International Journal of Computer Science and ...

Post-Fault Speed Sensor-Less Operation Based on Kalman Filter for a Six-Phase Induction Motor Islam M. Soliman 1, Elhussien A. Mahmoud 2, Ayman S. Abdel-Khalik 3, Hussein F. Soliman 4 1

Department of MEA-Systems & Infrastructure, Alstom Company, Department of Offshore Operation, National Drilling Company, 3 Department of Electrical Engineering, Alexandria University, 4 Department of Electrical Engineering, Ain Shams University,

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Abstract—This study introduces a post-fault speed estimator for asymmetrical six-phase (6-ph) induction machines (IM) under single open phase condition. The proposed technique is based on Kalman Filter (KF) estimator. The multiphase machine model scheme is associated with proportional integral (PI) speed control. Also, the indirect field-oriented control (IFOC) is intended to be used and followed by a hysteresis current controller (HCC). Different operating conditions have been carried out to investigate the estimator fidelity. The simulation study is performed using MATLAB/ SIMULINK platform. The simulations results show a promising performance of the proposed speed estimator. Keywords—asymmetric six phases, multiphase machine, Kalman filter, sensorless operation, speed estimation I. INTRODUCTION All Electrical motors are a vital part for any electrical system, especially in the industrial applications. Many developments are carried out to enhance motor operation, control and protection. AC induction motor is the most common and practical motor among the other types of the electrical motors. Also, it can be considered as the best choice in terms of robustness, lower cost, minimal maintenance and lower weight at a relatively wide power range. Multiphase AC induction motor were released in the middle of 1990s due to the need of extra high power applications, including railway traction industry, wind generation and electric ship propulsion, etc.,[1,2]. Multiphase winding layout can be broadly classified into symmetrical or asymmetrical winding layouts. The phase belt angle between two adjacent phases is known to be the main factor to identify the machine winding scheme [3, 4]. Reliability is the main concern in the most of industrial applications. Therefore, studying the electrical drives behaviour during a fault condition is the key to ensure the system sincerity [5, 6]. So far, vector control is usually the basic technique used for induction machine control [7, 8]. Also, speed sensor is commonly required for the indirect field oriented control (IFOC) in order to measure the rotor position. Moreover the flux sensors are expensive and unreliable [9].Thus, several methods are presented to eliminate the speed sensor for the six-phase induction motor. The fuzzy logic control was shown insensitive to parameter variations but has a limited adaptable range [10-13]. Another method is the model reference adaptive system (MRAS) which is one of the famous methods used thanks to its high robustness and fast response Nevertheless, this method suffers from noise and disturbances affecting the system [14]. Also, high control efforts and chattering are the main problems for sliding mode observer method [15]. Therefore, this paper proposes an analysis of a speed estimation method with Kalman filter to replace the speed sensor. Kalman filter (KF) is suitable algorithm to the schemes which has unknown noises such as current ripple by pulse width modulation (PWM), noise by modelling error and measurement

DOI:10.23883/IJRTER.2018.4061.ZZ9SP

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International Journal of Recent Trends in Engineering & Research (IJRTER) Volume 04, Issue 02; February - 2018 [ISSN: 2455-1457]

error. The proposed estimator is investigated in different scenarios. This is carried out not only for loading variation and speed transitions from rated speed into very low speed, but also tested during the post fault operation. II. MODELLING OF SIX-PHASE INDUCTION MOTOR An asymmetrical six-phase winding can be obtained by splitting the stator windings of a three phase stator into two identical halves (dual three phase groups). The dual three phase groups denoted as A,B,C phase group and D,E,F phase group, have an angular displacement of 30 electrical degrees. The mathematical representation (α-β model) of a six-phase induction motor can be obtained using the decoupling (Clarke’s) transformation matrix C  , shown in equation (1)

1 cos 0 sin  1 1 cos5 C    3 0 sin5 1 0  1 0 , where

cos4 sin4 cos8 sin8 1 0

cos5 sin5 cos sin 0 1

cos8 sin8 cos4 sin4 1 0

cos9  sin9  cos9   sin9  0   1 

(1)

     [16].

The Clark’s transformation converts the original six phase currents to a new set of orthogonal current components called sequence currents. These sequence currents consist of three pairs. Each pair of current components form an independent subspace, namely, the fundamental, third and zero sequence plans. The fundamental plan components are denoted by the suffix α and β. While, the secondary plan components are referred by the suffix x and y. And the zero sequence plan components are given the suffix 0- and 0+. The fundamental plan is the only energy conversion plan in the sinusoidal distributed multiphase machines. While, the zero sequence components 0- is ignored in the isolated star machines. The resulting model for a sinusoidal distributed winding six phase machine with two isolated star connection is given in equation (2, 3). v s   Rs  pLs v   0  s     0   pM     0   r M

0 Rs  pLs r M pM

 vxs   Rs  pL1s v   0  ys     0   Rs  pL1r    0 0 

0  ixs    Rs  pL1s  iys  x  ixr  0    Rs  pL1r  iyr 

pM 0 Rs  pLs r M

0  i s    pM  i s  x r M  i r     Rs  pLs  i r 

(2)

(3)

, where R s and R r are the stator and rotor resistances, L s and L r are the stator and rotor inductances, and L m is the mutual inductance. The voltage equation (2) can be rewritten as;

@IJRTER-2018, All Rights Reserved

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1   1 d   dt isd   ' isd  sisq   rd   prq   L vsd  s r s   (4) d  1   1  dt isq   ' isq  sisd   rq   prd   L vsq  s r s   , where vsd , vsq , isd , isq are the stator voltage and current dq components respectively and

λrd, λrq are the rotor flux components, and  is the rotor angular speed. Also, Lr M M2 M2 Ls τ  μ  , , τ  , r & Rs eq  Rs  2 Rr σ  1 Rr Ls Lr s Rs eq Ls Lr Lr

The torque equation is given by:

Tm 

pM λ i λ i Lr  rd sq rq sd 

(5)

III. PROPOSED KALMAN FILTER SPEED ESTIMATOR Kalman filter (KF) is used for the sensorless operation of the six phase induction motor under study. KF is one of the estimation techniques that use a series amount of measurements over a certain time period. The algorithm of the Kalman filter has several advantages; this filter is able to take into account quantities that are partially or completely neglected in other techniques (such as the variance of the initial estimate of the state and the variance of the model error). It provides information about the quality of the estimation by providing, in addition to the best estimate, the variance of the estimation error. Its recursive structure allows its real-time execution without storing observations or past estimates. The drawbacks of KF method are the high memory and processing speed requirements due to matrices manipulation. Two parameters are important in the KF approach. The first parameter is the order of the KF matrices, since it determines the size of the memory required to store the data, and the speed of updating the value of the estimated rotor speed. The second parameter is the rotor speed which included in the state vector. If the second parameter is not included in the state vector that means it is considered as a constant and this leads to a poor estimation in the transient condition. KF can be used as an observer in order to estimate the rotor angular speed in the sensor-less operation of six-phase induction motors. Two sources of noise may affect KF performance. The first is the process noise such as thermal noise, while the second is the measurement noise [17]. The predictive model of the KF can be formulated as in equations (6, 7) [18, 19].

xk  Axk1  Buk1  wk1 zk  Hxk  vk

(6) (7)

where x : State of the system, u : A known input to the system, z : Measured output. k : Time index. w: Process noise. v : Measurement noise. A, B&H : Time-varying dynamic coefficient, input coupling, and measurement sensitivity matrices respectively ,


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The goal of the KF is to estimate the state vector x which cannot be directly measured, where the measurement vector z is alternatively measured. The state vector is related to the measurement vector by the measurement equation (4), while the system is governed by the process equation (3). The KF can estimate the state vector even if the measurements and process are contaminated by noise and even if the system model is not accurate. The mathematical form of the Kalman filter consists of the following five equations [11, 12]: (8) xˆk   Axˆk 1  Buk

Pk   APk1AT  Q

Kk  Pk   H T   HPk  H T  R 

(9) 1

(10)

xk  xˆk   Kk  zk  Hxˆk  

Pk   I  Kk H  Pk

(11)



(12)

, where

Q&R K P I The “–“ The “^“ T

: Process and measurement noise covariance matrices respectively, : Kalman gain, : Error covariance matrix and : Identity matrix. : means a prior estimation. : means estimated value. : Matrix transposes.

IV. PROPOSED SENSORLESS CONTROLLER The proposed system structure is shown in Fig.1. The system under study compromises a six-phase induction motor connected to six phase inverter. A PI speed controller is used to determine the command torque based on the speed error. For the sake of comparison, the speed feedback may be taken from the actual or the estimated speed. The feedback speed is whether the actual speed from the speed sensor or the estimated speed calculated from Kalman Filter observer. The command torque is utilized to generate the required dq current components based on standard indirect rotor field oriented control (IRFOC). The reference currents i*d and i*q are transformed to their stationary frame using Park’s transform. Clark’s transformation is then used to obtain the corresponding reference phase values. Hysteresis current controller (HCC) is then used to control the six-phase inverter. The parameters of the six-phase induction machine used in the simulation study are given in Table (1). Table 1: Parameters of the six-phase induction machine Parameter Stator resistance Rotor resistance Stator leakage inductance Rotor leakage inductance Mutual inductance Moment of inertia Number of pole pairs Rated torque Rated stator flux

Symbol Value Unit Rs 1 Ω Rr 1.1 Ω Lr 67.26 mH Ls 64.8 mH M 0.06 mH J 0.02 kg·m2 P 3 Tn 10 N·m Ψs 1 Wb·m

The case study considers starting the machine under normal healthy operation. After the machine reaches its steady-state speed of 1000 rpm, a single open phase fault is assumed to occur. The


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machine is then subjected to speed reduction to 500 rpm. Another reduction to 200 rpm is then applied. The last speed reduction is after 8 seconds from starting to reach to 100 rpm (10% from the machine rated speed). Also two scenarios of the machine loading are taken into account to investigate the estimator performance as follows: 4.1. Scenario 1  Starting at full load (10N.m)  The machine is subjected to loading reduction to the half of the machine rated load (5N.m) after 10 seconds  Finally, the machine loading increases again after 12 seconds to its rated load (10N.m) 4.2. Scenario 2  Starts and operate assuming a parabolic torque speed load curve.

Fig 1: Blocks diagram of the proposed model under study

V. SIMULATION RESULTS The simulation results are presented for the assumed scenarios. For each scenario, the following plots are shown:  Speed versus time: reference speed, actual speed and the estimated speed are presented during the whole time period with all speed reductions behaviour.  Torque versus time: the torque profile is also shown to describe the loading of the machine during the simulation time.  Percentage error between the reference speed and the actual speed: ω  ωact % error  ref x100 (13) ωref The aim for this ratio is to identify the effect of the estimator on the actual speed. The actual speed converges to the reference speed in all transition levels.  Percentage error between the actual speed and the estimated speed: ω  ωest % error  act x100 (14) ωact This error is considered as the main indication of the speed estimator efficiency and accuracy. @IJRTER-2018, All Rights Reserved

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Fig. 2 shows the results for scenario (1).This scenario is considered for dynamic loading which is the most severe case. However, the estimator shows a good response with all transition levels. The actual speed follows the reference speed, and the estimated speed keeps a good tracking to the actual speed for all speed transients from the rated speed till very low speed values. Although the machine is subjected to loading variation from the rated value to the half of the rating and then increased again to its rated load, the estimator dynamic performance seems acceptable. The percentage error is below 15% during steady state in general. This increase in the estimation error is due to the loading at very low speeds and under fault condition. Fig. 3 displays the results for scenario (2). This scenario is considered as the most practical one. A load with parabolic torque speed characteristics (centrifugal pump or propeller) has been proposed. Excellent results have also been obtained during healthy and faulty time periods. Also the estimator presents a good behaviour not only in different loading, but also in the very low speed operation. The percentage errors are also very good as they are below 2% during steady state. 20 Reference speed Actual speed Estimated speed

1000

Torque produced vs Time 15

Torque (N.m)

Speed (rpm)

800 600 400

10

5 200 0 0

5

10

0 0

15

5

10

Time (sec)

(2.a)

20

(2.b) 20

% error speed detection [(ref- act)/ref]

% error speed detection [(act - est)/act] 15 10

10

5

% error

% error

15

Time(sec)

0

0 -5

-10

-10 -15

-20 0

5

10 Time (sec)

(2.c)

15

-20 0

5

10

15

Time (sec)

(2.d)

Fig 2: Simulation results for scenario (1). (a) speed, (b) torque, (c) % error between actual and reference speed, (d) % error between estimated and actual speed


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Reference speed Actual speed Estimated speed

1000

20 Torque produced vs Time 15

Torque (N.m)

Speed (rpm)

800 600 400

10 5 0

200

-5 0 0

5

10

15

-10 0

Time (sec)

5

10

15

Time(sec)

(3.a)

(3.b)

10

10

% error speed detection [(ref- act)/ref]

% error speed detection [(act - est)/act] 5

% error

% error

5

0

-5

-10 0

0

-5

5

10 Time (sec)

15

-10 0

5

10

15

Time (sec)

(3.c)

(3.d)

Fig 3: Simulation results for scenario (2). (a) speed, (b) torque, (c) % error between actual and reference speed, (d) % error between estimated and actual speed

In general, These results reflects the excellent performance of the proposed Kalman filter estimator integrated with the six phase induction motor in both high speed and low speed conditions. The proposed speed estimator has also a good dynamics response under step loading. VI. CONCLUSIONS This paper presents the speed sensor less operation of an asymmetrical six-phase induction motor under single open phase fault based on Kalman filter estimator. Standard indirect rotor field oriented control was employed to generate the machine reference current components. The proposed system was simulated using MATLAB/Simulink. The proposed speed estimator has shown an acceptable tracking and a good dynamic response under both healthy as well as faulty cases. Future work will consider the experimental implementation of the proposed estimator. REFERENCES Bojoi, R., et al. Multiphase electrical machines and drives: A viable solution for energy generation and transportation electrification. in Electrical and Power Engineering (EPE), 2016 International Conference and Exposition on. 2016. IEEE. II. Baltatanu, A. and M.-L. Florea. Multiphase machines used in electric vehicles propulsion. in Electronics, Computers and Artificial Intelligence (ECAI), 2013 International Conference on. 2013. IEEE. III. Padmanaban, Sanjeevikumar, and Michael Pecht. "An isolated/non-isolated novel multilevel inverter configuration for a dual three phase symmetrical /asymmetrical star-winding converter." Engineering Science and Technology, an International Journal 19.4 (2016): 1763-1770. I.


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International Journal of Recent Trends in Engineering & Research (IJRTER) Volume 04, Issue 02; February - 2018 [ISSN: 2455-1457] IV. V. VI. VII. VIII.

IX. X.

XI.

XII.

XIII. XIV. XV.

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