The problem of voltage imbalance detection in a three-phase power system using phasor measurement unit (PMU) data is considered within a hypothesis testing framework. A general model for the PMU output with a downsampled negative sequence is presented. The new formulation takes into account computation complexity and tolerance of imbalance. A new monitoring tool, referred to as a generalized locally most powerful (GLMP) test, is proposed for detection in the presence of nuisance parameters. A closed-form expression of the GLMP test is developed for the detection of an imbalance problem, based on a single PMU's measurements. Numerical simulations show improved performance over benchmark techniques.