Voltage Sag and Swell Estimation Using ANFIS for Power ...
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한국철도학회논문집 제16권 제4호 ■ pp. 272-277 (2013년 8월)
JOURNAL OF THE KOREAN SOCIETY FOR RAILWAY VOL.16, NO.4 ■ pp.272-277 (August 2013)
ISSN 1738-6225(Print)
ISSN 2288-2235(Online)
Voltage Sag and Swell Estimation Using ANFIS for
Power System Applications
N. Malmurugan·Devarajan Gopal*·Young Hwan Lho
1. Introduction
Power quality has become a main area of interest in the
power engineering research community. Voltage sags and
swells cause severe damage to the subsystems of power sys-
tems and can subsequently bring the entire power system to
halt mode. Voltage sag is a decrease to between 0.1 and 0.9 pu
in RMS (Root Mean Square) voltage or current at the power
frequency for a duration of 0.5 cycles to 1 minute and voltage
swell is an increase to between 1.1 pu and 1.8 pu in RMS volt-
age or current at a power frequency duration from 0.5 to 1
minute [1]. Table 1 shows the categories and characteristics of
power system electromagnetic phenomena [2]. These sags and
swells are mainly due turn on/turn off operations of supply
lines and flow of inrush current during starting of different
loads, etc. [2]. Turn on/turn off can happen either from the sup-
ply or load side. In addition, lightning strikes and EMI (elec-
tromagnetic interference) can cause momentary acceleration of
sags/swells. Numerous solutions have been proposed to mit-
igate sags and swells, including use of a dynamic voltage
restorer that injects voltage in series with supply lines when
any sags or swells are detected. Experimental investigation of
voltage sag mitigation by an advanced static Var compensator
has been extensively discussed in [3]. The RMS voltage mea-
surement method is generally used to detect sag and swell
before any mitigation technique is employed. The main draw-
back of the RMS voltage measurement is that the RMS voltage
is measured through voltage sensors and fed to the ADC of the
microcontroller or DSP to be converted into a digital signal,
and the data that are used are therefore based on old data that
are system dependent.
The disadvantages associated with the RMS method are dis-
cussed in [4-5]. Also, power quality surveys show that voltage
sags are considered the dominant factor affecting power quality
[6]. Rapid sag detection [7] has been achieved through the use
of a nonlinear adaptive filter. The authors reported that the fil-
ter can track the amplitude of the sag in real time, which would
be highly useful for sag and swell mitigation. Comparisons of
statistical methods and wavelet energy coefficients for deter-
mining two common PQ disturbances of sag and swell are pre-
sented in [8]. A novel sag detection method [9] for a line-
interactive dynamic voltage restorer (DVR) has also been pre-
sented. However, none of the authors used ANFIS (Adaptive
Network based Fuzzy Inference System) with different mem-
bership function types that can detect the RMS voltage in real
Abstract Power quality is a term that is now extensively used in power systems applications, and in this context the volt-
age, current, and phase angle are discussed widely. In particular, different algorithms that are capable of detecting the volt-
age sag and swell information in a real time environment have been proposed and developed. Voltage sag and swell play an
important role in determining the stability, quality, and operation of a power system. This paper presents ANFIS (Adaptive
Network based Fuzzy Inference System) models with different membership functions to build the voltage shape with the
knowledge of known system parameters, and detect voltage sag and swell accurately. The performance of each method has
been compared with each other/other methods to determine the effectiveness of the different models, and the results are pre-
sented.
Keywords : Voltage sag and swell, ANFIS, Power quality, Power system applications
*Corresponding author.
Tel.: +91-94437-78825, E-mail: [email protected]
©The Korean Society for Railway 2013
http://dx.doi.org/10.7782/JKSR.2013.16.4.272
Table 1 Characteristics of electromagnetic phenomena of power
systems
Categories Typical durationTypical
magnitude
InstantaneousSag 0.5-30 cycles 0.1-0.9 pu
Swell 0.5-30 cycles 1.1-1.8 pu
Momentary
Interruption 0.5-3 sec. < 0.1 pu
Sag 0.5-3 sec. < 0.1 pu
Swell 0.5-3 sec. 1.1-1.8 pu
Temporary
Interruption 3 sec.-1 min. < 0.1 pu
Sag 3 sec.-1 min. 0.1-0.9 pu
Swell 3 sec.-1 min. 1.1-1.8 pu
Voltage Sag and Swell Estimation Using ANFIS for Power System Applications
한국철도학회논문집 제16권 제4호(2013년 8월) 273
time if the voltage system amplitude and frequency are known.
The present paper discusses different methods to alter the volt-
age shape and then to detect voltage sags and swells at dif-
ferent operating conditions. In addition, a description of
ANFIS and voltage sag and swell detection algorithms are pre-
sented, and the results of performance evaluations of different
methods are compared.
2. Necessity of Initial Voltage Measurement
Voltage measurement is an essential step to develop a math-
ematical model for the voltage profile. A 3 phase power quality
analyzer was used to measure the voltage over one electrical
cycle, which can then be employed to model different math-
ematical equations. The measured voltage for two electrical
cycles is shown in Fig. 1 and the corresponding data are shown
in Table 2. Voltage was recorded for a 5 minute duration and
the results are shown in Fig. 2.
Fig. 1 Voltage for two electrical cycles
Fig. 2 Voltage RMS for 5 min.
3. Adaptive Network Based Fuzzy
Inference System
ANFIS refers to the Sugeno Adaptive Network Based Fuzzy
Inference System (ANFIS) [10]. Here, the fuzzy inference sys-
tem under consideration has two inputs, time (t) and voltage
(V), and one-output predicted voltage (VP). Each input has nine
membership functions. The rule base contains eighty fuzzy
Takagi and Sugeno type if-then rules. The corresponding
ANFIS architecture is shown in Fig. 3.
Fig. 3 Structure of ANFIS
The ANFIS network is formed with five layers. Explanations
of the layers are respectively given below.
Layer 1: In this layer, each input has 9 membership func-
tions. The output of input membership function 1 is
Ok1 = µAk(t) and the output of input membership function 2 is
Ok2 = µBk(t), where time and voltage are the inputs. Ak and Bk
are the linguistic labels (mf1, mf2,…, mf9) associated with the
node functions.
The output of the input membership functions specifies the
variables of the t and V, and satisfies the quantifier Ak. In this
work the triangular shaped membership function µAk(t) is used
with a maximum equal to 1 and a minimum equal to 0. The
generalized triangular membership function of the flux linkage
is given by
Table 2 Voltage from real time measurement
Time (ms) Voltage (V) Time (ms) Voltage (V)
0 0 10 0
1 72.928 11 -72.928
2 138.7173 12 -138.7173
3 190.928 13 -190.928
4 224.4493 14 -224.4493
5 236 15 -236
6 224.4493 16 -224.4493
7 190.928 17 -190.928
8 138.7173 18 -138.7173
9 72.928 19 -72.928
N. Malmurugan·Devarajan Gopal·Young Hwan Lho
274 한국철도학회논문집 제16권 제4호(2013년 8월)
(1)
Similarly, the generalized triangular shaped membership
function of the current is given by
(2)
where ak, bk, and ck are adaptable variables known as param-
eters. As the values of these parameters change, the triangular
shaped functions vary accordingly, thus exhibiting various
forms of membership functions.
Layer 2: It implements the fuzzy AND operator, as in Eq.
(3).
(3)
where k = 1, 2,…, 9
Layer 3: It acts to scale or normalize the firing strengths, as
shown in Eq. (4).
(4)
Layer 4: The output of the fourth layer comprises a linear
combination of the inputs multiplied by the normalized firing
strength. The output of this layer is given by Eq. (5).
(5)
where is the output of layer 3 and the modifiable variables
mk, nk and rk are known as consequent parameters.
Layer 5: Layer 5 is a simple summation of the outputs of
layer 4. The overall output gives the rotor position (θ).
(6)
4. Sag/Swell Detection Algorithm
Each algorithm has respective capabilities to predict the volt-
age and is used to detect voltage sags and swells very quickly.
The step by step procedure for detecting the sag and swell is
presented below and a corresponding flow chart is given in
Fig. 4.
1) Start the algorithm for sag and swell
2) Identify the zero crossing point of the voltage
3) If the voltage magnitude is positive, then move to step 4,
else go to step 1
4) Start the counter count = count + 1
5) If the counter reaches the max value, reset the counter and
move to step 4, else go to step 6
6) Implement any one of the following functions
7) Calculate the sag/swell as per Table 1 and display the
results
Fig. 4 Sag/swell detection algorithm
5. Results and Discussion
The ANFIS models have been developed by MATLAB/
Simulink, wherein input and output data are fed to the ANFIS
model. Initially we considered a 9×9 triangular membership
µAkt( )
0 t ak
<
t ak
–
bk
ak
–-------------- a
kt b
k<≤
ck
t–
ck
bk
–-------------- b
kt c
k<≤
0 ck
t≤⎩⎪⎪⎪⎪⎨⎪⎪⎪⎪⎧
=
µBkt( )
0 V ak
<
V ak
–
bk
ak
–-------------- a
kV b
k<≤
ck
V–
ck
bk
–-------------- b
kV c
k<≤
0 ck
V≤⎩⎪⎪⎪⎪⎨⎪⎪⎪⎪⎧
=
Wk
µAkt( ) µB
kv( )×=
Wk
Wk
Wk
k 1=
9
∑
---------------=
Ok4
Wk fk Wk mkt n
kV r
k+ +( )= =
Wk
Ok5
Wk fk∑
Wkfk
k
∑
Wk
k
∑----------------= =
Voltage Sag and Swell Estimation Using ANFIS for Power System Applications
한국철도학회논문집 제16권 제4호(2013년 8월) 275
function and obtained the results. The rule viewer and surface
viewer for the 9×9 membership function are presented in Fig.
5 (a) and (b), respectively. Voltage RMS of 236V for different
degrees of voltage sags/swells are shown in Fig. 6 (a)-(e).
Similarly, 9×9 membership functions of trapezoidal, bell,
gaussian, and sigmoid functions have been implemented and
the results were obtained. From the results, the 9×9 triangular
membership function outperforms all other membership func-
tions, and the results are presented in Table 3. For example,
when the time is 8 msecs and the input voltage is 138.71 volts,
the absolute error computed by ANFIS using the triangular
membership function is -0.2774. Similarly, for ANFIS using
9×9 membership functions using trapezoidal, bell, gaussian,
and sigmoid functions, absolute error of -1.3872, -4.6096,
-18.9423, and -19.1315, respectively, is produced. The results
of all other inputs are shown in Table 1, and the absolute volt-
age error due to triangular, trapezoidal, bell shape, gaussian,
and sigmoid functions vs. time for one electrical cycle is pre-
sented in Fig. 7. It is evident that ANFIS with a 9×9 triangular
membership function outperformed all other functions, as
shown in Table 3 and Fig. 7.
Fig. 5 9×9 membership function
Fig. 6 Voltage RMS of 236 V vs. time (ms)
N. Malmurugan·Devarajan Gopal·Young Hwan Lho
276 한국철도학회논문집 제16권 제4호(2013년 8월)
6. Conclusion
Five membership functions with ANFIS models have been
developed and presented in this paper for a single phase power
system for detecting voltage sag and swells. The developed
methods have been compared with each other/other methods to
determine their respective effectiveness. This paper demon-
strates the ability of predicting the voltage from the knowledge
of input supply parameters.
It has been observed that triangular and trapezoidal functions
perform better than the other methods, because these are sim-
ple ANFIS models, thereby reducing time consumption in their
implementation. Furthermore, these models can be extended to
any supply system to achieve higher reliability and repeat-
ability in sag and swell detection. It is also noteworthy that
these models require only a few input parameters such as time,
voltage, and frequency magnitude with zero crossing infor-
mation. It was found that the developed algorithm detects sags
and swells accurately and quickly, within 2.2 msecs.
References
[1] M.H. J. Bollen (1999) Understanding Power Quality Prob-
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(2004) Electric Power Systems Quality, McGraw-Hill, NY.
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Table 3 Voltage error due to triangular, trapezoidal, bell shape, gaussian, and sigmoid functions vs. time for one electrical cycle
Time
(ms)
Measuted
voltage
Triangular
function
Error due to
triangular
function
Trapezoidal
function
Error due to
trapezoidal
function
Bell shape
function
Error due to
bell shape
function
Gaussian
function
Error due to
gaussian
function
Sigmoid
function
Error due to
sigmoid
function
0.0010 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.0000 72.9280 73.0739 -0.1459 73.6573 -0.7293 75.3514 -2.4234 82.8865 -9.9585 82.9860 -10.0580
2.0000 138.7173 138.9947 -0.2774 140.1045 -1.3872 143.3269 -4.6096 157.6596 -18.9423 157.8488 -19.1315
3.0000 190.9280 191.3099 -0.3819 192.8373 -1.9093 197.2725 -6.3445 216.9998 -26.0718 217.2602 -26.3322
4.0000 224.4493 224.8982 -0.4489 226.6938 -2.2445 231.9078 -7.4585 255.0985 -30.6492 255.4046 -30.9553
5.0000 236.0000 236.4720 -0.4720 238.3600 -2.3600 243.8423 -7.8423 268.2265 -32.2265 268.5484 -32.5484
6.0000 224.4493 224.8982 -0.4489 226.6938 -2.2445 231.9078 -7.4585 255.0985 -30.6492 255.4046 -30.9553
7.0000 190.9280 191.3099 -0.3819 192.8373 -1.9093 197.2725 -6.3445 216.9998 -26.0718 217.2602 -26.3322
8.0000 138.7173 138.9947 -0.2774 140.1045 -1.3872 143.3269 -4.6096 157.6596 -18.9423 157.8488 -19.1315
9.0000 72.9280 73.0739 -0.1459 73.6573 -0.7293 75.3514 -2.4234 82.8865 -9.9585 82.9860 -10.0580
10.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
11.0000 -72.9280 -73.0739 0.1459 -73.6573 0.7293 -75.3514 2.4234 -82.8865 9.9585 -82.9860 10.0580
12.0000 -138.7173 -138.9947 0.2774 -140.1045 1.3872 -143.3269 4.6096 -157.6596 18.9423 -157.8488 19.1315
13.0000 -190.9280 -191.3099 0.3819 -192.8373 1.9093 -197.2725 6.3445 -216.9998 26.0718 -217.2602 26.3322
14.0000 -224.4493 -224.8982 0.4489 -226.6938 2.2445 -231.9078 7.4585 -255.0985 30.6492 -255.4046 30.9553
15.0000 -236.0000 -236.4720 0.4720 -238.3600 2.3600 -243.8423 7.8423 -268.2265 32.2265 -268.5484 32.5484
16.0000 -224.4493 -224.8982 0.4489 -226.6938 2.2445 -231.9078 7.4585 -255.0985 30.6492 -255.4046 30.9553
17.0000 -190.9280 -191.3099 0.3819 -192.8373 1.9093 -197.2725 6.3445 -216.9998 26.0718 -217.2602 26.3322
18.0000 -138.7173 -138.9947 0.2774 -140.1045 1.3872 -143.3269 4.6096 -157.6596 18.9423 -157.8488 19.1315
19.0000 -72.9280 -73.0739 0.1459 -73.6573 0.7293 -75.3514 2.4234 -82.8865 9.9585 -82.9860 10.0580
20.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Fig. 7 Voltage error (triangular, trapezoidal, bell shape, gaussian,
and sigmoid functions) vs. time for one electrical cycle
Voltage Sag and Swell Estimation Using ANFIS for Power System Applications
한국철도학회논문집 제16권 제4호(2013년 8월) 277
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접수일(2013년 8월 7일), 게재확정일(2013년 8월 27일)
N. Malmurugan : [email protected]
Director(R&D), Mahendra Engineering College, Mallasamudram,
Tamilnadu, 637503, India
Devarajan Gopal : [email protected]
Department of Electrical & Computer Engineering, Mahendra Engi-
neering College, Mallasamudram, Tamilnadu, 637503, India
Young Hwan Lho : [email protected]
Department of Railroad Electricity System, Woosong University, 17-
2, Jayang-Dong, Dong-Gu, Daejeon, 300-718, Korea