A robust collaborative optimization method for virtual power plants considering uncertain demand response

Abstract

The present invention relates to the technical field of electric-carbon synergistic integrated energy systems, and specifically to a robust collaborative optimization method for a virtual power plant that takes into account uncertain demand response. The method establishes a demand response model that integrates multidimensional features, identifies and analyzes the characteristics of four dimensions, namely, time delay, adjustment speed, tracking power, and response energy, and their impact on the accuracy of demand response. By fitting a normal distribution function with historical data, the confidence interval of the uncertainty feature is estimated, and a multidimensional coupling deviation model is constructed to accurately characterize the dynamic profile of demand response. A two-stage optimization strategy is adopted, with the first stage being an instruction decomposition model and the second stage being an instruction tracking model. The operating cost and total penalty cost are minimized through mixed integer linear programming and energy storage system deviation compensation strategies. The present invention can effectively manage the uncertainty in demand response and improve the flexibility and economy of virtual power plants.

Description

Technical Field

[0001] The present invention relates to the technical field of uncertain demand response characterization and efficient collaborative regulation of virtual power plant flexible load operation optimization, and specifically to a robust collaborative optimization method for a virtual power plant taking into account uncertain demand response. Background Art

[0002] Faced with global energy shortages and environmental crises caused by fossil fuels, the need for sustainable alternative energy solutions has become particularly urgent. In this context, renewable energy sources (RES) have become a core strategy to alleviate energy shortages. In particular, flexible loads (FL) have attracted increasing attention due to their low-cost response and high flexibility potential. By implementing demand side management (DSM) on them, not only can the overall performance of renewable energy systems be effectively optimized, but a new approach can also be created to achieve energy supply and demand balance.

[0003] In regions such as Europe and the United States, DSM is well established, with limited capacity FL integrated into DSM through virtual power plants (VPPs) or load aggregators. Despite these advances, the diversity and uncertainty of load characteristics still hinder effective demand response (DR). To achieve accurate DR, in which FL power consumption is adjusted to strictly follow load commands, it is essential to improve the cost-effectiveness of DR projects and promote renewable energy consumption. However, load characteristics such as slow response speed and variable power tracking can lead to inaccurate DR. These diverse and complex characteristics mean that the load adjustment amount cannot always be accurately calculated, making DR strategies extremely complex.

[0004] Uncertainty, as a key influencing factor, is particularly important when evaluating the DR deviation of distributed energy. Although existing studies have initially explored systems with multiple uncertain load characteristics, the in-depth coupling analysis of these systems through nonlinear models is still insufficient, and the impact of complex interactions has not been fully refined. It is necessary to build a model that accurately describes these interactions and quantifies DR deviations. In addition, effective coordination of multiple flexibility resources and the establishment of incentive and constraint mechanisms are crucial for managing DR deviations. When the VPP's own regulation capacity reaches its upper limit, new energy operators may need to use additional flexible resources at higher costs to maintain the delicate balance of electricity supply and demand, which highlights the challenge of the lack of efficient coordination mechanisms and strategies. To this end, the present invention will focus on accurate coupling analysis models, as well as innovative resource allocation and incentive frameworks, to enhance VPP's ability to control DR deviations and optimize the flexibility and economy of the overall energy system in a highly uncertain environment.

[0005] DR-specific attributes are included in the optimization strategy. For example, the amplitude of Tracking Power (TP) directly maps the degree of response of Flexible Loads (FL) to DR commands. This dimension is indispensable in strategy design. Some studies explore the energy uncertainty inherent in transferable DR loads, regard deferrable loads as a medium for energy scheduling, and analyze how decisions are subject to various uncertainties. On this basis, reasonable coordinated regulation of flexible loads (FL) and energy storage systems (ES) is widely considered to be the optimal strategy for dealing with response energy (RE) fluctuations and tracking power uncertainty. It can not only improve the system's dynamic adaptability to DR commands, but also ensure the optimization of power quality and supply-demand balance.

[0006] In the face of rapid changes in power supply and demand, the short-term characteristics of demand response (DR), especially the regulation speed (RS), that is, the agility of power adjustment, are particularly critical to maintaining the balance between supply and demand. Its impact spans from seconds to minutes or even longer time spans. This characteristic has been significantly highlighted in many studies. In addition, as the lag period of FL's response to control instructions, related studies have deeply analyzed the impact of TD on the effectiveness of DR strategies and designed targeted enhancement schemes to improve the stability and economic benefits of the system after the access of new energy. Some studies have also introduced robust synchronous control strategies to deal with the randomness and delay in the DR process, consolidating the position of the DR mechanism in the dynamic management of modern power grids.

[0007] Therefore, the precise implementation of demand-side response (DR) faces several major challenges, including uncertainty in time delay, shortage of response energy, slow regulation rate, and extended delay period. From the perspective of optimization strategy, designing an efficient demand-side management (DSM) solution becomes the key to alleviating the above-mentioned deviation problems. The concept of virtual power plant (VPP) is adopted in the existing technology as a means of centralized regulation of diversified flexible resources, which integrates multiple operation optimization algorithms to enhance the diversity and complementary effects of resource combinations. Common simplified assumptions in DR research, such as fast regulation rate, negligible time delay, and sufficient response energy, are usually not met in real scenarios, especially in the multi-dimensional characteristics (covering energy, speed and time) and the traditional power regulation dimension of DR. The fine coupling model has yet to be established, which significantly weakens the prediction accuracy of the model. Although most of them focus on optimizing DR by solving uncertain tracking power, they often ignore the importance of managing multiple uncertainties at the same time, which is a necessary condition for achieving precise DR regulation. In addition, existing technologies use the flexibility resources of renewable energy systems (RES) to alleviate DR deviations. However, in terms of economic benefits, it is urgent to build a priority mechanism to promote the operation optimization and scheduling strategy of high-quality and efficient flexible loads within virtual power plants (VPPs), and to implement certain penalty measures for low-quality flexibility. Summary of the invention

[0008] In order to solve the problems existing in the background technology, the present invention provides a robust collaborative optimization method of a virtual power plant considering uncertain demand response, which comprises the following steps:

[0009] Step S1: Establish a demand response DR model with multi-dimensional feature fusion; the demand response DR represents the behavior of users in the power market responding to power price signals or incentive mechanisms to change their inherent power consumption patterns; in the demand response DR model, the characteristics of the demand response DR in four dimensions of time delay TD, regulation speed RS, tracking power TP and response energy RE are identified, and the impact of these characteristics on the accuracy of demand response is analyzed, as well as how uncertainty factors lead to demand response deviations;

[0010] Step S2: Characterization of DR uncertainty characteristics; specifically, including: fitting a normal distribution function using historical DR data or adopting typical value modeling, estimating and correcting the parameters of the distribution function, and calculating the confidence interval of each uncertainty characteristic by integrating the distribution probability density function to define its upper and lower limits;

[0011] Step S3: constructing a DR multi-dimensional coupling deviation model; specifically, including: constructing a coupling deviation model according to the characteristics of demand response in four dimensions, and dividing the model into a delay stage, a ramp-up stage, a stable stage, and an early termination stage, using a piecewise function to describe the dynamic and nonlinear characteristics of the DR power curve; defining the upper and lower limits of uncertainty of the flexible load FL in different dimensions;

[0012] Step S4: Robust collaborative optimization of virtual power plants; specifically including:

[0013] S41: Construct the virtual power plant VPP operation framework, integrating the flexibility of energy storage system ES and flexible load FL; design a two-stage optimization strategy of decomposition and tracking, determine the instruction decomposition model in the first stage, and design the instruction tracking model in the second stage;

[0014] S42: DR instruction decomposition; using the mixed integer linear programming MILP model to plan the optimal dispatch of the power system and minimize the operating cost; considering the capacity forecast and operation constraints of renewable energy systems RES such as photovoltaic and wind power, as well as the operation constraints of power interconnection lines and energy storage systems;

[0015] S43: DR instruction tracking; based on the results of DR instruction decomposition, analyze and calculate the power and energy differences caused by the uncertainties of FL characteristics; design the ES deviation compensation strategy of the energy storage system to minimize the total penalty cost of VPP and FL.

[0016] Further, the specific process of step S1 includes:

[0017] Among the four dimensions of DR characteristics, namely time delay, regulation speed, tracking power and response energy, tracking power is closely related to the power distribution of flexible loads, which is monitored by smart meters. The power dimension adopts continuous time variables. Represents, while the other three dimensions introduce discrete time variables n, where n=1,2,…24;

[0018] S11. In the tracking power dimension, the power size constraint and deviation equation are constructed to adapt to both adjustable and interruptible loads, which is specifically described as equation (1):

[0019] (1)

[0020] Where: The tracking power curve represented as a flexible load; is represented as a time variable; and They are respectively expressed as power variables of adjustable and interruptible loads; and Continuous and discrete variables represented as load curves; It is represented as a load reference curve; and They are represented as the minimum and maximum boundaries of DR power, respectively; It is expressed as the DR power deviation, which is usually 0 under deterministic conditions; Indicates that a DR command is given to VPP;

[0021] S12. When considering the response energy dimension and adjusting or transferring energy through the demand response (DR) mechanism, the participation of energy flexible loads (FL) such as thermal storage boilers is directly limited by the actual thermal energy demand. Even though thermal storage boilers have potential in power regulation, they cannot actually perform DR operations in the case of insufficient thermal power. The response energy inequality constraint equation is specifically described as formula (2):

[0022] (2)

[0023] In the formula, It is expressed as the response energy of the flexible load; It is expressed as the scheduling time scale; Represented as discrete time periods; and They are respectively represented as the flexible load response energy range; It is expressed as DR energy deviation;

[0024] S13. In the time dimension, the time delay characteristics of DR are analyzed in detail, and the time difference between the theoretical response instruction and the actual execution is quantified. In order to accurately manage the resulting DR deviation, it is usually considered that the impact on the overall DR effect can be ignored when the time delay TD is short, that is, within a few seconds to a few minutes. However, as TD is extended to a few minutes or longer, the deviation effect on the DR execution effect is significant. In order to describe the delay characteristics, a set of inequalities are used to characterize it. This model integrates the correlation between power and energy deviations, defines the time delay constraint, the DR power curve with time delay, and the power and energy deviations. The specific description is formula (3):

[0025] (3)

[0026] Where: Expressed as flexible load delay time; and It is expressed as the power and energy deviation due to TD;

[0027] S14. In the dimension of regulation speed, flexible load (FL) is the rate of change of power participating in demand side management (DSM); in order to improve the flexibility of renewable energy system (RES) on a short time scale (minutes or seconds), it is necessary to achieve rapid response (RS); on the contrary, the slower the RS, the greater the power and energy deviation in demand response (DR). Considering the general form of regulation speed DR power and the formula of power and energy deviation caused by regulation speed, the specific description is formula (4):

[0028] (4)

[0029] Where: It is expressed as the adjustment speed; and Expressed as power and energy deviation caused by adjusting speed.

[0030] Further, the specific process of step S2 includes:

[0031] For the key features of the uncertainty range of four demand response (DR), the normal distribution function or typical value modeling is adopted; the present invention uses historical DR data to fit, estimate and correct the distribution function and parameters; then, the distribution probability density function is integrated and the corresponding confidence interval is calculated, which can accurately define the upper and lower limits of each uncertainty feature, which is specifically described as formula (5):

[0032] (5)

[0033] Where: Represented as a set of uncertainty features; and and and They are the uncertainty variables of tracking power, response energy, delay and adjustment speed respectively; σ and μ are the expected value and standard deviation of the distribution;

[0034] In order to more accurately adapt to the uncertainty of power tracking and energy response, the original uncertainty range is adjusted by fully considering the provisions of domestic demand-side management policies that do not penalize over-response due to factors other than instructions; on this basis, the improved uncertainty boundary should reflect the exemption of incentives outside the (DSM) strategy, ensuring that the set interval can capture the uncertainty in real operation without triggering unnecessary compensation mechanisms; the specific description is formula (6):

[0035] (6)

[0036] Where: Expressed as a parameter for varying the size of the confidence level; for time delay uncertainty, lower than expected Some of them can be ignored, allowing FL to respond early; and They are represented as uncertain RS confidence parameters respectively; and are represented as DR normal distribution parameters respectively.

[0037] Further, the specific process of step S3 includes:

[0038] A multi-dimensional coupled dynamic model is established to depict the exact posture of the DR curve and define the uncertainty boundary of its power response. The piecewise function method is used to solve the dynamic and nonlinear characteristics of the DR power curve modeling. The DR dynamic profile is accurately characterized in four core dimensions, and the function is divided into four time periods: [0, t1], [t1, t2], [t2, t3], and [t3, Δt]. The length of the time period corresponds to the time variable related to each characteristic. , , and ;

[0039] The coupled multidimensional deviation model is expressed as a piecewise function; for the specified load command , there is a delay at the beginning , at this time the DR system output power is zero; in the climbing stage, the power starts from zero at a preset adjustment rate and responds quickly to ; in duration The DR power is kept constant and the load command In the third stage, due to resource allocation limitations, DR response may be It ends earlier than expected. The specific process is described by equations (7) and (8):

[0040] (7)

[0041] (8)

[0042] Where: , and Expressed as a time point;

[0043] By integrating equations (5) and (6), a dimensional deviation model at a specific confidence level is constructed. In this model, the upper and lower limits of the uncertainty of the flexible load FL are defined: the time delay is used as the lower limit indicator of certainty, while the adjustment speed, power tracking accuracy and duration of the response energy constitute the upper limit indicator of uncertainty. Therefore, the model is simplified by focusing on the two periodic dynamic characteristics of climbing and steady state and ignoring the potential early termination stage, which is specifically described as equation (9):

[0044] (9)

[0045] Where: It is expressed as the upper limit of flexible load FL; Indicates the upper limit of the adjustment speed;

[0046] Similarly, in order to accurately express the lower bound of DR uncertainty, the following segmented definition is followed: the uncertainties in power, energy, and speed are all measured with lower limits, while the uncertainty in the time dimension is measured with an upper limit; the specific description of the lower bound of DR uncertainty is formula (10):

[0047] (10)

[0048] Where: It is expressed as the lower bound of the flexible load FL; , and They are denoted as TP, RE and RS lower bounds respectively; Indicates the upper bound of the delay.

[0049] Furthermore, the specific process of step S41 includes: constructing a virtual power plant VPP operation framework, and correcting the power offset that may occur in the demand response DR process through the cost compensation energy storage system ES; this operation framework consists of two stages: decomposition and tracking. In the first stage, the command decomposition model is determined to rationally plan the optimal scheduling of the power system; in the second stage, a command tracking model is designed to dynamically adapt to the actual demand response changes; finally, the column generation nested algorithm C&CG is adopted, combined with the two-stage robust optimization technology, and the decomposition and tracking double-layer model is repeatedly solved iteratively to achieve high management of dynamic resources; within the system framework, the flexible loads of lighting, HVAC, heating boilers and industrial machinery that can be adjusted are integrated into the VPP as a supplement to the renewable energy system RES; the coordination between the flexible load FL and the energy storage system ES is strengthened to ensure that the two complement each other effectively and jointly manage DR deviations.

[0050] Further, the specific process of step S42 includes:

[0051] The first stage of DR instruction decomposition uses the MILP model to achieve economic optimization of diverse and flexible resources within the renewable energy system RES, and refine the virtual power plant VPP operation instructions; the main goal of the DR decomposition model is to minimize the comprehensive cost of operating RES, including solar photovoltaic PV, wind power generation, grid connection and thermal power and VPP, taking into account the fines for thermal power due to carbon emissions and the dispatching cost of power interconnection lines. In VPP, the ES cost indicator also takes into account charging and discharging losses and operating expenses;

[0052] Therefore, the optimal operating cost target of the first-stage model is described as formula (11):

[0053] (11)

[0054] Where: , , , , and They are respectively represented as photovoltaic, wind, thermal power, energy storage, power interconnection line and flexible load costs; , , and They are expressed as the unit costs of power generation, ES operation, power tie line dispatching and flexible load transfer respectively; and They represent the unit penalties for photovoltaic power curtailment and wind power curtailment respectively; Expressed as a carbon penalty; Expressed as unit loss for charging and discharging; and They are represented as predicted photovoltaic and wind power respectively; and They are represented as actual photovoltaic and wind power respectively; It is represented by the rated capacity of thermal power; λ is represented by the thermal-electric coupling depth; It is indicated as a heat source; Expressed as storage charging power; Expressed as discharge power; Expressed as the power of the electric power tie line;

[0055] The optimization constraints of the DR command decomposition model (11) are derived from the operating characteristics of the renewable energy system RES and the management specifications of the virtual power plant VPP; including: renewable energy capacity forecast, cogeneration unit operation constraints, energy storage system ES intelligent charging and discharging management constraints, and the capacity limit of the interconnection line as a power supply and demand balancing node; the specific description is formula (12):

[0056] (12)

[0057] Where: It is represented by the state of charge SOC of ES; It is expressed as ES initial SOC; and They are expressed as ES rated capacity and power respectively; Expressed as the rated power of the electric power interconnection line.

[0058] Further, the specific process of step S43 includes:

[0059] The second-stage DR command tracking model focuses on the flexible load FL command tracking and energy storage ES system deviation compensation; based on the first-stage results, the power and energy differences caused by the uncertainty factors of FL characteristics are analyzed and calculated; the four-period piecewise function is defined by combining equations (7) and (8); the DR power and energy deviation is specifically described as equation (13):

[0060] (13)

[0061] Where: and They are represented as DR power and energy deviation respectively; m is the four time periods of the piecewise function, where m=1~4 corresponds to TD, RS, TP and RE respectively;

[0062] The second-stage DR command tracking model corrects the demand response (DR) power deviation through the energy storage system (ES) device. Ideally, the compensation power and energy provided by the ES completely match the power and energy of the DR deviation. However, in actual scenarios, the compensation behavior is affected by the cost-effectiveness of the ES operation, resulting in the relaxation of the original strong constraints to adapt to the actual operation complexity. The specific description of the relaxed constraints is formula (14):

[0063] (14)

[0064] Where: and are ES compensation power and energy, respectively;

[0065] The objective function of the second-stage DR instruction tracking model and the involved deterministic and uncertain parameters are presented as shown in equations (15) and (16):

[0066] (15)

[0067] (16)

[0068] Where: Expressed as VPP and FL deviation penalty;

[0069] The objective function of the second-stage DR instruction tracking model focuses on minimizing the total penalty of VPP and FL. Specifically, any ES that fails to fully compensate for the DR residual deviation according to the established plan will be converted into a deduction item. Given that ES can assist FL in evading penalties, a reasonable share of DR benefits must be allocated to ES users and the VPP operation management team. The specific objective function is calculated by formula (17) as follows:

[0070] (17)

[0071] Where: It is expressed as the net deviation unit penalty after ES compensation; Expressed as DR deviation unit penalty;

[0072] The constraints in the second-stage DR instruction tracking model have been detailed in equations (7) to (10). To strengthen the integrity of the constraints, equation (18) supplements the additional power and energy deviation limit constraints:

[0073] (18)

[0074] Where: and They are respectively represented as the VPP net power and energy deviation after ES compensation;

[0075] The battery state of charge SOC interval restriction constraint with uncertain attributes is shown in formula (19):

[0076] (19)

[0077] In equations (7) to (10), due to the dynamic constraints of the adjustment rate and response energy, non-convex characteristics are presented. In order to achieve the matching adaptation between non-convex constraints and convex optimization algorithms, auxiliary variables and relaxation techniques are introduced in equation (20); although the load instruction It is used as a decision variable in the decomposition phase, but as a constant in the tracking phase, allowing it to be combined with the uncertainty variable and Direct multiplication;

[0078] (20)

[0079] Where: It is represented as an auxiliary variable for adjusting speed;

[0080] Figure 4 The whole process of the DR instruction decomposition and tracking method proposed in this invention is presented. The column generation nesting algorithm (C&CG) is used to feed back the results of the second stage to the first stage, forming a closed-loop iterative solution mechanism. For the VPP deviation penalty in the objective function of the first stage decomposition model, as shown in formula (21), an auxiliary variable is introduced. Difference penalty is imposed and new constraints are generated to enhance the efficiency and accuracy of model solution. The objective function with deviation penalty is described as formula (22):

[0081] (twenty one)

[0082] (twenty two)

[0083] Where: θ represents the auxiliary variable of the first-stage objective introduced into the C&CG algorithm;

[0084] The first-stage decomposition model optimization constraint (12) generates additional column variables and corresponding row constraints, which are specifically described as (23):

[0085] (twenty three)

[0086] Where: k represents the number of iterations, and They represent the generation of column variables for the kth iteration.

[0087] The beneficial effects achieved by the present invention are:

[0088] First, this paper proposes a robust collaborative optimization method for virtual power plants with a multi-dimensional uncertain DR deviation calculation model, which aims to achieve accurate distributed energy regulation DR in highly uncertain scenarios, thereby overcoming problems such as time delay, slow regulation rate, inaccurate power tracking and response energy shortage. First, an in-depth analysis of DR in actual scenarios is conducted, and four core uncertainty factors are characterized by constructing a coupling deviation model, which is then integrated into the control method design link. The strategy is executed in two stages: decomposition and tracking. In the decomposition stage, the load instructions and the charging and discharging plan of the energy storage system are calculated to maximize the comprehensive benefits of renewable energy RES and virtual power plants VPP; in the tracking stage, the energy storage system ES is used to effectively correct and compensate for DR deviations to minimize penalty costs. Finally, the entire process is driven by the column generation algorithm C&CG to drive the decomposition-tracking feedback iterative cycle to ensure the dynamic optimization of the proposed strategy, which significantly improves the flexible complementarity of flexible load FL and energy storage system ES in the virtual power plant VPP management framework.

[0089] In the first stage, a mixed integer linear programming MILP model is used to maximize the utilization rate of renewable energy RES and the economic benefits of VPP operation. The optimal operation of RES is combined with the decomposition of VPP commands. The input parameters include: RES energy consumption and energy production. The output is for VPP specific operation instructions, DR power scheduling indicators and detailed optimal planning of charging and discharging time, realizing the initial deployment of resource optimization. In the second stage, a robust optimization model is introduced with the help of convex relaxation technology. Based on the output results of the first stage, the inputs such as DR characteristics and uncertainty boundaries are combined to solve the possible deviations in FL execution and complete the ES compensation strategy. The advantages of the proposed model and method are that it can distinguish and process deterministic and uncertain decision variables. Through the decomposition of instructions on a long time scale of every hour and the instruction tracking operation on a short time scale of every minute, the complexity of high-dimensional data is effectively managed, ensuring the stability and efficiency of VPP operation at the practical level.

[0090] Second, the present invention introduces a multidimensional uncertainty model and integrates a new coupled uncertainty model within the distributed energy DR deviation framework. This model comprehensively covers the four key uncertain variables of time delay, regulation rate, power tracking accuracy and response energy supply, providing theoretical support for accurate modeling;

[0091] Third, the present invention adopts the decomposition and tracking nesting method, and designs a set of virtual power plant VPP robust collaborative optimization methods to address the challenges of multi-dimensional deviations. This method not only promotes the intelligent management of flexible loads, but also significantly optimizes the charging and discharging plan of energy storage devices, and improves the flexibility and efficiency of distributed systems;

[0092] Fourth, the present invention achieves carbon reduction and cost-effectiveness improvement. By fine-tuning the multi-dimensional DR deviations, it reduces the overall economic cost of virtual power plant operation, energy storage maintenance and flexible load response, bringing a new low-carbon solution to the field of distributed energy management. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 Schematic diagram of uncertainty analysis and characterization of demand response characteristics, in which (a) is the demand response power dimension, (b) is the demand response energy dimension, (c) is the demand response time dimension, and (d) is the demand response speed dimension;

[0094] Figure 2 Schematic diagram of a multi-dimensional coupled deviation model representing demand response;

[0095] Figure 3 A diagram showing the operation framework of a virtual power plant with uncertain demand response;

[0096] Figure 4 A full flow chart of a robust collaborative optimization method for a virtual power plant considering uncertain demand response according to the present invention is shown. DETAILED DESCRIPTION

[0097] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. In addition, the forms of the various structures recorded in the following embodiments are merely illustrative, and the present invention is not limited to the various structures recorded in the following embodiments. All other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0098] refer to Figure 1 - Figure 4 The present invention provides a robust collaborative optimization method for a virtual power plant considering uncertain demand response, and the specific implementation process is as follows.

[0099] A robust collaborative optimization method for a virtual power plant considering uncertain demand response includes the following steps:

[0100] Step S1: Establish a demand response DR model with multi-dimensional feature fusion; the demand response DR represents the behavior of users in the power market responding to power price signals or incentive mechanisms to change their inherent power consumption patterns; in the demand response DR model, the characteristics of the demand response DR in four dimensions of time delay TD, regulation speed RS, tracking power TP and response energy RE are identified, and the impact of these characteristics on the accuracy of demand response is analyzed, as well as how uncertainty factors lead to demand response deviations;

[0101] Step S2: Characterization of DR uncertainty characteristics; specifically, including: fitting a normal distribution function using historical DR data or adopting typical value modeling, estimating and correcting the parameters of the distribution function, and calculating the confidence interval of each uncertainty characteristic by integrating the distribution probability density function to define its upper and lower limits;

[0102] Step S3: constructing a DR multi-dimensional coupling deviation model; specifically, including: constructing a coupling deviation model according to the characteristics of demand response in four dimensions, and dividing the model into a delay stage, a ramp-up stage, a stable stage, and an early termination stage, using a piecewise function to describe the dynamic and nonlinear characteristics of the DR power curve; defining the upper and lower limits of uncertainty of the flexible load FL in different dimensions;

[0103] Step S4: Robust collaborative optimization of virtual power plants; specifically including:

[0104] S41: Construct the virtual power plant VPP operation framework, integrating the flexibility of energy storage system ES and flexible load FL; design a two-stage optimization strategy of decomposition and tracking, determine the instruction decomposition model in the first stage, and design the instruction tracking model in the second stage;

[0105] S42: DR instruction decomposition; using the mixed integer linear programming MILP model to plan the optimal dispatch of the power system and minimize the operating cost; considering the capacity forecast and operation constraints of renewable energy systems RES such as photovoltaic and wind power, as well as the operation constraints of power interconnection lines and energy storage systems;

[0106] S43: DR instruction tracking; based on the results of DR instruction decomposition, analyze and calculate the power and energy differences caused by the uncertainties of FL characteristics; design the ES deviation compensation strategy of the energy storage system to minimize the total penalty cost of VPP and FL.

[0107] The specific process of each step is as follows:

[0108] S1. Among the four dimensions of DR characteristics, time delay, regulation speed, tracking power and response energy, tracking power is closely related to the power distribution of flexible loads, which can be monitored by smart meters. Inaccurate tracking power, especially under uncertain conditions, will lead to significant DR deviation. Among them, the power dimension adopts a continuous time variable Represented by , while the other three dimensions introduce discrete time variables n (where n=1,2,…24)) to represent.

[0109] In the tracking power dimension, the power size constraint and deviation equation are constructed to accommodate both adjustable and interruptible loads, which is specifically described as equation (1):

[0110] (1)

[0111] Where: The tracking power curve represented as a flexible load; is represented as a time variable; and They are respectively expressed as power variables of adjustable and interruptible loads; and Continuous and discrete variables represented as load curves; It is represented as a load reference curve; and They are represented as the minimum and maximum boundaries of DR power, respectively; It is expressed as the DR power deviation, which is usually 0 under deterministic conditions; Indicates that a DR command is given to VPP.

[0112] When considering the response energy dimension and adjusting or transferring energy through the demand response (DR) mechanism, the participation of energy flexible loads (FL) such as thermal storage boilers is directly limited by the actual thermal energy demand. Even though thermal storage boilers have potential in power regulation, DR operations cannot actually be performed in the case of insufficient thermal power. The response energy inequality constraint equation is specifically described as equation (2): (2)

[0113] In the formula, It is expressed as the response energy of the flexible load; It is expressed as the scheduling time scale; Represented as discrete time periods; and They are respectively represented as the flexible load response energy range; Expressed as DR energy deviation.

[0114] In the time dimension, the time delay characteristics of DR are analyzed in detail, and the time difference between the theoretical response instruction and the actual execution is quantified. In order to accurately manage the resulting DR deviation, it is usually considered that the impact on the overall DR effect can be ignored when the time delay TD is short, that is, within a few seconds to a few minutes. However, as TD is extended to a few minutes or longer, the deviation effect on the DR execution effect is significant. In order to describe the delay characteristics, a set of inequalities is used to characterize it. This model integrates the correlation between power and energy deviations, defines time delay constraints, DR power curves with time delays, and power and energy deviations. The specific description is formula (3):

[0115] (3)

[0116] Where: Expressed as flexible load delay time; and It is expressed as the power and energy deviation due to TD.

[0117] In the dimension of regulation speed, flexible load (FL) is the rate of change of power participating in demand side management (DSM). In order to improve the flexibility of renewable energy systems (RES) on a short time scale of minutes or seconds, a fast response (RS) is required. On the contrary, the slower the RS, the greater the power and energy deviation in demand response (DR). Considering the general form of the regulation speed DR power and the formula of power and energy deviation caused by the regulation speed, the specific description is formula (4):

[0118] (4)

[0119] Where: It is expressed as the adjustment speed; and Expressed as power and energy deviation caused by adjusting speed.

[0120] S2. DR uncertainty characterization

[0121] like Figure 1 As shown in (a), the adjustment range of demand response (DR) of flexible load (FL) is greatly affected by the uncertainty of tracking power. In the energy dimension, this uncertainty causes the difference between load instructions and actual acceptable power, such as Figure 1 As shown in (b). Figure 1 (c) shows the time delay between the issuance of instructions and the actual execution of DR; if the time delay is known, the deviation can be effectively reduced or even eliminated through early intervention. Figure 1(d) shows that the lower response speed (RS) prolongs the time required for the initial power to reach the command value. Therefore, enhancing RS and reducing uncertainty factors are crucial to improving the flexibility of FL in the dimension of adjustment speed. For actual operation scenarios, attention should be paid to the time lag effect, tracking power accuracy, adjustment speed, and the certainty and uncertainty range of response energy during DR implementation. By analyzing these key features and formulating appropriate strategies accordingly, the regulation accuracy and effect of demand side management (DSM) will be greatly enhanced.

[0122] The four key features of the uncertainty range of demand response (DR) described in step S1 can be initially modeled by a normal distribution function or by using typical values. The present invention uses historical DR data to fit, estimate and correct distribution functions and parameters. Subsequently, the distribution probability density function is integrated and the corresponding confidence interval is calculated, which can accurately define the upper and lower limits of each uncertainty feature, specifically described as formula (5):

[0123] (5)

[0124] Where: Represented as a set of uncertainty features; and and and are the uncertainty variables of tracking power, response energy, delay and adjustment speed respectively; σ and μ are the expected value and standard deviation of the distribution.

[0125] In order to more accurately adapt to the uncertainty of power tracking and energy response, the original uncertainty range is adjusted by fully considering the provisions of domestic demand-side management policies that do not penalize over-response due to factors other than instructions. On this basis, the improved uncertainty boundary should reflect the exemption of incentives outside the (DSM) strategy, ensuring that the set interval can capture the uncertainty in real operation without triggering unnecessary compensation mechanisms. The specific description is formula (6):

[0126] (6)

[0127] Where: Expressed as a parameter for varying the size of the confidence level; for time delay uncertainty, lower than expected Some of them can be ignored, allowing FL to respond early; and They are represented as uncertain RS confidence parameters respectively; and are represented as DR normal distribution parameters respectively.

[0128] S3. Constructing DR multi-dimensional coupling deviation model

[0129] In steps S1 and S2, the four characteristics of DR were analyzed in depth from the perspectives of certainty and uncertainty, and the corresponding mathematical models were constructed accordingly. These characteristics show the complex interaction and coupling relationship of the four key dimensions, in which the change of any single characteristic can affect the time period covered by all four characteristics. Figure 2 Different periods of DR optimization scheduling are shown, from the initial response delay, the climbing period affected by the regulation speed (RS), to the stage of maintaining the target power stable, until the early termination that may be caused by insufficient regulation efficiency (RE), reflecting the multi-stage complexity of the process. The interaction of these features at the power level exacerbates the system coupling effect, and the uncertainty of a single feature can rewrite the subsequent power trajectory shape and intensity. Based on this, the present invention introduces a multi-dimensional coupled dynamic model, which not only depicts the exact posture of the DR curve, but also defines the uncertainty boundary of its power response. The piecewise function method is used to solve the problem of modeling the dynamic and nonlinear characteristics of the DR power curve, and the DR dynamic profile is accurately portrayed in four core dimensions, reflecting the effective expression and prediction of this model. The function is divided into four time periods: [0, t1], [t1, t2], [t2, t3], and [t3, Δt]. Figure 2 The length of the time period corresponds to the time variable associated with each feature. , , and .

[0130] Through Figure 2 The analysis is performed on each stage (1 to 4) shown in the figure, and the corresponding interval is integrated to express the coupled multidimensional deviation model as a piecewise function. , there is a delay at the beginning , at this time the DR system output power is zero; in the climbing stage, the power starts from zero at a preset adjustment rate and responds quickly to ; in duration The DR power is kept constant and the load command In the third stage, due to resource allocation limitations, DR response may be The process ends earlier than expected. The specific process is described by equations (7) and (8):

[0131] (7)

[0132] (8)

[0133] Where: , and Expressed as Figure 2 Mid time point.

[0134] By integrating equations (5) and (6), a dimensional deviation model at a specific confidence level is constructed. In this model, the upper and lower limits of the uncertainty of the flexible load FL are defined: the time delay is used as the lower limit indicator of certainty, while the adjustment speed, power tracking accuracy and duration of the response energy constitute the upper limit indicator of uncertainty. Therefore, focusing on the two periodic dynamic characteristics of climbing and steady state, ignoring the potential early termination stage, the model is simplified, which is specifically described as equation (9):

[0135] (9)

[0136] Where: It is expressed as the upper limit of flexible load FL; Indicates the upper limit of the adjustment speed.

[0137] Similarly, in order to accurately express the lower bound of DR uncertainty, the following segmented definition is followed: the uncertainties in power, energy and speed are all measured with lower limits, while the uncertainty in the time dimension is measured with an upper limit. Therefore, the lower bound of the multidimensional deviation model constructed by the present invention is divided into four consecutive stages, namely time, speed, power and energy. The specific description of the DR uncertainty lower bound is formula (10):

[0138] (10)

[0139] Where: It is expressed as the lower bound of the flexible load FL; , and They are denoted as TP, RE and RS lower bounds respectively; Indicates the upper bound of the delay.

[0140] S4. Robust collaborative optimization method for virtual power plants considering uncertain demand response

[0141] S41. Virtual power plant operation framework for uncertain demand response

[0142] First, a virtual power plant (VPP) operation framework was constructed to correct the power offset that may occur during the demand response (DR) process by cost-compensating the energy storage system (ES). This operation framework consists of two stages: decomposition and tracking. In the first stage, the command decomposition model was determined to rationally plan the optimal dispatch of the power system; in the second stage, a command tracking model was designed to dynamically adapt to the actual demand response changes. Finally, the column generation nested algorithm (C&CG) was used in combination with the two-stage robust optimization technology to iteratively solve the decomposition and tracking double-layer model to achieve high management of dynamic resources.

[0143] Within the system framework, controllable flexible loads such as lighting, HVAC, heating boilers and industrial machinery are integrated into the VPP as a supplement to the renewable energy system (RES). Given the complex and multi-dimensional characteristics of flexible loads (FL), deviations in demand response are inevitable in VPP operations. To this end, the coordination between flexible loads (FL) and energy storage systems (ES) is strengthened to ensure effective complementarity between the two and jointly manage DR deviations. Under the VPP operation configuration framework of enhanced DR, energy storage (ES) users not only follow their own charging and discharging plans, but also flexibly provide support for demand response (DR), forming the following: Figure 3 Efficient interaction mechanism shown.

[0144] In the initial stage, the VPP management system combines the flexibility of energy storage systems (ES) and flexible loads (FL) to balance the instantaneous power between non-flexible power sources and loads in the power grid. The VPP smart manager flexibly corrects the backup power capacity and energy storage plan based on the attributes of each load to ensure that sufficient energy storage margin is reserved to cope with sudden demand deviations and ensure system robustness. Subsequently, the flexible load tracks the instructions issued in real time, and the energy storage unit acts as a deviation adjustment device to efficiently compensate for any difference between actual execution and planned targets. Finally, the VPP manager openly and transparently allocates the economic benefits brought by demand response (DR) and potential deviation correction costs among many FL participants and ES users.

[0145] The technical method proposed in this invention is combined with the operation framework to realize the refined control of demand response (DR). A two-stage robust optimization algorithm is adopted to significantly improve the flexible complementarity of flexible load (FL) and energy storage system (ES) in the virtual power plant (VPP) management framework. In the first stage, a mixed integer linear programming (MILP) model is adopted to maximize the utilization rate of renewable energy (RES) and the economic benefits of VPP operation, and to combine the optimal operation of RES with the decomposition of VPP commands. The input parameters include: RES energy consumption and energy production, and the output is for VPP specific operation instructions, DR power scheduling indicators and detailed charging and discharging time optimal planning, so as to achieve the initial deployment of resource optimization. In the second stage, a robust optimization model is introduced with the help of convex relaxation technology. On the basis of the output results of the first stage, the inputs such as DR characteristics and uncertainty boundaries are combined to solve the possible deviations in FL execution and complete the ES compensation strategy. The advantages of the proposed model and method are that it can distinguish and process deterministic and uncertain decision variables, effectively manage the complexity of high-dimensional data through instruction decomposition with a long time scale of every hour and instruction tracking operation with a short time scale of every minute, and ensure the stability and efficiency of VPP operation at the practical level.

[0146] S42. Phase 1: DR instruction decomposition model and method

[0147] The first phase of DR instruction decomposition uses the MILP model to achieve economic optimization of diverse and flexible resources within the renewable energy system (RES) and refine the virtual power plant (VPP) operation instructions. The main goal of the DR decomposition model is to minimize the comprehensive cost of operating RES (e.g., solar photovoltaic (PV), wind power, grid-connected and thermal power) and VPP (e.g., ES and FL), taking into account the fines for thermal power due to carbon emissions and the dispatch costs of power interconnection lines. In VPP, the ES cost indicator also takes into account charging and discharging losses and operating expenses.

[0148] Therefore, the optimal operating cost target of the first-stage model is described as formula (11):

[0149] (11)

[0150] Where: , , , , and They are respectively represented as photovoltaic, wind, thermal power, energy storage, power interconnection line and flexible load costs; , , and They are expressed as the unit costs of power generation, ES operation, power tie line dispatching and flexible load transfer respectively; and They represent the unit penalties for photovoltaic power curtailment and wind power curtailment respectively; Expressed as a carbon penalty; Expressed as unit loss for charging and discharging; and They are represented as predicted photovoltaic and wind power respectively; and They are represented as actual photovoltaic and wind power respectively; It is represented by the rated capacity of thermal power; λ is represented by the thermal-electric coupling depth; It is indicated as a heat source; Expressed as storage charging power; Expressed as discharge power; Expressed as the power of the electric power interconnection line.

[0151] DR command decomposition model Equation (11) optimization constraints are derived from the operating characteristics of the renewable energy system (RES) and the management specifications of the virtual power plant (VPP). They include: renewable energy (such as solar and wind) capacity forecast, combined heat and power unit operation constraints, energy storage system (ES) intelligent charging and discharging management constraints, and the capacity limit of the tie line as a power supply and demand balancing node. The specific description is Equation (12):

[0152] (12)

[0153] Where: Expressed as the state of charge (SOC) of ES It is expressed as ES initial SOC; and They are expressed as ES rated capacity and power respectively; Expressed as the rated power of the electric power interconnection line.

[0154] S43. Phase II: DR instruction tracking model and strategy

[0155] The second-stage DR instruction tracking model focuses on flexible load (FL) instruction tracking and energy storage (ES) system deviation compensation. Based on the results of the first stage, the power and energy differences caused by the uncertainty factors of FL characteristics are analyzed and calculated. Combining equations (7) and (8) to define the four-period piecewise function. The DR power and energy deviation is specifically described as equation (13):

[0156] (13)

[0157] Where: and They are represented as DR power and energy deviation respectively; m is the four time periods of the piecewise function, where m=1~4 corresponds to TD, RS, TP and RE respectively.

[0158] The second-stage DR command tracking model uses energy storage system (ES) equipment to correct the demand response (DR) power deviation. Ideally, the compensation power and energy provided by ES completely match the power and energy of DR deviation. However, in actual scenarios, the compensation behavior is affected by the cost-effectiveness of ES operation, resulting in the relaxation of the original strong constraints to adapt to the actual operation complexity. The specific description of the relaxed constraint is formula (14):

[0159] (14)

[0160] Where: and Compensate power and energy for ES, respectively.

[0161] The objective function of the second-stage DR instruction tracking model and the involved deterministic and uncertain parameters are presented as shown in equations (15) and (16):

[0162] (15)

[0163] (16)

[0164] Where: Denoted as VPP and FL deviation penalties.

[0165] The objective function of the second-stage DR instruction tracking model focuses on minimizing the total penalty of VPP and FL. Specifically, any ES that fails to fully compensate for the DR residual deviation according to the established plan will be converted into a deduction item. Given that ES can assist FL in evading penalties, a reasonable share of DR benefits must be allocated to ES users and the VPP operation management team. The specific objective function is calculated by formula (17) as:

[0166] (17)

[0167] Where: It is expressed as the net deviation unit penalty after ES compensation; Expressed as DR deviation unit penalty.

[0168] The constraints in the second-stage DR instruction tracking model have been detailed in equations (7) to (10). To strengthen the integrity of the constraints, equation (18) supplements the additional power and energy deviation limit constraints:

[0169] (18)

[0170] Where: and They are respectively represented as the VPP net power and energy deviation after ES compensation.

[0171] The battery state of charge (SOC) interval restriction constraint with uncertain attributes is shown in formula (19):

[0172] (19)

[0173] In equations (7) to (10), due to the dynamic constraints of the adjustment rate and response energy, non-convex characteristics are presented. In order to achieve the matching and adaptation of non-convex constraints and convex optimization algorithms, auxiliary variables and relaxation techniques are introduced in equation (20). It is treated as a decision variable in the decomposition phase, but as a constant in the tracking phase, allowing it to be combined with uncertainty variables such as and ) are directly multiplied, thus simplifying the calculation process.

[0174] (20)

[0175] Where: Represented as an auxiliary variable for adjusting speed.

[0176] Figure 4The whole process of the DR instruction decomposition and tracking method proposed in this invention is presented. The column generation nesting algorithm (C&CG) is used to feed back the results of the second stage to the first stage, forming a closed-loop iterative solution mechanism. For the VPP deviation penalty in the objective function of the first stage decomposition model, as shown in formula (21), an auxiliary variable is introduced Deviation penalty is applied and new constraints are generated to enhance the efficiency and accuracy of model solving. The objective function with deviation penalty is described as formula (22):

[0177] (twenty one)

[0178] (twenty two)

[0179] Where: θ represents the auxiliary variable of the first stage objective introduced into the C&CG algorithm.

[0180] The first-stage decomposition model optimization constraint (12) generates additional column variables and corresponding row constraints, which are specifically described as (23):

[0181] (twenty three)

[0182] Where: k represents the number of iterations, and They represent the generation of column variables for the kth iteration.

[0183] Aiming at accurately characterizing the multi-dimensional uncertainty of demand-side response (DR) and how to coordinate and control the operation optimization of flexible loads in virtual power plants (VPPs) in a high-quality and efficient manner to alleviate the DR deviation problem, this invention innovatively proposes a robust collaborative optimization method for virtual power plants (VPPs) with enhanced demand response. The multivariate uncertain characteristics of flexible loads (FL), such as time delay, regulation rate, instantaneous power tracking and response energy, are deeply analyzed and refined, and a multi-dimensional coupling deviation model is constructed. A two-stage robust optimization algorithm is adopted to ensure precise control of demand response (DR) in VPP operations. Through the iterative feedback mechanism of decomposition and tracking in the two stages, with the help of the collaborative operation of the energy storage system (ES) and the flexible load, the DR deviation is effectively alleviated, demonstrating the robustness of the system.

[0184] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A robust collaborative optimization method for virtual power plants considering uncertain demand response, characterized in that: It includes the following steps: Step S1: Establishing a demand response DR model with multi-dimensional feature fusion; the demand response DR represents the behavior of users in the power market responding to power price signals or incentive mechanisms to change their inherent power consumption patterns; In the demand response DR model, the characteristics of the demand response DR in four dimensions, namely, time delay TD, regulation speed RS, tracking power TP and response energy RE, are identified, and the impact of these characteristics on the accuracy of demand response is analyzed, as well as how uncertainty factors lead to demand response deviations; Step S2: Characterization of DR uncertainty characteristics; specifically, including: fitting a normal distribution function using historical DR data or adopting typical value modeling, estimating and correcting the parameters of the distribution function, and calculating the confidence interval of each uncertainty characteristic by integrating the distribution probability density function to define its upper and lower limits; Step S3: constructing a DR multi-dimensional coupling deviation model; specifically, including: constructing a coupling deviation model according to the characteristics of demand response in four dimensions, and dividing the model into a delay stage, a ramp-up stage, a stable stage, and an early termination stage, using a piecewise function to describe the dynamic and nonlinear characteristics of the DR power curve; defining the upper and lower limits of uncertainty of the flexible load FL in different dimensions; Step S4: Robust collaborative optimization of virtual power plants; specifically including: S41: Construct the virtual power plant VPP operation framework, integrating the flexibility of energy storage system ES and flexible load FL; design a two-stage optimization strategy of decomposition and tracking, determine the instruction decomposition model in the first stage, and design the instruction tracking model in the second stage; S42: DR instruction decomposition; using the mixed integer linear programming MILP model to plan the optimal dispatch of the power system and minimize the operating cost; considering the renewable energy system RES, including the capacity forecast and operation constraints of photovoltaic and wind power, as well as the operation constraints of power interconnection lines and energy storage systems; S43: DR instruction tracking; based on the results of DR instruction decomposition, analyze and calculate the power and energy differences caused by the uncertainties of FL characteristics; design the ES deviation compensation strategy of the energy storage system to minimize the total penalty cost of VPP and FL.

2. The method for robust collaborative optimization of a virtual power plant considering uncertain demand response according to claim 1, characterized in that: The specific process of step S1 includes: Among the four dimensions of DR characteristics, namely time delay, regulation speed, tracking power and response energy, the tracking power is closely related to the power distribution of the flexible load, which is monitored by the smart meter. The power dimension is represented by a continuous time variable t(t∈[0,24]), while the other three dimensions introduce discrete time variables n, where n=1,2,…24; S11. In the tracking power dimension, the power size constraint and deviation equation are constructed, which can adapt to the adjustable load and interruptible load at the same time. The specific description is as formula (1): Where: P(t) represents the tracking power curve of the flexible load; t represents the time variable; x a and m I They are respectively represented as power variables of adjustable load and interruptible load; f a (x a ,t) and f I (m I ,t) is expressed as a continuous variable and a discrete variable of the load curve; P N (t) is represented as the load reference curve; γ min (t) and γ max (t) represent the minimum and maximum boundaries of DR power respectively; δ(t) represents the DR power deviation, which is usually 0 under deterministic conditions; P DR (t) indicates that a DR command is given to VPP; S12. When considering the response energy dimension and adjusting or transferring energy through the demand response DR mechanism, the participation of energy flexible loads such as heat storage boilers is directly limited by the actual heat demand. Even if the heat storage boiler has potential in power regulation, it is actually impossible to perform DR operation in the case of insufficient heat. The response energy inequality constraint equation is specifically described as formula (2): In the formula, E RE (n) represents the response energy of the flexible load; Δt represents the scheduling time scale; n represents the discrete time period; E neg (n) and E pos (n) represent the flexible load response energy range respectively; It is expressed as DR energy deviation; S13. In the time dimension, the time delay characteristics of DR are analyzed in detail, and the time difference between the theoretical response instruction and the actual execution is quantified. In order to accurately manage the resulting DR deviation, it is usually considered that the impact on the overall DR effect is ignored when the time delay TD is short, that is, within a few seconds to a few minutes; but as TD is extended to a few minutes or longer, the deviation effect on the DR execution effect is significant; to describe the delay characteristics, a set of inequalities is used to characterize it. This model integrates the correlation between power and energy deviations, defines the time delay constraint, the DR power curve with time delay, and the power and energy deviations; the specific description is formula (3): Where: t TD (n) represents the flexible load delay time; δ TD (t) and It is expressed as the power and energy deviation due to TD; S14. In the dimension of regulation speed, the flexible load FL is the power change rate of the demand side management DSM. In order to improve the flexibility of the renewable energy system RES on a short time scale of minutes or seconds, it is necessary to quickly respond to RS. On the contrary, the slower the RS, the greater the power and energy deviation in the demand response DR. Considering the general form of the regulation speed DR power and the formula of power and energy deviation caused by the regulation speed, it is specifically described as formula (4): Where: v RS (n) represents the adjustment speed; δ RS (t) and Expressed as power and energy deviation caused by adjusting speed.

3. The method for robust collaborative optimization of a virtual power plant considering uncertain demand response according to claim 1, characterized in that: The specific process of step S2 includes: For the key features of the uncertainty range of four demand response DRs, modeling is performed using normal distribution functions or typical values. The distribution functions and parameters are estimated and corrected using historical DR data fitting. Subsequently, the distribution probability density function is integrated and the corresponding confidence interval is calculated, which can accurately define the upper and lower limits of each uncertainty feature, as specifically described in formula (5): Where: X represents the uncertainty feature set; and and and They are the uncertainty variables of tracking power, response energy, delay and adjustment speed respectively; σ and μ are the expected value and standard deviation of the distribution; In order to more accurately adapt to the uncertainty of power tracking and energy response, the original uncertainty range is adjusted by fully considering the provisions of domestic demand-side management policies that do not penalize over-response due to factors other than instructions; on this basis, the improved uncertainty boundary should reflect the exemption of incentives outside the DSM strategy, ensuring that the set interval can capture the uncertainty in real operation without triggering unnecessary compensation mechanisms; the specific description is formula (6): Where: l is a parameter used to change the confidence level; for time delay uncertainty, the part below the expected μ is ignored, allowing FL to respond in advance; l u and l d They are represented as uncertain RS confidence parameters; σ u and σ d are represented as DR normal distribution parameters respectively.

4. The method for robust collaborative optimization of a virtual power plant considering uncertain demand response according to claim 1, characterized in that: The specific process of step S3 includes: A multi-dimensional coupled dynamic model is established to depict the exact posture of the DR curve and define the uncertainty boundary of its power response. The piecewise function method is used to solve the dynamic and nonlinear characteristics of the DR power curve modeling. The DR dynamic profile is accurately characterized in four core dimensions, and the function is divided into four time periods: [0, t1], [t1, t2], [t2, t3], and [t3, Δt]. The length of the time period corresponds to the time variable t related to each characteristic. TD ,t RS ,t TP and t RE ; The coupled multidimensional deviation model is expressed as a piecewise function; for the specified load command P DR , there is a delay t in the initial stage TD , at this time the DR system output power is zero; in the climbing stage, the power starts from zero at a preset adjustment rate and quickly responds to P DR ; During duration t TP The DR power is kept constant and is consistent with the load command P DR In the third stage, due to resource allocation limitations, DR response may be delayed. RE It ends earlier than expected. The specific process is described as equations (7) and (8): Where: t1, t2 and t3 represent time points; By integrating equations (5) and (6), a dimensional deviation model at a specific confidence level is constructed. In this model, the upper and lower limits of the uncertainty of the flexible load FL are defined: the time delay is used as the lower limit indicator of certainty, while the regulation speed, power tracking accuracy and duration of the response energy constitute the upper limit indicators of uncertainty. Therefore, the model is simplified by focusing on the two periodic dynamic characteristics of climbing and steady state and ignoring the potential early termination stage, which is specifically described as equation (9): Where: It is expressed as the upper limit of flexible load FL; Indicates the upper limit of the adjustment speed; Similarly, in order to accurately express the lower bound of DR uncertainty, the following segmented definition is followed: the uncertainties in power, energy, and speed are all measured with lower limits, while the uncertainty in the time dimension is measured with an upper limit; the specific description of the lower bound of DR uncertainty is formula (10): Where: P (n,t) represents the lower bound of the flexible load FL; P (n) E RE (n) and v S They are denoted as TP, RE and RS lower bounds respectively; Indicates the upper bound of the delay.

5. The method for robust collaborative optimization of a virtual power plant considering uncertain demand response according to claim 1, characterized in that: The specific process of step S41 includes: constructing a virtual power plant VPP operation framework, and correcting the power offset that may occur in the demand response DR process through the cost compensation energy storage system ES; this operation framework consists of two stages: decomposition and tracking. In the first stage, the command decomposition model is determined to rationally plan the optimal scheduling of the power system; in the second stage, a command tracking model is designed to dynamically adapt to the actual demand response changes; finally, the column generation nested algorithm C&CG is used, combined with the two-stage robust optimization technology, to iteratively solve the decomposition and tracking double-layer model to achieve high management of dynamic resources; within the system framework, the flexible loads of lighting, HVAC, heating boilers and industrial machinery that can be adjusted are integrated into the VPP as a supplement to the renewable energy system RES; strengthen the coordination between the flexible load FL and the energy storage system ES to ensure that the two complement each other effectively and jointly manage DR deviations.

6. The method for robust collaborative optimization of a virtual power plant considering uncertain demand response according to claim 5, characterized in that: The specific process of step S42 includes: The first stage of DR instruction decomposition uses the MILP model to achieve economic optimization of diverse and flexible resources within the renewable energy system RES, and refine the virtual power plant VPP operation instructions; the main goal of the DR decomposition model is to minimize the comprehensive cost of operating RES, including solar photovoltaic PV, wind power generation, grid connection and thermal power and VPP, taking into account the fines for thermal power due to carbon emissions and the dispatching cost of power interconnection lines. In VPP, the ES cost indicator also takes into account charging and discharging losses and operating expenses; Therefore, the optimal operating cost target of the first stage model is described as formula (11): Where: C PV , C WT , C TP , C ES , C TL and C FL They are respectively represented by photovoltaic, wind power, thermal power, energy storage, power interconnection line and flexible load costs; C TP , C ES , C TL and C FL are expressed as the unit costs of power generation, ES operation, power line dispatching and flexible load transfer respectively; P PV and P WT They represent the unit penalties for photovoltaic power curtailment and wind power curtailment respectively; P TP Expressed as carbon emission penalty; l ES Expressed as unit loss of charge and discharge; P PV,0 and P WT,0 They are respectively expressed as the predicted photovoltaic and wind power; P PV and P WT They are respectively represented as actual photovoltaic and wind power; P TP,N It is represented by the rated capacity of thermal power; λ is represented by the thermal-electric coupling depth; P TP Represented as heat source; I cha Expressed as storage charging power; I dis Expressed as discharge power; P TL Expressed as the power of the electric power tie line; The optimization constraints of the DR command decomposition model (11) are derived from the operating characteristics of the renewable energy system RES and the management specifications of the virtual power plant VPP; including: renewable energy capacity forecast, cogeneration unit operation constraints, energy storage system ES intelligent charging and discharging management constraints, and the capacity limit of the interconnection line as a power supply and demand balancing node; the specific description is formula (12): Where: S ES Expressed as the state of charge SOC of ES; S ES,0 Expressed as ES initial SOC; E ES,PEC and P ES,N Respectively represented as ES rated capacity and power; P TL,N Expressed as the rated power of the electric power interconnection line.

7. The method for robust collaborative optimization of a virtual power plant considering uncertain demand response according to claim 5, characterized in that: The specific process of step S43 includes: The second-stage DR instruction tracking model focuses on the flexible load FL instruction tracking and energy storage ES system deviation compensation; based on the first-stage results, the power and energy differences caused by the uncertainty factors of FL characteristics are analyzed and calculated; the four-period piecewise function is defined by combining equations (7) and (8); the DR power and energy deviation is specifically described as equation (13): Where: δ(m,n) and They are respectively represented as DR power and energy deviation; m is the four time periods of the piecewise function, where m = 1 to 4 correspond to TD, RS, TP and RE respectively; The second-stage DR command tracking model uses the energy storage system ES device to correct the demand response DR power deviation. Ideally, the compensation power and energy provided by the ES are completely matched with the power and energy of the DR deviation. However, in actual scenarios, the compensation behavior is affected by the cost-effectiveness of the ES operation, resulting in the relaxation of the original strong constraints to adapt to the actual operation complexity. The specific description of the relaxed constraints is formula (14): Where: P EC and E EC are ES compensation power and energy, respectively; The objective function of the second-stage DR instruction tracking model and the involved deterministic and uncertain parameters are presented as shown in equations (15) and (16): Where: C PD Expressed as VPP and FL deviation penalty; The objective function of the second-stage DR instruction tracking model focuses on minimizing the total penalty of VPP and FL. Specifically, any ES that fails to fully compensate for the DR residual deviation according to the established plan will be converted into a deduction item. Given that ES can assist FL in evading penalties, a reasonable share of DR benefits must be allocated to ES users and the VPP operation management team. The specific objective function is calculated by formula (17): Where: ND It is expressed as the net deviation unit penalty after ES compensation; ρ D Expressed as DR deviation unit penalty; The constraints in the second-stage DR instruction tracking model have been detailed in equations (7) to (10). To strengthen the integrity of the constraints, equation (18) supplements the additional power and energy deviation limit constraints: Where: P d and E d They are respectively represented as the VPP net power and energy deviation after ES compensation; The battery state of charge SOC interval restriction constraint with uncertainty attribute is shown in formula (19): In equations (7) to (10), due to the dynamic constraints of the adjustment rate and response energy, non-convex characteristics are presented. In order to achieve the matching adaptation between non-convex constraints and convex optimization algorithms, auxiliary variables and relaxation techniques are introduced in equation (20); although the load instruction P DR It is used as a decision variable in the decomposition stage, but as a constant in the tracking stage, allowing it to be related to the uncertainty variable υ′ RS and E RE Direct multiplication; Where: v′ RS It is represented as an auxiliary variable for adjusting speed; For the VPP deviation penalty in the objective function of the first-stage decomposition model as shown in formula (21), an auxiliary variable θ deviation penalty is introduced, and new constraints are generated to enhance the efficiency and accuracy of the model solution; the objective function with deviation penalty is described as formula (22): min(C PV +C WT +C TP +C ES +C TL +C FL +θ) (21) Where: θ represents the auxiliary variable of the first-stage objective introduced into the C&CG algorithm; The first-stage decomposition model optimization constraint (12) generates additional column variables and corresponding row constraints, which are specifically described as (23): Where: k represents the number of iterations, E EC (m,n,k) and P EC (m,n,k) represent the generated column variables for the kth iteration.

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