Designing a GA-Based Robust Controller For Load Frequency Control (LFC)
Koosha Soleimani
Electrical and Computer Engineering Department Isfahan University of Technology
Isfahan, Iran
Jalil Mazloum
Electrical Engineering Department
Shahid Sattari Aeronautical University of Science and Technology Tehran, Iran
Abstract—Power systems include multiple units linked together to produce constantly moving electric power flux. Stability is very important in power systems, so controller systems should be implemented in power plants to ensure power system stability either in normal conditions or after the events of unwanted inputs and disorder. Frequency and active power control are more important regarding stability. Our effort focused on designing and implementing robust PID and PI controllers based on genetic algorithm by changing the reference of generating units for faster damping of frequency oscillations.
Implementation results are examined on two-area power system in the ideally state and in the case of parameter deviation.
According to the results, the proposed controllers are resistant to deviation of power system parameters and governor uncertainties.
Keywords-load frequency control; LFC; drop characteristics I. INTRODUCTION
A power system includes multiple power plant units constantly connected to each other while power flux is moving among them. Power systems should be operated in such a way that they remain stable or return to stable condition as soon as possible. If the power system frequency -which is equal to the frequency of production units electrical power output- is deviated, this leads to a difference between the speed of stator and rotor rotating magnetic fields in the air gap of synchronous generators. If this difference is low or quickly eliminated, synchronous generator remains in stable condition but if this difference becomes greater, the rotating magnetic fields will not be stable in the coupled state. Any synchronous generator output power in the production unit will be injected into the power system. Following this, the load of generator will be eliminated. So, rotational speed of rotor shaft will suddenly increase, which is probable to cause damage like cracks in the rotor or even total destruction of the power system stability. So, frequency of different areas and the power flux between them can be considered as fundamental stability factors in a power system. When load increases, the turbine speed will be reduced. As long as governor coordinates input vapor with new load, speed reduction may lead the power system to instability.
Load Frequency Control (LFC) problem is a way to restore nominal values of frequency by adding PI or PID controllers as supplementary controller system.
II. LOAD FREQUENCY CONTROL
Since real power (P) with frequency (f) and reactive power (Q) with voltage amplitude (|V|) are associated, by considering the importance of keeping frequency and voltage amplitude at desirable level, control of real and reactive power is very important. As noted, for a power system to perform in favorable state it is necessary for the frequency to remain constant. In order to maintain frequency stability it is necessary to prevent deviation in the outflow of production units.
However, since power in a power system is supplied by a large number of generators, it is necessary the extra power requested to be divided appropriately among production units. Main speed control in each production unit is performed by governor. In other words, governor is the primary frequency controller. Higher control process is performed by other controllers added to the system as supplementary controllers.
This process is called load frequency control (LFC).
III. BACKGROUND AND SOLVING METHODS TAKEN FOR LFC PROBLEM
Several attempts to solve LFC problem have been carried out. The installation of photovoltaic (PV) in [1] and possible uncertainties caused by time delays in [2] can be mentioned. In [3] complex and nonlinear parameters of a decentralized LFC problem have been inspected. In [4] authors designed a differential controller based on fuzzy logic to solve the LFC problem in a restructured environment. In [5] the problem is solved using a method called SOA. In order to solve LFC problem PID controllers based on genetic algorithm are used.
In [6] a two-stage controller which prevents disorders from entering the power system is proposed. LFC solving methods are divided into following categories.
A. Classic Controller
In this method, error signal is based on the integrated control error. In the classical approach, to reach desirable gain margin (Km) and phase margin (φm) in Bode plot, Nyquist curve is used as reference locus. This controller is simple to implement but according to the results obtained in [7], power systems containing this controller have poor dynamic performance.
B.
con sys reg C.
un In par ada con D.
res sys con con sys on E.
hig sen im on im pro out
eng cha a pop can im fea val po pro obj tha val obt gen equ the chrpas ste po gen nu the
Adaptive Con Adaptive co ntrollers. Som stem [8], decli gard to hydro-t Robust Contr Significant e certainty para [12] desig rameterization aptive contro ntroller is pres Intelligent C Classical an sponse agent f
stems with lar ntrol methods ntrol method stem. In [19] i artificial neur Digital Cont In compariso gh accuracy a nsitive to noi mplement a com
power syste mportant result oblem and an
t control effor
GAs are one gineering prob ange variable
objective fun pulation (as in n be custom mplemented at atures than its lues that lead int. Let [x1,x2
oblem and F jective is to ac at finally F(x1, lue. At first, tained that ha nes. Using s uated to a con ese values in
romosome ca ss to the next eps are repeate
int or the ch nerations are mber of calcu ese steps for ea
ntroller ontrollers hav me examples a
ined adaptive thermal produ roller efforts to prot
meter changin gning a rob n is presented.
ollers, a new sented to solve Controller
d non-flexible for the problem
ge dimensions [15-17]. In [1 to raise the le intelligent hyb ral network an troller on to analog co and reliability,
ise and more mprehensive d ems is given
ts in the fiel indication that rts on power sy IV. GENET
e of the algor blems. The p values through nction. In th nitial generati mized. It is n
ttempts so th s ancestors. B d the objectiv
2,…,xn] be th F(x1,x2,…,xn) chieve xi value
,x2,…,xn) is lo for each xi a as N chromo specific criter ntinuous numer the objective an be judged.
generation an ed until the ob hanges in obj
meaningless.
ulations has to ach xi paramet
ve more flexi are adaptive m
controllers [9 uction units [10
ect controller ng in a power bust controlle
In [14] by co w design of e LFC problem
e controller c m of frequenc s. This led to t 18] authors pr evel of perform brid method us nd fuzzy logic i
ontrollers, digi , are more co e flexible. Th digital regulato in [20]. In ld of digital t determines th ystem stability
TIC ALGORITH
rithms used in purpose of a G
h generations his method, t ion) for each necessary to hat each gen Better property ve function to e parameters their object es to be determ ocated very cl a matrix with
somes and ea ria, each chr ric value. Then e function th . Most succes nd some of the
bjective functi ective functio It should be be done at eac ter must be car
ibility than c multipart cont 9] and adaptive
0].
system again system are [1 er based on ombining robu
a robust ada m.
cannot be a p cy control in p the use of intel
esented a - mance in cont sing a method is presented.
ital controllers ompact in size he first attem or for direct c
[21] authors modeling of he impact of c y.
HMS
n order to opt GA algorithm in order to opt the specific variable consi take a seri neration has y is the presen owards the op of an optimiz tive function.
mined in such ose to its min dimension N ach of them romosome wi n by putting ea he desirability
ssful chromos em are mutated ion reaches op on’s values th noted that a ch stage becau rried out in par
classic troller e with
nst the 1-13].
n Q- ust and
aptive
proper power lligent -based troller based
s have e, less mpt to control
s give f LFC carried
timize m is to timize initial idered ies of
better nce of ptimal
zation . The
a way nimum N×P is
has p ill be ach of y of a
somes d. The ptimal hough a huge
use all rallel.
freq elec acc [7].
obt
whe inp A.
of einto load etc.
elec
D
dam diag 2.
Fig.
B.
freq sho area confreq pow gov C.
load a d gov coe
In Figure 1 th quency with in ctric torque, celeration torq
.
Fig. 1.
If statements tained.
ere and PPe ut mechanical
Load Respons Load in a pow electrical equip o two catego
ds, etc.) and .). So, load va ctric power are
In (2), PL
r
is depend mping coeffic gram in Figur
2. The funct changes in
Isochronous G An isochron quency to its ould be noted a power system nflicts betwee
quency into it wer system s vernors known Governors by This governo d increase by d drop characteri
vernor. R is efficient of its
V. LFC
he relation betw nput and outpu
Tm is inpu que and H is t
Conversion fu
s with high
m e m
P P T
P are changem
l power respec se forFrequen wer system is pment. In gen ories, indepen frequency-de ariations equa e expressed as
e L
P P D
is independe dent on freque cient. Accord re 1 is amende
tion of speed an n load frequency
Governor nous governo
nominal value that this type ms. If it is use en production ts planned wi stability. To n as governors y Drop Charac or is equipped decreasing the istic of its ow drop charact inverse.
C MODELING
ween change o ut torques is s ut mechanica the constant o
unction of speed a
degrees are
m e
T T es of output el ctively.
ncy Deviation a combination neral, electrical ndent of frequ ependent loads al to change o s:
Dr
ent of frequen ency load cha ding to the ed as the block
nd power by con
or is restorin e by adjusting of governor ed in a multi-a n units to b ll emerge and
solve this p by drop chara cteristics
with a featur e speed. Each p wn. Figure 3 s teristic and T
of generator o shown. Te is o al torque, T of generator in
and torques
negligible, ( (1) lectrical powe
n of different l loads, are div uency loads s (electric mo of generator o
(2) ncy load cha anges and is above, the b k diagram in F
nsidering the imp
ng power sy g turbine valv can operate in area power sy bring the sy d could disrup problem, ame acteristics are u
re that respons production un shows this typ TG is equal
output output Ta is
nertia
1) is
er and
types vided (ohm otors, output
anges, s load block Figure
pact of
ystem ves. It n one ystem, ystem pt the ended
used.
ses to nit has pe of to a
dro
Fig cha
P the
po det un sys gen D.
pro dec concon sho
gov any loa un fac is psta sys lik tw
Fig. 3. B
The Divided op characterist
g. 4. Dividing aracteristics
If f is the P is change ofi
e above we ob
i i
P P P
1 2
2 1
P R
P R
1 2
P P
So, by chang wer per unit termined. Thi ique frequenc stem. So, unlik nerators final s Change in R According to oduction unit crease the os ntrolling the o ntrol is perfor own in Figure
Fig. 5
By changing vernor shifts u y given freque ad. Figure 6 s
it output powe ct, intervening
possible by ch abilization is d stem is unstab ke PI or PID. T o-machine sys
Block diagram of
produced pow tics of each go
power produce
change in freq f output powe tain (3)-(5).
i i
P f R
PL
ging ΔPL in lo t depending s type of gov cy f′ as a new ke isochronou
speed values a eference Load o Figure 4 the output electr scillation time output power rmed by chang
5.
5. Governor w
g the reference up or down. In ency can be ch shows the role er and drop ch g in the stabiliz hanging the ref done in the sho ble for less tim The overall blo
stem is given i
f governors by dro
wer in parallel overnor is show
d in parallel pro
quency, iPL er of productio
oad the contri on each dro ernor in LFC w operating p s governor in t are unequal.
d of Productio power system ric power are e damping o
of production ging the refere
with reference loa
load, drop ch n other words,
hanged by cha e of reference haracteristic o zation process ference load. T ortest time pos
me by the add ock diagram of
in Figure 7.
op charactristics
production un wn in Figure 4
oduction units b
is load change on unit i. Bas
(3)
(4) (5) ibution of pro op characteris problem lead point of the p this case, indiv nUnits m frequency an
related. A w f the frequen n units. This ty ence load of un
ad control
aracteristic cu the output pow anging the refe
load in contr of their govern s of a power s Therefore, des ssible and the p dition of contr f LFC problem
nits by 4.
by drop
es and sed on
duced stic is ds to a
power vidual
nd the way to ncy is ype of nits as
urve of wer at erence rolling nor. In ystem sirable power rollers m for a
Fig.
Fig
des the sys wit in freq the A.
unc erro
p imp in con dev osc obj the gen par algo in par osc them
6. The effec characteri
g. 7. Overall b
Based on gen signed in MA
power system tem’s respons thin first 40 se different stat quency contro uncertainties Controller De For the def certainties are
or as objective
0 TS
total
E
t where anf1 p12 is the poplemented in M Figure 8. D ntroller, it is viated. So, it cillations. To ective function
designing of netic algorithm rameters have orithm. The d the power sy rameter values cillations in z
m. According
t of changes in stic drop
block diagram of L
VI. SI
netic algorithm ATLAB. Desig
m. Simulation se to an increa econds after th tes. The defi ol can be divid
(ideal) and con esign in Ideal finition of er discarded. Equ e function of L
1 2
( f f
nd are freqf2
ower flux. T MATLAB by During system likely for po is possible to design PID n, (6) was use f the PID con m, are given in been achieve designed suppl
ystem at 80%
s. Figures 9-1 ones 1 and 2 g to Figures
setpoint of refer
LFC problem for
IMULATION
m PI and PID gned controlle n results of th ase of 0.02 pu he incident has inition of err ded in two mo
nsidering them State
rror signal th uation (6) give LFC problem.
12) |OP_1
p
quency oscilla The objective
using the blo m operation w
ower system o not achieve
controller’s p ed. Obtained o ntroller in ide n Table I. Th ed at the 222 lementary con
%, 100% and 11 correspond 2 and flux os 9-11, by de
rence load on go
a two-machine sy
D controllers rs were appli he enhanced p u in load in an s been investi ror signal in
odes, regardle m.
he power sy es the ideally I
1.0 (6)
ations of areas function can ock diagram sh with the desi
parameters t e optimal dam parameters fo optimum value eal state, by u
e obtained op th step of the ntroller was ap 120% of nom d to the frequ scillations bet esigning addit
overnor
ystem
were ed to power n area gated load ess of
ystem ITAE
s and n be hown igned to be mping
r the es for
using ptimal e GA pplied minal uency tween tional
con obt the and
Fig
ntrollers, opti tained. When eir nominal va
d the power sy
Fig. 8. B
g. 9. Applying (a) Δf1, (
imal damping the power sy alues, the osci ystem will bec
Block diagram to b
g ideally desig (b) Δf2 and (c) Flu
for 100% an ystem parame
illation dampi come unstable.
build ideal LFC o
gned controllers ux oscillations Δp
nd 120% valu eters are at 80 ing is inappro .
objective function
in nominal p12
(a
(b
(c
ues is 0% of opriate
values:
Fig.
Fig.
a)
b)
c)
10. Applying (a) Δf1, (b
11. Applying (a) Δf1, (b
ideally designed b) Δf2 and (c) Δp1
ideally designed ) Δf2 and (c) Δp12
d controllers in 0
12
d controllers in 1
2
0.8 of nominal v
1.2 of nominal v (a)
(b)
(c)
(a)
(b)
(c) values:
values:
T
B.
no ter 20
diause val of res con alg con of Ac wit osc PID dam con it.
TA
T
TABLE I. O
Controller D To achieve minal mode, i rms of maxim
% deviated. In
0
0
0
S
S
S
T total
T
T
E t
which can be agram shown i ed to design th lues obtained
uncertainties spectively. Op
ntroller has be gorithm respec
ntrollers in cas system param ccording to th
th regard to cillations and D controller mping. Since ntrol process
ABLE II. OP C
Are Are
TABLE III. O C
Ar Ar
OPTIMAL PID CON S PID p Area 1
Area 2
Design by Cons a robust co it is required to mum possible n this case, the
1 2
1
1
( ( (
S
S
f f
t f f
t f f
e implemented
in Figure 12. O he PI and PID
for the design and by using G ptimal values een achieved a
ctively. The r ses of 100%, 8 meters are give e results, if th uncertainties, power flux b acts more fa the difference of PID contro
PTIMAL VALUES O CASE OF CONSIDE PID pa ea 1
P I D ea 2
P I D
OPTIMAL VALUES O CASE OF CONSIDE
PI pa rea 1
rea 2
NTROLLER PARAME STATE
arameters P 26.0
I 85.3 D 19.
P -29.
I 0.0 D -0.9
sidering Unce ontroller syste o investigate t deviation -wh e objective fun
12 _
2 12
2 12
) | ) | ) |
OP
OP
OP
p
f p
f p
d in MATLAB Objective func D controller pa n of PID and P GA are given
for the desi at 236th and 17
results of app 80% and 120%
en in Figures he controller d optimal dam between areas favorable than e is insignifica oller is done b
OF PID CONTROLLE ERING UNCERTAIN
arameters
P 9
72
D 19
P -2
D -0
OF PI CONTROLLE ERING UNCERTAIN arameters
P -13 I 1 P -30 I
ETERVALUESIN ID
051 352 .71
356 007
986
ertainties em in additio the power syst
hen paramete nction is:
0.8
_1.0
_1.2 P
P
(7)
B by using the ction in (7) has arameters. Opt PI controllers in
in Tables II a gn of PID an 79th step of th plying the des
% of nominal v 13-15 respect design is cond mping in freq
s will be ach n PI in oscil ant, the main r by the existing
ER PARAMETERS I NTIES
9.455 2.852 9.363 9.667
0 0.414
ER PARAMETERS IN NTIES
3.586 1.69 0.463
0
DEAL
on to tem in
rs are
block s been timum n case and III nd PI he GA signed values tively.
ducted quency hieved.
llation role in g PI in
IN THE
N THE
Fig.
Fig.
12. Block diag
13. Applying considerin
gram of LFC obje
designed contro ng uncertainties: (
ective function co
ollers in nominal (a) Δf1, (b) Δf2 an
onsidering uncerta
values in the c nd (c) Δp12
(b) (a)
(c) ainties
case of
Fig
Fig
C.
and 20
g. 14. Applying of consid
g. 15. Applying of consid
Deviation in The results d PID controll
% are given in
g designed contro dering uncertaintie
g designed contro dering uncertaintie
Operating Po of the implem lers when gov n Figure 16.
ollers in 0.8 of no es
ollers in 1.2 of no es
oint of Govern mentation of i vernor paramet
ominal values in t
ominal values in t
nor
ideally design ters are deviat
(b) (a)
(c) (b) (a)
(c)
the case
the case
ned PI ted by
Fig.
gov som sys
sys imp nor entr con osc sys ord of par the achpow sup con resu in i are
16. Implemen parameter
According to vernor operatio mewhat unfav
tem instability
Frequency st tems. Contro plemented to rmal condition ries and dis ntrollers like cillation dampi
tem is unstab der to obtain th
uncertainties rameters the de
face of pow hieve a robust wer system pplementary c ntroller in com
ults with bette ideal controlle
not a threat to
ntation of ideally rs deviation
o the results on point, area vorable but th
y.
VII. CO
tability is one ller systems ensure powe ns but also af orders. There
PI or PID w ing in the shor ble less time.
he controller p in the design esigned contro wer system pa controller sys
parameter controllers. O mparison with er oscillation d er design, dev o stability and j
designed controll
in the case a frequency os his event did
ONCLUSION
e of major ne in production er system stab fter the occurr efore, it is
with optimize rtest time poss
In this paper, parameters. H ning of PI a oller system w arameter devia
stem, it is nec deviation a On the other h the PI cont damping. Resu viations of go just cause low
lers with 20% go
of deviation scillations eme not cause p
ecessities in p n units shoul bility not only
rence of unw necessary to ed parameter sible, so that p
GAs was us However, regar and PID contr will be vulnerab ations. In ord cessary to con among desig r hand, the troller gives f ults show that overnor param wer damping.
(b) (a)
(c)
overnor
ns in erged power
power ld be
y for anted
add s for power
ed in rdless
roller ble in der to nsider
gning PID faster even meters
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