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This article presented a convex relaxation approach for the optimal power flow problem. The proposed approach leveraged the second-order cone programming (SOCP) relaxation to tackle the non-convexity within the feasible region of the power flow problem. Recovering an optimal solution that is feasible for the original non-convex problem is challenging for networks with cycles. The main challenge is the lack of convex constraints to present the voltage angles within a cycle. This article aims to fill this gap by presenting a convex constraint enforcing the sum of voltage angles over a cycle to be zero. To this end, the higher-order moment relaxation matrix associated with each maximal clique of the network is formed. The elements of this matrix are utilized to form a convex constraint enforcing the voltage angle summation over each cycle. To keep the computation burden of leveraging the higher-order moment relaxation low, a set of second-order cone constraints are applied to relate the elements of the higher-order moment relaxation matrix. The case study presented the merit of this work by comparing the solution procured by the introduced approach with other relaxation schemes.

Microgrids with AC/DC architecture benefit from advantages of both AC and DC power. In this paper, daily operation problem for a zero-carbon AC/DC microgrid in presence of electric vehicles (EVs) is considered. In this framework, EVs' batteries are mobile energy storage systems, which allow desirable operation of the microgrid during peak demand hours. This study shows in absence of storage system, EVs' batteries can be properly managed to satisfy the system requirements. In the case studies, several sensitivity analyses based on variations in battery degradation costs, solar irradiance, and inverter capacity are investigated., Comment: ITEC 2021

This paper investigates the impact of the changes in the demand of power systems on the quality of the solution procured by the convex relaxation methods for the AC optimal power flow (ACOPF) problem. This investigation needs various measures to evaluate the tightness of the solution procured by the convex relaxation approaches. Therefore, three tightness measures are leveraged to illustrate the performance of convex relaxation methods under different demand scenarios. The main issue of convex relaxation methods is recovering an optimal solution which is not necessarily feasible for the original non-convex problem in networks with cycles. Thus, a cycle measure is introduced to evaluate the performance of relaxation schemes. The presented case study investigates the merit of using various tightness measures to evaluate the performance of various relaxation methods under different circumstances., 6 Pages, 16 Figures, This paper is accepted for the 52nd North American Power Symposium

In this paper, a smaller battery and flywheel storage system was used to reduce the cost of using large flywheel storage to respond to fast load fluctuations. The droop control method is used for coordination between the flywheel, battery, and diesel. This method has been used to control the flywheel and the battery, respectively, with their speed and state of charge (SOC). Accordingly, by correctly coordinating the components of the microgrid, it is possible to reduce the high investment costs so that the efficiency of the microgrid is not reduced to respond to rapid changes in load.