Performance analysis of three phase induction motors under supply voltage unbalance conditions is normally conducted using the well-known symmetrical components analysis. In this analysis, the voltage unbalance level at the terminals of the machine is assessed by means of the NEMA or IEC definitions. Both definitions lead to a relatively large error in predicting the performance of a machine. A method has recently been proposed in which, in addition to the voltage unbalance factor (VUF), the phase angle has been taken into account in the analysis. This means that the voltage unbalance factor is regarded as a complex value. This paper shows that although the use of the complex VUF reduces the computational error considerably, it is still high. This is proven by evaluating the derating factor of a three phase induction motor. A method is introduced to determine the derating factor precisely using the complex unbalance factor for an induction motor operating under any unbalanced supply condition. A practical case for derating of a typical three phase squirrel cage induction motor supplied by an unbalanced voltage is studied in the paper. (c) 2007 Elsevier Ltd. All rights reserved.