In the existing research on the dispatch and control strategies of park micro-energy grids, the dispatch and control characteristics of controllable energy units, such as response delay, startup and shutdown characteristics, response speed, and sustainable response time, have not been taken into account. Without considering the dispatch and control characteristics of the controllable energy units, substantial deviation will occur in the execution of optimized dispatch and control strategies, resulting in economic losses in the electricity market and adverse effects on the safe operation of power systems. This paper proposes a unified model to describe the dispatch and control characteristics of various types of controlled energy units, based on which we develop a three-tier optimization dispatch and control strategy for the micro-energy grid, involving day-ahead, intra-day, and real-time stages. The day-ahead and intra-day optimization dispatch strategy is implemented to obtain the optimal reference values in the real-time stage for each controllable energy unit. In the real-time stage, a minimum variance control strategy based on d-step prediction is proposed. By considering the multi-dimensional control characteristics of controllable energy units, the real-time predictive control strategy aims to ensure that the controllable energy units can precisely follow the optimized dispatch plan. The simulation results show that when compared with the dispatching method optimized by the improved quantum particle swarm algorithm, the adoption of the optimal dispatch and control strategy proposed in this paper resulted in a 45.79% improvement in execution accuracy and a 2.38% reduction in the energy cost.