Resumo:
This work presents the implementation of classic (WLS) and robust (SHGM) estima tors in the complex domain, considering remote monitoring of hybrid measurements via
PMU and SCADA. For this, Wirtinger Calculus was the mathematical basis for turn ing non-analytical functions (power flow equations) concerning complex variables into
multi-differentiated functions for complex and conjugate variables. Therefore, it enables
expansion in the Taylor series. Thus, the classical (WLS) and robust (SHGM) estimation
algorithms are derived in the complex domain, paying attention also to the processing
of gross errors. In the classic complex estimator, the efficiency of the largest normalized
residual test in identifying and recovering erroneous measurements is attested. For the ro bust complex estimator, a slight change in the former algorithm for calculating statistical
projections is proposed for strengthening against bad leverage points. Projection statis tics algorithm applied to a real- or a complex-valued Jacobian matrix provides different
numbers and weightings assigned to leverage points. In addition, this work shows an ef ficient algorithm for analyzing the algebraic observability of the employed test systems,
highlighting the applications in MATLAB and the potential contributions of such appli cations. The performance of complex-valued estimators was evaluated comparing with the
same estimators built in the real plane. The test systems evaluated are IEEE-14, -30, -57,
-118 and the SIN equivalents of 340, 730 and 1916 buses. Results show the computational
advantages of the complex-valued estimator in scenarios of purely real, hybrid, or purely
phasor measurements. Furthermore, the disparity between these numerical domains be comes more clear as the size of the system increases.
