It is quite important to improve the energy saving of air source heat pump heating system through optimal operation and system engineering method. In this work

the nonlinear dynamic model of heat pump heating process is established and the integral optimal objective function is then formulated to balance the control accuracy and energy saving. To solve the differential and algebraic optimization problems (DAOPs) efficiently

a simultaneous method is used to discretize the problem by collocation of finite elements. Then

the problem is analyzed with different weights and an optimal strategy to dynamically adjust the weight of objective function is proposed for further energy cost reduction. Computing results show that the potential energy saving of more than 16% can be achieved under permitted indoor temperature tracking error of 0.85 ℃; the ambient temperature and electricity price have significant effect on the optimal operation and performance of the heat pump heating system; and considering the characters of these factors

the proposed strategy of dynamically adjust the weight of objective function can further reduce energy cost for about 4.7%. Our research is of significant meaning for the optimal operation of heat pump heating system under dynamical conditions.