1. College of Electrical Engineering Zhejiang University Hangzhou 310027 China;
2. Zhejiang Provincial Key Laboratory of Electrical Machine Systems Hangzhou 310027 China
Permanent magnet synchronous machines (PMSMs) are widely used for its high operating efficiency. During the application, the parameters of PMSMs may vary a lot when considering the effect of temperature, magnetic saturation and so on. In such a case, the performance of some optimal control strategies, such as the maximum efficiency control and current decoupling control, may decay. So, in order to achieve high performance control, online parameters identification is important. However, there are few parameters identification methods considering the ferromagnetic loss, as well as its variation with currents, while the ferromagnetic loss occupies a great proportion in the PMSMs’ loss. To solve the problem, this paper integrates the ferromagnetic loss and copper loss as electromagnetic loss, and then, proposes an improved DC-signal-injection-based online parameters identification considering the variation of equivalent electromagnetic loss resistance.
Firstly, the magnetic saturation of PMSMs and the variation of electromagnetic loss with current are discussed. Due to the magnetic saturation characteristic of ferromagnetic materials, the magnetic permanence of PMSMs may be decreased as the current rises, and then the inductance and flux linkage may be affected. Besides, when considering the change of current vectors, the copper loss may be variable due to the proximate effect, while the ferromagnetic loss may also vary with the changeable magnetic distribution. To describe such characteristics, an improved series electromagnetic loss resistance model is proposed, which uses apparent flux linkage and incremental inductance to characterize the magnetic saturation, and uses change rates of the equivalent resistance to characterize the variation of electromagnetic loss.
Secondly, in order to realize the full identification of the proposed model’s parameters, 4 groups of d-/q-axis operating currents are chosen based on the criterion of alternating changes of d-/q-axis currents. According to the analysis, once the current increment of each change is not 0, then the steady-state voltage equations of these 4 groups are linearly independent, that is the corresponding coefficient matrix is full-rank and the full parameters identification can be achieved.
Thirdly, a least mean square (LMS) algorithm is adopted to solve the 4 groups of steady-state voltage equations, due to the complexity of the high-rank coefficient matrix’s analytical computation. According to the LMS algorithm, it calculates the gradient of voltage estimation errors’ mean square to each model parameters at first, based on the measured voltages, currents and speeds. Then, the model parameters are updated iteratively based on the corresponding gradients at each step. After a period of iteration, the model parameters which meet the preset voltage estimation accuracy can be obtained.
Finally, a prototype PMSM is used to validate the accuracy of the proposed method. Experimental results show that, when compare with the sinusoidal-signal-injection-based method and the traditional DC-signal-injection-based method, the proposed method is more precise in the identification of electromagnetic resistance and apparent flux linkage, with an average relative error of less than 2.3%. In addition, the proposed method also has high identification accuracy for torque and incremental inductance, with average relative errors less than 0.9% and 3.5%, respectively. However, the identification performance for the change rate of the equivalent resistance is not good enough, and needs further improvement.
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