Ijartes v2-i4-001

International Journal of Advanced Research in Technology, Engineering and Science (A Bimonthly Open
Access Online Journal) Volume2, Issue4, July-Aug, 2015.ISSN:2349-7173(Online)
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Investigation of Response of Load
frequency Controller in Two Area
Restructured System with Non-Linear
Governor Characteristics
Veena Yadav1
and Manbir Kaur2
___________________________________
Abstract-The objective of automatic generation control
(AGC) is to maintain the system frequency and tie line
flows within the scheduled values. Adaptive control of
frequency has become more significant owing to
increased size, complexity and restructure of power
system. In this paper, a framework of automatic
generation control with linear and non-linear governor
characteristics in restructured power system has been
presented. Conventional AGC with non-linear governor
characteristics is reported to be dynamically unstable.
To stabilize the frequency and tie-line power
oscillations, the frequency stabilizer equipped with
energy storage system is modeled. The gains of the
integral controller and PID controller and parameters
of frequency stabilizer are optimized with genetic
algorithm. The transient response of optimized load
frequency controller is simulated for two area system
comprising non-linear hydro-hydro and hydro-thermal
systems. The response of simulated model is also
studied under different Poolco transactions and
bilateral transactions in restructured electricity market.
___________________________________
Keyword – AGC, SMES, TCPS, deregulation, hydro
___________________________________
I. Introduction
The interconnected power system requires the
matching of total generation with the total load and
the associated system losses. The normal operation
of a power system is continuously disturbed due to
sudden load perturbations which cause variations in
system frequency and tie-line power exchanges.
The main goal of load frequency controller (LFC)
or automatic generation control (AGC) is to re-
establish the frequency to its nominal value and
minimize unscheduled tie-line power flows
between neighboring control areas.
_________________________________________
First Author: Veena Yadav, Thapar University, Patiala,
Punjab.
Second Author: Manbir Kaur,Thapar University,
Patiala, Punjab.
________________________________________
The literature survey for AGC reveals that most of
the earlier work pertains to the interconnected two-
area thermal-thermal or hydro-thermal system and
relatively lesser attention has been given for hydro-
hydro system which has widely different
characteristics from thermal units. The normal
AGC operation for hydro-hydro system fails and
requires fast-acting energy storage systems and
FACT devices for the restoration of variations. In
order to enhance the system dynamic stability and
for effective transient frequency stabilization AGC
along with several FACTS devices has been
reported such as SMES, SSSC, TCPS [2].
The objective of this paper is to modify the two-
area interconnected system with linear governor
characteristics into non-linear governor
characteristics of hydro system and addition of
compensators to stabilize the steady-state
frequency and power deviations in two-area system
with non-linear governor characteristics. In
addition to this, we have seen the effects of linear
and non-linear governors in deregulated
environment.
This paper is organized as follows. In section II, we
explain the traditional AGC scenario in two-area
system with linear governor characteristics. In
section III, we explain the Linearized model of
two-area system with non-linear governor
characteristics. In Section IV, we explain how the
bilateral transactions are incorporated in the
traditional AGC system leading to a new block
diagram. Mathematical Problem Formulation is
presented in Section V. Simulation results are
presented in Section VI. This followed by
conclusion in Section VII.
II. AGC in Two-area system with linear
governor characteristics
The closed loop transfer function of area 1 of the
control system is given by:
∆ ( )
∆ ( )
=
( )( )
( )( )( )
(1)
The simulation results of two-area system are
shown in table 1. [5]

III. AGC in Two-area system with non-linear
governor characteristics
A. Test System
The governors of hydraulic units require
transient droop compensation for stable speed
control performance. The initial power surge of a
hydro turbine is opposite to that desired. A change
in the gate position at the foot of the penstock
causes the pressure across the turbine to reduce.
However, the flow does not change immediately
due to water inertia causing the power of the
turbine to reduce temporarily. Because of this
phenomenon, during a generation deficit situation,
the decelerating power is higher for a hydro turbine
compared to steam turbine. Therefore, the system
performance of hydraulic generation units for AGC
is different. The Linearized model of
interconnected two-area multiple units’ hydro-
hydro system is shown in figure.1
Figure1. Linearized model of interconnected
hydro-hydro system with SMES and TCPS
For dynamic performance analysis of the test
system, 10% step load perturbation is considered in
area I. It is observed that under the occurrence of
load change, the frequency is heavily disturbed
from its operating point and does not regain its
stable state. The eigenvalues for the system is
shown in Table I. The positive real parts in some
eigenvalues indicate that the system is small signal,
dynamically unstable. TABLE I.
Sl.No. Eigen values of test
system
1 -4.0422+1.179i
2 -4.0422-1.179i
3 -3.9869+0.9624i
4 -3.9869-0.9624i
5 0.4613+0.7098i*
6 0.4613-0.7098i*
7 0.4062+0.6832i*
8 0.4062-0.6832i*
9 -5
10 -2
11 -0.0103
B. Linearized model of TCPS
The tie-line power flow equation after including
TCPS may be written as:
∆ ( ) = ∆ ( ) − ∆ ( ) +
! "
#
∆ ( ) (2)
The structure of TCPS as a frequency stabilizer
is shown in figure 3. The input signal for the
frequency stabilizer is the p.u. rotor speed deviation
∆ωi=1,2. Kf is the gain block having value equal to
the nominal system frequency.
Figure2. Structure of TCPS as a frequency
controller
C. Linearized model of SMES
The structure for SMES as frequency stabilizer
is modeled as the second order lead-lag
compensator is shown below. The SMES is
connected at the load point and there are six
parameters such as stabilization gain KSMES, and
time constants TSMES, T1, T2, T3, T4 are to be
optimized for the optimal design of the coordinated
frequency stabilizer. The structure of SMES as a
frequency controller is shown in figure 4. The
application of SMES as frequency controller is
described in [1].
Figure3. Structure of SMES as a frequency
controller
IV. Restructured System
In restructured environment, GENCOs sell
power to various DISCOs at competitive prices.
Thus, DISCOs have the liberty to choose any
GENCOs for contracts. They may or may not have
contracts with the GENCOs in their own area. This
makes various combinations of DISCO-GENCO
contracts. The concept of “DISCO participation
matrix “makes the visualization of contracts easier.
DPM is the matrix where number of rows equal to
number of GENCOs and the number of columns
equal to the number of DISCOs in the system. The
sum of all the entities in a column in this matrix is
unity. DPM shows the participation of a DISCO in
a contract with a GENCO; hence the name
“DISCO participation matrix”.
A. Block Diagram Formulation
Whenever a load demanded by a DISCO
changes, it is reflected as a local load in area to
which this DISCO belongs. This corresponds to the
local load ∆PL1 and ∆PL2 and should be reflected in

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the deregulated AGC system block diagram at the
point of input to the power system block. As there
are many GENCOs in each area, ACE signal has to
be distributed among them in proportion to their
participation in the AGC. Coe
distribute ACE to several GENCOs are termed as
“ACE participation factors” (apfs)
Where,
∑ %&'(
)
(* = 1
m is the number of GENCOs
Further the detailed discussion and
mathematical equations are described in [5].
The block diagram for AGC in the deregulated
environment is shown in the figure 6:
Figure4. Two-area AGC system block diagram in
restructured scenario
V. Mathematical Problem Formulation
The objective of AGC is to re-establish system
frequency to its nominal value and minimize the
tie-line power flow oscillations between
neighboring control areas. In order to satisfy the
above requirements the gains (KI1, K
controller, (Kp, KI, KD) of PID controller,
parameters of TCPS (,-, Tps)and parameters of
SMES (KSMES, TSMES, T1, T2, T3, T4
optimized. An integral square error (ISE) criterion
is used to minimize the objective function defined
as,
Minimize . =
(4)
Where, m is the number of area in the system
Further we can write,
/01 = 2 ∆' ∆ 3343
(5)
/01 2 ∆' ∆ 3343
(6)
Where, ACE1, 2 is the area control error, B
is the bias factor ∆f1, ∆f2 is the incremental change
in frequency of area 1 and area 2 and
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the deregulated AGC system block diagram at the
point of input to the power system block. As there
are many GENCOs in each area, ACE signal has to
be distributed among them in proportion to their
participation in the AGC. Coefficients that
distribute ACE to several GENCOs are termed as
(3)
Further the detailed discussion and
equations are described in [5].
The block diagram for AGC in the deregulated
environment is shown in the figure 6:
area AGC system block diagram in
V. Mathematical Problem Formulation
establish system
frequency to its nominal value and minimize the
line power flow oscillations between
neighboring control areas. In order to satisfy the
, KI2) of integral
) of PID controller,
)and parameters of
4) are also to be
optimized. An integral square error (ISE) criterion
is used to minimize the objective function defined
5 ∑ /01)
*
Where, m is the number of area in the system
is the area control error, B1, B2
is the incremental change
in frequency of area 1 and area 2 and ∆Ptie1-2error is
the incremental change in tie
objective function is minimized with the help of
Genetic Algorithm.
VI. Simulation results
A. Simulation results of two-area system with
linear governor characteristics
The two-area interconnected system when
implemented with the Feedback control whose
gains are controlled by Genetic Algorithm in the
Matlab code following optimized gains is
in table 1:
Genetic Algorithm based optimal values
Control
Areas
Integral
Controller
Ki K
Area-1 0.7612 0.9998
Area-2 0.0117 0.9997
Factors Integral
∆f1
∆f2
Table 1. Simulation results of two
with linear governor characteristics
B. Simulation results of two-area system with non
The two-area interconnected systems with non
controlled by Genetic Algorithm in the Matlab
code following optimized gains are provided in
table 2:
TCPS-SMES coordination with Integral
Controller
Area 1
,- Tps
0.2857 0.3601
Area 2
KSMES TSMES T1
0.3886 0.03 0.0981
T4 Ki2
0.1076 0.0780
TCPS-SMES coordination with PID controller
Area 1
,- Tps Kp
0.3012 1.6864 0.0852
0 5 10 15 20 25 30 35 40
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0 5 10 15 20 25 30 35 40
-0.2
-0.15
-0.1
-0.05
0
0.05
7173(Online)
Page 3
the incremental change in tie-line power. The
objective function is minimized with the help of
area system with
area interconnected system when
implemented with the Feedback control whose
gains are controlled by Genetic Algorithm in the
following optimized gains is provided
PID controller
Kp Ki KD
0.9998 0.9996 0.9997
0.9997 0.9995 0.9994
PID
. Simulation results of two-area system
with linear governor characteristics
area system with non-
area interconnected systems with non-
linear governor characteristics whose gains are
controlled by Genetic Algorithm in the Matlab
d gains are provided in
SMES coordination with Integral
Ki1
0.0431
T2 T3
0.0303 0.1745
SMES coordination with PID controller
KI KD
0.0852 0.0509 0.017
8
45 50 0 5 10 15 20 25 30 35 40 45 50
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
45 50 0 5 10 15 20 25 30 35 40 45 50
-0.045
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005

Area 2
KSMES TSMES T1 T2 T3
0.213 0.03 0.1510 0.1248 0.175
2
T4 Kp KI KD
0.116 0.0417 0.0485 0.0265
Factors Integral PID
∆f1
∆f2
Table 2. Simulation results of two-area system with
non-linear governor characteristics
C. Simulation results of two-area system in
Deregulated Environment
The simulation results of two-area system in
Deregulated Environment have been plotted with
the use of Integral (I) and Proportional Integral
Derivative Controller (PID). The system data
related to the block diagram parameters of linear
and non-linear governor characteristics is used for
simulation. Both areas are assumed to be identical.
The governor-turbine units in each area are
assumed to be identical. Under consideration 3
cases has been taken. The detailed discussions
about these cases are given in [5]. The simulation
results and optimized parameters of each case are
given below:
Case 1: Base Case
With reference to the figure 4 the simulation results
for linear and non-linear governor characteristics
are shown below:
Factors Linear Governor
(Integral)
Linear Governor
(PID)
∆f1
∆f2
Tie-line
GENCO1
GENCO2
GENCO3
GENCO4
Factors Non-linear
Governor
(integral)
Non-linear
Governor (PID)
∆f1
∆f2
Tie-line
GENCO1
GENCO2
GENCO3
GENCO4
Table 3
0 10 20 30 40 50 60 70 80 90 100
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0 10 20 30 40 50 60 70 80
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0 10 20 30 40 50 60 70 80 90 100
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
x 10
-3
0 10 20 30 40 50 60 70 80
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
x 10
-3
0 5 10 15 20 25 30 35 40 45 50
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0 5 10 15 20 25 30 35 40 45 50
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0 5 10 15 20 25 30 35 40 45 50
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0 5 10 15 20 25 30 35 40 45 50
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0 5 10 15 20 25 30 35 40 45 50
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0 5 10 15 20 25 30 35 40 45 50
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0 5 10 15 20 25 30 35 40 45 50
0
0.02
0.04
0.06
0.08
0.1
0.12
0 5 10 15 20 25 30 35 40 45 50
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 5 10 15 20 25 30 35 40 45 50
0
0.02
0.04
0.06
0.08
0.1
0.12
0 5 10 15 20 25 30 35 40 45 50
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 5 10 15 20 25 30 35 40 45 50
-4
-2
0
2
4
6
8
10
12
14
x 10
-3
0 5 10 15 20 25 30 35 40 45 50
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0 5 10 15 20 25 30 35 40 45 50
-4
-2
0
2
4
6
8
10
12
14
x 10
-3
0 5 10 15 20 25 30 35 40 45 50
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0 5 10 15 20 25 30 35 40 45 50
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0 5 10 15 20 25 30 35 40 45 50
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0 5 10 15 20 25 30 35 40 45 50
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
x 10
-3
0 5 10 15 20 25 30 35 40 45 50
-4
-3
-2
-1
0
1
2
x 10
-3
0 5 10 15 20 25 30 35 40 45 50
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 5 10 15 20 25 30 35 40 45 50
-2
-1.5
-1
-0.5
0
0.5
1
0 5 10 15 20 25 30 35 40 45 50
-0.1
-0.05
0
0.05
0.1
0.15
0 5 10 15 20 25 30 35 40 45 50
-0.1
-0.05
0
0.05
0.1
0.15
0 5 10 15 20 25 30 35 40 45 50
-0.1
-0.05
0
0.05
0.1
0.15
0 5 10 15 20 25 30 35 40 45 50
-0.1
-0.05
0
0.05
0.1
0.15
0 5 10 15 20 25 30 35 40 45 50
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0 5 10 15 20 25 30 35 40 45 50
-8
-6
-4
-2
0
2
4
x 10
-3
0 5 10 15 20 25 30 35 40 45 50
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0 5 10 15 20 25 30 35 40 45 50
-8
-6
-4
-2
0
2
4
x 10
-3

The optimized gains of controller and parameters
are shown in table 4.
Control
Areas
Integral
Controller
PID controller
Ki Kp Ki KD
Area-1 0.0388 0.9935 0.1430 0.9075
Area-2 0.0140 0.0082 0.0083 0.8868
TCPS-SMES coordination with Integral Controller
Area 1
,- Tps Ki1
0.1342 1.6536 0.0070
Area 2
0.7983 0.03 0.1390 0.1042 0.1270
T4 Ki2
0.1683 0.8760
Area 1
,- Tps Kp KI KD
0.0863 0.1211 0.0487 0.0105 0.0469
Area 2
0.2189 0.03 0.1876 0.0615 0.0996
T4 Kp KI KD
0.1986 0.0143 0.0210 0.0149
Table 4
Case 2: The trajectories reach the respective
desired generations in the steady state as shown in
table 5-6
(Integral)
Linear Governor
(PID)
∆f1
∆f2
Tie-line
Factors Non-linear
Governor
(Integral)
Non-linear
Governor (PID)
∆f1
∆f2
Tie-line
Table 5
Control
Areas
Integral
controller
PID controller
Ki Kp Ki KD
Area-1 0.0352 0.2785 0.9071 0.9703
Area-2 0.0026 0.8926 0.0013 0.7205
TCPS-SMES coordination with integral controller
Area 1
,- Tps Ki1
0.1184 0.4424 0.0183
Area 2
0.4279 0.03 0.1479 0.1071 0.0172
T4 Ki2
0.1375 0.9142
Area 1
,- Tps Kp KI KD
0.1593 0.2576 0.0436 0.0352 0.0382
Area 2
0.9194 0.03 0.0248 0.0119 0.0986
T4 Kp KI KD
0.0512 0.0269 0.0485 0.0180
Table 6
Case 3: Contract Violation
The respective results and optimized gains of the
controller are given in table 7-8.
(Integral)
Linear Governor
(PID)
∆f1
0 5 10 15 20 25 30 35 40 45 50
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0 5 10 15 20 25 30 35 40 45 50
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0 5 10 15 20 25 30 35 40 45 50
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0 5 10 15 20 25 30 35 40 45 50
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0 5 10 15 20 25 30 35 40 45 50
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0 5 10 15 20 25 30 35 40 45 50
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0 10 20 30 40 50 60 70 80 90 100
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0 5 10 15 20 25 30 35 40 45 50
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0 10 20 30 40 50 60 70 80 90 100
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0 5 10 15 20 25 30 35 40 45 50
-7
-6
-5
-4
-3
-2
-1
0
1
x 10
-3
0 10 20 30 40 50 60 70 80 90 100
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0 5 10 15 20 25 30 35 40 45 50
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0 5 10 15 20 25 30 35 40 45 50
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0 5 10 15 20 25 30 35 40 45 50
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02

∆f2
Tie-line
Factors Non- linear
Governor (integral)
Non-linear
Governor (PID)
∆f1
∆f2
Tie-line
Table 7
Control
Areas
Integral
Controller
PID controller
Ki Kp Ki KD
Area-1 0.2572 0.9755 0.9948 0.99
48
Area-2 0.3831 0.9948 0.9948 0.36
46
TCPS-SMES coordination with Integral
Controller
Area 1
,- Tps Ki1
0.3824 0.1108 0.0377
Area 2
KSME
S
TSME
S
T1 T2 T3 T4
0.76
30
0.03 0.1925 0.0582 0.1433 0.041
0
Ki2
0.63
19
Area 1
,- Tps Kp KI KD
0.0734 0.474
6
0.0466 0.0416 0.0326
Area 2
0.8150 0.03 0.0954 0.0338 0.1637
T4 Kp KI KD
0.1593 0.0485 0.0443 0.0441
Table 8
VII. Conclusion
This paper work gives an overview of AGC with
linear and non-linear governor characteristics and
the application of both in deregulated environment.
To stabilize the frequency and tie-line oscillations
the coordinated controllers TCPS-SMES are very
effective against the varying system parameters
particularly for low tie-line synchronizing
coefficient. The optimized gains and parameters of
the compensators provide less overshoot and
minimum settling time with the help of PID
controller as compared to Integral controller using
the optimization technique Genetic algorithm. In
restructured environment some adaptations are
require in current AGC strategies to satisfy the
general needs of the different market organizations.
The existing market-based AGC configurations and
new concepts are briefly discussed and an updated
frequency response model for restructured AGC
market was introduced.
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x 10
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