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Compensation in Complex Variables for Microgrid Power Flow

The solution of the distribution network power flow in practical applications is based either on the forward–backward sweep method for radial networks, or the current injection method for meshed networks. While the power flow in microgrids that operate in grid-connected mode could be resolved using the above-mentioned approaches, their operation in island mode would require simulating local generation droop controllers for sharing the complex power load and network loss among the generators. This letter proposes a complex power compensation approach, which is based on Wirtinger calculus, for extending the applicability of practical distribution power flow methods to microgrids operating in island mode. Supporting numerical results are reported on microgrids with up to 3139 nodes.