IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 6, NO. 2, SUMMER-FALL 2007
98
A Robust Adaptive Sliding-Mode Controller for Slip Power Recovery Induction Machine Drives J. Soltani and A. Farrokh Payam
S
I. INTRODUCTION
the vector control (VC) and Direct torque control (DTC) methods have been applied to the three phase squirrel cage induction machine drives [1]. Although the field oriented control method in the stator or magnetizing reference frame are applied to the DFIM drives [2], [3], little attention has been given to the DTC and flux control of these types of drives. In field oriented methods applied to DFIM drives, the voltage drop across the stator leakage impedance is neglected. Such an assumption, forces a steady-state error both in motoring and generating modes of operation. In [4] the bang-bang DTC control method is combined with direct rotor flux field oriented control method and is applied to an adjustable doubly fed induction motor drive. In [4], the controller is designed based on neglecting the voltage drop across the rotor resistance. In [5], [6], a backstepping tracking controller has been introduced for a DFIM drive. The control method of [5], [6] is used only in generating mode of operation upon unity of power factor, measured on the stator side of the machine. This paper describes a nonlinear controller for DFIM drives based on combination of SM control and adaptive backstepping control approaches. The SM control forces the system state nominal trajectories to follow a linear reference model
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TABLE I DFIM SYSTEM MODES OF OPERATION
Mode Speed Sub-Synchronous Super- Synchronous
Generating
Motoring
Ps < 0 , Pr > 0 Ps < 0 , Pr < 0
Ps > 0 , Pr < 0 Ps > 0 , Pr > 0
DFIM drive while the adaptive backstepping controller makes the drive system performance robust and stable subject to the parameter variations and external load torque. The nonlinear control approach described in this paper has the following advantages: 1. The motor generated torque becomes linear with respect to system control states. 2. The rotor flux can be easily regulated in order to increase the machine efficiency. 3. The system robustness can be achieved against the parameters uncertainty. The overall system stability is proved by Lyapanouv theory. It is worthwhile mentioning that the above control strategy has been applied to a three-phase squirrel cage induction machine [7]. The research work presented in this paper is in fact a continuation of research work described in [7], with main objective of achieving a robust DTC and flux control for DFIM drives, using two back-to-back two level SVM-PWM voltage source inverters in the rotor circuit, the proposed control method can be applied for motoring and generating modes of operation below and above synchronous speed. In addition the rotor dc link voltage is maintained constant, using a rotating reference frame with d axis in coincide with the space voltage vector of the main ac supply. The dc link voltage is maintained constant based on input-output feedback linearization control method.
of
Index Terms—Doubly fed induction machine, nonlinear sliding-mode, adaptive backstepping, torque, flux control.
Fig. 1. Electrical circuit configuration of the DFIM system.
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Abstract—In this paper a robust nonlinear controller is presented for Doubly-Fed Induction Machine (DFIM) drives. The nonlinear controller is designed based on combination of Sliding-Mode (SM) and Adaptive-Backstepping control techniques. Using the fifth order model of DFIM in a stator d,q axis reference frames with stator currents and rotor flux components as state variables, First a SM controller is designed in order to follow a linear reference model. Then, the SM control and adaptive backstepping control approach are combined to derive a robust composite nonlinear controller for DFIM, which makes the drive system robust and stable against the parameters uncertainties and external load torque disturbance. In this drive system two back-to-back voltage source two level SVM-PWM inverters are employed in the rotor circuit, to make the drive system capable of operating in motoring and generating modes below and above synchronous speed. Computer simulation results obtained, confirm the effectiveness and validity of the proposed control approach.
Manuscript received June 13, 2006; revised December 9, 2006. J. Soltani is with the Department of Electrical Engineering, University of Malaya (UM), Kula-Lumpur, Malaysia. A. Farrokh Payam is with the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran (e-mail:
[email protected]). Publisher Item Identifier S 1682-0053(07)1525
II. DFIM MODEL The electrical configuration of a DFIM drive system is depicted in Fig. 1. This system consists of a three-phase wound rotor induction machine connected through a backto-back converter scheme, which in turn is connected to the main ac supply. The drive system shown in Fig. 1 can operate as a motor or a generator below and above the synchronous speed. The different modes of operation of this drive system are shown in Table I [8].
1682-0053/07$10 © 2007 JD
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SOLTANI AND FARROKH PAYAM: A ROBUST ADAPTIVE SLIDING-MODE CONTROLLER FOR …
Under assumption of linear magnetic circuits and balanced operating condition, the equivalent two-phase model of the symmetrical DFIM with stator connected to line, represented in fixed stator d-q reference frame is dids R RL 2 RL = −( s + r 2 m )ids + r2 m ψ dr + dt Lσ Lr Lσ Lr Lσ
diqs dt
ψ qr +
uds L − m udr Lσ Lr Lσ
Rs Rr Lm RL + )iqs + r2 m ψ qr − Lσ Lr 2 Lσ Lr Lσ
ωr Lm Lr Lσ
ψ dr +
uqs Lσ
−
(1)
Lm uqr Lr Lσ
h2 ( x) = ψ dr + ψ qr
RL R = r m iqs − r ψ qr + ωrψ dr + uqr dt Lr Lr
(2)
ive
where P is number of poles. The mechanical equation is given by
(3)
]T
Ar
[
ch
where J and B denote the moment of inertia and friction coefficient, respectively, T L is the external load torque and ωm is the rotor mechanical angular speed ( ω r = ( P / 2)ω m ). Let
x = ids
iqs ψ dr ψ qr
(4)
be the state vector and for generated torque Te defined by y = Te =
(9)
2
z1 = h2 ( x)
3P Lm (ψ dr iqs − ψ qr ids ) 2 Lr
(5)
Then, the dynamic model of DFIM in new coordinates is given by ⎡ z1 ⎤ ⎡ L f h2 ⎤ ⎡ Lg1h2 ⎢ z ⎥ = ⎢ L h ⎥ + ⎢ L h ⎣ 2 ⎦ ⎣ f 1 ⎦ ⎣ g1 1
(6)
(11)
where
L f h2 = 2 L f h1 =
ωr Lm Lr Lσ
Rr Lm R (idsψ qr − iqsψ dr ) − 2 r (ψ dr2 + ψ qr2 ) Lr Lr
3 P Lm 2 Lr
× ( −(
Rs Rr Lm 2 Rr + + )(iqsψ dr − idsψ qr ) − Lσ Lr 2 Lσ Lr
(ψ dr 2 + ψ qr 2 ) − ωr (ψ qr iqs + ψ dr ids ) +
uqsψ dr Lσ
−
udsψ qr Lσ
))
Lg1h2 = 2ψ dr Lg 2 h2 = 2ψ qr Lg1h1 =
L 3P Lm (iqs + m ψ qr ) 2 Lr Lr Lσ
Lg 2 h1 = −
(12)
L 3P Lm (ids + m ψ dr ) 2 Lr Lr Lσ
Furthermore, a nonlinear state feedback control inputs is employed as ⎡uˆdr ⎤ ⎡ Lg1h2 ( x)udr + Lg 2 h2 ( x)uqr ⎤ ⎢uˆ ⎥ = ⎢ L h ( x)u + L h ( x)u ⎥ . dr g2 2 qr ⎦ ⎣ qr ⎦ ⎣ g1 1
(13)
⎡ z1 ⎤ ⎡ L f h2 ( x)⎤ ⎡1 0⎤ ⎡uˆdr ⎤ ⎢ z ⎥ = ⎢ L h ( x) ⎥ + ⎢ ⎥⎢ ⎥ . ⎣ 2 ⎦ ⎣ f 1 ⎦ ⎣0 1⎦ ⎣uˆqr ⎦
(14)
From (14) the reference model is introduced as zm = Am zm + Bm uref
where x is defined in (4) and ⎡ Rs Rr Lm 2 ωL RL u ⎤ + 2 )ids + r2 m ψ dr + r m ψ qr + ds ⎥ ⎢− ( Lr Lσ Lσ ⎥ Lr Lσ Lr Lσ ⎢ Lσ 2 ⎥ ⎢ R u ω R L R L L ⎢− ( s + r m )iqs + r m ψ qr − r m ψ dr + qs ⎥ 2 2 Lr Lσ Lσ ⎥ Lr Lσ Lr Lσ f ( x) = ⎢ Lσ ⎥ ⎢ Rr Lm Rr ⎥ ⎢ ids − ψ dr − ωrψ qr Lr Lr ⎥ ⎢ ⎥ ⎢ Rr Lm Rr ψ ω ψ i − + ⎥ ⎢ qs qr r dr Lr Lr ⎦ ⎣
Lg 2 h2 ⎤ ⎡udr ⎤ Lg 2 h1 ⎥⎦ ⎢⎣uqr ⎥⎦
Then, the dynamic system (11) becomes
III. NONLINEAR SLIDING MODE CONTROL Equation (1) in compact form rewritten as x = f ( x) + g1udr + g 2uqr
(10)
z2 = h1 ( x)
of
3P Lm (ψ dr iqs −ψ qr ids ) 2 Lr
dω m + Bω m + T L = Te dt
(8)
T
Introducing the new variables as
where i s , ψ r , us , u r , R and L denote stator current, rotor flux linkage, stator terminal voltage, rotor terminal voltage, resistance and inductance, respectively. The subscripts s and r stand for stator and rotor while subscripts d and q stand for vector component with respect to a fixed stator reference frame. ωr denotes the rotor electrical angular speed and L m is mutual inductance. Lσ = L s (1 − ( L2m / L r L s )) is the redefined leakage inductance. The DFIM generated torque can be expressed in terms of stator currents and rotor flux linkage as follows
J
⎤ 0 1⎥ ⎦
3P Lm (ψ dr iqs −ψ qr ids ) 2 Lr 2
dψ qr
T
Assuming the machine torque Te and the norm of the 2 2 2 rotor flux modulus ψ r = ψ dr are to be the system +ψ qr control outputs. Based on input-output feedback linearization h1 ( x) =
dψ dr Rr Lm R ids − r ψ dr − ωrψ qr + udr = dt Lr Lr
Te =
⎤ 0 1 0⎥ ⎦
⎡ L g 2 = ⎢0 − m Lr Lσ ⎣
2
= −(
⎡ L g1 = ⎢ − m ⎣ Lr Lσ
D
Lr Lσ
and
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ωr Lm
99
(7)
⎡ zm1 ⎤ ⎡ −am1 ⎢ z ⎥ = ⎢ 0 ⎣ m2 ⎦ ⎣
0 ⎤ ⎡ zm1 ⎤ ⎡ am3 + − am 2 ⎥⎦ ⎢⎣ zm 2 ⎥⎦ ⎢⎣ 0
0 ⎤ ⎡ψ r ∗2 ⎤ (15) ⎢ ⎥ am 4 ⎥⎦ ⎣ Te∗ ⎦
where a m1 , a m 2 , a m3 and a m 4 are the positive constants. Using (14) and (15) the system error dynamics is obtained as
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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 6, NO. 2, SUMMER-FALL 2007
(16)
where ez = [z1 − zm1
z 2 − z m 2 ]T = [ez1
ez 2 ]T
(17)
with ⎡ L f h2 ( x) ⎤ A( x ) = ⎢ ⎥ ⎣ L f h1 ( x) ⎦
⎡1 0 ⎤ B( x) = ⎢ ⎥ ⎣0 1 ⎦
⎡udr ⎤ ⎡uˆ + am1 zm1 − am 3ψ r∗ ⎤ U = ⎢ ⎥ = ⎢ dr ∗⎥ ⎣uqr ⎦ ⎣⎢ uˆqr + am 2 zm 2 − am 4Te ⎦⎥ 2
(18)
(19)
2×2
is a constant linear matrix so that the where S ∈ ℜ inverse of SB (x) must exist for all x , i.e., det( SB ( x )) ≠ 0 for all x . Combining (16) and (19), gives
σ = Sez = SA( x ) + SBU = −Q sgn(σ ) − Kσ
(20)
where
⎡q Q=⎢ 1 ⎣0
0⎤ ⎡k K =⎢ 1 ⎥ q2 ⎦ ⎣0
0⎤ , q , k > 0, i = 1, 2 k2 ⎥⎦ i i
(21)
where as
σ >0
(22)
as
ez1 = L f h2 ( x) + udr + φ1d1 ( x) ez 2 = L f h1 ( x) + uqr + φ2 d 2 ( x)
σ 0 and ρ1 is chosen as follows
ρ1 .d 1 ( x) ≥ (φˆ1 − φ1 ) .d 1 ( x) when φˆ1 is in transient and the adaptation law of φˆ1 is given by
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SOLTANI AND FARROKH PAYAM: A ROBUST ADAPTIVE SLIDING-MODE CONTROLLER FOR …
φˆ1 = γ 1ez1d1 ( x )
(31)
where γ 1 > 0 is the adaptation gain. Similarly, the q axes SM control is designed as uqr = − L f h1 ( x ) − φˆ2 d 2 ( x ) − k 2 ez 2 − ρ 2 sgn(ez 2 )
(32)
where k 2 is positive constant feedback gain and φˆ2 = γ 2 ez 2 d 2 ( x )
(33)
where γ 2 > 0 is the adaptation gain and ρ 2 is chosen as follows
ρ 2 .d 2 ( x) ≥ (φˆ2 − φ 2 ) .d 2 ( x)
Derivative (34) with respect to time t and combining with (29), gives V1 = ez1 ⎡⎣ L f ( x ) h2 ( x) + udr + φˆ1d1 ( x) − (φˆ1 − φ1 )d1 ( x) ⎤⎦ 1 1 + (φˆ1 − φ1 )φˆ1 + (φˆ2 − φ2 )φˆ2
γ2
ive
Substituting the control laws (30) and (32) and the adaptation laws (31) and (33) into (35), the following inequality can be deduced (36)
Defining the following equation
ch
M (t ) = k1ez12 + k 2 ez 2 2 ≥ 0
Furthermore,
(37)
Ar 0 t
(38)
= V1 (e(0), φˆ(0)) − ∫ M (τ )dτ 0
[
]
T where e = [e z1 , e z 2 ] and φˆ = φˆ1 , φˆ2 . From the definition of the Lyapanouv function V1 (t ) ≥ 0 and the above equation, one can obtain that
t
∫
lim M (τ )dτ ≤ V1 ( e(0), φˆ(0)) < ∞
t →∞
(42)
as result, the system error dynamic is vd R v − id + ωe iq − d 1 − id∗ L L L (43) vq1 ∗ R − iq e2 = − iq − ωe id − L L Defining the ac side inverter reference voltages as
D
e1 =
vd R − id + ωe iq − id∗ − ke1 ) L L R vq1 = L(− iq − ωe id − iq∗ − ke2 ) L vd 1 = L(
(39)
0
Based on the Barbalat’s Lemma [10],we can obtain M (t ) → 0 as t → ∞
(44)
Linking (43) and (44), gives e1 = −ke1 e2 = − ke2
(45)
Considering a Lyapanouv function as
1 2 1 2 e1 + e2 2 2 therefore V = e e + e e = − k ( e 2 + e 2 ) < 0 V=
1 1
2 2
1
2
(46)
(47)
Based on above control strategy the block diagram of rotor dc link voltage controller is depicted in Fig. 2. VI. ACTIVE AND REACTIVE STATOR POWER CONTROL IN GENERATING MODE
t
V1 (t ) = V1 (e(0), φˆ(0)) + ∫ V1 (τ ) dτ
T
e1 = id − id∗
of
+ ez 2 ⎣⎡ L f ( x ) h1 ( x ) + uqr + φˆ2 d 2 ( x) − (φˆ2 − φ2 )d 2 ( x) ⎦⎤ (35)
V 1= −k1ez12 − k2ez 2 2 ≤ 0
did 1 = (vd − Rid + ωe Liq − vd 1 ) dt L (41) diq 1 = (− Riq − ωe Lid − vq1 ) dt L One may note that in this reference frames the d axis is in coincided with the main space voltage vector. Considering id∗ , i q∗ as reference currents, therefore
SI
1⎡ 2 1 1 ˆ 2 2 2⎤ ⎢ez1 + ez 2 + (ϕˆ1 − φ1 ) + (φ2 − φ2 ) ⎥ (34) 2⎣ γ1 γ2 ⎦
γ1
current equations corresponding to main ac power supply are give by
e2 = iq − iq∗
when φˆ2 is in transient. Theorem 2: Using the controller described by (30)-(33), the torque and flux amplitude DFIM is stable and robust subject to the parameters mismatched uncertainties. Proof: Defining the following Lyapanouv function V1 =
101
For electric energy generation, it is usually required to regulate the stator active-reactive power, whose references are assumed to be Ps∗ and Q s∗ respectively. These quantities in a special two axis rotating reference frame which is defined in the previous section are given by [11] 3 Qs∗ 2U 3 Ps∗ id∗ = 2U iq∗ =
(48)
Therefore, flux references calculated from (40)
That is, e z1 and e z 2 will converge to zero as t → ∞ . Therefore, the proposed controller is stable and robust, even if parameters uncertainties exist. V. STABILIZATION OF ROTOR DC-LINK VOLTAGE Using the method described in [9], the d and q axis
ψ d∗ = ψ q∗ =
1
βω0 1
(− (
Rs
σ
Rs
βω0 σ
iq∗ − ω0 id∗ )
id∗ − ω0 iq∗ −
1
σ
(49) U)
so rotor flux reference and torque reference are calculated as below
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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 6, NO. 2, SUMMER-FALL 2007
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Fig. 2. DC link voltage controller.
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Fig. 3. The overall block diagram of the proposed nonlinear controller.
ψ r∗ = (ψ d∗ 2 + ψ q∗2 )
Te∗ = µ (ψ d∗ iq∗ −ψ q∗id∗ )
(50)
VII. SYSTEM SIMULATION The overall block diagram of the proposed control approach is shown in Fig. 3. A C++ computer program was developed to model this system on P.C. In this program, a static Runge-Kutta fourth order method is used to solve the system equations. The effectiveness and validity of the proposed approach is tested for a three-phase 5 kW, 380 V, six poles,50 Hz DFIM drive [11] by simulation. Simulation results shown in Fig. 4 are obtained for the system motoring mode of operation below and above synchronous speed. These results are obtained in the condition of an exponentional speed reference from 0 to 260 (rad/sec) rise up to 350 (rad/sec) at t=2 sec with
τ ω = .07 sec, and reference flux signal that is construct from active and reactive power is shown in Fig. 4, a load torque reference profile which is also shown in Fig. 4 and Rr = Rrn , Rs = Rsn . Fig. 5 shows the system performance in the motoring mode of operation below and above synchronous speed. These results are obtained for the same condition described for Fig. 4 but for a Rr = 2 Rrn , Rs = 2 Rsn . Also in the all mode of operations, the torque and rotor reference flux signals are obtained based on desired active and reactive power reference profiles which are injected to the stator from main ac supply. Fig. 6 shows the drive system performance in the generation mode of operation above synchronous speed. These results are obtained for Rr = 2 Rrn , Rs = 2 Rsn and torque reference profile and reference flux signal shown in Fig. 6 and a constant ω r = 375 (rad/sec). Fig. 7 shows the drive system performance in the generation mode of operation below synchronous speed.
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SOLTANI AND FARROKH PAYAM: A ROBUST ADAPTIVE SLIDING-MODE CONTROLLER FOR …
Ps∗
(W )
Qs*
(Var)
t(sec)
t (sec)
(W )
Ps
103
Qs
(Var)
t (sec)
t(sec)
(a) Te , T L
ωr (rad
sec
)
(Nm)
t (sec)
ψ r∗
t (sec)
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ψr
of
(Wb − turn)
(Wb )
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Fig. 6. Drive system performance for the generating mode of operation above synchronous speed.
t (sec)
t (sec)
Te , T L
ωr sec
)
(Nm)
(Wb )
t (sec)
ψr
Fig. 7. Drive system performance for the generating mode of operation below synchronous speed. t (sec)
VIII. CONCLUSION
(Wb − turn)
Ar
ψ r∗
ch
( rad
ive
(b) Fig. 4. (a) Simulation results for motoring mode of operation, and (b) Simulation results for motoring mode of operation.
t (sec)
t (sec)
Fig. 5. Simulation results for motoring mode of operation.
These results are obtained for the same condition described for Fig. 6 and a constant ωr = 280 (rad/sec). One may note that in Figs. 6 and 7, the average active power injected to rotor circuit is positive. That is because of high rotor copper losses obtained by rotor resistance of Rr = 2 Rrn . Also in the above simulation results, Te is the machine generated torque, ω r is the rotor speed in electrical ( rad / sec ), ψ r is the rotor flux linkage, Pr is the power injected into the rotor circuit, E is the rotor dc link voltage, Ps and Q s are active and reactive power injected to the stator from ac supply.
In this paper a robust nonlinear controller has been designed for DFIM drives. The proposed controller is derived based on combination of SM control and adaptive backstepping control approach. The proposed composite control forces the system states trajectories to follow the nominal states which are obtained by a desired reference model, in spite of stator and rotor resistance uncertainties. The nonlinear control method has been tested for motoring and generating mode of operation bellow and above synchronous speed using two back-to-back two level SVM-PWM voltage sources inverters in rotor circuit. Furthermore the rotor dc link voltage is maintained constant also based on input-output control method, using a rotating synchronous reference frame with d axis coincide with the direction of space voltage vector of the main ac supply. Computer simulation results obtained, confirm the validity and capability of the proposed control approach.
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IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 6, NO. 2, SUMMER-FALL 2007
D. Casrdei, F. Profumo, G. Serra, and A. Tani, "FOC and DTC:tow viable schemes for induction motors torque control," IEEE Trans. Power Electron., vol. 17, no. 5, pp. 779-787, Sep. 2002. [2] B. Hopfensperger, J. Atkinson, and R. A. Lakin, "Stator-fluxoriented control of a doubly-fed induction machine with and without position encoder," IEE Proc. Electr. Power Appl., vol. 147, no. 4, pp. 241-250, Jul. 2000. [3] L. Xu and W. Cheng, "Torque and reactive power control of a doubly-fed wound rotor induction machine by position sensorless scheme," IEEE Trans. Ind. Appl., vol. 31, no. 3, pp. 636-642, May/Jun. 1995. [4] Z. Wang, F. Wang, M. Zong, and F. Zhang, "A New control strategy by combining direct torque control with vector control for doubly fed machines," in Proc. IEEE-Powercon’2004, pp. 792-795, Singapore, Nov. 2004. [5] S. Peresada, A. Tilli, and A. Tonielli, "Robust active-reactive power control of a doubly-fed induction generator," in Proc. IEEEIECON’98, pp. 1621-1625, Aachen, Germany, Sep. 1998. [6] S. Peresada, A. Tilli, and A. Tonielli, "Indirect stator flux-oriented output feedback control of a doubly fed induction machine," IEEE Trans. Contr. Sys., vol. 11, no. 6, pp. 875-888, Nov. 2003. [7] H. J. Shieh and K. K. Shyu, "Nonlinear sliding-mode torque control with adaptive backstepping approach for induction motor drive," IEEE Trans. Ind. Electr., vol. 46, no. 2, pp. 380-389, Apr. 1999. [8] J. Soltani and S. Mirzaei, "Computer simulation of a vector controlled slip-energy recovery induction machine drives," Iranian J. of Science & Technology, Trans. B, vol. 27, no. B4, pp. 737-750, Oct. 2003. [9] R. Pena, J. C. Clare, and G. M. Asher, "Doubly fed induction generator using back to back PWM converter and its application to variable-speed wind energy generator," IEE Proc. Electr. Power. Appl., vol. A3, no. 3, pp. 231-241, Nov. 1996. [10] M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, New York: Wiley, 1995. [11] S. Peresada, A. Tilli, and A. Tonielli, "Robust output feedback control of a doubly fed induction machine," in Proc. of the 25th Annual Conf. of the IEEE Industrial Electronics Society, pp. 13481354, 1999.
A. Farrokh Payam received the B.Sc. degree in electrical engineering from the K. N. Toosi University of Technology, Tehran, Iran, in 2002 and M.Sc. degree in electrical engineering from the Isfahan University of Technology, Isfahan, Iran, in 2006 and currently he is a Ph.D. student in electrical engineering in the University of Tehran, Tehran. His research interests include NEMS & MEMS, applied nonlinear control, electrical drives & machines, power electronics, and applied nanotechnology on power engineering.
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[1]
J. Soltani received the B.Sc. and M.E. degrees in electrical engineering from the University of Tabriz, Iran in 1973 and 1974, respectively, and the M.Sc. and Ph.D. degrees in Electrical Power system and Electrical Machine and drive from UMIST, Manchester, UK, in 1984 and 1987, respectively. From 1975 to 1978, he was employed as a shift and operator engineer atn120MW thermal Power Station in Iranian Steel-Mill Co-operation in Isfahan-Iran. In 1979 he joined to the department of electrical and computer engineering of Isfahan University of Technology (IUT) in Isfahan- Iran, as a lecturer and was promoted to Associate Professor and Professor in 1997 and 2002 respectively. From Oct.1999 up to Oct. 2000, he was on sabbatical leave at the University of McMaster in Hamilton, Ontario, Canada. In the early year of 2007, he applied to be retired from IUT and then in June 2007 he joint to the University of Malaya (UM), Kula-Lumpur, Malaysia where he is now a Professor in the Department of Electrical Engineering in the faculty of engineering. His research interests include electrical machine and motion drive, power electronics, power System dynamic, and power-system transient. Dr. Soltani is a senior member of the Institute of Electrical and Electronics Engineers (IEEE) and also is an Association member of IEE.
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REFERENCES
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