Estimação de estados usando o método holomórfico com base em medições fasoriais sincronizadas

Abstract

This work introduces the Holomorphic Embedding State Estimation Method (HESEM), a new technique for state estimation in electric power systems. It supports different measurement types, including data from Phasor Measurement Units (PMUs). The approach formulates the algebraic equations that describe network operation directly in terms of the bus voltage phasors to be estimated. These equations are then converted into holomorphic expressions by introducing an auxiliary complex variable, which ensures the resulting functions are analytically differentiable over the complex domain. Next, all nodal voltages are represented as a sum of terms in a Maclaurin series. The series coefficients are computed sequentially through a recursive procedure: each term of order n is obtained from the term of order n − 1. To obtain a unique solution while computing only a limited number of terms, the method applies analytic continuation using Padé approximants, which effectively enlarges the convergence region of a complex series from a reduced set of Maclaurin coefficients. Among the main advantages of HESEM is its constructive, non-iterative solution process, which ensures uniqueness and can reduce computational time when compared to traditional approaches such as Weighted Least Squares (WLS). In addition, the state variables are expressed as voltage phasors in rectangular coordinates. Unlike iterative methods, where a Jacobian matrix with multiple derivatives must be recomputed at every iteration, HESEM relies on a single matrix that remains unchanged throughout the entire solution procedure. The feasibility and effectiveness of the proposed method are validated through simulations on different test systems. The classic IEEE 14-bus and IEEE 33-bus networks illustrate the applicability of HESEM, while a 107-bus equivalent of the brazilian transmission system is used to assess performance and scalability.