IRJET- An Investigative Study of Generator-Load Tie-Line Model of Speed Governing System and Overview of Design of Conventional Controllers for LFC of Electrical Power Systems

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 06 | June 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1470
An Investigative Study of Generator-Load Tie-Line Model of Speed
Governing System and Overview of Design of Conventional Controllers
for LFC of Electrical Power Systems
B. Prakash Ayyappan1, Dr. R. Kanimozhi2
1Ph.D Scholar (Electrical), Anna University
2Assistant Professor (EEE), Anna University (BIT Campus)
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - A real power (active power) control is an
important control strategy to be performed during normal
operation of the power system to meet the power generation
with the continuously changing load, in order tomaintainthe
system frequency to within  1%. The frequencychanges due
to change in system load, which leads to the change in the
speed of turbine generator systems of all the units. The main
purpose of operating Automatic Generation Control (AGC) or
Load Frequency Control (LFC) is to keep uniformly the
frequency changes during the load changes. In this paper,
Automatic Load Frequency controloftwoareapowersystems
using Proportional, Integral, Proportional Integral,
Proportional Derivative and Proportional integral and
derivative tuning technique designing method are analyzing
along with generator load and tie line model. Two main
objectives of LFC are to maintain the real frequency and the
desired power output in the interconnected power system
and, to control the change in tie line power between control
areas. The advantages PID controller has the ability to
provide high adaption for changing conditionsandtheability
for making quick decisions. The PID controller is used to
improve the dynamic response as well as to reduce or
eliminate the steady-state error.
Key Words: Speed Governing System, Tie-line, Area Control
Error (ACE), Proportional (P), Proportional Integral (PI) and
Proportional Integral Derivative(PID),LoadFrequencyControl
(LFC) or Automatic Generation Control (AGC).
1. INTRODUCTION
The need for satisfactory operation of power stations
running in parallel and the relation between system
frequency and the speed of the motors has led to the
requirement of close regulation of powersystemfrequency.
Since the control of system frequency and load depends
upon the governors of the prime movers are understand by
the model of the governor. There are two types of control,
Primary Control and Secondary Control. The system speed
change from synchronous speed initiates the primary
control action resulting in all the participating turbine-
generator units taking up the change in load and stabilizes
with the system frequency. The secondary control action
needs to adjust the load reference set points of selected
turbine-generator units and to maintain the nominal value
of frequency. The objective of frequencycontrol isthespeed
control of the machines in the generating stations. The
system frequency is depends upon the speed at which the
entire generators. The prime movers are steam or hydro
turbines are coupledwithspeedgovernorswhicharepurely
mechanical sensitive device, which is to adjust the gate or
control valve opening or closing for constant speed of the
system. Generator synchronous speed, N=
p
f120 . The
system frequency can be varied by changing the speed of
the turbine. The frequency is closely related to real power
balance of overall network. In the normal operating
conditions, generators run synchronously and generate
power and then meet all the loads and real power losses.
Power system operation at al lower frequency than the
specified maximum allowable change in frequency is ± 0.5
Hz which affects the quality of power supply. The load
frequency control on a power system becomes one of
changing the control valve or gate openings of the prime
movers as a function of load changes in order to maintain
the system frequency constant. All the generators speed up
and slow down together maintaining their relative power
angles, which maintains the system frequency, such system
is called as a control area. The system generator unit’s
performances are dependent on the performance of all the
auxiliary drives associated with fuel, feed water and
combustion air supply system. The inter connected system,
two or more areas in addition to control of frequency, the
generation within each area has to be controlled and to
maintain the scheduled power interchange in the power
system.
II. MODELLINGOFSPEEDGOVERNINGMECHANISM
2.1 Model of Speed Governor and Turbine
The real power in a system is being controlled by
controlling the driving torques of the individual turbines of
the system. The speed governor is the main primarytool for
the load frequency control, whether the machine is used
alone to feed a smaller system or it is a part of the most
elaborate arrangement. By controlling the position of the
control valve or gate, we can exert control over the flow of
high pressure steam (or water) through the turbine. The
speed governor is a mechanical speed sensitive device, it
sense speed changes and moves through linkage point B.
The speed changer provides facilitytosettheturbineoutput

at desired level. A small downward movementofthelinkage
point A corresponds to an increase ΔPc in the reference
power setting. The hydraulic amplifier consists of low level
pilot value movement is converted into high power piston
movement. The input to this amplifier is the position XD of
the pilot valve. The output is the position XE of the main
piston.
Figure 1. Functional diagram of Speed Governing System
The steam is operating under steady state and is delivering
power PG from the generator at nominal frequency. Let us
assume that raise command ΔPc to the speed changer the
point A be moved downwards by a small amount ΔXA ,
which causes the turbine power output to change.
ΔXA = Kc ΔPc ------ (2.1)
Let us assume, that positive direction for downward
movement and negative direction for upward movement.
ΔXA = contributes 





1
2
I
I
ΔXA = K1KcΔPc; An increase in
frequency Δf causes the fly balls to move outwards, so that
point B moves downwards by a proportional amount K2 Δf.
Therefore, ΔXA = K1KcΔPc + K2 Δf ------ (2.2)
Then the movement of ΔXD is the amount by which the pilot
valve opens, thereby moving the main piston and opening
the steam valve by ΔXE .
ΔXD =








43
4
II
I ΔXC +








43
3
II
I ΔXE ------ (2.3)
ΔXD = K3ΔXC + K4 ΔXE
As the value of oil admitted to the cylinder is thus,
proportional to the line integral of ΔXD .
ΔXE = K5 dt)X(
1
0
D  ------ (2.4)
By taking Laplace transform,
ΔXC (s) = K1KcΔPc (s) + K2 ΔF (s) ------ (2.5)
ΔXD (s) = K3ΔXc (s) + K4 ΔXE (s) ------ (2.6)
and ΔXE (s) =
s
K5
ΔXD (s) ------ (2.7)
Substituting the above two equations,
ΔXE (s) =
s
K5
[K3ΔXc (s) + K4 ΔXE (s) ]
ΔXE (s)







s
KK 54
1 =
s
KK 35
ΔXC (s)
ΔXE(s) 






s
KK 54
1 =
s
KK 35 [K1KcΔPc(s)+K2ΔF(s)]
ΔXE (s)





 
s
KKs 54 = 




 
s
sFKKKsPKKKK Cc )()( 352135
ΔXE (s) =






















54
54
1
2
135
1
)()([
KK
s
KK
sF
KK
K
sPcKKK
C
ΔXE (s) =














54
1
2
4
13
1
)()([
KK
s
sF
KK
K
sP
K
KKK C
C
C
----- (2.8)
It can be written as,
ΔXE(s) = )(
1
)([ sF
R
sPC  ] x
G
G
sT
K
1
------ (2.9)
Where,
Speed regulation of the governor (R) =
2
1
K
KK C
in Hz/MW
Gain of speed governor (KG) =
4
31
K
KKK C
Time constant of speed governor (TG) =
54
1
KK
The value of TG is less than 100 m sec.
The generating unit output at a given system frequency
can be varied only due to changing its “load reference or

control point” and it is integrated into the speed governing
system. The reference set point is adjusted by operatingthe
speed changer motor. This effect leads to move the speed
loop characteristics up and down. A non-reheat turbine
model which relates the position of the valve that controls
the emission of steam into the turbine to the power output
of the turbine system.
2.2. Generator Load Model
The mathematical model ofanisolatedgenerator,which
can only supplying local load and is not supplying power to
another area suppose there is a real load change of DP .
Due to the action of the turbine controllers, the generator
increases its output by an amount GP . The net surplus
power ( GP - DP ) will be absorbed by the system in two
categories.
(a) By increasing the kinetic energy in the rotor.
(b) When the frequency changes, the motor load
changes being sensitive to speed.
The rate of change of load with respect to frequency
is B
f
PD


 ; where B = Damping coefficient in MW/Hz. The
value of damping coefficient is positive value for motoring
load.
ΔPG – ΔPD = B Δf ------ (2.10)
The power balance equation is
ΔPG – ΔPD =
0
2
f
HPr
)( f
dt
d
 + B Δf ------ (2.11)
Divide by Pr, we get,
ΔPG p.u–ΔPD p.u =
0
2
f
H
)( f
dt
d
 + Bp.u Δf ----- (2.12)
Taking laplace transform on both sides,
)()(
2
)()(
0
sfBsF
f
Hs
sPsP DG 
]
2
)[()()(
0
B
f
Hs
sFsPsP DG 
]
]
)2
1[
)()(
[)(
0Bf
Hs
B
sPsP
sF DG



]
1
)[()()(
P
P
DG
sT
K
sPsPsF

 ----- (2.13)
Where, Power system gain (KP) =
B
1
Power system time constant (TP) =
0
2
Bf
H
The combination of governor model, turbine model
and generator model is the complete block diagram model
of LFC of an isolated power system.
Figure 2. Model of LFC of Single Area System
III. TIE-LINE MODEL OF TWO AREA POWER
SYSTEMS
A two area system consists of two single area
systems, connected through a power line called tie-line.
Figure.3 shows a two area power system where each area
supplies to its own area and the power flow between the
areas are allowed by the tie line. For two area power
system, the individual areas are strong, the tie line which
connects the two area is weak and a single frequency is
characterized throughout.
Figure 3. Simulink diagram for Two area interconnected
power system
3.1 Area Control Error (ACE)
Area Control Error (ACE) of the ith area is commonly
defined as

ACEi = (T1i – T0i) – (F1i - F0i) --------- (3.1)
Existence of Area Control Errors shows that there is
excessordeficiencyofgenerationinacontrolareaandcontrol
isrequiredtorestorethesystemfrequencyandtielineflowto
scheduled value.
Figure 4. Two Area Power System
The tie-line equation in normal operation of power
system is
Pij = )sin( ji
ji
X
VV
  ------ (3.2)
There should be small deviations in the angles i and
j . Therefore, the tie-line power equation changes with
small amount.
∆Pij = ))(cos( jiji
ji
X
VV
  ----- (3.3)
The synchronizing coefficient of a line is,
0
T )cos( ji
ji
X
VV
  in MW ------ (3.4)
The tie-line power equation becomes,
∆Pij =
0
T )( ji   in MW
The frequency deviation ∆f is given is related to the
reference angle ∆δ.
)(
2
1 0



dt
d
f ----- (3.5)
)(
2
1



dt
d
f in Hz
Taking integration on both sides,
 
t t
f
0 0
2 

t
dtf
0
.2 in rad
Then the tie-line power deviation becomes,








  dtfdtfTP
tt
ij ..2
0
2
0
1
0
 in MW ----- (3.6)
Taking the Laplace transformation on both sides,





 



s
sf
s
sf
TPij
)()(
2 210

 )()(
2
21
0
sfsf
s
T
Pij 

----- (3.7)
IV. CONTROLLER
The controllers are set for a particular operating
condition and they take care of small changes in load
demand without voltage and frequency exceeding the pre-
specified limits. If the operating conditions change
materially the controllers must be re-set either manuallyor
automatically. A Controller is a device introduced in the
system to modify the error signal and to produce a control
signal. The controller modifies the transient responseofthe
system. The controllers may be electrical, electronic,
hydraulic or pneumatic depending on the nature of signal
and the system.
4.1 Proportional (P) Controller
The proportional controller is a device that
produces a control signal u(t) proportional to the input
error signal e(t).
In P-controller, u(t)  e(t)
U(t) = KP e(t) ------ (4.1)
On taking Laplace transform,
U(s) = KP E(s)
PK
)(
)(

sE
sU ------ (4.2)
The P-controller amplifies the error signal by an amountKP.
Also the introduction of the controller on the system
increases the loop gain by an amount KP. The increase in
loop gain improves the steady state tracking accuracy,
disturbance signal rejection and the relative stability and
also makes the system less sensitive to parameter
variations. But increasing the gain to very large values may

lead to instability of the system. The main drawback in P-
controller is that it leads to a constant steady state error.
4.2 Integral (I) Controller
The integral controller is a device that produces a control
signal u(t) which is proportional to integral of the input
error signal e(t).
In I-controller, u(t)  
dtte )(
;
U(t) = Ki
 dtte )( ------- (4.3)
U(s) = Ki
s
sE )(
------- (4.4)
The integral controller removes or reduces the steady error
without the need for manual reset. Hence the I-controller is
sometimes called automatic reset. The drawback inintegral
controller is that it may lead to oscillatory response of
increasing or decreasing amplitude which is undesirable
and the system may become unstable.
4.3 Proportional plus Integral (PI) Controller
The proportional plus integral controller produces
an output signal consisting of two terms. One is
proportional to error signal and the other is proportional to
the integral of error signal.
In PI-controller, U(t)    dttete )()( ;
U(t) =  dtte
T
K
teK
i
P
P )()( ------ (4.5)
U(s) =
s
sE
T
K
sEK
i
P
P
)(
)(  ------ (4.6)
)
1
1(K
)(
)(
P
sTsE
sU
i
 ------ (4.7)
The advantages of both P-controller and I-controller are
combined in PI-controller. The proportional action
increases the loop gain and makes the system less sensitive
to variations of system parameters. The integral action
eliminates or reduces the steady state error. The integral
control action is adjusted by varying the integral time. The
change in value of PK affects both the proportional and
integral parts of control action. The inverse of the integral
time iT is called the reset rate.
4.4 Proportional plus Derivative(PD) Controller
The proportional plus derivative controller
produces an output signal consisting of two terms. One is
proportional to error signal and the other is proportional to
the derivative of error signal.
In PD-controller, U(t)  



 )()( te
dt
d
te ;
U(t) = )()( te
dt
d
TKteK dPP  ------ (4.8)
U(s) = )()( ssETKsEK dPP  ------ (4.9)
)1(K
)(
)(
P sT
sE
sU
d ------ (4.10)
The derivative control acts on rate of change of error and
not on the actual error signal. The derivative control action
is effective only during transient periods and so it does not
produce corrective measures for any constant error. Hence
the derivative controller is never used alone, but it is
employed in association with proportional and integral
controllers. The derivative controller does not affect the
steady state error directly but antipates the error, initiates
an early corrective action and tends to increase thestability
of the system. While derivative control action has an
advantage of being anticipatory it has the disadvantagethat
it amplifies noise signals and may cause a saturation effect
in the actuator. The derivative control action is adjusted by
varying the derivative time. The change in the value of
PK affects both the proportional and derivative parts of
control action. The derivative control is also called rate
control.
4.5 Proportional plus Integral plus Derivative (PID)
Controller
The PID-controller produces an output signal
consisting of three terms. One is proportional to error
signal, another one is proportional tointegral oferrorsignal
and the third one is proportional to derivative of error
signal.
In PID-controller, U(t)  



  )()()( te
dt
d
dttete ;

U(t) = )()()( te
dt
d
TKdtte
T
K
teK dP
i
P
P   ---- (4.11)
U(s) = )(
)(
)( ssETK
s
sE
T
K
sEK dP
i
P
P  ----- (4.12)
)
1
1(K
)(
)(
P sT
sTsE
sU
d
i
 ------ (4.13)
The combination of proportional control action, integral
control action and derivative control action is called PID
control action. This combined action has the advantages of
the each of the three individual control actions. The
proportional controller stabilizes the gain but produces a
steady state error. The integral controller reduces or
eliminates the steady state error. The derivative controller
reduces the rate of change of error.
4.6 PID Controller Design
A proportional integral derivative controller is a
control loop feedback mechanism (controller) widely used
in industrial control systems. A PID controller calculates an
error value as the difference between a measured process
variable and a desired set point. The controller attempts to
minimize the error by adjustingtheprocessthroughuseof a
manipulated variable. There are several methodsfortuning
a PID loop. The most effectivemethodsgenerallyinvolve the
development of some form of process model, and then
choosing P, I, and D based on the dynamic model
parameters. The Ki and Kd gains are first set to zero. The
proportional gain is increased until it reaches the ultimate
gain, Ku, at which the output of the loop starts to oscillate.
The PID controller encapsulatesthreeofthemostimportant
controller structures in a single package. The parallel form
of a PID controller has transfer function. In the case of a
single generator supplying power to a single service area,
and consider three types of turbine used in generation. We
are interested in tuning PID controllers to improve the
performance of load frequency control system. In two area
system, two single area systems are interconnected via tie-
line. Interconnections established increases the overall
system reliability. Even if some generating units in onearea
fail, the generating units in the other area can compensate
to meet the load demand. The PID controller improves
steady state error simultaneously allowing a transient
response with little or no overshoot. As long as error
remains, the integral output will increase causing the speed
changer position, attains a constant value only when the
frequency error has reduced to zero. The SIMULINK model
of a two area interconnected power system using PID
controller is shown in Figure 4.
Figure 4. Block diagram of PID Controller
The PID controller improves the transient response so asto
reduce error amplitude with each oscillation and then
output is eventually settled to a final desired value. Better
margin of stability is ensured with PID controllers. The
mathematical equation for the PID controller is given as,
)()()()(
0
te
dt
d
KddeKitKpety
t
   ----- (4.14)
Where y(t) is the controller output and u (t) is the error
signal. Kp, Ki and Kd are proportional, integral and
derivative gains of the controller. The limitation
conventional PI and PID controllers are slow and lack of
efficiency in handling system non-linearity. But in the case
deregulated environment large uncertainties in load and
change in system parameters is often occurred. The
optimum controller gains calculated previously may not be
suitable for new conditions, which results in improper
working of controller. So to avoid such situations the gains
must be tuned continuously.
V. CONCLUSION
The model of load frequency control gives relation
between the changes in frequency as a result of change in
generation when the load changes by a small amount. From
this study it is found that if a load changes in an area, the
frequency and interchangeerrorsinthatarea havethesame
sign while these have opposite signsfortheotherarea.Thus
the relative signs of the frequency and interchange
deviations help to identify the area where the load has
changed. A PID controller is designed and its feasibility is
studied by varying system parameters.Ithasbeenobserved
that responses of the system with PID controller gives
better results in terms of dynamic parameters such as peak
overshoot and settling time. PID gives better response by
reducing settling time. The ability of two area
interconnected power system of PID controller is improved
as the settling time is reduced in PID as compared to PI.
When compared with PI controller than PID controller of
deregulated power system gives more rapidly and
responsive results. Effectiveness of PID controller with the
deregulated system is used to improve the stability of the
system. Simulation results presented justify the connection

of PID controller in deregulated system for stable and
quality power.
NOMENCLATURE
KG = Gain of speed governor
TG = Time constant of speed governor
R = Speed regulation of the governor in Hz/MW
Tt = Time constant of the turbine
Kt = Gain constant
Kp = Power system gain
Tp = Power system time constant
N = Speed in rpm
F = Frequency in Hz
P = Number of poles
V1&V2 = End voltages
δ1 & δ2 = Angles of end voltages
X = Reactance
ACE = Area Control Error of ith area in MW
T1i = Net interchange of area in MW, power output
is considered positive
T0i = Scheduled net interchange of area 1 in MW
Power output is considered positive
Bi = Bias setting of area in MW/ Hz and is
Considered Negative
F1i = System frequency in Hz
F0i = System frequency schedule in Hz
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AUTHORS
Dr. R.KANIMOZHI, Ph.D ., Assistant
Professor, Department of Electrical
and Electronics Engineering,
University College of Engineering,
Anna University, Bharathidasan
Institute of Technology (BIT) Campus,
Tiruchirapalli.
B. PRAKASH AYYAPPAN, Part-time
Research Scholar (Electrical), Anna
University, Chennai and working as a
Assistant Professor, Department of
Electrical and Electronics Engineering,
Chendhuran College of Engineering
and Technology, Pudukkottai.

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