Study of PID Controllers to Load Frequency Control Systems with Various Turbine Models

Abdul Shariq Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 5, Issue 8, (Part - 5) August 2015, pp.92-98
www.ijera.com 92 | P a g e
Study of PID Controllers to Load Frequency Control Systems
with Various Turbine Models
Abdul Shariq*, Shanti Bayyavarapu**
*(Department of Electrical Engineering, A.U.College of Engineering, Andhra University, Visakhapatnam)
** (Department of Electrical Engineering, A.U.College of Engineering, Andhra University, Visakhapatnam)
ABSTRACT
This paper studies the load frequency control problem for various systems under various controller design
methods. Frequency should remain nearly constant for satisfactory operation of a power system because
frequency deviations can directly impact on a power system operation, system stability, reliability and
efficiency. A Load Frequency Control (LFC) scheme basically incorporates an appropriate control system for an
interconnected power system, which is having the capability to bring the frequencies of system to original set
point values or very nearer to set point values effectively after any load change. This can be achieved by the use
of conventional and modern controllers. In this proposed paper PID controller has been applied for LFC power
systems. The parameters of the PID controller are tuned by different methods names as Ziegler-Nichols (Z-N)
Method, and IMC method for better results. We use various tuning formulae in Z-N method and certain model
approximation methods and the responses of LFC with model approximation are studied. It is seen that the
results obtained are as good as the conventional controller.
Keywords – Integral Model Controller(IMC), Load Frequency Control(LFC), PID controllers, Zielger-Nichols
Method
I. INTRODUCTION
THE problem of controlling the real power
output of generating units in response to changes in
system frequency and tie-line power interchange
within specified limits is known as load frequency
control (LFC).
The Objectives of LFC are to provide zero
steady-state errors of frequency and tie-line exchange
variations, high damping of frequency oscillations
and decreasing overshoot of the disturbance so that
the system is not too far from the stability. The load
frequency control of a multi area power system
generally incorporates proper control system, by
which the area frequencies could brought back to its
predefined value or very nearer to its predefined
value so as the tie line power, when the is sudden
change in load occurs
Due to the increased complexity of modern
power systems, advanced control methods were
proposed in LFC, e.g., optimal control; variable
structure control; adaptive and self-tuning control;
intelligent control; and robust control. Recently, LFC
under new deregulation market, LFC with
communication delay, and LFC with new energy
systems received much attention. Improved
performance might be expected from the advanced
control methods, however, these methods require
either information on the system states or an efficient
online identifier thus may be difficult to apply in
practice.
Here, PID controllers for LFC were studied due to
their simplicity in execution. Certain papers
suggested fuzzy PI controllers for load frequency
control of power systems; proposed a derivative
structure which can achieve better noise-reduction
than a conventional practical differentiator thus load
frequency controller of PID type can be used in LFC;
proposed a PID load frequency controller tuning
method for a single-machine infinite-bus (SMIB)
system based on the PID tuning method proposed and
the method is extended to two-area case. It is shown
that the resulted PID setting needs to be modified to
achieve desired performance. In this paper, methods
to design and tune PID load frequency controller for
power systems with non-reheat, reheat and hydro
turbines using Revised Zielger-Nichols(RZ-N) tuning
and Integral Model Controller (IMC) will be
discussed. The methods are flexible in that the
performance and robustness of the closed-loop
systems are related to single tuning parameter in IMC
and two tuning parameters in RZ-N. These methods
can also be extended to multi-area power systems.
Tuning Methods
A thorough study of papers based on PID
controller tuning methods and stabilization of LFC
using PID Controllers has been carried out.
The basics of PID controllers have been studied
using references [1] –[2]. The various tuning methods
used in PID controllers like Ziegler-Nichols Tuning
Formula, revised and Modified Z-N tuning formulae
RESEARCH ARTICLE OPEN ACCESS

are used thoroughly studied and algorithms and
programs were developed to use them for various
systems. Approaches for identifying the equivalent
first-order plus dead time model, which is essential in
some of the PID controller design algorithms, will be
presented. A modified Ziegler–Nichols algorithm is
also given. Some other simple PID setting formulae
such as the Chien–Hrones–Reswick formula, Cohen–
Coon formula, refined Ziegler–Nichols tuning,
Wang–Juang–Chan formula and Zhuang–Atherton
optimum PID controller will be presented.
The study of Model approximation methods, to
approximate a given plant to First Order Plus Dead
Time (FOPDT) or First Order Integral Plus Dead
Time (FOIPDT) formulae for FOIPDT (first- order
lag and integrator plus dead time) and IPDT
(integrator plus dead time) plant models, rather than
the FOPDT (first-order plus dead time) model, will
be given in sections .
IMC controller with Single Degree of Freedom
and Two degree of Freedom are studied using and
their methods of implementations are presented.
Load Frequency Controller Operation, the derivation
of various transfer functions in LFC, the importance
of stabilization are studied and presented. The
implementation designs of PID Controllers on LFC
under various systems like non-reheated, reheated,
hydrothermal systems with and without drooping
characteristics are studied.
II. LFC-PID DESIGN
We consider 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
Fig. 2.1.Linear model of a single-area power system.
performance of load frequency control system,
i.e.,
( )u K s f   find a control law , where K(s)
takes the form
1
( ) 1p d
i
K s K T s
T s
 
   
  (2.1)
In practice, to reduce the effect of noise, the PID
controller should be implemented as a practical one
1
( ) 1
1
d
P
i
T s
K s K
T s Ns
 
   
  (2.2)
Where N is the filter constant
(11
( ) 1
Ts
d
p
i
T e
K s K
T s T

 
   
  (2.3)
where T is a small sampling rate.
Since for the load-frequency control problem the
power system under consideration is expressed only
to relatively small changes in load, it can be
adequately represented by the linear model. (obtained
by linearizing the plant around the operating point).
The droop characteristic is a feedback gain to
improve the damping properties of the power system,
and it is generally set to 1/R before load frequency
control design. So there are two alternatives for LFC
design, i.e.,
1) Design controller
~
( )K s for the power system
without droop characteristic, and then subtract 1/R
from
~
( )K s ,i.e., the final controller will be
~
( ) ( ) 1/K s K s R  (2.4)
If
~
( )K s is of PID type, then the final proportional
gain of the PID controller just needs to be decreased
by 1/R.
Design controller K(s) directly for the power
system with droop characteristic.
The model dynamics for the two cases are different
so the final result might be different if the tuning
parameters are not carefully chosen. We will discuss
the two alternatives in detail.
2.1 LFC Design Without Droop Characteristic
2.1.1 Non-Reheated Turbine:
The plant for a power system with a non-
reheated turbine consists of three parts:
• Governor with dynamics:
1
( )
1
g
G
G s
T s


(2.5)
• Turbine with dynamics:
1
( )
1
t
T
G s
T s


(2.6)
• Load and machine with dynamics:
( )
1
P
p
P
K
G s
T s


(2.7)
Now the open-loop transfer function without droop
characteristic for load frequency control is
~
( )
( 1)( 1)( 1)
P
p t g
P T G
K
P s G G G
T s T s T s
 
  
(2.8)

From the TDF-IMC-PID design procedure, since
~
P
is minimum-phase, the set point-tracking IMC
controller takes the form
1~
3
1
( ) ( )
( 1)s
Q s P s




3
( 1)( 1)( 1)
( 1)
P T G
P
T s T s T s
K s
  

 (2.9)
To improve the disturbance response another degree
of freedom Qd(s) is used. We observe that the load
demand
( )dP s
must pass through
/ ( 1)P PK T s 
to affect the frequency deviation
( )f s , in order to
have a fast disturbance rejection; we choose Qd to
cancel the pole s=-(1/Tp) .
Let
1 1
1
d
d
s
Q
s




 then 1 should satisfy
~
1(1 ( ) ( ) ( )) |
P
d
s
T
P s Q s Q s


(2.10)
that is,
3
1 1 1 1 d
P
P P
T
T T


    
             (2.11)
By choosing suitable parameters  and d ,
TDF-IMC controllers Q(s) and Qd(s) can be obtained
and the corresponding PID controller can be obtained
by the procedure described in the previous section.
2.1.2 Reheated Turbine:
For reheated turbines, the turbine dynamics
becomes
1
( )
( 1)( 1)
r
t
r T
cT
G s
T s T s


  (2.12)
where Tr is a constant and is the portion (percentage)
of the power generated by the reheat process in the
total generated power. In such case the open-loop
transfer function without droop characteristic
becomes
~ ( 1)
( )
( 1)( 1)( 1)( 1)
P r
p t g
P T r G
K cT s
P s G G G
T s T s T s T s

 
   
(2.13)
and the set point-tracking IMC takes the form
3
( 1)( 1)( 1)( 1)
( )
( 1)( 1)
P T r G
P r
T s T s T s T s
Q s
K cT s s
   

  (2.14)
The disturbance-rejecting IMC Qd has the same
structure as the non-reheat turbine case, and 1 can
be computed in the same way as in .
2.1.3 Hydro Turbine:
For hydro turbines, the turbine dynamics is
Table : 3.1 Non Reheated Turbine System
Parameters.
1
( )
1 0.5
t
T s
G s
T s




 (2.15)
where is a constant. In this case the open-loop
transfer function without droop characteristic
becomes
~
( ) p t gP s G G G
(1 )
( 1)(0.5 1)( 1)
P
P G
K T s
T s T s T s




   (2.16)
the transfer function contains a right-half-plane zero,
so the setpoint-tracking IMC takes the form
2
( 1)(0.5 1)( 1)
( )
(1 )( 1)
P G
P
T s T s T s
Q s
K T s s

 
   
  
   (2.17)
The disturbance-rejecting IMC has the same
structure as the non-reheat turbine case, however, in
this case the parameter 1 must satisfy
2
1 1 1 1 / 1d
P
P P P
T
T
T T T


      
                  (2.18)
2.2 LFC Design With Droop Characteristic
In this case the plant model used in LFC design
is
( )
1 /
g t p
g t P
G G G
P s
G G G R


(2.19)
Where Gg is the governor dynamics ,Gp is the load
and machine dynamics, and Gt is the turbine
dynamics for non-reheated turbines, for reheated
turbines, and for hydro turbines.
S.no Parameter Power
System
1
Speed Regulation due
to governor action R
(Hz/p.u.MW)
2.4
2
Electric System
Gain(Kp)(s)
120
3
Electric System Time
Constant(Tp)(s)
20
4
Turbine Time
Constant(Tt)(s)
0.4
5
Governor Time Constant
(Tg)(s)
0.08

Unlike
~
( )P s discussed in the previous subsection,
which has a non-oscillatory step response for all
kinds of turbines, the step response of P(s) is
generally oscillatory, even unstable in some cases for
hydro turbines, so the LFC design is more
complicated. It was shown that for LFC tuning
purpose, the transfer function of the power systems
can be approximated with a second-order oscillatory
model, and a PID tuning procedure can be done
based on the TDF-IMC method. We note that the
approximation to a second-order model is not
necessary, and the process only works well for power
systems with non-reheated turbine.
Here we can directly apply the TDF-IMC design
method to the plant model. To achieve good
disturbance rejection performance, we need to use Qd
to cancel the undesirable poles of P(s) . MATLAB-
based programs for general TDF-IMC design and
PID reduction are available for such purpose and
good measure of robustness of the PID controllers.
III. NUMERICAL STUDIES
3.1 Non-Reheated Turbine
Consider a power system with a non-reheated
turbine. The model parameters are given by
The plant model without droop characteristic is
120
(0.08 1)(0.3 1)(20 1)s s s  
------3.1
By the LFC-PID design procedure discussed, we get
the following
3.1.1 Non-Reheated Turbine without droop
PID controller:
Modified Zielger-Nichols Tuning
For
45
0.45
o
b
br
 

1.155
0.8557 0.1586s
s
 
. ...............3.2
Figure 3.1 Bodeplot of Non Reheated Turbine
System with PID (MZ-N) (No Droop)
3.1.2 Integral Model Controller
Tf = 10
0.014
0.1037 0.028s
s
  ............3.3
System with PID (IMC) (no droop)
3.1.2 Non Reheated With Droop
LFC-PID can also be tuned for the plant model
with droop characteristic, which is
3 2
250
15.88 42.46 106.2s s s   ............ 3.4
The model has a pair of complex poles at with
damping ratio 0.459. So the response is oscillatory.
We get the following PID controller:
PID controller:
For
45
0.45
o
b
br
 

0.987
0.732 0.136s
s
 
.......................... 3.5
System with PID (MZ-N) droop
Integral Model Controller
Tf = 10
1.14
1.081 0.125
s
 
……........... 3.6

System with PID (IMC) droop
They are very small which mean that the closed-
loop systems with the tuned PID controllers are quite
robust.
Both guarantee stability and performance of the
closed-loop system under parameter variations.
3.2 Reheated Turbine
Consider a power system with a reheated turbine.
The model Parameters are given by
3.2.1 REHEATED TURBINE WITHOUT
DROOPING
120(1.47 1)
(0.08 1)(0.3 1)(20 1)(4.2 1)
s
s s s s

    ..................3.7
By the LFC-PID design procedure discussed,
we get the following PID controller:
For
45
0.45
o
b
br
 

0.13
0.3983 0.303s
s
 
...............3.8
Figure 3.5 Bodeplot of Reheated Turbine System
with PID (MZ-N) Without droop
Tf = 10
0.076
0.7249 0.36
s
  ................3.9
Figure 3.6 Bodeplot of Reheated Turbine System
with PID (IMC)
3.2.2 REHEATED TURBINE WITH DROOP
LFC-PID can also be tuned for the plant model
with droop characteristic, which is
4 3 2
87.5 59.52
16.12 46.24 48.65 25.3
s
s s s s

    .................3.10
By the LFC-PID design procedure discussed,
we get the following PID controller:
For
2.349
1.904 0.385s
s
 
...............3.11
Figure3.7 Bodeplot of Reheated Turbine System
with PID (MZ-N) With droop
S.no Parameter Power
System
1
Speed Regulation due to
governor action R
(Hz/p.u.MW)
2.4
2
Electric System Gain(Kp)
(s) 120
3
Electric System Time
Constant(Tp) (s) 20
4
Turbine Time Constant
(Tt)(s) 0.4
5
Governor Time Constant
(Tg)(s) 0.08
6
Constant of Reheat
Turbine (Tr) (s) 4.2
7
Pecentage of power
generated in Reheat
Portion (c)
0.35

Tf = 10
1.132
2.823 0.37s
s
 
...........3.12
Figure3.8 Bodeplot of Reheated Turbine System
with PID (IMC) With droop
3.3 Hydro Turbine
Consider a hydro-turbine power system with the
following parameters
Table 3.3 Hydro Turbine System Parameters.
S.no
Parameter Power
System
1
Speed Regulation due to
governor action R
(Hz/p.u.MW)
0.05
2 Electric System Gain(Kp)(s) 1
3 Electric System Time
Constant(Tp)(s)
6
4 Hydro Turbine Time
Constant(Tw)(s)
0.4
5 Governor Time Constant
(Tg)(s)
0.5
3.3.1 Hydro Turbine without droop
3 2
1 4
2.4 13.6 8.2 1
s
s s s

   .......................3.13
For
45
0.45
o
b
br
 

0.059
0.6113 1.59s
s
  
.................3.14
Figure 3.9 Bodeplot of hydro Turbine System with
PID (MZ-N) Without droop
Tf = 10
0.068
0.3997 0.555s
s
  
................3.15
Figure3.10 Bodeplot of hydro Turbine System with
PID (IMC) Without droop
3.3.2 Hydro Turbine with droop
LFC-PID can also be tuned for the plant model with
droop Characteristic
The model has two unstable poles at 0.312 and 3.09.
We get the following PID controller:
The plant model with droop
Characteristic is basically unstable and requires two
degree freedom IMC for stabilizing the plant then
designing the parameters.
IV. CONCLUSION
The two tuned PID controllers achieve
comparable performance with a manual re-tuning.
For the tuned PID setting, the robustness measure of
the closed-loop systems with the tuned PID
controllers is less, which guarantees that the closed-
loop systems are reasonably robust. Stability and
performance of the closed-loop system under
parameter variation are guaranteed.
The individual use of controller can be extended
to multi-Area systems and stability and range of
application can be increased by application of two
degree freedom method IMC Design which can
stabilize an unstable system.
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