THE NATURE OF SHORT CIRCUIT CURRENTS – PROTECTIVE RELAYING CONSIDERATION

Under normal system conditions, the equivalent circuit of Figure 2-1 may be used to calculate load currents. Three impedances determine the flow of current.

Zs and Zc are the impedances of the source and circuit, respectively, while Zl is the impedance of the load. The load impedance is generally the largest of the three, and it is the principle determinant of the current magnitude.

Load impedance is also predominantly resistive, with the result that load current tends to be nearly in phase with the driving voltage. A short circuit may be thought of as a conductor that shorts some of the impedances in the network while leaving others unchanged.

This situation is depicted in Figure 2-2. Because Zs and Zc become the only impedances that restrict the flow of current, the following observations may be made:

a) The short-circuit current is greater than load current.

b) Because Zs and Zc are predominately inductive, the short-circuit current lags the driving voltage by an angle approaching the theoretical maximum of 90°. 

 

The change in state from load current to short-circuit current occurs rapidly. Fundamental physics demonstrate that the magnitude of current in an inductor cannot change instantaneously. This conflict can be resolved by considering the short-circuit current to consist of two components:

— A symmetrical ac current with the higher magnitude of the short-circuit current

— An offsetting dc transient with an initial magnitude that is equal to the initial value of the ac current, but which decays rapidly

The initial magnitude of the dc transient is directly controlled by the point on the voltage wave at which the short circuit occurs. If the short circuit occurs at the natural zero crossing of the driving voltage sinusoid, the transient is maximized.

However, the transient is a minimum if the fault occurs at the crest of the voltage sinusoid. At any subsequent time, the magnitude of the dc transient is determined by the time constant of the decay of the dc, which is controlled by the ratio of reactance to resistance in the impedance limiting the fault.

Equation (2-2) can be used to calculate the instantaneous magnitude of current at any time. For the protection engineer, the worst case initial current includes the full dc transient.

The driving voltage depicted in Figure 2-1 and Figure 2-2 is the Thevenin equivalent opencircuit voltage at the fault point prior to application of the short circuit. This voltage includes sources such as remote generators with voltage regulators that maintain their value regardless of the presence of a short circuit on the system as well as nearby sources whose voltages decay when the short circuit is present.

The amount of decay is determined by the nature of the source. Nearby generators and synchronous motors with active excitation systems sustain some voltage, but because the short circuit causes their terminal voltage to drop, the current they produce is gradually reduced as the fault is allowed to persist.

At the same time, induction motors initially participate as short-circuit current sources, but their voltages decay rapidly as the trapped flux is rapidly drained. Figure 2-3 shows the generic tendencies of various kinds of short-circuit current sources and a composite waveform for the symmetrical ac current decay.  

 

Figure 2-4 depicts the most realistic case of the decaying symmetrical ac current combined with the decaying dc transient. From this figure, a generalized short-circuit current may be described in the following terms:

— High initial magnitude dc transient component of current, which decays with time

— High initial magnitude symmetrical ac current, which diminishes gradually with time

— Symmetrical ac current lags driving voltage by a significant angle, approaching 90°