Distributed Slack-Bus Based DC Optimal Power Flow with Transmission Loss: A Second-Order Cone Programming Approach and Sufficient Conditions

This paper proposed sufficient conditions of the zero duality gap for the second-order conic programming approach of the DC optimal power flow that quadratically embeds the transmission loss. The mechanism of the changes for locational marginal price with differently selecting the slack bus is revisited, based on which a load-weighted distributed slack bus method is introduced. Furthermore, a second-order conic programming-based convexification method is proposed by employing the duality analysis. A favorable property of the proposed method is that mild sufficient conditions of the zero duality gap can be derived by the analysis of Karush-Kuhn-Tucker conditions. Numerical results illustrate the effectiveness of the proposed method and physically prove the proposed sufficient conditions. Compared with traditional and similar market-clearing methods, the proposed method has better performance on convergence, robustness, and accuracy. Note to Practitioners-This paper was motivated by the problem of the pricing mechanism in the deregulated electricity market but it is also applicable to rapidly solving the power flow of power systems with sufficient reactive power. Existing approaches use the B-coefficient to estimate the transmission loss in the model non-linearly. In this paper, an improved approach considering transmission loss is proposed, which further introduces the distributed slack bus method and subsequently employs the second-order cone programming algorithm. The proposed method hedges the risk of appearing multiple solutions or lack of accuracy. Rigorous mathematical proofs are derived to support the method. For industrial practice, three sufficient conditions suitable for different kinds of power systems are given, indicating when the proposed approach can be efficiently applied. The proposed method can be integrated into the existing electricity market trading platform for independent system operators and facilitates real-Time market clearing and electricity price calculation. Future research is expected to improve the accuracy of the model based on nodal power balance equations.