Optimal Dispatch of Regional Integrated Heating and Power System Based on Differential Thermal Inertia Model

. As the physical carrier of Energy Internet, regional integrated energy system (RIES) has become an important role for improving comprehensive energy utilization efficiency. First, a subtle thermodynamic model of buildings and water-heating network was constructed based on differential thermal inertia model. Different from the traditional single-layer wall thermal inertial model, this paper constructed multi-layer wall thermal model. Then, an optimization scheme combining electricity and heat was established. The optimization results show that, compared with the traditional single-layer wall thermal inertia model, the proposed multi-layer wall thermal inertia model has better performance. The proposed comprehensive energy optimization scheme can reduce the cost of electricity while maintaining indoor comfort, and can provide a reference for the system operation status for distribution network dispatching.


Introduction
The regional integrated energy system (RIES) is considered to be the main form of energy for future human society. The RIES is mainly composed of energy supply networks, energy exchange links, energy storage links and a large number of users. As an efficient measure to improve energy efficiency, the RIES have gained rapid development in recent years [1].
Over the years buildings have gradually evolved into multi-energy carriers owing to their significant thermal load. In order to achieve higher utilization efficiencies, combined cooling, heating and power (CCHP) systems have been identified as potential solutions [2]. In reference [3], an integrated electricity-gas-heat network model was developed, but the piecewise friction coefficient model of a water-heating network was not considered. Reference [4] uses embedded wall-type pipes to heating the building and improves the building energy storage. Air conditioners are also involved in voltage regulation, demand response. If the air-conditioning load is controllable, an optimized scheduling model can be proposed, which can not only reduce the peak load, but also dispatch quickly and accurately in an emergency [5]. At the same time, due to the thermal inertia of the building, the change of air conditioning load in a short time will not affect people comfort [6]. Therefore, when the thermal inertia process is modeled more accurately, the airconditioning load can be effectively dispatched economically [7].
The traditional single-layer wall thermal inertia model is quite different from the actual heat transfer process. This paper proposes a layered thermal inertia model to simulate the heat in the system in detail. In addition, this paper introduces the water-heating network model considering the piecewise fiction coefficient.
For the above problems, this paper first introduces multi-layer wall thermal inertia model as a thermal model of the building integrated energy system. Then this paper introduces the water-heating network model considering the piecewise fiction coefficient. Based on the building thermal inertia model combined with grid constraints and water-heating network constraints, an optimized plan for the RIES is established. Finally, the analysis results based on the IEEE-13 bus system show that the multi-layer wall thermal inertia model proposed in this paper can accurately describe the heat transfer process. The proposed RIES optimization scheme can reduce the users' electricity purchase cost while maintaining indoor comfort. It can also optimize the power flow of distribution network, which is of great significance to the safe and stable operation of power system.

Thermal Model of RIES
In this paper, wall and floor are modeled according to the thermal inertia model. We take the wall as an example to introduce the thermal inertia model.

Multi-layer Thermal inertia model
Reference [8] proposed to use the thermal resistance and thermal capacity model to simulate the heat transfer process of the room. The traditional thermal inertia model does not consider the heat transfer process inside the wall, so there is a big gap with the actual process. In order to simulate the heat absorption and release process of the Suppose that as the heat passes through the wall, each wall will absorb some of the heat and then release it. Therefore, in the thermal inertia model of multilayer wall, the dynamic relationship between the temperature and heat of each part can be expressed as equations (1) -(4): ( ) ac Q t is the heat generated by the air-conditioning. In this paper, the energy efficiency coefficient is multiplied by the electric power of the air-conditioning to calculate the cooling capacity generated by the airconditioning [9].

Water-heating network model
For water-heating network model, we assume that it has only one heat source and one loop.
We define three types of temperatures variables [10]: The supply temperature s T is the temperature of hot water flowing into the load node. The outlet temperature o T is the temperature of hot water flowing out of the node. The return temperature r T is the temperature of hot water following the mixing of hot water flowing out of the load node with hot water in other pipelines.
The thermal power is: where n  is the thermal load power at load node and p C is the specific heat of water. As hot water flows from the beginning to the ending of the pipeline, the temperature of the hot water drops. Supposing that the thermal model does not have the thermal dynamic process. The relationship between the start and end temperatures is given by [11]: where start T and end T denote the node start temperature and node end temperature;  is the pipe line heat transfers coefficient. In order to clearly explain the formulation, we introduce three new variables: where K denotes pipeline drag coefficient. K can be calculated using the friction coefficient f as follows: where L denotes the pipeline length, D denotes pipeline diameter,  denotes the density of water, g is the acceleration caused by gravity, and f depends on the Reynolds number [12].

Objective function
The optimization goal is to minimize the daily building electricity bills under peak and valley pricing. The formulation is as follows: where c indicates the daily building electricity bills; ( ) c n is the electricity price at time n ; ( ) building P n is total electrical power of the room at time n ; t  is the time interval.

Example analysis
In this section, the wall thermal inertia model and waterheating network model are tested on modified IEEE-13 case, as shown in figure 6. In alternating current (AC) systems, the power flow model for on-load transformers, transmission lines, and distributed generator can refer to reference [13]. System structure and detailed parameters of test case can refer to [14]. There are 1000 smart houses connected to load bus 13, and each house uses the optimization strategy proposed in this paper. For waterheating network connected to bus 5 in this case, it has only one heat source and one loop.
Based on different thermal inertia models of the wall and floor, we compared two schemes, scheme 1 selects the single-layer wall and floor and scheme 2 selects the multilayer wall and floor. With a cycle of 24 hours a day, the time step is 1 hour.
The problem is mixed integer nonlinear programming (MINLP) problem. We use GAMS/KNITRO [15] to solve the MINLP problem, the version is 24.7.4.

Scheme 1
In scheme 1, the thermal resistance of wall (including windows) and floor is equivalent to total thermal resistance, respectively. Heat transfer within the walls is ignored. The initial temperature of the ambient temperature, wall, floor and room temperature is 5 ℃, 10 ℃, 20 ℃ and 22 ℃ respectively. The change curves of ambient, wall, floor and room temperature in scheme 1 are shown in figure 2.

Scheme 2
In scheme 2, the thermal resistance of wall (including windows) and floor is also equivalent to total thermal resistance, respectively. Heat transfer within the walls is ignored. The initial temperature of the ambient temperature, external wall, internal floor and room temperature is 5 ℃, 5 ℃, 20 ℃ and 22 ℃ respectively. The change curves of room, wall, floor and ambient temperature in scheme 2 are shown in figure 3.

Comparison of two schemes
In this section, we compare the room temperature with 24 hours between the two schemes. As can be seen from figure 4, the room temperature within the time period of 1:00~10:00 of scheme 2 is higher than that of scheme 1. It shows that the multi-layer wall and floor thermal inertia model has better heat storage performance than singlelayer model at the same outdoor temperature.  We compare the air-conditioning power change curves in the two schemes within 24 hours. As shown in figure 5, we can see that due to the poor heat storage performance of the single-layer model in scheme 1, the indoor heat loss is rapid, which leads to the increase of air conditioning power consumption.   Figure 7 is the calculation result of the bus 5 voltage amplitude within 24 hours of the day when the RIES optimization scheme 2 is adopted in the modified IEEE-13 test case. It can be seen that the power fluctuations at each node in the network cause the three-phase voltage amplitude of the node to fluctuate within a certain range, but the voltage amplitudes of bus 5 at all times are within the range allowed by the safe operation of the system, and can be maintained. This verifies the feasibility of the RIES optimization scheme proposed in this paper.

Conclusion
This paper has developed a multi-layer wall thermal model based on thermal inertia model and water-heating network model considering the piecewise fiction coefficient. Based on the buildings thermal inertia model combined with grid constraints and water-heating network constraints, this paper establishes an optimal plan for the RIES. The multi-layer wall thermal model has better performance, which is reflected in more consistent with the actual temperature changes. And the proposed RIES optimization scheme based on multi-layer wall thermal model can reduce the electricity purchase cost while E3S Web of Conferences 256, 02018 (2021) PoSEI2021 https://doi.org/10.1051/e3sconf/202125602018 maintaining indoor comfort. The robustness and effectiveness of the RIES optimization scheme proposed in this paper have been verified by the test cases.