Robust optimal scheduling of integrated energy systems considering multiple uncertainties

Multiple uncertainties such as renewable energy output, energy purchase prices and integrated demand responses have brought about severe challenges to the safe and economic operation of integrated energy system (IES). To meet this challenge, this study takes the combined cooling heating and power as an example of IES and proposes an optimization model considering multiple uncertainties. First, the structure of IES is given, and these mathematical models and constraints are listed according to the energy supply characteristics. Second, considering uncertain factors such as the wind and solar output, comprehensive demand response and energy purchase price, the different characterization methods are selected to model the uncertainty sources by identifying the characteristics of multiple uncertainty sources. Then, combining the stochastic scenario method and robust optimization method, a day‐ahead optimal scheduling model of IES with multiple uncertainties is established, and the whale optimization algorithm is improved to obtain the optimal solution of the model. Finally, the actual data of an IES is selected to verify the rationality and effectiveness of the model. Meanwhile, the influence of uncertain factors on scheduling is introduced to verify the perfect coordination of economy and robustness of the model at runtime.


| INTRODUCTION
With the intensification of global warming, fossil energy, mainly coal, oil and natural gas, has been difficult to meet the requirements of low-carbon environmental protection.At the same time, renewable energy, represented by wind power and photovoltaic, has developed vigorously in recent years and is promoting the reform of the power system worldwide.Sustainable development of energy systems and the efficient use of energy have become the focus of energy research.The integrated energy system (IES) couples cooling, heating, electricity and gas.Through the coordination and optimization of energy production, transmission, storage, conversion, distribution and consumption, it realizes the cascade utilization of energy, improves the efficiency of energy utilization and meets the diversified energy demand of industrial production and residents' life. 1,2n the IES, optimizing scheduling is one of the key links in energy production arrangements.Due to the randomness and volatility of renewable energy output, dispatchers must adopt relatively conservative power generation plans and reserve sufficient system reserve capacity to cope with the uncertainty of renewable energy.This has led to many problems such as low load rate of heating power units and limited space for renewable energy consumption. 3With the increasing penetration rate of renewable energy, its uncertainty is gradually increasing, and the above problems are becoming increasingly prominent.The scheduling of IESs urgently need to shift from deterministic optimization to uncertain optimization. 4n the scheduling problem of IES, the purpose of using the uncertain optimization is to obtain a better solution than the deterministic scheduling based on more accurate uncertainty characteristics of the renewable energy output and considering more regulation means.There are many kinds of uncertain optimization.According to the different modeling of uncertain factors, it can be generally divided into two categories: stochastic optimization (SO) and robust optimization (RO).SO uses the probability distribution function to describe the uncertainty of the renewable energy output, and then generates the scenario tree of the renewable energy output by sampling.The solution obtained from optimization is the optimal solution in the average sense of each scenario.Birge et al. 5 first applied SO to the unit commitment problem of day-ahead.They dealt with the uncertainty of load and solved it through Lagrangian relaxation.Tuohy et al. 6 considered a large-scale wind power access in the unit commitment problem.Khodayar et al. 7 proposed a two-stage SO to optimize the system containing wind power and pumped storage, and verified the role of pumped storage in improving the schedulability of wind power.SO has also been applied in intra-day scheduling, 8,9 but it does not break away from the framework of Look-ahead Economic Dispatch.The problem of SO is that when the uncertainty dimension in the system is high, it becomes difficult to build a scenario tree. 10Too large scenario trees will also lead to the problem of computing explosion, so it is often necessary to use scenario reduction methods. 11,12More importantly, the performance of SO largely depends on the probability distribution function fitted according to historical data, and there is often error with the actual situation, so the effect of SO solution in actual operation is often worse than the expected values. 13O is another method to deal with the uncertainty.Compared with stochastic optimization, RO assumes that uncertain parameters take values in the uncertainty set.The goal is to find a solution so that the values of any uncertain parameters meet the constraints, and the cost in the worst case is the minimum.Professor Aharon Ben Tal of Northwestern University and Professor Dimitris Bertsimas of MIT have done a lot of work in this field, and their achievements have attracted extensive attention in the engineering field. 14,15The advantage of RO is that it does not need to obtain the probability distribution function in advance, and it avoids the generation of scenario trees, which is suitable for a large-scale practical system.
To solve the problem that real distribution is difficult to obtain, Delage et al. 16 proposed the distributed robust optimization (DRO).Unlike the optimization of SO under a given distribution, DRO is optimized under a family of distributions to minimize the expected value of the objective function corresponding to the worst distribution.According to the different choices of distribution families, DRO can be divided into three categories: the moment based, the function distance based, and the kernel function based.Xiong et al. 17 and Zhu et al. 18 proposed the unit commitment DRO model based on the moment and the Wasserstein distance respectively, which is more robust to the data interference than SO.
Robust unit commitment (RUC) is the main application of RO in the field of power dispatching.Its structure is a two-stage optimization problem.The first stage is UC, which mainly determines the startup sequence of units.According to the specific problems, it can also include the unit standby, 19 the state of charge plan for energy storage, 20 the day-ahead market contract, 21 ad so forth.These are the decisions that must be made before the day-ahead.The second stage is the economic dispatch (ED), which solves the zero-sum game problem of the wind power and decision-makers.Given a day-ahead plan, the decisionmakers need to determine the optimal response after observing the actual output of wind power, such as the unit output, the charging and discharging power of storage, the regulating power of active load, 22 etc.While the wind power needs to find the worst scenario that makes the daily operating cost the highest, and its equilibrium solution will be returned to the first stage.As an evaluation of the dayahead plan, it will be iterated repeatedly until convergence.This kind of RUC problem is also called Adaptive Robust Unit Commitment (ARUC).The early work of ARUC can be seen in the literature, 23 in which a two-stage robust unit commitment model considering the pumped storage was proposed.The unit startup and pumped storage status were determined in the day-ahead phase, and the unit power regulation and the power of pumped storage were determined in the intra-day phase.Finally, it was solved through Benders decomposition.Subsequently, Zeng et al. 24 proposed the Column and Constraint Generation (C&CG).By continuously solving the limit scenario in the intra-day stage and adding the limit scenario to the dayahead stage, a new set of variables (columns) and constraints were formed, so as to continuously narrow the lower bound of the day-ahead stage until it converged.Compared with the Benders decomposition method, C&CG had fewer iterations and simpler implementation.][27] Although there have been some research on the uncertainty of the IES, the current research mainly focuses on the uncertainty analysis of renewable energy output and load forecasting, and less comprehensive consideration is given to the characterization and modeling of multiple uncertainty sources such as the wind power output, the energy purchase price and the integrated demand response, which reduces the economy and security of system operation.Therefore, it is of great theoretical and engineering significance how to use the reasonable modeling methods to build an optimization model for robust scheduling of IESs based on the analysis of multiple uncertainties.
Based on the above background, this paper takes the IES consisting of the wind and photovoltaic generator, gas turbine, gas boiler, electric chiller, absorption chiller, energy storage device, heating exchanger, cooling, heating and power load and other energy supply and energy consumption units as the research objects.According to the characteristics of multiple uncertainty sources in the IES, the different modeling methods are used to build a robust stochastic optimization model for multiple uncertainty environments.The multiobjective whale algorithm is used to solve the model.The results of the example verify that the proposed scheduling strategy can effectively improve the economy and security of IES operation by reasonably considering the characteristics of multiple uncertainty sources.This paper is organized as follows: In Section 1, a brief description of the theoretical background, and the motivation and the purpose of this paper are given.In Section 2, it establishes an IES model of combined cooling heating and power (CCHP).In Section 3, by identifying the characteristics of multiple uncertainty sources, the different characterization methods are selected to model the uncertainty sources.In Section 4, the optimization model of IES is established with the objective of minimizing operating cost and carbon dioxide emission, and an improved whale optimization algorithm is proposed to solve the model.In Section 5, the effectiveness of the optimization model is verified by the operation results of examples, and the influence of uncertain factors on the scheduling and economic security of IESs is deeply analyzed.Lastly, a brief conclusion and discussion are given in Section 6.
The novelties of this work include three aspects: 1.According to the structure of the IES and the conversion characteristics of each equipment, the mathematical models of each equipment are established.Considering the operation constraints of each equipment, a multiobjective optimization model is established with the minimum operation cost and the minimum carbon dioxide emission as the objectives, taking into account the dual requirements of the system operation economy and ecology.2. Compared with the deterministic scheduling model previously studied and the model only considering single uncertainty, according to the characteristics of uncertainty sources, a modeling method considering multiple uncertainty sources is proposed.At the same time, the multiobjective whale optimization algorithm is improved to solve the model, which improves the search ability on the large-scale optimization problem.3. Considering the impacts of the uncertainty of renewable energy output, the uncertainty of integrated demand response and the uncertainty of energy purchase price on IES scheduling, the model can effectively coordinate the economy and robustness of scheduling results.In addition, combined with the change of the uncertain budget set, we analyze its impact on the overall economy and security of the system.

| System structure
Figure 1 shows the structure of a typical CCHP-type IES.In Figure 1, the gas turbines use natural gas as fuel to provide electricity to users.At the same time, the high temperature The structure of combined cooling heating and power-type integrated energy system.
flue gas and cylinder water generated by them will transfer the waste heating to the absorption chiller and heating exchanger to meet the cooling and heating load requirements of users.In addition, the photovoltaic panels, the batteries and the urban power grids also participate in the supply of electric energy.The heating storage tank can store and release the heating as required, and the gas boiler and electric chiller can supply the heating and cooling.Next, we conduct the mathematical modeling for each energy supply unit in the IES.

| Gas turbine
As the main energy supply equipment of the system, the operating efficiency of gas turbine varies greatly under the different load rates, and its mathematical model is 28 where V mt is the consumption of natural gas, m 3 ; P mt is the output of electric power, kW; Q mt is the power of waste heating, kW; η mtP and η mtQ refer to the efficiency of power generation and the efficiency of waste heating respectively; L gas is the calorific value of natural gas.In this paper, the calorific value of natural gas is 9.7 kWh/m 3 ; Δt is the time scale of scheduling, which is taken as 1 h; T is the number of scheduling periods.
Taking the TCG2016 V16C micro gas turbine of MWM Company as an example, according to the actual test data, the functional relationship between the efficiency of power generation, the efficiency of waste heating and the load rate can be obtained by polynomial curve fitting with Matlab.
where P mt0 is the rated generating power of the gas turbine, kW.

| Absorption chiller
The mathematical model of absorption chiller is 29 where Q ac is the cooling power, kW; Q ac_in is the input heating power, kW; COP ac is the coefficient of performance.

| Energy storage device
The mathematical model of energy storage devices such as the battery and the heating storage tank is 30 where S S (t) is the residual energy of the energy storage device in t period, kWh; P S,chr (t) and P S,dis (t) are the input and output power of the stored energy in t period respectively, kW; τ S is the loss coefficient of the energy storage; η S,chr and η S,dis are the input and output conversion efficiency of the stored energy respectively.

| Gas boiler and heating exchanger
The mathematical model of gas boiler and heating exchanger is 30 where Q ex_in is the input heating power of heating exchanger, kW; Q ex is the output heating power of heating exchanger, kW; Q gb is the heating power of gas boiler, kW; V gb is the gas consumption of gas boiler, m 3 ; η gb and η ex refer to the efficiency of gas boiler and heating exchanger respectively.

| Electric chiller
The relationship between the refrigeration power of the electric chiller and the electric power consumed is 29 where Q ec is the cooling power, kW; P ec is the power consumption, kW; COP ec is the energy efficiency ratio.

| Calculation model of the energy flow
According to the structure of the IES and the mathematical model of each equipment, the calculation model of the energy flow is constructed as shown in the following equation: where k mt is the proportion of waste heating from the gas turbine allocated to the absorption chiller for refrigeration; Q load.c, Q load.h and P load are the cooling, heating and electric loads respectively, kW; P op is the self consumed power of the system, kW; k op is the self consumption rate of the system; P grid is the power purchased from the grid, kW; Q hs is the heating release power of the heating storage tank, kW; P es is the battery discharge power, kW; P re is the output power of wind and solar energy, kW.

| MODELING OF THE UNCERTAINTY SOURCES IN THE INTEGRATED ENERGY SYSTEM
The uncertainty factors considered in this study mainly include the uncertainty of wind and solar output, the uncertainty of energy purchase price and the uncertainty of the integrated demand response.For the load of multi energy flow, the current forecasting technology is relatively mature.Therefore, this study ignores the uncertainty of the load of multienergy flow and only analyzes the above three uncertainties.In this section, by identifying the characteristics of multiple uncertainty sources, the different characterization methods are selected to model the uncertainty sources.

| Uncertainty modeling of wind and solar output
The research shows that the regional conditions, weather, real-time temperature and humidity, air pressure and other factors have the great impact on the wind and solar output.The influence of meteorological factors leads to low accuracy and strong volatility of the prediction of wind and solar energy.At the same time, the output of wind and solar energy directly participates in the power balance of the system's electrical load.If the uncertainty of wind and solar output is modeled using the random scenario method, it is easy to cause the obtained dispatching results to exceed the safety limit during the actual operation, resulting in high penalty costs. 31Therefore, based on the uncertainty characteristics of wind and solar output, this study uses the robust optimization method to model it.The actual output values of wind and solar energy are shown in the following formula:

| Uncertainty modeling of the integrated demand response
The IES studied in this paper includes a variety of energy flow forms, including cooling, heating, electricity and gas.Its regulation potential is no longer limited to the traditional electric load.Therefore, based on the nature of the load and the ability of the load to participate in the response, this study divides the loads into the fixed load, the transferable load and the replaceable load from the perspective of the demand transfer of the same load and the energy substitution of the different loads, The integrated demand response (IDR) model which is established is shown in the following equation: where X L is the load after implementing the demand response; X L f is the fixed load; X L p is the transferable load; X L r is the alternative load.
For the fixed load, due to its high priority of load type, it is not allowed to interrupt and transfer during the dayahead scheduling process.Therefore, the value of fixed load has nothing to do with the price information and can be expressed as the following formula: where X L f0 is the value of fixed load before implementing the demand response.
For the transferable load, the user can increase or decrease the part of the load at the current time according to the energy price, or use the energy storage device to shift and adjust the energy at a certain time.The price response characteristics can be expressed as the following equation: where For the alternative load, the users can comprehensively compare various energy prices to change the types of energy consumption, and determine the load value participating in the demand response based on their own wishes.Taking the alternative electric load as an example, the users can determine the load value participating in IDR based on the comprehensive consideration of electricity price, gas price, heating price and cooling price.The price characteristics can be expressed as the following formula: where P t L, r0 is the alternative load before the demand response at time t; λ ei is the conversion efficiency between the electric energy and the other energies; ε t ei is the cross elasticity coefficient; X refers to the other energy flows except the electric energy; X t i L, is the load value of energy flow i at time t; ρ t i , and ρ t i0 , represent the actual price and benchmark price of the energy flow i at time t'.
For the uncertainty of the integrated demand response, its fluctuation range is directly related to the elastic range of user demand, the rate of price change and the level of price incentive.The regional difference of probability distribution function is large.At present, the integrated demand response is during the initial application stage, and its uncertainty lacks the credible and open historical data, and the information source is insufficient. 32,33It is unable to generate a discrete scenario set to describe the uncertainty of the integrated demand response.Meanwhile, in the model, the integrated demand response affects the power balance constraint and the spinning reserve constraint of IES, and its uncertainty directly affects the economy and security of IES operation.Considering that the uncertainty characteristics of the integrated demand response are mainly shown in the demand response X Δ L , this study uses the robust optimization method to model the fluctuation of the demand response and obtain the value set of the actual demand response.
where X Δ L is the actual value of demand response; X Δ L is the predicted value of demand response; X Δ L − and X Δ L + are the upper and lower limit of demand response fluctuation; u t DR− and u t DR+ are the indicator variables of upward fluctuation and downward fluctuation; ψ X DR is the uncertainty budget set of demand response.

| The uncertainty modeling of energy purchase price
Compared with the uncertainty of wind and solar output and the uncertainty of integrated demand response, the uncertainty of energy purchase price mainly affects the operating profit of IES in the model, and there is no actual operation beyond the limit.Meanwhile, the energy purchase price of IES has a large amount of historical information and open data sources, which can fully describe all the realization possibilities of the uncertainty and the information about the specific probability distribution of uncertainty by establishing the scenarios.
During the scenario generation process, due to the errors in the day-ahead prediction of wind and solar output and the cooling, heating, and electricity loads, this study regards the actual value of wind and solar output and the load as the sum of the predicted value and the predicted error, with the expression: Assuming that the wind and solar output and load forecasting errors follow the normal distribution with the mean value of 0, the standard deviations of wind and solar output and load forecasting errors are taken as where σ re.j.t , σ L.j.t is the standard deviation between the wind and solar output error and the load prediction error in the jth scenario during time t, respectively; P ren is the rated capacity of wind and solar power.
Real-time electricity price is formulated and published by the power grid company based on the load and output forecasts of the next day, and the users will arrange the electricity consumption time and quantity of the next day based on the published electricity price information and their own electricity demand.Compared with time-of-use electricity prices, real-time electricity prices have more flexible and diverse daily time slots, which can basically compensate for the deviation between electricity demand and supply caused by insufficient refinement of electricity prices.This study divides real-time electricity prices into the following daily periods:

| Construction of the uncertainty sets
In the study, the power deviation between the source and load is used as an uncertainty variable.This section takes the wind and solar power deviation as an example to illustrate how to construct an uncertainty set.We used the power deviation of wind and solar output to construct an uncertainty set, as shown in the following equation: where ‖‖ represents an infinite norm; ‖‖ 1 represents a 1-norm constraint, corresponding to the spatial clustering effect of wind and solar power output in practice.Here, the uncertainty spatial constraint parameter Γ t re of wind and solar output is introduced.γ i t , re is the deviation coefficient of the i-th wind and solar output at time t.Similarly, for other uncertainty variables in the IES, the uncertainty sets are constructed using the same method.

| THE OPTIMIZATION MODEL OF IES AND SOLUTION
The CCHP-type IES studied in this paper includes four energy forms: cooling, heating, electricity and gas, mainly including the gas turbine, the electric refrigerator, the absorption chiller, the heating exchanger, the wind turbine unit, the gas boiler, the integrated energy storage device and other equipment.In addition, IES implements the integrated demand response on the user side, guides the users to change their energy consumption mode through energy price change signals, indirectly controls the reduction, transfer and transformation of multiple energy flows, and improves the flexibility of system operation. 34To deal with the uncertainty characteristics of multiple scheduling resources during IES operation, the study combines the random scenario method and robust optimization method to establish the IES day ahead optimal scheduling model for multiple uncertainties, and uses the improved whale optimization algorithm to obtain the worst case of the uncertainty of wind and solar output and the comprehensive demand response, and obtain the robust cost under multiple energy purchase price scenarios.The model comprehensively considers the uncertainty characteristics of wind and solar output, energy purchase price and integrated demand response.

| Objective function
Goal 1 is to minimize the system operation cost in the scheduling cycle, and the expression is where f 1 is the total operating cost of the system; P s is the probability of scenario s; k is the number of scenarios; F gas (t,s), F grid (t,s) and F op (t,s) are respectively the fuel cost, the purchase cost of power grid and the maintenance cost in the scenario s during the period t.For a certain scenario, the specific expression is where C gas is the price of natural gas; C grid is the market electricity price; C mt , Cre, C ac , C ec , C ex , C es , and C hs are, respectively, the operation and maintenance costs of gas turbine, wind and solar units, absorption chiller, electric chiller, heating exchanger, battery and heating storage tank.Goal 2 is to minimize the total carbon dioxide emission of the system, and its expression is where f 2 is the total carbon dioxide emission of the system; F co2,gas (t,s) and F co2,grid (t,s) are, respectively, the equivalent carbon dioxide emission generated by the gas and the electricity purchased by the grid.For a scenario, the calculation formula is Where, K co2,gas and K co2,grid are, respectively, CO 2 conversion coefficients of gas and electricity, and the units are kg/m 3 and kg/kWh.

| Constraints
To ensure the safety and stability of the operation of IES, it is also necessary to consider the energy balance constraints of the system and the operation constraints of each equipment.Among them, the operation constraints of each equipment have been described in Section 2. In any scenario, the balance constraint expression of cooling, heating and electric energy is

| Multiobjective whale optimization algorithm
Whale optimization algorithm (WOA) has the characteristics of few parameter settings and strong optimization performance.It is superior to solve the accuracy and convergence speed, 35 and has been successfully applied to some large-scale optimization problems.The search range of whales is the global solution space, and it is necessary to first determine the position of the prey to surround it.Due to the fact that the position of the optimal design in the search speed is not a priori known, the WOA algorithm assumes that the current optimal candidate solution is the target prey or close to the optimal solution.After defining the best search agent, other search agents will attempt to update their location to the best search agent.This behavior is governed by the following equation: where t represents the current number of iterations, A and C are coefficient vectors, x*(t) is the position vector of the currently obtained optimal solution, x(t) vector is the position vector.If there is a better solution, then x*(t) should be updated in each iteration.The calculation method for vectors A and C is as follows: During the entire iteration process, a linearly decreases from 2 to 0; r 1 and r 2 are the random vectors in [0,1].
Although the WOA has a strong ability to search for global solutions, it cannot effectively balance the global and local search capabilities, resulting in a loss of diversity and insufficient convergence ability in the later stages of iteration.Therefore, the corresponding improvement strategy is proposed in this study.The improved WOA (IWOA) algorithm is as follows: Algorithm: IWOA Input: Np (the population size); D (dimension); G (maximum number of iterations); A_constant; X (the initial population) Output: x* (the optimal individual) 1. F←Calculate the fitness of X; x*←Select the best individual from X; 2. While (stop condition of the iteration is not satisfied) do 3. Update a, A, C, l by the Equations ( 26) and ( 27 where G iter and G max are the current and maximum iterations, respectively; r is a random number of (0, 1.0); The coefficients A and C are calculated by the convergence factor a, which decreases from 2 to 0 with the number of iterations; l is the helix coefficient; b is the parameter of spiral shape.Set the fixed value A_constant of the search.When A ≥ A_constant, the global search is performed, and vice versa.With the help of the cooperation and competition of individuals in the differential evolution algorithm to guide the optimization search, the spiral motion and linear motion are carried out respectively, and the update mode is as follows:

| Solution process
The overall solution of the model includes the constraint processing flow, as shown in Figure 2. First, it is necessary to set the parameters for IES operation and initialize the algorithm and population; Next, the objective function values are calculated in the optimization model and the nondominated sequence and crowding entropy are obtained in the population; Then, based Flowchart of solution process.IES, integrated energy system.
on the boundary constraints of each energy supply device in the model, the algorithm will update the external elite archive and determine whether the iteration termination condition is met.If the condition is met, it will return the optimal Pareto solution set, and we can extract the optimal compromise solution.On the contrary, the IWOA algorithm is used to continue updating the population, increasing the number of iterations by 1, and then performing boundary constraint processing in the IES, continuously cycling until the iteration termination condition is met, the optimal solution is outputted.The multiobjective whale algorithm uses the elite retention strategy in NSGAII for reference, and uses the external archives to preserve the nondominant solutions found in the evolution process.When the external archive exceeds the setting maximum capacity, the Pareto solution set is clipped by the crowding entropy. 36his method considers the distribution of adjacent solutions and can reasonably reflect the degree of congestion between the nondominant solutions.Starting from the reality of the problem, it is necessary to obtain a solution that meets each objective, extract the optimal compromise solution by the fuzzy mathematics, and select a linear function as the membership function.

| Parameter setting of the example
The example selected the actual data of an IES in a region, and called CPLEX to solve the problem in MATLAB environment to verify the rationality and effectiveness of the model established in this paper.The CCHP structure of the IES is shown in Figure 1, and the parameters of the equipment in the system are shown in Table 1.Time-of-use (TOU) price is adopted in the electric purchase market, as shown in Table 2.
The daily scheduling cycle is divided into 24 periods, and the scheduling time scale is 1 h. Figure 3 shows the electric load, heating load and cooling load and the wind and solar output during the dispatching period of the IES.The prediction error of the wind and solar output and the uncertainty fluctuation range of the integrated demand response are 20%.

| Analysis of model scheduling results
The scheduling results of power, heating and cooling scheduling of IES and the capacity change of energy storage are shown in Figure 4.In this scenario, the scheduling model uses the robust optimization method to model the uncertainty of wind and solar power and integrated demand response, and uses the scenario method to model the uncertainty of energy purchase price.The optimized operation result shows that the operating cost is ¥9276 and the average slack power is 863 kW.
IES meets the electrical load requirements through gas turbines, wind and solar generation, storage batteries and power purchases from the external grid.The gas load requirements are met by purchasing natural gas.The heating load requirements are met through the gas boiler, heating storage tank and heating exchanger.The cooling load requirements are met by the electric chiller and the absorption chiller.
It can be seen from Figure 4, 00:00-08:00 and 22:00-24:00, the electric load of the system is small and  most of the electricity purchase market is in the range of valley price.At this time, considering the optimal operating cost, the electric load is mainly met by the electricity purchase, wind and solar energy.Meanwhile, the purchase of gas is mainly used for the gas boiler, because the heating load during this period is mainly borne by the gas boiler.To ensure the economic requirement of the system operation, while meeting the various load requirements, the system stores the energy for each energy storage equipment through the purchase of electricity, and then releases energy during the peak of electricity price or the peak of load.From 8:00 to 18:00, this period is during working hours, the electric load of the system is relatively large, and most of the electric purchase market is in the peak and flat range of the electricity price.To save operating costs and reduce carbon emissions, the various loads are mainly met by the gas turbine, gas boiler, electric chiller, absorption chiller, and the insufficient part is supplemented by the energy storage equipment such as the battery and heating storage tank.Since this period is in the daytime, the solar generation starts to play an important role.The integrated demand response alleviates the peak demand for electricity by increasing the electricity price.In addition, according to the energy storage dispatching curve, the energy storage equipment has the output characteristics of "low storage and high release" and the flexible power regulation capability.At the same time, its characteristics of cooling, heating and electricity combined supply can effectively cooperate with the various equipment to optimize the economy and flexibility of system operation.
From 18:00 to 22:00, the electrical purchase market is in the range of peak prices.Considering the operation cost, the electrical load is mainly provided by the gas turbine.The gas turbine works in the mode of the electricity determining heating.To reduce carbon emissions, the excess heating is recovered through the heating exchanger.Meanwhile, the heating load is mainly supplied by the gas turbine, and the insufficient part is supplemented by the gas boiler.In terms of cooling, the use of electric chiller is reduced and the proportion of refrigeration capacity of absorption chiller is increased.
During the whole dispatching cycle, the energy storage device and the integrate demand response will store and release energy as well as increase, decrease and transfer the load demand according to the energy purchasing market price and the load fluctuation, so as to alleviate the problem of time staggering between the renewable energy supply and the regional load demand, improve the renewable energy consumption capacity, and effectively improve the economic efficiency of the operation of the IES.

| Uncertainty impact on the model scheduling
To illustrate the improvement of the effectiveness and superiority of the scheduling strategy after considering the uncertainty factors comprehensively, this section sets up four scenarios according to the modeling method of uncertainty sources, and compares and analyzes the impact of considering the uncertainty of renewable energy output, the uncertainty of integrated demand response and the uncertainty of energy purchase price on the scheduling results of the IES.The specific scenario settings are described below.| 3425 integrated demand response.The fixed electricity price is used as the energy purchase price.Scenario 4: In the dispatching model, the robust optimization method is used to model the uncertainty of wind and solar output and the uncertainty of integrated demand response.The stochastic scenario method is used to model the uncertainty of energy purchase price.
In the four scenarios, the scheduling model adopts the different types of combinations.The output of each generator in the IES is shown in Figure 5.
When scenario 1 is adopted, the scheduling model is a deterministic scheduling model that does not consider the influence of uncertain factors.Therefore, the internal unit output of the system is relatively stable, and the impact on operating costs and carbon emissions only depend on the output regulation among each power generation unit.
When scenario 2 is adopted, the uncertainty of energy purchase price is modeled in the scheduling model, and the wind and solar power and integrated demand response are taken as the predicted values.Considering the factor of the operating cost, the system is affected by the purchase of time-of-use electricity prices, and the priority of purchased electricity is higher than that of micro gas turbine power generation.If considering the environmental factors, due to the lower carbon emissions of gas turbine compared with the external power generation, the system will prioritize using gas turbines for power generation.
When scenario 3 is adopted, the robust optimization method is used to model the uncertainty of wind and solar output and the uncertainty of integrated demand response, and the fixed price is used for energy purchase.During the peak periods of wind and solar power output, the system will convert energy into multiple types through energy storage, to achieve the goal of maximizing the absorption of wind and solar energy.During the low periods of wind and solar power generation, the system will fully mobilize gas turbines and hybrid energy storage to meet the internal load demands.Due to the lower carbon emissions of gas turbines compared with the purchased electricity and the fact that the system is not affected by time-ofuse electricity prices, the gas turbines are prioritized for power generation, and the shortage of system load is compensated by the purchased electricity.
When scenario 4 is adopted, the robust optimization method is used to model the uncertainty of wind and solar power output and integrated demand response, and the uncertainty of energy purchase price.Considering the opposition between the minimum operating cost of the system and the optimal goal of carbon emissions, when the optimization goal is to minimize the operating cost, the efficiency of the energy storage system is limited by the cost and cannot effectively consume the wind and solar energy.When the optimization goal is to minimize carbon emissions, the energy storage system will achieve the consumption of the wind and solar energy through energy conversion.In the multiobjective optimization, although the operation of the energy storage system increases the operating cost of the system, it achieves multilevel energy utilization, reduces energy loss, and thus improves the overall optimization effect.
The comparison of the operating costs and CO 2 emissions of the four scenarios is shown in Figure 6.It can be seen intuitively that, compared with scenario 1 and scenario 2, after considering the uncertainty factors of energy purchase price, the system's purchased electricity can be flexibly adjusted according to the electricity price of real-time market, reducing the operating cost by ¥441 and the carbon emission by 355 kg.Compared with scenarios 2 and 4, considering the uncertainty of wind and solar output and integrated demand response, the operating cost increased by ¥634 and the carbon emission increased by 537 kg.The robustness of the model was improved by sacrificing certain economic and ecological benefits.Compared with scenarios 3 and 4, after the implementation of TOU, the users reduced the power consumption in the peak hours and increased the power consumption in the valley hours, thus reducing the system's operation cost and carbon emission.

| Uncertainty impacts on the economy and safety of IES
To study the impact of the uncertainty of wind and solar output and integrated demand response on the operating economy and safety of IES, this section calculates the operating cost and the average slack power of IES respectively according to the different values of uncertain budget set ψ RE and ψ DR .The operating results are shown in Figure 7.
It can be seen from Figure 7 that, with the increase of the values of uncertain budget set, the operating cost of IES shows an increasing trend, while the average slack power also decreases.This shows that the larger value of uncertain budget set can improve the security of IES operation, but also increase the system operation cost.The operators of IES may make trade-offs between the economy and robustness of system operation according to the actual situation, and achieve the coordinated optimization of economy and robustness through the reasonable values of uncertain budget set.
Further research on the scheduling results under the different values of ψ RE and ψ DR shows that, compared with the change of uncertain budget set of wind and solar output, the change of uncertain budget set of integrated demand response has a greater impact on the operating   | 3429 cost and average slack power of IES.In the model, the integrated demand response is involved in the power balance constraint of the heating and cooling loads, and its uncertainty is directly related to the operating economy and safety of electric, heating and cooling subsystems.To sum up, in the uncertain budget set, the changes of the integrated demand response have a greater impact on the overall economy and security of the system.

| Pareto frontier and multiattribute decision-making
On the basis of typical scenario 4, we can use IWOA algorithm to find Pareto solution set, as shown in Figure 8.
After getting the Pareto solution set, we adopted the Technology for Order Preference by Similarity to an Ideal Solution (TOPSIS) method and information entropy method to select the optimal solution from the Pareto solution set.The specific steps of TOPSIS method and information entropy method are shown in literature. 37he selected optimal solution has been marked in the red box in Figure 8.It can be seen that the Pareto solution set obtained by using the improved whale optimization algorithm is more evenly distributed on the front of Pareto with good distribution.Each point in the solution set of Pareto corresponds to the optimal operation strategy of IES and each equipment.According to the different situations in practice, the system dispatcher may make some decisions and find an appropriate optimal compromise solution to balance the operation cost of IES and CO 2 emission.
The study also adopted NSGA-II and WOA to solve the model.The solution sets of Pareto obtained by the different algorithms are shown in Figure 9.
It can be seen from Figure 9 that the IWOA algorithm, compared with the NSGA-II and WOA algorithms, can achieve lower operating cost and lower CO 2 emission of IES under the same user needs, so it is more suitable for solving the optimization model with more decision variables.

| CONCLUSION
This paper comprehensively considers multiple uncertainty sources such as the uncertainty of wind and solar output, the uncertainty of energy purchase price and the uncertainty of integrated demand response in IES.On the basis of identifying the characteristics of the uncertain sources, the stochastic scenario method and robust optimization method are used to model the uncertain sources, and the engineering game theory is combined to establish a robust economic dispatch model of the IES facing multiple uncertainties.The results of an example show that: 1. Compared with the deterministic scheduling model and the single uncertainty model, the economic scheduling model considering multiple uncertainties proposed in this paper can further improve the economy and security of the system operation according to the characteristics of uncertainty sources.2. After considering the uncertainty of energy purchase price, the operators of IES may select an appropriate energy purchase plan in real time according to the specific implementation scenario of energy purchase market, so as to improve the economy of system operation.3. The model can effectively coordinate the economy and robustness of dispatching results by reasonably adjusting the values of uncertain budget sets of wind and solar output and integrated demand response.Among them, the change of uncertain budget set of the integrated demand respond has a greater impact on the overall economy and security of the system.

F G U R E 3 4
Forecast of renewable energy and load.The scheduling results of the optimization model.The scheduling results of (A) power dispatching, (B) heating scheduling, (C) cooling scheduling, and (D) energy storage dispatching.Scenario 1: The dispatching model is deterministic and does not consider the impact of uncertain factors.Scenario 2: In the dispatching model, the stochastic scenario method is used to model the uncertainty of energy purchase price.The wind and solar output and the integrated demand response are taken as the predicted values.Scenario 3: In the dispatching model, the robust optimization method is used to model the uncertainty of the wind and solar output and the uncertainty of HU ET AL.

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I G U R E 5 The optimization results for the various scenarios.(A) The optimization results for scenario 1, (B) scenario 2, (C) scenario 3, and (D) scenario 4.

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I G U R E 5 (Continued).
HU ET AL.

6
Comparison of the operating costs and CO 2 emissions in the four scenarios.(A) Operation costs in the different scenarios and (B) CO 2 emissions in the different scenarios.

F I G U R E 7
Impact of the uncertain budget set.(A) Impact of the uncertain budget set on the operating costs and (B) impact of the uncertain budget set.F I G U R E The solution set of Pareto. , , R is the time set; ρ t p is the transferable load before the demand response at time t; ε tt Lp , is the mutual elasticity coefficient of load price at time t and time t'; T re.j.t and P refo.j.t are the actual and predicted output of wind and solar power in the jth scenario during time t; ξ re.j.t is the the wind and solar prediction error; P L.j.t and P Lfo.j.t are the actual and predicted values of the load in the jth scenario during time t; ξ L.j.t is the load prediction error.
valley are the peak, flat, and valley electricity prices during time t; C t base is the basic electricity price during time t; T 1 , T 2 , and T 3 are the corresponding periods of peak, flat, and valley load respectively; α and β are the limit values for real-time electricity price.
T A B L E 1 System parameters.