Novel Polarization Index Evaluation Formula and Fractional-Order Dynamics in Electric Motor Insulation Resistance

Abstract

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 t2 > 0 minutes (IRt2) from t1 > 0 minutes (IRt2) for t2 > t1 > 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 t1 and t2 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.

Methods of Diagnosing the Insulation of Electric Machines Windings

“…As standard, this measurement is performed after 60 s. Depending on the value of the rated voltage of the tested machine, the insulation resistance measurement is performed at a different value of the test voltage. The values are presented in Table 1 [7,26,27]. The values of the insulation resistance in relation to the condition of the insulation system are presented in Table 2 [7].…”

“…Electrical machines for which the PI index value < 2.0 are rarely suitable for further operation. However, Table 5 contains the minimum values of the PI polarization index for various insulation classes [26,27]. The PI values in Tables 4 and 5 apply to both DC and AC electrical machines.…”

Analisis Winding Insulation Pada Performa Induksi Motor Tiga Phase Berbasis Logika Fuzzy

“…Hasil akhir penelitian menyatakan kondisi motor dalam tiga keadaan yaitu motor baik, motor rusak dan kotor rusak parah. Gonzalez et al, (2018) menjelaskan tentang penghitungan nilai dari polarization index dan fractional order dynamics pada insulation electric motor. Pengujian dilakukan dengan menggunakan magnet permanen motor sinkron 418VAC, dinamika fraksional dari resistansi isolasi elect motor dapat diwakili oleh model orde fraksional dan resistansi mengikuti fungsi Mittag-Leffler daripada fungsi eksponensial.…”

Exact bounds for robust stability of output feedback controlled fractional‐order systems with single parameter perturbations

“…For example, a novel fractional‐order model for batteries was established, of which the accuracy and stability are better than those of integer‐order models in the work of Liu et al 6 Fractional‐order filters of order and were designed to obtain more flexibility in shaping the filter response compared with traditional integer‐order filters in the work of Radwan et al 7 The main reasons lie in the historical dependence and global correlation of fractional derivatives and integrals 8 . FOSs were extensively explored in interdisciplinary areas such as robotics systems, 9 viscoelastic systems, 10 electric motors, 11 and so on 12 . Furthermore, the design and application of many fractional‐order controllers enhanced the performance and robustness of FOSs in engineering.…”