] Furthermore, the deterministic equivalent transformation of the chance constraint through the inverse cumulative distribution function described in step S1 specifically involves: Based on the inverse cumulative distribution function of the normal distribution, the opportunity constraints of node voltage upper and lower limits and line capacity constraining the feasible region are equivalently transformed into deterministic expressions, the specific expressions of which are: (twenty one) (twenty two) In the formula, (·) is the inverse cumulative distribution function of the normal distribution; The standard deviation of node voltage fluctuation; branch road ij Apparent power in the inward approximation polygon c Standard deviation of fluctuation along the stripe direction; (twenty three) (twenty four) (25) In the formula, This is the covariance matrix of the photovoltaic and load forecasting errors for all nodes in the entire network. For nodes i The sensitivity coefficient vector of voltage to the injected power at each node of the entire network; , and Branch roads ij The sensitivity vectors of apparent power, active power, and reactive power.

[0009] Furthermore, the approximate characterization of the feasible region of aggregation flexibility described in step S1 specifically includes: (1) Initialization process: Construct an initial approximate polyhedron, select multiple initial vertices within the real aggregate feasible region to form an initial solution set, and determine a polyhedron as an estimate of the initial feasible region through convex combination characterization. (26) (27) (28) In the formula, The area of ​​the initial polyhedron; for t Initial feasible region plane for the time period; for tInitial feasible domain vertices for the time period; v Number the vertices; Ω (0) The initial feasible domain polyhedral expression for all time steps considering temporal coupling characteristics; The bilinear term in the objective function is linearized using the McCormick Envelope method, which introduces auxiliary variables. w t,v and υ t,v The linearized objective function is: (29) In the formula, w t,v for Linearized approximation of the term; υ t,v for Linearized approximation of the term; and They represent The upper and lower bounds; and They represent The upper and lower boundaries.

[0010] (2) Iterative expansion process: Based on the initial feasible region, the boundary of the approximate polyhedron is gradually expanded from the inside out to approximate the actual feasible region boundary; the search starts at the midpoint of each edge of the current polyhedron boundary, the search direction is the outward normal vector of each edge, and the search objective is to maximize the projected area of ​​the feasible region in this direction. (30) In the formula, For the first k After the second iteration t The area of ​​the time-space plane; det[·] is the determinant of the matrix; for t The total number of vertices in the feasible region at any given time; For the first k After the second iteration e v The direction of the external normal vector; It is the midpoint of the corresponding edge; is a parameterized variable representing the feasible region expansion scale, and its value range is [0, +∞]. e v For the first k The vertex obtained in the next iteration ( , )and( , The edges formed by ) For the edge ev The new vertices obtained from the baseline search, where, v' Indicates by the first v vertices and v The new vertex number obtained by searching for +1 vertex; Indicates the first The new vertex number obtained by searching the first vertex and the first vertex.

[0011] Merge the feasible vertices found in the current iteration with the original vertex set, update the polyhedral approximation model of the feasible region, and start a new round of iteration. All vertices after the update are still numbered in counterclockwise order. (3) Termination conditions: The rate of change of the total area is used to determine whether the approximate feasible region has sufficiently approximated the true boundary. When the rate of change of the total area resulting from two consecutive expansions is lower than a preset threshold, the boundary is considered to have stabilized, and the iteration ends. (31) In the formula, For the first k Obtained in the next iteration t Aggregate feasible region area over time period; r FR,1 The preset threshold for the rate of change of total area; The feasible region expression for the convex polyhedron obtained by approximating the true feasible region from the inside out based on vertex search is as follows: (32) In the formula, Ω PCC-V is the flexible feasible region based on vertex characterization; conv(·) is the convex hull of the point set; for t The vertex of the feasible region at any given time.

[0012] Furthermore, the specific expression for the optimized scheduling model of the aggregator's distributed resources described in step S2 is as follows: (33) (34) (35) (36) In the formula, The total cost of scheduling internal distributed resources for the aggregator; , , They are respectively tThe cost required for aggregators to schedule various photovoltaic systems, scalable flexible loads, and energy storage systems within a given time period; , , , , They are respectively t Unit adjustment cost parameters for active and reactive power of various resources during different time periods; , , They are respectively t Time period nodes i The active power reduction and reactive power adjustment of photovoltaic systems; , They are respectively t Time period nodes i This can reduce both active and reactive power of the load; , They are respectively t Time period nodes i The charging and discharging power of the energy storage system.

[0013] Furthermore, the optimal scheduling model of the aggregator's distributed resources is transformed into a Lagrangian function, and based on duality theory and KKT conditions, the expression for the marginal electricity price of feasible points within the aggregate feasible region is derived. This transforms the physical potential for flexibility into an economic signal for market transactions and scheduling, specifically: (37) In the formula, π sub-P and π sub-Q represents the marginal active and reactive electricity prices for the aggregator's flexibility. Let Lagrange function be the objective function corresponding to the optimized scheduling objective function of the aggregator's distributed resources. and These represent the changes in active and reactive power at the coupling point between the aggregator and the distribution network, respectively.

[0014] Furthermore, in step S3, The expression for the area change rate of the feasible region of aggregation flexibility is: for t Any vertex of the feasible region of time-segment aggregation Its adjacent l Rate of change of area of ​​a polygon formed by points for: (38) (39) In the formula, As vertex At,v Its adjacent l The area of ​​the polygon formed by the points. l For the vertex A t,v The number of adjacent vertices, if Smaller indicates that the vertex A t,v To the top A t,v+l It has very little impact on the local shape of the boundary; The expression for the marginal electricity price change rate is: Based on the calculated marginal electricity price of the aggregation node, the vertex A t,v With adjacent vertices A t,v+1 and A t,v-1 Electricity price change coefficient for: (40) In the formula, It is a 2-norm. As vertex A t,v The corresponding marginal electricity price vector of the aggregation node, As a benchmark normalized electricity price, if this peak touches the boundary of network security or equipment output extreme values, its corresponding shadow price will undergo a jump, causing... Significantly increased; The vertex comprehensive importance function is: (41) In the formula, and These are the weighting coefficients for area and electricity price characteristics, respectively. Let the sparsity synthesis threshold be... r FR,2 ,when At that time, the vertex A t,v The impact on the feasible region area and the aggregated marginal electricity price is relatively small, so it is identified as a redundant vertex and deleted. The algorithm starts from a certain initial vertex A t,v Begin by gradually incorporating the next adjacent vertex, forming... l For polygons with values ​​of 2, 3, 4…, calculate the comprehensive importance function for each vertex in turn. The comprehensive importance function is considered when it first exceeds a threshold. r FR,2When the newly added point has a significant impact on the boundary profile or marginal electricity price, only the first and second-to-last points in the polygon are retained, and the remaining intermediate points are considered redundant and deleted. The algorithm then uses the last retained point as the new starting point and continues to iterate backward until the entire boundary point set is traversed. After a vertex is deleted, the point set number corresponding to the convex hull boundary needs to be updated again in a counterclockwise direction.

[0015] A distributed resource flexibility quantification system based on feasible domain and economy includes: The module for characterizing the feasible region of aggregate flexibility is used to perform a deterministic equivalent transformation of the chance constraint through the inverse cumulative distribution function, and then to approximate characterize the feasible region of aggregate flexibility. The module for expressing the economic characteristics of the aggregation flexibility feasible domain is used to construct an optimized scheduling model for the distributed resources of the aggregator with the goal of minimizing the total scheduling cost of the aggregator for each distributed resource, and to obtain the marginal electricity price based on the coupling node between the aggregator and the distribution network. The aggregate flexibility feasible region boundary sparsification module is used to calculate the area change rate and marginal electricity price change rate of the aggregate flexibility feasible region, construct the comprehensive importance function of the vertices, and simplify the boundary of the feasible region by adopting the feasible region vertex sparsification process strategy.

[0016] A computer-readable storage device, wherein computer program instructions are permanently stored therein, and when the computer program instructions are invoked and loaded by a processor and executed, the method described in any one of claims 1 to 7 is performed.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. Comprehensive description of the spatiotemporal characteristics of flexibility: This method constructs an aggregated flexibility feasible domain, which can accurately describe the spatial distribution and temporal coupling characteristics of distribution network flexibility, overcoming the problem that traditional index quantification methods simply add up the data and have weak spatial characterization capabilities.

[0018] 2. Efficient handling of uncertainty: By adopting the opportunity constraint deterministic transformation, the problem of excessively conservative boundaries caused by the reliance on robust worst-case scenarios in traditional feasible region methods is solved, thereby improving the flexibility of space utilization while ensuring safety.

[0019] 3. Achieve unified representation of physical feasible region and economic characteristics: Embed the marginal electricity price of coupled nodes as an economic signal into the feasible region, solving the problem that traditional methods only focus on physical capabilities and lack economic value mapping, so that flexibility can be directly used for market transactions and scheduling. When the vertices are sparsified, the key physical boundaries of the feasible region and the marginal electricity price jump points are preserved at the same time, avoiding the distortion of economic boundaries caused by traditional geometric simplification.

[0020] 4. Improve the efficiency of distribution network resource allocation: Through precise quantification and economic signal conversion, distributed resources can flexibly and effectively participate in system scheduling. Attached Figure Description

[0021] Appendix Figure 1 This is a flowchart illustrating the execution of the method in this embodiment. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0023] As attached Figure 1 As shown, an aggregated distributed resource flexibility quantification system based on temporally coupled feasible domain characterization and economic characteristic representation is presented. The method includes the following steps: Step 1: Based on the linearized power flow constraints within the aggregator, typical resource constraints including temporal coupling characteristics, and network security opportunity constraints based on the prediction error of normally distributed source loads, a realistic feasible region for aggregation flexibility is constructed. Then, based on this, the opportunity constraints are transformed deterministically using the inverse cumulative distribution function. The specific process is as follows: Aggregators extract the overall adjustable capacity boundary within their jurisdiction. Considering time-series coupling characteristics and source-load prediction errors, they construct an aggregated feasible region to quantify the aggregation flexibility of local resources. This represents the range of active and reactive power adjustment achievable by the aggregator at the coupling node with the upper-level grid. The flexibility provided by the aggregator stems from the various distributed resources it aggregates, including photovoltaic systems, reducible flexible loads, and energy storage systems in this invention. These resources, under power flow constraints, self-regulation constraints, and network security constraints, collectively constitute a feasible space. Due to the energy continuity of the energy storage system's cross-time-period adjustment devices, the physical boundaries of flexibility at different times are interconnected. Historical scheduling behavior directly compresses or expands the adjustable space in subsequent time periods. Using the time-series trajectories of active and reactive power achievable at the coupling node between the aggregator and the upper-level grid throughout the entire scheduling cycle as the observation dimension, the true aggregated flexibility feasible region Ω is defined. PCC-E To constrain the boundary depth of each time period and cover the entire scheduling cycle, 2 T 3D time-series trajectory polyhedron.

[0024] (1) In the formula, P PCC = [ , …, ] T and Q PCC = [ , …, ] TThese are the active and reactive power vectors of the coupled nodes, respectively; T Representing a moment; A * B * and β The coefficient matrix and vector, jointly determined by all network and resource constraints, serve as the boundaries characterizing the flexibility of the coupled node PCC under multi-time-period association. Specific constraints include: 1) Distribution network linearization power flow constraints: (2) In the formula, i and j Branch roads ij Sending node number and receiving node number; and They are respectively t Time is determined by nodes i Calculated branches ij Active power and reactive power; r ij and x ij Branch roads ij Resistance and reactance; and They are respectively t Time Node i and j The voltage; and These are the sets of all nodes and branches in the network.

[0025] 2) Node power balance constraints: (3) (4) In the formula, and They are respectively t Time Node i Active and reactive power are injected into the upper part; and They are respectively t Time Node i The actual active and reactive power output of photovoltaic panels; , and , They are respectively t Time Node i The actual active and reactive power consumed by energy storage and scalable flexible loads.

[0026] The demand for photovoltaic power output and reducible flexible load consists of a forecast baseline value and a random forecast error, with the forecast error following a normal distribution with a mean of zero. t The time expression is: (5) (6) In the formula, , They are respectively t Time Node i The above forecasts photovoltaic output and demand for scalable flexible loads; , These are the active power reductions from photovoltaic and reduceable flexible loads, respectively. , These are the standard deviations of the prediction errors for the two methods.

[0027] 3) Opportunity constraints on the upper and lower limits of node voltage: (7) (8) In the formula, P (·) represents the probability measure function; and These are the upper and lower limits of the system's allowed voltage operation, respectively; , This is used to describe the risk thresholds for system voltage exceeding upper and lower limits under uncertain conditions.

[0028] Based on the inverse cumulative distribution function of the normal distribution, the chance constraints of the upper and lower limits of the node voltage constraining the feasible region are transformed into deterministic expressions: (9) (10) In the formula, (·) is the inverse cumulative distribution function of the normal distribution; The standard deviation of node voltage fluctuation; This is the covariance matrix of the photovoltaic and load forecasting errors for all nodes in the entire network. For nodes i The voltage sensitivity coefficient vector of the injected power to each node in the network.

[0029] 4) Line capacity opportunity constraints based on polygonal approximation linearization: (11) In the formula, branch road ij Maximum allowed capacity; α c ,β c and γ c These represent the coefficients after linearization; c The numbering of the edges of the inner approximation polygon; This is used to describe the risk threshold of system line capacity exceeding limits under uncertain conditions.

[0030] (12) (13) (14) In the formula, branch road ij Apparent power in the inward approximation polygon c The standard deviation of the fluctuation along the direction of the line segment; , and Branch roads ij The sensitivity vectors of apparent power, active power, and reactive power.

[0031] 5) Constraints of photovoltaic systems: (15) (16) (17) In the formula, for t Nodes for time prediction i Maximum output power of photovoltaic panels; For nodes i The maximum power factor angle of the photovoltaic inverter; Equation (12) is the linearized expression of Equation (11); 6) Reducible flexible load constraints: Reducible flexible loads provide flexibility by directly reducing power during operation, enabling rapid and flexible dispatch responses, including non-critical loads such as building lighting and garage ventilation systems; (13) (14) (15) In the formula, and They are respectively t Time Node i The maximum acceptable reduction in active and reactive loads for reducible flexible loads; and They are respectively t Time Nodei The reduction in active and reactive power of the flexible load can be reduced. For nodes i The power factor of the flexible load that can be reduced; 7) Constraints of energy storage systems including time-series coupling characteristics: Energy storage systems offer flexibility through their inter-period charge and discharge behavior. Their state is constrained not only by charge and discharge power boundaries but also by time-coupled states of charge, as expressed in the following constraint expression: (twenty one) (twenty two) (twenty three) (twenty four) (25) In the formula, and They are respectively t and t -1 time node i The actual electricity generated by the energy storage system; and These are the charging and discharging efficiencies of the energy storage system; and They are respectively t Time Node i The active power of the energy storage system during charging and discharging; For time intervals; and Maximum charge and discharge power limits for energy storage systems; This represents the maximum capacity of the energy storage system. and These are the upper and lower limits of the state of charge of the energy storage system. and These are the reactive power and power factor angle of the energy storage system, respectively.

[0032] Subsequently, an initial convex polyhedral feasible region is constructed within the real feasible region using the McCormick Envelope linearization technique. Based on this initial feasible region, a vertex search method is used to gradually approximate the real boundary from the inside out, thus proposing a method for characterizing the feasible region of aggregated distributed resource flexibility.

[0033] Using a vertex search method, approximate Ω from the inside out. PCC-E The specific steps are as follows: 1) Initialization phase: Construct an initial approximate polyhedron. Select multiple initial vertices within the real aggregate feasible region to form an initial solution set, and determine a polyhedron as an estimate of the initial feasible region through convex combination characterization.

[0034] (26) (27) (28) In the formula, The area of ​​the initial polyhedron. for t Initial feasible region plane for the time period for t Initial feasible domain vertices for the time period; v Number the vertices; Ω (0) The initial feasible region polyhedral expression for all time steps considering temporal coupling characteristics.

[0035] The bilinear term in the objective function is linearized using the McCormick Envelope method, which introduces auxiliary variables. w t,v and υ t,v The linearized objective function is: (29) In the formula, w t,v for Linearized approximation of the term; υ t,v for Linearized approximation of the term; and They represent The upper and lower bounds; and They represent The upper and lower boundaries.

[0036] 2) Iterative Expansion: Based on the initial feasible region, the boundary of the approximate polyhedron is gradually expanded from the inside out to approximate the true feasible region boundary. The search starts at the midpoint of each edge of the current polyhedron boundary, the search direction is the outward normal vector of each edge, and the search objective is to maximize the projected area of ​​the feasible region in this direction (i.e., the expansion of the approximate feasible region).

[0037] (30) In the formula, For the first k After the second iteration t The area of ​​the time-space plane; det[·] is the determinant of the matrix; for t The total number of vertices in the feasible region at any given time; For the first k After the second iteration ev The direction of the external normal vector; It is the midpoint of the corresponding edge; is a parameterized variable representing the feasible region expansion scale, and its value range is [0, +∞]. e v For the first k The vertex obtained in the next iteration ( , )and( , The edges formed by ) For the edge e v The new vertices obtained from the baseline search, where, v' Indicates by the first v vertices and v The new vertex number obtained by searching for +1 vertex; Indicates the first The new vertex number obtained by searching the first vertex and the first vertex.

[0038] Merge the feasible vertices found in the current iteration with the original vertex set, update the polyhedral approximation model of the feasible region, and start a new round of iterations. All vertices after the update are still numbered in counterclockwise order.

[0039] 3) Termination condition: The total area change rate is used to determine whether the approximate feasible region has sufficiently approximated the true boundary. When the total area change rate resulting from two consecutive expansions is lower than a preset threshold, the boundary is considered to have stabilized, and the iteration ends.

[0040] (31) In the formula, For the first k Obtained in the next iteration t Aggregate feasible region area over time period; r FR,1 This is a preset threshold for the rate of change of total area.

[0041] The feasible region expression for the convex polyhedron obtained by approximating the true feasible region from the inside out based on vertex search is as follows: (32) In the formula, Ω PCC-V is the flexible feasible region based on vertex characterization; conv(·) is the convex hull of the point set; for t The vertex of the feasible region at any given time.

[0042] Step 2: With the goal of minimizing the total scheduling cost of the aggregator for each distributed resource, construct an aggregator resource optimization scheduling model. Based on duality theory and KKT conditions, calculate the marginal electricity price of the aggregator and the coupled nodes of the distribution network, describe the economic characteristics of each point within the feasible region of aggregation, and transform the physical potential of flexibility into economic signals for market transactions and scheduling.

[0043] The specific process is as follows: The aggregator uses the total scheduling cost of its internal distributed resources... The goal is to minimize the amount of resources allocated.

[0044] (33) (34) (35) (36) In the formula, The total cost of scheduling internal distributed resources for the aggregator; , , They are respectively t The cost required for aggregators to schedule various photovoltaic systems, scalable flexible loads, and energy storage systems within a given time period; , , , , They are respectively t Unit adjustment cost parameters for active and reactive power of various resources during different time periods; , , They are respectively t Time period nodes i The active power reduction and reactive power adjustment of photovoltaic systems; , They are respectively t Time period nodes i This can reduce both active and reactive power of the load; , They are respectively t Time period nodes i The charging and discharging power of the energy storage system.

[0045] By constructing the Lagrangian function of the objective function and calculating the partial derivatives of the Lagrangian function with respect to the active and reactive power output of the aggregated resources, the expression for the marginal electricity price can be obtained, as shown in Equation (37). The marginal electricity price of the aggregator directly corresponds to the shadow price of active and reactive power at the coupling point. πsub-P and π sub-Q .

[0046] (37) In the formula, Let Lagrange function be the objective function corresponding to the optimized scheduling objective function of the aggregator's distributed resources. and These represent the changes in active and reactive power at the coupling point between the aggregator and the distribution network, respectively.

[0047] Step 3: Calculate the area change rate and aggregate marginal electricity price change rate of each vertex in the feasible region, construct the comprehensive importance function of the vertices, and delete vertices that have little impact on the boundary profile or marginal electricity price. This effectively reduces the computational dimension of the model while achieving high-fidelity preservation of important physical boundaries and economic characteristic points.

[0048] The specific process is as follows: for t Any vertex of the feasible region of time-segment aggregation Its adjacent l Rate of change of area of ​​a polygon formed by points for (38) (39) In the formula, As vertex A t,v Its adjacent l The area of ​​the polygon formed by the points. l For the vertex A t,v The number of adjacent vertices. If Smaller indicates that the vertex A t,v To the top A t,v+l It has very little impact on the local shape of the boundary.

[0049] Based on the calculated marginal electricity price of the aggregation node, the vertex A t,v With adjacent vertices A t,v+1 and A t,v-1 Electricity price change coefficient for (40) In the formula, It is a 2-norm. As vertex A t,vThe corresponding marginal electricity price vector of the aggregation node, This serves as the benchmark normalized electricity price. If this peak touches the boundary of network security or equipment output extreme values, its corresponding shadow price will undergo a jump, causing... Significantly increased.

[0050] Based on the dual characteristics of the area change rate and the aggregate marginal electricity price change rate of each vertex, a comprehensive importance function for the vertices is constructed: (41) In the formula, and These are the weighting coefficients for area and electricity price characteristics, respectively. Let the sparsity synthesis threshold be... r FR,2 ,when At that time, the vertex A t,v The impact on the feasible region area and the aggregated marginal electricity price is relatively small, so it is identified as a redundant vertex and deleted.

[0051] The algorithm starts from a certain initial vertex A t,v Begin by gradually incorporating the next adjacent vertex, forming... l For polygons of size 2, 3, 4…, calculate the comprehensive importance function for each vertex in turn. The comprehensive importance function is considered when it first exceeds a threshold. r FR,2 When a newly added point has a significant impact on the boundary profile or marginal electricity price, only the first and second-to-last points of the polygon are retained, while the remaining intermediate points are considered redundant and deleted. The algorithm then iterates backward from the last retained point as the new starting point until the entire boundary point set has been traversed. After a vertex is deleted, the point set number corresponding to the convex hull boundary needs to be updated counterclockwise. This method effectively reduces the computational dimensionality of the model while achieving high-fidelity preservation of important physical boundaries and economic characteristic points of the feasible region.

[0052] Based on the above method embodiments, the present invention provides a system for performing the above methods.

[0053] One embodiment of the present invention provides a distributed resource flexibility quantification system based on feasible domain and economy, including: a module for characterizing the feasible domain of aggregate flexibility, a module for expressing the economic characteristics of the feasible domain of aggregate flexibility, and a module for simplifying the boundary of the feasible domain of aggregate flexibility; The module for characterizing the feasible region of aggregate flexibility is used to perform a deterministic equivalent transformation of the chance constraint through the inverse cumulative distribution function, and then to approximate characterize the feasible region of aggregate flexibility. The module for expressing the economic characteristics of the aggregation flexibility feasible domain is used to construct an optimized scheduling model for the distributed resources of the aggregator with the goal of minimizing the total scheduling cost of the aggregator for each distributed resource, and to obtain the marginal electricity price based on the coupling node between the aggregator and the distribution network. The aggregate flexibility feasible region boundary sparsification module is used to calculate the area change rate and marginal electricity price change rate of the aggregate flexibility feasible region, construct the comprehensive importance function of the vertices, and simplify the boundary of the feasible region by adopting the feasible region vertex sparsification process strategy.

[0054] This application also provides an electronic device, which may include at least one processor and at least one memory. The processor may include one or more processing cores. The processor connects to various parts of the server using various interfaces and lines, and performs various functions of the server and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory, and by calling data stored in the memory.

[0055] This application also provides a computer-readable storage medium storing instructions. When executed by one or more processors, these instructions cause an electronic device to perform one or more of the methods described in the above embodiments.

[0056] Furthermore, the functional units in this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0057] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and the disclosure of practical truth. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for quantifying the flexibility of distributed resources based on feasible domain and economics, characterized in that, Specifically, the following steps are included: S1 constructs the real aggregate flexibility feasible region, performs deterministic equivalent transformation of chance constraints through inverse cumulative distribution function, and then constructs an initial convex polyhedral feasible region inside the real aggregate flexibility feasible region. The vertex search method is used to gradually approximate the real aggregate flexibility feasible region from the inside to the outside, so as to achieve an approximate characterization of the aggregate flexibility feasible region. S2 constructs an optimal scheduling model for distributed resources of aggregators, with the goal of minimizing the total scheduling cost of each distributed resource by the aggregator, and obtains the marginal electricity price based on the coupling nodes of the aggregator and the distribution network according to duality theory and KKT conditions. S3 calculates the rate of change of the feasible region area and the rate of change of the marginal electricity price associated with each vertex, constructs the comprehensive importance function of the vertex, and simplifies the boundary of the feasible region.

2. The distributed resource flexibility quantification method based on feasible domain and economy according to claim 1, characterized in that, The construction of the real aggregation flexibility feasible region mentioned in step S1 specifically means that the real aggregation flexibility feasible region is a 2-dimensional region that is constrained by the boundary depth of each time period and covers the entire scheduling cycle. T The specific expression for the 3D time-series trajectory polyhedron is as follows: （1）， In the formula, P PCC and Q PCC These are the active and reactive power vectors of the coupled nodes, respectively; T Representing a moment; A * B * and β The coefficient matrix and vector, jointly determined by all network and resource constraints, are used to characterize the boundaries of the flexibility of the coupled node PCC under multi-time-period association.

3. The distributed resource flexibility quantification method based on feasible region and economy according to claim 2, characterized in that, The constraints of the feasible region of true aggregation flexibility include: (1) Power flow constraints for linearization of distribution network: （2）， In the formula, i and j Branch roads ij Sending node number and receiving node number; and They are respectively t Time is determined by nodes i Calculated branches ij Active power and reactive power; r ij and x ij Branch roads ij Resistance and reactance; and They are respectively t Time Node i and j The voltage; and These are the sets of all nodes and branches in the network, respectively. (2) Node power balance constraints: （3）， （4）， In the formula, and They are respectively t Time Node i Active and reactive power are injected into the upper part; and They are respectively t Time Node i The actual active and reactive power output of photovoltaic panels; , and , They are respectively t Time Node i The actual active and reactive power consumed by energy storage and scalable flexible loads; The demand for photovoltaic power output and reducible flexible load consists of a forecast baseline value and a random forecast error, with the forecast error following a normal distribution with a mean of zero. t The time expression is: （5）， （6）， In the formula, , They are respectively t Time Node i The above forecasts photovoltaic output and demand for scalable flexible loads; , These are the active power reductions from photovoltaic and reduceable flexible loads, respectively. , These are the standard deviations of the prediction errors of the two variables; (3) Opportunity constraints on the upper and lower limits of node voltage: （7）， （8）， In the formula, P (·) represents the probability measure function; and These are the upper and lower limits of the system's allowed voltage operation, respectively; , This describes the risk thresholds for system voltage exceeding upper and lower limits under uncertain conditions; (4) Line capacity opportunity constraints based on polygonal approximation linearization: （9）， In the formula, branch road ij Maximum allowed capacity; α c , β c and γ c These represent the coefficients after linearization; c The numbering of the edges of the inner approximation polygon; This is a threshold used to describe the risk of system line capacity exceeding limits under conditions of uncertainty; (5) Constraints of photovoltaic systems: （10）， （11）， （12）， In the formula, for t Nodes for time prediction i Maximum output power of photovoltaic panels; For nodes i The maximum power factor angle of the photovoltaic inverter; Equation (12) is the linearized expression of Equation (11); (6) Reduceable flexible load constraints: Reducible flexible loads provide flexibility by directly reducing power during operation, enabling rapid and flexible dispatch responses, including non-critical loads such as building lighting and garage ventilation systems; （13）， （14）， （15）， In the formula, and They are respectively t Time Node i The maximum acceptable reduction in active and reactive loads for reducible flexible loads; and They are respectively t Time Node i The reduction in active and reactive power of the flexible load can be reduced. For nodes i The power factor of the flexible load that can be reduced; (7) Constraints of energy storage systems including time-series coupling characteristics: Energy storage systems offer flexibility through their inter-period charge and discharge behavior. Their state is constrained not only by charge and discharge power boundaries but also by time-coupled states of charge, as expressed in the following constraint expression: （16）， （17）， （18）， （19）， （20）， In the formula, and They are respectively t and t -1 time node i The actual electricity generated by the energy storage system; and These are the charging and discharging efficiencies of the energy storage system; and They are respectively t Time Node i The active power of the energy storage system during charging and discharging; For time intervals; and Maximum charge and discharge power limits for energy storage systems; This represents the maximum capacity of the energy storage system. and These are the upper and lower limits of the state of charge of the energy storage system. and These are the reactive power and power factor angle of the energy storage system, respectively.

4. The distributed resource flexibility quantification method based on feasible region and economy according to claim 3, characterized in that, The deterministic equivalent transformation of the chance constraint using the inverse cumulative distribution function described in step S1 specifically involves: Based on the inverse cumulative distribution function of the normal distribution, the opportunity constraints of node voltage upper and lower limits and line capacity constraining the feasible region are equivalently transformed into deterministic expressions, the specific expressions of which are: （21）， （22）， In the formula, (·) is the inverse cumulative distribution function of the normal distribution; The standard deviation of node voltage fluctuation; branch road ij Apparent power in the inward approximation polygon c Standard deviation of fluctuation along the stripe direction; （23）， （24）， （25）， In the formula, This is the covariance matrix of the photovoltaic and load forecasting errors for all nodes in the entire network. For nodes i The sensitivity coefficient vector of voltage to the injected power at each node of the entire network; , and Branch roads ij The sensitivity vectors of apparent power, active power, and reactive power.

5. The distributed resource flexibility quantification method based on feasible region and economy according to claim 4, characterized in that, The approximate characterization of the feasible region of aggregation flexibility described in step S1 includes the following steps: (1) Initialization process: Construct an initial convex polyhedron feasible region, select multiple initial vertices within the real aggregate feasible region to form an initial solution set, and determine a polyhedron as an estimate of the initial feasible region through convex combination characterization. （26）， （27）， （28）， In the formula, The area of ​​the initial polyhedron; for t Initial feasible region plane for the time period; for t Initial feasible domain vertices for the time period; v Number the vertices; Ω (0) The initial feasible domain polyhedral expression for all time steps considering temporal coupling characteristics; The bilinear term in the objective function is linearized using the McCormick Envelope method, which introduces auxiliary variables. w t,v and υ t,v The linearized objective function is: （29）， In the formula, for Linearized approximation of the term; for Linearized approximation of the term; and They represent The upper and lower bounds; and They represent The upper and lower bounds; (2) Iterative expansion process: Based on the initial feasible region, the boundary of the approximate polyhedron is gradually expanded from the inside out to approximate the actual feasible region boundary; the search starts at the midpoint of each edge of the current polyhedron boundary, the search direction is the outward normal vector of each edge, and the search objective is to maximize the projected area of ​​the feasible region in this direction. （30）， In the formula, For the first k After the second iteration t The area of ​​the time-space plane; det[·] is the determinant of the matrix; for t The total number of vertices in the feasible region at any given time; For the first k After the second iteration ev The direction of the external normal vector; It is the midpoint of the corresponding edge; is a parameterized variable representing the feasible region expansion scale, and its value range is [0, +∞]. ev For the first k The vertex obtained in the next iteration ( , )and( , The edges formed by ) For the edge ev The new vertices obtained from the baseline search, where, v 'Indicates by the first v vertices and v The new vertex number obtained by searching for +1 vertex; Indicates the first The new vertex number obtained by searching the first vertex and the first vertex; Merge the feasible vertices found in the current iteration with the original vertex set, update the polyhedral approximation model of the feasible region, and start a new round of iteration. All vertices after the update are still numbered in counterclockwise order. (3) Termination conditions: The rate of change of the total area is used to determine whether the approximate feasible region has sufficiently approximated the true boundary. When the rate of change of the total area resulting from two consecutive expansions is lower than a preset threshold, the boundary is considered to have stabilized, and the iteration ends. （31）， In the formula, For the first k Obtained in the next iteration t Aggregate feasible region area over time period; r FR,1 The preset threshold for the rate of change of total area; The feasible region expression for the convex polyhedron obtained by approximating the true feasible region from the inside out based on vertex search is as follows: （32） In the formula, Ω PCC-V is the flexible feasible region based on vertex characterization; conv(·) is the convex hull of the point set; for t The vertex of the feasible region at any given time.

6. The distributed resource flexibility quantification method based on feasible region and economy according to claim 1, characterized in that, The specific expression for the optimized scheduling model of the aggregator's distributed resources described in step S2 is as follows: （33）， （34）， （35）， （36）， In the formula, The total cost of scheduling internal distributed resources for the aggregator; , , They are respectively t The cost required for aggregators to schedule various photovoltaic systems, scalable flexible loads, and energy storage systems within a given time period; , , , , They are respectively t Unit adjustment cost parameters for active and reactive power of various resources during different time periods; , , They are respectively t Time period nodes i The active power reduction and reactive power adjustment of photovoltaic systems; , They are respectively t Time period nodes i This can reduce both active and reactive power of the load; , They are respectively t Time period nodes i The charging and discharging power of the energy storage system.

7. The method for quantifying the flexibility of distributed resources based on feasible domain and economy according to claim 6, is characterized in that, The optimal scheduling model of the aggregator's distributed resources is transformed into a Lagrangian function, and based on duality theory and KKT conditions, the expression for the marginal electricity price of feasible points within the aggregate feasible region is derived. This transforms the physical potential for flexibility into an economic signal for market trading and scheduling. Specifically: （37）， In the formula, π sub-P and π sub-Q represents the marginal active and reactive electricity prices for the aggregator's flexibility. Let Lagrange function be the objective function corresponding to the optimized scheduling objective function of the aggregator's distributed resources. and These represent the changes in active and reactive power at the coupling point between the aggregator and the distribution network, respectively.

8. The distributed resource flexibility quantification method based on feasible region and economy according to claim 1, characterized in that, In step S3, The expression for the area change rate of the feasible region of aggregation flexibility is: for t Any vertex of the feasible region of time-segment aggregation Its adjacent l Rate of change of area of ​​a polygon formed by points for: （38）， （39）， In the formula, As vertex At,v Its adjacent l The area of ​​the polygon formed by the points. l For the vertex At,v The number of adjacent vertices, if Smaller indicates that the vertex At,v To the top At,v+l It has very little impact on the local shape of the boundary; The expression for the marginal electricity price change rate is: Based on the calculated marginal electricity price of the aggregation node, the vertex A t,v With adjacent vertices A t,v+1 and A t,v-1 Electricity price change coefficient for: （40）， In the formula, It is a 2-norm. As vertex A t,v The corresponding marginal electricity price vector of the aggregation node, As a benchmark normalized electricity price, if this peak touches the boundary of network security or equipment output extreme values, its corresponding shadow price will undergo a jump, causing... Significantly increased; The vertex comprehensive importance function is: （41）， In the formula, and These are the weighting coefficients for area and electricity price characteristics, respectively. Let the sparsity synthesis threshold be... r FR,2 ,when At that time, the vertex A t,v The impact on the feasible region area and the aggregated marginal electricity price is relatively small, so it is identified as a redundant vertex and deleted. The algorithm starts from a certain initial vertex A t,v Begin by gradually incorporating the next adjacent vertex, forming... l For polygons with values ​​of 2, 3, 4…, calculate the comprehensive importance function for each vertex in turn. The comprehensive importance function is considered when it first exceeds a threshold. r FR,2 When the newly added point has a significant impact on the boundary profile or marginal electricity price, only the first and second-to-last points in the polygon are retained, and the remaining intermediate points are considered redundant and deleted. The algorithm then uses the last retained point as the new starting point and continues to iterate backward until the entire boundary point set is traversed. After a vertex is deleted, the point set number corresponding to the convex hull boundary needs to be updated again in a counterclockwise direction.

9. A distributed resource flexibility quantification system based on feasible domain and economics, characterized in that, For performing the method as described in any one of claims 1 to 8, comprising: The module for characterizing the feasible region of aggregate flexibility is used to perform a deterministic equivalent transformation of the chance constraint through the inverse cumulative distribution function, and then to approximate characterize the feasible region of aggregate flexibility. The module for expressing the economic characteristics of the aggregation flexibility feasible domain is used to construct an optimized scheduling model for the distributed resources of the aggregator with the goal of minimizing the total scheduling cost of the aggregator for each distributed resource, and to obtain the marginal electricity price based on the coupling node between the aggregator and the distribution network. The aggregate flexibility feasible region boundary sparsification module is used to calculate the area change rate and marginal electricity price change rate of the aggregate flexibility feasible region, construct the comprehensive importance function of the vertices, and simplify the boundary of the feasible region by adopting the feasible region vertex sparsification process strategy.

10. A computer-readable storage device, characterized in that, The storage device contains computer program instructions, which are invoked and loaded by the processor and executed to perform the method as described in any one of claims 1 to 8.

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