Parameter Estimation in Buildings: Methods for Dynamic Analysis of Measured Energy Use

Dynamic analysis of energy data can help improve the efficiency of buildings in several ways: evaluation of proposed modifications of a building or its operation (e.g., changes in thermostate setpoints); verification of performance on the basis of short-term measurements (corrected for weather); diagnostics and optimal control of HVAC equipment (real-time comparison of actual and predicted performance can be a powerful diagnostic tool). For this purpose one would like a simple building model whose parameters can readily be adjusted by a statistical fit to the data. This paper reviews the available methods: thermal networks, modal analysis, differential equations, ARMA (autoregressive moving average) models, Fourier series, and calibrated computer simulations. The basic models can be applied in several ways, differing in choice of dependent variable, number of coefficients, statistical criterion, time step, finite differencing scheme, and implementation as linear or nonlinear algorithm. The relation between the various approaches is examined. It is shown how the results of each of these methods can be presented in a standardized format that maximizes their physical interpretation, in terms of time constants and admittances (including heat loss coefficient and solar aperture). A general proof is given that the effective heat capacity equals the heat loss coefficient multiplied by a sum of time constants. The methods are tested with data from an office building. Special attention is focused on difficulties, due to air exchange or solar gains, that are likely to arise in practice.