electric governor.pdf,MODELING,OFELECTRICAL

THIS IS ELECTRICGOVERNOR

1. IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006 187
SomeNewFindingsonAutomaticGeneration
ControlofanInterconnectedHydrothermal
SystemWithConventionalControllers
Janardan Nanda,Senior Member, IEEE, Ashish Mangla, and Sanjay Suri
Abstract—This paper deals with automatic generation control
of an interconnected hydrothermal system in continuous-discrete
mode using conventional integral and proportional-integral con-
trollers. Appropriate generation rate constraint has been consid-
ered for the thermal and hydro plants. The hydro area is con-
sidered with either mechanical or electric governor and thermal
area is considered with either single or double reheat turbine. Per-
formances of mechanical governor, electric governor, and single
stage reheat turbine and two stage reheat turbine on dynamic re-
sponses have been explored. Further, selection of suitable value of
speed regulation parameter R and sampling period has been in-
vestigated. System performance is examined considering 1% step
load perturbation in either thermal or hydro area.
Index Terms—Automatic generation control, conventional con-
trollers, reheat turbine, sampling time period.
NOMENCLATURE
f Nominal System Frequency.
I Subscript referred to area i (1, 2).
∗ Superscript denotes optimum value.
P
ri Area Rated Power.
H
i inertia constant.
∆P
Di Incremental load change in area i.
∆P
gi Incremental generation change in area i.
D
i ∆PDi/∆fi.
T
12 Synchronizing coefficient.
R
i Governor speed regulation parameter.
T
g Steam governor time constant, second.
T
G Mechanical governor response time, second.
T
R Mechanical governor reset time constant, sec-
ond.
σ Mechanical governor permanent droop, per
unit.(R =σf).
δ Mechanical Governor Temporary Droop, per
unit.
K
r Steam turbine reheat constant.
T
r Steam turbine reheat time constant.
T
t Steam turbine time constant.
B
i Frequency bias constant.
T
pi 2Hi/f
∗
Di.
K
pi 1/Di.
K
I Integral gain.
Manuscript received June 9, 2004. Paper no. TEC-00170-2004.
The authors are with Department of Electrical Engineering, Indian Insti-
tute of Technology, Delhi, India (e-mail: janardan
[email protected]; mangla
[email protected]; [email protected]).
Digital Object Identifier 10.1109/TEC.2005.853757
KP Proportional gain.
K
d,Kp,KiElectric governor derivative, proportional, and
integral gains, respectively.
β
i (Di+1/R i); area frequency response charac-
teristics.
T
w Water starting time.
ACE
i Area control error of area i.
a
12 −Pr1/Pr2.
J Cost index.
T Sampling time period.
I. I
NTRODUCTION
G
ENERATION in large interconnected power system com-
prises of thermal, hydro, nuclear, and gas power gener-
ation. Nuclear units owing to their high efficiency are usually
kept at base load close to their maximum output with no par-
ticipation in system automatic generation control (AGC). Gas
power generation is ideal for meeting varying load demand.
However, such plants do not play very significant role in AGC
of a large power system, since these plants form a very small
percentage of total system generation. Gas plants are used to
meet peak demands only. Thus the natural choice for AGC falls
on either thermal or hydro units. The characteristics of hydro
turbine differ from steam turbine in many respects [1]–[3].
1) The transfer function of the hydro turbine represents a non-
minimum phase system.
2) In a hydro-turbine, relatively large inertia of water, used
as the source of energy, causes a greater time lag in the
response of the change in prime mover torque to a change
in gate position. Moreover, there is an initial tendency for
the torque to change in a direction opposite to that finally
produced. In addition, the response may contain oscillating
components caused by compressibility of water or surge
tank.
3) The hydro governor is provided with a relatively large tem-
porary droop and long washout time.
4) The typical value of permissible rate of generation for hydro
plant is relatively much higher (a typical value of generation
rate constraints (GRC) being 270%/min for raising genera-
tion and 360%/min for lowering generation), as compared
to that for reheat type thermal units having GRC of the order
of 3%/min [4].
A literature survey shows that most of the earlier works in the
area of AGC pertain to interconnected thermal systems and
relatively lesser attention has been devoted to the AGC of
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2. 188 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006
interconnected hydrothermal system. Concordia and Kirch-
mayer [1] and Kirchmayer [2] have studied the AGC of a
hydrothermal system considering nonreheat turbine and me-
chanical governor in hydro system, neglecting generation rate
constraints. Kothariet al.[5] are possibly the first to consider
GRC to investigate the AGC problem of a hydrothermal sys-
tem with conventional integral controllers. They have discussed
about finding the optimum integral controller settings and their
sensitivity to GRC, speed regulation parameter, water starting
time constant, base load condition etc. Kothariet al.[6] have also
studied the AGC problem of hydrothermal system, considering
GRC where their main contribution is to explore the best value
of speed regulation parameter (R). All the above research works
discussed consider the system & controllers in the continuous
mode strategy. Nanda, Kothari, and Satsangi [7] have discussed
the AGC problem in both continuous and discrete mode with
classical integral controllers and compared the responses. Their
main finding shows that the optimum integral controller gains
achieved in the continuous mode are totally unacceptable in
the discrete mode for sampling time period used in practice.
In the interconnected hydrothermal system used by them, the
thermal system uses reheat turbine and the hydro system uses a
mechanical governor.
Many of the existing hydro power stations are equipped
with mechanical governors. Modern hydro units are normally
equipped with electric governors in which the electronic appa-
ratus is used to perform low power functions associated with
speed sensing and droop compensation [12]. A literature survey
shows that no comparison has been made for the performances
of mechanical and electric governor to critically appreciate their
operation. It would be of practical significance to explore the
system performance if a mechanical governor is replaced by an
electric governor.
Kothariet al.[8] have investigated the effect of variation in
sampling period on the performance of AGC of an intercon-
nected two area thermal system considering GRC and reheat
turbines. Their investigations reveal that a relatively large sam-
pling time period to a tune of 20 s is permissible to provide
more or less best system performance instead of small sampling
period of 2 to 4 s used in practice. Such finding about sam-
pling period in a thermal-thermal system may not hold good in
a hydrothermal system which needs further investigations.
Hariet al.[14] investigate proper selection R for intercon-
nected reheat thermal-thermal system in continuous-discrete
mode considering appropriate GRC. Their findings reveal that
there is no necessity for going for a low value of R, since a large
value R with corresponding optimum integral controller gain
settings can be preferred to provide better dynamic response of
AGC. They advocate very strongly that for the governor design
consideration, it is better to adopt as large value of R as permis-
sible without jeopardizing the dynamic responses. Higher value
of R makes the realization of the governor simpler and reduces
its cost [15] such finding about R in a thermal-thermal sys-
tem may not hold good in a hydrothermal system which needs
further investigations.
In reheat turbines, the reheating may be in a single stage or in
multistage [11]. A transfer function model for single stage reheat
turbine has been given by Kundur [11]. What would be the model
for a two stage reheat turbine? How would the performance of
a two stage reheat turbine compare to performance of a single
stage reheat turbine? Literature survey does not provide any
answer to these questions.
In a realistic situation, the system works in the continu-
ous mode whereas the controllers work in the discrete mode.
Therefore, it is of practical significance to consider the realis-
tic continuous-discrete model for the system for any further
investigations to avail more meaningful results. To the best
of the authors’ knowledge, no work has been reported in the
literature for AGC of a hydrothermal system in the continuous-
discrete mode. In view of the above discussion, the following
are the main objectives of the present work.
i) To compare the performances of an optimum integral and
proportional-integral (PI) controllers for AGC of a hy-
drothermal system in continuous-discrete mode consider-
ing GRC, electric governor in the hydro area and reheat
turbine in the thermal area.
ii) To study the performance of mechanical governor and
selection of suitable value of temporary droop(δ)for a
given permanent droop(σ), considering perturbation in
either area.
iii) To compare the performances of mechanical and electric
governors.
iv) To develop a model for two stage reheat turbine and hence
to compare its responses with that of a single stage re-
heat turbine considering GRC, electric governor in hydro
area and optimum integral controllers in both hydro and
thermal areas.
v) To examine maximum permissible value of speed regu-
lation parameter R without practically affecting dynamic
responses.
vi) To examine the effect of change in sampling time period
on system performance and hence to decide appropriate
sampling period.
All investigations have been carried out for hydrothermal system
in continuous-discrete mode.
II. S
YSTEMINVESTIGATED
The AGC system investigated consists of two generating ar-
eas of equal size, area 1 comprising a reheat thermal system and
area 2 comprising a hydro system. GRC of the order of 3%/min
for thermal area and 270% per minute for raising and 360%
per minute for lowering generation in hydro area has been con-
sidered. Fig. 1 shows the AGC model with single stage reheat
turbine in thermal area and electric governor in hydro area. A
bias setting ofB
i=βiis considered in both hydro and thermal
areas. Matlab version 6.1 has been used, to obtain dynamic re-
sponses for∆f
1,∆f2,∆Ptiefor 1% step load perturbation in
either area. The system data has been taken from [9] and [10]
and given in Appendix. The optimum values of derivative, pro-
portional and integral gains for the electric governor have been
taken from the work of Nandaet al.[5] and given in the Ap-
pendix. For the system analysis, 1% step load perturbation has
been considered either in thermal or hydro area. Controllers in
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3. NANDAet al.: INTERCONNECTED HYDROTHERMAL SYSTEM WITH CONVENTIONAL CONTROLLERS 189
Fig. 1. Transfer function model of an interconnected two-area hydrothermal
system.
Fig. 2. Tandem-compound double reheat turbine. (a) Schematic diagram. (b) Approximate linear transfer function.
both the areas have been optimized using integral square error
(ISE) criterion. For ISE technique, the objective function used is
J=
2000
∆
n=0
δ
∆P
2
tie
+∆f
2
1
+∆f
2
2
β
∆T
where∆T =small time interval during sample (0.1 sec),
n=iteration count,∆P
tie=incremental change in tie power,
∆f =incremental change in frequency. The sampling time
period used for all investigations is 2 s otherwise stated.
III. T
RANSFERFUNCTIONMODEL FORTWO-STAG E
REHEATTURBINE
The transfer function model for a two stage reheat turbine
is developed and discussed here. Fig. 2(a) shows the schematic
diagram of a two-stage tandem-compound reheat turbine [11].
This two stage reheat turbine has four cylinders very high pres-
Fig. 3. Comparison of integral and PI controller responses with 1% step load
perturbation in thermal area. (a)∆f
1= f(t).(b)∆P tie= f(t).(c)∆P g1=
f(t).
sure VHP, high pressure HP, intermediate pressure IP and low
pressure LP having the p.u. Mw ratings ofα, β, γ, andµ, respec-
tively. It may be noted thatα+β+γ+µ=1.0. For a change
in control valve position∆P
v, the VHP turbine shall contribute
the power component
∆P
T(VHP) =α·∆X E·
1
1+sT t
Mw
whereT
trepresents time delay due to steam chest and inlet
piping. The HP turbine shall contribute the power component
as
∆P
T(HP) =β·∆X E·
1
1+sT t
·
1
1+sT r1
Mw
whereT
rjrepresents the time delay due to reheaterj(j=1,2).
The time constant due to crossover,T
cis very small as compared
to other time constants. So, total power contributed by IP and
LP sections will be
∆P
T(IP + LP) = (1−α−β)·∆X E
·
1
1+sT t
·
1
1+sT r1
·
1
1+sT r2
Mw.
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4. 190 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006
Fig. 4. Comparison of integral and PI controller responses with 1% step load
perturbation in hydro area. (a)∆f
2= f(t).(b)∆P tie= f(t).(c)∆P g2=
f(t).
Fig. 5. Transfer function model of mechanical governor.
The total power is obtained by adding the above three compo-
nents. Fig. 2(b) shows the approximate linear transfer function
model of the tandem compound two stage reheat steam turbine.
The overall turbine transfer function for a double reheat tur-
bine is given by
G
T(s)=
∆P
T(VHP) + ∆P T(HP) + ∆P T(IP + LP)
∆XE(s)
i.e.,
G
T(s)=
1
1+sT
α
α+
β
1+sT r1
+
1−α−β
(1 +sT r1)(1 +T r2)
γ
.
More simply
G
T(s)=
1+s{K
r1(Tr1+Tr2)+K r2Tr2}+s
2
Tr1Tr2
(1 +sT t)(1 +sT r1)(1 +sT r2)
Fig. 6. Comparison of mechanical and electrical governor performances with
1% step load perturbation in thermal area. (a)∆f
1= f(t).(b)∆f 2= f(t).(c)
∆P
tie= f(t).
whereK r1=αandK r2=β.αandβare reheat coefficients
i.e., fraction of the power generated for very high pressure and
high pressure cylinders.
The transfer function models for electric governor and hydro
turbine penstock are given in [3] and [12].
IV. R
ESULT ANDANALYSIS
The optimum value of integral controller gains for the ther-
mal area 1 and the hydro area 2 are found to beK
∗
I1
=0.048
andK
∗
I2
=0.012, respectively, using ISE Criterion. Using the
ISE technique for PI controller, the optimum value of gains for
thermal area are found to beK
∗
P1
=0.2040,K
∗
I1
=0.0484and
for the hydro area, the optimum value of the gains are found to
beK
∗
P2
=0.001andK
∗
I2
=0.0108, respectively. Fig. 3(a)–(c)
shows the responses for∆f
1,∆P tie, and∆P g1for 1% step
load perturbation in thermal area and Fig. 4(a)–(c) shows the
responses for∆f
2,∆P tieand∆P g2for the same perturbation
in the hydro area. Examining the responses it is seen that
they take more settling time when same perturbation occurs
in the hydro area than in the thermal area. Also, irrespective
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5. NANDAet al.: INTERCONNECTED HYDROTHERMAL SYSTEM WITH CONVENTIONAL CONTROLLERS 191
Fig. 7. Comparison of mechanical and electrical governor performances with
1% step load perturbation in hydro area. (a)∆f
1= f(t).(b)∆f 2= f(t).(c)
∆P
tie= f(t).
of controller, whether conventional integral controller or PI
controller, maximum peak deviation and settling time are
practically same. Thus, no distinct advantage is seen for a PI
controller over an integral controller. All further studies are
carried out with an integral controller.
Fig. 5 shows the transfer function model of mechanical gov-
ernor [13]. The governor speed regulation parameter (R) for
both the areas is taken as 2.4 Hz/p.u. Mw. The temporary droop
(δ)in mechanical governor plays a very important role in the
stability of the system.
An improper selection ofδwill make the system unstable. The
approach for finding out the suitable value ofδfrom stability
consideration is as follows.
i) Consider both the areas uncontrolled, it is seen that any
value ofδless than 0.7 and greater than 1.1 makes the
system unstable. Whenδis increased beyond 0.7, the
system become stable and more or less the best response
is obtained atδ=0.95.
ii) In the presence of optimum integral controller in both ar-
eas, thisδis varied around 0.95. Responses reveal that
δ=0.95again provides more or less the best response.
Fig. 8. Comparison of single and double reheat turbine performances with 1%
step load perturbation in thermal area. (a)∆f
1=f(t).(b)∆f 2=f(t).
Fig. 9. Comparison of single and double reheat turbine performances with 1%
step load perturbation in hydro area. (a)∆f
1= f(t).(b)∆f 2= f(t).
From the investigations, it is construed that the optimum
value ofδobtained in uncontrolled mode (absence of sup-
plementary controllers) works well in the controller mode
(presence of supplementary controllers).
The dynamic responses obtained with mechanical governor
usingδ=0.95is compared with that obtained with electric
governors, considering the optimum integral controller for the
areas. Fig. 6(a)–(c) shows the responses for∆f
1,∆f2, and
∆P
tie, respectively, for 1% step load perturbation in thermal
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6. 192 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006
Fig. 10. Comparison of R Parameters 1% step load perturbation in thermal
area. (a)∆f
1= f(t). (b)–(c)∆P tie= f(t).
Fig. 11. Comparison of R Parameters 1% step load perturbation in hydro area.
(a)∆f
1= f(t). (b)–(c)∆P tie= f(t).
Fig. 12. Comparison of sampling time periods with 1% step load perturbation
in thermal area. (a)∆f
1= f(t).(b)∆f 2= f(t).
Fig. 13. Comparison of sampling time periods with 1% step load perturbation
in hydro area. (a)∆f
1= f(t).(b)∆f 2= f(t).
area and Fig. 7(a)–(c) shows the same responses when same
perturbation occurs in the hydro area.
It is clearly seen that electric governor provides much better
response compared to a mechanical governor, although both the
governors are taking same settling time. Mechanical governor
gives very fast oscillations which is the absent with electric
governor.
In Section III-A, the transfer function for two-stage reheat
turbine is discussed, which is now used in the block diagram
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7. NANDAet al.: INTERCONNECTED HYDROTHERMAL SYSTEM WITH CONVENTIONAL CONTROLLERS 193
of Fig. 1 for the thermal system to obtain responses. Fig. 8(a)
and (b) shows dynamic responses∆f
1,∆f2with 1% step load
perturbation in thermal area and Fig. 9(a) and (b) shows dynamic
responses∆f
1,∆f2with 1% step load perturbation in hydro
area. Comparing these responses, they are seen to be more or
less the same from the view point of maximum peak deviation
and settling time. Thus, in large modern turbines, where a two
stage reheat is used, for all practical purposes, it can be modeled
as a single-stage reheat.
Fig. 10(a) and (b) shows the dynamic responses for
∆f
1,∆Ptiefor 1% step load perturbation in thermal area, with R
varying from 4% to 8%, Fig. 10(c) shows the dynamic response
for∆P
tiefor R=10%. Fig. 11(a) and (b) shows the dynamic re-
sponses for∆f
2and∆P tiefor 1% step load perturbation in hy-
dro area with R varying from 4% to 8% while Fig. 11(c) shows
the dynamic response for∆P
tieforR=10%. Examinining
these responses, it is clearly seen thatR=8% provides better
dynamic responses in terms of peak deviations and settling time
thanR=4% used in practice. The value greater thanR=8%
provides fast oscillations in the system dynamic responses, and
hence undesirable. Also, a value greater thanR=12% makes
the system unstable. Hence, it is construed that for realistic con-
tinuous discrete-mode, one can go for as a large value ofRas
is permissible in continuous or discrete mode with conventional
integral controllers.
Fig. 12(a) and (b) shows the responses for 1% step load per-
turbation in thermal area for sampling period(T)in the range of
2 s to 25 s. It is interesting to note that higher values of sampling
period(T)provide better responses thanT=2s used in prac-
tice. A sampling period(T)of the order of 10 s seems to work
satisfactorily. Sampling period greater than 20 s increases the
settling time. It may be noted that the amplitudes of oscillations
forT=10s are smaller as compared to those forT=2s.
Fig. 13(a) and (b) shows the dynamic responses for different
sampling period with 1% step load perturbation in hydro area.
It is again seen thatT=2s does not provide the best dynamic
responses. The sampling period ofT=10second provides best
frequency responses. Thus considering perturbation in either
thermal or hydro area, the more or less best sampling period is
found to be 10 s. A higher sampling period reduces effort on the
sampler and improves its longevity.
V. C
ONCLUSION
The following are the significant contributions.
i) In continuous-discrete mode strategy for a hydrothermal
system, considering electric governor in hydro area, reheat
turbine in thermal area and appropriate GRC in both ar-
eas, the dynamic responses with integral and proportional-
integral controller are more or less the same from the view
point of peak deviation and settling time.
ii) The optimum value of temporary droop for a mechanical
governor in hydro area evaluated in the uncontrolled mode
works well in the controlled mode.
iii) The performance of electric governor is found to be quite
superior to a mechanical governor, although both take
more or less same settling time. Mechanical governor pro-
vides very fast oscillations which are absent in electric
governor.
iv) The dynamic responses for double reheat & single reheat
turbines are close to each other. Thus for all practical
purposes, a double reheat turbine can be modeled as a
single reheat one.
v) Investigations reveal that in a hydrothermal system, irre-
spective of small perturbation in either area, it is permis-
sible to chose a much higher sampling period than used in
practice that provides better system performances.
vi) Investigations reveal that in a hydrothermal system, it is
permissible to choose a much higher sampling period than
used in practice.
A
PPENDIX
Nominal parameter pf hydrothermal system investigated:
f=60Hz R
1=R2=2.4Hz/per unit MW
T
g=0.08 s P tie,max= 200 MW
T
r=10.0s K r=0.5
H
1=H2=5s Pr1=Pr2= 2000 MW
T
t=0.3s K p=1.0
K
d=4.0K i=5.0
T
w=1.0s D 1=D2=8.33∗10
−3
p.u.MW/Hz
a
12=−1T 12=0.086 p.u.Mw/rad
T
R=5s K p1=Kp2= 120 Hz/p.u.Mw
T
p1=Tp2=20s T 1=48.75 s,T 2=0.513 s.
R
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Janardan Nanda(SM’90) has been a Professor with the Department of Electri-
cal Engineering, Indian Institute of Technology (IIT), Delhi, India, since 1973.
He was Head of Electrical Engineering Department and Dean (UGS) at IIT
Delhi from 1984 to 1990.
Dr. Nanda is a Fellow of Indian National Academy of Engineering and a Fel-
low of Indian National Science Academy. His field of interest comprises power
system analysis, dynamics, control, optimization, and application of computa-
tional intelligence to power system problems.
Ashish Manglawas born on May 4, 1981. He graduated from Kurukshetra
University, India, in 2002. Currently, he is graduate student in the Electrical
Engineering Department, Indian Institute of Technology (IIT), Delhi, India.
Sanjay Suriwas born on November 17, 1967. He received the B.Sc. and B.E.
degrees in 1988 and 1995, respectively. Currently, he is pursuing the M.S. degree
at the Indian Institute of Technology (IIT), Delhi, India.
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