Smoothing Techniques in Dynamic Building System Simulation

Efficiently, robustly, and accurately solving systems of nonlinear differential algebraic equations (DAE) for dynamic building system simulation is becoming more important due to the increasing demand to simulate large-scale problems including the integration of multiple buildings. However, in some building system simulations, the formulation of DAEs can include discontinuous variables and equations, and thus, derivatives. Even if these occurrences are infrequent, the presence of a discontinuity in a building system simulation can result in loss of efficiency and robustness in calculating solutions. This issue becomes more burdensome as problem sizes grow. In this paper, a smoothing technique that attempts to remove function discontinuity in dynamic building system simulation, enabling desirable numerical behaviour while preserving physical accuracy, is investigated. The impact of the smoothing technique on the numerical simulation is demonstrated in an example employing the HVACSIM+ environment: smoothing of a discontinuous coil component model. This example shows that the smoothing technique can greatly improve the efficiency and robustness of the numerical simulation with similar solution accuracy to the original, discontinuous model, while it is argued that the method does not deviate far from physical reality.