Chapter 5 On-line parameter estimation of a three-phase induction machine
5.4.1 Case 1 – Constant induction machine parameters 127
This case assumes that the IM parameters are constant. The simulation results of the estimated IM parameters are in Figures 5.6-5.10. These figures show that the percentage errors of the estimated IM parameters are always less than 5% using the five RLS algorithms. Nevertheless, it is obvious that the assumption of constant IM parameters is impractical. The IM parameters vary during operation. Thus, the on-line parameter estimation problem is considered next with variations of the IM parameters.
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0
0.55 0.552
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.2 0.4
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.722
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.2 0.4
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.07
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.065
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4
Time (s)
Lm (%)
Figure 5.6 Results using the standard RLS algorithm for the case of constant IM parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.55 0.65
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.74
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.078
0.068
0
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.073
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Time (s)
Lm (%)
Figure 5.7 Results using the RLS algorithm with a constant forgetting factor for the case of constant IM parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0
0.55 0.552
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.2 0.4
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.722
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.2 0.4
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.07
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.066
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4
Time (s)
Lm (%)
Figure 5.8 Results using the RLS algorithm with a time-varying forgetting factor for the case of constant IM parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.55 0.6
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.74
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0682
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.5 1
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.068
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Time (s)
Lm (%)
Figure 5.9 Results using the RLS algorithm with multiple forgetting factors for the case of constant IM parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0
0.55 0.56
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4
Rs (%)
Percentage error of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.73
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0682
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.5 1
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.066
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4
Time (s)
Lm (%)
Figure 5.10 Results using the RLS algorithm with multiple time-varying forgetting factors for the case of constant IM parameters
5.4.2 Case 2 - Time-varying induction machine parameters with the same variation rate
In this case, the IM parameter variations are shown in Table 5.4.
Table 5.4 Description of the time-varying IM parameters with the same rate (30%)
IM parameters Stator resistance,
Rs (Ω)
Rotor resistance,
Rr (Ω)
Stator inductance,
Ls (H)
Magnetizing inductance,
Lm (H)
t = 0 – 2 (s) 0.550 0.720 0.0680 0.0630
t = 2 – 5 (s) 0.715 0.936 0.0884 0.0819
All IM parameters are assumed to increase by 30% at t = 2 s. Simulation results are shown in Figures 5.11-5.15 using the five RLS algorithms. In Figures 5.11-5.12, it can be realised that the estimated parameters cannot track the IM parameter variations using the standard RLS algorithm and the RLS algorithm with a constant forgetting factor.
The percentage errors of the estimated parameters are greater than 10% for all the estimated IM parameters using the standard RLS algorithm, Figure 5.11, and greater than 10% for the estimated stator and rotor resistances, 5% for the estimated stator and magnetizing inductances using the RLS algorithm with a constant forgetting factor, Figure 5.12. The forgetting factor, λ, is set to 0.98 in the RLS algorithm with a constant forgetting factor. However, the effectiveness of the forgetting factor is not significant in this case. As a consequence, the tracking capability of the algorithm has been reduced.
This also shows that the issue of choosing the appropriate forgetting factor is important and there are no clear recommendations for selecting this factor.
Figure 5.13 shows the estimation results and the percentage errors of the IM parameters using the RLS algorithm with the time-varying forgetting factor. The tracking ability of the RLS algorithm has been significantly improved when compared with the standard RLS algorithm and RLS algorithm with a constant forgetting factor. All the percentage errors are less than 10% for the estimated parameters using the RLS algorithm with the time-varying forgetting factor. These estimation results have confirmed the effectiveness of the time-varying forgetting factor in the RLS algorithm. Nevertheless, the percentage errors of the IM parameters are still significant. The reason for the poor performance using this algorithm is that when an error is detected, the parameter estimates are updated without differentiating between the errors of the estimated parameters. This causes overshoot or undershoot in the estimates, Figure 5.13.
Figures 5.14-5.15 show the estimation results and the percentage errors of the IM parameters using the two RLS algorithms with multiple forgetting factors and multiple time-varying forgetting factors. The forgetting factors λ1, λ2 and λ3 are set to 0.98, 0.99 and 0.95 respectively in the RLS algorithm with multiple forgetting factors whereas these forgetting factors are time-varying in the RLS algorithm with multiple time- varying forgetting factors. All the percentage errors of the estimated parameters are always less than 5% using these two algorithms. Unlike the estimation results with the standard RLS algorithm, RLS algorithm with a constant forgetting factor and RLS algorithm with the time-varying forgetting factor, the estimates are smoother and converge faster when the IM parameters are varied. Obviously, their performance has
been enhanced significantly when compared with the other RLS algorithms. The benefits of the two RLS algorithms with multiple forgetting factors and multiple time- varying forgetting factors have been confirmed in on-line parameter estimation of the IM where the IM parameters are varied with the same rate. Another case of different variations in the IM parameters is considered in the next section.
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.55 0.715 0.8
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 25 50
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.936
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 25 50
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0884 0.1
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 25 50
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0819 0.1
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 25 50
Time (s)
Lm (%)
Figure 5.11 Results using the standard RLS algorithm for the case of time- varying IM parameters with the same rate
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0
0.55 0.715 0.8
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 25 50
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.936
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 25 50
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0884 0.1
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 30 50
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0819 0.1
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 30 50
Time (s)
Lm (%)
Figure 5.12 Results using the RLS algorithm with a constant forgetting factor for the case of time-varying IM parameters with the same rate
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.55 0.715
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.936
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0884
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2.5 5
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0819
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Time (s)
Lm (%)
Figure 5.13 Results using the RLS algorithm with a time-varying forgetting factor for the case of time-varying IM parameters with the same rate
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0
0.55 0.715
Parameter values
Rs (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2.5
5 Percentage errors of the estimated parameters
Rs (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.936
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2.5 5
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0884
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2.5 5
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0819
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2.5 5
Time (s)
Lm (%)
Figure 5.14 Results using the RLS algorithm with multiple forgetting factors for the case of time-varying IM parameters with the same rate
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.55 0.715
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 0.936
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0884
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0819
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Time (s)
Lm (%)
Figure 5.15 Results using the RLS algorithm with multiple time-varying forgetting factors for the case of time-varying IM parameters with the same rate
5.4.3 Case 3 - Time-varying induction machine parameters with different variation rates
In this case, the IM parameter variations are assumed as in Table 5.5 and Figure 5.16.
Table 5.5 Description of the time-varying IM parameters with different rates
IM parameters
Stator resistance,
Rs (Ω)
Rotor resistance,
Rr (Ω)
Stator inductance,
Ls (H)
Magnetizing inductance,
Lm (H)
t = 0 – 2 (s) 0.550 0.720 0.0680 0.0630
t = 2 – 2.5 (s) 0.715 0.720 0.0680 0.0630
t = 2.5 – 3 (s) 0.715 1.080 0.0680 0.0630
t = 3 – 5 (s) 0.715 1.080 0.0816 0.0756
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.55 0.715
Rs (Ohm)
Reference parameter values
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 1.08
Rr (Ohm)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0816
Ls (Henry)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0756
Time (s)
Lm (Henry)
Figure 5.16 IM parameter values for the case of time-varying IM parameters with different rates
-The IM parameters, Rs, Rr, Ls and Lm, are constant for t = 0 – 2 s.
-The IM stator resistance, Rs, is increased by 30% at t = 2 s. The remaining parameters, Rr, Ls and Lm, are constant.
-The IM rotor resistance, Rr, is increased by 50% at t = 2.5 s. The stator resistance, Rs, remains at its varied value. The remaining parameters, Ls and Lm, are constant.
-The stator and magnetizing inductances, Ls and Lm, are increased by 20% at t = 3 s. The stator and rotor resistances, Rs and Rr, remain at their varied values, 30% and 50%
respectively.
Figures 5.17-5.19 show the estimation results of the IM parameters using the standard RLS algorithm, RLS algorithm with a constant forgetting factor and RLS algorithm with the time-varying forgetting factor. It can be seen that the percentage errors are larger than 20% for the stator and rotor resistances and 5% for the stator and magnetizing inductances. When the IM parameters vary in this manner, the effectiveness of the time-varying forgetting factor has not been established. Obviously, the algorithm does not take into account the estimation errors of each IM parameter and the corrections have then been applied for all IM parameters with the same rate. This results in large errors for the estimations.
The estimation results using the RLS algorithm with multiple forgetting factors are shown in Figure 5.20. The forgetting factors, λ1, λ2 and λ3, are set to 0.98, 0.99 and 0.95 respectively in this algorithm. The percentage errors are larger than 5% in this case.
This means that the values of the forgetting factors above are not appropriate for this application when the IM parameters vary in this manner. A different set of forgetting factors needs to be assigned so that the percentage errors can be reduced. Once again, it can be realised that the issue of choosing appropriate forgetting factors is important. It is not easy to choose good forgetting factors. The RLS algorithm with multiple time- varying forgetting factors is the best choice for this application. The estimation results using the RLS algorithm with multiple time-varying forgetting factors are shown in Figure 5.21. The forgetting factors are time-varying which depend on the input signals and the value of the covariance matrix. The percentage errors of the estimated IM parameters are less than 5% in this case. This confirmed the effectiveness of the proposed RLS algorithm when the IM parameters are time-varying with different rates.
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0
0.55 0.715
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 20 40
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 1.08
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 20 40
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0816
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0756
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 20
Time (s)
Lm (%)
Figure 5.17 Results using the standard RLS algorithm for the case of time- varying IM parameters with different rates
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.55 0.715
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 20 40
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 1.08
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 20 40
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0816
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0756
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 20
Time (s)
Lm (%)
Figure 5.18 Results using the RLS algorithm with a constant forgetting factor for the case of time-varying IM parameters with different rates
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0
0.55 0.715
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 20 40
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 1.08
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 20 40
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0816
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 20
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0756
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 20
Time (s)
Lm (%)
Figure 5.19 Results using the RLS algorithm with a time-varying forgetting factor for the case of time-varying IM parameters with different rates
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.55 0.715
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 1.08
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 20 30
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0816
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 20
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0756
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 10 20
Time (s)
Lm (%)
Figure 5.20 Results using the RLS algorithm with multiple forgetting factors for the case of time-varying IM parameters with different rates
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0
0.55 0.715
Rs (Ohm)
Parameter values
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rs (%)
Percentage errors of the estimated parameters
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.72 1.08
Rr (Ohm)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Rr (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.068 0.0816
Ls (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Ls (%)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.063 0.0756
Time (s)
Lm (Henry)
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 5 10
Time (s)
Lm (%)
Figure 5.21 Results using the RLS algorithm with multiple time-varying forgetting factors for the case of time-varying IM parameters with different rates 5.5 Conclusion
This chapter introduced a regressive model which is simple and appropriate for on-line parameter estimation of the IM. The RLS algorithm with multiple time-varying forgetting factors was proposed in this chapter to solve the on-line parameter estimation problem. When using the proposed RLS algorithm, the percentage errors of the estimated parameters are always less than 5%. This confirmed the benefit of the proposed algorithm for the on-line estimation application, especially for the case of time-varying IM parameters with different rates. Regarding the RLS algorithm with multiple time-varying forgetting factors, the disadvantages of the existing RLS algorithms such as covariance matrix vanishing, the covariance “wind-up” problem and the overshoot or undershoot problem in the estimations were overcome. The proposed RLS algorithm is better than the other RLS algorithms for on-line parameter estimation of the IM.
5.6 References
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353-364, May 2002.
[5.5] T. Iwasaki and T. Kataoka, “Application of an extended Kalman filter to parameter identification of an induction motor”, Conference Record of the 1989 IEEE Industry Applications Society Annual Meeting, pp. 248-253, 1-5 October 1989.
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[5.11] M. Velez-Reyes, K. Minami and G. C. Verghese, “Recursive speed and parameter estimation for induction machines”, Conference Record of the 1989 IEEE Industry Applications Society Annual Meeting, pp. 607-611, 1-5 October 1989.
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[5.13] J. Stephan, M. Bodson and J. Chiasson, “Real-time estimation of the parameters and fluxes of induction motors”, IEEE Transaction on Industry Applications, vol. 30, no. 3, pp. 1-12, May/June 1994.
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CHAPTER 6
ENERGY EFFICIENT CONTROL OF A THREE-PHASE INDUCTION MACHINE
6.1 Introduction
Energy efficient control of the induction machine (IM) has received significant attention in recent years because of concerns regarding energy saving and environmental pollution reduction as presented in Chapter 1. Basically, the IM operational efficiency is high for rated conditions of the load, speed and flux. Nevertheless, the IM drive systems usually operate at light loads most of the time. In this case, if the rated flux is still maintained at light loads, the core loss will increase dramatically. This results in poor IM efficiency. In order to solve this problem, it is well-known that the IM efficiency can be improved by reducing the flux level when it operates at light load conditions [6.1].
Various approaches have been researched to enhance the IM efficiency at light loads.
Two basic control approaches, known as model-based control and search control have been introduced.
The model-based control approach uses an IM loss model to define an optimal flux for each operational point at a given load torque and machine speed. This approach has a fast response time. However, it is not robust to parameter variations of the IM. A neural network [6.2]-[6.7], a genetic algorithm [6.8]-[6.9] and a particle swarm optimization algorithm [6.10] have allowed an optimal flux level to be defined for energy efficient control using the IM loss model. In the model-based control approach, the IM loss model is usually formed by the IM loss components such as the stator and rotor copper losses, core loss, stray loss and mechanical losses [6.4]-[6.6] and [6.9]-[6.10].
The search control approach is based on a search of optimal flux levels which ensure minimization of the IM input power measured for a given load torque and machine speed. It can be realised that this approach is insensitive to parameter variations of the IM and does not require a priori knowledge of the IM parameters. Nevertheless, the response for obtaining an optimal flux value is slow. Additionally, input power
measurement noise can affect the algorithm performance. A fuzzy logic [6.11]-[6.16]
and a golden section technique [6.17] have been applied for this control strategy.
It is obvious that there are always disadvantages for model-based control and search control approaches. This is why hybrid controllers [6.18]-[6.24] have recently been examined for energy efficient control of the IM. These are a combination of the model- based control and search control approaches. By using hybrid controllers, the energy efficient control strategy always remains optimal. Nevertheless, it can be realised that the structure of these controllers is complex.
This chapter proposes an energy efficient control strategy for the IM based on the model-based control approach. A loss model is introduced for energy efficient control which is not formed by the IM loss components, such as the stator and rotor copper losses, core loss, stray loss and mechanical losses. Additionally, in order to adapt to the IM parameter variations, an on-line parameter estimator for the IM is proposed to perform together with the energy efficient controller. The energy efficient control strategy then always remains optimal regardless of the IM parameter variations. The on- line parameter estimator uses the RLS algorithm with multiple time-varying forgetting factors which was presented in Chapter 5. The derivative technique and the chaos PSO algorithm are utilised to define an optimal IM flux level for a certain load and machine speed. Simulations and comparisons are performed to confirm the effectiveness of the proposed energy efficient control strategy in this chapter.
6.2 Energy efficient control
6.2.1 Induction machine model for energy efficient control
In the model-based control approach, most of the previous energy efficient control strategies were based on the model of the IM loss components which are the stator and rotor copper losses, core loss, stray loss and mechanical losses. This chapter introduces a loss model for energy efficient control of the IM which is more general and simpler than others. This loss model is described as follows.