Sensorless Loss Model Control of the Six-Phase Induction Motor in All Speed Range by Extended Kalman Filter

This paper proposes a simple extended Kalman filter (EKF) loss model controller (LMC) for efficiency improvement of a six-phase induction machine in all speed ranges. The proposed method is fast and can be operated online. If the machine parameters are changed during the operation, the EKF algorithm is activated to find the parameters to ensure optimal efficiency operation. Not only is the motor speed measurement difficult at low speeds but it is also difficult to calculate the machine efficiency at the same speeds. Thus, the EKF model can estimate speed, load, and motor efficiency at low speed ranges so that optimization can be done in all loads and speed ranges. Unlike the conventional LMC method, the proposed method is independent of parameter variations. Because of the independency of this method against the parameter variations, it works similarly to the search based efficiency control methods. Two DSP boards including estimator and controller are used to achieve high accuracy and speed in estimating and controlling machines. The simulation and experimental results verify the robustness of the sensorless method against parameter variations.

Voltage vector T e , T l Electromagnetic and load torque ω Electrical rotor speed s, r Subscript for stator and rotor quantities ψ s , ψ r Stator and rotor flux J Moment of inertial R s , R r Stator and rotor resistance L s , L r Self stator and rotor inductance T r Rotor time constant T s Sample time M Magnetizing inductance The associate editor coordinating the review of this manuscript and approving it for publication was Chunlong He .

Number of pole pair L ls
Stator leakage inductance X 1 , Y 1 , U 1 the state vectors of the system w 1 , w 2 the system noises Q, R, and w u Covariance matrices of the system, measurement, and input noise k h , ke Hysteresis and eddy current coefficient Six-phase and five-phase machines are two usual types of multi-phase machines that have several applications [1]- [4].
Increasing machine phases has several advantages, such as higher redundancy and lower torque pulsation. Field-oriented control (FOC) and direct torque control (DTC) techniques are implemented for six-phase and five-phase machines [7]- [11], which speeds up the application of the multiphase machines. These methods cannot achieve good performance in low-speed applications due to the speed measurement difficulty and parameters variation. In low-speed VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ applications, a suitable method is required to estimate parameters and speed [12]- [14]. The EKF is robust in estimating past, present, and future states of nonlinear systems [25]- [28]. It can be used to estimate various parameters and outputs while there are not any sensors to measure. To estimate the parameters, some of the system outputs are measured by sensors; then, the estimation error is deduced and the Kalman filter coefficients are improved. If the sensors are not accurate enough to measure some parameters, the EKF can be used to improve the accuracy of the measurements [29]- [30]. The Kalman filter and EKF have been used in many research works to estimate motor parameters and outputs of servo systems [31]- [32]. Nowadays, with the increase in processing speed in DSP, the online experiment of EKF has been rendered possible. Induction motors have stochastic properties, so the EKF can easily be used to model it. Also, it can be employed to control machines when they are used at low speeds or the machine parameters are changed. Other estimators are used to estimate the parameters of induction machines [33]- [36].
When a motor operates at a low speed or light load, the system will demonstrate very low efficiency. It is, therefore, essential to use an appropriate method to improve efficiency. The proposed method should be useful at all speed ranges, especially at low-speed ranges. Typically, the efficiency improvement methods of electrical machines are divided into two general categories: loss model control (LMC) [15]- [21] and search control (SC) [22], [23]. Although the SC method is independent of machine parameters, it is time-consuming to implement. Therefore, the SC method cannot be used in highly dynamic applications. In contrast, the LMC technique is relatively fast to implement in a real-time manner; thus, it is suitable for highly dynamic cases, but it depends on machine parameters and offers high computation speed. It is of the practical significance to employ an appropriate method to estimate motor parameters and to improve the LMC method performance. Efficiency improvement of six-phase induction machines has been dealt with in some research papers [23] and [37]. The efficiency improvement method considering highly dynamical applications and all speed ranges of the six-phase induction motors has rarely been reported before to the best knowledge of the authors.
This paper aims to improve the efficiency of a six-phase induction machine (6PIM) in all speed ranges with highly dynamical applications. The EKF is employed to estimate the parameters and states of the motor, which is needed by the LMC to improve the efficiency of the system in the light load conditions. The efficiency improvement method is based on the sensor-less field-oriented control (FOC) framework for 6PIM. The advantage of EKF is not only estimating the speed in the low-speed range with high precision but also estimating the variant parameters, like resistance, to achieve better robustness performance. The innovation of this paper is extending a simple EKF model for 6PIM to achieve high efficiency using the LMC-based FOC of the motor.
In the rest of this paper, a six-phase induction motor modeling and field-oriented control of a 6PIM are first deduced, and EKF modeling of the 6PIM is described in Section II. A suitable loss model control of the 6PIM using the parameters estimated by the EKF is explained in Section III. Finally, extensive simulation results and experiment results are given to validate the correctness of the analysis and the effectiveness of the proposed methods in all speed ranges in Section IV.

II. SIX-PHASE INDUCTION MOTOR MODEL A. MODELING AND FOC OF MOTOR
The Vector space decomposition (VSD) method is a popular method in the modeling 6PIMs [1]. The technique has been used in several papers as it is simple and suitable for the controller design of 6PIMs. Using this method and applying 6 * 6 matrices, the six-phase voltage, current, and flux equations are transformed into three subspaces. These subspaces The FOC of the 6PIM is implemented in the (d − q) subspace and the references of the other current subspaces are set to zero. The 6PIM model using the VSD method in that subspace is given below: According to [32], the dynamic model of the 6PIM in the (α − β) subspace can be given as: where X 1 , Y 1 , and U 1 are the state vector of the system, the measured parameter of the motor, and the input vector in the (α − β) subspace, respectively. All noises of the drive system and measurement equipment in that subspace are modeled with w 1 and w 2 .
in which The machine model in the (z 1 − z 2 ) subspace has only copper loss and it is modeled as follows: in which X 2 , Y 2 , and U 2 denote the state vector of the system, the measured parameter of the motor and the input vector in the (z 1 − z 2 ) subspace, respectively. All noises of the drive system and measurement equipment in that subspace are modeled with w 1 andw 2 .
A discrete model of the motor is needed for the DSP-based digital control of the motor. The discrete model of the 6PIM is deduced by discretizing the state vectors. If the sampling time is T s , the discrete state vector in the (α − β) subspace will be as below Also, the discrete state vector in the (z 1 − z 2 ) subspace is: When the speed is low, the accuracy of speed sensing and calculation is decreased to a great extent. The EKF is a powerful estimator in this case. The EKF model of the 6PIM is given by recursive equations as below: in which where three covariance matrixes (Q, R, and w u ) are used to model the system, measurement, and input noise of the system. These equations are run recursively to decrease the estimation error.

III. LOSS MODELING OF MACHINE
Electrical and mechanical losses are two parts of a drive system. The motor loss decreases the system efficiency and causes the motor temperature to increase. The loss in the machine not only increases the power consumption of the machine but also reduces the operating life of the motor. Electrical motors are designed to have maximum efficiency near the nominal conditions. If a motor load or speed is less than the nominal ones, the motor loss increases. An appropriate method can increase machine efficiency in light load conditions. Previous papers have generally focused on increasing efficiency only under light load conditions, and low speed and light load condition has not been addressed. To this end, a suitable model is used to model the motor losses according to [14]. The total loss of a 6PIM, including stator and rotor copper losses, rotary power loss, and core loss, can be calculated as below [37]:  From (2), (17), and (18), the total loss is calculated as: where: If the temperature of the machine is increased during the working process, the stator and rotor resistance will be changed. Thus, the loss model control of the machine has many errors. According to Figure 1, the loss model of the machine is calculated from the parameter estimation of the EKF estimator.P in whichÂ,B,Ĉ,R s ,R r ,ω 2 r represent the estimated parameters of the EKF estimator and are defined as below: The estimated power differential efficiency optimization of the machine is as below: which can be used in Figure 1 to achieve efficiency improvement.

IV. SIMULATION AND EXPERIMENTAL RESULTS
In this section, the EKF modeling of a 6PIM at low and high-speed is first shown in Figure 2. In these simulations, the motor speed reference is 1 rad/sec at low speed and 90 rad/sec at high-speed. The EKF algorithm is active and estimates all states. According to this Figure, the load is varied at 1.25 sec to 2 N.m at t = 1.25 sec and then to 1.25 N.m at t = 2.5 sec. Also, the stator resistance is changed from 15 to 25 at t = 3 sec, but the EKF algorithm can estimate these variations. The simulation is run with and without the LMC algorithm and the results are shown in Figures 3 and 4, respectively. In these figures, the EKF modeling of a 6PIM is active in high-speed and the motor speed reference is 130 rad/sec and load torque is varied. According to results, the load is varied at t = 1.25 sec to 3 N.m and then to 1.25 N.m at t = 3 sec. In figure 3, the LMC algorithm is inactivated and efficiency is low at all load torques. In figure 4, the proposed optimization algorithm is activated after 0.3 sec; thus by changing the load of the 6PIM, the motor currents are varied to the optimal value. Efficiency, input power, motor currents, motor speed, and load torque in the proposed loss model control method are shown in Figure 4(a)-(f). The comparison of Figures 3(a) and 4(a) shows the advantage of the proposed method to improve the efficiency of the 6PIM. According to Figures 3(a) and 4(a), after running the optimization algorithm, the motor efficiency is changed from 13% to 38%. Also, the proposed method increases the motor efficiency from 63% to 64.5% and from 43% to 58% when the load torque is 3 N.m and 1.25 N.m, respectively.
In Figure 5, the LMC is added to the EKF model of the 6PIM at low speed and the efficiency is improved. This Figure illustrates the performance of the proposed algorithm at low speed and load variations. The proposed algorithm is run at 1 second. After running the optimized algorithm, the stator current in the d-axis is changed to the optimal value. while the optimization algorithm is off, the load torque is changed to 0.5 N.m at 2.5 econd. The optimization algorithm is run again at t = 3.5 second while the optimization algorithm is off from t = 5 sec to t = 6 sec, the load torque is changed at 5 sec.
The optimization algorithm is run again at t = 6 second and efficiency is optimized as depicted in Figure 5(a). Also, this figure shows the efficiency improvement, input power, current in the (α − β) subspace, rotor flux, load torque, and motor speed in the LMC of the FOC of the 6PIM. The experimental results of the proposed method at a high-speed are displayed in Figure 6. The motor speed is 100 rad/sec and the motor load is 0.5N.m which is changed to 1.5 N.m at t = 1.7 sec. The proposed efficiency improvement algorithm is run at t = 0.8sec and is active until t = 1.7sec. Then, the efficiency improvement is deactivated and run at t = 2.3sec again.
Also, the stator resistance is varied from 15 to 18 at t = 2.7sec. According to the results, the proposed algorithm is active after stator resistance variation and optimal  efficiency is obtained. Also, the experimental results at lowspeed are shown in Figure 7. The motor speed is 1.8 rad/sec and the motor load is varied at t = 2.4 sec. The proposed efficiency improvement algorithm is run at t = 0.8sec and is active until the load change. Then, the efficiency improvement is deactivated and run at t = 3.4 sec again.
Besides, the stator resistance is varied from 15 to 18 at t = 3.9 sec. According to the results, the proposed algorithm VOLUME 8, 2020  is active at all speed ranges and can minimize the power loss very fast. In addition, the proposed method is independent of parameter variations and optimal efficiency is obtained with parameter variations.
The proposed technique to improve efficiency has been developed and tested in an experimental set-up. The structure of the implemented hardware is illustrated in Figure 8. The test-bench is composed of a 6PIM and load. This machine  is fed by a six-phase DC-AC VSI. The 6PIM is made of a three-phase induction motor by rewinding the stator as an asymmetrical structure. The motor specification parameters are shown in Table 1.
To perform the 6PIM closed-loop vector control, the six stator phase currents are sensed using LEM current sensors. Four current sensors are used to measure the phase currents of VSI. The outputs of sensors VOLUME 8, 2020  are digitized using six 12-bit A/Ds in the TMS board.
TMS3206713 is a floating point processor with 225 MHZ clock time that can execute real-time algorithms. Tms320F2812, which is a fixed point microcontroller, has favorable performance in motor control by useful peripherals. If the control and estimation algorithms are implemented in one DSP board, the execution time and sampling time will be large. To reduce sampling time, the control algorithm is implemented in EZDSP2812 board and the EKF algorithm is implemented in the DSK6713 board.
For the high-speed interface of two DSP boards, a parallel interface is used. To this end, an HPI port in DSK6713 is connected to P2 (XINTF) in EZDSP2812. The host port interface (HPI) is a parallel port in DSK6713 for rapidly sending and receiving data. The host processor can directly access the CPU memory space by the HPI port.
The proposed loss model control method has been compared with other power loss minimization strategies. Table 2 summarizes the improvements caused by some of the methods available in the literature. In this table, the announced results are the average values for load torque, efficiency before loss minimization, and efficiency after loss minimization methods with different load torques.
According to table 2, the proposed loss minimization method has a good response in low load conditions than other methods. Also, if the stator resistance is varied the proposed method can estimate the optimal current very well. Compare of efficiency improvement of various methods with 30% stator resistance variations are shown in Table 3. According to the results, the proposed method has the  best response in various loads. If motor parameters are changed without parameter estimation, the motor efficiency is decreased.

V. CONCLUSION
The EKF loss model control of a 6PIM presented in this paper gives optimal efficiency at all speed ranges. According to the results, the proposed method is active under load variations and the variations of parameters. If the motor speed is low, the proposed method estimates the speed and optimal flux to reduce the loss and improve efficiency. Also, the proposed method is fast and can estimate machine parameters and motor loss online. The proposed method is independent of parameter variations and optimal efficiency is obtained with parameter variations. This technique has some the advantage against the usual efficiency improvement methods. This method is as fast as the LMC method and the proposed method is independent of motor parameters like the SC techniques. The performance of the proposed method is proven with simulations and experimental results perfectly. He was a Visiting Professor with the University of Alberta, Canada, from January 2019 to April 2019, and then, he joined to Xi'an Technological University. His current research interests include modeling, analysis, and control of power converters, motor drives and control, and multiphase machine drives, multilevel inverter, power electronic systems for renewable energy sources, process control, DSP and FPGA-based system designs, hardware in the loop, and computer-aided control.