A distributed resource aggregation feasible region approximation method considering network constraints

Abstract

The application discloses a kind of distributed resource aggregation feasible region in-approximation method considering network constraint, belong to power system operation optimization and dispatching control technical field.Based on the power-energy coupling relationship of distributed resource, construct cumulative energy constraint matrix and dimension matching energy boundary constant vector, form distributed resource initial aggregation base set;Max-min double-layer optimization model is constructed to identify default point, search the maximum distance of current aggregation base set in accurate aggregation feasible region and default point, solve the security boundary reference point of corresponding default direction, contract the boundary constant vector corresponding to the effective boundary plane to the normal projection value outside the security boundary reference point;Iterative execution default point identification and boundary contraction update, ensure that the aggregation interface power point in the obtained in-approximation aggregation feasible region can meet network constraint constraint, and can improve the description accuracy of multi-period distributed resource adjustable capacity while reducing the scale of upper distribution network dispatching optimization model.

Description

Technical Field

[0001] This invention relates to the field of power system operation optimization and dispatch control technology, specifically to an approximate method within the feasible domain for distributed resource aggregation considering network constraints. Background Technology

[0002] In recent years, distributed energy resources (DERs) have been massively integrated into distribution networks, gradually forming a new power system characterized by a high proportion of new energy sources and the coordinated operation of multiple types of flexible resources. Distributed resources such as distributed photovoltaics, energy storage, adjustable loads, and micro gas turbines can effectively improve the grid's regulation margin and smooth out fluctuations in new energy sources. However, the dispersed locations, small individual capacities, and significant differences in operational constraints of these massive distributed resources present multiple bottlenecks for traditional refined centralized dispatching models. On the one hand, modeling all distributed resources individually would significantly increase the number of optimization variables and constraints, resulting in large model sizes and long solution times, making it difficult to meet the timeliness requirements of day-ahead and rolling dispatching. On the other hand, uploading the underlying distributed resource operating parameters and control status to the dispatching master station would increase communication and data storage pressure and may lead to the risk of leakage of user energy consumption data and distributed asset information.

[0003] To address the challenges of high computational load, communication pressure, and privacy protection difficulties arising from the refined modeling of massive distributed resources, distributed resource aggregation modeling technology has gained increasing attention. This technology equates multiple heterogeneous distributed resources within a region to a single aggregation unit. By quantifying the power range within which the aggregation unit can operate safely—the aggregation feasible region—it achieves model dimensionality reduction, decreases the number of scheduling optimization variables, and shortens model solution time. Simultaneously, it provides a standardized and equivalent interactive interface for distributed resources to participate in grid dispatch and virtual power plant market transactions.

[0004] However, existing aggregate feasible region construction schemes typically only consider the upper and lower limits of output of distributed resource entities and energy storage constraints, directly ignoring or roughly simplifying network constraints such as power flow, node voltage, and branch capacity. This leads to a deviation between the generated aggregate feasible region and the actual safe operation boundary of the distribution network. If the aggregation model completely ignores network constraints, the scheduling scheme obtained based on the relaxed aggregate feasible region may cause node voltage exceeding limits or line overload. On the other hand, if all resource constraints and network constraints are fully embedded in the upper-level scheduling model, the model size will increase significantly, weakening the advantages of lightweight and fast solution of the aggregation method.

[0005] Furthermore, in multi-period scheduling scenarios, distributed resources such as energy storage and adjustable loads exhibit cross-period temporal coupling relationships. The charging and discharging power, energy storage state, and continuous response state of the adjustable load in the current period are all affected by decisions made in previous and subsequent periods, resulting in a complex, high-dimensional polyhedral structure for the actual aggregated feasible domain. Existing methods, which only set independent power boundaries for each period, cannot fully characterize the power-energy coupling relationship between consecutive periods, thus leading to errors in the assessment of regional adjustable capacity. Summary of the Invention

[0006] The purpose of this invention is to provide an approximate method for the aggregated feasible region of distributed resources that considers network constraints. Under the premise of distribution network security constraints, the method uses an inner approximation solution mechanism to ensure that the obtained aggregated feasible region is located inside the exact aggregated feasible region. This ensures that the aggregated interface power points within the inner approximate aggregated feasible region can satisfy distributed resource operation constraints, distribution network power flow balance equation constraints, and safe operation constraints. Furthermore, it can improve the accuracy of characterizing the multi-time period distributed resource adjustability while reducing the scale of the upper-level distribution network scheduling optimization model.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] An approximate method for distributed resource aggregation within the feasible domain considering network constraints includes the following steps:

[0009] S1. Initial Aggregate Base Set Construction: Define the aggregate interface power as the net active power exchange between the distributed resource aggregation area and the upper-level power grid at the common connection point, and form an aggregate interface power vector by arranging the aggregate interface power of each scheduling period in chronological order; construct an energy change model based on the power-energy coupling relationship of distributed resources, and solve for the upper and lower boundary values ​​of the cumulative energy of the aggregate interface power within any consecutive scheduling period interval; construct a cumulative energy constraint matrix formed by stacking forward and reverse cumulative power constraints according to the coverage of each consecutive scheduling period interval, and construct an energy boundary constant vector that matches the dimension of the cumulative energy constraint matrix; the cumulative energy constraint matrix and the energy boundary constant vector together form the initial aggregate base set of distributed resources.

[0010] S2. Default Point Identification: Based on the distribution network operation state variable vector and the distributed resource internal decision variable vector, distributed resource operation constraints, the correlation mapping between the aggregation interface power vector and the distributed resource internal decision variable vector, the distribution network power flow balance equation constraints, and safe operation constraints, an accurate aggregation feasible region is constructed. Based on robust optimization, a max-min two-level optimization model is constructed. The current aggregation basis set is used as the feasible region of the outer maximization problem. The inner problem calculates the shortest distance from the candidate aggregation power point to the accurate aggregation feasible region, and searches for the default point with the largest distance relative to the accurate aggregation feasible region in the current aggregation basis set.

[0011] S3, Boundary Shrinkage Update: For the default point with the largest distance, solve for the feasible aggregation interface power point within the precise aggregation feasible region that is closest to the default point, and determine the feasible aggregation interface power point as the safe boundary reference point of the precise aggregation feasible region in the corresponding default direction; determine the effective boundary plane of the default point in the current aggregation basis set, and shrink the corresponding boundary constant vector to the projection value of the safe boundary reference point in the normal direction outside the effective boundary plane;

[0012] S4. Iterative Update: Iteratively execute the default point identification and boundary shrinkage update, continuously shrinking the current aggregation base set boundary inward until the shortest distance from the candidate aggregation power point in the current aggregation base set to the precise aggregation feasible region does not exceed the preset tolerance, thus obtaining an approximate aggregation feasible region within the distributed resources that satisfies the distribution network constraints.

[0013] Furthermore, the present invention also includes the following steps:

[0014] S6. Embedding of Upper-Level Distribution Network Scheduling Optimization Model: An aggregated interface power vector is introduced into the upper-level distribution network scheduling optimization model. The approximate aggregated feasible region within the distributed resources obtained by iterative update is used as an embedded constraint. The upper-level distribution network scheduling optimization model is solved to obtain the optimal aggregated interface power command. The optimal aggregated interface power command is then decomposed and allocated to each distributed resource to form an executable scheduling scheme. The upper-level distribution network scheduling optimization model includes a day-ahead scheduling model, a rolling scheduling model, or a primary-distribution coordinated scheduling model.

[0015] Furthermore, the distribution network operation status variable vector includes node voltage, branch active power, and branch reactive power, and the safe operation constraints include node voltage constraints and branch capacity constraints; the distributed resource internal decision variable vector is formed by stacking photovoltaic output, energy storage charging and discharging power, energy storage energy status, and adjustable load reduction amount according to time periods.

[0016] Furthermore, the process of solving for the upper and lower boundary values ​​of the aggregated power cumulative energy within any continuous scheduling time interval includes: defining the internal decision variable vector of the distributed resource. The distributed resource internal decision variable vector The distributed resource operation constraints are formed by stacking photovoltaic output, energy storage charging and discharging power, energy storage status, and adjustable load reduction according to time periods.

[0017]

[0018] in, This is the distributed resource operation constraint coefficient matrix. The distributed resource operation limit vector includes photovoltaic output limits, energy storage charge / discharge power limits, energy storage energy limits, and adjustable load response limits. This distributed resource operation limit vector differs from the energy boundary constant vector used to define the initial aggregation base set boundary. An aggregation interface power vector is then established. With distributed resource internal decision variable vector The association mapping between them is used to solve the upper and lower boundary values ​​of the cumulative energy of the aggregated interface power within any continuous scheduling time interval based on the distributed resource operation constraints.

[0019] Furthermore, the aggregation interface power vector With distributed resource internal decision variable vector The association mapping between them is as follows:

[0020]

[0021] in, For aggregated interface power vectors, For the first Aggregated interface power for each scheduling period Number of scheduling periods; This is the aggregate power mapping matrix. Let represent the coefficient vector in the matrix, and The aggregated power mapping matrix The In the row, with the first The coefficients corresponding to the photovoltaic output, energy storage discharge power, and adjustable load reduction during the time period are positive, and are consistent with the first... The coefficient corresponding to the time period energy storage charging power is negative, while the coefficient corresponding to the energy storage state and variables that do not directly form interface power is zero.

[0022] Furthermore, the upper and lower boundary values ​​of the cumulative energy of the aggregated interface power within any continuous scheduling time interval are solved using the following linear programming models:

[0023]

[0024]

[0025] in, , The length of a single scheduling period. For the first Aggregated interface power for each scheduling period and Represents any continuous scheduling time interval The upper and lower boundary values ​​of the internal cumulative energy, where st indicates that it is subject to the constraint Fy <= f.

[0026] Furthermore, let the number of all continuous scheduling time intervals be . For any continuous scheduling time interval Define row vectors ,when At that time, the row vector of the first row... The elements are When t does not belong to [t1, t2], the row vector of the first position... All elements are zero; stack all row vectors and their opposites sequentially to form the cumulative energy constraint matrix. The upper and lower boundary values ​​of the cumulative energy for each consecutive scheduling period are stacked sequentially to form an energy boundary constant vector. This forms the initial aggregate base set.

[0027]

[0028] Furthermore, the precise aggregated feasible region includes a vector of distribution network operating state variables. and distributed resource internal decision variable vector and includes aggregated interface power vector With distributed resource internal decision variable vector The relationships between them, the operational constraints of distributed resources, the power flow balance equation constraints of the distribution network, and the safety operation constraints are expressed as follows:

[0029]

[0030] in, A mathematical symbol representing existence. This includes node voltage, branch active power, and branch reactive power. This represents the constraint of the power flow balance equation in the distribution network. This indicates safety operation constraints, including node voltage constraints and branch capacity constraints. , , and For the corresponding constraint coefficient matrix, and This is the corresponding constraint constant vector.

[0031] Furthermore, the first The current aggregation base set in the next iteration is The max–min two-level optimization model is as follows:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] in, and Representing the candidate aggregation interface power vectors respectively Relative to the positive and negative offsets of the power vector that can achieve aggregation, The degree of default of the current aggregation basis set relative to the maximum norm of the exact aggregation feasible region; This represents a vector whose elements are all 1s. For the first The energy boundary constant vector for the next iteration.

[0039] Furthermore, by performing a dual transformation on the inner layer problem of the max–min bilayer optimization model, a single-layer optimization model is obtained:

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] in, The dual variables corresponding to the aggregate power mapping equation are used to characterize the default direction. For the non-negative dual variable corresponding to the distributed resource operation inequality, These are the free dual variables corresponding to the power flow balance equation constraints of the distribution network. The non-negative dual variables corresponding to the safety operation constraints; the default direction variable for each scheduling period is discretized as follows: , and By introducing binary variables and product auxiliary variables, and using the upper and lower bounds of the power of the aggregation interface to construct linearization constraints, the single-layer optimization model is transformed into a mixed integer linear programming model for solution.

[0047] Furthermore, the feasible region is precisely aggregated along the safety boundary reference points in the corresponding default direction. The following least-2 norm optimization model is used to obtain:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] in, To simultaneously satisfy distributed resource operation constraints and distribution network constraints, and to address the default point The power vector of the nearest feasible aggregation interface; To find the optimal solution for p when it is minimized.

[0054] Furthermore, shrinking the corresponding boundary constant vector to the projection value of the safety boundary reference point in the out-of-plane normal direction includes: [reducing the cumulative energy constraint matrix]. The Travelogue , No. The direction of breach at each effective boundary plane is its outward normal direction. The boundary constant vector is updated according to the following formula:

[0055] .

[0056] The present invention has the following beneficial effects:

[0057] This invention addresses the technical challenges of implementing network constraints, computationally complex high-dimensional models, and difficulty in ensuring scheduling security in solving feasible regions for distributed resource aggregation. It achieves a balance between operational security, computational efficiency, and approximate accuracy by constructing an initial low-dimensional basis set and iteratively shrinking the default point.

[0058] 1. Ensure scheduling security from the root cause; internal approximation characteristics completely avoid the risk of exceeding limits.

[0059] This invention employs an internal approximation-based core solution logic, resulting in an aggregated feasible region that is a subset of the precise feasible region. All aggregated interface power schemes falling within this precise feasible region naturally satisfy the operational constraints of distributed resources, power flow balance constraints of the distribution network, and safe operation constraints. The upper-level power grid dispatch directly uses the common connection point exchange power plan formulated based on this precise feasible region, avoiding issues such as line overload, node voltage exceeding limits, and equipment capacity overruns. This model avoids the safety hazards of traditional external approximation and equivalent aggregation models, which are theoretically feasible but practically exceed limits, and is particularly well-suited to the core requirement of prioritizing power grid dispatch safety.

[0060] 2. Significantly reduces computational complexity, enabling efficient low-dimensional solutions to high-dimensional problems.

[0061] Traditional exact aggregation of feasible regions requires simultaneously solving for distributed resource internal decision variables, distribution network state variables, and interface power variables. This results in high variable dimensionality and large constraint scale, making it difficult to support online scheduling applications. This invention achieves a leap in efficiency through a two-stage order reduction:

[0062] Based on the power-energy coupling relationship, the initial aggregate base set is constructed using only the aggregate interface power vector as the core variable, which transforms the high-dimensional underlying device constraints into low-dimensional cumulative energy linear constraints, directly compressing the problem dimension and constraint scale.

[0063] Employing an iterative mechanism that identifies the furthest default point and shrinks the boundary accordingly, it eliminates the need to traverse and solve all boundaries of the feasible region. Instead, it precisely corrects the boundary only for the default direction with the largest deviation, allowing it to quickly approximate the accurate feasible region with a small number of iterations. This significantly reduces computational overhead and makes it suitable for engineering-level scheduling scenarios involving multiple time periods and large-scale distributed resources.

[0064] 3. Fully incorporates distribution network constraints, filling the practical deficiencies of traditional aggregation models.

[0065] Existing distributed resource aggregation methods often only consider the power and energy constraints of the resources themselves, neglecting network constraints such as distribution network line current carrying capacity and node voltage. This results in aggregation results that cannot directly adapt to the actual operating requirements of the distribution network. This invention incorporates the distribution network power flow balance equation and safe operation constraints into the criteria for determining the precise feasible region. Throughout the entire process of default point identification and boundary contraction, network constraints are satisfied as the basis for feasibility determination. The final output feasible region can directly match the actual operating limitations of the distribution network, maximizing the release of the control potential of distributed resources while ensuring grid security.

[0066] 4. It inherently supports temporal coupling characteristics, enabling continuous scheduling decisions across multiple time periods.

[0067] This invention uses the power vector of a multi-time-period aggregated interface as the modeling object. Through forward / reverse cumulative energy constraints across continuous time intervals, it comprehensively characterizes the power-energy temporal coupling law of distributed resources such as energy storage and flexible loads (e.g., upper and lower limits of state of charge, total adjustable capacity limits, and continuous adjustment capability constraints). The constructed feasible region is a holistic feasible region with multi-time-period linkage, rather than an independent power range for a single time period. When upper-level scheduling formulates continuous multi-time-period plans such as day-ahead and intraday rolling plans, it can directly satisfy the temporal operation constraints of distributed resources, avoiding the drawbacks of single-time-period scheduling that fragments energy balance.

[0068] 5. Strong engineering adaptability, balancing robustness, controllable accuracy, and user-friendly interface.

[0069] Standardized output format: The final feasible region is presented as a linear convex polyhedron of constraint matrix and boundary constant vector, which can be directly embedded into various power system optimization and scheduling models and is compatible with mainstream solvers; at the same time, it does not require disclosure of detailed parameters of the underlying distributed resources, which facilitates standardized interaction between aggregators and power grid dispatch centers and takes into account data privacy.

[0070] Robustness is guaranteed: The max-min dual-layer optimization framework is used to identify the farthest default point, which can locate the most severe extreme conditions in the current base set that deviate from the precise feasible region. This ensures that the feasible region after boundary shrinkage still has safety under the most severe scenarios, and adapts to the robust scheduling requirements under the fluctuation of distribution network operation.

[0071] Precision is flexible and controllable: By pre-setting tolerance control for iteration termination conditions, the calculation speed and approximate accuracy can be flexibly balanced according to the needs of engineering scenarios, taking into account application scenarios with different accuracy requirements such as offline planning and online scheduling. Attached Figure Description

[0072] Figure 1 This is a flowchart of the feasible region approximation method for distributed resource aggregation considering network constraints according to the present invention.

[0073] Figure 2 This is a schematic diagram of the 10 kV power distribution feeder structure used in an embodiment of the present invention. Detailed Implementation

[0074] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0075] Example 1:

[0076] like Figure 1As shown, this embodiment provides an approximate method for distributed resource aggregation within the feasible region considering network constraints. For consistency, in the following text, "initial aggregation base set" refers to the initial polyhedron set formed solely based on the power-energy coupling relationship of the distributed resources themselves; "exact aggregation feasible region" refers to the set of executable aggregation interface power that simultaneously satisfies distributed resource operation constraints, distribution network power flow balance equation constraints, and safe operation constraints; and "current aggregation base set" refers to the initial aggregation base set... The set of candidate polyhedra after the second boundary contraction; "default point" refers to the aggregation interface power point located in the current aggregation base set but not belonging to the exact aggregation feasible region; "boundary constant vector" refers to the vector on the right-hand side of the cumulative energy constraint matrix inequality used to limit the aggregation power boundary.

[0077] An approximate method for distributed resource aggregation within the feasible domain considering network constraints includes the following steps:

[0078] S1. Construction of the initial aggregate base set

[0079] The aggregated interface power is defined as the net active power exchange between the distributed resource aggregation area and the upper-level power grid at the point of common connection. The aggregated interface power of each scheduling period is arranged into an aggregated interface power vector in chronological order. An energy change model is constructed based on the power-energy coupling relationship of distributed resources to solve for the upper and lower boundary values ​​of the cumulative energy of the aggregated interface power within any consecutive scheduling period. According to the coverage of each consecutive scheduling period, a cumulative energy constraint matrix is ​​constructed, which is formed by stacking forward and reverse cumulative power constraints. An energy boundary constant vector matching the dimension of the cumulative energy constraint matrix is ​​also constructed. The cumulative energy constraint matrix and the energy boundary constant vector together form the initial aggregated basis set of distributed resources.

[0080] The distribution network operation status variable vector includes node voltage, branch active power and branch reactive power, and the safe operation constraints include node voltage constraints and branch capacity constraints; the distributed resource internal decision variable vector is formed by stacking photovoltaic output, energy storage charging and discharging power, energy storage energy status and adjustable load reduction according to time periods.

[0081] Furthermore, in one embodiment of the present invention, the initial aggregation base set construction described in step S1 specifically includes:

[0082] An energy change model is constructed based on the power-energy coupling relationship of distributed resources:

[0083] For any continuous scheduling time interval The cumulative energy satisfies:

[0084]

[0085] Arbitrary continuous scheduling time interval Upper boundary value of cumulative energy of internal aggregation interface power With lower boundary value The solution process includes:

[0086] definition To access the internal decision variable vectors of all distributed resources within the aggregation region, the internal decision variable vectors of distributed resources are... It is formed by stacking photovoltaic output, energy storage charging and discharging power, energy storage state of energy, and adjustable load reduction according to time periods. Distributed resource operation constraints are constructed:

[0087]

[0088] In the formula, This is the distributed resource operation constraint coefficient matrix; This is a distributed resource operation limit vector. This includes limits on photovoltaic output, energy storage charging and discharging power, energy storage capacity, and adjustable load response, as well as a vector of distributed resource operation limits. Unlike the energy boundary constant vector used to define the boundaries of the initial aggregate base set. It is used to carry data such as the upper limit of photovoltaic output, the upper and lower limits of energy storage charging and discharging power, the upper and lower limits of energy storage energy, the initial state of energy storage, charging and discharging efficiency, and adjustable load response limits. It should be noted that... This is a constant vector on the right-hand side of the distributed resource operation constraints, which will be discussed later. The two constant vectors belonging to the right-hand side of the feasible region boundary have different meanings and dimensions.

[0089] The aggregation interface power is defined as the net active power exchanged between the distributed resource aggregation area and the upper-level power grid at the point of common connection. A positive value indicates that the aggregation area outputs active power to the upper-level power grid, while a negative value indicates that the aggregation area absorbs active power from the upper-level power grid. The aggregation interface power of each scheduling period is then arranged into an aggregation interface power vector in chronological order.

[0090]

[0091] Establish aggregation interface power vector With distributed resource internal decision variable vector The association mapping between them

[0092]

[0093] Among them, the aggregated power mapping matrix

[0094]

[0095] in, For aggregated interface power vectors, For the first Aggregated interface power for each scheduling period Number of scheduling periods; It is the aggregate power mapping matrix, and ;when When stacked in the order of "photovoltaic output, energy storage charging power, energy storage discharging power, energy storage energy status, and adjustable load reduction", the aggregated power mapping matrix The During the journey, With the The coefficients corresponding to the photovoltaic output, energy storage discharge power, and adjustable load reduction during the specified time period are positive. With the The coefficient corresponding to the time-limited energy storage charging power is negative. The coefficients corresponding to the energy storage state and variables that do not directly form interface power are zero.

[0096] Therefore, the above mapping relationship provides a mapping from the internal decision variables of distributed resources to the power of the aggregation interface. Used only to illustrate vectors Scalar of each time period The two are not two different aggregate power variables.

[0097] Arbitrary continuous scheduling time interval Upper boundary value of cumulative energy of internal aggregation interface power With lower boundary value Solve using the following linear programming models respectively:

[0098]

[0099]

[0100] in, , and These are the start and end times of the continuous scheduling time interval, respectively. The length of a single scheduling period. For the first Aggregated interface power for each scheduling period and Represents any continuous scheduling time interval The upper and lower boundary values ​​of the cumulative energy of the internal aggregation interface power.

[0101] The two linear programming models mentioned above only consider the operational constraints of the distributed resources themselves and are used to generate the energy boundary constant vector of the initial aggregate base set.

[0102] Furthermore, in one embodiment of the present invention, a cumulative energy constraint matrix is ​​constructed based on the coverage of each continuous scheduling time interval, which is formed by stacking forward cumulative power constraints and reverse cumulative power constraints, and an energy boundary constant vector matching the dimension of the cumulative energy constraint matrix is ​​constructed. The cumulative energy constraint matrix and the energy boundary constant vector together form the initial aggregate base set of distributed resources.

[0103] Specifically, the complete scheduling cycle is discretized into... Given a set of equal-length time intervals, let the total number of all continuous scheduling time intervals be . For any continuous scheduling time interval Define row vectors , its first The elements are:

[0104]

[0105] when At that time, the row vector of the first row... The elements are When t does not belong to [t1, t2], the row vector of the first position... Each element is zero;

[0106] All intervals All corresponding row vectors The cumulative energy constraint matrix is ​​formed by stacking the numbers and their opposites in sequence. :

[0107]

[0108] The upper and lower boundary values ​​of the cumulative energy for each consecutive scheduling time interval are then determined according to the cumulative energy constraint matrix. The same intervals are stacked sequentially to form the energy boundary constant vector. ,

[0109]

[0110] Therefore, the initial aggregate base set is represented as:

[0111]

[0112] Cumulative energy constraint matrix Each line describes a continuous time interval and its positive or negative cumulative direction, and the energy boundary constant vector. The corresponding element gives the cumulative energy boundary in that direction, and the two are in one-to-one correspondence.

[0113] S2, Default Point Identification

[0114] Based on the distribution network operation state variable vector and the distributed resource internal decision variable vector, the distributed resource operation constraints, the correlation mapping between the aggregation interface power vector and the distributed resource internal decision variable vector, the distribution network power flow balance equation constraints, and the safe operation constraints, an accurate aggregation feasible region is constructed. Based on robust optimization, a max-min two-level optimization model is constructed. The current aggregation basis set is used as the feasible region of the outer maximization problem. The inner problem calculates the shortest distance from the candidate aggregation power point to the accurate aggregation feasible region, and searches for the default point with the largest distance relative to the accurate aggregation feasible region in the current aggregation basis set.

[0115] Furthermore, in one embodiment of the present invention, the identification of the breach point in step S2 specifically includes:

[0116] Based on the initial aggregation base set, all network constraints of the distribution network operation are introduced to construct the exact aggregation feasible region:

[0117]

[0118] In the formula, A mathematical symbol representing existence. This is a vector of distribution network operating state variables, including node voltage, branch active power, and branch reactive power; It is a vector of decision variables within distributed resources, formed by stacking photovoltaic output, energy storage charging and discharging power, energy storage energy status, and adjustable load reduction according to time periods; For power flow balance equation constraints in distribution networks; For safe operation, constraints include upper and lower limits for node voltage and upper limit for branch capacity. , , and For the corresponding constraint coefficient matrix, and This is the corresponding constraint constant vector.

[0119] Therefore, the aforementioned precise aggregation feasible region simultaneously includes the correlation mapping constraint between the aggregation interface power vector and the internal decision variable vector of the distributed resource, the distributed resource operation constraint, the distribution network power flow balance equation constraint, and the distribution network safe operation constraint.

[0120] No. The current aggregate base set of the next iteration is denoted as:

[0121]

[0122] For the first The energy boundary constant vector for the next iteration.

[0123] To find the candidate polymerization power point furthest from the exact polymerization feasible region in the current polymerization basis set, a max-min two-level optimization model is constructed based on robust optimization, which is used to optimize the current polymerization basis set. As the feasible region of the outer maximization problem, the candidate aggregation power points are calculated from the inner problem to the exact aggregation feasible region. The shortest distance, and in the current aggregate base set Searching within the feasible region relative to exact aggregation The furthest point from the default point;

[0124] max–min two-level optimization model:

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] in, To achieve an aggregated interface power vector that satisfies resource and network constraints, and Representing the candidate aggregation interface power vectors respectively Relative to the positive and negative offsets of the power vector that can achieve aggregation, The degree of default of the current aggregation basis set relative to the maximum norm of the exact aggregation feasible region; For the first The energy boundary constant vector for the next iteration.

[0132] By performing a dual transformation on the inner layer problem of the above max–min bilayer optimization model, we can obtain a single-layer optimization model:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] in, For the equation of power mapping The corresponding dual variables are used to characterize the direction of default in each scheduling period; Inequality for Distributed Resource Operation The corresponding non-negative dual variable; For power flow balance equation constraints in distribution networks The corresponding free dual variables; Constraints for safe operation The corresponding non-negative dual variable. The second dual feasibility equation in the above single-layer optimization model adopts... This is consistent with the inequality direction and the definition of the nonnegative dual variable adopted.

[0140] In one embodiment of the present invention, the default direction variable for each scheduling period is discretized as follows: , and For each Introducing binary variables and and product auxiliary variables And order:

[0141]

[0142]

[0143]

[0144] It is an auxiliary variable for the product.

[0145] The linearization constraints are constructed using the upper and lower bounds of the aggregated interface power, transforming the single-layer optimization model into a mixed-integer linear programming model for solution.

[0146] make , The first aggregation base set can be obtained from the initial aggregation base set. Time-of-use aggregation interface power upper and lower bounds The exact linearization of the product of a binary variable and a continuous auxiliary variable can be achieved using the following McCormick linearization constraints:

[0147]

[0148]

[0149]

[0150]

[0151] Will Replace with The single-layer optimization model is transformed into a mixed-integer linear programming model:

[0152]

[0153] Its constraints include The dual feasibility constraints, binary encoding constraints, and product linearization constraints in the above single-layer optimization model.

[0154] Solving the mixed-integer linear programming model yields the maximum default degree in the current aggregation basis set relative to the exact aggregation feasible region. and the corresponding distance to the maximum default point .

[0155] S3, Boundary Shrinkage Update

[0156] For the default point with the largest distance, find the feasible aggregation interface power point that is closest to the default point within the precise aggregation feasible region, and determine the feasible aggregation interface power point as the safe boundary reference point of the precise aggregation feasible region in the corresponding default direction; determine the effective boundary plane of the default point in the current aggregation basis set, and shrink the corresponding boundary constant vector to the projection value of the safe boundary reference point in the normal direction of the effective boundary plane;

[0157] Furthermore, in one embodiment of the present invention, the boundary shrinkage update in step S3 specifically includes:

[0158] Precise aggregation of feasible regions The inherent safety boundary reference point corresponding to the direction of default That is, safety boundary reference point To accurately aggregate feasible regions Within and at the maximum point of default The nearest feasible aggregation interface power point is obtained using the following least-norm 2 optimization model:

[0159]

[0160]

[0161]

[0162]

[0163]

[0164] in, To simultaneously satisfy distributed resource operation constraints and distribution network constraints, and to address the default point The nearest accurate aggregation feasible domain feasible interface power vector, and used as the safe boundary reference point that can be retained in this default direction; To find the optimal solution for p when it is minimized.

[0165] Determine the point of breach In the current aggregation base set The effective boundary plane in the definition is:

[0166]

[0167] In the formula, Cumulative energy constraint matrix row index, To preset the tolerance, the cumulative energy constraint matrix is ​​used. The The row is represented as a row vector. Then the outward normal direction of the effective boundary plane This corresponds to the direction of the default;

[0168] The corresponding boundary constant vector is shrunk to the safety boundary reference point. In the effective boundary plane The projection value along the outward normal direction, and the updated boundary constant vector are:

[0169]

[0170] This update only shrinks the effective boundary that leads to the default point, and does not change the cumulative energy constraint matrix. The structure; by taking a smaller value, it is ensured that the updated current aggregation base set does not expand outward.

[0171] S4, Iterative Update

[0172] The default point identification and boundary shrinkage update are performed iteratively, continuously shrinking the current aggregation base set boundary inward until the shortest distance from the candidate aggregation power point in the current aggregation base set to the precise aggregation feasible region does not exceed the preset tolerance, thus obtaining an approximate aggregation feasible region within the distributed resources that satisfies the distribution network constraints.

[0173] Furthermore, in one embodiment of the present invention, the iterative update of step S4 specifically includes:

[0174] Let the initial value of the iteration number be... ,make Iteratively execute the default point identification described in S2 and the boundary shrinkage update in S3, continuously shrinking the boundary of the current aggregation base set inward. When the shortest distance from the candidate aggregation power point in the current aggregation base set to the precise aggregation feasible region does not exceed a preset tolerance, the shortest distance is adopted. Representation, that is, satisfying:

[0175]

[0176] Cumulative energy constraint matrix row index Forming the effective boundary plane index set ; For the first The l-th row of the energy boundary constant vector in the next iteration. This is the preset tolerance.

[0177] Then stop iterating and output the approximate aggregated feasible region within the distributed resources that satisfies the distribution network constraints. :

[0178]

[0179] in ; This is the final (after iterative convergence) energy boundary constant vector.

[0180] S5, Upper-level distribution network dispatch optimization model embedding

[0181] In the upper-level distribution network scheduling optimization model, an aggregated interface power vector is introduced. The approximate aggregated feasible region within the distributed resources obtained by iterative update is used as an embedded constraint. The upper-level distribution network scheduling optimization model is solved to obtain the optimal aggregated interface power command. The optimal aggregated interface power command is then decomposed and allocated to each distributed resource to form an executable scheduling scheme. The upper-level distribution network scheduling optimization model includes a day-ahead scheduling model, a rolling scheduling model, or a primary-distribution coordinated scheduling model.

[0182] Furthermore, in one embodiment of the present invention, step S5, embedding the upper-level distribution network scheduling optimization model, specifically includes:

[0183] The feasible region is approximated by the inner approximation after iterative convergence. Embedded in the upper-level distribution network dispatch optimization model. The aggregation interface power vector in the upper-level distribution network dispatch optimization model is denoted as... It is similar to the aforementioned The superscript "agg" is added only to indicate that the aggregated interface power vector is located in the upper-level distribution network scheduling optimization model, representing the same physical quantity. The approximate aggregated feasible region within the distributed resources obtained through iterative updates is used as an embedded constraint.

[0184]

[0185] The upper-level distribution network scheduling optimization model with embedded constraints can be expressed as:

[0186]

[0187]

[0188]

[0189] In the formula, Other decision variables in the upper-level distribution network dispatch optimization model besides the aggregation interface power include conventional unit output, power purchased and sold, and distribution network exchange power; The objective function for upper-level scheduling can represent operating costs, power purchase costs, curtailment costs, or comprehensive scheduling costs. and This is the upper-level scheduling constraint coefficient matrix; This is the upper-level scheduling constraint limit vector; the embedded aggregation capability constraint is used to limit the multi-time adjustable power range of the aggregation region.

[0190] After the upper-layer scheduling is completed, the power command is based on the optimal aggregation interface. Solve for the satisfaction , , and The lower-level decomposition problem allocates the optimal aggregation interface power command to various distributed resources, including photovoltaics, energy storage, and adjustable loads, to form an executable scheduling scheme. The upper-level distribution network scheduling optimization model includes a day-ahead scheduling model, a rolling scheduling model, or a primary-distribution coordinated scheduling model.

[0191] Application example:

[0192] To verify the engineering adaptability of the method of this invention, this application example uses a 10 kV radial distribution feeder containing distributed photovoltaic, energy storage and adjustable load as the implementation object. The structural diagram of the implementation object is shown below. Figure 2 As shown, the implementation object is connected to the upper-level distribution network via a tie transformer, and multiple nodes are connected to photovoltaic, energy storage, and adjustable load resources. A scheduling cycle of 24 hours and a scheduling step size of 1 hour are set, resulting in 24 consecutive scheduling periods. Using the method of this invention, a distributed resource aggregation feasible region that satisfies network constraints is constructed.

[0193] The results are as follows:

[0194] In the constructed test system, the method of this invention was compared with the box set-based aggregation method and the centralized modeling method. The box set-based method constructs the aggregation feasible region by independently characterizing the upper and lower bounds of power in each time period, while the centralized method performs unified modeling and solving for all distributed resources and network constraints.

[0195] As shown in Table 1, the solution time of the method of the present invention is shorter than that of the centralized method, and the total cost is lower than that of the box set-based method, achieving a good balance between computational efficiency and scheduling economy.

[0196] Table 1 Comparison of different methods .

Claims

1. A distributed resource aggregation feasible region approximation method considering network constraints, characterized in that, Includes the following steps: S1. Initial Aggregation Base Set Construction: Define the aggregation interface power as the net active power exchange between the distributed resource aggregation area and the upper-level power grid at the common connection point, and form an aggregation interface power vector by arranging the aggregation interface power of each scheduling period in chronological order; construct an energy change model based on the power-energy coupling relationship of distributed resources, and solve for the upper and lower boundary values ​​of the cumulative energy of the aggregation interface power within any consecutive scheduling period interval. Based on the coverage of each continuous scheduling time interval, a cumulative energy constraint matrix is ​​constructed, which is formed by stacking forward cumulative power constraints and reverse cumulative power constraints. An energy boundary constant vector matching the dimension of the cumulative energy constraint matrix is ​​also constructed. The cumulative energy constraint matrix and the energy boundary constant vector together form the initial aggregate base set of distributed resources. S2. Default Point Identification: Based on the distribution network operation state variable vector and the distributed resource internal decision variable vector, distributed resource operation constraints, the correlation mapping between the aggregation interface power vector and the distributed resource internal decision variable vector, the distribution network power flow balance equation constraints, and safe operation constraints, an accurate aggregation feasible region is constructed. Based on robust optimization, a max-min two-level optimization model is constructed. The current aggregation basis set is used as the feasible region of the outer maximization problem. The inner problem calculates the shortest distance from the candidate aggregation power point to the accurate aggregation feasible region, and searches for the default point with the largest distance relative to the accurate aggregation feasible region in the current aggregation basis set. S3, Boundary Shrinkage Update: For the default point with the largest distance, solve for the feasible aggregation interface power point within the precise aggregation feasible region that is closest to the default point, and determine the feasible aggregation interface power point as the safe boundary reference point of the precise aggregation feasible region in the corresponding default direction; determine the effective boundary plane of the default point in the current aggregation basis set, and shrink the corresponding boundary constant vector to the projection value of the safe boundary reference point in the normal direction outside the effective boundary plane; S4. Iterative Update: Iteratively execute the default point identification and boundary shrinkage update, continuously shrinking the current aggregation base set boundary inward until the shortest distance from the candidate aggregation power point in the current aggregation base set to the precise aggregation feasible region does not exceed the preset tolerance, thus obtaining an approximate aggregation feasible region within the distributed resources that satisfies the distribution network constraints.

2. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 1, characterized in that, It also includes the following steps: S5. Embedding of Upper-Level Distribution Network Scheduling Optimization Model: An aggregated interface power vector is introduced into the upper-level distribution network scheduling optimization model. The approximate aggregated feasible region within the distributed resources obtained by iterative update is used as an embedded constraint. The upper-level distribution network scheduling optimization model is solved to obtain the optimal aggregated interface power command. The optimal aggregated interface power command is then decomposed and allocated to each distributed resource to form an executable scheduling scheme. The upper-level distribution network scheduling optimization model includes a day-ahead scheduling model, a rolling scheduling model, or a primary-distribution coordinated scheduling model.

3. The approximate method for distributed resource aggregation within the feasible region considering network constraints according to claim 1, characterized in that, The distribution network operation status variable vector includes node voltage, branch active power and branch reactive power, and the safe operation constraints include node voltage constraints and branch capacity constraints; the distributed resource internal decision variable vector is formed by stacking photovoltaic output, energy storage charging and discharging power, energy storage energy status and adjustable load reduction according to time periods.

4. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 1, characterized in that, The process of solving for the upper and lower boundary values ​​of the aggregated power cumulative energy within any continuous scheduling time interval includes: defining the internal decision variable vector of the distributed resource. The distributed resource internal decision variable vector The distributed resource operation constraints are formed by stacking photovoltaic output, energy storage charging and discharging power, energy storage status, and adjustable load reduction according to time periods. in, This is the distributed resource operation constraint coefficient matrix. This is a distributed resource operation limit vector, which includes photovoltaic output limits, energy storage charging and discharging power limits, energy storage energy limits, and adjustable load response limits. An aggregation interface power vector is then established. With distributed resource internal decision variable vector The association mapping between them is used to solve the upper and lower boundary values ​​of the cumulative energy of the aggregated interface power within any continuous scheduling time interval based on the distributed resource operation constraints.

5. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 4, characterized in that, The aggregation interface power vector With distributed resource internal decision variable vector The association mapping between them is as follows: in, For aggregated interface power vectors, For the first Aggregated interface power for each scheduling period Number of scheduling periods; This is the aggregate power mapping matrix. Let represent the coefficient vector in the matrix, and The aggregated power mapping matrix The In the row, with the first The coefficients corresponding to the photovoltaic output, energy storage discharge power, and adjustable load reduction during the time period are positive, and are consistent with the first... The coefficient corresponding to the time period energy storage charging power is negative, while the coefficient corresponding to the energy storage state and variables that do not directly form interface power is zero.

6. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 5, characterized in that, The upper and lower boundary values ​​of the cumulative energy of the aggregated interface power within any continuous scheduling time interval are solved using the following linear programming model: in, , The length of a single scheduling period. For the first Aggregated interface power for each scheduling period and Represents any continuous scheduling time interval The upper and lower boundary values ​​of the internal cumulative energy, where st indicates that it is subject to the constraint Fy <= f.

7. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 6, characterized in that, Let the total number of continuous scheduling time intervals be . ; For any continuous scheduling time interval Define row vectors ,when At that time, the row vector of the first row... The elements are When t does not belong to [t1, t2], the row vector of the first position... All elements are zero; stack all row vectors and their opposites sequentially to form the cumulative energy constraint matrix. The upper and lower boundary values ​​of the cumulative energy for each consecutive scheduling period are stacked sequentially to form an energy boundary constant vector. This forms the initial aggregate base set. 。 8. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 7, characterized in that, The precise aggregation feasible region includes a vector of distribution network operating state variables. and distributed resource internal decision variable vector and includes aggregated interface power vector With distributed resource internal decision variable vector The relationships between them, the operational constraints of distributed resources, the power flow balance equation constraints of the distribution network, and the safety operation constraints are expressed as follows: in, A mathematical symbol representing existence. This includes node voltage, branch active power, and branch reactive power. This represents the constraint of the power flow balance equation in the distribution network. This indicates safety operation constraints, including node voltage constraints and branch capacity constraints. , , and For the corresponding constraint coefficient matrix, and This is the corresponding constraint constant vector.

9. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 8, characterized in that, No. The current aggregation base set in the next iteration is The max–min two-level optimization model is as follows: in, and Representing the candidate aggregation interface power vectors respectively Relative to the positive and negative offsets of the power vector that can achieve aggregation, The degree of default of the current aggregation basis set relative to the maximum norm of the exact aggregation feasible region; This represents a vector whose elements are all 1s; For the first The energy boundary constant vector for the next iteration.

10. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 9, characterized in that, By performing a dual transformation on the inner layer problem of the max–min bilayer optimization model, a single-layer optimization model is obtained: in, The dual variables corresponding to the aggregate power mapping equation are used to characterize the default direction. For the non-negative dual variable corresponding to the distributed resource operation inequality, These are the free dual variables corresponding to the power flow balance equation constraints of the distribution network. The non-negative dual variables corresponding to the safety operation constraints; the default direction variable for each scheduling period is discretized as follows: , and By introducing binary variables and product auxiliary variables, and using the upper and lower bounds of the power of the aggregation interface to construct linearization constraints, the single-layer optimization model is transformed into a mixed integer linear programming model for solution.

11. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 10, characterized in that, Precisely aggregate the safe boundary reference points of the feasible region in the corresponding default direction. The following least-2 norm optimization model is used to obtain: in, To simultaneously satisfy distributed resource operation constraints and distribution network constraints, and to address the default point The power vector of the nearest feasible aggregation interface; To find the optimal solution for p when it is minimized.

12. The approximate method within the feasible region for distributed resource aggregation considering network constraints according to claim 11, characterized in that, Shrinking the corresponding boundary constant vector to the projection value of the safety boundary reference point in the out-of-plane normal direction includes: [reducing the cumulative energy constraint matrix]. The Travelogue , No. The direction of breach at each effective boundary plane is its outward normal direction. The boundary constant vector is updated according to the following formula: Cumulative energy constraint matrix row index Forming the effective boundary plane index set ; For the first The energy boundary constant vector of the nth iteration OK.

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