11-05-2012, 12:14 PM
Power System Fault Analysis
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Introduction
The fault analysis of a power system is required in order to provide information for the
selection of switchgear, setting of relays and stability of system operation. A power
system is not static but changes during operation (switching on or off of generators and
transmission lines) and during planning (addition of generators and transmission lines).
Thus fault studies need to be routinely performed by utility engineers (such as in the CEB).
Faults usually occur in a power system due to either insulation failure, flashover, physical
damage or human error. These faults, may either be three phase in nature involving all
three phases in a symmetrical manner, or may be asymmetrical where usually only one or
two phases may be involved. Faults may also be caused by either short-circuits to earth or
between live conductors, or may be caused by broken conductors in one or more phases.
Sometimes simultaneous faults may occur involving both short-circuit and brokenconductor
faults (also known as open-circuit faults).
Balanced three phase faults may be analysed using an equivalent single phase circuit.
With asymmetrical three phase faults, the use of symmetrical components help to reduce
the complexity of the calculations as transmission lines and components are by and large
symmetrical, although the fault may be asymmetrical.
Fault analysis is usually carried out in per-unit quantities (similar to percentage quantities)
as they give solutions which are somewhat consistent over different voltage and power
ratings, and operate on values of the order of unity.
In the ensuing sections, we will derive expressions that may be used in computer
simulations by the utility engineers.
EE 423 - Power System Analysis: Faults – J R Lucas – October 2005 2
2.1 Equivalent Circuits - Single phase and Equivalent Single Phase Circuits
In a balanced three phase circuit, since the information relating to one single phase gives
the information relating to the other two phases as well, it is sufficient to do calculations in
a single phase circuit. There are two common forms used. These are (i) to take any one
single phase of the three phase circuit and (ii) to take an equivalent single phase circuit to
represent the full three phase circuit.
Single Phase Circuit
Figure 2.1 - Single Phase Circuit
Figure 2.1 shows one single phase “AN” of the three phase circuit “ABC N”. Since the
system is balanced, there is no current in the neutral, and there is no potential drop across
the neutral wire. Thus the star point “S” of the system would be at the same potential as
the neutral point “N”. Also, the line current is the same as the phase current, the line
voltage is √3 times the phase voltage, and the total power is 3 times the power in a single
phase.
I = IP = IL, V = VP = VL/√3 and S = SP = ST/3
Working with the single phase circuit would yield single phase quantities, which can then
be converted to three phase quantities using the above conversions.
Equivalent Single Phase Circuit
Of the parameters in the single phase circuit shown in figure 2.1, the Line Voltage and the
Total Power (rather than the Phase Voltage and one-third the Power) are the most
important quantities. It would be useful to have these quantities obtained directly from the
circuit rather than having conversion factors of √3 and 3 respectively. This is achieved in
the Equivalent Single Phase circuit, shown in figure 2.2, by multiplying the voltage by a
factor of √3 to give Line Voltage directly.
Figure 2.2 - Equivalent Single Phase Circuit
The Impedance remains as the per-phase impedance. However, the Line Current gets
artificially amplified by a factor of √3. This also increases the power by a factor of (√3)2,
which is the required correction to get the total power.
Thus, working with the Equivalent single phase circuit would yield the required three
phase quantities directly, other than the current which would be √3 IL.
Revision of Per Unit Quantities
Per unit quantities, like percentage quantities, are actually fractional quantities of a
reference quantity. These have a lot of importance as per unit quantities of parameters tend
to have similar values even when the system voltage and rating change drastically. The per
unit system permits multiplication and division in addition to addition and subtraction
without the requirement of a correction factor (when percentage quantities are multiplied
or divided additional factors of 0.01 or100 must be brought in, which are not in the original
equations, to restore the percentage values). Per-unit values are written with “pu” after the
value.