A multistage recursive approach in time- and frequency-domain for thermal analysis of thermochromic glazing and thermostatic control systems in buildings

The frequency-domain analysis is an effective approach to analyze the steady-periodic heat transfer in buildings. Auxiliary load in buildings can be calculated using the indoor temperature in a frequency-domain analysis. However, both auxiliary load and indoor temperature are usually unknown in building analysis, which makes computing the indoor temperature and auxiliary load with the presence of heating and cooling setpoints are challenging in a frequency-domain analysis. A similar problem applies to the calculation of the auxiliary loads of buildings with dynamic materials, such as thermochromic materials. This paper proposes and implements a recursive approach in time- and frequency-domain to calculate the indoor temperature in an office space with dual setpoint and thermochromic glazing systems with different critical transition temperatures and tinted-to-clear transmissivity ratios. This method allows for capturing the free-floating fluctuations of the indoor temperature within the deadband as well as determining the points-in-time when the indoor temperature equals heating or cooling setpoint temperatures. A multistage procedure is defined to account for the varying window transmittance. The proposed method accounts for the time-dependent response of a thermostat and thermochromic glazing within a finite number of adjustments without requiring to carry out time-domain temperature or load calculations. Results revealed reductions in the annual cooling energy use and increases in the annual heating energy consumption using thermochromic glazing systems with the total annual energy savings of up to 1.22 kWh/m(2)-yr for the tau-ratio of 0.65, 3.50 kWh/m(2)-yr for the tau-ratio of 0.30, and 5.22 kWh/m(2)-yr for the hypothetical case with zero tau-ratio.