Short Circuit Study | An Introduction to Circuit Breaker Sizing
Power systems appear in various sizes and levels of complexity. Because of this, careful design considerations and studies such as load flow are exhaustively conducted. This is to ensure that the system will be operating as designed, thus maintaining a very high level of continuity of service. But despite all these efforts, unavoidable conditions that result to short circuit on the system cannot be entirely eliminated.
Power System States
A power system can be in any of the following states: normal, abnormal, and faulted state. In a normal state, the system is operating within the designed limits and maximum equipment life is expectancy is anticipated. An abnormal state is when the system operates outside the designed limits for short periods that may accelerate equipment aging. A faulted state is when the system is subjected to severe stress and where equipment failure is very likely. A faulted state maybe caused by natural events, accidents, deterioration of insulation and other causes that are impossible or impractical to avoid.
A faulted state can be distinguished generally by a sudden and significant increase in current. It is because of this high current that the system is subjected to high levels of stress given that mechanical and thermal stress are functions of the square of the current, i2. Short circuit current is usually supplied from utility transmission system, generators, and synchronous and induction motors.
Anatomy of A Short Circuit Current
A faulted power system can be simplified into an equivalent circuit with an ideal sinusoidal voltage source, and a resistance and inductance connected in series. The closing of the switch in figure 3, simulates a short circuit condition.
By Kirchhoff’s Voltage Law,
where
E is the magnitude of the voltage source in rms
i(t) is the instantaneous current at any time t
R is the resistance of the circuit in ohms
L is the inductance of the circuit in henry
t is the time in seconds
α is the phase angle of the voltage source when the switch is closed
ω is equal to 2πf at system frequency
Solving for the instantaneous current i(t),
where
The instantaneous short circuit current i(t) is composed of two components, the transient dc component and the steady-state ac component. While the steady-state ac component is symmetrical, the transient dc component decays exponentially with time based on the system X/R ratio. This makes the fault current asymmetrical. It is important to note that the magnitude of the dc and ac component is dependent on phase angle of the voltage source when the fault occurs, and together with the system X/R ratio, the degree of the fault current asymmetry.
As an example, for a purely inductive system, the fault current waveform is shown in figures 4 and 5. Figure 4 shows a short circuit current waveform with the voltage source phase angle equal to 0° at the time of fault while figure 5 shows a short circuit current with the voltage source phase angle equal to 90° at the time of fault. Notice that the maximum asymmetry occurs when the voltage source phase angle is equal to 0° at the time of fault. This is true for any system X/R. For a purely resistive circuit, the transient dc component is forced to zero.
Figure 6 shows a typical short circuit current waveform with the voltage source phase angle equal to 27° at the time of fault and a system X/R ratio of 15.
The ‘Half-Cycle’ Current
When conducting a short circuit study, the maximum fault current is of particular interest because circuit breakers are sized according to this value. Most of the computer programs adopt the ‘Half-Cycle’ current assumption to determine the peak and rms values of the maximum fault current available. The ‘Half-Cycle’ current assumes a purely reactive system where the maximum fault current occurring exactly one-half cycle after the onset of a fault. However this assumption may underestimate the maximum fault current because in practical systems, the current is usually lagging the applied voltage by an angle based on the system X/R. This will result to the fault current reaching its maximum value before one-half cycle.
At t = 0.5 cycle with α = 0°, the maximum peak fault current is determined.
Let
Similarly, the maximum rms fault current can be determined using
This is the concept behind the commonly used multiplying factors in determining the momentary short circuit current and protective device duties at the ½ cycle after the fault.
The calculated short circuit current by applying these multiplying factors can be used for the verification of circuit breaker close and latch capability, bus bracing capability, relay instantaneous overcurrent protection, and interrupting capabilities of fuses and low voltage circuit breakers.
References
G. Pradeep Kumar (2006), Principles of Transformer Protection, notes on Power System Protection Training, Visayan Electric Company, Cebu City, Philippines.
Blackburn, J. (2014). Protective Relaying Principles and Application, 4th ed. Boca Raton, FL: CRC Press.
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