To develop novel theories and methods of power system dispatch, this paper constructs a hydro-thermal-wind- photovoltaic-storage coupled dispatching system, one that integrates cascade hydro-wind-photovoltaic-pumped storage (CHWPPS). When analysing such a coupled dispatching system, it is easy for the traditional solution method to fall into a local optimum and it is challenging to arrive at a feasible solution within a satisfactory time. This paper proposes a greedy strategy, adaptive crossover operator and adaptive t-distribution variation-based moth search algorithm (GCTMSA) to overcome these shortcomings. GCTMSA combines the adaptive crossover operator with the Lévy flight strategy, introduces an adaptive t-distribution variation in flight straight strategy, and uses the greedy strategy to enhance the global search capability and speed. The case studies conducted on a modified IEEE 6-machine and 30-bus system and a provincial simplified power system show that the GCTMSA has more substantial search capability and stability than the traditional moth search, genetic or particle swarm algorithms, as well as biogeography-based optimization. The impact of CHWPPS and battery storage on the system is analyzed. The related discussion and conclusion can provide a reference for developing multi-energy complementary technologies such as dispatching hydro-thermal-wind-photovoltaic-storage coupled systems. This work is supported by the National Natural Science Foundation of China (No. 51967004).