Date of Award


Publication Type

Doctoral Thesis

Degree Name



Electrical and Computer Engineering


Multi-phase PMSM, Parameter estimation, Performance improvement, Thermal protection


Narayan N.C. Kar




This thesis investigates novel multi–parameter estimation schemes for dual three–phase permanent magnet synchronous machine (PMSM) towards condition monitoring and torque performance improvement. First, the vector space decomposition (VSD) based dual three–phase PMSM model in the synchronously rotating reference frame is introduced and presented. According to VSD transformation, the fundamental and harmonic components in voltage, current and flux vectors are projected to three subspaces that are orthogonal to each other. However, the challenges associated with parameter estimation, such as voltage source inverter (VSI) nonlinearity and magnetic saturation, are systematically derived and summarized. Subsequently, an updated machine model with consideration of the aforementioned nonlinearities is proposed. To further improve the parameter estimation accuracy and reduce the computational cost, the DC component–based model is incorporated in the updated machine model to identify parameters having fast and accurate convergence. The key to accurately estimating machine parameters is to resolve the rank deficiency issue in the estimation of more than two machine parameters simultaneously irrespective of the kind of algorithm employed. Based on the proposed machine model, a current injection–based estimation scheme is proposed for identifying multiple machine parameters, in which a recursive least square (RLS) algorithm is applied to reduce the mean square error to achieve the objectives of: 1) constructing a full–rank estimation model incorporating voltage source inverter nonlinearity model; 2) estimating the stator winding resistance and permanent magnet flux linkage by taking temperature effect into account; 3) estimating the inductances with consideration of magnetic saturation; and 4) improving the overall estimation accuracy. Then, a massive redundant measurements–based estimation scheme is proposed to elaborate the inductance model which does not need to interfere with the motor drive system. Specifically, this method benefits machine testing process without additional information from the motor manufacturers. Thus, the proposed parameter estimation strategies are applicable to both online and offline applications. Based on the proposed estimation method, the use of estimated machine parameters contributes to practical applications such as condition monitoring and performance determination. Firstly, efficient permanent magnet (PM) temperature models are derived due to temperature–dependence of PM flux linkage. A look–up table (LuT) is employed to assist in tracking the PM temperature variation. Moreover, by taking the advantages of additional decoupled harmonic subspace, the winding temperature estimation with the cancellation of the VSI nonlinearity effect is proposed, in which a set of DC currents is injected into the harmonic subspace. Considering the aforementioned concepts, a simultaneous stator winding and PM temperature estimation scheme is developed to avoid the use of look–up table. To achieve a better estimation performance, the Kalman filter is incorporated into the aforestated temperature tracking methods. In addition to thermal condition monitoring, better parameter estimation can help maximize torque production which consumes minimum stator current through the maximum torque per ampere (MTPA) technique. It is worth noting that the proposed estimation method can effectively reduce the parameter dependency of the machine model. To this end, the proposed optimal current angle searching algorithm can instinctively take magnetic saturation, VSI nonlinearity and temperature effect into account. During the thesis investigations, different parameter estimation schemes and thermal condition monitoring and MTPA strategies are extensively evaluated and validated on a laboratory dual three–phase PMSM under different speeds, load, and temperature conditions.