Joint frequency and phasor estimation under the KCL constraint

In this letter, we consider the problem of joint off-nominal frequency and phasor estimation that incorporates Kirchhoff's Current Law (KCL) as a constraint. We develop the constrained maximum likelihood (CML) and constrained weighted least-squares (CWLS) estimators for this problem and derive the corresponding constrained Cramér-Rao bound. The KCL constraint is shown to behave as a noise cancellation factor for the phasors estimation. We show that the KCL CML is based on the classical periodogram subtracting the average current periodogram. The results indicate significant performance improvement compared to the unconstrained maximum likelihood (ML) and unconstrained weighted least-squares (WLS).