An optimal scheduling method for integrated power and heat system with multiple thermal flexibilities

Integrated power and heat system (IPHS) is a typical multi-energy system which involves power system and district heating system (DHS). The utilization of thermal flexibilities in the joint operation of power system and district heating system has shown the potential to improve energy efficiency and economic performance. In this paper, an optimal scheduling method for IPHS with multiple thermal flexibilities is proposed. Thermal flexibilities of electric boilers and district heating network (DHN) are modelled and analysed, in which the flexibility of DHN is described by a detailed node-based quasidynamic model. The proposed scheduling method is to minimize the operation cost of IPHS. Case study is carried out on a typical IPHS with a 6-node power system and a 12-node DHS. Simulation results show that the scheduling method can reduce the operation cost of IPHS and improve wind accommodation.


Introduction
Integrated power and heat system (IPHS) is one of the most common form of multi-energy system, which combine power system and district heating system (DHS) [1], as shown in Fig. 1. And thermal flexibilities in IPHS can improve economic efficiency, system reliability and wind accommodation [2].
Thermal flexibility is a promising option to improve IPHS operation performance, which has increasingly gained attention. On the one hand, thermal equipment such as electric boiler, heat pump and thermal storage device can offer thermal flexibility. A scheme of configuring electric boilers for thermal power plants to increase wind power accommodation is evaluated in [3]. Energy balance in IPHS integrated with large capacity thermal energy storage is analysed in [4]. On the other hand, thermal inertia of district heating network (DHN) can offer additional operational flexibility of heat source. A unit commitment model of IPHS considering the thermal inertia of DHN is proposed in [5], which improves wind power accommodation. An MLIP model to evaluation the annual performance of DHS to use DHN flexibility as short-term thermal energy storage is proposed in [6].
This paper proposed an optimal scheduling method for IPHS with multiple thermal flexibilities. In the following sections, flexibility from DHN is analysed and described as a quasi-dynamic model. Then the optimal scheduling model is proposed and testes on a IPHS with a 6-node power system and a 12-node DHS. Case study verifies the effectiveness of our scheduling model.   Fig. 2, DHN is composed of primary pipe network and secondary pipe network, which is similar to transmission network and distribution network in power system. The primary pipe network is not connected directly to the secondary pipe network in DHN, and thermal energy is exchanged through a heatexchanger station. Because the heat storage capacity of primary pipe network is considerably larger than that of secondary pipe network, only the thermal dynamics in primary pipe network is considered. Besides, each heatexchanger station and the following secondary pipe networks are denoted as a heat load.

Primary pipeline model
The quasi-dynamic pipeline model needs to reflect transmission delay and heat loss character of pipelines. Transmission delay of a pipeline is the time interval that heat carrier needs to flow from the inlet to the outlet. In this paper DHS is assumed to operate in a constant flow rate mode, in which the transmission delay is constant in the dispatch process. The calculation of transmission delay is stated as: where j  is the transmission delay of pipeline j , h; j l is the length of pipeline j , m; j v is the velocity of heat carrier, m/s. Taking transmission delay into account, the relationship between inlet temperature and outlet temperature can be denoted as: where out , ' t j T is the outlet temperature of pipe j at time t that ignore transmission loss, ℃; in , ℃. Transmission loss occurs when heat carrier flows through the pipeline, and it is related to heat loss coefficient and ambient temperature, which is formulated as follow: where , out t j T is the outlet temperature of pipeline j at time t , ℃; am t T is the ambient temperature at time t , ℃; j k is the heat loss coefficient of pipeline j , W/(mꞏ℃); w c is the specific heat capacity of heat carrier, kJ/(kgꞏ℃); j q is the mass flow rate of heat carrier in pipe line j , kg/s.

Temperature mixing model
According to the thermal energy conservation, the thermal energy flowing into one node is equal with the thermal energy flowing out. The temperature mixing can be concluded as: where pipen S and pipe+ n S are the sets of pipelines starting from node n and pipelines ending at node n , respectively.
In addition, the thermal carrier in the DHN should satisfy the node continuity equation: the amount of the fluid flowing into one node is equal with the fluid flowing out, which can be denoted as:

Heat-exchanger station model
The heat-exchanger station realizes the heat transfer between primary pipelines and secondary pipelines in the DHN, which can specifically meet the demand of the user's heat load by adjusting the flow rate in the secondary network. The heat exchange of heatexchanger station is formulated as:

Objective function
The optimal scheduling model of the IPHS with multiple thermal flexibilities has the objective function to minimize the total operational cost of the IPHS. At the same time, in order to promote the accommodation of wind power, the penalty cost of wind curtailment is added to the total operating cost, which reflects the principle of giving priority to the wind power. The expression of the objective function is stated as: are the minimum spinning reserve required by power system at time period t , kW.

DHS constraints
In addition to (3), (5)-(7), DHS also need temperature constraints for supply and return heat carrier, which is denoted as: are the upper and lower limit of return temperature, ℃.

Generation constraints
CHP, thermal unit, wind turbine and electric boiler are considered in the proposed scheduling method, and their constraints are shown as follows.
1)CHP Back-pressure CHP has a fixed power-to-heat ratio, its power and heat output constraints is stated as: 2)Thermal unit Thermal unit constraints include power limit and ramping limit, as shown below: In this paper, a 6-node electric power system and a 12node heating system are used as a test system [8], and the structure is shown in Fig. 3. The second heatexchanger stations are built at Nd1~7, and the first heat exchange station are built at Nd8. The heating network pipeline parameters are shown in Table 1. The electrothermal coupling equipment includes CHP units and electric boilers located at grid node 6/heating network node 8. Electricity load, heat load and wind power forecast output are shown in Fig. 4 [9], the parameters of the system's conventional units, CHP units and electric boilers are shown in Table 2 [10]. The scheduling period is 24h, and the scheduling interval is 1h. The heating network temperature can still return to the initial value after a scheduling cycle.    7000  2  9  1  250  1000  3  9  10  700  6000  4  10  2  250  1000  5  10  3  700  1000  6  10  11  500  4000  7  11  4  700  1000  8  11  5  250  1000  9  11  12  700  2000  10  12  6  250  1000  11  12  7 700 1000  To demonstrate the effect of optimal scheduling method for IPHS with multiple thermal flexibilities, three cases are introduced.
Case I is the proposed model in this paper, which considers thermal flexibilities of electric boilers and DHN.
Case II considers thermal flexibilities of DHN, without electric boilers.
Case III ignores thermal flexibilities of electric boilers and DHN.

Economic analysis
The comparison results of the costs under the above three cases are shown in Table 3 during a dispatching cycle. Compared with case II and case III, the power unit operating cost, CHP unit operating cost and wind curtailment cost have all decreased in case I. In the scheduling cycle, the total operating cost of case I is reduced by 0.7% compared with case II and 3.6% compared with case III. Case Ⅰ has 65MW less wind curtailment than case II, and 339MW less wind curtailment than case III. The dispatching scheme under case 1 can reduce wind curtailment, and the total operation cost is reduced.

Wind power consumption analysis
The optimization results of the electrical power in the three cases are shown in Fig. 5-7. Comparing Fig. 5-7 and Fig. 4, it can be seen that during the period of 1:00-8:00 when the wind power is relatively high, the heat load is relatively high, which leads to a relatively highpower output generated by the CHP unit. Power units have minimum power generation that cannot be further peaked, resulting in insufficient space for the system to absorb wind power. In case II, equipped with electric boilers, the excess wind power can be used for heating, which increases the wind power consumption, reduces the necessary power generated by the CHP unit. Considering the thermal flexibility of the heating network, the CHP can adjust its power output according to the variations of wind power. For example, during the periods of high wind power and low electrical load, CHP appropriately reduce their own power and heat output to increase wind power consumption, and at the same time, the insufficient heat output is suppressed by the heat network. Case I has been coordinated by the source and network of the electricity-heat integrated energy system, and the electricity load is more provided by wind power, achieving the wind power consumption.

Conclusion
This paper proposed an optimal scheduling method for IPHS with multiple thermal flexibilities. A detailed formulation of the DHN model is proposed as a quasidynamic model. The results of case study show that our scheduling method can reduce the total cost and improve wind accommodation for IPHS. And both the flexibility of electric boiler and DHN can enhance IPHS operational flexibility.