topic 8 fault calculation methods

7/31/2019 Topic 8 Fault Calculation Methods

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Topic 8: Fault Calculation

Methods

Problems in electrical circuits

Open circuits Supply is disconnected to the load

Short circuits Supply bypasses the load

Very dangerous Lead to high fault currents

Disastrous effects on equipment

Thermal heating

Electromechanical effects

Fires

Protection must detect abnormal fault currents Isolate in a time consistent with short circuit fault

current

Therefore fault current must be accurately predictedfor a fault in any location


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Types of short-circuits and their currents

Balanced three-

phase short-circuit

Line-to-line short-

circuit

Types of short-circuits and their currents

Line-to-line short-circuit

with earth connection

Line-to-earth short-circuit


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Comparison of magnitude of short-

circuit currents

Fault type Magnitude

3-phase (most severe) (E/Z) x multiplier

Line-to-line 0.87 x 3-phase fault

Line-to-ground(usually least severe)

Depends on systemgrounding

Per Unit System

Fault calculations must be done using per-unit system

Vpu = V/VB VB is the voltage base

Ipu = I/IB IB is the current base

Spu = S/SB SB is the kVA base

Zpu = Z/ZB ZB is the impedance base

Usually base values VB and SB are specified

IB and and ZB are determined from VB and SBIB = SB/VBZB = VB

2/SB = VB/IB VB is taken as the rated system voltage

SB is arbitrarily specified (100/10/1 MVA)

Rating of transformer is normally used as the base


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Use of pu system

For balanced symmetrical 3-phase faults

Fault calculation must be done on single phase

basis

Use the pu phase impedance of one-line

diagram

Care must be taken to ensure the proper phase kVA

and voltage levels are used in the calculation

IB = (SB/3)/(VB/3) = SB/ (3 VB)

ZB = [(VB/3)2]/(SB/3) = VB2/SB

Where VB is the line voltage

And SB is the three phase kVA value

Change of base

Fault calculations must include all significant components ofimpedance

Must be expressed in pu terms using the appropriate base value

Sometimes may need to be changed if they are expressed usingdifferent bases, e.g transformer impedances

Zpu = Z/ZB = Z(SB/VB2)

For change of kVA base (SB): Zpu(new) = Zpu(old)[SB(new)/SB(old)]

Change of voltage base (VB): Zpu(new) = Zpu(old)[VB2

(old)/VB2

(new)]

Change of both kVA and voltage bases at the same time:

Zpu(new) = Zpu(old)[SB(new)/SB(old)][VB2

(old)/VB2

(new)]

Impedances of transformers, motors, etc will be given in puterms based on their rated voltage and power levels

Impedances of cables, overhead lines, etc will be given in ohmsand must be converted to pu with the appropriate base


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Fault Calculation Effects and Requirements

Fault levels in a power system must be calculated atthe design stage to determine:

Overcurrent protection

Peak electromagnetic forces

Thermal heating effects

Maximum and minimum fault current

Time discrimination requirements of protection

Touch voltages on earth objects

Sources of fault currents

Electrical utility supply system

In-house generation systems operating at time of fault

Motors operating within the system at time of fault

Any electrical storage elements in the system, e.g.capacitors

Fault current contribution

Static equipment are not sources of fault

current

Inverters, converters, transformers, induction

heaters

Capacitors and battery operated UPS are low-

level sources of fault current

Supply utility and in-house generation providesconstant fault current (stiff source)

Motors will provide decaying fault current as

their magnetic excitation fields collapse


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Fault current contribution from motors

Time-varying impedance

Sub-transient reactance (Xd) effective impedance in

first few cycles

Transient reactance (Xd) - effective impedance in 2 20

cycles

Synchronous reactance (Xs) impedance in steady state

Synchronous reactance is generally not used since

protection will operate before it comes into effect

For synchronous motors, only the sub-transient and

transient reactance are normally used

For induction motors, only the sub-transient reactance is

used

DC Offset

Must be included in fault calculations,

especially LV systems

DC offset can increase initial current levels

substantially

Magnitude of DC offset depends on X/R ratio

of fault circuit


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Short-circuit current waveforms

(far from generator short-circuit)

Short-circuit current waveforms

(near to generator short-circuit)


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Short-circuit current waveforms from

different sources

Utility

Generator

Synchronous

motor

Induction

motor

Symmetrical short-circuit current from 3 sources(utility, motors and generator combined into a total)


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Fault calculation methodsTo simplify calculations, the following assumptions are made:

Fault is balanced 3-phase symmetrical

Pu impedances are pure reactances for MV

systems, any resistance is neglected

For LV systems where resistance is important,

impedance is [Z] = (R2 + X2)1/2

All significant component impedances are

included

The fault itself has zero impedance (i.e. boltedshort circuit)

Fault calculation methods

Earth circuit impedance is neglected

balanced 3-phase nature of fault eliminates earth

impedance

Rated voltage is used as the voltage base

X/R for all equipment

used to calculate level of DC offset multiplier

after symmetrical fault current has been calculated

Convert all impedances to pu values Use these to draw single line diagram of fault circuit

All possible sources modeled as ideal voltage source

With appropriate source impedance value connected


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Fault calculation methods

Circuit simplification

Impedance diagram reduced to single pu

impedance Zf

Connected to true earth and to ideal voltage

source

Fault current (pu):

If (pu) = Vpu/Zf(pu)

= 1/Zf(pu) (since Vpu = 1) If= If(pu) . IB Amps

Parameters for fault calculation


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topic 8 fault calculation methods

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