Dynamic state estimation of electrical power systems - unified solution in the complex domain

Abstract

For decades, the numerical solution of network analysis applications has invariably occurred in the real number domain. However, the phasor nature of electrical quantities allows these problems to be formulated directly in the complex domain. This thesis proposes a comprehensive framework for Dynamic State Estimation (DSE) in complex-conjugate coordinates, leveraging Wirtinger calculus to linearize functions involving complex and conjugate variables. The algebraic-differential modeling of network dynamics is presented, incorporating classical and two-axis synchronous machine models with voltage and speed regulators. The work evaluates the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) in complex-conjugate coordinates, introducing structural optimizations such as the Decoupled EKF (D-EKF) to mitigate the computational burden of augmented complex statistics. Furthermore, robust versions of these algorithms are developed to handle gross errors, bad leverage points, and communication failures, ensuring high reliability in adverse operational scenarios. The methodology also integrates real-time frequency estimation, which is critical for the operational security of low-inertia systems. Numerical simulations conducted on the IEEE 3-bus system for detailed validation, followed by scalability analyses on the IEEE 39-bus, IEEE 118-bus, and a 340-bus equivalent of the Brazilian Interconnected Power System (SIN-340), demonstrate that while the DEKF significantly reduces execution times, making complex-domain linearization-based filters computationally viable, the complex-domain UKF achieves superior computational performance in large-scale systems.