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: gdrajan33@gmail.com

©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-

lems: Voltage Sags and Interruptions, IEEE Press, Vol. I, NY.

[2] Roger Dugan, Surya Santoso, Mark McGranaghan, H. Beaty

(2004) Electric Power Systems Quality, McGraw-Hill, NY.

[3] P. Wang, N. Jenkins, M. H. J. Bollen (1998) Experimental

investigation of voltage sag mitigation by an advanced static

VAr compensator IEEE Trans. Power Del., 13(4), pp. 1461-

1467.

[4] X. Xiangning, X. Yonghai, L. Lianguang (2000) Simulation

and analysis of voltage sag mitigation using active series volt-

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 : n.malmurugan@gmail.com

Director(R&D), Mahendra Engineering College, Mallasamudram,

Tamilnadu, 637503, India

Devarajan Gopal : gdrajan33@gmail.com

Department of Electrical & Computer Engineering, Mahendra Engi-

neering College, Mallasamudram, Tamilnadu, 637503, India

Young Hwan Lho : yhlho@wsu.ac.kr

Department of Railroad Electricity System, Woosong University, 17-

2, Jayang-Dong, Dong-Gu, Daejeon, 300-718, Korea