Local Energy Optimum of Warm Water Loop in the Heat Pump Heating System

Abstract

The paper presents the analytical energy optimization procedure of the warm water loop of heat pump heating system. The analytical optimization method is applied based on the 'first derivate equals to zero' principle. The objective function is the heating system's coefficient of performance ( COP). In the optimization procedure, three types of mathematical models are used: the basic, the modified and the optimizer model. All three models contain: condenser, circulation pump, piping, compressor mathematical description. The models forming equations are coupled, non-linear and algebraic. The solution can be obtained using e.g. the iterative, Newton-Taylor linearization, Gaussian elimination numerical methods. Moreover, with exact mathematical derivation the condition equation of local energy optimum with respect to the circulating pump's power and the warm water mass flow rate have been determined.