Promulgating of Voltage Fluctuations along Practical Power ......Key-words: power quality, voltage sag, swell, wavelet analysis, distribution system 1 Introduction A voltage sag, as

Promulgating of Voltage Fluctuations along Practical Power Distribution Systems

QIAN AI� DANZHEN GU CHUANWEN JIANG CHEN CHEN

Department of Electrical Engineering Shanghai Jiaotong University, Shanghai

CHINA �

Abstract: Voltage fluctuations, such as sags and swells, are the most widespread power quality issues affecting electrical power distribution systems. This paper describes details of sag characteristics due to different types and locations of faults in one practical power distribution system. The results can not only give utility engineers very useful information when they deal with area of vulnerability, but also assist the facility personnel to make decisions on purchasing power quality mitigation equipment. At the same time, one special wavelet analysis is utilized to detect voltage sags and swells. Characteristics of investigated signals are measured on a time-frequency plane. The results are very satisfied. Key-words: power quality, voltage sag, swell, wavelet analysis, distribution system 1 Introduction A voltage sag, as defined in the IEEE Std. 1346-1998 [1], is a momentary decease in the RMS voltage magnitude, usually caused by a remote fault somewhere on the power system, with a duration ranging from half a cycle to few cycles (less than one second). Longer the voltage sag lasts, the more probable the chances of malfunction. Much more attention has been paid to this under the deregulated environment. Voltage sags are the most widespread quality issues affecting distribution systems, especially industries where involved losses can reach very high values. A very short and shallow voltage sag can produce dropout of a whole factory, being necessary a long time for the full plant recovery (cleaning and reach the steady state), sometimes as long as several hours. In general, it is possible to consider voltage sags as the origin of between 70 and 90% of the industrial power quality problems [2]. Accurate estimates of sag magnitude and duration probabilities help system designers to select appropriate equipment specifications for critical processes. The obtained sag information can be used by the utility engineers to understand the ‘weak locations’ (area of vulnerability) of the electrical supply system and to assist the facility personnel to take decisions on purchasing power quality mitigation equipment. Faults cause voltage sags that can disrupt sensitive equipment and these problems continue until

equipment is made less sensitive. Since the utility faults cannot be eliminated completely, solutions to the voltage sag problems on the utility side include fault prevention activities and modification of fault clearing practices; and on customer side, a power line conditioning equipment is required to be used to provide ride-through capability for highly sensitive loads. Modest change in equipment specifications through design practices also provides the equipment ride-through [2,3]. This paper firstly describes the voltage sag characteristics in one practical distribution system. The feature of voltage sags and unbalance is summarized including factors influencing the voltage sag magnitude, such as, different types of faults, faults locations, loading conditions. There are the several algorithms that have been used in the analysis of electrical signals, the Fast Fourier Transform (FFT), the Kalman filtering, the Least Squares (LS) method, and the Finite Impulse filtering can be quoted. However, in presence of non-stationary signals, the performance of these techniques is limited. J.Morlet and A. Grossmann have initiated wavelets, in the beginning of the eighties last century. The last ten years have seen the interest in wavelets growing at an explosive rate. Wavelets have been successfully applied in several fields due to their advantages better than those traditional signal analysis tools. In the last part of this paper, a recursive wavelet [7,8] is applied in detecting the start and end of voltage disturbance

Proceedings of the 5th WSEAS Int. Conf. on Power Systems and Electromagnetic Compatibility, Corfu, Greece, August 23-25, 2005 (pp66-71)

events, such as sags and swells. It is shown that wavelets are well suited to the analysis of the non-stationary signals measured by the protection devices. Moreover, the fast implementation of the recursive wavelet transform allows the design of fast digital relays. Some papers show how the spectral contents as a function of time can be obtained by using the short-time Fourier transform (STFT)[11]. But the STFT has a fixed frequency resolution for all frequencies once the size of the window is chosen. Apparently, the recursive wavelet proposed here has advantages over STFT: characteristics of investigated signals are measured on a time-frequency plane. In section II of this paper, general methodology to calculate voltage sag is presented. Section III presents the model of one part of a practical distribution system. Some simulation results are concluded in Section IV. In section V, a recursive wavelet and transform are described, and applications of this wavelet are also presented. It is also shown how wavelets can be useful to detect the changes or time location in signal disturbances. 2 Voltage Sags In Power Quality Problem And General Methodology Better understanding of the voltage sag characteristics of the electric power system offers the opportunity to evaluate alternate system configuration, and small modifications in equipment specifications can reduce the number of nuisance outages due to voltage sag. Hence there is a definite need for utility companies to provide more information regarding voltage sags to their customers in today’s competitive environment. A voltage sag is most of the time described by two essential characteristics, one magnitude and one duration. The magnitude is determined by the electrical distance to the fault and the duration by the fault clearing time. However, a fault in a power system not only leads to a drop in voltage magnitude, but also to a change in phase angle of the voltage (jump in phase angle). This so-called phase angle jump can be calculated as the argument of the complex voltage. The impact of sag depends on equipment sensitivity. For a faulted redial system, one can calculate the voltage sag at the point of interest by using the impedance divider principle. These are some factors influencing the voltage sag magnitude [4,5]:

1) Fault location: any fault closer to the substation

produces severe sag than the fault far from the substation.

2) Types of faults: Three phase (3LF) and Single line to ground fault (SLGF) are normally considered in the analysis. Two line to ground fault (LLGF) is included in this paper as well.

3) Effect of transformer connections: three phase transformer connected delta wye or wye delta alters unbalanced voltage sags.

General methodology for voltage sag analysis basically consists of: 1) load flow, a load flow representing the existing or modified system is required; 2) voltage sag calculation, a standard short circuit program is utilized for this purpose. The calculation scheme can be summarized as follows: 1. Read network line data, power transformer data,

load data, feeder sending voltage at substation, pre-fault voltage, fault impedance.

2. Perform load flow analysis and compute bus voltages for converged load flow.

3. Perform short circuit analysis for different faults on different locations of faults simulated.

4. Compute voltage sag characteristics which can give sag magnitude at bus bar for both types of faults and for different simulated fault locations.

5. Compute sag magnitude at the customer bus using the given transformer connection and three phase load connection.

6. Repeat step-5 for different simulated fault locations. Plot a graph: fault distance v.s. sag magnitude at customer bus.

3 Model Of One Practical Distribution System The system is illustrated below. Feeder 1 has three loads. The lengths of the cables between loads are all 1 km. Feeder 2 has four loads. The loads all connect with bus bar through transformers and 1km cable. The major transformers are Star/Star to earth through a ‘tank’. The ‘tank’ acts as a Tertiary delta winding providing path for zero-sequence currents. The distribution transformers are all Delta/Star to earth, as shown in Figure 1. The types of loads respectively are static load, dynamic, and mixture of two, for calculating their impact on the voltage sags at the same fault and same fault position.

S

1

1

1 1

2 30 Feeder 1


Fig.1 distribution system structure The faults occur respectively at position 0 (bus bar), 1, and 2 on feeder 1. The types of fault comprise of: (i) single phase to ground, (ii) two phases to ground, (iii) phase to phase and (iv) three phases to ground. The measurement positions are load side on feeder 2. 4 Summary Of Simulation Results The simulation results can be broken down according to the types of fault: 4.1 Single line to ground fault (SLGF) The single line-to-ground fault is the most probable type of faults and, through a delta-wye transformer, is transferred as a two-phase voltage sag, in which case voltage sags should be considered as a case of unbalanced transient supply. This paper gives some results when single line to ground fault occurs on different positions of Feeder 1. Figure 2 shows that the sags are the function of fault location or electrical distance between the bus bar and fault position.

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.670

80

90

100

110

120

130

140SLGF( phase A)

time (s)

RM

S

0 1

2

Fig.2 RMS changes following different fault

locations (phase A)

4.2 Two phase-to-ground faults (LLGFs or 2LGFs) When the double line-to-ground fault or line-line fault occurs, through the transformer, the voltages at custom side have special characteristics: One phase voltage drops greatly and the other phases have smaller sags. When the LLGF occurs at position 1, RMS changes corresponding to fault locations are shown in Figure 3.

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.60

20

40

60

80

100

120

1402LGF

time (s)

RM

S

0

1 2

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.670

80

90

100

110

120

1302LGF

time (s)

RM

S

0 1

2

Fig. 3 RMS changes at different fault locations

(phase A and B)

4.3 Three-phase-to-ground faults (3LGFs) Apparently, the voltage sags are balanced. The bus bar voltages are shown as below when 3LGF occurs on position 1. The change of RMS voltage is shown in Fig.4 by following different positions of faults.

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.60

20

40

60

80

100

120

1403LGF

time(s)

RM

S

Fig. 4 RMS changes following different fault

locations In Figure 5, the fault location is on position 1, only the fault type is different. It clearly shows that three phase voltage sags will depend on the fault types.


From mild to severe, the voltage sags deviates from SLGFs to 3LGFs.

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.60

20

40

60

80

100

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140Phase A

time (s)

RM

S

SLGF

LLGF

3LGF

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.60

20

40

60

80

100

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140Phase B

time (s)

RM

S

SLGF

LLGF

3LGF

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.60

20

40

60

80

100

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140Phase C

time (s)

RM

S

LLGF

SLGF

3LGF

Fig.5 Three-phase voltage sags under different faults 5 Detection Of Sags And Swells Via Wavelet Analysis The currently known method for detecting power quality disturbances is based on a point-to-point comparison of adjacent cycles. This method inherently suffers from the drawback that it fails to detect and identify periodic disturbances, such as phase controlled load voltage wave shapes. Past research has considered the applications of neural networks to classification of waveforms due to high and low impedance faults, magnetizing inrush and power quality issues. In this paper, we propose a new approach to detect and localize various types of power quality disturbances by using wavelet analysis introducing below. This method can achieve satisfied results. 5.1 Recursive Continuous Wavelet Transform A recursive continuous wavelet transform algorithm defined in [6,7] is programmed in this paper. This algorithm has been chosen over the wide range of time-frequency computation tools from a qualitative study of new signal processing tools used for electrical disturbance analysis [8]. This recursive continuous wavelet uses the Chaari complex mother wavelet h given below,

tjts eetststh 0)2

1()( 22

ω−++= , (1)

and ⎪⎩

⎪⎨⎧

=

=

32

20

ππω

s (2)

The continuous wavelet transform coefficient of a signal x at time b and scale a is:

,( , ) ( ) ( )hx a bCWT a b x t h t dt

+∞

−∞= ∫ (3)

with ,

1( ) ( )a b

t bh t h

aa−

= (4)

Fig.6 Presents the wavelet when a equals to 1 and b equals to 0. We set a/1 equal to a frequency f, and ‘T’ the sampling period and ‘k’ and ‘n’ are integers. For a chosen frequency ‘f’, and for ‘b=kT’, the formula (3) becomes:

( , ) ( ) [ ( )]h

x

n

CWT f kT x nT f h f nT kT T= ⋅ ⋅ − ⋅∑ (5)

So the wavelet in fig.6 has a frequency f= 1/a=1Hz. A wavelet coefficient is defined for one time and one frequency. The only way to present a wavelet transform is a three-dimensional representation, as such in the Fig.7, second graph (Fig.7 (b)) and the level curves of the wavelet transform magnitude are presented in the third graph of Fig.7 (Fig.7(c)) which is so called time-frequency plane. Some tests of this wavelet transform are presented as below.

-4 -3 -2 -1 0 1 2 3 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Recursive Wavelet (a=1,b=0)

time (s)

Mag

nitu

de

Fig.6. Real part (solid line) and imaginary part (dashed line) of complex wavelet (a=1, b=0)

5.2 Tests The examples include voltage sag and swell. In order to detect a fault in a signal, a clear time-frequency plane is obtained for each computed power disturbance. This time-frequency plane represents a meaningful signature of each kind of electrical fault. Fig.7(c) shows the time-frequency plane of a voltage sag and Fig9(c) of a voltage swell. This particular time-frequency plane points out the main signal characteristics change in the 50Hz signal and at high frequency. The sharp increases at all high


frequencies are corresponding to the changes in the behavior of the voltage sag.

The profiles at 50Hz, 100Hz and 150Hz are plotted in fig.8 and fig.10 respectively. A part of the signal, assumed to be disturbance-free, is taken as reference. When the fault occurs, the magnitude of the 50 Hz signal changes very slowly and shows the basic characteristics of the events, such as, sag or swell. The high frequency peaks correspond to sharp changes in the signal. So these peaks are used to detect changes or time location in signal disturbances.

Fig.7 (a) Example of a sag, X, time, Y, Magnitude

(b) 3D illustration, X, time, Y, frequency, Z, Magnitude

(c) Time-frequency plane, X, time, Y, frequency.

0.05 0.1 0.15 0.2 0.25 0.30

100

200

300

400

500

60050Hz

Time (s)

Mag

nitu

de

0.05 0.1 0.15 0.2 0.25 0.30

10

20

30

40

50

60

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90

100100Hz

time(s)

Mag

nitu

de

0.05 0.1 0.15 0.2 0.25 0.30

10

20

30

40

50

60150Hz

time(s)

mag

nitu

de

Fig.8 Profiles at 50Hz, 100Hz and 150Hz., Y label is

Magnitude

In both cases, values of the continuous wavelet transform at high frequencies indicate the discontinuities of the signal (beginning and end of voltage sag, swell). These discontinuities are major aspects of these power disturbances. Furthermore, this method enables an accurate classification of power quality events, and characterstics are easily read from the time-frequency plane. It is shown that wavelets are well suited to the analysis of the non-stationary signals measured by the protection devices. Moreover, the fast implementation of the recursive wavelet transform allows the design of fast digital relays.

Fig. 9.(a) example of a swell, (b) 3D illustration, (c)

time-frequency plane

0.05 0.1 0.15 0.2 0.25 0.3450

500

550

600

650

700

750

800

850

90050Hz

time (s)

Mag

nitu

de

0.05 0.1 0.15 0.2 0.25 0.30

20

40

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120

140100HZ

time (s)

Mag

nitu

de

0.05 0.1 0.15 0.2 0.25 0.310

15

20

25

30

35

40

45

50

55150Hz

Fig.10 Profiles at 50Hz, 100Hz and 150Hz


6 Conclusions An awareness of the importance of power quality problem with focus on voltage sag analysis is highlighted. The voltage sags are unbalanced during single phase to ground and two-phase faults. The characteristics of sags are also different between above two different types of faults. Only voltage sags of three phase faults are symmetrical. The details are concluded as follows: When single phase (A phase) to ground faults occur at different positions on feeder 1, the voltage dips at phase A and C on customer side are same but much severe than phase B. Actually, the voltage of phase B does not have any changes during the faults. When two phases (A and B phases) to ground or phase-to-phase faults occur, phase A voltage at customer side drops very great, but B and C phase voltage drop smaller than A phase. The voltage dips of LLGFs are higher than these of SLGFs. All of three phase voltages drop at the same degree. And the farther the fault positions from bus bar, the less the voltages drop.

The voltage sags at customer side are proportional to these sags at bus bar according to the electrical distance from the faults. Namely, a fault on a given remote line segment will be characterized by its location and its fault resistance. Recursive continuous wavelet transform has been developed for detecting and measuring power quality events, such as, sags and swells. This algorithm enables very accurate time location and magnitude measurements of voltage sags and swells. References [1] IEEE Standard 1346, IEEE Recommended

Practice for Evaluating Electric Power System Compatibility with Electronic Process Equipment, 1998.

[2] M.F. Mcgranahan, D.R. Mueller, M.J. Samotyj, Voltage sags in industrial systems, IEEE Transactions on Industry Applications, v.29, No.2, March/April 1993, pp397-402.

[3] A.C. Parsons, W.M. Grady, E.J. Powers, J.C. Soward, A direction finder for power quality disturbances based upon disturbance power and energy, IEEE Transactions on Power Delivery, v.15, No.3, July 2000, pp. 1081-1086.

[4] G.T. Heydt, Power quality engineering, IEEE Power Engineering Review, September 2001, pp. 5-7.

[5] M.H.J. Bollen, Voltage sags in three-phase systems, IEEE Power Engineering Review, September 2001, pp. 8-11.

[6] O. Chaari, M. Meunier, F. Brouaye, Wavelets: a new tools for the resonant grounded power distribution systems relaying, IEEE Transactions on Power Delivery, Vol.11, No.3, July 1996, pp. 1301-1308.

[7] O. Poisson, P. Rioual, M. Meunier, Detection and measurement of power quality Disturbances using wavelet transform, IEEE Transactions on Power Delivery, v.15, No.3, July 2000, pp. 1039-1044.

[8] O. Poisson, P. Rioual, M. Meunier, New signal processing tools applied to power quality analysis, IEEE Transactions on Power Delivery, v.14, No.2, April 1999, pp. 561-566.

[9] D.O. Koval, R.A. Bocancea, and M.B. Hughes, Canadian national power quality survey - frequency of industrial and commercial voltage sags, IEEE Trans. on Industry Applications, vol.35, September 1998, pp.904-910,

[10] D.S. Dorr, M.B. Hughes, T.M. Gruzs, R.E. Jurewicz, and J.L. McClaine, Interpreting recent power quality surveys to define the electrical environment, IEEE Trans. on Industry Applications, vol.33, November 1997, pp.1480-1487,

[11] F. Jurado, J. R. Saenz, Comparison between discrete STFT and wavelets for the analysis of power quality events, Electric Power Systems Research, Vol.62, 2000, pp.183-190


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Promulgating of Voltage Fluctuations along Practical Power ......Key-words: power quality, voltage sag, swell, wavelet analysis, distribution system 1 Introduction A voltage sag, as