## 2 Spatiotemporal Characteristics of Diversified Loads in Multiple Functional Areas
### Characteristics of the Loads Suitable for Internal Transmission in Functional Areas  
#### 2.1.1 Characteristics of the Heating Loads  
Since the propagation medium of the heating systems is generally hot water or steam with low speed, there is a large time inertia constant in the heating systems, meaning the transmission of the heating loads are delayed, and a heating system composed of heating source, heating network, and heating building has a large heating inertia, which means a heating system has a certain'storage' capability for heating energy, and its 'energy storage' effect depends on its heating inertia. This heating inertia could be utilized to coordinate with the operation of the power system. A heating network could store heating power, so the heat supply could be controlled on the time scale and then thermal-electric decoupling could be realized and the consumption rate of renewable energy could be improved. The human body's perception of temperature has ambiguity. When the temperature rises or drops in a certain range, heating users are difficult to detect, which could improve the flexible adjustability of the heating loads. The temperature of a heat transfer medium gradually decreases with the increase of the distance during a transmission process, so the transmission distance of heating loads is limited, and it is generally considered that high efficiency of central heating is attained within 5-8 km [18]. Since each functional area is relatively large, it is not appropriate to establish a heating network between functional areas, but a heating network could be built inside each functional area to achieve the balance of heating loads. The characteristics of heating loads vary in different functional areas. For example, the heating loads of the residential area, the office area, and the commercial area are mostly ordinary heating loads, while the heating loads of the industrial area are mostly productive heating loads. The elasticity of ordinary heating loads can be judged by the predicted mean vote (PMV), which represents the average value of the thermal sensation of most people in the same environment. The PMV index [19] is divided into seven levels corresponding to the seven thermal sensations of the human body, as shown in Table 1:  
The mathematical equation for the PMV index [20] is represented as  
\[ \begin{array}{ll}\lambda_{\text{PMV}}&=(0.303\text{e}^{-0.036M}+0.028)\left( M-W-3.05\times 10^{-3}\times[5733-6.99(M-W)-P_{\text{a}}]-0.42[(M-W)-58.15]\right.\\ &\left.-1.7\times 10^{-5}M(5867-P_{\text{a}})-0.0014M(34-t_{\text{a}})-3.96\times 1 0^{-8}f_{\text{cl}}[(t_{\text{cl}}+273)^{4}-(t_{\text{b}}+273)^{4}]-f_{\text{cl }}t_{\text{cl}}(t_{\text{cl}}-t_{\text{a}})\right)\end{array}  \tag{1}\]  
The heating supply is focused in this paper, and temperature is the most intuitive experience of the human body for indoor thermal comfort. Therefore, except for the air temperature around the human body, the other parameters are given. When the PMV index is 0, it corresponds to the optimal thermal comfort state of the indoor thermal environment. The PMV index should be between \(-1\) and \(+1\)[21], which means that it is allowed to be slightly cool and slightly warm, so the heating demand and the heating supply do not have to be strictly balanced in real-time, and it could be satisfied within a certain range. The thermal inertia [22] could be described by the autoregressive and moving average (ARMA) model as  
\[T_{\text{h},t}=\sum_{j=1}^{J}\alpha_{j}T_{\text{n},t-j}+\sum_{j=0}^{J}\beta_{j} T_{\text{g},t-j}+\sum_{j=0}^{J}\gamma_{j}T_{\text{w},t-j} \tag{2}\]  
\[T_{\text{n},t}=\theta_{1}T_{\text{n},t-1}+\phi_{1}T_{\text{g},t-1}+\omega_{1} T_{\text{w},t-1} \tag{3}\]  
It shows that the indoor temperature of a heating building in a certain period of time is the result of the combined action of heat supply of the heating network in the past several periods.