A method for depicting the aggregation feasible region and cost of virtual power plant under space-time decoupling

Abstract

The application discloses a method for depicting the feasible region and cost of a virtual power plant (VPP) in space-time decoupling, which is used for the VPP and comprises the following steps: receiving operation information of distributed energy resources (DERs) in a power distribution network, and uploading the information of maximum output of the DERs to a distribution system operator (DSO) to calculate a demand of operation energy (DOE); receiving the DOE issued by the DSO; constructing a PCC point aggregation PFR depiction model based on operation constraints of the DERs; decoupling time coupling constraints existing in the operation constraints and converting the PFR depiction model to calculate the PFR after decoupling; performing safety checking on the PFR after decoupling by using the DOE; performing uniform sampling on output points in the PFR after safety checking; constructing a minimum aggregation cost model based on a DER operation cost function, and substituting each sampling point into the minimum aggregation cost model to calculate a cost value; and obtaining a three-dimensional active-reactive-cost point set and constructing a convex hull after calculating all the sampling points to depict the aggregation cost. The method can realize fast and accurate depiction of the PFR while ensuring the safety of the power distribution network.

Description

Technical Field

[0001] This invention relates to the field of power technology, and specifically to a method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling. Background Technology

[0002] With the continuous advancement of new power systems and electricity market construction, Virtual Power Plants (VPPs) can aggregate distributed energy resources (DERs) such as large-scale distributed power sources, distributed energy storage, and adjustable loads through advanced communication and control technologies to participate in optimized dispatch and market transactions. Before conducting decision optimization, it is necessary to aggregate DERs and characterize their overall adjustable range. However, due to the inconsistent operating characteristics of different resources, especially the significant time coupling constraints of some resources, it is difficult to characterize the adjustable range through aggregation. Furthermore, to obtain diversified market benefits, VPPs need not only to describe the adjustable boundary after resource aggregation but also to reflect the actual operating costs under different output levels. Therefore, it is necessary to further construct an aggregation cost function for DERs.

[0003] The assessment of VPP aggregation adjustability can be achieved through power feasible region (PFR) characterization. Existing research on feasible region characterization can be divided into two categories: PFR considering only active power and PFR considering both active and reactive power. 1) PFR considering only active power ignores the reactive power component. DERs can provide reactive power resources to the system through inverters to participate in distribution network losses and voltage regulation, and can also obtain revenue from the reactive power ancillary service market. Therefore, PFR needs to consider both active and reactive power. 2) For active-reactive power PFR, existing research has explored various aspects such as geometric modeling, optimization solutions, uncertainty modeling, and multi-time dynamic characterization. However, most active-reactive power PFR studies ensure distribution network safety by directly embedding distribution network power flow constraints into the feasible region characterization model. In practice, due to considerations such as data security and market fairness, distribution network data is monopolized by the distribution system operator (DSO), and VPPs do not have the authority to access it. Therefore, the method of directly embedding distribution network power flow constraints into the feasible domain to characterize the model is difficult to implement in actual operation and cannot guarantee distribution network security.

[0004] Regarding the characterization of cost functions, existing research has explored cost modeling for VPP aggregation. However, overall, the characterization of VPP aggregation cost functions still primarily focuses on the active power dimension, which to some extent limits the economic analysis and decision support for VPP participation in the reactive power ancillary service market. Although some studies have begun to consider reactive power opportunity costs, these typically only reflect the revenue loss caused by DERs reducing active power output due to reactive power output, without fully accounting for the additional operating costs incurred by DERs in providing reactive power support. Therefore, it is necessary to further construct a comprehensive active power-reactive power-cost characterization model for aggregated VPPs. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling, so as to achieve rapid and accurate characterization of PFR while ensuring the safety of the distribution network.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A method for characterizing the feasible domain and cost of a virtual power plant (VPP) under spatiotemporal decoupling, the method comprising:

[0008] Receive the operating information of DERs in the distribution network and upload the maximum output information of DERs to the DSO to calculate DOE;

[0009] Receive the DOE sent by the DSO;

[0010] Based on the operational constraints of DERs, a PCC point aggregation PFR characterization model is constructed; the time coupling constraints existing in the operational constraints are decoupled and the PFR characterization model is transformed to calculate the decoupled PFR; the decoupled PFR is then subjected to safety verification using DOE.

[0011] Within the PFR after safety verification, output points are uniformly sampled; based on the DERs operating cost function, a minimum aggregate cost model is constructed and each sampled point is substituted into the minimum aggregate cost model to calculate the cost value; after calculating all sampled points, a three-dimensional active-reactive-cost point set is obtained and a convex hull is constructed to characterize the aggregate cost.

[0012] Optionally, the DOE is the power transmission range given by the DSO for each distribution network node, within which the DERs can arbitrarily adjust their output.

[0013] DSO uses the Lyapunov optimization method to decouple time-coupled constraints.

[0014] DSO uses a convex piecewise linear fitting method to characterize polymerization costs.

[0015] The DSO classifies DERs into DERs with time coupling constraints and DERs without time coupling constraints.

[0016] The DSO defines time-coupled DERs as distributed energy storage, distributed generators, and shiftable loads; the DSO defines time-coupled DERs as distributed photovoltaics and load shedding.

[0017] The DSO decouples the time coupling constraints and transforms the PFR characterization model to calculate the decoupled PFR; the decoupled PFR is then subjected to a safety check using DOE, including:

[0018] 1) Initialize the virtual queue and the set of unit vectors corresponding to the search directions in the first loop as follows: ,in Indicates the number of search rounds. , , They represent the first The set of search direction numbers in the wheel, the first A set of unit vectors and search directions;

[0019] 2) Calculate and solve the corresponding coefficients in the virtual queue for each search direction in the direction set; from The virtual queue is updated periodically to obtain the corresponding PCC and distribution network node. Output points, and save them to their respective vertex sets. , ,in Equal to node The sum of the outputs of the next DERs;

[0020] 3) If ,make (And proceed to step 4); otherwise, proceed to step 5).

[0021] 4) To The points are sorted counterclockwise and the perpendicular bisectors of adjacent output points are calculated. The direction of the extension of the perpendicular bisectors is taken as the search direction for the s-th round, and then the process returns to execute steps 2)-3).

[0022] 5) To Construct the convex hull and calculate its area. Check whether the convergence condition is met time interval by time. If it is met, proceed to step 6); otherwise, And return to step 4).

[0023] 6) Exit the loop iteration to obtain the time-decoupled PFR of PCC and distribution network nodes;

[0024] 7) Perform DOE verification on the time-decoupled PFR.

[0025] Optionally, in step 5), the convergence condition is set as follows:

[0026] In the formula: , Time periods No. The convex hull area and the change in convex hull area obtained after round search; For area calculation; This is the convergence threshold.

[0027] Optionally, the security verification of the decoupled PFR using DOE includes:

[0028] To a single node Its corresponding runtime envelope Take the intersection to obtain the final feasible region of a single resource that satisfies the DOE constraints. ;

[0029] For all The final feasible region of PCC is obtained by performing Minkowski summation. :

[0030] In the formula: This is the set of distribution network nodes containing DERs.

[0031] 10. The method for characterizing the feasible region and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 4, characterized in that the method of characterizing the aggregation cost using a convex piecewise linear fitting method includes:

[0032] 3D point set exist Construct its convex hull in three-dimensional space: ,in, The lower surface is composed of several triangular facets. composition: ,in Let be the total number of pieces; The general form of the plane is:

[0033] Select the facets that face outward along the negative direction of the cost axis as the lower surface facet set: Local planes together constitute the set of candidate support planes for the aggregation cost surface; for any ,because The plane is rewritten as:

[0034] Based on the affine functions corresponding to all lower surface patches, the time period is defined. The piecewise linear approximation function for aggregation cost is:

[0035] Introducing auxiliary variables This indicates that efforts were made in the application process. The approximate value of the polymerization cost is as follows:

[0036] When the objective function minimizes the cost term Or in maximizing profits When the form appears, the optimal solution automatically has: .

[0037] Compared with the prior art, the advantages of this invention are as follows:

[0038] This invention addresses the challenges of complex PFR (Power Flow Rate) calculation and constraint satisfaction caused by the heterogeneous characteristics of massive DERs (Distribution Network Controllers), time-coupled constraints, and power flow spatial coupling. It employs a dynamic operating envelope (DOE) for power flow spatial decoupling and verification. This decouples time-coupled constraints within the operational constraints and transforms the PFR characterization model, achieving rapid and accurate PFR characterization. The full-time PFR obtained after time decoupling meets the effectiveness requirements of actual VPP (Vehicle Power Utility) operation. Using DOE for safety verification and spatial decoupling ensures distribution network safety and protects sensitive data while characterizing PFR without incorporating power flow constraints into the model. The convex piecewise approximation of the aggregation cost function effectively characterizes the nonlinear relationship between aggregation cost and active and reactive power output. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the feasible domain and cost characterization method for virtual power plant aggregation under spatiotemporal decoupling in the embodiments of this application.

[0040] Figure 2 A flowchart is provided to characterize the PFR of VPP under spatiotemporal decoupling. Detailed Implementation

[0041] It should be noted that in this application, VPP and DSO both refer to terminals capable of information exchange, namely, virtual power plant terminals and distribution network operator terminals, respectively. Terminals include, but are not limited to, smart terminals such as mobile phones, computers, and tablets.

[0042] Example:

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0044] See Figure 1 As shown in this embodiment, the method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling is used for VPP. The method includes:

[0045] (1) Receive the operating information of DERs in the distribution network and upload the maximum output information of DERs to DSO to calculate DOE; DOE is the power transmission range given by DSO for each distribution network node. Within DOE, DERs can adjust their output at will while ensuring the safety of the distribution network.

[0046] (2) Receive the DOE sent by the DSO; the calculation of DOE ensures the power flow safety of the distribution network, and at the same time realizes the decoupling of the spatial coupling caused by the power flow constraints of the original DERs. That is, the DERs under any distribution network node only need to run in their own DOE and are not affected by the output of other nodes.

[0047] (3) Based on the operational constraints of DERs, a PCC (Point of Common Coupling) aggregated PFR characterization model is constructed; the time coupling constraints in the operational constraints are decoupled and the PFR characterization model is transformed to calculate the time-decoupled PFR. The full-time PFR obtained after time decoupling can meet the effectiveness requirements of the actual operation of VPP; the time-decoupled PFR is verified by DOE. The spatial decoupling method of using DOE for safety verification can ensure the power flow safety of the distribution network and protect sensitive data when characterizing PFR in VPP without including power flow constraints in the model.

[0048] (4) Perform uniform sampling of output points within the PFR after safety verification; construct the minimum aggregate cost model based on the DERs running cost function and substitute each sampling point into the model to calculate the cost value; after calculating all sampling points, obtain the three-dimensional active-reactive-cost point set and construct the convex hull, and use the convex piecewise linear fitting method to characterize the aggregate cost.

[0049] Therefore, this method addresses the challenges of complex PFR (Power Flow Rate) calculation and constraint satisfaction caused by the heterogeneous characteristics of massive DERs, constraint temporal coupling, and power flow spatial coupling. It employs a dynamic operating envelope (DOE) for power flow spatial decoupling and verification. This decouples temporally coupled constraints within the operational constraints and transforms the PFR characterization model, achieving rapid and accurate PFR characterization. The full-time PFR obtained after temporal decoupling meets the effectiveness requirements of actual VPP (Vehicle Power Utility) operation. Using DOE for safety verification and spatial decoupling ensures distribution network safety and protects sensitive data while characterizing PFR without incorporating power flow constraints into the model. The convex piecewise approximation of the aggregation cost function effectively characterizes the nonlinear relationship between aggregation cost and active and reactive power output.

[0050] In one specific embodiment, VDERs are divided into DERs with time coupling constraints and DERs without time coupling constraints. DERs with time coupling constraints include: distributed energy storage (ES), distributed generator (DG), and shiftable load (SL); DERs without time coupling constraints include: distributed photovoltaic (PV) and curtailable load (CL).

[0051] The above five typical distributed resource operation models are as follows:

[0052] The above five typical distributed resource operation models are as follows:

[0053] 1) ES: Capacity upper and lower limits constraints, capacity change constraints, initial and final capacity constraints, charge / discharge state constraints, charge / discharge power upper and lower limits constraints, and apparent power upper limit constraints: (1) (2)

[0054] In the formula: , , , , , , Energy storage The charging status, discharging status, charging power, discharging power, active power, reactive power, and battery capacity; , , , These are the maximum charge / discharge power, the maximum apparent power, and the charge / discharge efficiency, respectively. For time intervals; This represents the total number of time periods.

[0055] 2) DG: Ramp-up constraints, power upper and lower limits constraints, and apparent power upper limit constraints:

[0056] Taking micro gas turbines and diesel generators as examples, DG can also supply reactive power to the grid through inverters, with the following output boundaries: (3); (4)

[0057] In the formula: , , , , , Generators The active power, reactive power, maximum active power, maximum apparent power, and maximum ramp rate.

[0058] 3) SL: Limits on shiftable power, constraints on cumulative unmet demand, limits on cumulative demand, and constraints on cumulative demand at the beginning and end of the process. (5); (6)

[0059] In the formula: , , , , , , These are respectively movable loads The original power, translation power, accumulated amount of unmet demand, upper and lower limits of translation power, and upper and lower limits of accumulated amount.

[0060] 4) PV: Power upper and lower limits constraints, power factor constraints, apparent power upper limit constraints:

[0061] Adjustable loads include two types: SL and CL. Generally, they can only regulate active power, and their output boundaries are as follows: (7)

[0062] In the formula: , , , , Photovoltaics The active power, reactive power, maximum active power, maximum power factor angle, and maximum apparent power.

[0063] 5) CL: Power upper and lower limit constraints can be reduced: (8)

[0064] In the formula: , , They are respectively load reduction The power reduction, the minimum power consumption to meet user needs, and the original power consumption.

[0065] In one specific embodiment, the PCC (Point of Common Coupling) aggregated PFR characterization model includes:

[0066] A vertex search method is used to characterize the feasible region, so as to obtain a search model in a single direction under time coupling, as follows:

[0067] Objective function: Maximize the output power projection at the power coupling point along the search direction. :

[0068] (9)

[0069] Constraints: DERs operating constraints (1)-(8), PCC equivalent output constraints (10), and power variation limitation constraints (11): (10); (11)

[0070] In the formula: , These are the aggregated equivalent active and reactive power on the PCC, respectively. , , , , These are the total numbers of ES, SL, DG, PV, and CL, respectively. , These are the active and reactive power of the midpoint of the adjacent points after the previous round of search; , These are the horizontal and vertical coordinate components of the unit vector corresponding to the search direction, ensuring that the power on the PCC changes along the search direction.

[0071] It is important to note that when a component in the unit vector of the search direction is zero, the power of PCC in the direction corresponding to that component is equal to the power of the midpoint, and the power of each resource in that direction is also equal to the power of the resource corresponding to the midpoint. The specific proof is as follows:

[0072] Record the output of PCC as ,make , Let each point be an adjacent point after the previous search round. According to the PCC equivalent output constraint, we know that: (12)

[0073] In the formula: It is a coefficient matrix; , , Let the decision variable vector be: The midpoint between the two adjacent points mentioned above is: For convex optimization, we can obtain: That is, the internal decision solution corresponding to the midpoint is the mean of the internal solutions of the two adjacent points. When ,Require: .by For example, at this time Therefore Only optimization is needed Additionally, when k=1, the midpoint of all search directions is the origin. In this case: .

[0074] Due to the existence of time-coupling constraints (1), (3), and (6), under the same search direction, the search model in the time period It will also be determined The solution is available for a specific time period, but this solution is often related to its specific time period. The results obtained when solving them individually differ. This is because the time period... The search essentially revolves around maximizing the PFR (Progressive Feasibility Rate) in the current time period, without directly considering the impact of this decision on the PFR in subsequent time periods. For resources with cross-time-period coupling characteristics, releasing more adjustment capacity in the current time period usually means a reduction in the available adjustment space in subsequent time periods. Therefore, under time-coupled constraints, the aggregated feasible region obtained by time-period search tends to be too large, making some application decisions difficult to implement in actual operation. To address this issue, the Lyapunov optimization method is used to decouple the time-coupled constraints.

[0075] For resources of both ES and SL that simultaneously have capacity (cumulative) change constraints and start-end capacity (cumulative) constraints, the time-coupled constraint equations (1) and (6) representing the two types of resources are rewritten as time-period cumulative constraints: (13)

[0076] because , Therefore, the following is required: (14)

[0077] For the time coupling constraint equation (3) of DG, its form is difficult to rewrite directly in the above manner, so it is equivalently reconstructed as follows: (15)

[0078] In the formula: , , , Generators Ascent and descent rates and state variables. , ,in It is a constant, numerically equal to the last period of the previous day. The winning power. Further relaxation to time-period cumulative constraint: (16)

[0079] because ,therefore: (17)

[0080] Construct virtual queues for the three types of resources respectively:

[0081] 1) Construct a virtual queue for Elasticsearch that reflects capacity changes. : (18)

[0082] In the formula: For bias; , , The value can guarantee the components in any direction. superior All conditions are met: .

[0083] 2) Virtual queues for SL construction to address unmet cumulative load demands. : (19)

[0084] 3) Construct virtual queues reflecting the cumulative power change violations for the upper and lower bounds of the cumulative constraint during the DG period: , : (20)

[0085] By constructing a virtual queue, the constraints (14) and (17) originally expressed in the form of time-based accumulation can be equivalent to the virtual queue having a net change of zero, and further transformed into the stability problem of the virtual queue.

[0086] Construct a Lyapunov function to characterize the crowding level of the virtual queue: (twenty one)

[0087] Further, Lyapunov drift is constructed to characterize the difference in crowding levels between adjacent time periods: (twenty two)

[0088] The smaller the value, the more stable the queue, but it is difficult to calculate directly. This can be addressed by constructing an upper bound for the drift. and control As small as possible It can also be restricted to meet queue stability requirements. For example, let's perform an upper bound analysis on it: (twenty three)

[0089] Similarly, we can conclude that: (twenty four)

[0090] Taking the upper bound virtual queue of DG as an example, this explains why the time-period accumulation constraint can be guaranteed by transforming the stability problem: The smaller the value, the more stable the queue is, i.e., it has... ,available This is consistent with the requirements of the time-period cumulative constraint.

[0091] To balance feasible region search and virtual queue stability, the search objective and Lyapunov drift term need to be considered simultaneously in the original aggregation model. Based on this, the objective function in equation (9), originally in the form of maximization, is rewritten as a minimization function, and the Lyapunov drift term is incorporated into the objective function, thus constructing the following optimization model: (25)

[0092] In the formula: , , , where are the non-negative weight coefficients for each queue, representing the trade-off between the original objective function and Lyapunov drift. Where: , In addition, regarding Even with a reasonable value, SL can still fail to meet the cumulative requirement. satisfy Further, the objective function is transformed into an upper bound form: (26)

[0093] In the formula: The sum of the constant terms in the Lyapunov drift is calculated using the following formula: (27)

[0094] Through the above transformation, the time-coupling constraints of the three resource types (ES, DG, and SL) can be decoupled. Simultaneously, by controlling the values ​​of the non-negative weight coefficients in the objective function, some upper and lower bound constraints are eliminated. The final time-coupling constraint decoupling model based on Lyapunov optimization is summarized as follows:

[0095] Objective function: Equation (26).

[0096] Constraints: Equations (2), (4), (5), (7), (8), (10), (11).

[0097] Compared to the traditional PFR characterization model, the Lyapunov-optimized time-coupled constraint decoupling model described above does not directly incorporate power flow security constraints into the distribution network. During the model solution phase, the outputs of DERs at each distribution network node are independent. Furthermore, subsequent DOE verification after the solution is completed ensures the safe and stable operation of the distribution network. Therefore, it decouples the spatial coupling constraints caused by the direct inclusion of power flow security constraints in the traditional model. Additionally, the search model only targets a single search direction; to obtain the PFR vertex set, it is necessary to solve for all search directions and update the search directions round by round. The overall solution steps are as follows:

[0098] 1) Initialize the virtual queue and the set of unit vectors corresponding to the search directions in the first loop as follows: ,in Indicates the number of search rounds. , , They represent the first The set of search direction numbers in the wheel, the first A set of unit vectors and search directions.

[0099] 2) Calculate and solve for the corresponding coefficients in the virtual queue for each search direction in the direction set; from The virtual queue is updated periodically to obtain the corresponding PCC and distribution network nodes. Output points, and save them to their respective vertex sets. , ,in Equal to node The sum of the outputs of the DERs.

[0100] 3) If ,make (And proceed to step 4); otherwise, proceed to step 5).

[0101] 4) To The points are sorted counterclockwise and the perpendicular bisectors of adjacent output points are calculated. The direction of the extension of the perpendicular bisectors is taken as the search direction of the s-th round, and then the process returns to execute steps 2)-3).

[0102] 5) To Construct the convex hull and calculate its area. Check whether the convergence condition is met time interval by time. If it is met, proceed to step 6); otherwise, And return to step 4).

[0103] Convergence condition setting: As The increase, As the number of interior points increases, the area of ​​the convex hull they construct also increases. After reaching a certain value, the increase in area will be very small or even approach zero. At this point, it is assumed that PFR no longer changes, and the model converges. (28)

[0104] In the formula: , Time periods No. The convex hull area and the change in convex hull area obtained after round search; For area calculation; This is the convergence threshold.

[0105] 6) Exit the loop iteration to obtain the time-decoupled PFR of PCC and distribution network nodes, i.e.: , , This refers to the convex hull operation for a point set.

[0106] 7) Perform DOE verification on the time-decoupled PFR.

[0107] The purpose of DOE verification is to correct and constrain the output of distribution networks (DERs) when VPPs are difficult to embed directly into the aggregation model, thereby ensuring the safe and stable operation of the distribution network. This embodiment uses DOE and set operations to verify PFR. The specific verification process is as follows.

[0108] In the search model, there is no coupling of DERs output between distribution network nodes. Therefore, the active and reactive power outputs of DERs at each distribution network node are independent at the modeling level. Furthermore, as shown in equation (10), the equivalent output at PCC is obtained by the linear superposition of the outputs of each node. Based on these characteristics, the DOE's verification of PFR can be performed by... Set operations between DOE and other libraries: This allows you to perform set operations on a single node. Its corresponding runtime envelope By taking the intersection, we obtain the final feasible region of a single resource that satisfies the DOE constraints. Finally, for all The final feasible region of PCC is obtained by performing Minkowski summation. The expression is as follows: (29)

[0109] In the formula: This is the set of distribution network nodes containing DERs.

[0110] The parameters that ES needs to determine and prove are: , , The specific proof process is as follows:

[0111] For the initial capacity of ES According to mathematical induction, we assume Then it is only necessary to prove Proof can be obtained immediately , , The value can satisfy the upper and lower limits of the ES capacity. :

[0112] 1. When When, the objective function right and Find the partial derivatives separately: (30)

[0113] make , The results that cause the signs of the partial derivatives to change are obtained respectively. Threshold: (31)

[0114] according to The symbols are used for further derivation:

[0115] ①When hour, The two thresholds are required to be within the range of 0. Inside, then: , ,Right now: (32)

[0116] If equation (32) holds, then it is required that At the same time, it is necessary to ensure ,Right now: (33)

[0117] because Therefore, it is required ,Right now: .

[0118] right The possible values ​​are discussed in intervals:

[0119] a.When At this time , For the minimization function In other words, there exists , ,but: (34)

[0120] Require ,get: .

[0121] b. When hour, , For the minimization function In other words, there exists , ,but: ,at this time Heng was established.

[0122] c. When hour, , For the minimization function In other words, there exists , ,but: (35)

[0123] Require ,get: .

[0124] Further discussion , , , Size: Because the maximum sustainable charge and discharge power meets ,therefore: , ,because It is also necessary to ensure that: ,Right now: (36)

[0125] get: (37)

[0126] because ,Require ,Right now: (38)

[0127] get: (39)

[0128] because Only proof is needed That's all. ,in , .right Differentiate: .because Therefore, in superior , Strictly increasing, therefore its upper bound is: ,so Heng was established.

[0129] In conclusion, when At that time, the range of each parameter is obtained: , , Because different energy storage batteries vary in maximum sustainable charge / discharge power and capacity, the `max` and `min` results in the parameter range need to be adjusted accordingly based on the actual battery parameters. For ease of calculation, the midpoint value of each parameter range is taken as the final value, i.e.: (40)

[0130] ②When Similarly, the ranges of each parameter can be obtained as follows: , , .in , , , The calculation formula is as follows: (41)

[0131] For ease of calculation, let ,but: , , The final values ​​of each parameter are as follows: (42)

[0132] 2. When At that time, according to the power change constraint equation (11), if in the first round If this occurs during a search, then ,Right now ,at this time The requirements are met.

[0133] If this situation occurs during k>1 rounds of search, then ,Right now , .for as well as In other words, it must already exist: ,at this time: (43)

[0134] It also meets the requirements.

[0135] The parameters that SL needs to determine and prove are: The specific proof process is similar to that of ES, and will not be repeated here. The parameter range after derivation is as follows: (44)

[0136] The final values ​​of the set parameters are as follows: (45)

[0137] The reason for characterizing aggregation costs is that when a VPP participates in market transactions to submit volume and price declarations or respond to scheduling commands to obtain compensation, it needs not only to understand the physical feasible boundary of its aggregated output but also to clarify the true minimum scheduling cost at different aggregation output points. The aggregation cost function essentially describes the minimum total operating cost for a VPP to coordinate internal DERs to meet its own operational constraints and network security constraints, given a given aggregation output level. It should be noted that the aggregation cost function characterized in this paper is a monetary function of the "output-cost" mapping, rather than a price function of the "output-price" mapping.

[0138] DERs operating costs consist of two parts: active power and reactive power. The operating cost functions for various resources are as follows:

[0139] 1) PV: Active power output cost is zero, reactive power output cost is the cost converted from inverter losses: (46)

[0140] In the formula: For PV operating costs; This is the unit reactive power output inverter loss reduction factor.

[0141] 2) ES: Active power output cost is the cost of charging and discharging losses of the energy storage battery; reactive power output cost is the cost of inverter losses converted to equivalent values. (47)

[0142] In the formula: , , These are the operating costs of ES, active power output costs, and reactive power output costs, respectively. , These are the battery loss cost coefficient per unit of active power output and the inverter loss conversion coefficient per unit of reactive power output, respectively.

[0143] 3) DG: Active power output cost is secondary fuel cost, reactive power output cost is inverter loss-based cost: (48)

[0144] In the formula: , , These are the operating costs of DG, active power output costs, and reactive power output costs, respectively. , , This is the DG fuel cost coefficient; This is the conversion factor for inverter losses per unit of reactive power output (DG).

[0145] 4) SL: Power shifting requires operation off the baseline load curve; compensation is provided for this shift. (49)

[0146] In the formula: For SL operating costs; This is the offset unit power compensation cost coefficient.

[0147] 5) CL: Cost calculated based on the unit price for power reduction compensation: (50)

[0148] In the formula: For CL operating costs; To reduce the unit price of power compensation.

[0149] The aggregation cost function, like the PFR, is also time-based. The aggregation cost function is characterized by the following model:

[0150] Objective function: at the point that satisfies PCC Given the output, find the minimum aggregation cost value. : (51)

[0151] Constraints: DERs operating constraints and operating cost function: equations (2), (4), (5), (7), (8) and PCC equivalent output constraint equation (10). In equation (10) Should be replaced with .

[0152] Through Uniform sampling within the area can construct a set of sampling points. After constructing the sampling point set, the above model is solved point by point to calculate the corresponding aggregation cost value, resulting in a three-dimensional point set: ,in This represents the number of sampling points.

[0153] Will exist Construct its convex hull in three-dimensional space: ,in, The lower surface is composed of several triangular facets. composition: ,in Let be the total number of pieces. The general form of the plane is: (52)

[0154] Select the facets that face outward along the negative direction of the cost axis as the lower surface facet set: These local planes collectively constitute the set of candidate support planes for the aggregation cost surface. For any ,because The plane can be rewritten as: (53)

[0155] According to the property of convex functions: any convex function can be represented as the upper envelope of all its supporting hyperplanes. Based on the affine functions corresponding to all lower surface patches, the time interval is defined. The piecewise linear approximation function for aggregation cost is: (54)

[0156] To avoid directly appearing in subsequent application decision-making models Calculation, introducing auxiliary variables This indicates that efforts were made in the application process. The approximate value of the polymerization cost is given below. Then we have: (55)

[0157] When the objective function minimizes the cost term Or in maximizing profits When the form appears, the optimal solution automatically has: .

[0158] Thus, by adopting the VPP aggregation cost function with convex piecewise approximation, the nonlinear law of aggregation cost variation with active and reactive power output can be well characterized.

[0159] The above embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made based on the essence of the content of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for characterizing the feasible region and cost of virtual power plant aggregation under spatiotemporal decoupling, for VPP, characterized in that, The method includes: Receive the operating information of DERs in the distribution network and upload the maximum output information of DERs to the DSO to calculate DOE; Receive the DOE sent by the DSO; Based on the operational constraints of DERs, a PCC point aggregation PFR characterization model is constructed; the temporal coupling constraints in the operational constraints are decoupled and the PFR characterization model is transformed to calculate the time-decoupled PFR; the time-decoupled PFR is then subjected to safety verification using DOE. Within the PFR after safety verification, output points are uniformly sampled; based on the DERs operating cost function, a minimum aggregate cost model is constructed and each sampled point is substituted into the minimum aggregate cost model to calculate the cost value; after calculating all sampled points, a three-dimensional active-reactive-cost point set is obtained and a convex hull is constructed to characterize the aggregate cost.

2. The method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 1, characterized in that, The DOE is the power transmission range given by the DSO for each distribution network node. Within the DOE, DERs can arbitrarily adjust their output.

3. The method for characterizing the feasible region and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 1, characterized in that, The Lyapunov optimization method is used to decouple the time coupling constraints.

4. The method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 1, characterized in that, The polymerization cost is characterized by a convex piecewise linear fitting method.

5. The method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 1 or 2, characterized in that, The DERs are divided into DERs with time coupling constraints and DERs without time coupling constraints.

6. The method for characterizing the feasible region and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 5, characterized in that, The DERs with time-coupled constraints include distributed energy storage, distributed generators, and shiftable loads; the DERs without time-coupled constraints include distributed photovoltaics and load shedding.

7. The method for characterizing the feasible region and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 1, characterized in that, The time coupling constraints are decoupled, and the PFR characterization model is transformed to calculate the decoupled PFR; the decoupled PFR is then subjected to a safety check using DOE, including: 1) Initialize the virtual queue and the set of unit vectors corresponding to the search directions in the first loop as follows: ,in Indicates the number of search rounds. , , They represent the first The set of search direction numbers in the wheel, the first A set of unit vectors and search directions; 2) Calculate and solve the corresponding coefficients in the virtual queue for each search direction in the direction set; from The virtual queue is updated periodically to obtain the corresponding PCC and distribution network node. Output points, and save them to their respective vertex sets. , ,in Equal to node The sum of the outputs of the lower DERs; where: , These are the active and reactive power outputs of VPP aggregation and a single distribution network node, respectively. 3) If ,make And proceed to step 4); otherwise, proceed to step 5). 4) To The points are sorted counterclockwise and the perpendicular bisectors of adjacent output points are calculated. The direction of the extension of the perpendicular bisectors is taken as the search direction for the s-th round, and then the process returns to execute steps 2)-3). 5) To Construct the convex hull and calculate its area. Check whether the convergence condition is met time interval by time. If it is met, proceed to step 6); otherwise, And return to step 4); 6) Exit the loop iteration to obtain the time-decoupled PFR of PCC and distribution network nodes; 7) Perform DOE verification on the time-decoupled PFR.

8. The method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 7, characterized in that, In step 5), the convergence condition is set as follows: ； In the formula: , Time periods No. The convex hull area and the change in convex hull area obtained after round search; For area calculation; This is the convergence threshold.

9. The method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 1 or 7, characterized in that, The security verification of the decoupled PFR using DOE includes: To a single node Its corresponding runtime envelope Take the intersection to obtain the final feasible region of a single resource that satisfies the DOE constraints. ; For all The final feasible region of PCC is obtained by performing Minkowski summation. : ； In the formula: This is the set of distribution network nodes containing DERs.

10. The method for characterizing the feasible domain and cost of virtual power plant aggregation under spatiotemporal decoupling as described in claim 4, characterized in that, The method of using convex piecewise linear fitting to characterize aggregation cost includes: 3D point set exist Construct its convex hull in three-dimensional space: ,in, The lower surface is composed of several triangular facets. composition: ,in Let be the total number of pieces; The general form of the plane is: ； Select the facets that face outward along the negative direction of the cost axis as the lower surface facet set: Local planes together constitute the set of candidate support planes for the aggregation cost surface; for any ,because The plane is rewritten as: ； Based on the affine functions corresponding to all lower surface patches, the time period is defined. The piecewise linear approximation function for aggregation cost is: ； Introducing auxiliary variables This indicates that efforts were made in the application process. The approximate value of the polymerization cost is as follows: ； When the objective function minimizes the cost term Or in maximizing profits When the form appears, the optimal solution automatically has: .

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