107 zayegh aupec01 paper revised

7/28/2019 107 Zayegh AUPEC01 Paper Revised

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VOLTAGE DIP CALCULATIONS USING SPREADSHEETS

V. MIJATOVIC, R. COULTER*, A. ZAYEGH, A. KALAM

School of Communications and Informatics

Victoria University

PO Box 14428 MC, Melbourne, 8001

*Manager Technology Development, POWERCOR, Australia

Abstract

The analysis of voltage dips is an important technique in the determination of power quality. Thispaper deals with the use of spreadsheets to calculate voltage dips in a distribution network. It is shown

that the graphs generated are essential tools in helping to understand the characteristics of voltage dips.

1. INTRODUCTION

Voltage dips are short-duration rms voltage caused by

faults in the electricity supply system and the starting of

large loads [1]. The interest in voltage dips is mainly

due to the problems they cause on many types of

equipment.

Characteristics typically analyzed when discussing

voltage dips are its magnitude and duration. However,

during voltage dips, there is a phase shift associated with

the drop in voltage, which is not included in the normal

characteristics. This characteristic is based on a balanced

voltage dip, whereas most voltage dips are a result of

unbalanced faults occurring on the system. Both these

factors play an important role in the disturbance of

equipment operation [4].

One of the most powerful tools for dealing with classical

unbalanced systems is the theory of symmetricalcomponents. This theory allows us to analyze the system

response when dealing with both symmetrical and

unsymmetrical faults. In this paper, the theory of

symmetrical components will be applied to voltage dips

due to single line to ground fault (SLGF) and line to line

fault (LLF).

Using a simple radial high voltage distribution network

at no load as the base model (Figure 1), phase voltage

characteristics are derived for both faults. Using data

provided with the base model and alternating thetransformer from delta-delta () to star-delta (Y), thephase voltage characteristics are then determined in

terms of magnitude and angle. Comparing the phase

voltage to the pre-fault phase voltages will give the

voltage dip in terms of magnitude and phase change.

Figure 1 Base model of a distribution network.

2. UNBALANCED FAULTCHARACTERISTIC

For simplified symmetrical component analysis it is

assumed that the positive and negative sequence

networks have the same impedance (Z1=Z2) [2].

However for the purpose of determining phase voltages

we shall initially label both the positive and negative

impedances separately.

The analytical equations for the three phase voltages are

derived via the voltage matrix.

=

2

1

0

2

2

1

1

111

R

R

R

B

Y

R

V

V

V

V

V

V

(1)

where = 1120 and 2 = 1240


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Therefore

VR= VR0 + VR1 + VR2

VY = VR0 + 2VR1 + VR2 (2)

VB = VR0 + VR1 + 2VR2

From the SLGF sequence network it can determined that

VR0 = -IFZ0

VR1 = ER1 - Z1IF (3)

VR2 = -IFZ2

where IF = ER1 / (Z1 + Z2 + Z0 + 3ZF)

For the LLF the sequence network is

VR0 = 0

VR1 = IF (Z2 + ZF) (4)

VR2 = IFZ2

where IF = ER1 / (Z1 + Z2 + ZF)

Thus the sequence voltages at the fault point F and bus

R, for given networks, can be determined using theabove equations (2)(3) and (4). To determine the voltage

at bus LD the transformer connections are taken into

account.

If the transformer is Y connected there is a phase shiftof +30 in the positive sequence and a shift of 30 inthe negative sequence [3]. There is no phase shift for the

connected transformer. Also taken into account isthe change in the zero sequence network due to

transformer connections.

3. EXCEL SPREADSHEET FOR VOLTAGE DIP

CALCULATIONS

Using the relevant equations obtained from the previous

section it is possible to calculate the voltage dip

expected at varying fault points (0 20km) at bus LD

for both SLGF and LLF using either transformer.

Firstly it is known that pre-fault values of the phase

voltages are equivalent to

VRN = 1 30VYN = 1270VBN = 1150

VRY = 160VYB = 1 -60

VBR = 1180

Subtracting the fault voltage from its relevant pre-fault

voltage determines the voltage dip magnitude and angle.

To calculate the voltage dip at various fault points

requires changing the line impedance, due to the fact

that as the line length increases so does the line

impedance.

The advantage of using spreadsheets is that the data can

be graphed in order to show the behaviour of the voltage

dip. In the next section plots are generated which show

the trend in voltage magnitude vs. phase change, change

in voltage magnitude vs. distance and phase change vs.distance. The line voltages at particular fault points are

displayed as sinewave graphs so that comparison

between pre-fault, fault and post-fault conditions can

physically be seen. The advantage of this is that it is

poss ible to see voltage dip effects.

Using MATLAB tool Excel Link, the data in Excel can

be used to represent, in MATLAB, the three pre-fault

and fault voltages as vector diagrams for the fault points.

4. RESULTS

The following graphs are for both SLGF and LLF using

either transformer, however due to these graphs being

only examples we have only used the three line-ground

voltages (VRN, VBN,VYN) as data. Please note that VRN is

represented by a grey line, VBN by a light grey line and

VYN by a black line.

4.1 Magnitude change vs. phase change

Figures 2 to 5 are useful in determining the phase

change experienced in the line when the fault voltageincreases or decreases, and vice versa. It is also possible

to see the difference that the transformer connections

will make on the voltage dip.

4.1.1 SLGF

Figure 2 Magnitude change vs. phase change forconnection


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4.2 Magnitude vs. distance

The graphs shown in this section help determine the

voltage dip magnitude at certain distances. Thus, given

the distance, it is possible to estimate what the voltage

dip magnitude will be.

4.2.1 SLGF

Figure 3 Magnitude change vs. phase change for Yconnection. Note: VYN located origin.

4.1.2 LLF

Figure 4 Magnitude change vs. phase change forconnection. Note: VRN located at 0-30

Figure 5 Magnitude change vs. phase change for Yconnection.

Figure 6 Magnitude vs. distance for connection.

Figure 7 Magnitude vs. distance for Y connection.


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4.2.2 LLF

Figure 8 Magnitude vs. distance for connection.

Figure 9 Magnitude vs. distance for Y connection.

4.3 Phase vs. distance

Figure 10 - 13 show what phase change the system will

experience over a certain distance

4.3.1 SLGF

Figure 10 Phase vs. distance for connection.

Figure 11 Phase vs. distance for Y connection.

4.3.2 LLF

Figure 12 Phase vs. distance for connection.

Figure 13 Phase vs. distance for Y connection.


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4.4 Sinewave graphs

The data used for the following graphs are taken at a

fault distance of 0km. These graphs give a better

understanding of the line voltage values at pre-fault,

fault and post-fault conditions. Please note that transienteffects are not taken into account.

4.4.1 SLGF

Figure 14 connection, at observation point.

Figure 15 Y connection, at observation point

4.4.2 LLF

Figure 16 connection, at observation point


4.5 Vector diagrams

The vector diagrams visually clarify the change in

magnitude and phase in comparison to its initial value.Please Note that the data used is once again for a fault

distance of 0km.

4.5.1 SLGF



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4.5.2 DLGF



5. CONCLUSION

As can be seen, by using a simple radial high voltage

distribution network at no load as the base model, the

phase voltage characteristics where derived for bothfaults using spreadsheets. Using the voltage dip data

obtained from the spreadsheets it was graphically

represented in order to give us a better understanding of

its characteristics, especially noting its behaviour when

the transformer connection was changed from to Y.

The advantage of using spreadsheets is that the graphs

generated help us to physically see the comparison

between pre-fault and fault conditions as well as the

difference between fault location points. Thus it helps us

in determining the effects of voltage dips on the system.

Another advantage of using spreadsheets, especially for

students, is its ease of use and it is also relativelyaffordable and obtainable compared to other simulation

packages.

6. REFERENCES

[1] L. Zhang, and M.H.J. Bollen, Characteristic in

Voltage Dips (sags) in Power Systems,IEEE

Trans. on Power Delivery, vol.2, pp 827-832, April

2000.

[2] H. Saadat,1999,Power System Analysis,

WCB/McGraw-Hill.

[3] J.J. Grainger, W.D. Stevenson, 1994,Power SystemAnalysis, McGraw-Hill.

[4] M.H.J. Bollen, P. Wang, and N. Jenkins, Analysisand consequences of the phase angle associated

with a voltage sag,IEEE Trans. on Power Systems

Computation Conf., Dresden, Germany, Aug 1996.

107 zayegh aupec01 paper revised

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