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Efficient and Robust Optimization for building energy simulation



Shokouh Pourarian, Jin Wen, Anthony J. Kearsley, Amanda Pertzborn


Efficiently, robustly and accurately solving large sets of structured, non-linear algebraic and differential equations is one of the most computationally expensive steps in the dynamic simulation of building energy systems. Here, the efficiency, robustness and accuracy of two commonly employed methods are compared. The comparison is conducted within the HVACSIM+ simulator, a component based simulation tool. The HVACSIM+ program currently employs Powell's Hybrid method to solve the system of nonlinear algebraic equations whose solution leads to dynamic energy simulation of buildings. As some of the case studies show, this method does not always converge to a desirable solution. Since a myriad of numerical methods are available to solve systems of nonlinear algebraic equations, like the ones encountered by HVACSIM+, the question arises as to which method is most appropriate for building energy simulation. This paper argues that considerable computational benefits can be gained by studying these nonlinear systems and selecting solvers carefully. As an example, a variant of the Levenberg-Marquardt algorithm is shown to perform differently than Powell's Hybrid method when deployed in HVACSIM+. The numerical results provide supporting evidence that the accuracy and robustness of Levenberg-Marquardt are superior to Powell's Hybrid and suggest it as a reasonable candidate for replacement of the Powell's Hybrid method in HVACSIM+.
Energy and Buildings


Building energy systems, HVAC simulation, Numerical method, Efficiency, Robustness, Powell’s Hybrid method, Levenberg-Marquardt method


Pourarian, S. , Wen, J. , Kearsley, A. and Pertzborn, A. (2016), Efficient and Robust Optimization for building energy simulation, Energy and Buildings, [online],, (Accessed July 24, 2024)


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Created June 14, 2016, Updated October 12, 2021