Study of the impact of analytical modelling based on electric heating loads and differential equations for power regulation

In this study, an equivalent model of room temperature variation is established, and the switching state function, thermal power function and time variables are introduced to construct an analytical model of electric heating for a typical user, which in turn obtains the dynamic evolution of the steady state solution. Specifically, due to the large specific heat capacity of the wall, its temperature changes are small; the room temperature and heating power show periodic changes, while the power and thermal resistance are positively correlated to the room temperature fluctuation, and the heat capacity is generally negatively correlated. When the outdoor temperature reaches 15°C, the power consumption and cost reach the highest point. We also constructed an analytical model for power regulation based on differential equations, taking into account the thermal inertia of the building and the model temperature constraints, and found that the initial upward and downward adjustments had smoother changes in the available durations. When the time reaches 15 hours, the down-regulation durations show a decreasing trend, while the indoor temperatures rapidly approach the wall temperatures until they reach relative equilibrium. Especially noteworthy is that, when the outdoor temperature is lower, the power up-regulation is larger in order to keep the temperature within this range because the que value is set between 18°C and 22°C; conversely, the power up-regulation is smaller when the outdoor temperature is higher. It provides useful insights for the future development of green, efficient and intelligent electric heating systems.