Rotor resistance estimation methods for high performance IM drive – A Review
Three phase induction motors are the most prominently used drives due to their reliability and cost.Indirect field oriented control (IFOC)scheme is of industrial standard and is being used in high performance IM drives...
- S. Himavathi, Chitra. A
During the past three decades, the adjustable speed AC drive technology has gained a lot of momentum. It is well recognized that AC motor drives account for more than 50% of all the electrical energy consumed in developed countries. Induction motors (IM), and permanent magnet synchronous motor are the best candidates for variable speed drive applications. This is because induction motors rugged and require less maintenance. But at the same time they are non-linear, parameter varying, multivariable with coupling effect and has complex dynamics of higher order. After the invention of vector control, it has been demonstrated that induction motor could be controlled like a separately excited DC motor. For a practical drive, the instantaneous response (torque or speed) is not possible due to electrical and mechanical inertia of the drive and also due to variations of motor parameters. The estimation of parameters under different operating conditions makes the system possible to trackthe command trajectory with good dynamic response.
Need for rotor resistance estimation
Three phase induction motors are the most prominently used drives due to their reliability and cost.Indirect field oriented control (IFOC)scheme is of industrial standard and is being used in high performance IM drives. However, the performance of the IFOC drive depends on the accuracy of the estimated rotor flux from the measured stator currents.The accuracy of the estimated rotor flux is greatly influenced by the value of the rotor resistance which is not constant. Thus the major problem is the variation in rotor resistance. Rotor resistance may vary due to the rotor heating and recovering this information either with a thermal model or a temperature sensor is difficult. In addition rotor resistance can change significantly with rotor frequency due to skew and proximity effect. The problem related to rotor resistance adaptation has been investigated by various authors.
Fig.1 Classification of Rr estimation methods
a. Spectral analysis technique:
This method encompasses all of the cases where the identification 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/or voltages of the motor are sampled and the parameters are derived from the spectral analysis of these samples. In the case of spectral analysis, a perturbation signal is used because under no-load conditions of the induction motor, the rotor induced currents and voltages become zero, so slip frequency becomes zero, and hence, the rotor parameters cannot be estimated. The main drawback of this method is that the hostile effect of the injected signal on the motor dynamics. Also this requires an additional hardware for the signal injection.
b. Observer based technique:
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 requiresterminal and rotor speed measurements and is useful for auto tuning an indirect 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. This is similar to a previously mentioned method that injected perturbationin the system, except that in this case, the perturbation is not provided externally. Instead, the wide-band harmonics contained in a PWM inverter output voltage serve as an excitation. This method works on the assumption that when the motor speed changes, the machine model becomes a two-input/two output time-varying system with superimposed noise input. The drawbacks are that this method is computationally intensive.
c. Model reference adaptive system (MRAS) based technique:
The third major group of online rotor resistance adaptation methods is based on the principles of model reference adaptive control scheme. This is the approach that has attracted most of the attention due to its relatively simple implementation requirements. The basic block diagram used in this method is given in Fig.2.
Fig.2 Rrestimation using model reference adaptive system based technique
The basic idea is that one quantity can be calculated in two different ways. The first value is calculated from references inside the control system. The second value is calculated from the measured signals. One of the two values is independent of the rotor resistance (rotor time constant). The difference between the two is an error signal, whose existence is assigned entirely to the error in rotor resistance used in the control system. The error signal is used to drive an adaptive mechanism (PI or I controller) which provides correction of the rotor resistance.
d. Heuristic techniques:
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.
Need for Intelligent estimator:
One of the common features that all the methods of this group share are that rotor resistance adaptation is usually operational in steady state only and is disabled during transients. In addition to the above methods, there are also a few techniques proposed which cannot be classified in the above three categories. Even these identification methods are valid only for steady state operation of the induction motor. Recently, few authors have proposed a new technique for on-line estimation of rotor resistance in induction motor drives using AI techniques.
a. Fuzzy logic system:
Fuzzy logic systems have the capability of extracting knowledge out of heuristics. In the past three decades, fuzzy systems have supplanted conventional technologies in many applications. One major feature of fuzzy logic is its ability to express the amount of ambiguity in human thinking. Thus, when the mathematical model of the process does not exist, or exists but with uncertainties, fuzzy logic is an alternative way to deal with the unknown process.
The fuzzy based estimator is proposed by B. Karanayil is shown in Fig. 3, which involves voltage and current model of the induction motor. The current model equations involve Rr, hence the flux ( ) obtained through this acts as the actual flux. The flux ( ) calculated using the voltage model equations acts as the reference flux. The error between the actual and the reference flux is one input to the fuzzy estimator. The other input to the fuzzy estimator is the change in error. The fuzzy estimator is designed to generate the incremental rotor resistance.
Fig. 3 Fuzzy logic based rotor resistance estimator
In the signal conditioning block the incremental rotor resistance from the fuzzy estimator is continuously added to the previously estimated rotor resistance and then it is passed through a low pass filter and limiter. Here the fuzzification stage variables are flux error and change in flux error and the output variable is change in resistance.
b. Neural based estimator:
Advancements in neural network have increased its application for the control, modelling and identification of nonlinear dynamic systems. Their capability to approximate a wide range of non-linear functions to any desired degree of accuracy has been proved. They also offer the advantages of extremely fast parallel computation, immunity from input harmonic ripples, and fault tolerant characteristics.
Two independent estimators are used to estimate the rotor fluxvectors of the induction motor as shown in Fig. 4a. Equation (1) based on stator voltages and currents arecalled as voltage model equation. As this is independent of Rr, the flux estimated using this serves as the desired state variable. Equation (2) is based on stator currents and rotor speed called as current model equations.As this is dependent on Rr, the flux estimated from this serves as actual state variable. The total error between the desired and actual state variables is then back propagated to adjust the weights of the neural model, so that the output of this model tracks the actual output. The rotor resistance of an induction motor is estimated using the neural network structure as shown in Fig 4b.
Fig.4 (a) Rrestimation using NL-MRAS based estimator (b) Neural Network structure for Rr estimation
Here T is the sampling period, Tr is the rotor time constant, r is electrical rotor angular velocity, dr and qr are d-axis and q-axis rotor fluxes, Ids and Iqs are d-axis and q-axis stator currents, Vds and Vqs are d-axis and q-axis stator voltages, Lr, Ls, and Lm are the rotor, stator and magnetizing inductances, Rs is the stator resistance and is called leakage coefficient. The neural network structuredesigned shown in Fig 4b is based on the discrete currentmodel equations given (3) and (4) , where W1, W2, W3 represent the weights of the neural network. In the network, W2 is already known and W1 and W3 need to be updated.The Rr can be found using the equation (5).
The weights between neurons, W1and W3 are trained, so as to minimize the energy function E. The energy function is given in equation (6).
Where the rotor flux is obtained using voltage model equations, and is the rotor flux estimated using current model equations. For updating the weights, neural learning algorithms are employed which is discussed in the next section.
Conventional Neural learning algorithms:
The task of training the network can be thought of in terms of an optimization problem. The variables to manipulate are the various weight factors while the variable we are seeking to minimize is the NN output error. The variants of back propagation learning algorithms are
1. Back propagation with momentum (BP with momentum)
2. Back propagation with variable learning rate (BP with VLR)
3. Quick propagation (Quick prop)
The change in weight updates for all the neural algorithms are coded as m-File in Matlab. The voltage model equations are implemented in simulink model file. The neural model estimator is updated at a sampling frequency of 10 kHz, so the sampling period for on-line rotor resistance estimator is T = 0.0001 sec. The weight W2 is fixed and the weights W1 and W3 are updated in such a way that the energy function E is minimized. The induction motor has been modeled using T-model equations in Matlab/Simulink to incorporate the variations in rotor resistance as in the practical case.The update equations for the conventional back propagation algorithm with momentum are given by (7) to (10).
Where, is the learning rate and is momentum constant. In BP with VLR adaptive learning rate helps in fast convergence irrespective of the start values. This is one of the heuristic methods to accelerate the convergence rate of the gradient descent algorithm.The quick prop is another heuristic technique to accelerate the convergence rate of gradient descent technique. This technique employs a dynamically changing momentum factor. The acceleration rate is determined by the successive difference between the slope values. This is similar to newton’s method since it considers the second order gradient also. Hence in all this conventional algorithms the number equations involved increases, as convergence rate is increased.
Modified neural learning algorithm proposed by the authors:
In this algorithm the back propagation learning technique is used to update the weight W3 and the weight W1 is found from the value of W3. Here the initial transients are reduced in the estimation and also this shows excellent tracking performance.The update laws for the proposed constraint based back propagation algorithm are through (11) to (13). In the proposed constraint based BP only W3 is updated and the other weight W1 is obtained from the equation (13). Hence it is clear that the number of equations have been reduced in the case of the proposed algorithmwhich in turn yields fast convergence.
Among all these methods the proposed constraint based back propagation is concluded to be the most suitable learning algorithm for neural based rotor resistance estimator. Though the BP with VLR provides comparable performance with the proposed method, the computation complexity involved in VLR increases the time taken for estimation. Also here the number of equations gets reduced from which simplifies the process.
The advantages of the proposed constraint based back propagation are
Superior tracking performance
Less rigorous computation
This is well proven from the simulation results presented in the coming section.
Observations and Results:
The induction motor has been modeled using T-model equations in Matlab/simulink to incorporate the variations in rotor resistance as in the practical case. The simulation results for the rotor resistance estimation using various learning strategies are studied for the following cases. The linear change in rotor resistance due to gradual variation in temperature can be considered as ramp change and sudden change in rotor resistance due any rotor bar breakage because of excessive temperature can be considered as step change.
1. With 40% step change in Rotor Resistance
2. With 40% trapezoidal change in Rotor Resistance
The simulation studies are carried out for the above cases with rotor resistance estimator trained using conventional algorithms and proposed algorithm.Since BP with VLR is exhibits better response in the conventional algorithms, the performance of the neural based rotor resistance estimator using back propagation with VLR is presented in Fig. 5a and 6a. The performance of the neural based rotor resistance estimator using proposed learning algorithm is shown in the Fig. 5b and 6b. In both the cases the results are shown for 40% step change in Rr and 40% trapezoidal change in Rr. Though the BP with VLR provides comparable performance with BP with constraint the complex computation involved in VLR shows its limitation on digital implementation.
Fig. 5 Estimation ofRr with 40% step change in Rr (a) using BP with variable learning rate(b) using constraint based BP
Fig. 6 Estimation of Rr with 40% trapezoidal change in Rr(a) using BP with VLR (b) using constraint based BP
The simulation results are consolidated in a pictorial form in the Fig.7. The estimation error(%) and estimation time(ms) for 40 % step change in Rrwith conventional and proposed learning algorithm are shown in Fig. 7a. Similarly in Fig. 7b the error and estimation time are shown for 40 % trapezoidal change with conventional and proposed learning algorithms.
Fig. 7. Estimation error and estimation time with conventional and proposed algorithms with (a) Step change (b) Trapezoidal change
From the results the actual and estimated value of rotor resistance, accuracy of estimation in terms of percentage error and time taken for estimation are presented for all the learning techniques.It can be seen from the results the performance factors such as speed of estimation and percentage error are found to be better with the proposed learning method namely constraint based back propagation. Hence this can be the appropriate learning method for neural network based rotor resistance estimator.
Digital implementation is desired because of higher accuracy, high repeatability, low noise sensitivity, better testability, higher flexibility, and compatibility with other types of preprocessors. Digital implementation is possible either with a general purpose Digital SignalProcessor (DSP) or with a Field Programmable Gate Array (FPGA). DSP is preferred, as it is general purpose hardware at low cost and also involves simple implementation. The proposed neural based rotor resistance estimator is first implemented in a low cost DSP. As the estimation speed of this estimator is not faster enough to improve the dynamic performance of the drive, the implementation is carried out in FPGA. The two implementation schemes have been compared in terms of estimation error and estimation time in Fig. 8.
Fig, 8 Performance comparisons of FPGA and DSP based implementations
Though the estimation error is almost same with both implementation methods the time taken for estimation is large in the DSP implementation due its sequential processing nature. The faster tracking in the FPGA based implementation is because of its parallel computing units. Hence the FPGA implementation is found to be suitable for the proposed neural estimator.
The various methods employed for rotor resistance estimation in induction motor drives are presented. Well accepted methods from the spectral analysis till the intelligent mode of estimation have been reviewed. The neural based estimator is expanded along with the neural algorithms. A modified neural learning algorithm namely constraint based BP for rotor resistance estimation is presented.
The neural based rotor resistance estimator has been trained with various learning strategies and the results are compared in terms of time taken for estimation, accuracy of estimation and complexity. The proposed algorithm and VLR algorithm are shown to perform well in terms of accuracy and tracking. Through extensive simulation for step, ramp and trapezoidal changes in Rr the proposed algorithm is shown to be better than the VLR algorithm in terms of computational complexity and tracking capability.
The proposed Rr estimator is implemented using DSP and FPGA. The DSP implementation is carried out using F2812 processor and the time taken for estimation is found to be 1.4sec. To further improve the speed of estimation the estimator is implemented using Spartan 3E FPGA. In FPGA the time taken for implementation is obtained to be 0.0089sec. Both DSP and FPGA estimate Rr with good accuracy but the FPGA is 157 times faster than the DSP. As Rr varies online the speed of estimation is crucial for the drive performance.Hence FPGA is concluded to be the most suitable digital hardware for Rr estimation.
Department of Electrical and Electronics Engineering,
Pondicherry Engineering College.
School of Electrical Engineering,
VIT University, Vellore, India
If you want to share thoughts or feedback then please leave a comment below.