Novel polarization index evaluation formula and fractional-order dynamics in electric motor insulation resistance

One of the common test metrics prescribed by IEEE Std 43 for testing motor insulation is the Polarization Index (P.I.) which evaluates the "goodness" of the machine's insulation resistance by getting the ratio of the insulation resistance measured upon reaching t ₂ > 0 minutes (IR _t2 ) from t ₁ > 0 minutes (IR _t2 ) for t ₂ > t ₁ > 0, after applying a DC step voltage. However, such definition varies from different manufacturers and operators despite of decades of research in this area because the values of t ₁ and t ₂ remain to be uncertain. It is hypothesized in this paper that the main cause of having various P.I. definitions in literature is due to the lack of understanding of the electric motor's dynamics at a systems level which is usually assumed to follow the dynamics of the exponential function. As a result, we introduce in this paper the fractional dynamics of an electric motor insulation resistance that could be represented by fractional-order model and where the resistance follows the property of a Mittag-Leffler function rather than an exponential function as observed on the tests done on a 415-V permanent magnet synchronous motor (PMSM). As a result, a new PMSM health measure called the Three-Point Polarization Index (3PPI) is proposed.