Optimal Dispatch of Integrated Energy System Considering Demand Response and Load Inertia

Renewable energy has the characteristics of strong anti-peak regulation and uncertainty, which cause severe challenges to system peak shaving and renewable energy accommodation. To cope with the challenges of system peak shaving and renewable energy accommodation, this paper proposes an optimal dispatch model of integrated energy system (IES), which considers the price-based demand response and load inertia. Firstly, the impact of changes in energy price on users’ energy consumption is analyzed, and the cool and heat loads inertias are considered in their unbalanced constraints. Secondly, the objective function of the minimum operation costs of the IES is established, including the penalty cost of wind power and photovoltaics curtailments, and operation costs. Finally, the optimal dispatch model of IES is established and solved by YALMIP and GUROBI, respectively. The proposed model is compared with other conventional models. The accommodation capacity of renewable energy with the proposed model is enhanced.


Introduction
Renewable energy power accommodation is limited due to its uncertainty [1]. Peak loads are shifted to the valley with the demand response and the cooling and heating loads inertias in the integrated energy system (IES) [2]. Therefore, it is of great significance to study the impact of demand response and heat and cool loads inertias on improving renewable energy accommodation in the IES. Users adjust their energy consumption behaviors and habits according to changes in energy price with the demand response [3]. The effect of electricity price demand response on users' electricity consumption behaviors is analyzed [4]. However, the effects of gas. price changes on user gas consumption and renewable energy accommodation are not considered. References [5] study the effect of gas price on user gas consumption behaviors, but the effects of gas price changes on user electricity consumption are not studied. Reference [6] analyzed the impact of changes in gas price on user electricity consumption and electricity price on user gas consumption. However, the impact of pricebased demand response on renewable energy accommodation is not studied. The supply and demand of the cool and heat loads can be staggered in time with the cool and heat loads inertias [7]. The supply and demand of the cool and heat loads are balanced at all times, which limits the renewable energy accommodation [8]. References [9] study the effects of the cool and heat loads inertias on the renewable energy accommodation and the operation costs of the IES. However, the effects of price-based demand response and cool and heat loads inertias on renewable energy accommodation and operation costs of the IES are not studied. On the basis of the abovementioned studies, in this paper, we propose an optimal dispatch model of IES that considers the demand response and load inertia to enhance renewable energy accommodation. The effects of demand response and load inertia on renewable energy accommodation are fully considered.

Price-based demand response
The price-based demand response includes self-price elasticity and cross-price elasticity demand response. The electric load demand response is obtained by (1).
where r el P is the electric load demand, P el is the electric load demand without demand response, and △ P el is the electricity price-based load changes. The gas load demand response is expressed by (2).
where r gl P is the gas load demand, P gl is the gas load demand without the demand response, and △P gl is the price-based load changes. The elastic loads can be shown in (3).     are the self-price and cross-price elasticity matrix of gas load, △P ec,t is the electricity price change in period t, P ec,t is the electricity price in period t without demand response, △P gc,t is the gas price change in period t, and P gc,t is the gas price in period t without demand response.

load inertia
The actual temperature of heat load may be higher or lower than the standard temperature, due to the heat inertia. The heat power of the heating system considering thermal inertia is limited by (6).
where Ph,t is the heat power of the heating system at time t, μ and ν are the inertia coefficients of the heating system, Phl,t is the heat power load. The elasticity of human thermal comfort can be expressed by the predicted mean vote (PMV) index. The PMV index calculation formula is expressed by (7).
where T is the standard heating temperature. The heat power unbalance is calculated by (9).
,min ,m ax , , , The cool load, similar as the heat load, has the inertia. The cool power unbalance is limited by (10).
where Pc,t is the cooling power of the cooling system at time t, ψ and ω are the inertia coefficients of the cooling system, Pcl,t is the cool power load.

Integrated energy system model 1) Combined heat and power (CHP) model.
The CHP has the constraint of "setting power with heat". The electric-heat characteristics of CHP can be described in (11) [10] .
where P e,t is the electric power of CHP at time t, P e,min and P e,max are the min and max electrical power of CHP, P h,t is the heat power of CHP at time t.
The constraints of CHP are expressed by (12).
where r l and r u are the lower and upper ramp rate limits.
where Pgs,t is the gas power generated by P2G at time t, and α is a conversion coefficient. The constraints of P2G are expressed by (14).
where Pmts,t is the gas power consumed at time t, ηmt is a conversion coefficient, Pmth,t is the heat power . The power and ramp rate constraints of the micro gas turbine are as follows.
,min ,max where P mt,min and P mt,max are the lower and upper power limits for the micro-gas turbine, r l,mt and r u,mt are the lower and upper ramp rate limits, respectively.

Objective function
The objective function of the minimum operation costs of the IES are established by (17).
( ) where C 1 is the operation cost of CHP, a 1 , b 1 and g are the operation cost coefficients of CHP.
2) Operation cost of P2G. where C 2 is the operation costs, c 1 is the operation costs coefficients of P2G.
3) Operation costs of micro gas turbine. where C 4 is the cost of wind curtailment, a 4 is a cost coefficient of wind power curtailment, and P cwind,t is the wind power curtailment at time t. 5) Cost of photovoltaics curtailment.
where C 5 is the cost of photovoltaics curtailment, a 5 is a cost coefficient of photovoltaics curtailment, and P cpv,t is the wind power curtailment at time t.

Constraints 1) Electric power balance.
Total generations and electric loads must be balanced at each operation period as described in (23).
The upper and lower limits of the electricity price and the gas price change range do not exceed ±50%. The load and air load response do not exceed 10% of the load.

The setup of simulation
The simulation parameters of the IES are shown in Table 1. Fig. 1 shows the forecasts of load demand, wind power and photovoltaics, and forecasts data are taken from the comprehensive demonstration area in Liaoning Province, China.

Optimization model dispatch results analysis
To verify the effectiveness of the proposed optimal dispatch model, two models are compared in this paper. Model 1: An optimal dispatch model that with demand response and load inertia. Model 2: An optimized dispatch model that without demand response and load inertia. Figs. 2-5 show the comparison of electricity price, gas price, electric load, and gas load with two models. During the high-wind power and low-electric load period of (1:00 -4:00) and (22:00 -24:00), the electricity price is reduced and the gas price is increased, and the electric load demand is increased. Users transfer the self-elastic response electric load demand to the trough, and transfer the crosselastic response gas load demand to the electric load, which increase the wind power accommodation. During the period of (5:00 -6:00), (15:00), (20:00), the electricity price and gas price are increased, and the user reduce the electricity and gas consumption according to the increase in the electricity and gas price. The self-elastic response power load and gas load are transferred to the trough period, so the electric load demand and the gas load demand are reduced. Therefore, the effect of peak shaving is achieved. During the high-electric and low-gas period load demand of (7:00 -10:00), (16:00 -19:00) and (21:00), the electricity price is increased and gas price is reduced. User transfers the self-elastic response electric load during this period to the trough period. The self-elastic response gas load in other peak periods is transferred to this time period, and the electric load of the cross-elastic response is transferred to the gas load. The electric load demand is reduced and the gas load demand is increased, which has a peak-shaving effect on electric load demand, and the demand for gas load has the effect of filling the valley. During the high-wind power, high-photovoltaics, high-electric load demand and high-gas load demand period of (11:00 -14:00), the electricity price is reduced and the gas price is increased, user transfer the self-elastic response electric load of other peak periods to this period, so the electric load demand is increased. According to the comparison of electricity price and gas price, the user transfers the gas load demand of the cross-elastic response during this period to the electric load demand. Therefore, the electric load demand is increased and the gas load demand is reduced, and the wind power and photovoltaic accommodation are enhanced. Figs. 6-7 show the comparison of heat load and cool load optimization with two models. During the high wind power and heat load period, the heat load demand is reduced due to the heat load inertia. The heat output of is reduced, and wind power accommodation is improved. During the high-wind power and photovoltaic period, the heat load demand is lower, the heat load demand and the heat output is reduced, and photovoltaic accommodation is improved. Power MW Figure 6. Comparison of heat load optimization with two models. With the demand response, the electricity price and gas price are optimized, and users are guided to transfer the electric energy during peak hours to the low period. The electric load and gas load during this period are transferred, which improve wind power and photovoltaics accommodation.

Conclusion
Aiming at improve the wind power and photovoltaics accommodation, an optimal dispatch model of IES based on demand response and the cool and heat loads inertias is proposed in this paper. The proposed model can reduce the peak load, fill the trough load, and the supply and demand of the cool and heat loads fluctuate within a certain range, so the wind power and photovoltaics accommodation are increased. The simulation results show that, with the proposed model, the wind power and photovoltaics accommodation are increased. Compared Model 1 with Model 2, the wind power and photovoltaics accommodation are increased due to the demand response and the cool and heat loads inertias.