Resumo:
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.
