Pyramidal approximation for power flow and optimal power flow

Power flow equations (PFEs) are the fundamental of power flow (PF) calculations and optimal PF (OPF) for power system analysis, but existing PFEs suffer from the trade-off among various requirements in practice. This study presents a novel pyramidal approximation (PA) for PF and OPF. A multi-sided pyramid is used to approximate the feasible region of PFEs. The PA-based PFEs not only guarantee the linearity, tightness, and no dependence on the initial guess but also have high solution accuracy. The rotation-and-fold strategy is developed to balance the computational efficiency and approximation accuracy, so that the problem for a relatively large power system can be solved in a reasonable time. Case studies in different test systems validate the tightness and accuracy of the proposed PA method. The balance of accuracy and efficiency is also discussed, and the PA has a good performance in the small or medium power systems.