new short circuit studies dr. nitin dhote · 2019. 1. 8. · assumptions in short circuit studies:...

SHORT CIRCUIT STUDIES

Dr. Nitin Dhote

Dr. Nitin Dhote, SVPCET, Nagpur

NECESSITY OF SHORT CIRCUIT STUDIES:

1. THE CURRENTS AND VOLTAGES AT DIFERENT POINTS ON THE

SYSTEM DURING FAULT CONDITION.

2. TO DESIGN POWER SYSTEM EQUIPMENT INSULATION LEVEL AND

CONDUTOR DIAMETER.

3. DESIGN EFFECTIVE AND ADEQUATE RELAYING AND SWITCHING

SYSTEM.

4. IT PROVIDES THE INFORMATION ABOUT SHORT CIRCUIT MVA

CAPACITY REQUIRED FOR CIRCUIT BREAKER AT DIFFERENT POINTS.

5. PLANNING , DESIGN AND OPERATION OF THE SYSTEM.Dr. Nitin Dhote, SVPCET, Nagpur

ASSUMPTIONS IN SHORT CIRCUIT STUDIES:

1. ALL THE SHUNT ELEMENTS INCLUDING LOADS IN THE POWER

SYSTEM ARE NEGLECTED (I L(0) = 0).

2. SYSNCHRONOUS MACHINE IS REPRESENTED BY CONSTANT

VOLTAGE BEHIND REACTANCE.

3. RESISTANCES OF ALL ELEMENTS ARE NEGLECTED.

4. POSITIVE AND NEGATIVE SOURCE REACTANCES OF ALL ROTATING

MACHINES ARE EQUAL(X1=X2)

5. TRANSFORMERES ARE REPRESENTED BY THEIR NOMINAL RATIOS

ONLY.


G1

G2

Gn

L1 L2 Lm

machines

Loads Ep

Ei

3-Ø Transmission system

i

p

abc

abc

abc

1

E1


machines

Ep

Ei

Transmission system with series reactances

i

p

abc

abc

Gn

G1

1

E1abc

++

+


E1(0)

][ ,, cbaZf

Including machines reactances

machines

Ep(0)

Ei(0)

i

p

abc

abc

abc

1

Zf

[ZBUS]


For a power system containing m number of buses,Bus voltages during fault at bus P are given by

)()0()( abcabcabcabc IbusZbusEbusEbus

E1(+)

E2(+)

Ei(+)

EP(+)

Em(+)

=

E1(0)

E2(0)

Ei(0)

EP(0)

Em(0)

-

Z11 Z12 Z1i Z1p Z1m

Z21 Z22 Z2i Z2p Z2m

Zi1 Zi2 Zii Zip Zim

Zp1 Zp2 Zpi Zpp Zpm

Zm1 Zm2 Zmi Zmp Zmm

0

0

0

0

0

Ip(+)

0

0

Neglect prefault load currents, Fault current If =Ip(+)

abc abc abc abc

abcabcabcabcIfZppEpEp )0()( …… (a)

Voltage at fault bus is given by


Voltage at fault bus P is also given by

abcabcabcIfZfEp .)( …… (b)

From a&b, abcabcabcabcabc IfZppEpIfZf )0(.

)1.......()0(.)(

).()0(

1 abcabcabcabc

abcabcabcabc

EpZppZfIf

IfZppZfEp

)2........(.)0()(abcabcabcabc

IfZipEiEi

Putting values of If in voltage at any other bus Ei(+) and voltage at fault bus Ep(+), we get

)3........(.)(abcabcabc

IfZfEp Dr. Nitin Dhote, SVPCET, Nagpur

If the network is expressed in sequence components 0,1,2 ,Equations 1,2&3 are modified by replacing the suffix abc by 012 asfollows:

)1.......()0(.)(0121012012012

EpZppZfIf

)2........(.)0()(012012012012

IfZipEiEi

)3........(.)(012012012

IfZfEp


In many types of faults , Fault impedance Zf is unidentified( Infinite). Equations are obtained in terms of Fault admittance


For a power system containing m number of buses,Bus voltages during fault at bus P are given by

)()0()( abcabcabcabc IbusZbusEbusEbus

E1(+)

E2(+)

Ei(+)

EP(+)

Em(+)

=

E1(0)

E2(0)

Ei(0)

EP(0)

Em(0)

-

Z11 Z12 Z1i Z1p Z1m

Z21 Z22 Z2i Z2p Z2m

Zi1 Zi2 Zii Zip Zim

Zp1 Zp2 Zpi Zpp Zpm

Zm1 Zm2 Zmi Zmp Zmm

0

0

0

0

0

Ip(+)

0

0

Neglect prefault load currents, Fault current If =Ip(+)

abc abc abc abc

)(..........)0()( aIfZppEpEpabcabcabcabc

Voltage at fault bus is given by


).......()(. bEpYfIfabcabcabc

Fault current in terms of admittance is given by

From a&b, we get

)1........()0(.).()(

)0()().(

))(..()0()(

1 abcabcabcabc

abcabcabcabc

abcabcabcabcabc

EpYfZppUEp

EpEpYfZppU

EpYfZppEpEp

)3........(.)0()(abcabcabcabc

IfZipEiEi

Putting values of Ep(+) in fault Current If , we get

)2.......()(.abcabcabc

EpYfIf

Putting values of If in voltage at any other bus Ei(+) , we get


Ea = Ii (Zf +Zg)

)( ZgZfIi

EaZf

aa


Since the fault is symmetrical all transfer impedance are the

same.


into which is given by

The fault current at the faulted bus p using equation is given by


=Assuming pre fault bus voltage as 1p.u.

=assuming abc sequence


• Assuming all the power system element are balanced. The Zpp 012 have only the diagonal term


Simply the voltage at faulted bus is given by


similarly the voltage at any other bus during fault is given by

for i = 1, 2,--- n--

--Ei(+) 012 =

0

√3

0

--


=


• Let a single line to ground fault occurs on phase a at bus ‘p’ through impedance Zf as shown in fig. below

a cb

Zf


• THE FAULT IMPEDANCE [ZF ABC] CAN BE CALCULATED BY USING

THE DEFINITION OF DRIVING POINT AND TRANSFER IMPEDANCE

a cb

Zf


Zfaa = Zf = Ea/Ia

Since b & c are open ckt to ground.

Zfbb = Zf

cc= ∞

And all transfer impedances are zero.

Therefore

Zfabc=

To avoid the multiplication by infinity the solution should be carried out in form of Yf

abc

Zf

∞

∞


1/ Zf 0 0 Yf 0 0

Yfabc = 0 0 0 = 0 0 0

0 0 0 0 0 0

where Yf = 1/Zf .

Yf012 =Ts

*t . Yfabc. Ts

= 1 1 1 Yf 0 0 1 1 1

1/√3 1 α α2 0 0 0 1/√3 1 α2 α

1 α2 α 0 0 0 1 α α2


1 1 1 Yf Yf Yf Yf Yf YfYf

012= 1/3 1 α α2 0 0 0 = 1/3 Yf Yf Yf1 α2 α 0 0 0 Yf Yf Yf

1 1 1

Yf012= Yf/3 1 1 1

1 1 1

voltage at faulted bus P during the fault is given by

Ep(+)012 = [ U + Zpp012 .Yf012 ] -1 Ep (0) 012


1+ (Yf/3)Zpp(0) (Yf/3)Zpp(0) (Yf/3)Zpp(0) -1 0

Ep(+)012= (Yf/3)Zpp(1) 1+(Yf/3)Zpp(1) (Yf/3)Zpp(1) √3

(Yf/3)Zpp(2) (Yf/3)Zpp(2) 1+(Yf/3)Zpp(2) 0

With solving we get

-Zpp(0)

Ep(+)012 = √3/(3Zf+Zpp(0)+Zpp(1)+Zpp(2)) 3Zf+Zpp(0)+Zpp(2)

-Zpp(2)

:. Zpp(1)= Zpp(2)

-Zpp(0)

Ep(+)012= √3/(3Zf+Zpp(0)+2Zpp(1)) 3Zf+Zpp(0)+Zpp(1)

-Zpp(1)


If012 = [Yf

012 ].Ep(+)012

1 1 1 -Zpp(0)

If012 =Yf/3 1 1 1 * 1 √3/(3Zf+Zpp(0)+2Zpp(1)) 3Zf+Zpp(0)+Zpp(1)

1 1 1 -Zpp(1)

1

If012 = √3 / (3Zf+Zpp(0)+2Zpp(1)) 1

1

Voltage at any other buses during fault

Ei (+)012 = Ei(0)012 – Zip012 .If012

Fault current


0 Zip(0) 0 0 1

Ei(+)012= √3 - 0 Zip(1) 0 * √3/(3Zf+Zpp(0)+2Zpp(1)) 1

0 0 0 Zip(2) 1

0 Zip(0)

= √3 - √3/(3Zf+Zpp(0)+2Zpp(1)) Zip(1)

0 Zip(2)

Zip(0)

= √3/(3Zf+Zpp(0)+2Zpp(1)) 1- Zip(1)

-Zip(2)

By pre multiplying [Ts] matrix with fault current If 012, voltage of fault bus Ep(+) 012 , voltage of any other bus Ei(+) 012, current and voltages in phase quantities a bc can be obtained.

Ep(+) abc =Ts* Ep(+) 012 , If abc =Ts* If 012 & Ei(+) abc =Ts* Ei(+) 012Dr. Nitin Dhote, SVPCET, Nagpur

new short circuit studies dr. nitin dhote · 2019. 1. 8. · assumptions in short circuit studies:...

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