Initialised load-flow analysis based on Lagrange polynomial approximation for efficient quasi-static time-series simulation

This study presents a developed formulation for solving the quasi-static time-series simulation in unbalanced power distribution systems. This simulation is very important for analysing a set of given daily load curves under various operating conditions. The Lagrange polynomial approximation is implemented to predict an initial guess of both voltage magnitude and phase angle at time instants in vicinity of the given power-flow solutions. The developed methods are categorised based on the required number of power-flow solutions to predict the initial guess. The linear approximation of the Lagrange polynomial requires the knowledge of two power-flow solutions, whereas the non-linear approximation requires three power-flow solutions. The predicted values of both voltage magnitudes and angles are corrected using power-flow engine. The adopted power-flow solver uses the forward/backward sweep. The developed methods were tested using the unbalanced IEEE 123-node and 33-node test feeders with a set of daily load curves and intermittent distributed energy resources. The developed methods are compared with the method which utilises the previous power-flow solution as an initial guess. The results show that the number of iterations and computation time of quasi-static time-series simulations are greatly reduced.