Restarted holomorphic embedding load-flow model based on low-order Padé approximant and estimated bus power injection

Abstract The holomorphic embedding load-flow model (HELM) is a noniterative method based on the computation of a Taylor power series that is a function of an embedded parameter. In this method, a continuous function based on a Pade approximant is used to replace this series, extending the radius of convergence. However, depending on the problem and how it is solved, the convergence can demand a high-order series or have a stagnated solution for the case of the continued equivalent function. In this paper, a restarted HELM (RHELM) is introduced. The method works with a very much reduced number of coefficients of the bus voltage Taylor series, different from HELM. Additionally, in the problem formulation, the power balance equations (PBEs) are embedded, considering a parameter and an estimated bus-injected power. This injected power is computed from a voltage estimate whose value is updated at every restarting point. The restart process allows for an approximate solution of the voltages computed via Pade approximation to be used as a new starting point. It is expected that at a new restarting point, the estimated power tends to converge toward the effective power injection of the bus. Tests to accept a given result for a voltage are evaluated for each of two consecutive new coefficient power series that are calculated. The coefficients are calculated until a given specified power mismatch is achieved. In the event that this tolerance is not reached up to a user-defined number of coefficients, the process is then restarted. The method’s performance is evaluated for a wide variety of test systems including a 13659-bus network model. The obtained results reveal that in comparison with the traditional iterative methods based on Newton’s method and the HELM, the proposed formulation is very efficient for computations involving large-scale systems and presents fast convergence.