The contributions of this article include a new concept, a new question and a new method. This article proposes the concept of functional community, which is different from conventional topological community. Functional community is defined with two meanings: (1) tighter internal coupling for better efficiency within the same community; (2) more internal transmission from source to sink nodes within the same community. Then a new question about how to detect functional communities in power grids is analyzed, and most existing algorithms are not applicable. Therefore, a new method is put forward. Corresponding to meaning 1, Electrical Coupling Strength (ECS) is defined to replace conventional adjacency matrix; corresponding to meaning 2, Power Supply Strength (PSS) is defined and integrated with ECS to form the newly defined Electrical Functional Strength (EFS). Based on these two changes, we apply the proposed power supply modularity as a benchmark to evaluate any partitioning of power grids. The capability of the proposed partitioning method is demonstrated via the IEEE-118, IEEE-300 bus systems, and an Italian power grid. We argue that the conventional topological modularity may exaggerate the community characteristics of power grids and is inferior to the power supply modularity in detecting some functional features in communities. The work can also give inspirations to other engineering networks for functional communities.