Abstract-In this paper, a detailed study on the Model Reference Adaptive Controller (MRAC) utilizing the reactive power is presented for the online estimation of rotor resistance to maintain proper flux orientation in an Indirect Vector Controlled Induction Motor Drive. Selection of reactive power as the functional candidate in the MRAC automatically makes the system immune to the variation of stator resistance. Moreover, the unique formation of The MRAC with the instantaneous and steady-state reactive power completely eliminates the requirement of any flux estimation in the process of computation. Thus, the method is less sensitive to integrator-related problems like drift and saturation (requiring no integration). Simulation results have been presented to confirm the effectiveness of the technique.
THE indirect field oriented (IFO)-controlled induction motor (IM) drive is widely used in high performance industry applications [1], [2] due to its simplicity and fast dynamic response. However, feedforward adjustment of the slip frequency, which requires rotor resistance, makes this scheme dependent on machine parameters. Of all the parameters, the rotor resistance undergoes considerable variation and if care is not taken to compensate for the change, the flux orientation is lost, resulting in coupling between the d- and q-axes variables. As is well known, the coupling makes the performance of the drive system sluggish. Attention is focused to enforce field orientation through online estimation of the machine parameters [3]-[6]. Many online parameter estimation schemes are available in literature [7]-[20]. They are broadly classified as follows
Spectral analysis technique
Observer based techniques
Model reference adaptive system based techniques
Heuristic methods
Reactive power based technique
In one class of method, estimation of rotor time constant is done using the spectral analysis techniques. This group of methods is based on the measured response to a deliberately injected test signal or an existing characteristic harmonic in the voltage/current spectrum. Stator currents and voltages of the motor are sampled and the parameters are derived from the spectral analysis of these samples. The second classification of rotor resistance identification scheme used observer based techniques. Most of the methods have used the Extended Kalman Filter, which is a computationally intensive technique [11] and [12].
Loron and Laliberté describe the motor model and the development and tuning of an extended Kalman filter (EKF) for parameter estimation during normal operating conditions without introducing any test signals. The proposed method requires terminal and rotor speed measurements and is useful for auto tuning an indirect field-oriented controller or an adaptive direct field-oriented controller. Zai, DeMarco, and Lipo propose a method for detection of the inverse rotor time constant using the EKF by treating the rotor time constant as the fifth state variable along with the stator and rotor currents. The drawbacks are that this method is computationally intensive.
The third group of on-line rotor resistance adaptation methods is based on principles of model reference adaptive control. This is the approach that has attracted most of the attention due to its relatively simple implementation requirements [13] and [14].
In addition to the above methods, there are also a few techniques proposed which cannot be classified in the above three categories. These may be based on the measurement of steady state stator voltage, current and motor speed, the rotor resistance can then be calculated algebraically from the equations derived. These methods are grouped to be Heuristic methods.
The main drawback for the above techniques is that the Rotor Resistance depends on d and q axis axis rotor flux which in turn depends on Stator Resistance. Therefore if any error occurs in the Stator Resistance, the accuracy of rotor flux deteriorates which in turn affects the accuracy of estimated Rotor Resistance.
Reactive power based rotor resistance estimator [1] overcomes the disadvantage of above problem. Selection of reactive power as the functional candidate in the Model Reference Adaptive Controller (MRAC) automatically makes the system immune to the variation of Stator Resistance. The unique formation of the MRAC with the instantaneous and steady-state reactive power eliminates the requirement of any flux estimation in the process of computation.
2. MRAS based rotor resistance estimation for vector controlled induction motor drives
The parameter can be calculated by the model reference adaptive system (MRAS), where the output of a reference model is compared with the output of an adjustable or adaptive model until the errors between the two models vanishes to zero. The error signal is used to drive an adaptive mechanism (PI or I controller) which provides correction of the rotor resistance. In MRAS, the plant's response is forced to track the response of a reference model, irrespective of the plant's parameter variation and load disturbance effect. Such a system is defined as a robust system. The reference model may be fixed or adaptive.
Selection of reactive power as the functional candidate in the Model Reference Adaptive Controller (MRAC) automatically makes the system immune to the variation of Stator Resistance. The unique formation of the MRAC with the instantaneous and steady-state reactive power completely eliminates the requirement of any flux estimation in the process of computation. Thus, the method is independent of Stator Resistance estimation and integration drift problems.
Fig 1 Basic structure of MRAS
In the proposed MRAC (Fig. 1), the reference model and adjustable model compute instantaneous reactive power ( ) and steady-state reactive power ( ) respectively. Note that the reference model is independent of slip frequency ( ) whereas the adjustable model depends on ( ). The error signal ( ) is fed to the adaptation mechanism block, which yields estimated slip speed ( ). Rotor resistance ( ) is then computed from ( ).
2.1 Theoretical Development of the Proposed Scheme
The d and q axis voltages for IM referring to the synchronously rotating (ωe) reference frame can be expressed as
(1)
(2)
The instantaneous reactive power (Q) can be expressed as
(3)
Substituting (1) and (2) in (3), the new expression of Q is
(4)
It is worthwhile to mention that the above expressions of Q are free from stator resistance, which is a notable feature of any reactive power-based scheme. In steady state the derivative terms are zero.
Therefore, the expression of estimated reactive power ( ) is obtained as reduces to
(5)
2.2 Ratings and Parameters of Induction Motor
The parameters of the induction machine used for simulation are given in the Table shown below.
Table 2.3 Parameters of 2.2KW 150V, 50Hz 6 Pole Induction Machine
Parameters
Values
Stator Resistance (Rs)
Rotor Resistance (Rr)
Magnetizing Inductance (Lm)
Stator Inductance (Ls)
Rotor Inductance (Ls)
Inertia Jtot
Friction B
Rated Current
Rated Torque
6.03Ω
6.085Ω
0.4893H
0.5192H
0.5192H
0.007187Kgm2
0.0027Kgm2/s
2.9Amps
7.5Nm
2.3 Simulation Results
The Performance of MRAS based rotor resistance estimator using reactive power method for vector controlled induction motor drives is analyzed with various changes in rotor resistance for the operating condition of 415V/50Hz with rated load torque of 7.5Nm
With 100% step change in Rotor Resistance.
With 100% ramp change in Rotor Resistance.
With 100% trapezoidal change in Rotor Resistance
Fig 2 Actual and Estimated Rotor Resistance for 100% step change Rr
Fig 3 Actual and Estimated Rotor Resistance for 100% ramp change Rr
Fig 4 Actual and estimated rotor resistance for 100% trapezoidal change Rr
From the results, it is observed that estimated rotor resistance is tracking with actual rotor resistance. MRAS based Rotor resistance estimator using reactive power method is studied and designed for vector controlled induction motor drives. The performance of rotor resistance estimator using reactive power is analyzed extensively for various changes in rotor resistance. From the results obtained, it is observed the error between that actual and estimated rotor resistance is always found to be less than 0.9% and the settling time is found to be approximately 1 sec.
3. Analysis of vector controlled drive performance with and without estimator
Vector control is also known as the "field oriented control", "flux oriented control" or "indirect torque control". Using field orientation (Clarke-Park transformation), three-phase current vectors are converted to a two-dimensional rotating reference frame (d-q) from a three-dimensional stationary reference frame. The "d" component represents the flux producing component of the stator current and the "q" component represents the torque producing component. These two decoupled components can be independently controlled by passing though separate PI controllers. The outputs of the PI controllers are transformed back to the three-dimensional stationary reference plane using the inverse of the Clarke-Park transformation. The corresponding switching pattern is pulse width modulated driving a Voltage source Inverter. This control simulates a separately exited DC motor model, which provides an excellent torque-speed curve. The transformation from the stationary reference frame to the rotating reference frame is done and controlled with reference to a specific flux linkage space vector (stator flux linkage, rotor flux linkage or magnetizing flux linkage). In general, there exists three possibilities for such selection and hence, three different vector controls. They are: Stator flux oriented control, Rotor flux oriented control and magnetizing flux oriented control.
As the torque producing component in this type of control is controlled only after transformation is done and is not the main input reference, such control is known as "indirect torque control". The most challenging and ultimately, the limiting feature of the field orientation, is the method whereby the flux angle is measured or estimated. Depending on the method of measurement, the vector control is divided into two subcategories: direct and indirect vector control.
In direct vector control, the flux measurement is done by using the flux sensing coils or the Hall devices. This adds to additional hardware cost and in addition, measurement is not highly accurate. Therefore, this method is not a very good control technique. The more common method is indirect vector control. In this method, the flux angle is not measured directly, but is estimated from the equivalent circuit model and from measurements of the rotor speed, the stator current and the voltage.
One common technique for estimating the rotor flux is based on the slip relation. This requires the measurement of the rotor position and the stator current. With current and position sensors, this method performs reasonably well over the entire speed range. The most high-performance VFDs in operation today employ indirect field orientation based on the slip relation. The advantages of the vector control are to better the torque response compared to the scalar control, full-load torque close to zero speed, accurate speed control and performance approaching DC drive, among others. This chapter gives complete details about indirect vector control scheme.
Fig 4 Vector controlled Induction Motor Drives
The indirect field oriented control presented here is rotor flux oriented control. Figure 4 shows the complete schematic of rotor resistance estimation for indirect field oriented control of induction motor drives. The torque command is generated as a function of the speed error signal, generally processed through a PI controller. The torque and flux command are processed in the calculation block. The three phase reference current generated from the functional block is compared with the actual current in the hysteresis band current controller and the controller takes the necessary action to produce PWM pulses. The PWM pulses are used to trigger the voltage source inverter to drive the Induction motor.
3.3 Simulation Results
The IFOC drive performance is analyzed without and with estimator for the operating condition.
Reference speed = 100rad/sec
Reference rotor flux = 0.9wb
Load torque = 7.5Nm(constant)
Rotor Resistance = 100% step change in rotor resistance is given at
1 second.
3.3.1 Simulation result for decoupled stator current for operating condition I with and without rotor resistance estimator
Fig 3.3 d and q axis of stator current for operating condition I without Rr estimator
Fig 3.4 d and q axis of stator current for operating condition I with Rr estimator
3.3.2 Simulation result for torque for operating condition I with and without rotor
resistance estimator
Fig 3.5 Actual and reference torque for operating condition I without Rr estimator
Fig 3.6 Actual and reference torque for operating condition I with Rr estimator
3.3.3 Simulation result for rotor flux for operating condition I with and without
rotor resistance estimator
Fig 3.7 Actual and reference rotor flux for operating condition I without Rr estimator
Fig 3.8 Actual and reference rotor flux for operating condition I with Rr estimator
3.5 Significance of Estimation time on the drive performance
In the implementation of the estimators, the time taken for estimation is an important parameter. Faster tracking will lead to better dynamic performance. The cost of the estimator should be low to keep the cost of the drive system within the permissible levels. Hence a study on the drive performance has been done for various estimation times and the torque and the flux responses are observed. The results are tabulated in Table 3.2 and 3.3.
The estimation time decides the transient performance indices like settling time and peak overshoot in both torque and flux responses of the vector controlled drive. The estimation error has less impact on the transient performance. However the steady state error in both torque and flux response mainly decided by the estimation error.
The drive performance is analyzed with various estimators in which the estimation error is kept constant at 1% and time of estimation is varied. The estimation error and estimation time of the vector controlled induction motor drive is analyzed for the operating condition for reference speed 100rad/sec, reference rotor flux 0.9wb, the rated load torque(7.5Nm) is reduced to 5.5Nm,40% step change in rotor resistance is given at 2 second.From this the transient response in torque and flux are studied.
Table 3.3 Flux Response for Various Estimation Times
Table 3.2 Torque Response for Various Estimation Times
ESTIMATION TIME(sec)
SETTLING TIME (sec)
PEAK OVERSHOOT
(%)
No delay
-
-
8*10-3
0.2
0.45
20*10-3
0.23
1.55
30*10-3
0.25
4.95
80*10-3
0.27
6.75
100*10-3
0.55
8.29
1
1.2
11.25
ESTIMATION TIME(sec)
SETTLING TIME (sec)
PEAK OVERSHOOT
(%)
No delay
-
-
8*10-3
0.11
2.95
20*10-3
0.14
6.55
30*10-3
0.17
10.72
80*10-3
0.2
16.33
100*10-3
0.55
16.55
1
1.15
16.65
Table 3.5 Flux Response for Various Estimation Errors
Table 3.4 Torque Response for Various Estimation Errors
ESTIMATION ERROR(%)
STEADY STATE ERROR (%)
0
0
0.4
0
1
0.26
1.5
0.44
2
0.65
3
0.71
5
1.03
ESTIMATION ERROR(%)
STEADY STATE ERROR (%)
0
0
0.4
0
1
0.39
1.5
0.50
2
0.70
3
0.95
5
1.11
Similarly with same operating conditions the steady state analysis of the torque and flux response of the drive can be done by having the estimation time as constant with various estimation errors. The performance is studied with a constant estimation time of 20ms. The Torque and the flux responses for the above conditions are tabulated in Table 3.4 and 3.5. The bold numbers shown in table 3.2, 3.3, 3.4 and 3.5 are the optimum permissible values of the estimation time and estimation error.
It is obvious that as the estimation time and the estimation error are increased the drive performance is being deteriorated. However it is quiet appealing to settle down with the maximum allowable estimation time and estimation error, so that the drive performance is satisfactory. Thus from the results it can be concluded that the performance of the drive is satisfactory with the maximum estimation time of 20ms and an estimation error of 1.5%.
4. Conclusion
The MRAS based Rotor resistance estimator using reactive power method is studied and designed for vector controlled induction motor drives. The performance of rotor resistance estimator using reactive power is analyzed extensively for various changes in rotor resistance. From the results obtained, it is observed the error between that actual and estimated rotor resistance is always found to be less than 0.9% and the settling time is found to be approximately 1 sec.
The performance of Vector Controlled Induction Motor Drive with and without Rotor Resistance estimator is studied. From the results, it is observed that the without rotor resistance estimator, the decouple control is lost which leads to significant deteriorates in the performance of vector controlled induction motor drives while with rotor resistance estimator, the decouple control is achieved and the performance of IFOC is really enhanced. The maximum permissible estimation error and estimation time for rotor resistance estimation that does not deteriorate the performance of IFOC is found to be 1.5% and 20ms respectively.
