Optimal Operation Model of Park Integrated Energy System Considering Uncertainty of Flexible Electrical, Thermal and Gas Load

Flexible Load (FL) of electricity, heat and gas can improve the operation economy, flexibility and reliability of PIES. Aiming at the uncertainty of FL in the actual operation of the park integrated energy system (PIES), an optimal operation model of PIES with uncertainty of FL is proposed. Firstly, the uncertainty models of shiftable electric load and transferable load response are established, respectively. And then an adjustable heat load response model considering the uncertainty of solar radiation intensity is established. On this basis, an optimal operation model of PIES considering the uncertainty of the FL with the goal of maximizing the total revenue is constructed and is solved by the enhanced-interval linear programming method. Simulation indicate that FL can improve the operating economy of PIES and renewable energy consumption.


Introduction
The traditional demand response (DR) is gradually developing to integrated demand response (IDR) [1][2][3][4][5]. IDR can promote the cascade utilization of energy in different energy systems and improve the overall energy efficiency of the system [3]. Most of the research on IDR in the park integrated energy system (PIES) are based on the optimal planning. An optimal scheduling model of regional integrated energy system considering the demand response of electricity, gas and heat is proposed in reference [6]. In reference [7], a multi-objective dayahead comprehensive optimal dispatch model of energy hub is established. It is verified that the flexible load can reduce the economic cost and carbon emission of the system. At present, there are still some deficiencies in the research of IDR in PIES. There is seldom research on IDR uncertainty [8][9][10][11]. 2. It is difficult to determine the subjective fuzzy membership function and random distribution function when Fuzzy theory and probability theory are used [12]. In view of the above deficiencies, considering the uncertainty of IDR in PIES, this paper adopts interval optimization method to model IDR. Firstly, the uncertainty of IDR is analysed. Then, considering consumer psychology, the demand response uncertainty models of transferable and replaceable loads are established. Next, this paper constructs the optimal operation model of PIES considering the uncertainty of IDR and uses the enhanced interval programming method to solve it. Finally, an example is given.
p T , f T and v T represent peak, average, and valley periods, respectively. e, 0 t L and e, 1 t L  respectively represent the predicted load and fitting load of t period before and after the implementation of Time of Use price (TOU price). pv   , pf   and fv   represent the interval numbers of peak valley, peak flat and valley load transfer rate. p L and f L are the average value of peak load and period load before the implementation of

Uncertainty of Alternative Load Response
As can be seen from Figure 3, L and g,t L  represent electric load and gas load in t period before and after electrical replacement.

Uncertainty of Adjustable Heat Load Response
Considering the heat inertia of heating buildings and the dynamic change process of room temperature, this paper uses interval number to describe the uncertainty of solar radiation, and establishes the uncertainty model of adjustable heat load, as shown in equations 11 to 14 [11][12] .
w , ri, 1 ri, +1 r ri, s, ci, ve, t nt t nt n t n t n n n n t n t T  represent the indoor and outdoor temperature in t and the temperature of the n wall, respectively. s,t Q  , ci,t Q  and ve,t Q  represent the heat supply of the system, the heat loss of cold air infiltration and ventilation in t, respectively. t  indicates the unit scheduling time, the n wall is exposed to solar radiation, it is 1, otherwise it is 0. wn A , n  and , n t G  indicate the area, radiation absorption coefficient and the light intensity of the nth wall. N is the total number of walls. w R , w C and r C are wall heat resistance, heat capacity and room heat capacity. ci N and en V are the number of air changes per hour and the ventilation rate. r V represents the volume of a heating building. p c is specific heat capacity of cold air. ro ,t  represents the outdoor air density in time t.

Objective Function
Taking the maximum total income as the optimization objective, which is expressed by Equation 15 to 20, including income from energy sales S C  , reduced purchasing cost P C  , operating cost OM C  , the cost of carbon emissions CE C  , cost of abandoned wind turbine (WT) and photovoltaic (PV) Ab C  and T is the total operation hours, T=24. k = e, h, g are electricity, heat and gas respectively. , k t c and , k t L  are the selling price and selling energy of k energy in t period respectively. E,t c and G ,t c are the price of power and gas respectively. e,t P  and g,t P  represent the power purchase and gas purchase in t period respectively. NG L is low calorific value of natural gas. om, j c is the operating cost of the j equipment unit. , j t P  is the output of j in t period.  is the treatment cost per unit mass of CO 2 . e  and g  represent the equivalent carbon emission coefficients of electricity purchase and gas purchase respectively.  is the cost of abandoned WT and PV. Ab,t P  is the amount of abandoned WT and PV. max etr P is the reserved power   T and min ri,t T represent the limit value of indoor temperature in t respectively. max ch T is the maximum change of room temperature in the adjacent period.

Enhanced-interval Linear Programming
In this paper, an enhanced interval linear programming (EILP) model in reference [9] are selected. The general form of EILP model are shown in Equation 36: EILP model assumes that when j=1,2,…,k, 0 j c   , and when j=k+1,k+2,…,n, 0 j c   .

1) The first sub model is shown in Equation 37
: To ensure that the optimal solution ,opt The model is solved by CPLEX [9] .

Case Conditions
In this paper, an IES system in northern China is selected as an example for simulation analysis. Relative parameters are listed in Table 1~3 [8][9][10] . Gas price is 3 yuan/m 3 .

Analysis of Example Results
Three scenarios (scenario 1 is without IDR, scenario 2 is with deterministic IDR, and scenario 3 is with IDR uncertainty) are set for simulation and comparative analysis. Forecast curve of temperature, wind turbine and photovoltaic output and electricity, gas, and heat load is shown in Figure 4.      Comparison of heat load curves in each scenario. In Figure 5 to Figure 7, the implementation of IDR can calm peaks and valleys, improve the operation economy of PIES and the level of renewable energy consumption. In Figure 5, the difference between peak and valley of the original electric load is 2297.11kw, the difference is reduced to 1942.27kw after considering the deterministic IDR, with a decrease of 15.45%. The reason is that the alternative load chooses gas instead of electricity during the peak period. In table 4, considering the uncertainty of IDR in scenario 3, the total income of IEA fluctuates with the range of ± 1.24%. IDR's participation will increase the total income of IEA and the level of renewable energy consumption, while the uncertainty of IDR will make the total income of IEA fluctuate.

Conclusion
Considering the difference of consumer psychology of end users, this paper established the response uncertainty model of transferable electric load and replaceable load, and establishes the response uncertainty model of adjustable heat load.
(1) IDR's participation can achieve peak load reduction and valley filling, and effectively improve the economy of the system operation and the level of renewable energy consumption.
(2) Considering the uncertainty of IDR, it can more comprehensively and accurately analyse the actual effect of IDR in the process of system operation.
(3) The fluctuation degree of load has a direct influence on the system operation results, and the fluctuation degree dof electrical load has a great influence on the system operation and the stability of the total revenue of the integrated energy aggregators.
In the follow-up study, how to make risk decision according to the impact of IDR uncertainty on the optimal operation of PIES to reduce the risk of system operation would be studied.