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Abstract. This paper presents the closed form solution of the synchronous machine transients undergoing short circuit. That analytic formulation has been derived based on linearity and balanced conditions of the fault. Even though restrictive, the proposed method will serve somehow or other as a new resource for EMTP productivity. Indisputably superior, the closed-form formulation has some features inimitable by discretization such as continuity, accuracy and absolute numerical stability. Moreover, it enables us to calculate states at one specific instant independent of previous states or a snapshot, which any discretization methods cannot do.

Optimal reactive power dispatch (ORPD) is a way to improve power system performance. Determination of the optimal value of the control variable can reduce the objective function to be achieved. The optimization of the two objective functions simultaneously is called multi-objective ORPD (MORPD). This research has a major contribution in proposing and utilizing original ideas from new algorithms and new ideas from the old algorithm to solve more complex variables and challenging ORPD problems. The ORPD problem is formulated as a nonlinear model with variables consisting of continuous and discrete. The proposed multi-objective algorithm is time-varying particle optimization (MOTVPSO), ant lion objective (MOALO), dragonfly algorithm (MODA), grey wolf optimizer (MOGWO), and multi-objective multi-verse optimization (MOMVO). To measure the effectiveness of those algorithms, testing is performed on the IEEE 57-bus. The simulation results show that the MOTVPSO algorithm can contribute more dominantly from the statistical tests conducted compared to previous studies and all four algorithms in this work to minimize real power loss. Whereas the MOMVO has an advantage in computational time efficiency.

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