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miRNA-223-3p and let-7b-3p as potential blood biomarkers associated with the ischemic penumbra in rats

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Aliyu, Mr Sabo

International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.04, 2018 
17 
Anfis Coordination of Changes In Power Oscillation Damper Parameters with 
Variation In Power System Operating Point 
Dr I. I. Alabi 
Department of Electrical/Electronic Engineering 
Nigerian Defence Academy.  
Kaduna. Nigeria 
e-mail: alabiibitayo@yahoo.com 
Dr A. I. Araga, Mr Sabo Aliyu 
Department of Electrical/Electronic Engineering 
Nigerian Defence Academy.  
Kaduna. Nigeria 
e-mail: araga9393@gmail.com
 
 
Abstract—In this paper an Adaptive Neuro-Fuzzy Controller 
was designed to adaptively adjust the parameters of a power 
Oscillation Damper as the power system operating point 
changes due to change in operating point in a large 
interconnected Network fitted with FACTS device and Power 
Oscillation Damper. As a foundational work the generalized 
mathematic model of multi-machine power system with 
embedded FACTS was developes. The results obtained clearly 
reveals the effectiveness of this approach. 
Keywords-Neuro-Fuzzy Controller; Mathematic Model; 
Oscillation Damper; Interconnected Network 
I. INTRODUCTION 
Most of the FACTS based damping controllers belong to 
the PI (Proportional + Integral) type and work effectively in 
single machine system [1]. However, the performance of the 
above mentioned damping controllers deteriorates in multi-
machine power systems. The damping performance of the 
FACTS based damping controllers in multi-machine power 
systems can be improved by using fuzzy coordinated design 
[2]. Furthermore Power Oscillation Damper are designed for 
specific operating point, but operating point changes as 
demand changes for optimal performance the parameter of 
power oscillation damper must continually change with 
changes in operating point for this reason ANFIS is 
deployed to predict the future values of POD parameters 
based on large population of such parameters obtained from 
all possible operating scenarios. The structure of the 
proposed Adaptive Neuro Fuzzy coordinated controller is 
shown in Figure 1, where the inputs are speed deviation of 
synchronous machines and their acceleration. Thus, the 
conventional damping controllers are adaptively tuned by 
using ANFIS controllers.  
 
w
w
sT
sT
K
1 lag
lead
sT
sT


1
1
lag
lead
sT
sT


1
1
ANFIS
POD ADAPTIVE 
PARAMETER LEADT
LAGT
OPERATING
CONDITIONS
 𝑉𝑝𝑜𝑑  𝑖  
 𝑈 𝑖  
 𝑃𝑖  
𝑄𝑖  
𝑉 𝑖  
 
Figure 1. Proposed Adaptive POD Controller 
II. LITERATURE REVIEW 
An attempt has been made to apply hybrid neuro-fuzzy 
approach for the coordination between the conventional 
power oscillation damping (POD) controllers for multi-
machine power systems. With the help of MATLAB, a class 
of adaptive networks, that are functionally equivalent to 
fuzzy inference systems, is proposed. The proposed 
architecture is referred to as ANFIS (Adaptive Neuro-Fuzzy 
Inference System) [2]-[6]. An adaptive fuzzy inference 
system (ANFIS) based UPFC supplementary damping 
controller to superimpose the damping function on the 
control signal of UPFC for damping of power system 
electromechanical oscillations was proposed in [7]-[8]. 
The acronym ANFIS derives its name from adaptive 
neuro-fuzzy inference system. Using a given input/output 
data set, the toolbox function ANFIS constructs a fuzzy 
inference system (FIS) whose membership function 
parameters are tuned (adjusted) using either a back 
propagation algorithm alone, or in combination with a least 
squares type of method. This allows fuzzy systems to learn 
from the data they are modeling [8]. It has a network-type 
structure similar to that of a neural network. Thus, it maps 
inputs through input membership functions and associated 
DOI: 10.21307/ijanmc-2019-016
International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.04, 2018 
18 
parameters and then through output membership functions 
and associated parameters to outputs, can be used to 
interpret the input/output map. The parameters associated 
with the membership functions will change through the 
learning process. The computation of these parameters (or 
their adjustment) is facilitated by a gradient vector, which 
provides a measure of how well the fuzzy inference system 
is modeling the input/output data for a given set of 
parameters [9]-[10]. Once the gradient vector is obtained, 
any of several optimization routines could be applied in 
order to adjust the parameters so as to reduce some error 
measure (usually defined by the sum of the squared 
difference between actual and desired outputs) [11]-[12].  
III. PROPOSED METHOD 
A. Fuzzy System Modeling and Controller Philosophy 
 
             INPUT             OUTPUT
1x
nx
1y
 
ny
UNKNOWN SYSTEM
 
Figure 2. An unknown System as a Black Box 
In the unknown system in Figure 2 only a set of 
input,        and output        can be measured. The 
mathematical description relating the input to the output can 
be a mathematical formula, such as a mapping or a function 
that relates the input to the output in the form 
                      
   
            
or a set of differential equations in the form 
                     
  
                      
or a logical linguistic statement which can be quantified 
mathematically in the form: 
             IF (input    ) AND … AND (input    ) (3) 
THEN (output   ) AND …. AND (output   ) 
Fuzzy systems modeling is to quantify the logical form 
of equation (3.51) by using Fuzzy logic and the 
mathematical functional model of equation (3.49) or by 
using Fuzzy logic together with the differential equation 
model of equation (3.50). 
The fuzzy logic controller comprises of four stages: 
fuzzification, a knowledge base, decision making and 
defuzzification. The fuzzification interface converts input 
data into suitable linguistic values that can be viewed as 
label fuzzy sets. To obtain a deterministic control action, a 
defuzzification strategy is required. Defuzzification is a 
mapping from a space of fuzzy control actions defined over 
an output universe of discourse into a space of nonfuzzy 
(crisp) control actions. The defuzzification of the variables 
into crisp outputs is tested by using the weighted average 
method. 
After generating the fuzzy inference, the generated 
information describing the model’s structure and parameters 
of both the input and output variables are used in the ANFIS 
training phase. This information will be fine-tuned by 
applying the hybrid learning or the backpropagation 
schemes. The algorithm employed for ANFIS training is 
shown in Figure 3. 
International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.04, 2018 
19 
INVOKE THE COMMAND LINE 
ANFIS TRAINING ROUTINE AND 
PROVIDE THE FOLLOWING INPUT
ARGUMENT: EPOCH NUMBER, 
GENFIS OUTPUT, AND THE 
TRAINING DATA 
PLOT THE TRAINING DATA AND THE 
OUTPUT
IS OUTPUT 
SATISFACTORY ?
END
YES
INCREASE NO OF MEMBER 
FUNCTION AND EPOCH 
NUMBER
START
GENERATE
INPUT/
OUTPUT
TRAINING DATA
SET THE GENFIS INPUT PARAMETERS:NUMBER OF 
MEMBERSHIP FUNCTIONS, MEMBERSHIP FUNCTION 
TYPE e.t.c
NO
PLOT THE OUTPUT MEMBERSHIP
FUNCTION AND THE INPUT/OUTPUT
DATA
 
Figure 3. Flowchart of ANFIS Training 
 
IV. RESULTS AND DISCUSSIONS 
Power Oscillation Dampers were designed for UPFC 
embedded in two test case study systems: 
a) Kundur Two Area System 
b) Nigerian 330kV National Grid 
However the optimal performance of these PODs are 
only guaranteed at the particular operating points under 
consideration, but at any other operating points, different 
values of time constant must be determined for the damping 
to be effective 
A. Result of ANFIS Training (Test System 1) 
The training data and check data are generated by 
randomly varying the load (multiplying the load with a 
factor of 0.1) in the two areas of the test system. At each 
operating point the actual values of POD parameters 
          were calculated. The ANFIS parameter settings 
are as shown in Table 1. Fig 4 is the plot of training data and 
ANFIS output for lead time constant while Figure 5 is the 
graph of check data and ANFIS output for lead time constant. 
The plot of the error associated with the training is shown in 
Figure 6 for both the check data and training data. The 
corresponding plots for lag time constant are shown in 
Figures 7 to Figure 9. 
TABLE I. ANFIS PARAMETER SETTINGS 
numMFs 5 
mfType 'gbellmf' 
epoch_n 20 
 
International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.04, 2018 
20 
 
Figure 4. Training Data and ANFIS Output: Lead Time Constant 
 
 
Figure 5. Check Data and ANFIS Output: Lead Time Constant 
 
 
Figure 6. Prediction Error for Training Data and Check Data: Lead Time Constant 
 
3.79 3.8 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88
0.13
0.135
0.14
0.145
0.15
0.155
0.16
MODULUS OF EIGENVALUE
LE
AD
 T
IM
E 
CO
NS
TA
NT
PLOT OF TRAINING DATA AND ANFIS OUTPUT:LEAD TIME CONSTANT
 
 
TRAINING DATA
ANFIS OUTPUT
3.7 3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86 3.88 3.9
0.13
0.14
0.15
0.16
0.17
0.18
0.19
PLOT OF CHECK DATA AND ANFIS OUTPUT:LEAD TIME CONSTANT
LE
AD
 T
IM
E 
CO
NS
TA
NT
MODULUS OF EIGENVALUE
 
 
CHECK DATA
ANFIS OUTPUT
3.79 3.8 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88
-4
-2
0
2
4
x 10
-4 TRAINING DATA ERROR FOR LEAD TIME CONSTANT
ER
RO
R
MODULUS OF EIGENVALUE
3.7 3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86 3.88 3.9
-2
0
2
4
x 10
-4 CHECK DATA ERROR FOR LEAD TIME CONSTANT
ER
RO
R
MODULUS OF EIGENVALUE
International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.04, 2018 
21 
 
Figure 7. Training Data and ANFIS Output: Lag Time Constant 
 
Figure 8. Check Data and ANFIS Output: Lag Time Constant 
 
Figure 9. Prediction Error for Training Data and Check Data: Lag Time Constant 
B. Result of ANFIS Training (Test System 2) 
The data for training were obtained by randomly varying 
the load in different areas by a factor of 0.01 from low to 
medium and high values for about 500 scenarios, the data 
were divided into training data and check data. The lead-lag 
time constants were recorded as they change with operating 
conditions as well as the lead and lag time constants that 
provide the best damping under different operating 
conditions. The results obtained for lag time constant are as 
shown in Figures 10 to 12. Figure 13 to 14 are the 
corresponding results for lead time constant. Figure 15 is the 
graph of the input membership function while Figures 16 
and 17 are the graphs of the ANFIS adjusted membership 
function that gives the exact simulation of the training data 
for the lag time constant and lead time constant respectively. 
3.79 3.8 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88
0.44
0.45
0.46
0.47
0.48
0.49
0.5
0.51
0.52
0.53
MODULUS OF EIGENVALUE
LA
G 
TI
M
E 
CO
NS
TA
NT
PLOT OF TRAINING DATA AND ANFIS OUTPUT:LAG TIME CONSTANT
 
 
ANFIS OUTPUT
TRAINING DATA
3.7 3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86 3.88 3.9
0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
0.52
0.54
MODULUS OF EIGENVALUE
LA
G 
TIM
E C
ON
ST
AN
T
PLOT OF CHECK DATA AND ANFIS OUTPUT:LAG TIME CONSTANT
 
 
ANFIS OUTPUT
CHECK DATA
3.79 3.8 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88
-1
-0.5
0
0.5
1
x 10
-3 TRAINING DATA ERROR FOR LAG TIME CONSTANT
ER
RO
R
MODULUS OF EIGENVALUE
3.7 3.72 3.74 3.76 3.78 3.8 3.82 3.84 3.86 3.88 3.9
-5
0
5
10
x 10
-4 CHECK DATA ERROR FOR LAG TIME CONSTANT
ER
RO
R
MODULUS OF EIGENVALUE
International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.04, 2018 
22 
 
 
Figure 10. Plot of ANFIS Data and Training Data: Lag Time Constant 
 
 
Figure 11. Plot of ANFIS Data and Check Data: Lag Time Constant 
 
 
Figure 12. Prediction Error for Training Data and Check Data 
 
3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89
0.215
0.22
0.225
0.23
MODULUS OF EIGENVALUE
LA
G 
TI
M
E 
CO
NS
TA
NT
PLOT OF TRAINING DATA AND ANFIS OUTPUT:LAG TIME CONSTANT
 
 
TRAINING DATA
ANFIS OUTPUT
3.8 3.85 3.9 3.95
0.205
0.21
0.215
0.22
0.225
0.23
0.235
MODULUS OF EIGENVALUE
LA
G 
TI
M
E 
CO
NS
TA
NT
PLOT OF CHECK DATA AND ANFIS OUTPUT:LAG TIME CONSTANT
 
 
ANFIS OUTPUT
CHECK DATA
3.8 3.85 3.9 3.95
-4
-2
0
2
4
x 10
-4 CHECK DATA ERROR FOR LAG TIME CONSTANT
ER
RO
R
MODULUS OF EIGENVALUE
3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89
-1
-0.5
0
0.5
1
x 10
-4 TRAINING DATA ERROR FOR LAG TIME CONSTANT
ER
RO
R
MODULUS OF EIGENVALUE
International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.04, 2018 
23 
 
Figure 13. Plot of ANFIS Output and Training Data: Lead Time Constant 
 
Figure 14. Plot of ANFIS Data and Check Data: Lead Time Constant 
 
Figure 15. Prediction Error for Training Data and Check Data 
 
Figure 16. Input Membership Function 
3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89
0.0805
0.081
0.0815
0.082
0.0825
0.083
0.0835
0.084
0.0845
0.085
0.0855
MODULUS OF EIGENVALUE
LE
AD
 TI
ME
 C
ON
ST
AN
T
PLOT OF TRAINING DATA AND ANFIS OUTPUT:LEAD TIME CONSTANT
 
 
ANFIS OUTPUT
TRAINING DATA
3.8 3.85 3.9 3.95
0.078
0.08
0.082
0.084
0.086
0.088
0.09
MODULUS OF EIGENVALUE
LE
AD
 T
IM
E 
CO
NS
TA
NT
PLOT OF CHECK DATA AND ANFIS OUTPUT:LEAD TIME CONSTANT
 
 
ANFIS OUTPUT
CHECK DATA
3.8 3.85 3.9 3.95
-2
0
2
4
x 10
-4 CHECK DATA ERROR FOR LEAD TIME CONSTANT
ER
RO
R
MODULUS OF EIGENVALUE
3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89
-1
-0.5
0
0.5
1
x 10
-4 TRAINING DATA ERROR FOR LEAD TIME CONSTANT
ER
RO
R
MODULUS OF EIGENVALUE
5.422 5.424 5.426 5.428 5.43 5.432 5.434 5.436
0
0.2
0.4
0.6
0.8
1
INPUT: MODULUS OF EIGENVALUES
DE
GR
EE
 O
F M
EM
BE
RS
HI
P
in1mf1 in1mf2 in1mf3 in1mf4 in1mf5
International Journal of Advanced Network, Monitoring and Controls          Volume 03, No.04, 2018 
24 
 
Figure 17. ANFIS Adjusted Membership Function: Lag Time Constant 
 
Figure 18. ANFIS Adjusted Membership Function: Lead Time Constant 
 
V. CONCLUSION 
In this work an adaptive neuro fuzzy controller has been 
developed for the purpose of coordinating the changes in 
power oscillation damper parameters with variation in power 
system operating point. The accuracy with which the 
controller was able to predict the values of POD parameters 
clearly reveals the effectiveness of the proposed approach. 
 
REFERENCES 
[1] Chia, B.H.K., S. Morris and P.K. Dash, 2004. “A Fuzzy-Feedback 
Linearizing Nonlinear Control of CSI Based STATCOM for 
Synchronous Generator Stabilization”, Proceedings of the IEEE 
International Conference on Control Applications, vol. 2, September, 
pp 1473-1478. 
[2] External Neuro-control for a Series Capacitive Reactance 
Compensator Based on a Voltage Source PWM Converter in 
Damping Power Oscillations”, IEEE Transactions on Industrial 
Electronics, vol. 54, no. 1, February 2007, pp. 77-85. 
[3] J. R. Jang, “ANFIS Adaptive-netwok-Based Fuzzy Inference 
System”, IEEE Transactions on Systems, Man and Cybernetics, vol. 
23, no. 3, 1993, pp. 665-685. 
[4] S. P. Ghoshal, “Multi-Area Frequency and Tie-Line Power Flow 
Control with Fuzzy Logic Based Integral Gain Scheduling”, IE (I) 
Journal-EI, vol. 84, December 2003, pp. 135-141. 
[5] Fuzzy Logic Toolbox—for Use with Matlab, The Mathworks Inc, 
1999. 
[6] T. R. Sumithira and A. Nirmal Kumar, “Elimination of Harmonics in 
Multilevel Inverters Connected to Solar Photovoltaic Systems Using 
ANFIS: An Experimental Case Study”, Journal of Applied Research 
and Technology, vol. 11, no. 1, February 2013, pp. 124-132. 
[7] Jyh-Shing Roger Jang.: ‘ANFIS: Adaptive-Network-Based Fuzzy 
Inference System’, IEEE Trans. Syst. Man and Cyber., 23, (3), 
1993,pp. 665-685 
[8] E.V. Larsen, Juan.J, Sanchez-Gasca and Chow.J.H.‘Concept for 
design of FACTS controllers to damp power swings’, IEEE 
Transactions 1995,PWRS-2 (10), pp.948-956. 
[9] C R Houck,  J Joines and M Kay.” Genetic Algorithm Optimization 
Toolbox, User’s Manual”  Version 5.0, 1996 
[10] Jang, J.-S. R. and N. Gulley, "Gain scheduling based fuzzy controller 
design," Proc. of the International Joint Conference of the North 
American Fuzzy Information Processing Society Biannual 
Conference, the Industrial Fuzzy Control and Intelligent Systems 
Conference, and the NASA Joint Technology Workshop on Neural 
Network and Fuzzy Logic, San Antonio, Texas, Dec. 1994. 
[11] Jang, J.-S. R. and C.-T. Sun, "Neuro-fuzzy modeling and control, 
Proceedings of  the IEEE, March 1995. 
[12] Jang, J.-S. R. and C.-T. Sun, Neuro-Fuzzy and Soft Computing: A 
Computational Approach to Learning and Machine Intelligence, 
Prentice Hall, 1997. 
[13] Kaufmann,  A. and M.M. Gupta, Introduction to Fuzzy Arithmetic, 
V.N. Reinhold, 1985. 
 
 
5.422 5.424 5.426 5.428 5.43 5.432 5.434 5.436
0
0.2
0.4
0.6
0.8
1
INPUT: MODULUS OF EIGENVALUES
DE
GR
EE
 O
F 
M
EM
BE
RS
HI
P
in1mf1 in1mf23 45
ADJUSTED MEMBERSHIP FUNCTIONS: LAG TIME CONSTANT
5.422 5.424 5.426 5.428 5.43 5.432 5.434 5.436
0
0.2
0.4
0.6
0.8
1
INPUT: MODULUS OF EIGENVALUES
DE
GR
EE
 OF
 ME
MB
ER
SH
IP
in1mf1in1mf2in1mf3 in1mf4 5
ANFIS ADJUSTED MEMBERSHIP FUNCTION: LEAD TIME CONSTANT


Anfis Coordination of Changes In Power Oscillation Damper Parameters with Variation In Power System Operating Point

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