Determination of the economical insulation thickness of building envelopes simultaneously in energy-saving renovation of existing residential buildings

When the energy saving rate of existing residential buildings renovation is determined, the thermal performances of external walls, windows, and roof interact with each other. Therefore, it is necessary to study the determination of economical insulation thickness of building envelopes considering the interaction among building envelope performances. The objective function and its bound of envelope thermal performance optimization in the energy-saving renovation of existing residential buildings in severe cold and cold zones in China were established. It is the conditional extremum problem and can be solved through Lagrange’s method of multipliers to determine the economical insulation thickness of external walls and roofs simultaneously. The method is proved to be feasible by an existing residential building in Beijing. When the same window types are selected, the energy-saving renovation program of the building envelope determined by the Lagrangian optimization method can produce the minimum investment in insulation, minimum investment payback period, and the largest net present value (NPV) of the life cycle.