AGC System Design Using a New Model Reference
Adaptive Control
A. A.Gharaveisi1 , M. Rashidi-Nejad2,3, S. H. Seyyad-Mousavi
Electrical Engineering Department, Shahrood University of Technology – Iran
2
Electrical Engineering Department, Shahid Bahonar University of Kerman, Kerman
3
International Research Center for Hi-Tech and Environmental Sciences, Mahan
1
Abstract: - Automatic generation control (AGC) is an important part of ancillary services in power systems area.
To maintain system reliability as well as security of power systems, AGC system design is a crucial issue. In this
paper, model reference adaptive control (MRAC) method is generalized to design an AGC or Load frequency
control (LFC). The proposed controller system eliminates the frequency error due to any load disturbances, while
it improves the relative stability of power systems. Simulation results can prove a desirable performance of the
proposed system within a wide range of variations for specified parameters. These results show the effectiveness
of the proposed criterion for AGC system designation
Key-Words: - Automatic Generation Control, Load Frequency Control, Model Reference Adaptive Control
1
figure turbine and governor blocks are modeled by
their transfer functions
Introduction
The dynamic performance evaluation of power
systems can be addressed to stability of frequency
regarding to AGC or LFC. The controller commonly
used in the AGC is integral type [2] with
functionality which is affected via a great trend in
power systems development. A large variety of
researches are carried out to solve this problem,
where among them some can be addressed to new
developed methods such as: artificial neural
networks [3], variable structure control [4], genetic
algorithm [5], robust control [6], fuzzy logic
controller [7].
In this paper, a new method for LFC design
considering an adaptive type of controller is
proposed. Adaptive control method as an important
field in automatic control systems [8] is applied in
this research.
A generalized model reference
adaptive controller is implemented to solve the AGC
problem. Numerical results derived through this
study show that our proposed controller possesses a
desirable performance.
2
G p (s) 
G g (s) 
kp
1  sT p
1
1  sT g
, Gt ( s ) 
, kp 
1
,
1  sTt
1
, TP  2 H
D
Df S
Where pd indicates stepped variations of
load disturbances
Figure 1- Single Area of a Power System
3
AGC Model in Power Systems
Proposed Model Reference
Adaptive Controller
In adaptive control method, controller
parameters are subjected to be variable; hence it is
necessary to use a mechanism to regulate these
parameters to proper values. Model reference
A general block diagram of a power system
including one area is shown in figure 1. In this
1
adaptive control (MRAC), as shown in figure 2, is
one of the adaptive control methods. Typical block
diagram of this controller consists of four major
parts as the following:
3.3 Controller:
There are several adjustable parameters for the
controller, by which via choosing different values,
different family of the controller can be obtained.
To achieve to the convergence in tracking, it is
necessary for controller to fulfill enough capability
of perfect tracking. For given parameters of the
plant, it should be assigned such a range of values
for controller parameters so that the output of the
plant agrees the output of model reference.
Reciprocally in the case of unknown parameters for
the controller, adaptation mechanism is responsible
for adjusting the controller parameters. In fact, it is
in a manner in which the so called asymptotically
acute tracking be obtained. To guarantee both the
tracking convergence and stability in accordance to
adjustable parameters, control law is needed to be
linear.
ym
r
Model
Reference
y
Plant
T
R
S
R
Figure 2- Conventional Model Reference Controller
3.1 Plant
3.4 Adaptation mechanism:
The structure of the model is assumed to be
known, and its parameters are presumed unknown
by default. In linear systems, such an assumption
means that the number of poles and zeros of the
plant is known, but their locations are unknown. In
terms of non-linear systems it means that the
structure of dynamic equations of the model is
known, but some of its parameters are unknown.
Adaptation mechanism intends to adjust the
controller parameters based on error signal between
model reference response and the plant under
control. This mechanism should be designed in such
a way to maintain three needs:
 Producing credible parameters for controller
 Assuring tracking error to zero
 Stability Improvement
Based upon figure 2, the objective of the MRC
design, is tracking of desirable input signal (r) by
means of plant output (y) as resemblance as model
3.2 Model Reference
The model reference shows the ideal response
of the plant caused by the external signals while the
adaptation mechanism is running. The question is
how to select model reference, which is one of the
most important parts of MRAC structure. In general
model reference must satisfy two important issues:
1. It must show the ideal characteristics of function
of controller such as rise time, settling time, the
percent of overshoot, etc.
2. Ideal behavior should be achievable.
In the other words, there should not be a significant
difference between the order and / or degree of the
model reference, as well as the relative order and /
or degree of the plant.
reference output (ym), assuming
y ( s ) ym ( s )

 1.
r (s)
r (s)
This structure is shown in figure 3. In this research
the input (r) signal is considered as an undesired
signal. a disturbance signal, that is assumed to be
input spuriously to the plant, in addition to inputting
to the model reference block. So, total strategy of
designing the controller can be wrapped up as
follows:
y( s) y m ( s)

(1)
d ( s) d ( s)
lim s0 sy ( s)  lim s0 sym ( s)  0
d
Model
(2)
ym
y
2
Plant
T
S
tends to increase, transient characteristics of the
power system should be improved.
Load Disturbance
Figure 5- State diagram for model reference
considered for AGC problem
4
Design Procedure for the Proposed
Controller for AGC
As shown in figure 4, in conventional AGC
controller by making a proper variation in
parameter ke , a suitable performance of the system
can be achieved. A proposed method for model
reference controller design procedure is presented in
the following section.
4.2 Design the Controller
Referring to the proposed structure of the
MRAC as shown in figure 3, the state diagram of the
AGC system is chosen as illustrated in figure 6.
Considering the transfer function of the AGC system
B
, and the transfer function of model reference
A
Bm
as
, the proposed controller is designed
Am
T (s)
S (s)
through transfer functions
and
. These
R1 ( s )
R2 ( s )
as
transfer functions have to meet the equation (3) and
(4).
f
f
B B
  m  m
pd A Am pd
lim s0 sf ( s)  lim s0 sf m (s)  0
Figure 4- AGC of Power system using integral controller
(3)
(4)
4.1 Select the Model Reference
Two features should be complied by a suitable
model reference:
A) Simplicity of implementation
B) Selecting based on an acceptable
performance of the plant
C) Proper performance
Considering these items, a model reference is
selected, which the state diagram is illustrated in
figure 5. It is defined Dm  D  De where De is the
incremental value for which the damping in the
model reference is considered. While the damping
Figure 6- State Diagram for Proposed System
3
Referring to the state diagrams of figure 5 and 6, and
using Mason’s gain formula [9] equations (5) and
(6) can be derived as following:
Bm
s 4 m
Am

4.3 Choosing Adaptation Mechanism
Since the operating point and power system
parameters are often changing continuously, it is
reasonable to use the adaptation mechanisms to
adjust controller parameters. In the mechanism
selected in this paper, considering AGC time
constant, and in order to adjust controller
parameters, the following steps are to be executed
once a few minutes:
A) Identifying the power system parameters
B) Adjusting model reference parameters
C) Adjusting controller parameters using
equations (7) and (8)
s4m
m  
fs
s 1 s 1
s 2
[1 


]
2H
Tg
Tt
Tg Tt
m 1
D f s 1
s 1 s 1
s 2


 m s

Tg
Tt
Tg Tt
2H
Dm f s s  2
D f s  2 Dm f s s 3
 m s


2 HT g
2 HTt
2 HT g Tt
f s s 3
k f s 4
 e s
2 HT g Tt R 2 HT g Tt
(5)
B
s 4
 4
A
s 
  m 
5
f s s 3 T (s)
(
)
2 HTgTt R1 ( s )
  m 
To check the functionality performance of the
proposed method, the single area power system is
indicated in figure 1. The parameters related to this
model are given as followings [1]:
De f s s 1 De f s s  2 De f s s  2



2H
2 HTg
2 HTt
De f s s  3 ke f s s  4
f s s 3
T (s)


(
)
2 HTgTt 2 HTgTt 2 HTgTt R2 ( s )
H  5 Sec.
( 6)
l s 3  l 2 s 2  l1 s  l0
S (s)
 3
R2 ( s )
fss
l1 
De f s
ke f s
, l0 
2 HT g Tt
2 HT g Tt
It can be said that the transfer function
H  5 Sec.
D  0.01 p.u.MW / Hz
Tt  0.4991 Sec.
R  3.003 Hz / p.u.MW
(7 )
Tg  0.3991Sec.
D  0.01005 p.u.MW / Hz
The next job is determining parameters related to the
model reference. Let increase amount of damping
( De ) be considered as 0.1. A comparison is
performed between numerical results achieved from
the proposed method and conventional integral
controller method, and resulted curves are indicated
in figures 7-12 for %5 stepped load variation.
Analyzing these curves shows the following
consequents:
A) In the nominal conditions (i.e. nominal
parameters of the power system), the
proposed controller has a better performance
than the integral controller. (see figure 7)
S (s)
is not
R2 ( s )
realizable. To overcome to the problem, two very far
poles from the imaginary axis are included to the
transfer function, by which equations (8) is obtained.
T ( s)
0
R1 ( s )
l3 s 3  l 2 s 2  l1 s  l 0
S ( s)

R2 ( s )
f s s (1  T p1 s )(1  T p2 s )
Tg  0.4 Sec. f s  50 Hz
Additionally, the typical integral control index for
this system is set to k I  0.09 . Identification of the
parameters of power system is made before
designing the proposed controller. This is done in
once in each few minutes. The results of such
identification using recursive least square method, in
the case that system parameters meet nominal
ratings, leads to the following results:
T (s)
0
R1 ( s )
De f s
De f s
De f s
, l2 

2H
2 HT g
2 HTt
Tt  0.5 Sec.
R  3 Hz / p.u.MW
Consequently, by substitution equations (5) and
(6) in the equations (3) and (4), then it leads to
equations (7), which describes a controller with the
least degree.
l3 
Validity Check and Performance
Analysis of the Proposed Method
(8)
4
Interconnected Reheat Thermal System”, Proc.
IEE, Vol. 138, Nov. 1991.
[6] M. Azzam, “ Robust Automatic Generation
Control”, 98 Simulation Int. Conf., 30Sep.-2Oct.,
pp. 253-258, 1998.
[7] G.A. Chown & R.C. Hartman, “Design and
Experience with a Fuzzy Logic Controller for
Automatic Generation Control (AGC)”, Power
Industry Computer App., 1997, 20th int. conf.,
11-16 May, pp. 352-357, 1997.
[8] K.S. Narendra & A.M. Annasawamy, “ Stable
Adaptive Control”, Jhon Wiley, New York, 1987.
B) Assuming the generation rate constraint
(GRC) to be 5% for the output of turbine,
the functionality and performance of the
conventional integral controller gets
undesirable, while the proposed adaptive
controller eliminates frequency variations
properly. (see figure 8)
C) If primary control loop is open and does not
function ( r   ), the integral controller
causes oscillating behavior of power system,
while the proposed adaptive controller
demonstrates a perfect response of the
system. (see figure 9)
D) General variations in the parameters of
power system, results in undesirable
functioning of integral controller system,
while proposed adaptive control system
shows a desirable performance. (see
figures 10 to12)
6
Conclusions
In this paper, the model reference controller for
AGC or LFC system is designed by a generalization
approach in the structure of model reference
adaptive controller. The results of simulation of
power system demonstrated that the proposed
adaptive controller is not only able to eliminate the
frequency errors, but also presents desirable
functioning and performance against extensive
variations of the system parameters.
Figure 7- Relative frequency variations
f/f0 for load disturbance due 5%
References:
[1] A.J. Wood & B.F. Wollenberg , “Power
Generation Operation and Control”, Jhon
Wiley,New York,1993.
[2] J. Nanda & B.L. Kaul, “Automatic Generation
Control of an Interconnected Power System”,
IEE Proc. , 1978 , pp. 385-390.
[3] Mohammad Bagher Menhaj, Aref Dorudi,
“Applying Nerve Networks in Load-Frequency
Controllers” , 11th International Iranian
Electrical Conference , pp. 380-388, 1996.
[4] S. Matsushida & et al, “ Automatic Generation
Control Using GA Considering Distributed
Generation”, IEEE/PES, Vol. 3, 6-10 Oct., pp.
1579-1583, 2002.
[5] D. Das & et al, “Variable Structure Control
Strategy to Automatic Generation Control or
Figure 8- Relative frequency variations f/f0 for load
disturbance due 5%, and limited generation rate
5
Figure 9- Relative frequency variations f/f0 for
5% load disturbance & open frequency control
loop
Figure 11- Relative frequency variations
f/f0 for load disturbance due 5%, and100%
of variations in Tg
Figure 10- Relative frequency variations f/f0
for5% load disturbance & 100% variations in Tg
Figure12- Relative frequency variations f/f0
for load disturbance due 5%, and 50% of
variations in H
6