a nonlinear voltage regulator with one tunable parameter for multimachine power systems
TRANSCRIPT
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1186 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 3, AUGUST 2011
A Nonlinear Voltage Regulator With One TunableParameter for Multimachine Power Systems
Gurunath Gurrala, Graduate Student Member, IEEE, and Indraneel Sen
AbstractThis paper proposes a nonlinear voltage regulatorwith one tunable parameter for multimachine power systems.Based on output feedback linearization, this regulator can achievesimultaneous voltage regulation and small-signal performanceobjectives. Conventionally output feedback linearization has beenused for voltage regulator design by taking infinite bus voltageas reference. Unfortunately, this controller has poor small-signalperformance and cannot be applied to multimachine systemswithout the estimation of the equivalent external reactance seenfrom the generator. This paper proposes a voltage regulatordesign by redefining the rotor angle at each generator with respectto the secondary voltage of the step-up transformer as referenceinstead of a common synchronously rotating reference frame.
Using synchronizing and damping torques analysis, we show thatthe proposed voltage regulator achieves simultaneous voltageregulation and damping performance over a range of system andoperating conditions by controlling the relative angle between thegenerator internal voltage angle and the secondary voltage ofthe step up transformer. The performance of the proposed voltageregulator is evaluated on a single machine infinite bus system andtwo widely used multimachine test systems.
Index TermsFeedback linearization, power system stabilizers,small-signal stability, transient stability.
NOMENCLATURE
Rotor angle (in electrical radians).
Rotor (electrical) speed, corresponding to
the time derivative of .
Rotor angle with respect to the secondary
voltage of the transformer.
Slip speed .
w.r.t. center of inertia (COI)
.
w.r.t. center of inertia
.
Mechanical and electrical torques.
Damping coefficient.
Transient induced voltages due to field
flux-linkages.
Manuscript received December 25, 2009; revised January 01, 2010, January05, 2010, April 09, 2010, and July 02, 2010; accepted July 20, 2010. Date ofpublication October 14, 2010; date of current version July 22, 2011. Paper no.TPWRS-01007-2009.
The authors are with the Department of Electrical Engineering, Indian In-stitute of Science, Bangalore 560012, India (e-mail: [email protected];[email protected]).
Digital Object Identifier 10.1109/TPWRS.2010.2069930
d, q-axis components of stator current.
d, q-axis open circuit time constants.
d, q-axis reactances.
Field voltage.
Voltage measured at the generator terminal.
Voltage measured at the secondary of the
transformer.
Reference voltage.
PSS input.
Armature resistance.
Transformer and transmission line
reactances.
d, q-axis components of terminal voltage.
Gain and time constants of static excitation
system.
Inertia constant of machine.
Power factor at the transformer bus.
Real and reactive powers at machine andtransformer secondary terminals.
PSS Power system stabilizer.
AVR Automatic voltage regulator.
FBL Feedback linearization.
SMIB Single machine infinite bus system.
GEN, SYS Generator, system.
I. INTRODUCTION
TRADITIONALLY, the automatic voltage regulator (AVR)and power system stabilizer (PSS) have been designed
separately using the linearized models of power system. The
AVR tries to modulate reactive power and PSS tries to modu-
late real power, since both strategies are executed through field
voltage, simultaneous achievement of both goals is not pos-
sible [1], [2]. The linearized models on which the controllers are
based depend upon the system operating condition. Any signif-
icant deviation from this nominal operating condition can con-
siderably degrade the performance of the controllers.
In order to overcome these difficulties, feedback lineariza-
tion (FBL) technique has been widely used for generator ex-
citation system design [3][9]. Most of the nonlinear control
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designs based on FBL have formulated the excitation control
problem as a regulator problem and terminal voltage regulation
was not considered in the design objective. As this formulation
results in poor voltage regulation [2], [8], [10], [11], researchers
have proposed several alternative methods for voltage regula-
tion in addition to FBL, such as using observed decoupled state
space, switching an additional controller after the fault, etc. [2],[5][8], [11][14]. Most of these controllers require complete
system information for the design, and at least two variables
need to be tuned for better performance. It is always desirable
to have a single controller with minimum tunable parameters
that can simultaneously achieve better terminal voltage regula-
tion and good small signal performance. The first attempt in this
direction was made in [10]. Unfortunately, this controller has
poor small-signal performance and cannot be applied to multi-
machine systems without the estimation of equivalent external
reactance seen from the generator terminals.
In [15], a power system stabilizer based on feedback lin-
earization has been proposed by taking secondary voltage of
the step up transformer as reference instead of the infinite busvoltage. This PSS tries to control the oscillations by controlling
the angle , the angle between generator internal
voltage , and secondary voltage of the step up transformer
. This work has been patented [16] with hardware imple-
mentation details. In [17], this concept has been used for de-
veloping fixed parameter power system stabilizers for multima-
chine systems.
In this paper, a nonlinear voltage regulator design for mul-
timachine systems has been proposed by taking the secondary
voltage of the step-up transformer (high-voltage bus) as refer-
ence [16], [17] instead of a common synchronously rotating ref-
erence frame [infinite bus voltage in the case of single machineinfinite bus system (SMIB)]. Using the concepts of synchro-
nizing and damping torques, it has been shown that the tuning
parameter of the proposed controller can be varied in a wide
range as opposed to the controller in [10] which allows effective
tradeoff between the voltage regulation and small-signal per-
formance objectives. The performance of the proposed voltage
regulator has been evaluated on an SMIB test system and two
most widely used multimachine test systems, IEEE ten-gener-
ator 39-bus system and IEEE 16-generator 59-bus system over
a wide range of operating conditions.
II. PROPOSED APPROACH
In this paper, a generator connected to an external power
system through a step-up transformer as shown in Fig. 1 has
been considered for the nonlinear AVR design [15], [17]. In the
present design, IEEE Model 1.0 [18], [19] is used to represent
the synchronous generator. This results in a third-order dynamic
model for a power system. The use of third-order model is jus-
tified as it sufficiently represents the essential dynamics of the
system. In systems equipped with static excitation systems, the
complexity of higher order models is largely due to the pres-
ence of amortisseur windings which always contribute to posi-
tive damping. The adequacy of third-order model has been ex-
perimentally verified recently in [20] and a large number of non-
linear excitation controllers are designed based on this model
[17], [21].The generator rotor angle with respect to the secondary
voltage of the transformer is defined as .
The expressions for are given below [17]. Subscript
refers to the th machine in a multimachine environment:
(1)
where and is
power factor angle at the high-voltage bus:
(2)
The expressions for and are as follows:
(3)
where
Now the expression for terminal voltage is given by (4) at the
bottom of the page.
The variables have standard meaning as indicated in the
nomenclature. We use input-output feedback linearization to
derive the nonlinear control law for the field voltage. For a
control affine system with output ,
the basic approach of the input-output feedback linearization is
to differentiate the output function repeatedly until the input
appears and then design to cancel the nonlinearity. The
number of differentiations required for the input to appear is
called the relative degree of the system. Defining the tracking
(4)
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Fig. 1. Generator connected to external network through a step-up transformerand proposed control structure.
error as , where is the desired output, a
fixed gain parameter can be chosen such that the error
dynamics as . Solving the error dynamics
equation gives the nonlinear control law as
(5)
Derivatives of the output (4) are taken successively until the
control input appears in the equation. In this case, relative
degree is one. Taking derivative of (4), we get
(6)
Equation (6) can be written in control affine form as
(7)
Here the output to be tracked is the steady-state terminal voltage
(the reference voltage). So the tracking error is defined as
. Following assumptions are made in the design.
1) is replaced with . This
is to enable a damping torque component to be produced
on the rotor.
2) . This assumption is to avoid singularity in the
nonlinear control law during sudden changes in terminalvoltage.
Solving the error dynamics equation, one can get the nonlinear
control law from (5) for field voltage as given in the fol-
lowing:
(8)
The subscript 0 indicates initial operating condition. The pro-
posed control structure has been shown in Fig. 1. The control
law tries to control instead of . The proposed controller can
assess the system disturbances such as changes in system con-
figuration or load variations based on the deviations in com-
puted from the power flow and voltage at the high-voltage bus
of the step-up transformer [15], [17]. In general, it is very diffi-
cult to get the measurements of and in the field. However,
the proposed approach enables us to realize the control law inmultimachine environment by computing (1)(3) from
and measurements at the high-voltage bus of each machine.
This makes the control law decentralized. Usage of (1) and (2)
for power system control applications has been patented [16].
The conventional nonlinear AVR proposed in [10] and the
proposed AVR have the same control format except that the
former is a function of and the later is a function of
. The proposed controller has shown much better performance
than the conventional nonlinear AVR and the linear
controller. In the following section, the concepts of synchro-
nizing and damping torques have been used to understand the
reason for better performance of the proposed controller.
III. ANALYSIS OF THE PROPOSED NONLINEAR AVR
To understand the small-signal behavior of the proposed non-
linear AVR at different operating conditions, the control law (8)
is linearized using the conventional Taylor series approxima-
tion. The analysis is performed for SMIB system (subscript i
is dropped). Linearization of (8) gives
(9)
In implementing the nonlinear control law (8), terminal
voltage is obtained from the measurements at the generator
terminals, so the linearized equation of is
(10)
(11)
(12)
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While linearizing , it is considered as a function of
and . While linearizing , we consider and as state vari-
ables and as a variable quantity. So linearizing given in
(3) results in
(13)
It can be observed that an additional term also comes in the
expression to account for the variations in and the respective
constants are functions of and :
(14)
substituting (10) and (13) in (9) and rearranging the terms, one
can arrive at (15) where and
. This equation can be rewritten as (15)and (16) at the bottom of the page.
Fig. 2 shows the block diagram representation of (16). From
the block diagram, the proposed controller can be interpreted
as a high gain , fast exciter with negligible delay. It has
four components negatively affecting the torque angle loop, two
components due to the deviations in rotor angle and relative
rotor angle denoted by and , respectively. One com-
ponent due to the deviations in flux linkages denoted by
and one component denoted by due to the deviations in
voltage magnitude of the high-voltage bus . and are
standard Heffron Phillips model parameters [23]. It also con-
tains an additional component from the deviations in slip
speed as shown with dashed circle in Fig. 2. This compo-
nent contributes positively to the torque angle loop just like
a power system stabilizer. In case of a conventional FBLAVR
,the components and are contributed by and the com-
ponent is zero as is constant.
For simplifying the analysis, though and have dif-
ferent magnitudes, one can combine the effect of these com-
ponents by taking . This does not affect the
Fig. 2. Proposed feedback linearization based AVR.
synchronizing and damping torques analysis as and arein-phase quantities.
Variations of parameters and are plotted by
varying generator power from 0.5 p.u. to 1.1 p.u. for various
values of . The terminal voltage is fixed at 1 p.u. Figs. 3
and 4 show the variations of and , respectively,
with . Gain of the proposed controller is fixed at 20 so
that the variation of and is almost the same as that of the
linear AVR parameters and . Observe that and are
always positive. and onthe other handcan bepositive or
negative (see Fig. 3). Here the negative damping contribution of
has to be compensated by the component for damping.
These plots for conventional FBLAVR are not shown due to
space limitations; however, they are observed to be more or less
identical to that of the proposed FBLAVR.
Fig. 5 shows the variation of with for different values
of . Solid lines show the variations for the proposed non-
linear AVR. Dashed lines show the variation for the conven-
tional nonlinear AVR. It can be seen that the damping com-
ponent of conventional FBLAVR reduces significantly with in-
crease in external impedance and with increase in system
(15)
(16)
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Fig. 3. Variation of with for various values of .
Fig. 4. Variation of with for various values of .
loading. However, the damping term contribution of the pro-posed AVR is more or less constant with increase in loading
as well as system external reactance. The proposed controller,
therefore, offers good damping performance over a wide range
of operating and system conditions. It has been observed that for
in the range of 0.2 p.u. to 0.8 p.u., lies between 620
and 950. Higher values of gain give higher synchronizing torque
and better voltage regulation but at the expense of damping
torque [23]. It has been observed that , which represents the
effect of variation in the magnitude of the voltage of the trans-
former bus, varies between 5e-4 to 13e-4. It means that the vari-
ation in voltage magnitude of the high-voltage bus on system
dynamic performance is not of much significance. Neglecting
variation while deriving the proposed control law (assump-tion 2) is thus justified.
Fig. 5. Variation of with of proposed FBLAVR and conventionalFBLAVR.
A. Synchronizing and Damping Torques AnalysisThe component of electrical torque produced by voltage reg-
ulator action due to variations in rotor angle through can be
expressed as [26]
(17)
The first component can be treated as the torque that
would have been produced by a static AVR with a gain equal
to and low time constant. The second component
can be considered as the torque produced by due to the non-
linear AVR action. Substituting (complex eigen-
value corresponding to the rotor mode of system matrix that
can be easily obtained) and , one can ob-
tain the following expressions for synchronizing and damping
torque coefficients [26]:
(18)
(19)
Total synchronizing torque coefficient can be obtained by
adding to (18).
Figs. 6 and 7 show the variation of total synchronizing anddamping torque coefficients and with for various
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Fig. 6. of proposed FBLAVR and conventional FBLAVR.
Fig. 7. of proposed FBLAVR and conventional FBLAVR.
values of . It can be observed that the variation of the
proposed AVR is the same as that of a conventional nonlinear
AVR except for . decreases with increase in
for both controllers; however, for the proposed AVR, the is
always positive and much higher than that of the conventional
FBLAVR. Positive over the entire range of operating condi-
tions accounts for the better performance of the proposed non-
linear AVR.
Now we analyze the damping factor obtained from the total
and using the following expression [26]:
(20)
Fig.8 showsthecomparison of withincrease in for the pro-
posed FBLAVR and the conventional FBLAVR. Observe that
for both the controllers at every value of , the variation in
damping factor has an inverted v-shape. The value of at
which maximum damping occurs decreases with increase in .
Observe that variation with the proposed AVR is always pos-
itive. The maximum damping factor occurs at
for the nominal operating condition (
p.u., p.u., and p.u.). This is muchhigher than of conventional FBLAVR. In the
Fig. 8. Variation of damping factor , proposed FBLAVR.
case of proposed FBLAVR, the tuning parameter can be
varied in a wider range than the conventional nonlinear AVR
because even at , the damping factor is 0.17786 for
p.u., which is quite acceptable for power systems.
This allows an effective trade-off between voltage regulation
and damping improvement.
IV. SIMULATION RESULTS
A. SMIB System
The performance of the proposed AVR (8) has been exten-
sively evaluated on a SMIB system studied in [23]. Data for the
steam input SMIB given in [23] have been used here. Several
operating conditions are created to test the performance of the
proposed voltage regulator by varying from 0.2 p.u. to 0.8p.u. and from 0.5 p.u. to 1 p.u. by keeping and con-
stant at 1 p.u. Results of only a few representative test cases are
shown here.
Figs. 9 and 10 show the terminal voltage and the field voltage
responses of the nominal SMIB system (
p.u., p.u., p.u.) for a 0.1 p.u. step change in
. The system is operated with 1) nonlinear AVR proposed in
[10] (conventional FBLAVR), , 2) static
(linear ),and 3) proposed nonlinear AVR (proposed
FBLAVR or FBLAVR), . The system is unstable with
linear AVR alone. The system becomes stable with all the three
controllers. It can be observed that the performance of the pro-posed controller is comparable to the linear and the
conventional nonlinear AVR. Observe that all the controllers are
able to track the reference voltage perfectly. In Fig. 10, observe
that the control effort due to the proposed voltage regulator is
similar to that of the linear .
It has been observed in simulations that if assumption 1 is not
considered, then the performance of the proposed controller is
exactly the same as the conventional nonlinear AVR. Assump-
tion 1 is very crucial in this design as this enables the proposed
AVR to achieve good small signal performance.
Fig. 11 shows the responses of the SMIB with the same con-
ditions as above, following a fault cleared after two cycles
by tripping one of the parallel lines. After the fault is cleared,the system becomes weak with an equivalent external reactance
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Fig. 9. response, 10% step change in .
Fig. 10. response, 10% step change in .
Fig. 11. response, fault at transformer bus, cleared by line tripping.
. The system is more oscillatory with conventional
nonlinear AVR. The performance of the proposed AVR is better
than the performance of the linear .
B. Ten-Generator 39-Bus System
This is a most widely used test system, for validating controldesigns. The data for the system are taken from [19]. Though
Fig. 12. of GEN-9 for a 0.02 p.u. step change in at GEN-9, 10 GENSYS.
the controller is developed for third-order model, here the sim-
ulations are carried out using IEEE model 1.1 [18] neglecting
transient saliency. All the static excitation systems of the ten-
generator (GEN) system except GEN-2, which is an equivalent
representation of external network, are replaced with the pro-
posed nonlinear AVR. The performance of the proposed non-
linear AVR is compared with the performance of the system
equipped with linear AVR+PSS at varied operating conditions.
is selected such that
the terminal voltage response of each generator for a 0.02 p.u.
step change in is within % of the final value [24]. Sim-
ulation results of a few test cases are shown in this section.
Fig. 12 shows terminal voltage responses of GEN-9 with
the proposed AVR for a 0.02 p.u. step change in inputof GEN-9. The figure also contains the responses obtained
with a linear AVR and linear AVR+PSS. It can be observed
that the system is unstable with the linear AVR alone. The
response with the proposed AVR is comparable to that of the
linear performance. Observe that the response of
the proposed voltage regulator is much faster than linear AVR
and linear AVR+PSS. For this case, 0.1% steady-state error is
observed in the final value.
From extensive simulation studies, the lines 2122, 2629,
and 2829 are found to be critical for system stability, and
few results corresponding to contingencies on these lines are
presented. Fig. 13 shows the terminal voltage responses ofGEN-9 for a fault of 80 ms duration on bus 29 followed
by tripping of 2928. In this case, the system with linear
is more oscillatory. The voltage dynamics are
considerably improved with the proposed controller, and the
steady-state error in the post fault voltage is 0.003 p.u.
Fig. 14 shows the responses of GEN-7 to GEN-10
under heavy loading conditions. All the loads are increased
by 15%, and generation at generators 5 to 10 is increased by
15%. A fault of 70 ms duration on bus 21 followed by
tripping of 2122 is created. In this case, the system is more
oscillatory with linear . It has been observed
that the voltage dynamics are considerably improved. The
percentage voltage regulation calculated as the percentage de-viation from prefault voltage to the postfault voltage w.r.t. the
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Fig. 13. of GEN-9 for a fault of 80 ms at bus 29 cleared by tripping line2928, nominal loading, 10 GEN SYS.
Fig. 14. ofGEN-7to GEN-10for a fault of70 msat bus 21clearedby tripping line 2122, heavy loading, 10 GEN SYS.
prefault voltage at all generators except at GEN-2 is given by
which is less than %. Under
nominal loading conditions, the terminal voltage regulation
is always less than %. One can still obtain better voltage
regulation by increasing the gain with little compromise
on the damping performance; even then, the performance of the
proposed AVR would be better than the linear .
Fig. 15 show the rotor angle responses of GEN-1 to
GEN-3 w.r.t. center of inertia with the proposed AVR for a
fault of 100 ms duration on bus 11 followed by tripping of
11-2 under light loading conditions (all loads are decreased by
20% and generation at GEN-3 to 10 are decreased by 20%).
The figure also contains the responses obtained with a linear
AVR+PSS. It can be observed that the damping performance
of the proposed controller is similar to the performance of the
linear .
C. The 14-Generator 59-Bus System
This is a simplified model of the southern and eastern Aus-
tralian network as shown in Fig. 16. It consists of five areas in
which areas 1 and 2 are closely coupled. The system data aretaken from [25]. The six operating conditions given in [25] are
Fig. 15. of GEN-1 to GEN-3 for a fault of 100 ms at bus 11 clearedby tripping line 11-2, light loading, 10 GEN SYS.
Fig. 16. IEEE 14-generator 59-bus test system.
studied extensively. A few representative results corresponding
to case 1 (heavy load) and case 4 (light load) are given here. For
this system, also IEEE model 1.1 [18] is used for synchronous
generators including transient saliency. The nonlinear AVR gain
is se-
lected for simulations.
Fig. 17 shows the slip speed responses of area-3 gen-
erators GEN-6 and GEN-7 w.r.t. center of inertia for a 0.1 p.u.
step change in at GEN-6. This simulation corresponds tocase-1 operating condition. The small-signal performance of the
proposed nonlinear AVR is better than the linear
controller which are designed using the complete system infor-
mation.
At case-1 operating condition, the line 2931 is a heavily
loaded line carrying 2760 MW. Fig. 18 shows the responses
for a fault at bus 31 cleared after 35 ms by tripping one of
the parallel lines between 31-29. The slip speed responses
of area-5 generators GEN-13 and GEN-14 w.r.t. the GEN-9 of
area-4 are shown. The responses are well damped with the pro-
posed controller within 5 s. The inter area mode ( Hz)
oscillations of small magnitude persist until 20 s in the case of
linear . With increase in fault clearing times be-yond 35 ms, both of the controllers eventually fail to stabilize
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Fig. 17. responses of GEN-6 and GEN-7 for a 0.1 p.u. step change inat GEN-6, case-1, 14 GEN SYS.
Fig. 18. responses of GEN-13 and GEN-14 w.r.t. GEN-9, fault at bus31 cleared after 35 ms by tripping the line 31-29, case-1, 14 GEN SYS.
the system. This simulation clearly shows the ability of the pro-
posed nonlinear AVR in damping the interarea mode of oscilla-
tions. For this condition, a maximum terminal voltage deviation
of 3.7% has been observed at bus 36.
Fig. 19showsthe responses for a fault at bus55 for case-4,
which is a light loading condition. The fault is cleared after 100
ms by tripping one of the parallel lines between the buses 55
and 57. Here the responses of GEN-12 to GEN-14 areshown. The responses are well damped in about 3 s with the
proposed FBLAVR, whereas the oscillations persist until 6 s
with the linear .
Extensive simulation studies on multimachine systems have
clearly established the superiority of the proposed AVR in
damping interarea modes when compared to the conventional
nonlinear AVR and linear .
V. CONCLUSION
A nonlinear voltage regulator has been proposed in this
paper for multimachine power systems using output feedback
linearization approach by redefining the rotor angle at eachgenerator with respect to the secondary voltage of the step-up
Fig. 19. responses of GEN-12 to GEN-14, fault at bus 55 clearedafter 100 ms by tripping the line 55-57, case-4, 14 GEN SYS.
transformer as reference instead of a common synchronouslyrotating reference frame. Though the controller is designed
using third-order model, it has been validated on higher order
models. The proposed controller has shown better performance
when compared to the conventional AVR proposed in [10] as
well as static . From the synchronizing and damping
torques analysis, it is observed that the proposed AVR always
produces a positive damping torque and allows considerable
variation in the tuning parameter so as to get effective trade off
between the voltage regulation and small signal performance
objectives. The implementation of this controller is very simple
as it requires only local measurements. The proposed approach
for the nonlinear AVR design can replace the conventional
structure, as tuning a single parameter is alwayseasier than tuning multiple parameters of a power system
stabilizer in the structure.
REFERENCES
[1] K. T. Law, D. J. Hill, and N. R. Godfrey, Robust controller structurefor coordinated PowerSystem voltage regulator and stabilizer design,
IEEE Trans. Control Syst. Technol., vol. 2, no. 3, pp. 220232, Sep.1994.
[2] C. Zhu, R. Zhou, and Y. Wang, A new nonlinear voltage controller forpower systems, Int. J. Elect. Power Energy Syst., vol. 19, pp. 1927,1997.
[3] R. Marino, An example of a nonlinear regulator, IEEE Trans. Autom.Control, vol. AC-29, no. 3, pp. 276279, Mar. 1984.
[4] Q. Lu and Y. Sun, Nonlinear stabilizing control of multimachine sys-tems, IEEE Trans. Power Syst., vol. 4, no. 1, pp. 236241, Feb. 1989.
[5] J. W. Chapman, M. D. Ilic, C. A. King, L. Eng, and H. Kaufman, Sta-bilizing a multimachine power system via decentralized feedback lin-earizing excitation control, IEEE Trans. Power Syst., vol. 8, no. 3, pp.830839, Aug. 1993.
[6] C. A. King, J. W. Chapman,and M. D. Ilic, Feedbacklinearizingexci-tation control on a full-scale power system model, IEEE Trans. PowerSyst., vol. 9, no. 2, pp. 11021109, May 1994.
[7] Y. Guo, D. J. Hill, and Y. Wang, Global transient stability and voltageregulation for Power systems, IEEE Trans. Power Syst., vol. 16, no. 4,pp. 678688, Nov. 2001.
[8] D. J. Hill, Y. Guo, M. Larsson, and Y. Wang, Global Control of Com-plex Power Systems, ser. Lecture Notes in Control andInformationSci-ences. Berlin/Heidelberg, Germany: Springer, 2004, vol. 293.
[9] B. K. Kumar, S. Singh, and S. Srivastava, A decentralized nonlinear
feedback controller with prescribed degree of stability for dampingpower system oscillations, Elect. Power Syst. Res., vol. 77, no. 34,pp. 204211, Mar. 2007.
-
7/30/2019 A Nonlinear Voltage Regulator With One Tunable Parameter for Multimachine Power Systems
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GURRALA AND SEN: NONLINEAR VOLTAGE REGULATOR WITH ONE TUNABLE PARAMETER 1195
[10] F. K. Mak, Design of nonlinear generator excitors using differentialgeometriccontrol theories, in Proc. 31st IEEE Conf. Decision Control,Tuscon, AZ, 1992, pp. 11491153.
[11] Y. Wang, D. J. Hill, R. H. Middleton, and L. Gao, Transient stabilityenhancement and voltage regulation of power systems, IEEE Trans.Power Syst., vol. 8, no. 2, pp. 620627, May 1993.
[12] T. Lahdhiri and A. T. Alouani, Nonlinear excitation control of a syn-chronous generator with implicit terminal voltage regulation, Elect.
Power Syst. Res., vol. 36, pp. 101112, 1996.[13] L. Gao, L. Chen, Y. Fan, and H. Ma, A nonlinear control design forpower systems, Automatica, vol. 28, pp. 975979, 1992.
[14] C. Zhu, R. Zhou, andY. Wang, A new decentralized nonlinear voltagecontroller for multi-machine power systems,IEEE Trans. Power Syst.,vol. 13, no. 1, pp. 211216, Feb. 1998.
[15] M. Nambu and Y. Ohsawa, Development of an advanced powersystem stabilizer using a strict linearization approach, IEEE. Trans.Power Syst., vol. 11, no. 2, pp. 813818, May 1996.
[16] M. Nambu, United states patent 5 604 420, Feb. 1997.[17] G. Gurrala and I. Sen, Power system stabilizers design for intercon-
nected power systems, IEEE Trans. Power Syst., accepted for publi-cation.
[18] IEEE Task Force, Current usage and suggested practices in powersystem stability simulations for synchronous machines, IEEE Trans.
Energy Convers., vol. EC-1, no. 1, pp. 7793, 1986.[19] K. R. Padiyar, Power System Dynamics Stability and Control. New
York: Wiley/Interline, 1996.[20] M. Arjona, R. Escarela-Perez, G. Espinosa-Perez, and J. Al-
varez-Ramirez, Validity testing of third-order nonlinear modelsfor synchronous generators, Elect. Power Syst. Res., vol. 79, pp.953958, 2009.
[21] Q. Lu, Y. Sun, and S. Mei, Nonlinear Control Systems and PowerSystem Dynamics. Norwell, MA: Kluwer, 2001.
[22] J. J. E. Slotine and W. Li, Applied Nonlinear Control. EnglewoodCliffs, NJ: Prentice-Hall, 1991.
[23] F. P. Demello and C. Concordia, Concepts of synchronous machinestability as affected by excitation control, IEEE Trans. Power App.Syst., vol. PAS-88, no. 4, pp. 316329, 1969.
[24] I. A. Erinmez, Generator excitation system performance requirementsarising from grid system considerations, in Proc. IEE Colloq. Excita-tion and Stability of Generators, Jan. 28, 1992, pp. 19.
[25] M. Gibbard and D. Vowels, Simplified 14-Generator Model of the SEAustralian Power System, The University of Adelaide, Tech. Rep. Re-
vision 2, 21, May 2008. [Online]. Available: http://www.eleceng.ade-laide.edu.au/Groups/PCON/PowerSystems.[26] P. S. Kundur, Power System Stability and Control. New York: Mc-
Graw-Hill, 1994.
Gurunath Gurrala (GS09) received the B.Tech degree in electrical and elec-tronics engineering from S.V.H. College of Engineering, Nagarjuna University,Guntar, India, in 2001 and the M.Tech degree in electrical power systems fromJ.N.T.U. College of Engineering, Anantapur, India, in 2003.He is currentlypur-suing the Ph.D. at the Indian Institute of Science, Bangalore, India.
He worked as an Assistant Professor in Anil Neerukonda Institute of Tech-nology and Sciences (ANITS), Visakhapatnam, India, from 2003 to 2005. Hisresearch interests include power system stability, grid integration of renewables,flexible AC transmission systems, artificial intelligence applications to power
systems, and nonlinear and adaptive control of power systems.
Indraneel Sen received the Ph.D. degree from IISc, Bangalore, India, in 1981.He is currently an Associate Professor in the Department of Electrical En-
gineering at the Indian Institute of Science, Bangalore. His research interestsinclude power system stability, adaptive control, and energy management sys-tems.