## 4 Case Study
### Results and Analyses  
The change of battery, natural gas storage, and heat storage charge/discharge power in EH1 at a continuous time period are shown in Figure 6. During the valley price period (such as from 5:00 to 7:00), the battery is a state of charge, which can reduce the cost of electricity purchase, and also play a role in cutting peak demand (such as from 8:00 to 10:00 and from 17:00 to 18:00). However, the heat load demand is greater from 2:00 to 4:00, and heat storage, natural gas storage, and the battery are in a state of discharge so more electric energy and natural gas energy are converted to heat energy aiming to meet the heat demand peak, which reduces EH operation cost during the heat load peak period while the heat price is at the peak price. As a whole, battery, natural gas storage, and heat storage are in a state of charge from 11:00 to 16:00, meantime heat load, natural gas load, and electric load are experiencing valley demands. As shown in Figure 2, the power proportional coefficient of total natural gas bus energy flowing to the furnace/boiler unit in EH1 is denoted as G2H-EH1, and the power proportional coefficient of total electric bus energy flowing to the _P2H_ unit is recorded as _P2H_-EH1, which has the same notation in EH2. A change in the optimal distributive proportion coefficient for EH1 and EH2 in IES is shown in Figure 7. First of all, the _CHP_ unit in EH1 and EH2 are all in the shutdown states during the whole stable operation period according to the optimization results. This can be easily understood because the _CHP_ unit usually has a gas turbine, an internal combustion engine, or a micro-combustion machine as its main component and their energy conversion efficiency is low because of more energy loss during the energy conversion process compared to the direct use of electricity, heat, and _P2H_ and furnace/boiler units. The results shown in Figure 7 illustrate that the optimal allocation proportion coefficient of different EHs in stable and efficient operation can be obtained by the inner layer optimization strategy. During the period from 16:00 to 18:00, the furnace/boiler and _P2H_ units in EH1 are in the shutdown state, and the heat distribution system provides all the heat energy to meet the demand of the heat load. It can be clearly seen from Figure 7 that the variation trend of the same type curve is significantly different. Figure 5: Structure diagram of the IES based on an EH. As shown in Figure 8, an electricity transmission system includes four nodes and four transmission lines, where Nodes 1 and 2 are PQ nodes, Node 3 is the PV node, and Node 4 is the slack node. Optimization results of nodes voltage magnitudes (\(V\)) and nodes voltage angles (\(\theta\)) at a continuous time period are shown in Figure 8. The optimization results show that all nodes \(V\) are in the range of [0.9 p.u., 1.1 p.u. ], and all nodes \(\theta\) are in the range of [\(-8^{\circ},0^{\circ}\)]. The natural gas pressure at all nodes is decreased compared to the reference gas source Node 3. Figure 9 shows the pressure gradient diagram from source Node 3 to the consumer/natural gas load (from Node 1 to Node 2) at a continuous time period. Minimum pressure of the natural gas node observed under steady state is the furthest consumer (Node 2) at a continuous time period. The pressure of node 1 fluctuates up and down at 75 kPa, while that of node 2 fluctuates up and down at 58 kPa, but more violently than that of Node 1. The pressure of each node is mainly  
Figure 6: Change of diversified storage devices charge/discharge for EH1. Figure 7: Change of optimal distributive proportion coefficient for EH1 and EH2. influenced by integrated factors such as EH's natural gas load demand, natural gas pipeline flow, and pipeline resistance. Due to the limited length, only the temperature at the end of supply/return pipeline that is connected to the supply pipeline from 1 to 3 and return pipeline from 4 to 6 in the district heating system is given.