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Robot and Servo Drive Lab.
Analytical modelling and parametric sensitivity
analysis for the PMSM steady-state performance
prediction
Maryam Kazerooni1, Saeedeh Hamidifar2, Narayan C. Kar2
IET Electr. Power Appl., 2013, Vol. 7, Iss. 7, pp. 586–596
學
生:蔡景棠
指導教授:王明賢
2016/7/14
Department of Electrical Engineering
Southern Taiwan University of Science and Technology
Outline
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Abstract
Methods for determining the PMSM parameters with varying
level of accuracy
Parametric sensitivity analysis of the PMSM in steady-state
performance applications
Novel d–q axis model of the PMSM including the effect of
saturation and core losses
Conclusion
References
2016/7/14
Department of Electrical Engineering
Robot and Servo Drive Lab.
Southern Taiwan University of Science and Technology
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Abstract
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Inaccuracy in the permanent magnet synchronous motor (PMSM)
steady-state performance calculation corresponds to the parameter
error and model imprecision. Accurate determination of the PMSM
parameters may encounter various complications because of its
rotor structure and drive design.
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In addition, this study contributes to accurate performance
estimations of the PMSM by developing a precise model that
incorporates the saturation saliency and core losses. The accuracy
of the proposed model is compared with the conventional dq-axis
model and its higher accuracy is validated through experimental
results.
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Department of Electrical Engineering
Robot and Servo Drive Lab.
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Methods for determining the PMSM
parameters with varying level of accuracy
Calculation of armature resistance, Ra:
Calculation of the flux linkage constant, λf:
Calculation of the d- and q-axis armature inductances, Ld and Lq:
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Novel DC standstill test:
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Proposed on-load test:
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Parametric sensitivity analysis of the PMSM in
steady-state performance applications
Fig. 5 PMSM performance calculation employing various
methods of d- and q-axis inductances determination at 1500 rpm
a Output power
b Error in output power
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A numerical expression of the sensitivity is presented in (8). According to this
equation, the sensitivity of the performance factor, γ to the parameter, ρ is the ratio of
the performance factor error to the parameter error. In this equation, γex is the
measured performance factor, γcal is the calculated performance factor, ρact is the
actual value of the parameter which is obtained from manufacturer’s data and
ρdet is the determined value of the parameter.
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Fig. 6 PMSM performance calculation employing various
methods of flux linkage constant determination at 1500 rpm
a Output power
b Error in output power
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Fig. 7 PMSM performance calculation employing various methods of armature resistance
determination at 1500 rpm
a Output power
10
b Error
in output
power
Department
of Electrical
Engineering
Robot and Servo Drive Lab.
Southern Taiwan University of Science and Technology
2016/7/14
Department of Electrical Engineering
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Novel d–q axis model of the PMSM including
the effect of saturation and core losses
In a PMSM, the d- and q-axis currents are related to the internal voltage through (9).
The terminal voltage of the PMSM is related to the internal voltage and the terminal
current through (10).
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Solving the set of equations in (9) for the d- and q-axis internal voltages and substituting it
in (10), one can calculate the d- and q-axis voltages with respect to the d- and q-axis
currents as described in (11).
Where α is the ratio of the q-axis inductance to core loss resistance and ɛ can be
calculated by (12)
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Lq, Ld and Ra are equivalent parameters of the PMSM which incorporate the effect of core
losses and are defined by the set of equations presented in (13).
Solving the set of equations in (11) for currents, the d- and q-axis currents can be determined
by (14).
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Where kd and kq are the coefficients of the excitation voltage in the current equations and can
be calculated by (15).
The d- and q-axis excitation voltages displayed in this figure can be calculated by (16).
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Fig. 8 Modelling of the under excited
PMSM incorporating the
core losses
(a) Phasor diagram
(b) d- and q-axis model
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Fig. 9 Novel d–q-axis model of the
PMSM incorporating the core losses
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Conclusion
According to the experimental results, the PMSM’s output
power is highly sensitive to the flux linkage constant, whereas
its sensitivity to d- and q-axis inductances and armature resistance is
moderately low. A comprehensive study on desired accuracy of
performance calculations, performance sensitivity to the parameters and the
complexity of the parameter determination methods leads to an effective
selection of the appropriate method for parameter determination.
 Once the parameters are determined, the performance calculation
can be improved by enhancing the PMSM’s model accuracy. In
this study, a novel dq-axis model of the PMSM including the core
losses and saturation saliency was proposed. The proposed model
was applied to the laboratory PMSM and its higher accuracy in comparison
with the conventional dq-axis model was validated.
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References
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drive system incorporating structural and saturation saliencies’. Proc. Industry Applications
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2 Ying, Y., Jianguo, Z., Youguang, G., Jianxun, J.: ‘Numerical simulation of a PMSM model
considering saturation saliency for initial rotor position estimation’. Proc. 27th Chinese Control
Conf., 2008
3 Wang, Y., Zhu, J., Guo, Y.: ‘A comprehensive analytical mathematic model for permanentmagnet synchronous machines incorporating structural and saturation saliencies’, IEEE Trans.
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4 Jurkovic, S., Strangas, E.G.: ‘Design and analysis of a high-gain observer for the operation of
SPM machines under saturation’, IEEE Trans. Energy Convers., 2011, 26, (2), pp. 417–427
5 Sheikh-Ghalavand, B., Vaez-Zadeh, S., HassanpourIsfahani, A.: ‘An improved magnetic
equivalent circuit model for iron-core linear permanent-magnet synchronous motors’, IEEE
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6 Urasaki, N., Senjyu, T., Uezato, K.: ‘A novel calculation method for iron loss resistance
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2003, 18, pp. 41–477 Dlala, E.: ‘Comparison of models for estimating magnetic core losses in
electrical machines using the finite-element method
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8 Lee, B.-H., Kwon, S.-O., Sun, T., Hong, J.-P., Lee, G.-H., Hur, J.:‘Modeling of core loss
resistance for d-q equivalent circuit analysis of IPMSM considering harmonic linkage flux’, IEEE
Trans. Magn.,2011, 47, (5), pp. 1066–1069
9 Abbas, A., Yousef, H.A., Sebakhy, O.A.: ‘FE parameters sensitivity analysis of an industrial LS
interior PM synchronous motor’. Proc.IEEE Power and Energy Society General Meeting, 2008
10 Ansuj, S., Shokooh, F., Schinzinger, R.: ‘Parameter estimation for induction machines based
on sensitivity analysis’, IEEE Trans. Ind.Appl., 1989, 25, (6), pp. 1035–1040
11 Bargalló, R., Sust, J., Moron, J., Pujolras, J.C.: ‘Efficiency determination taking into account
the sensitivity of losses and measurement system’.Proc. XIX Int. Conf. on Electrical Machines,
6–8 September 2010,pp. 1–5
12 Liu, K., Zhang, Q., Chen, J., Zhu, Z.Q., Zhang, J.: ‘Online multiparameter estimation of
nonsalient-pole PM synchronous machines with temperature variation tracking’, IEEE Trans. Ind.
Electron., 2011, 58, (5), pp. 1776–1788
13 Ichikawa, S., Tomita, M., Doki, S., Okuma, S.: ‘Sensorless control of permanent-magnet
synchronous motors using online parameter identification based on system identification theory’,
IEEE Trans. Ind.Electron., 2002, 2, pp. 363–372
14 Morimoto, S., Sanada, M., Takeda, Y.: ‘Mechanical sensorless drives of IPMSM with online
parameter identification’, IEEE Trans. Ind. Appl.,2005, 1, pp. 1241–1248
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Robot and Servo Drive Lab.
Southern Taiwan University of Science and Technology
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