Parameter Sensitivity and Adaptation of the Proposed Core-Loss Model

For model-based analysis and design, the accuracy of the model parameters have important effects on the results. To study the effects of the parameter values on the simulated machine losses, a series of model parameter sensitivity tests are performed on the 1.5HP IM at three different speed and torque conditions as shown in TABLE III. In each simulation run, one of the six independent model parameters, Rs, Lls, Rr’, Llr’, Rc, Lm or Lms, is changed by -20%, -

10%, 10%, 20% from their nominal values. The results for the change of losses compared to using the nominal parameters are shown in Fig. 30, and the legend of Fig. 30 is explained in TABLE III due to limited space in the figure.

TAB LEIII.THE THR EE COND IT IO NS USED IN THE PAR AM E TER SE NS IT IV ITY TESTS

Speed Torque Line color + Marker

CD1 (Condition 1) 1735 RPM 6 N·m Purple + Dot

CD2 (Condition 2) 1735 RPM 1 N·m Green + Cross

CD3 (Condition 3) 600 RPM 1 N·m Orange + Square

It is found that, first, Rc mainly affects Pcore; Rs and Lm(Lms) mainly affect PCu; Lls and Llr’

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effect on Pcore. These effects increase as the parameter error increases. Second, the increase of TL

mainly increases PCu. Thus, ∆PCu in percentage is less sensitive to parameters’ variation in high-

torque condition due to the increased value of PCu. Similarly, the increase of speed increases

Pcore. Thus, ∆Pcore in percentage is less sensitive in the high-speed condition. Third, due to the

reasons in the previous point, the estimation deviation can exceed 20% in the sensitive low- torque low-speed condition, while the estimation deviation is less than 10% in the relatively insensitive high-torque high-speed condition for the same changing degree of the model parameters. Fourth, the effects of the model parameters on the power loss estimation are monotonous and almost linear before saturation. Thus, if the increase of a certain parameter increases the power loss estimation, then the decrease of the same parameter will decrease the same type of the power loss estimation in almost the same degree.

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Fig. 30. Model sensitivity test results for (a) Rs; (b) Ll s; (c) Rr’; (d) Ll r’; (e) Rc; (f) Lm(Lm s). (Solid line: ∆Pc u; Dashed line: ∆Pc o r e; Dotted line: ∆Pt o t a l)

3.1.5.2 Parameter Adaptation of the Proposed Core-Loss Model

As shown in the previous section that the value of model parameters will affect the proposed model’s accuracy and the estimated machine losses. Therefore, it is important to accurately characterize the model parameters, or adapt the model parameters with the change of frequency and flux level. The adaptation of the model parameters with different frequencies and flux levels are shown next, where the Pacific AC source is used to adjust the input sinusoidal excitation as needed.

First, different frequencies are applied in the characterization tests while rated V/f ratio is used. The input voltage increases along with the frequency until rated value. The extracted machine parameters are shown in Fig. 31. It is seen that Rs is constant from the DC test. Lls and

Llr’ are also almost constant with respect to frequency. Moreover, Rr’ slightly increases with

frequency in general, since the practical stray loss, which is assumed to be zero in the no-load test, is included in the Rr’ determination. Lm slightly decreases with frequency. It is important to

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Pcore, it is expected that Pcore is a strong function of frequency. When the V/f ratio is constant, the

Pcore at different frequencies are shown in Fig. 32. As expected, Pcore increases with frequency.

Fig. 31. Parameters of the proposed core-loss model at different frequencies

Fig. 32. Core loss at different frequencies

Then, the operating frequency is fixed at 40Hz. The input voltage is decreased from rated value with the decrease of the V/f ratio until the input current starts to increase. The extracted machine parameters at different V/f ratios are shown in Fig. 33. It is seen that Rs is still constant

while Lls, Llr’ and Rr’ are also almost independent of the V/f ratio. Lm and Rc tend to have a

parabolic shape. On the other hand, Pcore at different flux levels are shown in Fig. 34. It is seen

that Pcore increases with the V/f ratio, or machine input voltage when the operating frequency is

fixed. Note that higher-order harmonics in the PWM excitation will also modify the model parameters beyond the values that are determined by the fundamental excitation component. Therefore, the model parameters obtained from the sinusoidal-fed characterization tests could be

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inaccurate for the corresponding inverter-fed conditions depending on the harmonics’ levels. Better accuracy of the core-loss model is expected with the inverter-fed characterization tests, which unfortunately are not available in any literature at the moment.

Fig. 33. Parameters of the proposed core -loss model at different flux levels

Fig. 34. Core loss at different flux levels