Voltage Event Detection and Characterization Methods: A Comparative Study

Voltage Event Detection and Characterization

Methods: A Comparative Study

commonly used methods of detection and analysis of voltage

events in power systems. The performance of the rms method, the

fundamental component estimation using Discrete Fourier

Transform and Kalman filtering and the use of wavelet analysis

for detection and estimation of magnitude and duration of

voltage events, are studied under simulation using voltage dips of

different magnitude, duration and point-on-wave of beginning in

a pure sinusoidal voltage supply and also for a voltage supply

with different harmonic distortion levels. The methods employed

are also tested using real voltage events measured in a low-

voltage distribution system discussing the results obtained.

Index Terms—Fourier Transform, Kalman filtering, Power

Quality, RMS, Wavelets.

I. INTRODUCTION

Voltage events, defined as an abnormal and temporary

variation of the magnitude of voltage supply, are one of the

most important power quality disturbances in power systems

because of their frequency of occurrence and the economical

impact on commercial and industrial customers.

The magnitude of voltage supply during a voltage event

can be computed using the r.m.s. magnitude, the fundamental

component magnitude or the peak voltage magnitude. The use

of any of these three methods will produce the same results in

the case of a pure sinusoidal voltage supply, but the presence

of harmonics and other disturbances in voltage waveforms

could produce different results depending on the signal

processing method used. The paper presents a comparative

study of the most common methods used for voltage event

detection and characterization in power systems: the r.m.s.

method, DFT method, Kalman filtering and the wavelet

analysis method.

II. REVIEW OF VOLTAGE EVENT DETECTION AND

CLASSIFICATION METHODS

This section reviews the performance of the main signal

processing methods used in voltage event detection and

analysis.

A. RMS method

The most common processing tool used for voltage

measurement in power system is the calculation of the root

mean square voltage.

This work was supported by the Spanish Ministry of Science and

Technology under grant DPI 2003-08869-C02.

E. Pérez and J. Barros are with the Department of Electronics and

Computers, University of Cantabria, Santander, Spain 39005. (e-mail:

[email protected]).

The main advantage of this method is its simplicity but the

main drawback is the dependency on the window length and

the time interval for updating the values. Depending on the

selection of these two parameters, the magnitude and the

duration of a voltage event can be very different [1]-[3].

IEC Standard 61000-4-30 has proposed the Urms(1/2)

magnitude as the basic measurement of a voltage event [4].

This magnitude is defined as “the r.m.s. voltage measured

over 1 cycle, commencing at a fundamental zero crossing, and

refreshed each half-cycle”. According to this standard, the

voltage dip begins when the Urms(1/2) magnitude goes below the

dip threshold and ends when this magnitude is equal to or

above the dip threshold plus the hysteresis voltage.

The efficiency in the detection and in the estimation of the

magnitude and duration of voltage events using the Urms(1/2)

method has been studied in [5]. As any other r.m.s. method, it

is simple and easy to implement, but shows a limited

performance in the detection of voltage events and in the

estimation of its magnitude and duration, especially for short

duration and less severe voltage events. Another limitation of

this method is that no phase-angle information nor the point-

on-wave where the event starts is given.

B. DFT method

The traditional method to obtain the fundamental and

harmonic components of a signal in a digital system is the

application of the Discrete Fourier Transform (DFT) to the

samples of the signal taken in a time window. As is well

known, the results obtained using DFT are incorrect in the

case of non-stationary signals, as is the case of the voltage

waveform in an event.

A way to overcome this problem is the use of the Short

Time Fourier Transform (STFT). The STFT partitions the

signal into time segments where the signal is considered

stationary, applying the DFT within each segment. Once the

size of the time window is selected, the time-frequency

resolution obtained is fixed and it is the same for the whole

frequency spectrum of the signal. To obtain different

resolutions in different parts of the spectra it would be

necessary to apply STFT using different window sizes. The

results obtained give information of the time evolution of the

harmonic components of the signal.

Different authors have studied the application of STFT for

the detection and characterization of voltage events in power

systems [6]-[8]. The results obtained show, as in the case of

the rms method, its dependency on the length of the time

window selected. An advantage of the STFT method is that it

gives information on the magnitude and phase-angle of the

fundamental and harmonic components of voltage supply

during the event.

1-4244-0288-3/06/$20.00 ©2006 IEEE

2006 IEEE PES Transmission and Distribution Conference and Exposition Latin America, Venezuela

Enrique Pérez, Senior Member, IEEE, and Julio Barros, Senior Member, IEEE

C. Kalman filtering method

Kalman filters have been used as an alternative method for

detection and analysis of voltage events in power systems. The

change in magnitude of the fundamental component of voltage

supply can be used as an efficient way to detect and analyze

voltage events. Unlike the r.m.s. method, the Kalman filtering

method gives information both on the magnitude and phase

angle of voltage supply during the event and the point-on-

wave where the voltage event begins. References [9], [10]

discusses the Kalman filtering modeling issues and compares

the speed of detection of voltage dips using linear Kalman

filters of different order.

References [11], [12] propose the use of a three twelve-

state Kalman filters (one per phase) for real-time detection and

analysis of voltage events in power system. The fundamental

component and odd harmonics from third to eleventh order are

used to have an accurate representation of voltage supply

during the event. A new value of fundamental magnitude and

phase angle of voltage supply is obtained in real-time with

each new sample of the voltage waveform. Reference [13]

shows the results obtained in several months monitoring of

voltage supply in a low-voltage distribution system.

The detection properties of Kalman filtering and the

accuracy in the estimation of the magnitude and duration of

voltage events depend both on the model of the system used

and on the magnitude, duration and point-on-wave where the

voltage event begins. In general, the detection of the end of a

voltage event could show worse performance than the

detection of the beginning, mainly for short duration or

multiple-step voltage events, because, in such a case, the

coefficients of the filter may not have converged to the new

stationary values when the transition associated with the end

of the voltage event arrives.

A possible solution to improve the performance of Kalman

filtering in the detection and analysis of voltage events is the

use of an Extended Kalman filter to better estimate the non-

linear process associate with a voltage event. Reference [14]

presents the performance of different Extended Kalman filters

in the estimation of simulated and real voltage events in power

systems.

D. Wavelet analysis

Wavelet analysis is a powerful signal processing tool

specially useful for the analysis of non-stationary signals.

Unlike the STFT, which provides the same time-frequency

resolution in the whole frequency spectrum of a signal, the

discrete wavelet transform provides a non-uniform division of

the time-frequency plane, giving short-time intervals for high-

frequency components and long-time intervals for low-

frequency components.

Wavelet analysis has been successfully applied to monitor

power quality disturbances in power systems [15]-[20]. One of

the key factors in the application of the discrete wavelet

transform is the selection of the most appropriate wavelet

function depending on the type of disturbance to be detected

and analyzed. As a general rule shorter wavelets are best

suited for detecting fast transients while slow transients are

better detected using longer wavelets [15].

References [19],[20] study the performance of different

wavelet functions for the analysis of voltage dips,

recommending the use of the Daubechies with 6 coefficients

as the mother wavelet and the detail coefficients of the first

level of decomposition of the wavelet decomposition tree to

detect the beginning and the end of a voltage dip. As can be

seen in these references, these coefficients are insensitive to a

steady-state signal but show a high variation in magnitude

associated with the high frequency components present at the

beginning and the end of a voltage dip.

Yoon and Devaney in [21] give the theoretical basis for

computing the rms magnitude of voltage or current waveforms

using the detail and approximation coefficients of the wavelet

analysis. An alternative way to compute the phasor of a signal

using the wavelet analysis can be seen in [22].

III. COMPARATIVE ANALYSIS

As an example of the different performance in the detection

and analysis of voltage events using the methods described in

the last section, Table I and Fig. 1 show the simulation results

obtained when a 60% magnitude and 21.25 ms duration

voltage dip is applied to a 230 V, 50 Hz pure sinusoidal

voltage waveform. The voltage dip starts after two cycles and

5.15 ms of the voltage waveform and the sampling frequency

used in the simulations is 6.4 KHz (128 samples/cycle in a 50

Hz power system).

The characteristics of the different signal processing

methods applied for the detection and analysis of voltage dips

were the following:

• The Urms(1/2) magnitude is computed in the way proposed

in IEC61000-4-30.

• The STFT is applied using a sampling window of 1 cycle

and the results are updated with each new sample taken,

using the algorithm proposed in [23].

• A 13-state Extended Kalman filter, with the in-phase and in-

quadrature components of the fundamental and odd harmonic

components from third to eleventh order of voltage supply

and the power system frequency as the state variables, has

been used to detect and to estimate the fundamental

component of voltage supply during the voltage dip [14].

• The discrete wavelet transform is applied to the voltage

samples using Daubechies with six coefficients as the

mother wavelet function. The detail coefficients of the first

level of decomposition of the signal are used to determine

the beginning, the end and the duration of the voltage dip

and also to compute the rms magnitude of voltage supply

using the method proposed in [22].

TABLE I

RESULTS OBTAINED IN THE DETECTION AND EVALUATION

OF 60% MAGNITUDE, 21.25 MS DURATION VOLTAGE DIP

Urms(1/2) STFT EKF DWT

Magnitude (%) 49.6 60 59.9 60

Duration (ms) 40.0 37.5 22.03 21.31

Detection time (ms) 5.15 1.87 0 0.156

a)

b)

c)

d)

e)

f)

Fig. 1. a) Voltage waveform with a voltage dip, b) ideal rms value c) rms

magnitude computed using Urms(1/2) d) fundamental component using STFT e)

fundamental component using Extended Kalman filtering (EKF) f) magnitude

of detail coefficients of discrete wavelet analysis (DWT).

As can be seen the results obtained are very different

depending on the method used, the worst results in the

detection and the estimation of the magnitude and duration of

the voltage dip are given by the Urms(1/2) method. The number

of detail coefficients in Fig. 1.f is half the voltage samples due

to the down sampling by two associated with the DWT

implementation.

In order to evaluate the performance of these methods,

rectangular voltage dips of different magnitude, duration and

different instant of beginning have been simulated in a 230 V,

50 Hz, pure sinusoidal voltage supply. For each simulation the

Urms(1/2) magnitude, the fundamental component in voltage

supply obtained using STFT and Extended Kalman filtering

and the r.m.s. value computed using the wavelet analysis, are

computed to detect the instant where the voltage dip begins

and to obtain its magnitude and duration. The maximum error

in the estimation of magnitude and duration and the maximum

delay in the detection of the beginning of the voltage event are

compared to show the accuracy and the limitations of these

methods for the complete characterization of voltage events.

Fig. 2 shows the maximum error in the magnitude of

voltage dips computed using the above mentioned methods for

voltage dip magnitudes from 10% to 90%, durations of 0.5,

0.75 and 1 cycles respectively and different instants of

beginning of the voltage event (from 0º to 360º in steps of 5º).

As can be seen the error in the magnitude is higher for

shorter and more severe voltage dips, the Urms(1/2) method

being the worst in the estimation of the magnitude of the

voltage dip. In all the cases considered the error in magnitude

using the DWT method is always 0%. The error in magnitude

is zero for voltage dips of 1 cycle or longer using the STFT

method and for voltage dip durations longer than 1.5 cycles

using the Urms(1/2) method. On the other hand, the maximum

error in magnitude for voltage dips longer than 1 cycle is less

than 2% using the EKF method.

The error in the computation of the magnitude of short

duration voltage dips using the Urms(1/2) and DTFT methods is

of such magnitude, that these voltage dips can be undetected

because, in such a case, the voltage dip detection threshold

might not be surpassed.

Another important aspect in the performance of the

different methods studied is how long it takes for the detection

of the beginning of a voltage event. Fig. 3 shows the

maximum delay in the detection of the beginning of a voltage

dip, for rectangular voltage dips of different magnitude,

duration and different point-on-wave of beginning in a 230 V,

50 Hz, pure sinusoidal voltage supply, using the Urms(1/2),

DTFT, EKF and DWT methods. In all cases, the detection

time is a function of the point-on-wave the voltage event

begins, it depends on the magnitude of the voltage event and it

is independent of its duration.

The maximum delay is the greatest using the Urms(1/2),

because in this method, the time interval for updating the rms

magnitude is a half-cycle of the voltage supply and in the

other methods, a new value of the rms or the fundamental

component in voltage supply is computed with each new

sample of the voltage waveform. On the other hand, the DWT

method shows the lowest delay in the detection, 0.3125 ms,

double the sampling period used in the simulations,

independently of voltage dip magnitude and duration.

Fig. 2. Maximum error in magnitude for voltage dips of 0.5, 0.75 and 1 cycles

and different point-on-wave of beginning using Urms(1/2), STFT, EKF and

DWT methods

Fig. 3. Maximum delay in the detection of a voltage dip using the Urms(1/2),

DTFT, EKF and DWT methods.

From the results reported in Figs. 2 and 3, the wavelet

analysis is the best processing tool for the detection and

analysis of voltage dips in the case of pure sinusoidal voltage

supply.

However, this is not the real situation in voltage supply,

where harmonic distortion, high frequency noise and other

disturbances modify the voltage supply from the pure

sinusoidal waveform. The performance of the methods used

for the detection and analysis of voltage events could be very

different when this type of power quality disturbances are

present in voltage waveforms, as will be seen in the next

section in the analysis of real voltage events, especially in the

case of the use of wavelet analysis.

IV. EXPERIMENTAL RESULTS

As an example of the performance of the methods

considered in the detection and analysis of real voltage events,

Fig. 4.a shows the waveform of voltage supply with a voltage

dip measured in the low-voltage distribution network of our

building, and Fig. 4.d and Fig. 4.c show the results obtained in

the application of these four methods.

As can be seen, the direct use, without any other

consideration, of the detail coefficients of the first level

decomposition of the wavelet analysis (Fig. 4.c), makes it

impossible to assess how many voltage dips are present in the

voltage waveform and when exactly they begin and end or if

the voltage dip is single or multiple step, as is the case in the

example considered.

The use of these coefficients for detection of the beginning

and the end of a voltage event requires the definition of an

adequate threshold that should be surpassed only in the case of

the high frequency transitions associated with the beginning

and the end of a voltage event. Unfortunately, these

coefficients are so sensitive that other very short, high

frequency disturbances in voltage waveform, produce similar

effect to the voltage events, making the use of wavelet

analysis very difficult in an automatic voltage event analysis

system [20].

On the other hand, the EKF method provides the best

estimation of voltage supply during the event and the shortest

detection time of the beginning of the event, and Urms(1/2)

shows the worst performance in any case.

a)

b)

c)

Fig. 4. a) Voltage waveform of a voltage dip b) results obtained in the

application of Urms(1/2), STFT and EKF methods c) magnitude of detail

coefficients of wavelet decomposition level 1.

V. CONCLUSIONS

The paper studies the performance of the rms, STFT,

Kalman filtering and wavelet analysis methods for the

detection and analysis of voltage events in power systems.

The Urms(1/2) and the STFT methods always present a delay

in the detection of a voltage event function of the point-on-

wave the voltage event begins and also show a limited

performance for short duration and low magnitude voltage

events. The use of Extended Kalman filtering gives a good

performance both in the detection and in the estimation of the

magnitude and duration of voltage events. Finally, the wavelet

analysis shows the best performance in the detection and in

the estimation of the time-related parameters of a voltage

event, but the use of the high frequency coefficients of the

wavelet analysis require an auxiliary method to discriminate

voltage events from other high frequency disturbances.

A combination of wavelet analysis for the estimation of the

time related parameters of a voltage event and Kalman

filtering for obtaining its magnitude and phase angle appears

to be the best solution for the optimal characterization of

voltage events in an automatic on-line system.

VI. REFERENCES

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VII. BIOGRAPHIES

Enrique Pérez, received the M.Sc. degree in Physics in 1985 from the

University of Cantabria, Spain. His research areas include real-time computer

application in power systems, power quality and harmonic compensation in

power systems. At present he is pursuing his Ph.D. degree in the area of

power system applications and control.

Julio Barros (M’1996, SM’2002) received the M.Sc. and Ph.D. degrees in

Physics in 1978 and 1989 respectively, both from the University of Cantabria,

Spain. In 1989 he joined the Department of Electronics and Computers of the

University of Cantabria, Spain, where he is currently a Professor. His research

areas are real-time computer applications in power systems, harmonics and

power quality.