As the numbers of microgrids (MGs) and prosumers are increasing, many research efforts are proposing various power sharing schemes for multiple MGs (MMGs). Power sharing between MMGs can reduce the investment and operating costs of MGs. However, since MGs exchange power through distribution lines, this may have an adverse effect on the utility, such as an increase in peak demand, and cause local overcurrent issues. Therefore, this paper proposes a power sharing scheme that is beneficial to both MGs and the utility. This research assumes that in an MG, the energy storage system (ESS) is the major controllable resource. In the proposed power sharing scheme, an MG that sends power should discharge at least as much power from the ESS as the power it sends to other MGs, in order to actually decrease the total system demand. With these assumptions, methods for determining the power sharing schedule are proposed. Firstly, a mixed integer linear programming (MILP)-based centralized approach is proposed. Although this can provide the optimal power sharing solution, in practice, this method is very difficult to apply, due to the large calculation burden. To overcome the significant calculation burden of the centralized optimization method, a new method for determining the power sharing schedule is proposed. In this approach, the amount of power sharing is assumed to be a multiple of a unit amount, and the final power sharing schedule is determined by iteratively finding the best MG pair that exchange this unit amount. Simulation with a five MG scenario is used to test the proposed power sharing scheme and the scheduling algorithm in terms of a reduction in the operating cost of MGs, the peak demand of utility, and the calculation burden. In addition, the interrelationship between power sharing and the system loss is analyzed when MGs exchange power through the utility network.