ACSE Journal, Volume (6), Issue (2), June, 2006
Fuzzy STATCOM Control Strategies for Power System Stabilization A.H.M.A. Rahim1, E.P. Nowicki2, and J.M. Bakhashwain1 Dept. of Electrical Engineering, K.F. University of Petroleum & Minerals, Dhahran, Saudi Arabia.
[email protected],
[email protected] http://www.kfupm.edu.sa 2 Dept. of Electrical & Computer Engineering, University of Calgary, Calgary, AB, Canada
[email protected] http://www.ucalgary.ca
1
linearized models, nonlinear control strategies for STATCOM have also been reported recently [8]. STATCOM controls for stabilization have been attempted through complex Lyapunov procedures for simple power system models [10]. Applications of fuzzy logic and neural network based controls have also been reported [11-15]. The fuzzy logic control has been emerging in recent years as a complement to conventional controls because it can deal with the uncertainties in the power system effectively [11]. Effectiveness of the fuzzy strategies in damping power system oscillations often depends on the choice of inputs to the controller. In multi-machine system stabilization problems, additional factors to be taken into consideration are the number and location of the STATCOMs. In order to keep the control structure simple, preference should be given to decentralized control employing local measurements. This article investigates the stability enhancement problem of a power system considering multiple STATCOMs in the system and using signals local to the STATCOM. The fuzzy algorithms developed have been tested for their robustness over wide ranges of operation.
Abstract Fuzzy logic control of static synchronous compensators (STATCOM) to improve the damping of a power system is presented. The development of the fuzzy strategy starts through a simple single machine power system and then extended to a multi-machine system. The damping characteristics of the multimachine power system were also investigated with multiple STATCOMs in the system. Only variables local to each STATCOM were used as the input to the controllers. The proposed fuzzy strategy was found to damp the transients of the single machine as well as multi-machine systems effectively for wide ranges of operation. Keywords: Power System Stability, Damping Improvement, STATCOM, Fuzzy-logic Control.
1. Introduction The static synchronous compensator (STATCOM) is a power electronic based synchronous voltage generator that generates a three-phase voltage from a dc capacitor. By controlling the magnitude of the STATCOM voltage, the reactive power exchange between the STATCOM and the transmission line and hence the amount of shunt compensation in the power system can be controlled [1]. Use of STATCOM controller for reactive support of induction generators have also been reported recently [2]. The reactive power is provided by the ac inductors, dc bus capacitor and solid state commutating devices in the STATCOM. In addition to reactive power exchange, properly controlled STATCOMs can also provide damping to a power system [3, 4]. The modeling, operation and control fundamentals of the STATCOM have been extensively discussed in the literature [1, 5-8]. Harmonic analysis for large and small signal transfer of power with STATCOM control has been presented by Woods and Osauskas [9]. While most of the control designs are carried out with
2. Power System Models A single machine infinite bus system with a STATCOM installed at the mid-point of the transmission line is shown in Fig.1. The STATCOM consists of a step down transformer, a three phase GTO–based voltage source converter, and a DC capacitor. The STATCOM is modeled as a voltage sourced converter (VSC) behind a step down transformer. Depending on the magnitude the VSC voltage, the STATCOM current can be made to lead or lag the bus voltage. Generally, the STATCOM voltage is in phase with the bus voltage. However, some active power control may be possible through a limited control of phase angle. This would necessitate a power source behind the capacitor voltage.
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ACSE Journal, Volume (6), Issue (2), June, 2006
The configuration of a 4-genrator multi-machine system is shown in Fig. 2. STATCOMs are assumed to be connected at the middle of the line connecting the generator to the network. The dynamics for the multimachine system contains 5 differential equations similar to (1-2) for each generator. The network equations excluding the generators and the STATCOMs are expressed through the relationships, IBUS = YBUS VBUS
The current-voltage relations are normally expressed in terms of synchronously rotating (D-Q) frames. The (DQ) quantities relate to individual machine frame (d-q) variables by the transformation matrix T = diag [ej(δπ/2) ]. The non-state variables in the generator equations are eliminated by substituting the transformed equations and then the overall dynamics is expressed as, x = f(x, u) (4) Here, the state vector x is of the order 5 times the number of generators, and u is a vector of all STATCOM controls.
Fig.1 A single machine system with STATCOM .
δ = ωo ∆ω .
1 [Pm − Pe − D∆ω] M 1 e 'q = [Efd − eq' − (xd − xd' )Id ] Tdo' ω=−
.
Efd = −
(1)
3. Fuzzy Logic Control The fuzzy logic control (FLC) system, shown in Fig.3, contains four main components – the knowledge base (KB), the fuzzification interface (FI), the decisionmaking logic (DL), and the defuzzification interface (DI). The knowledge base contains knowledge about all the input and output fuzzy partitions. It includes the term set and the corresponding membership functions defining the input variables to the fuzzy ‘rule-base (RB)’ system and the output or decision variables to the plant.
K 1 (Efd − Efdo ) + A (Vto − Vt ) TA TA
The STATCOM capacitor voltage equation is,
dVdc Idc m = = ILod cosψ + ILoqsinψ dt Cdc Cdc
(
)
(3)
(2)
Combining (1) and (2), the dynamics of the single machine system is written as a 5th order state model. The state and the control vectors are given as, [ δ ω ∆ eq’ Efd Vdc]T and [m ψ]T, respectively. A list of symbols is included at the end of the article.
FLC
KB
RB Output
Input FI
PS
DL
DI
STATCO M
Fig.3 The fuzzy logic controller configuration The crisp stabilizing input signals are converted to fuzzy linguistic variables in the fuzzifier. These are then composed with the fuzzy decision variables. The decision-making logic generates the fuzzified control through various composition rules. The fuzzy control is then defuzzified and is used to fire the thyristors in the STATCOM.
Fig.2 Multi-machine system configuration
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ACSE Journal, Volume (6), Issue (2), June, 2006
The following steps are involved in designing the fuzzy STATCOM controller [14, 15]: 1.
2.
3.
Table 1 Decision table ∆α
Choose the inputs to the fuzzy STATCOM controller. Only two inputs, the generator speed deviation (∆ω) and acceleration (∆α), have been employed in this study. The output or decision variable is the pulse modulation index ‘m’ of the STATCOM voltage. The symbol u has been synonymously used to represent the output. Since control of ψ is known to provide no additional damping to the system, it has not been considered any further.
∆ω
Choose membership functions to represent the inputs in fuzzy set notation. Triangular functions are chosen in this work. Fuzzy representation of generator speed change is shown in Fig.4. Linguistic variables chosen are large positive (LP), medium positive (MP), small positive (SP), very small (VS), small negative (SN), medium negative (MN), and large negative (LN) at thresholds s1, s2, s3, 0, s4, s5, s6, respectively. Similar membership functions for the other inputs and the stabilizer output are also defined.
- s6
VS SP
SN
MP
LP
-s4 0
s3
s2
s1
VS
SP
M
LP
LN
LN
LN
LN
LN
M
SN
VS
M
LN
LN
MN
MN
SN
VS
SP
SN
LN
MN
SN
VS
SP
M
MP
VS
MN
MN
SN
VS
SP
M
MP
SP
MN
SN
VS
SP
SP
M
LP
MP
SN
VS
SP
MP
MP
LP
LP
LP
VS
SP
MP
LP
LP
LP
LP
FLC Output Membership values
x1
(LN,LN)
L N 1
x2
(LN,MN)
1
M N 0. 5 0. 5 ..
S N 0
VS
SP
LP
0
M P 0
0
0
0
0
0
0
..
..
..
..
..
1
0.5
0
0
0
0
..
..
..
x24
(VS,SN)
0
.. x48
..
..
0. 5 ..
..
..
..
..
..
(LP,MP)
0
0
0
0
0
1
x49
(LP,LP)
0
0
0
0
0
0. 5 0. 5
1
5. The membership values for the condition part of each rule are calculated from the composition rule as follows: µ(xi)= µ(∆ω is LP, and ∆α is LN) =min [µ (∆ω is LP),µ(∆α is LN)]; i=1,2, … N2 (5) Here, xi is the i-th value of the N2 possible states (input-combinations) in the FRM. 6. The membership values for the output characterized by the M linguistic variables are then obtained from the intersection of the N2 values of membership function µ(xi) with the corresponding values of each of the decision variables in the FRM. For example, for the decision LN ⊂ M and for state xi , we obtain, µ u (xi, LN)=min[µ(xi, LN), µ(xi)];
1
-s5
SN
FLC Input xi (∆ω,∆α)
µ(∆ω) MN
M
Table 2 Part of the fuzzy relationship matrix
A set of decision rules relating the inputs to the output are compiled and stored in the memory in the form of a ‘decision table’. The rules are of the form: IF ∆ω is large negative (LN), AND ∆α is large negative (LN); THEN control (u) is large negative (LN). The decision table is provided in Table 1.
LN
LN
∆ω
Fig.4 Fuzzy representation of speed signal 4. For N linguistic variables for each of ∆ω and ∆α, there are N2 possible combinations resulting into any of M values for the decision variable u. All the possible combinations of inputs, called states, and the resulting control are then arranged in a (N2xM) ‘fuzzy relationship matrix’ (FRM). The fuzzy relationship matrix for all the 49 states and the corresponding membership values of control are tabulated in Table 2.
i=1,2, … N2. (6) The final value of the stabilizer output ‘LN’ can be evaluated as the union of all the outputs in equation (6) given by the relationship (7) µ u (LN)= max { µ u s (xi, LN)}
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ACSE Journal, Volume (6), Issue (2), June, 2006
The membership values for the other M-1 linguistic variables are generated in a similar manner. 7.
110 100
The fuzzy outputs µ u (LN), µ u (LP), etc. are then
90
Angle (deg.)
defuzzified to obtain crisp u. The popular methods of defuzzification are the centroid and the weighted average methods. Using the weighted average method, the output of the FLC is then written as, M µ ( Ai ) x threshold values of Ai (8) u=∑ u ∑ µ u ( Ai ) i =1
80 a
70 b
60 c
50
The expert knowledge employed in the general fuzzy STATCOM design to stabilize a power system is that if the states are far from the origin, exertion of large control is required to bring the states to the origin; polarity of the control being decided roughly by the quadrants. Since a ∆ω - ∆α based control is generally known to damp transients, given enough time to iterate, this type of strategy will eventually converge.
d
40 30 20
0
0.5
1
1.5
2
2.5
3
3.5
4
Time (sec)
Fig.6 Generator rotor angle variations following a threephase fault on the remote bus for 0.2s
The robustness of the controller was tested by applying the fuzzy strategy to a number of operating conditions. Figs. 6 and 7 show the rotor angle and DC capacitor voltage variations in the STATCOM for the following 4 loading conditions - a) 1.1 pu power output at 0.9 pf lagging, b) 1 pu power at 0.95 pf lag, c) 0.9 pu power at 0.95 pf lag, and d) 0.6pu power at 0.85pf lagging. The disturbance considered was a three-phase fault on the remote bus for 0.2s. It can be observed the fuzzy control scheme gives very good damping profile over a range of operating conditions even for severe fault conditions.
4. Simulation Results Single Machine System: The single-machine infinite bus system considered in Fig.1 was tested with the fuzzy logic STATCOM control for a number of disturbances and for various operating conditions. The system data is given in the appendix.
3.9
D C C apacitor Volt.(pu)
3.85 3.8
c b
3.75 3.7 d
3.65 3.6
a
3.55 3.5
Fig. 5 The generator rotor angle variation following a three-phase fault for 0.2 sec duration, (a) no control, (b) with the proposed fuzzy STATCOM control
0
0.5
1
1.5
2
2.5
3
3.5
4
Time (sec)
Fig.7 DC capacitor voltage variation corresponding to Fig.7
Fig. 5 shows the rotor angle variation of the generator following a three-phase fault for a nominal load of 0.9 pu at 0.95 pf lagging with and without fuzzy logic control. Without control the system response is very oscillatory (a), while the fuzzy controller provides excellent damping to the system (b).
Multi-machine System with One STATCOM: The fuzzy control strategy for stabilization developed in section 3 was tested on the multi-machine system of Fig3. The STATCOM considered is connected to the circuit of generator 2. The speed deviation and acceleration of generator 2 were considered as input to the STATCOM control circuit. These quantities could 4
ACSE Journal, Volume (6), Issue (2), June, 2006
Gen 4
∆ ω 2 - ∆ ω 1 (% )
2 1 0
1
2
2.5
3
3.5
4
a
0
0.5
1
1
1.5
2
2.5
3
3.5
4
3
3.5
4
3
3.5
4
a b
0 -1 0
0
0.5
1
1.5
2 2.5 Time (sec)
3
3.5
0
0.5
2 1 0 -1
1
1.5
2
1
1.5
2
2.5
2
b
0
0.5
4
a
2.5
3
3.5
4
a
b
0 -2
a
0
0.5
1
1.5
2
2.5
Time(sec)
b 0
0.5
1
1.5
2
2.5
3
3.5
4
Time (sec)
Fig.10 Relative speed variation of the generators following a 4-cycles three-phase on generator 2 bus
Fig.8 Speed variations of the generators following a 100% torque pulse for 0.1sec with, a) no control, b)fuzzy logic control. Fig.8 shows that the response of the uncontrolled system is under damped. It is apparent that only one STATCOM provides significant damping to all the generators in the system. Damping provided to generators 2 and 3 is the most because of their electrical proximity.
The fuzzy control strategy was tested for robustness considering a number of loading conditions. Fig. 12 shows the relative angle variations of the generators for 4 widely different loading conditions given in the appendix. It can be seen that the proposed fuzzy controller with only one STATCOM, fed from signals local to it, is very effective in damping the multi-machine system oscillations for severe short circuit conditions.
4.2
b
4.5
4.15
4.4
S TA TC OM D C V oltage (pu)
STA TC OM D C Voltage (pu)
-1
b
1
-1
1.5
∆ ω2 - ∆ ω3
0.5
-1
2
b
2
b 0
a
0
0
-1
2 1
1
a
∆ω2 - ∆ω4
A b s o lu te S p e e d D e v . (% ) Gen 3 Gen 2
Gen 1
be tele-metered or reconstructed from the line flow. Fig. 8 shows the speed variations of the various generators in the power system with and without the fuzzy control for a 100% torque pulse for 0.1s on generator 2.
4.1
4.05 a
4
3.95
a 4.3 4.2
b
4.1 4 3.9 3.8 3.7
0
0.5
1
1.5
2
2.5
3
3.5
4
Time (sec)
3.6
Fig.9 DC STATCOM voltage variation for a 100% torque pulse disturbance corresponding to Fig.8
3.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Time(sec)
Fig.9 shows the variations of the DC control voltage of the STATCOM with and without fuzzy controls. For a 4-cycle three-phase fault at the terminal of generator 2, the relative speed variations of the different generators are shown in Fig. 10, while Fig 11 shows the dc control voltage variation.
Fig.11 DC capacitor control voltage corresponding to fault condition of Fig.10
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ACSE Journal, Volume (6), Issue (2), June, 2006
R elative Generator A ngle δ 2 - δ 1 (deg)
100
5. Evaluation of the Fuzzy Controller
a
PLANT
b
50
-
sTw 1 + sTw
c 0 d
KI s
Fig.14 PI controller for STATCOM -50
0
0.5
1
1.5
2
2.5
3
3.5
4
The damping properties of the fuzzy logic controller for the single machine case were compared with a conventional PI controller. Configuration of plant, the PI controller and an additional washout, which is used to eliminate any additional signal in steady state, is given in Fig.14. The parameters of the PI controller are ‘optimally’ tuned so that the dominant eigenvalues of the closed loop system give a damping ratio of approximately 0.3. In Fig.15, a comparison of the responses with the PI control and the fuzzy logic control are given for three operating conditions, (a) at 1.1 pu, (b) 0.9 pu and (c) 0.6 pu power outputs. The solid lines are with fuzzy control, while the dashed ones are with PI control. PI gains are calculated for the nominal loading of 0.9pu. Fig.16 shows the corresponding variations of the dc capacitor voltage with the fuzzy and PI controls. The PI controller generally gives reasonable response for the designed nominal case but the response worsens for operation away from nominal, and can even give rise to unstable situations as in (a). Fuzzy control, to the contrary, performs very well over a wide range of operation. Similar conclusions can de drawn for multimachine system also.
Time(sec)
Fig.12 Relative rotor angle variations following a 4cycle three-phase fault for 4 different loading conditions Multi-machine System with Two STATCOMs: The damping behavior of the multi-machine power system was investigated by activating fuzzy control on two STATCOMs in the system. The inputs to STATCOM controllers located in the circuits of generator 2 and 3 are considered to be the speed deviation and acceleration of the individual machines. Figure 13 shows a comparison of the relative speed variations of the generators with STATCOM controls applied independently, as well as with coordinated application. The disturbance considered was a 4-cycles three-phase fault at the terminal of generator 2. It can be observed that the individual controls themselves are very effective, the coordinated application giving the best damping profile. 2
∆ ω2 - ∆ ω1
KP +
c
b 0
120
a -2 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
100 c
a(PI)
a 0
Angle (deg.)
∆ ω2 - ∆ ω3
2
b -2
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
∆ ω2 - ∆ ω4
2
80 a b(PI)
60
c
b
b
c(PI)
0
40
c
a
-2 0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time(sec)
20
Fig.13 Relative speed variation of the generators following three-phase faults with, a) control on STATCOM 2, b) control on STATCOM 3, c) coordinated application of both controls.
0
0.5
1
1.5 2 Time (sec)
2.5
3
3.5
Fig.15 The rotor angle response for three loading conditions (a) 1.1 pu, (b) 0.9 pu, and (c) 0.6 pu following three-phase fault for 0.2 sec.
6
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ACSE Journal, Volume (6), Issue (2), June, 2006
Efdo, Vto Vdc,Idc
4
DC Capacitor Volt.(pu)
3.9
Cdc ILo m, ψ
b
3.8
b(PI) 3.7
c
IBUS VBUS YBUS
3.6
c(PI)
a 3.5
a(PI) 3.4
3.3
Nominal field, terminal voltage dc capacitor voltage, current of STATCOM Capacitance of dc capacitor Steady ac STATCOM current Modulation index, phase of STATCOM voltage Vector of injected current to the network Network bus voltage Bus admittance matrix of system excluding generator and STATCOM
9. References 0
0.5
1
1.5
2
2.5
3
3.5
[1] A.H. Noorazi and A.M. Sharaf, “Two control schemes to enhance the dynamic performance of the STATCOM and SSSC,” IEEE Trans. Power Delivery, vol. 20, no. 1, pp. 435-442, January 2005. [2] B. Singh, S.S. Murthy and S. Gupta, “Analysis and design of STATCOM-based voltage regulators for self-excited induction generators,” IEEE Trans. Energy Conversion, vol. 19, no. 4, pp.783-790, December 2004. [3] P. Rao, M.L.Crow and Z. Young, “STATCOM control for power system voltage control applications,” IEEE Trans. on Power Delivery, vol. 15, no. 4, pp. 1311-1317, October 2000. [4] P.S. Sensarma, K.R. Padiyar and V. Ram-narayanan, “Analysis and performance evaluation of a distribution STATCOM for compensating voltage fluctuation,” IEEE Trans. Power Delivery, vol. 16, no. 2, pp. 259-264, April 2001. [5] D.Shen and P.W. Lehn, “Modeling, analysis and control of a current source inverter-based STATCOM,” IEEE Trans. Power Delivery, vol. 17, no. 1, pp.248-253, January 2002. [6] Y. Ye, M. Kazerani and V.H. Quintana, “Current source converter based STATCOM: Modeling and control,” IEEE Trans. Power Delivery, vol. 20, no 2, pp.795-800, April 2005. [7] L. Cong and Y. Wang,“Coordinated control of generator excitation and STATCOM for rotor angle stability and voltage regulation enhancement of power systems,” IEE Proc- Gener. Transm. Distrib. vol. 149, no. 6, pp.659-666, November 2002. [8] D. Soto and R. Pena, “Nonlinear control strategies for cascaded multilevel STATCOM,” IEEE Trans. Power Delivery, vol.19, no. 4, pp. 1919-1927, October 2004. [9] A.R. Wood and C.M. Osauskas, “A linear frequency domain model of a STATCOM”, IEEE Trans. Power Delivery, vol.19, no. 3, pp.1410-1418, July 2004. [10] M.H.Haque and P. Kumkratng, “Application of Lyapunov stability criterion to determine the control strategy of a STATCOM,” IEEE Proc. – Gener. Transm. Distrib., vol.151, no. 3, pp.415 420, May 2004. [11] L.O.Mak, Y.X. Ni and C. M. Shen, “STATCOM with fuzzy controllers for interconnected power systems,” Electric Power Systems Research, vol.
4
Time (sec)
Fig.16 dc capacitor voltage for the fault condition corresponding to Fig.15
6. Conclusions A fuzzy logic STATCOM controller design for stabilization of power systems is presented. The control has been implemented on a single as well as a multi-machine power system and was found to provide very good damping characteristics over wide ranges of operation. It has been observed that the damping of a multi-machine power system can be significantly enhanced with proper control of only one STATCOM. However, coordinated application of multiple STATCOM controls provides superior transient response. Effective damping control for wide ranges of operation and for various disturbance conditions demonstrate the robustness of the fuzzy STATCOM control.
7. Acknowledgements The authors wish to acknowledge the facilities provided towards this research at the King Fahd University of Petroleum and Minerals, Dhahran, and the University of Calgary, Calgary, Canada.
8. List of Symbols δ Generator rotor angle ω Rotor speed ωo Base (synchronous) speed Pm Pe M D eq’ Tdo’ Efd xd, xd’ Id KA, TA Vt VL Vb
Mechanical power input Electrical power output Inertia constant Damping coefficient of generator Quadrature (q) axis internal voltage Open circuit field time constant Field voltage Synchronous, transient direct (d) axis reactance d-component of armature current Exciter gain, time constant Generator terminal voltage STATCOM bus voltage Network bus voltage 7
ACSE Journal, Volume (6), Issue (2), June, 2006
55, pp.87-95, 2000. [12] G.W.Kim and K.Y.Lee, “Coordination control of ULTC transformer and STATCOM based on an artificial neural network,” IEEE Trans. Power Systems,vol. 20, no. 2, pp.580-586, May 2005. [13] M. Mohaddes, A.M. Gole and P.G.McLaren, “A neural network controlled optimal pulse-width modulated STATCOM”, IEEE Trans. Power Delivery, vol.14, no. 2, pp.481-488, April 1999. [14] H.A.Toliat, J. Sadeh and R. Ghazi, “Design of augmented fuzzy logic power system stabilizers to enhance power system stability”, IEEE Trans. Energy Conversion, vol. 11, no.1, pp.97-103, 1996. [15] T.J. Ross, Fuzzy Logic with Engineering Applications, McGraw Hill, New York, 1995.
A 3: Generation and loading conditions P and Q are given in MW and MVAR. Gen
Case a
Case b
Case c
Case d
G1
232
119
307
226
68
19
123
31
G2
700
244
725
366
535
78
330
49
G3
300
193
575
336
165
74
165
105
G4
450
266
675
461
245
111
157
94
10. Appendix A 1: STATCOM data for single machine system H=3.0 s, Tdo′ = 6.3 s, xd = 1.0, xd′ = 0.3, xq = 0.6, D=0,
Loads
XTL= 0.3, XLB = 0.3, XSDT = 0.15, KA = 10, TA = 0.05s, Cdc = 1.0, mo = 0.25, ψo = 46.52o
SA
350
195
460
275
275
135
200
150
SB
350
195
460
275
175
135
125
175
SC
650
375
900
475
410
250
350
250
SD
325
155
450
220
150
100
125
75
Nominal plant operating conditions: Peo = 0.9, Vto = 1.0, pf = 1.0. All the quantities are in per unit, except as indicated
Case a
Case b
Case c
Case d
A 2: Multi-machine System Dat The STATCOM system data for the multi-machine system is identical to the single machine system. Xd
Xq
Xd1
Xd2
Xq2
1.000
0.9550
0.1219
0.026
0.033
0.552
0.3972
0.1845
0.029
0.026
1.244
1.1918
0.1655
0.026
0.033
2.769
2.6910
0.6017
0.269
0.335
H
Tdo1
Tqo1
Ka
Ta
6.50
3.48
0.50
75.0
0.01
2.55
8.62
0.10
75.0
0.01
3.28
6.11
0.50
75.0
0.01
3.17
7.39
0.10
75.0
0.01
11. Author Biographies Abu H. M. A. Rahim did his Ph.D. from the University of Alberta, Edmonton, Canada in 1972. Since his Ph.D., he has worked at the University of Alberta, Bangladesh University of Engineering, University of Strathclyde (Glasgow), University of Bahrain, DeVry Institute of Technology, Calgary and at the University of Calgary. Dr. Rahim is presently working at the King Fahd University of Petroleum and Minerals, Dhahran where he is a Professor. Dr. Rahim's main fields of interest are power system stability, control and application of artificial intelligence to power systems. Dr. Rahim is a senior member of the IEEE and Fellow of the Institute of Engineers, Bangladesh.
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ACSE Journal, Volume (6), Issue (2), June, 2006
Edwin P. Nowicki received his Ph.D. from University of Toronto in 1991. He worked at Inverter Controls ltd., Burlington, Ontario in the area of medium voltage induction motor drives before joining the University of Calgary in 1992, where he is presently an Associate Professor in the Department of Electrical and Computer Engineering. His current research projects include fuzzy logic controls and artificial neural networks to power electronic devices. Jamil M. Bakhashwain, is an Associate Professor and Chairman of Electrical Engineering Department at King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia. He received his Ph.D. from University of Colorado at Boulder in 1989. His areas of interests are control systems and its application and measurements and management of magnetic fields on transmission lines. He has published many journal and conference papers and authored or co-authored a number of technical reports. He has been involved in many research projects and studies on power system.
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