Energy optimization method for multi integrated energy system including shared energy storage

Abstract

Provided in the present application is an energy optimization method for a multi integrated energy system (MIES) including shared energy storage. A unified shared energy storage power station is established by the MIES, thereby saving on the initial investment costs of subsystems respectively establishing energy storage apparatuses; and shared energy storage is more conducive to electric energy transmission inside the system, thereby saving operation costs. In the present application, the optimization method for an MIES including shared energy storage is provided, i.e., a two-stage three-layer optimization model is established: the upper layer is a shared energy storage power station capacity configuration model, and the lower layer is an MIES optimization scheduling model. In the present application, an uncertain fuzzy set is constructed on the basis of a Wasserstein distance and moment information, such that first-order moment information is merged into a Wasserstein distance fuzzy set, thereby making the establishment of the fuzzy set more accurate. By means of the present application, an MIES including shared energy storage can be constructed, thereby saving on the initial investment costs of subsystems respectively establishing energy storage apparatuses; and shared energy storage is more conducive to electric energy transmission inside the system, thereby saving operation costs.

Description

An energy optimization method for a multi-integrated energy system with shared energy storage

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to a Chinese patent application filed with the Patent Office of China on February 5, 2024, with application number 202410164422.6 and invention name “An energy optimization method for a multi-integrated energy system with shared energy storage”, the entire contents of which are incorporated by reference into this application. Technical Field

[0003] The present application relates to the technical field of energy systems, and in particular to an energy optimization method for a multi-integrated energy system including shared energy storage. Background Art

[0004] Developing an integrated energy system (IES) with multiple complementary energies is an important way and means to transform the energy structure and reform energy. A multi-integrated energy system (MIES) refers to multiple interconnected IES, with each sub-member conducting point-to-point transactions and energy interaction, which is more conducive to alleviating the contradiction between supply and demand, reducing operating costs, and improving energy utilization efficiency.

[0005] IES aggregated energy storage devices can enable more flexible, reasonable, and timely control of system output. They can store excess energy when the system is operating at low load and release energy to meet energy load demands during high load operation, thereby shaving peak loads and filling valleys and alleviating system pressure. However, in MIES, traditional energy storage systems cannot achieve energy complementarity among multiple IES members, resulting in huge investment and operating costs. With the emergence of the sharing economy concept, the sharing economy concept and energy storage systems have been combined to propose a new service model for shared energy storage. Shared energy storage refers to the establishment of shared energy storage equipment within the MIES, fully considering the differences in electricity consumption among members, integrating the energy storage needs of different members through the dispatch center, storing idle electricity, and making more rational use of electricity.

[0006] Currently, there is little research on the optimal scheduling of MIES with shared energy storage. In existing technical literature, the article "Operational Optimization of Multi-Integrated Energy Systems Considering Electricity-Heat Interaction and Shared Energy Storage" establishes a MIES operation optimization model that considers electricity-heat interaction and shared energy storage. This model is solved using a mixed-integer linear programming approach. However, this model uses forecast data for wind speed, temperature, sunlight, and load, and does not account for the uncertainty of renewable energy output, making the accuracy of its scheduling results difficult to guarantee.

[0007] "Two-Tier Optimization of Integrated Energy Microgrids Considering Wind-Solar Output Correlation and Shared Energy Storage" proposes a two-tier optimization model for integrated energy microgrids that takes into account both wind-solar output correlation and shared energy storage. However, this model only considers the correlation of wind and solar output. For IES, load size is also uncertain due to the influence of user behavior and market policies. The relative relationship between renewable energy and load directly affects the system's scheduling strategy.

[0008] "Optimal Configuration of Multi-energy Complementary Microgrid System Integrating Wind and Solar Output Scenarios" studies the optimal configuration of multi-energy complementary microgrid system considering the uncertainty and correlation of wind and solar output, but only considers the charging and discharging conditions of energy storage, and does not fully utilize the idle time of energy storage.

[0009] Summary of the Invention

[0010] The present application aims to solve one of the technical problems in the related art at least to a certain extent.

[0011] To this end, the purpose of this application is to propose an energy optimization method for a multi-integrated energy system with shared energy storage, aiming to construct a multi-integrated energy system with shared energy storage, which can save the initial investment cost of establishing energy storage devices for each subsystem separately, and through shared energy storage, it is more conducive to the internal power transmission of the system and saves operating costs.

[0012] To achieve the above objectives, the present application provides an energy optimization method for a multi-integrated energy system including shared energy storage. The multi-integrated energy system includes multiple integrated energy systems, including:

[0013] The energy of the multi-integrated energy system with shared energy storage is optimized using a two-stage distributed robust optimization model;

[0014] Based on the historical data of observed wind and solar power output and electric and thermal load, an empirical distribution is established, the Wasserstein distance between the empirical distribution and the actual distribution is calculated, and an uncertain fuzzy set of uncertain factors that meet the conditions is constructed. The uncertainty of wind power is described by a fuzzy set composed of random distributions.

[0015] Construct the upper-level problem and the lower-level problem, integrate the uncertain fuzzy set into the two-stage problem, and form a two-stage three-level optimization model. Input the parameters of each unit and the cost coefficient.

[0016] The column and constraint generation algorithm C&CG is used to divide the model into main and sub-problems and solve them iteratively until the iterative convergence requirements are met;

[0017] Output decision results. The upper-level decision results are the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station. The lower-level decision results are the CHP unit output, electric heat pump output, shared energy storage power station charge and discharge volume, and transaction volume with the electricity market and heat market.

[0018] Among them, the two-stage distributed robust optimization model is divided into the first stage capacity configuration model and the second stage optimization scheduling model.

[0019] The first-stage capacity configuration model is used to calculate the optimal capacity and maximum charge and discharge power of the shared energy storage power station;

[0020] The second-stage optimization scheduling model is used to determine the output power of each integrated energy system in the multi-integrated energy system, the charging and discharging power of the shared energy storage, and the amount of electricity and heat traded with the electricity market and the heat market;

[0021] An uncertain fuzzy set is constructed based on the combination of Wasserstein distance and moment information, and the uncertain fuzzy set is integrated into the second-stage optimization scheduling model to form a two-stage three-layer optimization model. The first-stage capacity configuration model determines the maximum capacity, maximum charging and discharging power, and actual charging and discharging power of the shared energy storage power station. The second-stage optimization scheduling model calculates the worst scenario based on the uncertain fuzzy set, and obtains the model formula corresponding to the optimization scheduling strategy under the worst scenario; the column and constraint generation algorithm is used to solve the problem. The column and constraint generation algorithm divides the second-stage optimization scheduling model into two layers, setting the upper bound UB = +∞ and the lower bound LB = -∞. The upper layer is the main problem and the lower layer is the subproblem. The upper layer passes the obtained variables to the lower layer to obtain the upper layer objective function value and updates the lower bound at the same time. After the lower layer accepts the variables, it solves the subproblem and obtains the lower layer objective function value. The corresponding variables and constraints are added and passed to the upper layer, and the upper bound is updated. It is iterated repeatedly until the upper and lower bounds meet the conditions.

[0022] Among them, when the power generation of the first integrated energy system within the multi-integrated energy system is greater than the load, and the power generation of the second integrated energy system is less than the load, the shared energy storage integrates the electricity demand, virtualizes the charging and discharging, and transmits the multi-electricity of the first integrated energy system to the second integrated energy system. The difference is made up by the shared energy storage itself. If the total power generation is greater than the total load, the excess electricity of the integrated energy system will be charged into the shared energy storage, otherwise the shared energy storage will be discharged into the difference integrated energy system to realize the shared utilization of resources.

[0023] Among them, in order to maximize the use of shared energy storage, the priority is set as follows: trading with shared energy storage is greater than trading with the electricity market, that is, multiple integrated energy systems give priority to trading with shared energy storage, and when the shared energy storage power reaches the maximum charging capacity or the power reaches the maximum discharging capacity, it will trade with the electricity market.

[0024] Among them, the two-stage distributed robust optimization model is based on the uncertainty factor modeling of Wasserstein distance and moment information, and the uncertain fuzzy set is constructed by combining Wasserstein distance and moment information. Assume that Pi,t W 、P i,t V 、P i,t L 、H i,t L They are wind power output, photovoltaic output, electric load and thermal load in the i-th integrated energy system respectively. According to the historical sample set of wind power output and electric thermal load {ξ1, ξ2, …ξ N}, N is the total number of samples, and the following empirical distribution is established:

[0025] Among them, f N is the empirical distribution constructed based on the observed samples, δ ξ i is the Dirac measure on ξi. According to the law of large numbers, when N→+∞, the empirical distribution f N Approaching the true distribution f, f N The distance between f and is measured by Wasserstein distance, which is defined as:

[0026] Among them, ξ and They obey the empirical distribution f N and the random variables of the true distribution f, Ξ represents the random variables ξ and The support space, for ξ and The first-order norm between for ξ and The joint distribution of , inf is the lower bound function;

[0027] The uncertainty set based on Wasserstein distance is represented as an empirical distribution f N The Wasserstein sphere with centered and ε as radius has a fuzzy set represented as:

[0028] D0={f∈H(Ξ)|W(f,f N )≤ε} (3)

[0029] Where H(Ξ) is the set of all distributions with support set Ξ, and ε is the Wasserstein radius;

[0030] The selection method of Wasserstein radius ε follows the following confidence requirements:

[0031] Among them, P[W(f,f N)≤ε] is W(f,f N )≤ε, D is a constant, N is the number of sample groups, β is the confidence level, that is, the probability that the actual sample is within the Wasserstein sphere. The larger β is, the greater the probability is. α is a coefficient greater than zero, and μ is the sample mean.

[0032] In order to improve the reliability of uncertain fuzzy sets, the first-order moment information of uncertain factors is incorporated into the fuzzy sets constructed based on Wasserstein, that is, the first-order moment of the uncertain variables satisfies the following constraints:

[0033] Combining Equations (3) and (7), the final uncertain fuzzy set is expressed as:

[0034] D0={f∈H(Ξ)|W(f,f N )≤ε, P(ξ∈Ξ)=1, E(ξ-μ)=0} (8).

[0035] The first-stage capacity allocation model aims to minimize investment and operating costs, and the optimization variables are the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station.

[0036] The objective function of the first-stage capacity allocation model is:

[0037] Among them, C rl is the upper objective function, T is the scheduling period, t is the scheduling period, They are the average construction investment cost of the shared energy storage power station during the dispatch period, the interaction cost with multiple integrated energy systems, and the service income of the shared energy storage power station;

[0038] The construction cost of shared energy storage is expressed by converting the fixed asset investment cost into daily depreciation expenses. The average construction investment cost of a shared energy storage power station is:

[0039] Among them, c cl 、c s,1 、c s,2 are the unit costs of the maximum capacity, maximum charging power, and maximum discharging power of the shared energy storage power station, n is the economic and practical life of the shared energy storage power station, k is the line loss rate between the shared energy storage power station terminal and the electricity sales settlement point, SOC s max 、P s in,max 、P s out,max are the maximum capacity, maximum charging power and maximum discharging power of the shared energy storage power station, c es Daily operation and maintenance costs;

[0040] The cost of interacting with multiple integrated energy systems is:

[0041] Among them, c out 、c in are the unit prices for purchasing and selling electricity from the shared energy storage power station, are the discharge power and charging power of the shared energy storage power station respectively;

[0042] The revenue from shared energy storage power station services is:

[0043] Among them, c fu To pay the service revenue coefficient to the shared energy storage power station.

[0044] The column and constraint generation algorithm divides the second-stage optimization scheduling model into two layers, the upper layer constraints are:

[0045] Among them, SOC p,t+1 , SOC p,t The power of the shared energy storage power station at time t+1 and t, respectively, η p in ,η p out are the charging efficiency and discharging efficiency of the shared energy storage power station, P t in 、P t out are charging power and discharging power, SOC s min , SOC s max are the minimum and maximum capacities allowed for the shared energy storage power station, P s in,max 、P s out,max They are the maximum charging power and discharging power of the shared energy storage power station respectively.

[0046] Among them, the second-stage optimization dispatch model is modeled with the lowest MIES operating cost, wind and solar curtailment cost, load shedding cost, and transaction cost with the electricity and heat market as the objective function. The optimization variables are CHP unit output, electric heat pump output, shared energy storage power station charge and discharge capacity, and transaction volume with the electricity and heat markets. The objective function is:

[0047] Among them, N IES is the number of integrated energy systems within the multi-integrated energy system, C i,t CHP 、C i,t HP 、C i,t LS 、C i,t CW 、C i,t CP 、C i,t HG are CHP operating costs, electric heat pump operating costs, load shedding costs, wind curtailment costs, solar curtailment costs, and market transaction costs; α1, α2, α3, α4, α5, α6, α7, and α8 are unit cost coefficients, P i,t CHP 、H i,t CHP are the electrical output and thermal output of the CHP unit, P i,t HP is the output of the electric heat pump unit, P i,t LS is the load shedding power, P i,t CW 、P i,t CV are the amount of wind and solar power abandoned, P i,t G 、H i,t G are the amount of electricity and heat traded with the electricity market and the heat market respectively;

[0048] The constraints of the second-stage optimization scheduling model are:

[0049] The CHP unit operates in a heat-to-electricity mode, and the electric-to-heat output range is within the closed region ABCD of the CHP unit operating characteristic curve; wherein, in a coordinate system with thermal power and electric power as the horizontal and vertical coordinates, points C and D are on the vertical coordinate of the CHP unit operating characteristic curve;

[0050] The output constraints are:

[0051] Among them, c m 、c v 、c n They are the slopes of AB, BC and AD in the closed area ABCD of the CHP unit operating characteristic curve, h med is the thermal power of the CHP unit corresponding to point A, are the electric power and thermal power of the CHP unit at time t, p min 、 pmax are the upper and lower limits of CHP unit power output, h max is the maximum thermal power of the CHP unit;

[0052] The output constraint of the electric heat pump is:

[0053] in, are the electric power and thermal power of the electric heat pump unit at time t, η HP is the conversion efficiency of the electric heat pump unit, is the maximum electric power of the electric heat pump unit;

[0054] The transaction constraints in the electricity market and heat market are:

[0055] in, Electricity and heat are traded in the electricity market respectively. The value can be positive or negative. When it is positive, it means buying energy and paying the cost. When it is negative, it means selling energy and making a profit. The minimum and maximum values ​​allowed for trading in the electricity and heat markets, respectively;

[0056] Load shedding constraints:

[0057] in, are the electrical load cut-off and thermal load cut-off, are the maximum values ​​of the cut-off electrical load and the cut-off thermal load respectively;

[0058] Heat storage tank constraints:

[0059] Among them, HSOC i,t+1 HSOC i,,t are the heat storage tanks at time t+1 and t, respectively. are the minimum and maximum heat storage capacity of the heat storage tank, The heat storage tank stores and releases heat respectively. They are the minimum heat storage, maximum heat storage, minimum heat release and maximum heat release of the heat storage tank;

[0060] Energy balance constraints:

[0061] in, They are wind power generation, photovoltaic power generation, wind curtailment and solar curtailment. Electric and heating loads respectively.

[0062] The two-stage distributed robust optimization modeling of multiple integrated energy sources with shared energy storage integrates uncertain fuzzy sets into the lower-level optimization scheduling, forming a two-stage three-layer optimization model. The upper layer determines the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station. The lower layer calculates the worst-case scenario based on fuzzy sets, even if the cost is maximized, and then obtains the optimal scheduling strategy under the worst-case scenario. The two-stage model is as follows:

[0063] D0={f∈H(Ξ)|W(f,f N )≤ε,P(ξ∈Ξ)=1,E(ξ-μ)} (39)

[0064] Where x is the upper-level decision vector, y is the lower-level decision vector, z is the uncertainty vector, E(·) is the expectation, and the lower-level objective function is in brackets.

[0065] Different from the existing technology, the present application provides an energy optimization method for a multi-integrated energy system containing shared energy storage. By establishing a unified shared energy storage power station through the multi-integrated energy system, the initial investment cost of each subsystem to establish an energy storage device separately is saved. Shared energy storage is more conducive to the internal power transmission of the system, saving operating costs. The present application proposes an optimization method for a multi-integrated energy system containing shared energy storage, that is, a two-stage three-layer optimization model is established, the upper layer is a shared energy storage power station capacity configuration model, and the lower layer is a MIES optimization scheduling model. The present application proposes to construct an uncertain fuzzy set based on Wasserstein distance and moment information, and integrate the first-order moment information into the Wasserstein distance fuzzy set, so that the fuzzy set establishment is more accurate. Through this application, a multi-integrated energy system containing shared energy storage can be constructed, which can save the initial investment cost of each subsystem to establish an energy storage device separately. Shared energy storage is more conducive to the internal power transmission of the system, saving operating costs.

[0066] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] FIG1 is a schematic structural diagram of a multi-integrated energy system in an energy optimization method for a multi-integrated energy system with shared energy storage provided in the present application.

[0068] FIG2 is a flow chart of an energy optimization method for a multi-integrated energy system including shared energy storage provided in this application.

[0069] FIG3 is a schematic diagram of a CHP unit operating characteristic curve in an energy optimization method for a multi-integrated energy system with shared energy storage provided in the present application. DETAILED DESCRIPTION

[0070] The following describes in detail embodiments of the present application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0071] The following describes an energy optimization method for a multi-integrated energy system including shared energy storage according to an embodiment of the present application with reference to the accompanying drawings.

[0072] An embodiment of the present application provides an energy optimization method for a multi-integrated energy system with shared energy storage. The multi-integrated energy system involved in the present application includes multiple integrated energy systems, and the multi-integrated energy system with shared energy storage is specifically shown in Figure 1. It includes multiple integrated energy systems, shared energy storage; the electricity market in the upper power grid, and the heat market in the upper heat network; the multi-integrated energy system is formed by a combination of four integrated energy systems, each integrated energy system has different internal aggregation subjects, electric and thermal loads, and renewable energy outputs, thereby constituting differences in energy consumption and production capacity, providing an energy transmission basis for shared energy storage; in a specific embodiment, shared energy storage is specifically a shared energy storage power station.

[0073] The multi-integrated energy system internally aggregates cogeneration units, electric heat pump units, heat storage tanks, photovoltaic generators, wind turbines and user-end interruptible loads. The multi-integrated energy system exchanges electricity with shared energy storage through power transmission lines. The electricity market and heat market can trade with the multi-integrated energy system and shared energy storage respectively.

[0074] As shown in FIG2 , an energy optimization method for a multi-integrated energy system including shared energy storage provided in an embodiment of the present application includes:

[0075] The energy of the multi-integrated energy system with shared energy storage is optimized using a two-stage distributed robust optimization model;

[0076] Based on the historical data of observed wind and solar power output and electric and thermal load, an empirical distribution is established, the Wasserstein distance between the empirical distribution and the actual distribution is calculated, and an uncertain fuzzy set of uncertain factors that meet the conditions is constructed. The uncertainty of wind power is described by a fuzzy set composed of random distributions.

[0077] Construct the upper-level problem and the lower-level problem, integrate the uncertain fuzzy set into the two-stage problem, and form a two-stage three-level optimization model. Input the parameters of each unit and the cost coefficient.

[0078] The column and constraint generation algorithm C&CG is used to divide the model into main and sub-problems and solve them iteratively until the iterative convergence requirements are met;

[0079] Output decision results. The upper-level decision results are the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station. The lower-level decision results are the CHP unit output, electric heat pump output, shared energy storage power station charge and discharge volume, and transaction volume with the electricity market and heat market.

[0080] Specifically, the two-stage distributed robust optimization model is divided into the first-stage capacity configuration model and the second-stage optimization scheduling model.

[0081] The first-stage capacity configuration model is used to calculate the optimal capacity and maximum charge and discharge power of the shared energy storage power station;

[0082] The second-stage optimization scheduling model is used to determine the output power of each integrated energy system in the multi-integrated energy system, the charging and discharging power of the shared energy storage, and the amount of electricity and heat traded with the electricity market and the heat market;

[0083] An uncertain fuzzy set is constructed based on the combination of Wasserstein distance and moment information, and the uncertain fuzzy set is integrated into the second-stage optimization scheduling model to form a two-stage three-layer optimization model. The first-stage capacity configuration model determines the maximum capacity, maximum charging and discharging power, and actual charging and discharging power of the shared energy storage power station. The second-stage optimization scheduling model calculates the worst scenario based on the uncertain fuzzy set, and obtains the model formula corresponding to the optimization scheduling strategy under the worst scenario; the column and constraint generation algorithm is used to solve the problem. The column and constraint generation algorithm divides the second-stage optimization scheduling model into two layers, setting the upper bound UB = +∞ and the lower bound LB = -∞. The upper layer is the main problem and the lower layer is the subproblem. The upper layer passes the obtained variables to the lower layer to obtain the upper layer objective function value and updates the lower bound at the same time. After the lower layer accepts the variables, it solves the subproblem and obtains the lower layer objective function value. The corresponding variables and constraints are added and passed to the upper layer, and the upper bound is updated. It is iterated repeatedly until the upper and lower bounds meet the conditions.

[0084] When the power generation of the first integrated energy system within the multi-integrated energy system is greater than the load, and the power generation of the second integrated energy system is less than the load, the shared energy storage integrates the electricity demand, virtualizes the charging and discharging, and transmits the multi-electricity of the first integrated energy system to the second integrated energy system, wherein the difference is made up by the shared energy storage itself. If the total power generation is greater than the total load, the excess electric energy of the integrated energy system is charged into the shared energy storage, otherwise the shared energy storage is discharged into the integrated energy system with the difference, thereby realizing the shared utilization of resources. The electricity market and heat market involved in this application refer to the electricity market in the upper-level power grid and the heat market in the upper-level heat network.

[0085] The multi-integrated energy system internally aggregates cogeneration units, electric heat pump units, heat storage tanks, photovoltaic generators, wind turbines and user-end interruptible loads. The multi-integrated energy system exchanges electricity with shared energy storage through power transmission lines. The electricity market and heat market can trade with the multi-integrated energy system and shared energy storage respectively.

[0086] In order to maximize the use of shared energy storage, the priority is set as follows: transactions with shared energy storage are greater than transactions with the electricity market, that is, multiple integrated energy systems give priority to trading with shared energy storage, and when the shared energy storage reaches the maximum charging capacity or the power reaches the maximum discharging capacity, they will trade with the electricity market.

[0087] In the specific model, the two-stage distributed robust optimization model is based on the uncertainty factor modeling of Wasserstein distance and moment information, and the uncertain fuzzy set is constructed by combining Wasserstein distance and moment information. Assume that P i,t W 、P i,t V 、P i,t L 、H i,t L They are wind power output, photovoltaic output, electric load and thermal load in the i-th integrated energy system respectively. According to the historical sample set of wind power output and electric thermal load {ξ1, ξ2, …ξ N}, N is the total number of samples, and the following empirical distribution is established:

[0088] Among them, f N is the empirical distribution constructed based on the observed samples, δ ξi For i According to the law of large numbers, when N→+∞, the empirical distribution f N Approaching the true distribution f, f N The distance between f and is measured by Wasserstein distance, which is defined as:

[0089] Among them, ξ and They obey the empirical distribution f N and the random variables of the true distribution f, Ξ represents the random variables ξ and The support space, for ξ and The first-order norm between for ξ and The joint distribution of , inf is the lower bound function;

[0090] The uncertainty set based on Wasserstein distance is represented as an empirical distribution f N The Wasserstein sphere with centered and ε as radius has a fuzzy set represented as:

[0091] D0={f∈H(Ξ)|W(f,f N )≤ε} (3)

[0092] Where H(Ξ) is the set of all distributions with support set Ξ, and ε is the Wasserstein radius;

[0093] The selection method of Wasserstein radius ε follows the following confidence requirements:

[0094] Among them, P[W(f,f N )≤ε] is W(f,f N )≤ε, D is a constant, N is the number of sample groups, β is the confidence level, that is, the probability that the actual sample is within the Wasserstein sphere. The larger β is, the greater the probability is. α is a coefficient greater than zero, and μ is the sample mean.

[0095] In order to improve the reliability of uncertain fuzzy sets, the first-order moment information of uncertain factors is incorporated into the fuzzy sets constructed based on Wasserstein, that is, the first-order moment of the uncertain variables satisfies the following constraints:

[0096] Combining Equations (3) and (7), the final uncertain fuzzy set is expressed as:

[0097] D0={f∈H(Ξ)|W(f,f N )≤ε, P(ξ∈Ξ)=1, E(ξ-μ)=0} (8).

[0098] The first stage capacity allocation model aims to minimize investment and operating costs, and the optimization variables are the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station.

[0099] The objective function of the first-stage capacity allocation model is:

[0100] Among them, C rl is the upper objective function, T is the scheduling period, t is the scheduling period, They are the average construction investment cost of the shared energy storage power station during the dispatch period, the interaction cost with multiple integrated energy systems, and the service income of the shared energy storage power station;

[0101] The construction cost of shared energy storage is expressed by converting the fixed asset investment cost into daily depreciation expenses. The average construction investment cost of a shared energy storage power station is:

[0102] Among them, c cl 、c s,1 、c s,2 are the unit costs of the maximum capacity, maximum charging power, and maximum discharging power of the shared energy storage power station, n is the economic and practical life of the shared energy storage power station, k is the line loss rate between the shared energy storage power station terminal and the electricity sales settlement point, SOC s max 、P s in,max 、P s out,max are the maximum capacity, maximum charging power and maximum discharging power of the shared energy storage power station, c es Daily operation and maintenance costs;

[0103] The cost of interacting with multiple integrated energy systems is:

[0104] Among them, c out 、c in are the unit prices of electricity purchased and sold from the shared energy storage power station, P t out 、P t out are the discharge power and charging power of the shared energy storage power station respectively;

[0105] The revenue from shared energy storage power station services is:

[0106] Among them, c fu To pay the service revenue coefficient to the shared energy storage power station.

[0107] The column and constraint generation algorithm divides the second-stage optimization scheduling model into two layers, the upper layer constraints are:

[0108] Among them, SOC p,t+1 , SOC p,t The power of the shared energy storage power station at time t+1 and t, respectively, η p in ,η p out are the charging efficiency and discharging efficiency of the shared energy storage power station, P t in 、P t outare charging power and discharging power, SOC s min , SOC s max are the minimum and maximum capacities allowed for shared energy storage power stations, P s in,max 、P s out,max They are the maximum charging power and discharging power of the shared energy storage power station respectively.

[0109] The second-stage optimization dispatch model takes the lowest MIES operating cost, wind and solar curtailment cost, load shedding cost, and transaction cost with the electricity and heat market as the objective function. The optimization variables are CHP unit output, electric heat pump output, shared energy storage power station charge and discharge capacity, and transaction volume with the electricity and heat markets. The objective function is:

[0110] Among them, N IES is the number of integrated energy systems within the multi-integrated energy system, C i,t CHP 、C i,t HP 、C i,t LS 、C i,t CW 、C i,t CP 、C i,t HG are CHP operating costs, electric heat pump operating costs, load shedding costs, wind curtailment costs, solar curtailment costs, and market transaction costs; α1, α2, α3, α4, α5, α6, α7, and α8 are unit cost coefficients, P i,t CHP 、H i,t CHP are the electrical output and thermal output of the CHP unit, P i,t HP is the output of the electric heat pump unit, P i,t LS is the load shedding power, P i,t CW 、P i,t CV are the amount of wind and solar power abandoned, P i,t G 、H i,t G are the amount of electricity and heat traded with the electricity market and the heat market respectively;

[0111] The constraints of the second-stage optimization scheduling model are:

[0112] The CHP unit operates in a heat-to-electricity mode, and the electric-to-heat output range is within the closed region ABCD of the CHP unit operating characteristic curve. The CHP unit operating characteristic curve is shown in FIG3 , where, in a coordinate system with thermal power and electric power as the horizontal and vertical coordinates, points C and D are on the vertical coordinate.

[0113] The output constraints are:

[0114] Among them, c m 、c v 、c n They are the slopes of AB, BC, and AD in the closed area ABCD of the CHP unit operating characteristic curve in Figure 3, respectively. med is the thermal power of the CHP unit corresponding to point A, are the electric power and thermal power of the CHP unit at time t, p min 、p max are the upper and lower limits of CHP unit power output, h max is the maximum thermal power of the CHP unit;

[0115] The output constraint of the electric heat pump is:

[0116] in, are the electric power and thermal power of the electric heat pump unit at time t, η HP is the conversion efficiency of the electric heat pump unit, is the maximum electric power of the electric heat pump unit;

[0117] The transaction constraints in the electricity market and heat market are:

[0118] in, Electricity and heat are traded in the electricity market respectively. The value can be positive or negative. When it is positive, it means buying energy and paying the cost. When it is negative, it means selling energy and making a profit. The minimum and maximum values ​​allowed for trading in the electricity and heat markets, respectively;

[0119] Load shedding constraints:

[0120] in, are the electrical load cut-off and thermal load cut-off, are the maximum values ​​of the cut-off electrical load and the cut-off thermal load respectively;

[0121] Heat storage tank constraints:

[0122] Among them, HSOC i,t+1 HSOC i,,t are the heat storage tanks at time t+1 and t, respectively. are the minimum and maximum heat storage capacity of the heat storage tank, The heat storage tank stores and releases heat respectively. They are the minimum heat storage, maximum heat storage, minimum heat release and maximum heat release of the heat storage tank;

[0123] Energy balance constraints:

[0124] in, They are wind power generation, photovoltaic power generation, wind curtailment and solar curtailment. Electric and heating loads respectively.

[0125] The two-stage distributed robust optimization modeling of multiple integrated energy sources with shared energy storage integrates uncertain fuzzy sets into the lower-level optimization scheduling, forming a two-stage three-layer optimization model. The upper layer determines the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station. The lower layer calculates the worst-case scenario based on fuzzy sets, even if the cost is maximized, and then obtains the optimal scheduling strategy under the worst-case scenario. The two-stage model is as follows:

[0126] D0={f∈H(Ξ)|W(f,f N )≤ε,P(ξ∈Ξ)=1,E(ξ-μ)} (39)

[0127] Where x is the upper-level decision vector, y is the lower-level decision vector, z is the uncertainty vector, E(·) is the expectation, and the lower-level objective function is in brackets.

[0128] To verify the effectiveness of the proposed multi-energy system with shared energy storage and the two-stage distributed robust optimization method, this application sets up three system strategies for comparative experiments:

[0129] Strategy 1: Each sub-integrated energy system does not have energy storage, and relies entirely on participating in electricity and heat market transactions to make up for the difference between production capacity and energy consumption.

[0130] Strategy 2: Each sub-integrated energy system is equipped with its own energy storage device, relying on its own energy storage to complete the energy supply task, and does not exchange energy with other subsystems.

[0131] Strategy 3: Set up shared energy storage in multiple integrated energy systems and make up for the difference between production capacity and energy consumption through shared energy storage power stations.

[0132] Table 1 shows the costs of the three strategies:

[0133] Table 1 Cost of the three strategies (unit: yuan)

[0134] By comparing Strategy 2 with Strategy 1, we can see that although investing in energy storage power stations increases the construction cost of energy storage power stations, it reduces the operating costs of the units and reduces market transaction costs. By comparing Strategy 3 with Strategy 2, we can see that building a shared energy storage power station can significantly reduce the initial construction costs. Moreover, because the energy storage power station coordinates the various sub-integrated energy systems and promotes energy interaction between systems, the operating costs of the units are reduced, and profits can even be obtained when trading with the two markets, which greatly reduces the total cost.

[0135] From the above analysis, it can be seen that the multi-integrated energy system with shared energy storage and the two-stage distributed robust optimization method can effectively reduce costs, promote energy interaction, and reduce resource waste.

[0136] The beneficial effects are as follows:

[0137] (1) This application proposes a multi-integrated energy system with shared energy storage: the multi-integrated energy system establishes a unified shared energy storage power station, saving the initial investment cost of establishing energy storage devices for each subsystem separately. Shared energy storage is more conducive to the transmission of power within the system and saves operating costs.

[0138] (2) This application proposes an optimization method for a multi-integrated energy system with shared energy storage: a two-stage three-layer optimization model is established, the upper layer is a shared energy storage power station capacity configuration model, and the lower layer is a MIES optimization scheduling model.

[0139] (3) This application proposes to construct uncertain fuzzy sets based on Wasserstein distance and moment information, and integrate the first-order moment information into the Wasserstein distance fuzzy set, making the fuzzy set construction more accurate.

[0140] The collection, storage, use, processing, transmission, provision and disclosure of user personal information involved in this application are in compliance with relevant laws and regulations and do not violate public order and good morals.

[0141] It is important to note that personal information collected from users should be used for legitimate and reasonable purposes and should not be shared or sold beyond these legitimate uses. Furthermore, such collection / sharing should be conducted only after receiving the user's informed consent, including but not limited to notifying the user to read the user agreement / user notice and sign an agreement / authorization that includes the relevant user information before using the feature. Furthermore, any necessary steps must be taken to safeguard and secure access to such personal information and ensure that others with access to personal information comply with its privacy policy and procedures.

[0142] This application contemplates providing implementations that allow users to selectively block the use or access of personal information data. Specifically, this disclosure contemplates providing hardware and / or software to prevent or block access to such personal information data. Risks can be minimized by limiting data collection and deleting data once it is no longer needed. Furthermore, where applicable, such personal information can be de-identified to protect user privacy.

[0143] In the descriptions of the foregoing embodiments, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are mutually inconsistent.

[0144] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of such features. Throughout the description of this application, "plurality" means at least two, for example, two, three, etc., unless otherwise specifically defined.

[0145] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of optional embodiments of the present application includes additional implementations in which functions may be performed in a sequence other than as shown or discussed, including performing functions in a substantially simultaneous manner or in a reverse order depending on the functions involved, as should be understood by those skilled in the art to which the embodiments of the present application pertain.

[0146] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and a portable compact disc read-only memory (CDROM). Furthermore, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or processing it in another suitable manner if necessary, and then storing it in a computer memory.

[0147] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used to implement: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0148] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0149] In addition, the functional units in the various embodiments of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into a module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0150] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

Claims

1. An energy optimization method for a multi-integrated energy system with shared energy storage, wherein the multi-integrated energy system includes a plurality of integrated energy systems, characterized in that: include: The energy of the multi-integrated energy system with shared energy storage is optimized using a two-stage distributed robust optimization model; Based on the historical data of observed wind and solar power output and electric and thermal load, an empirical distribution is established, the Wasserstein distance between the empirical distribution and the actual distribution is calculated, and an uncertain fuzzy set of uncertain factors that meet the conditions is constructed. The uncertainty of wind power is described by a fuzzy set composed of random distributions. Construct the upper-level problem and the lower-level problem, integrate the uncertain fuzzy set into the two-stage problem, and form a two-stage three-level optimization model. Input the parameters of each unit and the cost coefficient. The column and constraint generation algorithm C&CG is used to divide the model into main and sub-problems and solve them iteratively until the iterative convergence requirements are met; Output decision results. The upper-level decision results are the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station. The lower-level decision results are the CHP unit output, electric heat pump output, shared energy storage power station charge and discharge volume, and transaction volume with the electricity market and heat market.

2. The energy optimization method for a multi-integrated energy system with shared energy storage according to claim 1, characterized in that: The two-stage distributed robust optimization model is divided into a first-stage capacity configuration model and a second-stage optimization scheduling model. The first-stage capacity configuration model is used to calculate the optimal capacity and maximum charge and discharge power of the shared energy storage power station; The second-stage optimization scheduling model is used to determine the output power of each integrated energy system in the multi-integrated energy system, the charging and discharging power of the shared energy storage, and the amount of electricity and heat traded with the electricity market and the heat market; An uncertain fuzzy set is constructed based on the combination of Wasserstein distance and moment information, and the uncertain fuzzy set is integrated into the second-stage optimization scheduling model to form a two-stage three-layer optimization model. The first-stage capacity configuration model determines the maximum capacity, maximum charging and discharging power, and actual charging and discharging power of the shared energy storage power station. The second-stage optimization scheduling model calculates the worst scenario based on the uncertain fuzzy set, and obtains the model formula corresponding to the optimization scheduling strategy under the worst scenario; the column and constraint generation algorithm is used to solve the problem. The column and constraint generation algorithm divides the second-stage optimization scheduling model into two layers, setting the upper bound UB = +∞ and the lower bound LB = -∞. The upper layer is the main problem and the lower layer is the subproblem. The upper layer passes the obtained variables to the lower layer to obtain the upper layer objective function value and updates the lower bound at the same time. After the lower layer accepts the variables, it solves the subproblem and obtains the lower layer objective function value. The corresponding variables and constraints are added and passed to the upper layer, and the upper bound is updated. It is iterated repeatedly until the upper and lower bounds meet the conditions.

3. The energy optimization method for a multi-integrated energy system with shared energy storage according to claim 1, characterized in that: When the power generation of the first integrated energy system within the multi-integrated energy system is greater than the load, and the power generation of the second integrated energy system is less than the load, the shared energy storage integrates the electricity demand, virtualizes the charging and discharging, and transmits the excess electricity of the first integrated energy system to the second integrated energy system. The difference is made up by the shared energy storage itself. If the total power generation is greater than the total load, the excess electricity of the integrated energy system will be charged into the shared energy storage. Otherwise, the shared energy storage will be discharged into the integrated energy system with the difference, thereby realizing the shared utilization of resources.

4. The energy optimization method for a multi-integrated energy system with shared energy storage according to claim 2, characterized in that: In order to maximize the use of shared energy storage, the priority is set as follows: transactions with shared energy storage are greater than transactions with the electricity market, that is, multiple integrated energy systems give priority to trading with shared energy storage. When the shared energy storage reaches the maximum charging capacity or the power reaches the maximum discharging capacity, it will trade with the electricity market.

5. The energy optimization method for a multi-integrated energy system with shared energy storage according to claim 1, characterized in that: The two-stage distributed robust optimization model is based on the uncertainty factor modeling of Wasserstein distance and moment information. The uncertain fuzzy set is constructed by combining Wasserstein distance and moment information. Assume that P i,t W 、P i,t V 、P i，t L 、H i，t L They are wind power output, photovoltaic output, electric load and thermal load in the i-th integrated energy system respectively. According to the historical sample set of wind power output and electric thermal load {ξ1, ξ2, …ξ N }, N is the total number of samples, and the following empirical distribution is established: Among them, f N is the empirical distribution constructed based on the observed samples, δ ξi For i According to the law of large numbers, when N→+∞, the empirical distribution f N Approaching the true distribution f, f N The distance between f and is measured by Wasserstein distance, which is defined as: Among them, ξ and They obey the empirical distribution f N and the random variables of the true distribution f, Ξ represents the random variables ξ and The support space, for ξ and The first-order norm between for ξ and The joint distribution of , inf is the lower bound function; The uncertainty set based on Wasserstein distance is represented as an empirical distribution f N The Wasserstein sphere with centered and ε as radius has a fuzzy set represented as: D0={f∈H(Ξ)∣W(f,f N )≤ε} (3) Where H(Ξ) is the set of all distributions with support set Ξ, and ε is the Wasserstein radius; The selection method of Wasserstein radius ε follows the following confidence requirements: Among them, P[W(f,f N )≤ε] is W(f,f N )≤ε, D is a constant, N is the number of sample groups, β is the confidence level, that is, the probability that the actual sample is within the Wasserstein sphere. The larger β is, the greater the probability is. α is a coefficient greater than zero, and μ is the sample mean. In order to improve the reliability of uncertain fuzzy sets, the first-order moment information of uncertain factors is incorporated into the fuzzy sets constructed based on Wasserstein, that is, the first-order moment of the uncertain variables satisfies the following constraints: Combining Equations (3) and (7), the final uncertain fuzzy set is expressed as: D0={f∈H(Ξ)∣W(f,f N )≤ε,P(ξ∈Ξ)=1,E(ξ-μ)=0} (8).

6. The energy optimization method for a multi-integrated energy system with shared energy storage according to claim 1, characterized in that: The first stage capacity allocation model aims to minimize investment and operating costs, and the optimization variables are the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station. The objective function of the first-stage capacity allocation model is: Among them, C rl is the upper objective function, T is the scheduling period, t is the scheduling period, During the scheduling period The average construction investment cost of shared energy storage power stations, the cost of interaction with multiple integrated energy systems, and the service revenue of shared energy storage power stations; The construction cost of shared energy storage is expressed by converting the fixed asset investment cost into daily depreciation expenses. The average construction investment cost of a shared energy storage power station is: Among them, c cl 、c s,1 、c s,2 are the unit costs of the maximum capacity, maximum charging power, and maximum discharging power of the shared energy storage power station, n is the economic and practical life of the shared energy storage power station, k is the line loss rate between the shared energy storage power station terminal and the electricity sales settlement point, SOC s max 、P s in，max 、P s out，max are the maximum capacity, maximum charging power and maximum discharging power of the shared energy storage power station, c es Daily operation and maintenance costs; The cost of interacting with multiple integrated energy systems is: Among them, c out 、c in are the unit prices of electricity purchased and sold from the shared energy storage power station, P t out 、P t out are the discharge power and charging power of the shared energy storage power station respectively; The revenue from shared energy storage power station services is: Among them, c fu To pay the service revenue coefficient to the shared energy storage power station.

7. The energy optimization method for a multi-integrated energy system with shared energy storage according to claim 1, characterized in that: The column and constraint generation algorithm divides the second-stage optimization scheduling model into two layers, the upper layer constraints are: Among them, SOC p,t+1 , SOC p,t The power of the shared energy storage power station at time t+1 and t, respectively, η p in ,η p out are the charging efficiency and discharging efficiency of the shared energy storage power station, P t in 、P t out are charging power and discharging power, SOC s min , SOC s max are the minimum and maximum capacities allowed for shared energy storage power stations, They are the maximum charging power and discharging power of the shared energy storage power station respectively.

8. The energy optimization method for a multi-integrated energy system with shared energy storage according to claim 1, characterized in that: The second-stage optimization dispatch model takes the lowest MIES operating cost, wind and solar curtailment cost, load shedding cost, and transaction cost with the electricity and heat market as the objective function. The optimization variables are CHP unit output, electric heat pump output, shared energy storage power station charge and discharge capacity, and transaction volume with the electricity and heat markets. The objective function is: Among them, N IES is the number of integrated energy systems within the multi-integrated energy system, C i,t CHP 、C i,t HP 、C i,t LS 、C i,t CW 、C i,t CP 、C i,t HG are CHP operating costs, electric heat pump operating costs, load shedding costs, wind curtailment costs, solar curtailment costs, and market transaction costs; α1, α2, α3, α4, α5, α6, α7, and α8 are unit cost coefficients, P i,t CHP 、H i,t CHP are the electrical output and thermal output of the CHP unit, P i,t HP is the output of the electric heat pump unit, P i,t LS is the load shedding power, P i,t CW 、P i,t CV are the amount of wind and solar power abandoned, P i,t G 、H i,t G are the amount of electricity and heat traded with the electricity market and the heat market respectively; The constraints of the second-stage optimization scheduling model are: The CHP unit operates in a heat-to-electricity mode, and the electric-to-heat output range is within the closed region ABCD of the CHP unit operating characteristic curve; wherein, in a coordinate system with thermal power and electric power as the horizontal and vertical coordinates, points C and D are on the vertical coordinate of the CHP unit operating characteristic curve; The output constraints are: Among them, c m 、c v 、c n They are the slopes of AB, BC and AD in the closed area ABCD of the CHP unit operating characteristic curve, h med is the thermal power of the CHP unit corresponding to point A, are the electric power and thermal power of the CHP unit at time t, p min 、p max are the upper and lower limits of CHP unit power output, h max is the maximum thermal power of the CHP unit; The output constraint of the electric heat pump is: in, are the electric power and thermal power of the electric heat pump unit at time t, η HP is the conversion efficiency of the electric heat pump unit, is the maximum electric power of the electric heat pump unit; The transaction constraints in the electricity market and heat market are: in, Electricity and heat are traded in the electricity market respectively. The value can be positive or negative. When it is positive, it means buying energy and paying the cost. When it is negative, it means selling energy and making a profit. The minimum and maximum values allowed for trading in the electricity and heat markets, respectively; Load shedding constraints: in, are the electrical load cut-off and thermal load cut-off, are the maximum values of the cut-off electrical load and the cut-off thermal load respectively; Heat storage tank constraints: Among them, HSOC i,t+1 HSOC i,,t are the heat storage tanks at time t+1 and t, respectively. are the minimum and maximum heat storage capacity of the heat storage tank, The heat storage tank stores and releases heat respectively. They are the minimum heat storage, maximum heat storage, minimum heat release and maximum heat release of the heat storage tank; Energy balance constraints: in, They are wind power generation, photovoltaic power generation, wind curtailment and solar curtailment. Electric and heating loads respectively.

9. The energy optimization method for a multi-integrated energy system with shared energy storage according to claim 1, characterized in that: The two-stage distributed robust optimization modeling of multiple integrated energy sources with shared energy storage integrates uncertain fuzzy sets into the lower-level optimization scheduling, forming a two-stage three-layer optimization model. The upper layer determines the maximum capacity, maximum charge and discharge power, and actual charge and discharge power of the shared energy storage power station. The lower layer calculates the worst-case scenario based on fuzzy sets, even if the cost is maximized, and then obtains the optimal scheduling strategy under the worst-case scenario. The two-stage model is as follows: D0={f∈H(Ξ)|W(f,f N )≤ε,P(ξ∈Ξ)=1,E(ξ-μ)} (39) Where x is the upper-level decision vector, y is the lower-level decision vector, z is the uncertainty vector, E(·) is the expectation, and the lower-level objective function is in brackets.

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