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Online equivalent parameter estimation using BPANN controller with lowfrequency signal injection for a sensorless induction motor drive
Journal of Electrical Systems and Information Technology volume 9, Article number: 20 (2022)
Abstract
The development of a sensorless induction motor drive is elaborated in this paper with a unique feature of online estimation of equivalent circuit parameters (ECPs) during its running condition. The cases like temperature rise of the motor, change in drive speed due to sudden changes in its loading, or even in supply voltage are the sources of error in accurate ECPs evaluation. The indirect fieldoriented control (IFOC) scheme is adopted in its controller to deal with these challenges. The drive controller is designed with a model reference adaptive system (MRAS) having two models—one is the plant model to estimate the ECPs during running conditions while the other one is the reference model. The HG diagram method is utilized in the reference model to estimate the reference ECPs (ECP_{R}) before starting without the need of performing any physical tests on the motor. During the transition period of the drive, the feedback signal is fed to the reference model to generate the ECP_{R}. The technique of the backpropagation algorithm with an artificial neural network (BPANN) is utilized in the plant model while its weight and gain parameters are tuned with the reference ECPs. The Adam rule is utilized for fast convergence of the BPANN weights during the transition period while stator temperature and speed feedback enhance the overall accuracy in ECPs. A discretetime lowfrequency signal injectionbased resistance assessment and sensorless speed estimation method to determine inductances are adopted for minimizing the ECPs errors. The results from MATLABbased simulation and a hardware prototype using a DSPIC microcontroller with different running conditions show the efficacy of the proposed algorithm.
Introduction
Nowadays IFOC schemes are generally adopted in ASD controllers of IM for better speed control, both during its transient and steadystate running [1]. Determination of accurate values of ECPs is essential based on which the time constant, slip speed relationship, dq axis currents, etc., can be evaluated for successful implementation of IFOC. But during running conditions some of the ECPs, stator, and rotor resistances, in particular, are getting changed due to harmonics heating effect, skin effect, change in load, and undervoltage running reasons [2, 3]. These changes in ECPs are the sources of errors resulting in the inaccurate generation of gate triggering pulses and hence proper control of speed could not be achieved. In IFOCbased VSIIM drive, accurate estimation of ECPs during steadystate and transient conditions is an ageold challenge. Moreover, highspeed DSPbased processors are also being utilized to process these ECPs data following the IFOC algorithm with the feedback of speed, temperature, loading conditions, etc. [4,5,6,7,8].
For estimation and optimization of IM parameters, various conventional methods like spectrum analysis and sinusoidal signal perturbation as well as intelligent control algorithms like GA, PSO and their hybrid form, bacterial foraging, anthill, GSA, etc., offline methods [9, 10] are proposed. These algorithms are easy to implement and support multiobjective optimization but the convergence time is large, which makes these algorithms incapable of online application. To overcome these problems, FLCs are used but the rulebased FLC requires all the possible variations of the motor condition. Hence FLC could not be able to produce a satisfactory result where all of this information is not available. Various other state observers like EKF, Luenberger observer and its extended form, polynomial regression method [11], etc., can estimate parameters efficiently but higher complexities make these algorithms timeconsuming and becoming difficult for their realtime implementation even with DSPbased processors [3, 4].
In works [12,13,14,15,16], ANN algorithms using highspeed DSPbased processors are proposed as these algorithms perform faster than other heuristic ones. The efficiency of the ANN algorithm depends upon its structure, chosen optimizer, and training logic. Accordingly, RNNs, LSTM, CNNs, encoderdecoderbased networks, and GNNs are preferred [12]. But these types of network are either unsupervised or selfsupervised type for which the training of these NN models is relatively slow and also needs extra memory to hold all the set of sampled data [12,13,14,15,16]. Besides, most of the NN, RNN, and GNN also suffer from exploding and vanishing gradient problems. To minimize these, some improved activation functions like Leaky ReLu [17] and Adam optimizers [18] are chosen to get a fast and stable convergence. However, the activation function like Leaky ReLu does not provide a satisfactory result with RNN.
For closeloop scalar or vector control methods, estimation of speed is very essential and any arrangement for speed sensor mounting makes the drive less reliable and costly. Without these sensors, it is possible to estimate speed from the feedback of stator voltage and current signals, but these processes are complex and their accuracy depends on motor parameters. Various methods have been proposed for sensorless speed estimation like slip calculation, EKF, Luenberger observer, AI, MRAS, sliding mode observers, flux linkage method, back emf method, etc. [19,20,21,22].
Temperature variation is the main cause of variation in the stator and rotor resistances. This may lead to inaccurate speed estimation and vector control logic may get detuned. Thus temperature correction of these resistances is essential. Various methods are proposed like dc signal injection, ac signal injection, Goertzel algorithm to the complex current and voltage space vectors, thermal observers, voltage disturbance observers, etc., to estimate the temperature or the stator resistance directly [23,24,25,26].
Getting motivated by these, the authors of this paper propose a model reference, the adaptive systembased plant model, where a BPANNbased efficient algorithm is adopted to estimate accurate equivalent circuit parameters. The ECPs are estimated both in prestarting in offline mode, during starting transient and running conditions as well in an online mode without the requirement of physical tests like noload and blocked rotor tests. The BPANNbased online estimation scheme is adopted to consider any change in parameters due to changes in the running conditions like temperature variation which in turn makes the drive more accurate and efficient. Adoption of the Adam method [18] makes the tuning of the weight factors of ANN at a faster convergence rate such that this tuning is completed during the starting of the motor irrespective of the capacity of the motor. The HG [27, 28] method is adopted for the evaluation of ECP_{R} in the reference model during starting the transient period with the help of nameplate data [29] and the feedback signals of voltage and current. This ECP_{R} is used to train the BPANN during motors starting transient period. Besides, for diagnosis purposes, a machine monitoring unit is also developed that interfaces with the DSPbased microcontroller and displays all the machine parameters, variables, and feedback values before and during running conditions. The proposed system has the following unique features: (i) The IFOC controller is broadly constituted with two models namely the reference model and the Plant model to generate ECPs independently. (ii) The ECPs have been generated accurately from M_{R} using motor nameplate data and the HG diagram method up to the starting transient period. (iii) The BPANN gain parameters of M_{P} are getting tuned during the starting transient period. After then, ECPs are evaluated during the entire running condition of the motor. (iv) To maintain the accuracy in ECPs evaluation from M_{P}, the estimation of motor resistance during running conditions as well as temperature using the SSI method as well as rotor speed using the sensorless scheme is adopted. (v) The various parameters during running conditions can be monitored from a remote GUI using its MMU module. This can also be used for diagnosis purposes.
The uniqueness of the proposed work is that an online accurate ECPs estimation scheme is developed with the help of a robust IFOC controller using BPANN based plant model along with their necessary corrections using feedback of sensorless estimated values of speed and motor temperature.
Proposed IFOC based induction machine drive
Equivalent circuit parameter model of IM
The steadystate per phase equivalent circuit of the IM referred to the stator side in the dq reference frame is shown in Fig. 1 where R_{s}, R_{r}, X_{s}, X_{r}, L_{s}, and L_{r} represent the stator and rotor resistance, reactive inductances while R_{m}, X_{c}, and L_{m} represent core resistance, reactance, and mutual inductance, respectively. The equivalent impedance of the system is given by Eq. (1)
To study the various dynamic conditions during the running of the motor, the IFOC scheme is generally adopted. To implement IFOC, this steadystate per phase equivalent circuit is represented by dynamic equivalent circuit in the synchronously rotating dq model as shown in Fig. 1, where the stator current I_{s} is represented by (i_{ds}, i_{qs}) and rotor current I_{r} as (i_{dr}, i_{qr}), the stator and rotor fluxes by (ψ_{ds}, ψ_{qs}) and (ψ_{dr}, ψ_{qr}), stator and rotor voltages by (v_{ds}, v_{qs}) and (v_{dr}, v_{qr}). The synchronous speed is ω_{s} and the rotor speed is ω_{r}.
Proposed schematic for IFOC drive
The schematic diagram of the proposed IFOC of the VSIIM drive, as shown in Fig. 2, has four major blocks—namely (i) power unit, (ii) control unit, (iii) sensor unit, and (iv) machine monitoring unit (MMU). The power unit is built with IGBTs in the HBridge configuration to provide the controlled power output to the IM. The control unit is built with a fast operating DSP microcontroller; the firmware of which estimates the proposed equivalent circuit parameter required to generate triggering pulses following IFOC algorithms with greater accuracy. The IFOC controller logics are described in detail in the following “The IFOC controller schematic” section to generate modulating signal corresponding to the SVM scheme. Accordingly, the generated triggering pulses are fed to the respective IGBTs through their proper gate driver circuit so that the desired speed of the IM can be achieved. To achieve better speed control, the feedback signals of voltage, current, and speed are fed to the IFOC logic. Thus, the sensor unit is equipped with voltage hall sensors for voltage sensing, a current hall sensor for current sensing, and an optical encoder for rotor speed sensing. To have a better understanding of the changes in the internal parameters of IM during ts running conditions, a PCbased data acquisition system is developed where the ECPs from IFOC is communicated serially. The MMU is a PCbased GUI to display, analyze and control various running states by collecting data from the microcontroller using serial communication. This stateoftheart GUI is extremely helpful in designing and debugging the control algorithm, for initial training of single layer BPANN weight factors, etc. From this GUI, the desired speed can also be set.
The IFOC controller schematic
The adopted IFOC controller schematic with independent paths for the torque and flux control using orthogonal currents i_{ds} and i_{qs} as shown in Fig. 3. The dq stator currents as reference are generated from flux and torque flow paths using Eq. (2) and (3).
where \(\psi_{{\text{r}}}\) is the rotor flux and T_{e} is the electromechanical torque, p is the number of poles, K_{1} and K_{2} are the gains of the flux flow path and torque flow path, respectively. In IFOC, the ψ_{qr} = 0 and ψ_{dr} = ψ_{r}. The gain K_{3} is used to generate the ω_{sl} following Eq. (4) which in turn helps to generate a unit vector for axis transformation as shown in Eq. (5)
As seen in Fig. 3, three PI controllers are used, in the torque and flux flow path along with i_{ds}^{*} and i_{qs}^{*} signals. The torque control can be achieved from speed error since the developed electromagnetic torque affects the speed dynamically. Applying PI controller into the error signal between reference and measured or calculated speed and current. The PI_{s} are the representation of the PI controller in the torque flow path.
The errors between the actual and reference values of i_{ds} and i_{qs} are fed to the respective PI controllers (PI_{f} and PI_{T}) to generate equivalent dq axis voltages (v_{ds}^{*}, v_{qs}^{*}).
The flux ψ_{r} is estimated with the V_{s} and ω_{r} from the nameplate data before the start of the motor and remains almost constant during running for which i_{ds} also remain constant. After transformation to v_{α} and v_{β}, the v_{svm} is generated for the SVM to produce PWM pulses for the inverter [1]. The v_{svm} and its inclination angle α [1, 2] are calculated as
Using Eq. (8) the switching instances of the space vector modulation (SVM) are determined as
where the modulation index M is given by
where T_{c} = T_{pwm}/2, and T_{pwm}. The instantaneous phase voltage is shown in Eq. (11) by time averaging of the space vectors during one switching period for the sector.
where T_{c} = T_{pwm}/2. It is evident from the above equations that the performance of the IFOC controller is primarily dependent on the equivalent parameters of the IM as well as the gains of the PI controllers. Thus evaluation of equivalent parameters of IM before starting, during the transition phase as well as during running is essential. Generally, no load and blocked rotor tests of IM are performed to estimate its equivalent parameters. But with our scheme, these tests are avoided as ECPs are evaluated using the proposed MRAS model during the stalled, transition, and running conditions.
Model reference adaptive system for ECPs estimation
To implement the IFOC scheme for the drive, the accurate estimation of the required ECPs is the most challenging task as these ECPs get changed with the running conditions of the motor.
The ECPs depend mostly on the slip, supply frequency, loading, and inside temperature of the motor, the accurate measurement of which are very much essential to get better control performance of the IFOC. Accordingly, an MRAS model [5, 7] for ECPs estimation is developed as shown in Fig. 4. In the form of BPANN, the Reference model and BPANNbased plant model are the two basic building blocks of the controller.
Formulation for reference model M _{R}
This model is used to generate ECP_{R} set, i.e. the reference values of ECPs namely R_{s1}, R_{r1}, L_{m1}, L_{s1}, L_{r1} during the prestart and poststart transition period up to the steadystate running condition of the induction motor. This ECP_{R} set is utilized to train the gains in the plant model during this entire transition period i.e. till the steadystate running of the motor up to the desired speed is achieved.
ECPR generation before start
The HG diagram method, IEEE 112, and the NEMA specification are used to generate the ECP_{R} set based on the nameplate data before starting the motor. The stator voltage V_{s}, stator current I_{s} (I_{a}, I_{b}), rotor speed N_{r}, input power factor p_{f}, and output power P_{out} are the nameplate data to be provided. The HG diagram is represented by an operating circle in the complex plane to analyze the power consumption scenario of an IM. The G and H functions [27] are having the dimension of inductance to represent the active and reactive power consumption status, respectively. The G function is directly related to developed torque and the H function is concerned with the magnetizing flux. The perphase equivalent circuit impedance of Eq. (1) is modified by ignoring R_{c} and is expressed as in Eq. (12). The ECP_{R} set is evaluated using the equations derived as follows:
Following the construction method of the HG diagram, the operating points on the diagram are a function of slip ω_{sl} and can be expressed as
Since G(ω_{sl}) and H(ω_{sl}) represent active and reactive power consumption, their locus describes a circle in the socalled HG plane for the variation in load or even change in the ECPs for any other reasons [17]. This circle is graduated with the ω_{sl} increasing from the purely synchronous point H_{0} to its point H_{∞}, from which stator inductance L_{s} and the total leakage coefficient σ can be derived using Eq. (15)
where the current I_{nl} can be evaluated from the nameplate data and NEMA specification without performing the real hardware test. It is assumed that σ is quite small for which H_{∞} ≈ 0, circle diameters become directly a function of the stator flux ψ_{s} as shown in Eq. (16). The HG diagram identifies the parameters in the (α, β) reference frame. The P and Q power components are estimated from the dot and cross product of the V_{s} and I_{s} vectors in the (α, β) reference frame using Clarke Transformation. The values of P and Q are obtained as
The values of G(ω_{sl}) and H(ω_{sl}) at any instantaneous point i can also be calculated from given P and Q as
where k is obtained from NEMA guidelines. The stator and rotor resistance R_{s1} and R_{r1} and rotor time constant τ_{r} can then be estimated from G(i) and H(i) as,
Thus the value of rotor inductance L_{r1} can be estimated from τ_{r} and R_{r1}. The mutual inductance can thus be evaluated as
The gain parameters of IFOC K_{1}, K_{2}, and K_{3} as shown in Eqs. (2)–(4) are evaluated using the ECP_{R} set from the nameplate data before starting.
ECPR generation during the transition phase
It is evident from Eq. (2) that the value of ψ_{r} is dependent on the mutual inductance. But the mutual inductance varies on variations in resistances and both of them vary due to variations in motor temperature during the running condition. This in turn causes a change in i_{ds} and IFOC logic accordingly. Thus though the HG diagram method is efficient enough for estimating the ECPs during the prestart condition, its use is not suggested during the running condition. Accordingly, during the transition phase, the feedback values like V_{s}, I_{a}, and I_{b} are provided as input to the reference model on basis of which the ECP_{R} is generated using equations are (16)–(21) to tune the plant model ECP_{p}. The value of I_{sαβ} (i_{α},i_{β}) and the V_{sαβ} (V_{α}, V_{β}) are evaluated using Clarke transformation as shown in figure vii7.
Formulation for plant model M _{P}
The estimated ECP_{R} set, using the abovedescribed method, provides accurate results so long the operating conditions, i.e. load demand, slip, temperature, supply frequency remain unaltered. But, as the values of R_{s1}, ω_{sl} varies with change in motor temperature and slip, the estimated ECP_{R} set, L_{m} value in particular, from the HG method produces an erroneous result. This needs a switchover of the ECPs estimation from the reference model to the plant model during the running condition of the motor. The plant model is built based on the backpropagation principle where ANN with an input layer of three neurons and three hidden layers of five, four, and two neurons respectively, and one output neuron model (35421) is used in its forward path as shown in Fig. 5. The value of each of the ECPs, i.e. R_{s}, R_{r}, L_{r}, L_{s}, and L_{m}, have been evaluated accurately during steady state. For working of BPANN, an input matrix [A]_{3×5} is constituted where each row contains three values of one of the parameters and each column represents each of the parameters of R_{s}, R_{r}, L_{r}, L_{s}, and L_{m}. Out of the three values of each row j, one value (a_{j}) is calculated by using the respective equations from (22) to (24) and the other two values are estimated considering a deviation range of ± €. This creates a set of values like [a_{j}−ε, a_{j}, a_{j}+ε] for each row j of [A]_{3×5} and is treated as the input neurons for the ANN module to estimate the parameter corresponding to that row j. As j can vary from 1 to 5 to represent R_{s}, R_{r}, L_{r}, L_{s}, and L_{m}, respectively, the ANN structure is to be utilized four times to estimate all the ECPs in a onetime step. The entire operation of the plant model can be divided into two subparts—namely (i) starting, i.e. start of the motor from standstill to the set speed achievement and (ii) running conditions of the motor. The functioning of ECPs under these conditions is described below.
ECPs evaluation during the transition period
Before start, the ECP_{R} values are utilized for input matrix [A]_{3×5} and the weight updation procedure begins offline so that the overall time of convergence can be minimized. After the offline training is done the IM is started with the parameters obtained from M_{R}. During this period, ECPs copy the values of ECP_{R} to generate the triggering pulses following IFOC schemes. It is considered that the value of L_{s} and L_{r} are assumed to be the same for small to medium motors whereas the ratio between these two parameters can be taken as per NEMA specifications for larger motors for their evaluation. The value of R_{s} and R_{r} is estimated using (22) where v_{ssi} and i_{ssi} are the voltage and current signals derived from the SSI method as illustrated in “Estimation of R_{s} using small signal injection method” section.
Therefore the inductances can be evaluated as
where slip s is changing with the estimated speed
Considering the inputs of each BPANN topology as
three such inputs for each j are mapped to the four neurons of the first hidden layer by their corresponding weight factor w. The selection of the weights is done in a random manner such that the neurons of this layer are initialized as in Eq. (26)
The BPANN structure is designed in such a way that the vanishing gradient and exploding gradient problems are minimum. For simplicity, the number of the hidden layer is considered to be two where Leaky Relu and Adam activation function is used for optimization. But in some work [30, 31] use of three hidden layers has also been considered to improve accuracy. The use of three hidden layers poses the problems like: (i) increase in network complexity, (ii) increase in convergence time, as well as the number of iterations to converge, (iii), increases the processor’s computational overhead, and accordingly, high power processors are required for its implementation. Whereas with the use of two hidden layers, these problems are very less and the system with two hidden layers can easily be implemented with a lowpower processor. But considering the accuracy aspects for the evaluation of ECPs of IM, three hidden layer system control structure is considered in this work. The activation function used here is Leaky Relu which is defined as S_{ir}(h) = h_{ir} for h_{ir} ≥ 0 or S_{ir}(h) = 0.01h_{ir} for h_{ir} < 0 where i represents the number of hidden layers and r represents the number of neurons in that particular hidden layer. For this design, i and r maybe 1 to 2 and 1 to 4, respectively. The second hidden layer neurons are represented similarly as given by
The output of the ECP_{pj} is expressed as
Besides, the BPANN algorithm is designed in such a way that the weight factors are trained during the speed transient period and/or starting period of the motor while these periods are identified till the desired set speed is achieved from the very start i.e. stopped or stalled condition of the motor.
For the training purposes, each of the output parameters from M_{P} is compared with the respective reference parameters coming out from M_{R} i.e. the error between the parameters of the M_{R} and M_{P} are E_{j} = (ECP_{Rj}ECP_{Pj}) are evaluated such that The loss or error functions are then generated following Eqs. (35) which are minimized using Adam rule to recalculate the weights in backpropagation manner,
where b_{j} is the loss function for each of the jth parameters. Thus the weight updation process or the training process continues until the difference between the output of all the elements of M_{R} and M_{P} will be less than or equal to the tolerance limit δ,
The basic weight updation rule as stated in the gradient descend (GD) method is expressed as in Eq. (32). This weight updation method is modified as per the ADAM rule as described in Eq. (35–38). This ADAM rule is a combined form of the Adagrad and RMSProp adaptive GD method, the details of which are explained in reference (25), and hence the description is not included in this paper.
where m_{n} is the momentum term and the value of m_{n} and r_{n} is given by
and
The BPANN gain tuning procedure continues till the weight updating rule is satisfied, the duration of which is well within the starting transition period of the motor.
ECPs evaluation during running
Once the training period is over, the ECPs estimation is started with the plant model by making a switch over to the selection of input towards sampled feedback of (V_{s}, I_{s}(I_{a}, I_{b})). The parameters are calculated using Eqs. (22)–(24) to form the input matrix of BPANN and then this [A]_{3×5} is used to evaluate ECP_{P}. The values of K_{1}, K_{2}, and K_{3} are also evaluated following Eq. (37), and all the IFOC dq voltage, current, flux, slip frequency, etc., are calculated using Eq. (2)–(11).
Stator resistance and speed estimation
Estimation of R _{s} using small signal injection method
The R_{s} measurement method is based on the injection of a very lowfrequency, low amplitude lockin signal to the stator along with the threephase supply fed to the motor using the converter. A basic lockin system consists of a lockin signal generator, an amplifier, a PSD, and a low pass filter, the schematic diagram of which is shown in Fig. 6. All the constituent blocks of Fig. 6 are grouped into DSPbased lockin signal generators with LIA for voltage and LIA for current, sensor unit, and power unit blocks for a better understanding of their working. The DSPgenerated lockin signal of very low amplitude is passed through the stator along with the stator voltage after their necessary modulation to produce a lockin stator current depending on the stator resistance. This lockin current is amplified to a level adequate for the PSD in the sensor unit and is then passed through an LPF to extract the noisefree return current signal. The stator resistance is estimated during running conditions with the ratio of the injected lockin voltage and the return current signal. The amplitude of lockin voltage v_{r} is made so small that it is unable to contribute any impact on the running of the motor while its frequency is made very low so that its inductive effect can be neglected and the return current I_{r} will be limited only by the stator resistance R_{s}. Besides, this kind of infinitesimally small impact is further reduced with the intricacies of intermittent injection of lockin signals. In its intermittent operation, the lockin signal is injected for its oneperiod duration at an interval of nT_{lc} making a duty cycle δ_{lc} such that δ_{lc} = T_{lc}/nT_{lc} where n is the number of cycles and T_{lc} = 1/f_{2} is the period of lockin signal of frequency f_{2}. The term f_{3} = 1/nT_{lc} can also be termed as refresh rate for R_{s} estimation. The v_{svm}(t) is added with a very small ac signal of amplitude v_{r}(t) and frequency (f_{2}) to produce a resultant voltage v(t) for δ_{lc} period such that
For detection purposes during δ_{lc} period, the DSPbased processor multiplies the feedback voltage V_{b}(t) with a modulating signal r(t) having the same amplitude and frequency as that of the v_{r}(t). The inphase component of v_{r}(t) is r_{x}(t) = sin(2πf_{2}t) and quadrature (90° shifted) r_{y}(t) = cos(2πf_{2}t) components which produces x_{vb}(t) and y_{vb}(t), respectively, so that
After this, both the signals are passed through the digital low pass filter to eliminate all the ac components and only the dc component is obtained of both inphase x_{vbdc} and quadrature component y_{vbdc}. Thus the voltage obtained after filtering is
The current i_{b}(t) is also sensed by the Hall sensor which contains the load current, harmonic distortion, and noise component. The i(t) is also multiplied by the same r(t).
After this, both the signals are passed through the digital low pass filter where the noise, harmonic distortion, and the other ac components get filtered and the only dc component is obtained as x_{ibdc} and y_{ibdc}. Thus the value of i_{ssi} is given by
The frequency (f_{2}), as well as the amplitude of v_{r}(t), is kept very low so that its contribution to the net flux production is negligibly small such that
Thus the stator resistance can thus be computed as follows
Thus this method of resistance estimation takes care of the temperature effect of the motor and thus the use of a temperature sensor is avoided. Again if the temperatures of the motor (T_{(lc+1)} and T_{lc}) are known at two different running conditions, the corresponding resistances can also be evaluated using equation ( 43) provided the coefficient of expansion λ is known
where R_{s(lc+1)} and t_{lc+1} represent the current value of the resistance and temperature, and R_{slc} and t_{lc} denote the precious value, respectively.
Sensorless speed estimation scheme
The performance of the IFOC scheme depends on the variation of temperature which varies due to environmental changes, the presence of harmonics, and overloading as both the stator resistance R_{s} and the rotor resistance R_{r} vary with it. Fluctuations in the speed may occur due to a change in load, change in the time constant due to temperature rise. For a variation of R_{r}, the time constant (τ_{r} = L_{r}/R_{r}) varies inversely. An increase in temperature in general increases the rotor and stator copper losses P_{rcl}, P_{scl} for which the total loss P_{loss} increases. Thus if the supply voltage V_{s} and the output power (P_{out}) remain constant, IM will draw more power from the input for which the motor efficiency will reduce and the stator and rotor currents (I_{s}, I_{r}) will also increase. In normal operating conditions, as the motor starts picking up with the speed the torque T_{e} becomes maximum at slip s_{m} before coming to the operating point following Eq. (45)
Thus the rotor speed varies with ECPs variation. At steady state, the dq axis voltages can be expressed by Eqs. (45) and (46) considering constant flux by neglecting the rate of change of flux.
The reactive power can be expressed as in Eq. (47)
By substituting the value of v_{ds}^{*} and v_{qs}^{*} in the above equation, the reference value of the reactive power is
assuming negligibly small measurement error, the reference values of (v_{ds}^{*}, v_{qs}^{*}, i_{ds}^{*}, i_{qs}^{*}) must be equal to the measured values (v_{ds}, v_{qs}, i_{ds}, i_{qs}), and hence the reactive power evaluated with reference values must be equal to the actual value. Thus by equating (47) and (48)
Accordingly, the shaft speed is estimated by
where ω_{sl}^{*} and ω_{sl} can be expressed as in Eq. (4). Before start, the ω_{r} is estimated by
To ensure accurate estimation of the ω_{sl}, a PI controller with gain k_{pωsl}, k_{iωsl} is introduced as in Eq. (51) Substituting this ω_{sl} in Eq. (51) the expression modified shaft speed expression will be.
With this accurate performance speed estimation is achieved. The PI controller here is tuned using the ZN method. The schematic of the speed estimation method is shown in Fig. 7.
Flowchart for the proposed BPANN based optimization method
Experimentation
The viability of the proposed controller development based on the Adam technique is tested in two stages—(i) in the first stage, the entire scheme is simulated using MATLAB/Simulink environment while (ii) the simulated development is tested with actual hardware implementation as well a customized graphical user interface (GUI) development for parameter monitoring purposes, all of which are described as follows.
Simulation results
Case 1: Avoidance of physical tests
The parameters of an IM are simulated using both GD and Adam algorithms based on the nameplate data viz. 3.3 kW, 3φ, 415 V, 50 Hz, 6.9A, 1415 rpm and pf = 0.8. For validation purposes, the equivalent circuit parameters of the motor are evaluated from conventional physical noload and blocked rotor tests (PT). The parameters estimated from PT, M_{R}, and M_{P} are presented in Table 1 along with the percentage error of ECPs with that of paper [12] for comparison purposes. It is evident from Table 1 that the errors are very similar between different methods suggesting the need of performing PT can be avoided.
The ECPs evaluated in Table 1 is based on the BPANN with three hidden layer structure of the plant model as shown in Fig. 5. But for simplicity in implementation purposes, two hidden layer structure is widely used. Thus to make a comparison in achieved accuracy the experiment is also performed with two hidden layers and the result of both two and three are tabulated in Table 2. It is evident from this Table 2 that betterment in accuracy for almost all of the parameters is achieved with a threelayer structure.
Case 2: Tracking performance
The performances of the drive like its speed response at a constant load torque as well as its sudden change are simulated and shown in Figs. 8 and 9 respectively during the running condition. It is evident from these Figs. 8 and 9 that the speed responses are similar both in their steadystate and transient conditions for all the BPANN methods.
Case 3: BPANN convergence
The convergence status for BPANN to evaluate the resistance of stator and rotor by using AD and GD methods is shown in Figs. 10 and 11, respectively. Figures 12 and 13 show the convergence graph of reactance L_{r}/L_{s} and L_{m}, respectively. Reaching the steadystate value is considered as the point of convergence. It is evident from these figures that the steadystate value is reached with AD at a faster rate than that with the GD method. This is the reason for which the AD method is adopted in this work.
Case 4: R_{s} estimation using SSI
The small ac signal of 1 V and 1 Hz is injected along with the A phase supply of V_{s} of 240 V, 50 Hz, for estimating temperature effect on R_{s}. The FFT analysis, as shown in Fig. 14, of the Aphase feedback data confirms the presence of this 1 Hz signal injection. As per the proposed design, the only voltage sensor and one of the two current sensors are used in the A phase, the other one is placed either in the B or C phase. The convolutions of V_{a} and I_{a} with v_{rx} and v_{ry} are used to demodulate the lockin signals while DLPFs are used to extract V_{ssi} and I_{ssi} for the estimation of the R_{s}. As stated in “Estimation of R_{s} using small signal injection method” section, this R_{s} estimation is done only during the δ_{lc} period of the lockin signal and is refreshed with frequency f_{3}. The motor temperature proportional values of R_{s} thus obtained are shown in Table 3 and are assumed to remain constant during the refresh period of the lockin signal. For this study, δ_{lc} is considered 1 s while the refresh rate is f_{3} = 0.1 Hz. The evaluated resistances are shown at four different temperatures at T, (T + 10), (T + 20), and (T + 25) where T is the room temperature (25 °C). The same is also estimated using the positive temperature coefficient of stator winding λ is the (3.83 × 10^{–3}/°C) [30] and the % error is evaluated for estimating the efficacy of the proposed SSI.
Case 5: Effect of resistance change
The effect of change in stator resistance on the other parameters of ECPs and speed is also shown in Table 3. It shows how the stator and rotor resistance and rotor time constant τ_{R} change with temperature. The change in speed indicates that a correction in the firing pulse modulation index is essential otherwise the desired speed can’t be achieved. Besides, independent ECPs evaluation using two models at different temperatures is also shown in Table 4. Since Eqs. (17)–(21) and Eqs. (22)–(24) are utilized for ECP_{R} and ECP_{P} evaluation, the ECPs values evaluated using these two methods are different for variation in the motor temperature. But considering the running of the motor with fixed load torque, the mutual inductance value should not be changed with temperature. But remarkable change is observed in ECPs evaluation through the M_{R} model. This suggests ECPs estimation with the HG diagram method where temperature variation is considered is not suitable during the running of the motor. This also justifies the use of BPANN based plant model in this proposed design.
The changes in stator and rotor resistance and rotor time constant τ_{R} with temperature change are shown in Table 3. It is observed from the ECPs values in the Table 4 that the modulation index (MI) is needed to be changed to incorporate the effect of temperature changes. If the correction in the MI for this temperature change is not considered, a fluctuation in the developed torque i.e. torque ripple is observed. In other words, there is a fluctuation in the speed as observed in Fig. 15. The reason behind it is that due to the increase in R_{s} with temperature rise, the developed torque, T_{e} is reduced, following Eqs. 2 and 6, resulting in a momentary decrease in rotor speed and this error is corrected by the controller and a fluctuation in torque or speed be the result. The no fluctuation in speed is also observed for correction in MI. On the other hand, the change in stator current I_{s} with and without correction in the MI with the change in R_{s} is also observed from the Fig. 16. This justifies that a temperature correction is essential to avoid any ripple in the speed or developed torque of the motor.
Experimental results with MMU GUI
Case 6: Hardware controller with MMU system
A DSPenabled digital signal controller (DSC) featured microcontroller (DSPIC33EP512MC502) with 70 MIPSbased control board is developed for this proposed motor drive system where SVM PWM trigger pulses are generated as per the proposed control algorithm along with the desired feedback signals. These pulses are utilized to control the IGBTbased 3 phase H bridge power hardware through its gate driver system. The IGBT gate driver has also the facility to detect any abnormal operation of the drive for protection purposes. The entire controller logic is embedded within the firmware of this DSC to make it a standalone drive controller. The PWM is designed to operate at 5 kHz (or 200 µs period) and it is observed that the duration for ECPs generation following the abovediscussed control algorithm is within 140–180 µs. This proves that the developed drive can be used for online controlling purposes. A snapshot of the developed hardware prototype is shown in Fig. 17. In addition, the values of the internal parameters are sent to a PC through serial communication at a speed of 115.2 kbps for their display in a customized GUI of MMU for monitoring and storage purposes. Some parameters, the nameplate data in particular for starting of the motor and the desired speed are sent to the controller from this GUI. A customized GUIbased MMU using visual basic is designed in such a way that it sends the machine nameplate data to the drive controller once these are fed. The controller then evaluates the equivalent parameters and retransmits them to the PC for its display in the GUI as shown in Fig. 18. The MMU receives the sample values for motor terminal voltage and current, estimated speed, and measured temperature for their evaluation and display in the GUI. Besides, it is also able to display and store the ECPs of the motor as received from the hardware controller.
The microcontroller acquires voltage and current signals through its inbuilt ADC and these data are also transmitted to the PC for monitoring purposes along with other parameter values. The MMU displays these normalized data as shown in Fig. 19 while it's part (a) shows the voltage waveforms and part (b) is for current. The voltage and current data are acquired using voltage (VH1K0T02) and current (HE025T01) sensors respectively. As shown, the lockin signal to be used to measure R_{s} is embedded within the acquired voltage or current signals. MMU also displays the estimated ECPs both from M_{P} and M_{R} models in its part (c) while its part (d) displays the measured values of voltage and current at an intermediate stage of speed change.
Case 7: ECPs estimation using drive controller
The ECPs values as evaluated by the hardware controller are communicated to the PC at a regular interval of 1 kHz once the training of the BPANN algorithm is completed. Out of all such values, Table 5 shows the ECPs values just after the completion of the training of BPAN along with the other values for comparison purposes. The ECPs data are obtained after taking the average of over 100 observations and accordingly appear very close to the simulated values. The data for % error of this table justifies the avoidance of PT for the evaluation of ECPs.
Case 8: Sensorless Speed estimation
The speed of the motor is estimated without any speed sensor based on the ECPs of the motor during its running condition as well as feedback values of voltage and current following Eq. (52). The estimated speed is tabulated for a wide range of reference speeds in Table 6. The same is verified with the speed estimated using an optical sensor mounted on the rotor shaft of the motor, the waveform of which is shown in Fig. 20. The y axis of the figure here represents the amplitude of the signal obtained from the optical sensor and the xaxis represents the time. The % error is computed for both the sensored and sensorless methods and it is observed that the sensorless method is equally applicable for speed estimation. The optical sensor has a resolution such that one complete revolution produces 60 pulses.
Conclusion
This paper elaborates on the automatic estimation of ECPs during the starting transients and running conditions of an induction motor. The result from Tables 1 and 2 reveals that the proposed scheme avoids any physical tests of the motor and applicable to all rated motors. The speed tracking errors performance shown in Figs. 8 and 9 and the convergence criteria of ECPs evaluation as shown in Figs. 10, 11, 12 and 13 prove the efficacy of the proposed HG and Adambased BPANN schemes. The variation in R_{s} and its impact on other ECPs with motor temperature is also shown in Tables 3 and 4. An intelligent SSI for R_{s} and sensorless speed estimation methods are adopted to incorporate the temperature and speed error correction schemes. A hardware prototype along with a PCbased GUI is developed for its standalone operation as shown in Figs. 17 and 18. The ripple in the torque or speed is reduced drastically with this BPANN controller as evident from Figs. 15 and 16. Thus the development of an intelligent controller for induction motor drive with online parameter estimation and GUIbased display facility is described.
Availability of data and materials
The data of the motor that has been considered here are taken from the nameplate of the motor. The NEMA specifications of AC machine IEEE 112 data have also been used.
Abbreviations
 AD:

Adam optimizer
 AI:

Artificial intelligence
 ANN:

Artificial neural network
 ASD:

Adjustable speed drive
 BPANN:

Backpropagation artificial neural network
 CNN:

Convolution neural network
 DLPF:

Digital low pass filter
 DSP:

Digital signal processing
 ECP_{P} :

Equivalent circuit parameters obtained from plant model
 ECP_{R} :

Equivalent circuit parameters obtained from the reference model
 ECP_{s} :

Equivalent circuit parameters
 EKF:

Extended Kalman's filter
 FLC:

Fuzzy logic controller
 FOC:

Fieldoriented control
 GA:

Genetic algorithm
 GD:

Gradient descent method
 GNN:

Graphical neural networks
 GSA:

Gravitational search algorithm
 GUI:

Graphical user interface
 IFOC:

Indirect fieldoriented control
 IM:

Induction motor
 LPF:

Low pass filter
 LSTM:

Long short term memory
 MMU:

Machine monitoring unit
 MRAS:

Model reference adaptive structure
 NN:

Neural network
 PSD:

Phasesensitive detector
 PSO:

Particle swarm optimization
 PT:

Physical test
 PWM:

Pulse width modulation
 RNN:

Recurrent neural network
 SSI:

Small signal injection method
 SVM:

Space vector modulation
 VSI:

Voltage source inverter
 B :

Loss function
 E :

Error
 f :

Frequency
 f _{2} :

Lockin signal of frequency in SSI
 f _{3} :

Refresh rate in SSI
 g _{ n } :

Gradient of the error
 h :

Hidden layer
 i _{dr}, i _{qr} :

Dq axis rotor current
 i _{ds} , ^{*} i _{qs} ^{*} :

Stator reference current in the dq axis
 i _{ds}, i _{qs} :

Dq axis stator current
 I _{nl} :

Noload current
 I _{r} :

Rotor current
 I _{s} :

Rated stator current
 K :

The ratio between R_{s} and R_{r}
 K _{1} :

Controller gain of the flux flow path
 K _{2} :

Controller gain of the torque flow path
 K _{3} :

Controller gain of the slip frequency
 K _{pIs}, K _{i} _{Is} :

PI controller gain in the torque flow path
 L _{m} :

Magnetizing inductance
 L _{r} :

Rotor inductance
 L _{s} :

Stator inductance
 L _{m1} :

Mutual inductance of M_{R}
 L _{r1} :

Rotor inductance of M_{R}
 L _{s1} :

Stator inductance of M_{R}
 M :

Modulation index
 m :

Momentum term in ADAM rule
 M _{P} :

Plant model
 M _{R} :

Reference model
 N _{r} :

Rated speed
 p :

Number of poles
 p _{f} :

Power factor rated condition
 p _{fnl} :

Power factor at no load
 P _{nl}, P _{rcl}, P _{scl}, P _{out} :

Noload power, rotor copper loss, stator copperloss, rated power
 P :

Active power referred to the αβ
 Q :

Reactive power referred to the αβ
 Q _{1} :

Reactive power in the dq axis
 R _{c} :

Core resistance
 R _{r} :

Rotor resistance
 R _{r1} :

Rotor resistance of M_{R}
 R _{s} :

Stator resistance
 R _{s1} :

Stator resistance of M_{R}
 r _{ n } :

Summation of the squared term of gradients
 r(t):

Modulating signal of SSI
 S :

Activation function
 s :

Slip
 s _{m} :

Maximum slip
 T :

Temperature at start
 T _{e} :

Electromechanical torque
 T _{pwm} :

Time period of PWM
 T _{lc} :

Period of lockin signal in SSI
 t _{1} ,t _{2} ,t _{0} :

Switching instances of SPWM
 V _{s} :

Rated stator voltage
 V _{an}, V _{bn}, V _{cn} :

Instantaneous phase voltages of VSI
 v _{dc} :

Dc supply voltage
 v _{dr}, v _{qr} :

Dq axis rotor voltage
 v _{dr}, v _{qr} :

Dq axis rotor voltage
 v _{ds} ^{*}, v _{qs} ^{*} :

Stator reference voltage in the dq axis
 v _{r} :

Lockin voltage
 V _{ssi}, i _{ssi} :

Voltage and current of SSI method
 v _{svm} :

Voltage vector of SVM
 v _{ α } ,v _{ β } :

αβ Axis voltage
 w _{ n } :

Current weight of nth iterations
 w _{(} _{ n } _{+1)} :

Modified weight after nth iterations
 X _{m} :

Magnetizing reactance
 x _{vbdc}, y _{vbdc} :

Dc component voltage inphase and quadrature component in SSI
 Y :

Output of the forward path of M_{P}
 Y _{MP} :

Output ECPs for plant model
 Y _{MR} :

Output ECPs for reference model
 Z _{eqP} :

Per phase impedance of M_{P}
 Z _{eq} :

Per phase impedance
 Z _{eqR} :

Per phase impedance of M_{R}
 δ :

Tolerance limit
 δ _{lc} :

Duty cycle in SSI
 η :

Learning rate
 σ :

Total leakage coefficient
 ψ _{ds}, ψ _{qs}, ψ _{qr}, ψ _{dr} :

Dq axis flux
 ω _{r} :

Rotor speed
 ω _{s} :

Synchronous speed
 ω _{sl} :

Slip Speed
 τ _{R} :

Rotor time constant
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Acknowledgements
We would like to thank Mr. Rakesh Das for his generous help for development of the hardware system.
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This is a selfsponsored project. There is no source of any funding for this research from any other external resources.
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The theory has been developed, and also the simulation and practical verification of the work is being done by the corresponding author. Prof (Dr) J.N. Bera has supervised the entire work. Both authors read and approved the final manuscript.
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Tista Banerjee received a B.Tech. degree in electrical engineering from Techno India in 2006, M.Tech. in electrical engineering from the University of Calcutta, in 2008. She has worked as an Assistant Professor in the College of Engineering and Management Kolaghat (2008–2009) and at B.P.Poddar Institute of Management and Technology, (2009–2017). Her research interest is on power electronics and control systems.
Jitendra Nath Bera is associated with the Department of Applied Physics of the University of Calcutta, Kolkata. He has obtained his B.Tech. and M.Tech. degrees from the University of Calcutta and Ph.D. degrees from Jadavpur University. He has more than 35 in national and international journals. His research areas include Power Electronics, Smart Grid, Electrical Machines, control system wireless communication, and Embedded Systems.
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Banerjee, T., Bera, J.N. Online equivalent parameter estimation using BPANN controller with lowfrequency signal injection for a sensorless induction motor drive. Journal of Electrical Systems and Inf Technol 9, 20 (2022). https://doi.org/10.1186/s43067022000603
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DOI: https://doi.org/10.1186/s43067022000603