Abstract
Large fluctuations may occur on the energy supply and the load sides when large-scale renewable energies are integrated, leading to great challenges in power systems. The renewable power curtailment is especially numerous in the integrated electricity-heat energy system (IEHES) on account of electricity-heat coupling. The flexible resources (FRs) on both the energy supply and load sides are introduced into the optimal dispatch of the IEHES and further modeled to alleviate the renewable fluctuations in this paper. On the energy supply side, three kinds of FRs based on electricity-heat coordination are modeled and discussed. On the load side, the shiftable electricity demand resource is characterized. On this basis, the solution for FRs participating in IEHES dispatch is given, with goals of maximizing the renewable penetration ratio and lowering operation costs. Two scenarios are performed, and the results indicate that the proposed optimal dispatch strategy can effectively reduce the renewable energy curtailment and improve the flexibility of the IEHES. The contribution degrees of different FRs for renewable integration are also explored.
IN recent years, renewable energy has received increasing attention from all over the world due to the deterioration of the ecological environment and the energy shortage crisis [
This phenomenon can be attributed to the strong random volatility and intermittence of wind power and photovoltaics [
Many researches have been carried out on electricity-heat coordination techniques. On CHP units, [
On the load side, demand response (DR) has been widely used to provide support for power system stability. Reference [
All the above researches have improved the operation flexibility of the electric power system (EPS) to a certain degree. However, the orderly classification and modeling for FRs and their contribution degrees for renewable penetration are seldom discussed. And the optimization solution for various FRs participating in IEHES dispatch is rarely mentioned in the literature. The contributions of this paper are described as follows. Firstly, different FRs are orderly classified and modeled for renewable penetration. Secondly, the solution for FRs participating in IEHES dispatch is given, with the goals of maximizing the renewable penetration ratio and lowering operation costs. Thirdly, the contribution degrees of different FRs for renewable integration are explored.
The remainder of this paper is organized as follows. Section II presents the detailed modeling and analysis of FRs in an IEHES. Section III presents the electricity-heat dispatch problem and solution in an IEHES. Section IV discusses cases that verify the effectivity of the proposed method. Section V provides the conclusion.
This paper studies an IEHES, which contains two subsystems, i.e., the EPS and the DHS, as shown in

Fig. 1 Schematic of IEHES.
Various technologies and methods that can promote the renewable penetration are introduced above such as heat pumps, EBs, and thermal inertia of heating pipe networks. Considering practicality and feasibility, two types of FRs are focused on in this paper. The first type is electricity-heat coordination resources (EHCRs), which contain the electricity decoupled by the HSD, the electricity decoupled by the heat storage in DHN, and the convertible electricity from the EB. The second one belongs to the load side and is called shiftable electricity demand resource (SEDR). The characteristics and models of the mentioned FRs are presented below.
1) Electricity Released by HSD
An HSD stores heat from CHP units when the electricity demand is greater than the electricity productions under the rated heating supply condition. The heat storage in the HSD compensates for the lack of heating from the CHP units when their electricity productions are limited. The heat storage capacity of the HSD determines the released electricity quantity. The constraints of heat storage and release power can be expressed as:
(1) |
(2) |
(3) |
where and are the heat storage and release power of HSD at time , respectively; and and are the maximum heat storage and release power of HSD , respectively. Moreover, the heat storage and release cannot occur simultaneously.
The constraints of heat storage are expressed as:
(4) |
(5) |
(6) |
(7) |
where is the heat storage of HSD at time ; is the upper limit of ; is the energy loss; is the time interval; and is the heat loss coefficient. In addition, the heat storage at the last time is equal to that at the initial time.
As shown in

Fig. 2 Electrothermal coupling characteristics of CHP unit with HSD.
2) Electricity Released by Heat Storage in DHN
1) Storage in DHN pipeline
The pipeline structure of the DHN is shown in
(8) |
(9) |

Fig. 3 Schematic of DHN pipeline connection.
where is the total heat input from the heat source at time ; and are the inlet and outlet water temperatures of the PHN, respectively; and are the mass flow rate and specific heat capacity of water in the PHN main pipeline, respectively; is the heat power transfer from the PHN to SHN at time t; and are the inlet and outlet temperatures of PHN branch pipeline at time , respectively; and is the mass flow rate of PHN branch pipeline at time .
The pipeline transmission time delay causes thermal inertia. The pipeline length of the PHN can reach several kilometers, so we can use a considerable amount of water in the pipeline to store or release heat.

Fig. 4 Thermal inertia of PHN.
2) Storage in building
The thermodynamic model of the equivalent building is introduced in [
(10) |
(11) |
where is the indoor temperature of equivalent building at time t; is the outside environment temperature; and are the thermal capacity and resistance of building , respectively; and is the heat lost to the outside environment of building at time . Part of the heat from the SHN is stored inside the building envelopes. The other part is lost to the external environment to maintain the indoor temperature.
As shown in

Fig. 5 Thermal inertia of equivalent building.
The thermal inertia of the PHN and equivalent buildings reflects the passive heat storage capacity of the DHS, which can adjust the heat load of the CHP unit, thereby indirectly alleviating the serious thermoelectric coupling and improving the scheduling flexibility of the IEHES.
3) Convertible Electricity by EB
EBs can convert electricity into heat power for the heating demand when the electricity productions are excessive. For direct heating EBs, the electricity from the EPS is directly converted to heat and sent to the DHS, thereby realizing energy conversion in the system. The electricity consumption is linearly related to the heat putout:
(12) |
(13) |
(14) |
where and are the electric power input and heat power output of EB at time , respectively; is the conversion coefficient of EB ; and and are the upper limits of the electric and heat power outputs, respectively.
EBs are usually installed near the CHP unit as a heat source. The electrothermal coupling characteristics of the CHP unit with the EB is shown in

Fig. 6 Electrothermal coupling characteristics of CHP unit with EB.
The orderly utilization of SEDR can reduce the electricity demand fluctuations and promote the renewable penetration. PDR is an efficient approach to motivating electricity consumers to participate in DR.
The load change rate and electricity price change rate are expressed as:
(15) |
(16) |
where is the electricity load change; is the original value of electricity; is the electricity price change; and is the original electricity price.
In economics, the relationship between price and load change rates is expressed as:
(17) |
(18) |
where and are the respective self-elastic and mutual-elastic coefficients of electricity and price, respectively, which represent the load DR to the electricity prices in current period or another period .
We use the elasticity matrix to describe the load DR to electricity prices in multiple periods:
(19) |
where and is the scheduling period; and E is the price-based demand elasticity matrix, in which the main diagonal is the self-elasticity coefficient, and the sub-diagonal is the mutual elasticity coefficient.
Considering the consumer satisfaction constraints, the electricity consumption satisfaction index is introduced to ensure that the electric load change is controlled within an acceptable range:
(20) |
(21) |
where Sat is the electricity consumption satisfaction index; and is the lower limit of Sat.
The sum of load changes in the entire scheduling period is zero, so the total load demand remains unchanged:
(22) |
The electricity price change at each time is limited to prevent excessive fluctuations:
(23) |
By adjusting the electricity price to change the load demand, we can improve the integration of renewable energy and the flexibility of the IEHES.
The objective of IEHES dispatch is to minimize the total cost:
(24) |
where is the total cost; and are the costs of coal consumption of the CHP and CTP units, respectively; and and are the curtailment penalty costs of wind power and photovoltaics, respectively.
The total cost consists of the unit operation and renewable energy curtailment costs. The purpose of adding renewable energy curtailment costs is to increase the renewable penetration. The penalty function is expressed as:
(25) |
(26) |
where and are the forecasting and actual values of wind power output, respectively; and are the forecasting and actual value of photovoltaic output, respectively; and and are the penalty factors.
The operation costs of CHP and CTP units can be expressed as a quadratic function of unit output:
(27) |
(28) |
where and are the cost coefficients of the CHP and CTP units, respectively; and are the electric power output and the extraction steam mass flow of CHP units, respectively; and is the electric power output of CTP units.
The electric power and heat source flow of CHP unit can be formulated by a convex combination of extreme points [
(29) |
(30) |
(31) |
where is the index set of the CHP units; is the electric power output of CHP unit at time ; is the extraction steam mass flow of CHP unit at time ; is the total number of extreme points of the feasible operation area; is the combination coefficient of extreme point for CHP unit at time ; and and are the electric power and extraction steam mass flow of corner point of CHP unit , respectively.
The power output of the CTP units is constrained by their generation capacity:
(32) |
where is the electric power of CTP unit at time ; and and are the upper and lower limits of , respectively.
The CTP and CHP units have ramping constraints in two adjacent scheduling intervals:
(33) |
(34) |
where and are the ramping capacities of the CTP and CHP units, respectively; and is the time interval.
The actual power outputs of wind turbines and photovoltaic units should be limited by the predicted available power:
(35) |
(36) |
where and are the actual power outputs of wind turbine i and photovoltaic unit i at time t, respectively; and and are the predicted available powers.
The transmission lines of the EPS have power flow constraints. The transmission power of each branch should not exceed its limit:
(37) |
(38) |
where is the transmission power of branch at time ; is the transmission power limit; is the element of the transfer distribution factor matrix of the DC power flow, representing the impact of the injected power of node on line ; Nu is the number of various types of power unit; is the power output of unit at time ; NL is the number of load nodes; and is the load demand of node j at time .
The total generated power of various units in the EPS should be balanced with the load demand:
(39) |
where is the EPS electric load at time ; is the number of the CTP units; is the number of wind turbines; is the number of photovoltaic units; and is the number of EBs.
The constraints of the PDR are defined in (15)-(23).
The extraction steam from the CHP unit is used for direct heating and heat storage. The heat transfer ratio links the extraction steam flow rate and the heat transfer power:
(40) |
(41) |
(42) |
(43) |
where and are the respective extraction steam flows for direct heating and heat storage, respectively; and are the corresponding heat power; and and are the heat transfer ratios that indicate the heat transfer capacity of the extraction steam for direct heating and heat storage, respectively.
(44) |

Fig. 7 Schematic of heat source.
where is the thermal power entering the DHN at time .
A general pipeline transmission model [
(45) |
where is the pipe outlet average temperature at time ; and are the pipe inlet temperatures at time and , respectively; k1, k2, and the coefficients a, b, c are related to the parameters of the pipeline; and the product of the soil temperature and the coefficient c represents the heat loss caused by the heat exchange between the pipe and the outside.
The temperature mixing constraints of the pipeline node model are used to ensure energy conservation:
(46) |
(47) |
where and are the outlet temperature and mass flow rate of pipeline at time , respectively; and are the inlet temperature and mass flow rate of pipeline at time , respectively; and are the outlet and inlet pipeline indices of node k, respectively; and is the index set of nodes in the DHN.
The water outlet and inlet temperatures in the pipeline cannot exceed their upper and lower limits:
(48) |
(49) |
To ensure the thermal comfort of heat consumers, the equivalent buildings have the following constraints:
(50) |
(51) |
(52) |
(53) |
where is the limit of temperature change in adjacent time; is the thermal comfort temperature related to the outside temperature and correlation coefficients and ; and is the indoor temperature limit.
Other constraints of the DHS are mentioned in (1)-(14).
As shown in

Fig. 8 Schematic of optimal scheduling process.
We choose a region in China for the simulation study. The electric load, outdoor temperature, and renewable energy output on a typical day are shown in

Fig. 9 Electric power and temperature curve on a typical day.

Fig. 10 Diagram of 6-bus EPS and 6-node DHS test system.
The HSD and the EB are generally installed near the CHP unit to provide assisting heat source, and we combine the two for investigation. The renewable integration before and after configuration is shown in

Fig. 11 Scheduling results with HSD and EB. (a) Wind power. (b) Photovoltaic. (c) Heat storage of HSD. (d) Heat power of EB.
As shown in

Fig. 12 Scheduling results with thermal inertia. (a) Wind power. (b) Photovoltaic. (c) PHN inlet and outlet temperatures. (d) Indoor temperature.
The PDR realizes synergy between the power supply and load demand through the shift of demand load.

Fig. 13 Scheduling results with PDR. (a) Wind power. (b) Photovoltaic. (c) Electric load. (d) Day-ahead electricity price.
The above simulation results indicate that the three types of FRs play an important role in reducing the curtailment of renewable energy. The contribution degrees of different FRs are compared in
After separately discussing the operation and influence of flexible scheduling resources, we further analyze the combination method.
1) Case 1: reference case, where none of the FRs are considered.
2) Case 2: the HSD and the EB are considered on the heat source side.
3) Case 3: the HSD and the EB on the heat source side and the thermal inertia of DHS are all applied in scheduling.
4) Case 4: three types of FRs are considered.

Fig. 14 Comparison of optimal scheduling results. (a) Wind power. (b) Photovoltaic. (c) Electric power of CHP unit. (d) Heat power of CHP unit.
The total integrations of renewable energy and system cost in four cases are listed in

Fig. 15 Renewable energy curtailment and cost reduction. (a) Wind power curtailment. (b) Photovoltaic curtailment. (c) Cost reduction.
As shown in

Fig. 16 Diagram of 30-bus and 12-node large system.
The 30-bus EPS consists of two CHP units, three CTP units, a wind farm, and a photovoltaic unit, which are located at buses 1, 2, 5, 8, 11, 13. Two CHP units, 4 HSDs, and 4 EBs form the heat source for DHS heating. There are six buildings in the 12-node DHS serving as the thermal loads in the IEHES.
Similar to 6-bus and 6-node test system, we use the 4 cases listed in

Fig. 17 Comparison of optimal scheduling results. (a) Wind power. (b) Photovoltaic.
All the simulations are performed on a computer with Intel Core i7 CPU and 16 GB memory under MATLAB R2016a and CPLEX environment. The simulation times of the 4 cases in both systems are listed in
In this paper, FRs on the power supply and load sides of an IEHES are introduced to IEHES dispatch for renewable penetration. Three kinds of EHCRs and the SEDR are modeled in detail. The solution for FRs participating in IEHES dispatch is furthermore given, with goals of maximizing the renewable penetration ratio and lowering operation costs. A 6-bus EPS and 6-node DHS test system is tested, and the contribution degrees of different FRs for renewable integration are also explored. The results show that the renewable curtailments are nearly eliminated after introducing FRs: the wind power curtailment rate decreases from 10.5% to 1.4%, and the photovoltaic curtailment rate decreases from 10.5% to 0.9%. Furthermore, a 30-bus and 12-node system is performed, and the results prove the universality of the proposed approach in real applications. In future work, IEHES optimization considering electricity storage together with the orderly dispatch and management for different FRs will be explored.
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