As a result of the increasing number of distributed energy resources (DER) in the electrical grid and their commitment to future market participation, control strategies for the optimal operation of DER gain importance. For this scenario a microgrid is a promising approach and forms a solution to this challenge. Microgrids are subsystems of the distribution grid including distributed generation (DG) units, storage devices and controllable loads, and can operate either connected or isolated from the utility grid. Ensuring a smooth, reliable and economic operation of a microgrid requires an energy management system that dynamically fits the production to the consumption in combination with storage. Quick response of the energy management strategy is crucial for a microgrid as compared to a conventional energy system. In this paper, a formulation of the environomic power dispatch approach in microgrids is proposed which uses multiobjective optimisation. The application aims to fulfill the time varying energy demand while minimising the costs and emissions of the local production and imported energy from the utility grid. With the introduction of a storage device, stored energy is controlled to balance the power generation of renewable sources, cover the overall microgrid demand and to optimise the overall power exchange between utility grid and microgrid. Operational constraints such as generator limits, start-up, operation and maintenance costs and the intermittency of renewable energy sources (RES) are to be satisfied. A representative microgrid structure is studied as an example and some simulation results are presented to demonstrate the performance of the microgrid environomic power dispatch approach.