In terms of the multi-area optimal power flow (OPF) problem

the optimized objectives are always a fuel cost function expressed by a second-order polynomial. However

the valve-point loading effect

whose cost curve is a transcendental function formed by the superposition of the sine and polynomial function

will make the objective function non-convex and non-differentiable. Conventional distributed optimization technologies can hardly make a solution directly. Therefore

it is necessary to realize a distributed solution for multi-area OPF from another point of view. In this paper

we constitute a new double-layer optimization mechanism. The proposed distributed meta-heuristic optimization (DMHO) algorithm is put on the top layer to optimize the dispatching of each area

and in each iteration a distributed power flow calculation method is embedded as the bottom layer to minimize the mismatch of power balance. Numerical experiments demonstrate that the proposed approach not only implements a multi-area OPF distributed solution but also accelerates the convergence rate

improves the solution accuracy and enhances the robustness. In addition

a fully decentralized computation experiment is performed in an actual distributed environment to test its practicability and computation efficiency.