  The problem of imbalance detection in a three-phase power system using a
phasor measurement unit (PMU) is considered. A general model for the zero,
positive, and negative sequences from a PMU measurement at off-nominal
frequencies is presented and a hypothesis testing framework is formulated. The
new formulation takes into account the fact that minor degree of imbalance in
the system is acceptable and does not indicate subsequent interruptions,
failures, or degradation of physical components. A generalized likelihood ratio
test (GLRT) is developed and shown to be a function of the negative-sequence
phasor estimator and the acceptable level of imbalances for nominal system
operations. As a by-product to the proposed detection method, a constrained
estimation of the positive and negative phasors and the frequency deviation is
obtained for both balanced and unbalanced situations. The theoretical and
numerical performance analyses show improved performance over benchmark
techniques and robustness to the presence of additional harmonics.
