An Adaptive Internal Model for Load Frequency Control using Extreme Learning Machine

TELKOMNIKA, Vol.16, No.6, December 2018, pp.2879~2887
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v16i6.11553  2879
Received August 6, 2018; Revised October 2, 2018; Accepted October 31, 2018
An Adaptive Internal Model for Load Frequency Control
using Extreme Learning Machine
Adelhard Beni Rehiara*1
, He Chongkai2
, Yutaka Sasaki3
, Naoto Yorino4
, Yoshifumi Zoka5
1,2,3,4,5
Graduate School of Engineering, Hiroshima University Higashi-Hiroshima, Japan
1
Electrical Engineering, University of Papua Manokwari, Indonesia
*Corresponding author, e-mail: ab-rehiara@hiroshima-u.ac.jp
Abstract
As an important part of a power system, a load frequency control has to be prepared with a
better controller to ensure internal frequency stability. In this paper, an Internal Model Control (IMC)
scheme for a Load Frequency Control (LFC) with an adaptive internal model is proposed. The
effectiveness of the IMC control has been tested in a three area power system. Results of the simulation
show that the proposed IMC with Extreme Learning Machine (ELM) based adaptive model can accurately
cover the power system dynamics. Furthermore, the proposed controller can effectively reduce the
frequency and mechanical power deviation under disturbances of the power system.
Keywords: IMC, MPC, ELM, LFC, power system.
Copyright © 2018 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
In the power system operation, deviation of frequency would be a critical issues since
the deviation could cause many troubles to devices connected to the power system. It is
reported that the frequency change will affect operation and speed control of both synchronous
and asynchronous motors, increase reactive power consumption and furthermore degrade load
performance,overload transmission lines, and finally interfere system protection. An LFC is a
main part of a power system to minimize frequency variation by maintaining power exchange
between power system areas. Some works have been done in the area of LFC [1-9],
including [1] designed a model predictive control (MPC) based LFC for a multi-area power
system considering wind turbines operation, [2] compare MPC and PI performance against a
conventional AGC system, [3] presented fuzzy controller for LFC of three area power system
and recently [4] discussed a new LFC method for multi-area power system.
Internal Model Control (IMC) is a well-established control structure and it is widely
applied in process control applications. An IMC incorporates a plant model into its structure as
an internal model so that the controller output will be based on the difference between internal
model and plant output. Morari in [10] has proved that the controller has dual stability,
zero offset, and perfect control properties. Since plant models are mostly linearized models, it is
almost impossible for an IMC to be a perfect control. An adaptive model will be a solution to be
close to the “perfect control” since it can be updated in a certain time to do corrections for the
existing model. Many previous researches have succeeded to apply the adaptive model into a
controller i.e. PI/PID [10-13], Fuzzy controller [14], or MPC [15].
Since introduced a decade before, extreme learning machine (ELM) has been used in
many cases and applications. It has accurate predictions in short time training compared to its
ancestor which is a feed-forward neural network. An adaptive internal model has been
introduced in [7] using prediction error minimization (PEM) algorithm. Due to time-consuming,
this method is not appropriated to be used in an online application. Therefore, an ELM with its
features is a good candidate to replace the PEM method. In this paper, an ELM based adaptive
IMC controller is built by employing an internal model in an adaptive scheme and an MPC as
the main controller to control a load frequency of a power system.

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TELKOMNIKA Vol. 16, No. 6, December 2018: 2879-2887
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2. Research Method
2.1. Model Predictive Control
MPC is an advanced control method that used a plant model to predict the optimal
movement of the plant. A Laguerre based MPC would be a solution for online computation
compare to classical MPC [16, 17]. In addition, a Laguerre based MPC can increase the
feasible region of the optimization problem [16]. Accurate approximation of control signal Δu
may need many parameters that cause poor numerical solutions and heavy computational load
when classical MPC is implemented in rapid sampling, complicated process dynamics and/or
high demand on closed-loop performance [16, 17].
The discrete Laguerre function is transformed from its original using invert
z-transformation as shown in (1). The Laguerre function vector and initial condition
shown in (2) and (3) respectively [6, 8, 17].
1
11
1
11
21
)(














N
az
az
az
a
z
N
(1)
)()1( kL
l
AkL  (2)
T
NaNaaa
T
L



  11)1(321)0(  (3)
Minimization of output errors for m sampling instant is done by taking a minimal solution
of an objective function J as in (4). Closed loop feedback control with optimal gain Kmpc (6) is
formulated in (5) and receding horizon control law is realized in (7).
 R
T
Np
m
kmkQxTkmkxJ 


1
)|()|( (4)
)()()1( kxBKAkx mpc (5)
 1
)0( T
mpc LK (6)
xKu mpc (7)
where,
0 0 0 0
0 0 0
0 0
2 0
0
2 3 4
a
a
a a
A
l a a a
N N N N Na a a a a

 
  
   
 
 
 
 
 
 
 
 
 
 
  



      
 1

L
T
RmNp
m Qm   )(1 )( 
m
ANp
m Qm  1 )(

TELKOMNIKA ISSN: 1693-6930 
An Adaptive Internal Model for Load Frequency Control... (Adelhard Beni Rehiara)
2881
The parameters of N, a, Al and L are the length of Laguerre network, time scaling factor,
a Toeplitz matrix with α = (1-a2), and Laguerre function’s state vector respectively. The matrices
of Q  ns x ns and R  ni x ni are weighting matrices, η  ns x N is the parameter vector of N
Laguerre function and  is a Hessian matrix. Np is the number of prediction horizon and Δu is a
vector of the control parameter.
2.2. Internal Model Control
An internal model that placed into a normal closed-loop control system, including
controller, plant and/or sensor, may perform Internal Model Control systems as shown in
Figure1. The difference between signal correction ŕ and set-point r is the command to the
controller to signal u to the plant. Control law applied for the IMC control can be written as
follows [18].
mdGQPQry )1(  (8)
mQdQru  (9)
mdGQrPQe )1()1(  (10)
The difference between IMC and the classical controller is that an IMC will correct the
actual output before it is fed back. An IMC can use the internal model to predict the future output
of the plant and also to make correction of the output. It can also work with another controller to
control a plant [10], to tune other controller [19], or to combine with the other controller such as
PI/PID[13, 18-22], Fuzzy controller [14, 23], Neural Network [24] or MPC [15, 24, 25].
An adaptive IMC controller refers to a model and/or controller that can be updated in a
certain time. By tuning a proper gain to the model and/or controller following the disturbance,
the controller can be adaptive to the disturbance. In order to perform adaptive scheme of an
IMC, another block for system identification should be presented inside the IMC structure as
appeared in the dotted block of Figure1.
Figure 1.IMC principle
2.3. Extreme Learning Machine
An ELM is basically a single hidden layer feed-forward neural network (SLFN) which
has an excellent training algorithm. Input weight and hidden layer biases are not necessarily
adjusted and those can be chosen arbitrarily in this algorithm. Then the output weight of the
SLFNs can be determined by a generalized inverse operation of the hidden layer output
matrices. In fact, this procedure has been fastening this algorithm.
Plant P
dm
Controller Q XX
XModel G
yr u
ym
ŕ
-
-
+
+
++

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For a given ñ training set samples (xj, tj) where xj=[xj1, xj2,…, xjñ]T and tj=[tj1, tj2,…, tjñ]T,
an SLFN with Ñ hidden neurons and activation function g(x) is expressed as [26, 27]
  

N
i
N
i
jijiiji njobxwgxg
~
1
~
1
'' ~...,,2,1,)()(  (11)
where wi=[wi1, wi2,…, wiñ]T, β’i=[β’i1, β’i2,…, β’iñ]T, bi, and oj are the connecting weight of
ith hidden neuron to input neuron, the connecting weights of the ith hidden neuron to the output
neurons, the bias of the ith hidden node, and the actual network output with respect to input xj
respectively. Because the standard SLFN can minimize the error between tj and oj, (11) can be
rewritten as follows.


N
i
jijii njtbxwg
~
1
' ~...,,2,1,)( (12)
In simple (12) can be Hβ’=T so that the output weight matrix β’ can be solved by least
square solution as in (13).
β’=H†
T (13)
The hidden layer output matrix H and the network output T are formulated as follows.
 













)()(
)()(
,
~~~1~1
~1~111
NnNn
NN
ii
bxwgbxwg
bxwgbxwg
bwH



, and











T
n
T
t
t
T
~
1
 (14)
2.4. Proposed Controller
As proposed in this research, an adaptive model will be used to provide an updated
model of the plant. The adaptive model is generated by using a classification based extreme
learning machine (ELM) algorithm by utilizing input and output data. The proposed controller
uses MPC controller as its main controller combining with an adaptive ELM model as the
internal model. The complete block diagram of the proposed controller is shown in Figure 2.
The ELM model was trained using controller output ∆u and frequency deviation ∆f as input and
output data respectively. After trained, the ELM model is used to predict frequency deviation ∆f
for a given controller signal ∆u. The algorithm for simulation is written in Algorithm 1.
Algorithm 1 : Adaptive IMC
1. set disturbances and noises
2. configure ELM model
3. for j=1 to simulation time
4. ⁞
5. for i=1 to n-area
6. calculate ∆u
7. update state matrix ∆ẋi
8. train ELM model
9. predict ELM output ∆ymi
10. calculate ∆ẏi=∆yi-∆ymi
11. ⁞
12. end
13. end
Rotating
Mass
∆PL
~
MPC
Controller
Model
Identification
X
Adaptive
ELM Model
∆f
∆fmf
-
+
+
-
+
+
Governor &
Turbine
∆Ptie
β
∆f/R
-
∆Ptie
∆u
-
+
Figure 2.Proposed Adaptive IMC Scheme
2.5. Power system model
A model of power system dynamics can be redrawn in Figure 3. The frequency
deviation of the power system, including tie-line power interchange, is expressed as follows.

2883
Controller
iACE
itieP ,
if
i
s
2
 ij
T
 
i
f
ij
T
ii DsH 2
1
1
1
, sT it
1
1
, sT ig
iR
1
imP ,
iLP ,
iCP ,
+
_
+
_
+
+
_
+ +
imP , g,i
Figure 3. Power system dynamics






  itieiiiLim
i
i
PfdPP
H
f ,,,
2
1 (15)
The prime mover Pm, governor output Pg, tie-line power interchange Ptie are for n areas
are formulated in (16-18). Area Control Error (ACE) is chosen as the controller input which is the
result of frequency f and tie-line power changes within a control area of the power system
defined in (19) [1].
im
it
ig
ig
im P
T
P
T
P ,
,
,
,
,
11 





















 (16)










 

 ig
i
i
iC
ig
ig P
R
f
P
T
P ,,
,
,
1 (17)












 





n
ij
j
n
ij
j
f jTijf iTijP itie
1 1
2,  (18)
iiitiei fPACE  , (19)
where PL,i is the load/disturbance, PC,i is the controller output, Hi is the equivalent inertia
constant, di is the damping coefficient, Ri is the speed droop characteristic and βi is the bias of
frequency. Tij is the tie-line synchronizing coefficient between area i and j, Tg,i is the governor
time constants and Tt,i is the turbine time constants of area i.
3. Results and Analysis
3.1. Simulation
The power system configuration for testing the proposed controller is based on [6, 8]
with the parameters as shown in Table 1 while the system dynamics are figured in Figure 4.
Simulations were done in two cases and the simulation setup is configured in Table 2, where
step and random disturbance are imposed on the load in all area. The random disturbance
implies load changes of white noise with a maximum 0.1 pu while step disturbance is assumed
as load change in constant for a certain time.

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Figure 4. Three-area power system
configuration
Table 1. Three Area Power System Parameters
Area
d
[pu/Hz]
2H
[pu s]
R
[Hz/pu]
Tg
[s]
Ti
[s] [pu/Hz]
Tij
[pu/Hz]
1 0.015
0.166
7
3.00 0.08 0.40 0.3483
T12=0.20
T13=0.25
2 0.016
0.201
7
2.73 0.06 0.44 0.3827
T21=0.20
T23=0.12
3 0.015
0.124
7
2.82 0.07 0.30 0.3692
T31=0.25
T32=0.12
Table 2. Simulation Setup
Case
Step
Disturbance [pu]
Random
Disturbance [pu]
I 0.2 0.1
II 0.2 -
A Laguerre function based MPC controller is built to control a three area power system
frequency. To ensure the MPC stability, the scaling factor a is tuned to 0.1 while network lengths
N is set to 4 for each area controller. The model will be updated each second with the
input-output data using ELM method. Overall simulation responses of frequency and
mechanical power deviation for both existing and proposed controller are plotted
in Figures 5 and 6.
3.2. Discussion
The controller performance is evaluated based on system responses and signal
measures. Standard deviation is also provided to indicate how sensitive the controller to
response the errors.
For the system responses based evaluation, overshoot and standard deviation are
analyzed and the results are provided in Table 3 as well as its visual in Figure 7 and 8 based on
system responses in Figure 5 and 6. According to the figures and table, it can be simply known
that the proposed controller has very good response overshoot of frequency and mechanical
power compared to the existing MPC controller in all areas of both cases. On the other hand,
the proposed controller slightly aggressive to the disturbances as shown in high standard
deviations in some areas and cases. These are the evidence that the proposed controller can
accurately cover the power system dynamics and also it shows the ability to increase controller
performance by sending proper feedback to the controller by utilizing the adaptive model.
By the treatment as same as in the case I, the other adaptive internal model for LFC
application introduced in [7] has overshoot responses 0.1465, 0.1729, and 0.1652 and standard
deviation 0.0294, 0.0443, and 0.0278 for area 1-3 respectively. Compared to the proposed
controller, it is proved that the proposed controller has smaller overshoot and higher standard
deviation compared. These are the indications that the proposed controller is more active to
maintain the frequency change during the simulation and so it only has a small overshoot on the
simulation.
Table 3. Frequency and Mechanical Power Deviation Analysis
Area
Frequency Deviation Mechanical Power Deviation
MPC Cases
Adaptive IMC
Cases
MPC Cases
Adaptive IMC
Cases
I II I II I II I II
Overshoot
1 0.1346 0.2190 0.0923 0.2047 0.3437 0.3401 0.3080 0.3109
2 0.0860 0.1162 0.0407 0.1147 0.4164 0.4165 0.3473 0.3484
3 0.1374 0.2530 0.1259 0.2384 0.4605 0.4625 0.4318 0.4340
Standard
Deviation
1 0.1762 0.1967 0.1767 0.1946 0.0372 0.0428 0.0442 0.0814
2 0.1786 0.1838 0.1795 0.1842 0.0418 0.0432 0.0354 0.0514
3 0.1714 0.2012 0.1714 0.1976 0.0522 0.0580 0.0450 0.0738
G1
Load1
G2
Load2
G3
Load3
Tie-line
Area 2
Area 1
Area 3

2885
(a) (b)
Figure 5. MPC controller responses (a) case i and (b) case II
(a) (b)
Figure 6. Adaptive IMC controller responses (a) case i and (b) case ii
Figure 7. Frequency deviation Figure 8. mechanical power deviation
0
0.05
0.1
0.15
0.2
0.25
0.3
Overshoot1 Overshoot2 Overshoot3 Std. Dev.1 Std. Dev.2 Std. Dev.3
Existing Controller Case I Case II Proposed Controller Case I Case II
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Overshoot1 Overshoot2 Overshoot3 Std. Dev.1 Std. Dev.2 Std. Dev.3
Existing Controller Case I Case II Proposed Controller Case I Case II

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The signal measured based evaluation of the proposed controller including Integral of
the absolute value of the error (IAE), Integral of the square value of the error (ISE) and Integral
of the time-weighted absolute value of the error (ITAE) are provided in Table 4. It is shown that
the proposed controller has small errors in IAE and ITAE index while it has high deviation in the
ISE index in both cases. These are the validation that the proposed controller has no persisting
high errors and it adaptively follows the load changes in the simulation.
The specifications of the machine to run the simulation runs are Intel Core i7 2.9 GHz
CPU and 16 GB RAM using MatLab 2016a under Windows 10 environment. CPU time for both
cases of MPC, and case I and II of adaptive IMC are 1.5509, 1.5446, 6.6927 and 6.4599
seconds respectively. It seems like the proposed controller will need time 4 times longer than
the existing controller since it needs to build its own model in a certain period which is in this
cases every second. This may not degrade the performance in real operation since the CPU
time is still littler than simulation setting time.
Table 4. Controller Index Analysis
Area
MPC Adaptive IMC
IAE ISE ITAE IAE ISE ITAE
Case I
1 1.9340 0.6858 10.6362 1.9039 0.6900 10.1068
2 1.6508 0.7028 6.9319 1.6532 0.7118 6.8517
3 2.1407 0.6593 14.1713 2.0966 0.6589 13.4449
avg 1.9085 0.6827 10.5798 1.8846 0.6869 10.1345
Case II
1 2.2608 0.7425 15.0622 2.2289 0.7444 14.4818
2 1.6748 0.7204 6.8818 1.6792 0.7297 6.8696
3 2.6418 0.7685 20.5055 2.5884 0.7626 19.6189
avg 2.1924 0.7438 14.1498 2.1655 0.7456 13.6567
4. Conclusion
A novel adaptive IMC controller based on ELM method has been introduced in this
paper. A three area power system is chosen to validate the controller in handling load frequency
control including step and random disturbance. Simulation results show that the proposed
controller presents superior responses in all areas of both cases compared to the existing MPC
controller.
Acknowledgments
The first author wishes to acknowledge the support of Papua University as well as the
Indonesian Ministry of Research, Technology and Higher Education Directorate via General of
Higher Education for his study and research in Hiroshima University.
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