Short Circuit Transients

Short Circuit Transients

It may be possible in practice that the alternator running with full excitation may undergo a sudden short circuit because of the abnormal conditions. Due to sudden short circuit of alternator, large mechanical forces are developed which may not be sustained by the alternator. These forces are proportional to square of the current value, hence large pressure is buit up between adjacent stator conductors. 

The short circuit transients in a synchronous machine is a complicated phenomenon due to number of circuits coupled to each other are involved. When a synchronous generator undergoes short circuit, it has a characteristic time varying behaviour. During short circuit, flux per pole dynamically changes. Thus the transients are seen in the field and damper windings. The alternator can be represented by an equivalent circuit wherein the reactance is seen to be changed from subtransient reactance to final steady state synchronous reactance.

When alternator undergoes a short circuit number of events take place which depends on various factors such as the instant in the cycle at which short circuit occurs, whether the machine is loaded or not, what is the excitation provided, how many phases are involved, whether it is occuring near to machine terminals or away from it and on the constructional features of the machine. Hence the evaluation of sudden short circuit current for the given conditions is complex and to some extent empirical process depending on values of resistances, self and mutural inductances which themselves are variable and difficult to assess.

After the moment of short circuit, the time period followed by it can be divided into three periods. The first one is very short period of one or two cycles the conditions of which are dependent on the flux linkages between stator and rotor during short circuit. The second interval is longer one which is nothing but transient decay of short circuit current which is affected by damping and rise of armature reaction. The final period is nothing but the steady state short circuit before which the generator is normally open circuited.

1. Constant Flux Linkage Theorem

The behaviour shown by the alternator just after short circuit can be understood by the use of constant linkages theorem. If a closed circuit with resistance r and inductance L is considered without a source then the equation obtained using KVL will beThis show that the flux linkages Li remain constant. In generator also the effective inuctance of stator and rotor windings is large compared to the resistance which can be neglected for first few cycles. The rotor circuit is closed through exciter while stator is closed by short circuit. Thus the flux linkag with either winding must remain constant irrespective of the rotation.

2. Analysis of RL Series Circuit

Consider RL series circuit excited by sinusoidal voltage as shown in the Fig. 3.18.1. At t = t₁ switch is closed.

The first term is steady state current (I_ss) while the second term is transient current (I_t). The waveforms are shown in the Fig. 3.18.2.

If voltage is switched on at t = t₁ when it is zero, then the transient term has greatest value. The approximate current in this case reaches 2I_m which is known as doubling effect compared to the switching instant of voltage when voltage is maximum.

Thus the current flowing in the circuit changes its waveform depending on the instant at which the voltage is applied, alternator subjected to short circuit condition.

3. Short Circuit Phenomenon

Consider a two pole elementary single phase alternator with concentrated stator winding as shown in Fig. 3.18.3.

The corresponding waveforms for stator and rotor currents are shown in the Fig. 3.18.4.

Let short circuit occurs at position of rotor shown in Fig. 3.18.3 (a) when there are no stator linkages. After 1/4 Rev as shown Fig. 3.18.3 (b), it tends to establish full normal linkage in stator winding. The stator opposes this by a current in the shown direction as to force the flux in the leakage path. The rotor current must increase to maintain its flux constant. It reduces to normal at position (c) where stator current is again reduces to zero. The waveform of stator current and field current shown in the Fig. 3.18.4 changes totally if the position of rotor at the instant of short circuit is different. Thus the short circuit current is a function of relative position of stator and rotor.

Using the theorem of constant linkages a three phase short circuit can also be studied. After the instant of short circuit the flux linking with the stator will not change. A stationary image of main pole flux is produced in the stator. Thus a d.c. component of current is carried by each phase. The magnitude of d.c. component of current is different for each phase as the instant on the voltage wave at which short circuit occurs is different for each phase. The rotor tries to maintain its own poles. The rotor current is normal each time when rotor poles occupy the position same as that during short circuit and the current in the stator will be zero if the machine is previously unloaded. After one half cycle from this position the stator and rotor poles are again coincident but the poles are opposite. To maintain the flux linkages constant, the current in rotor reaches to its peak value.

The stationary field produced by poles on the stator induces a normal frequency emf in the rotor. Thus the rotor current is fluctuating whose resultant a.c. component develops fundamental frequency flux which rotates and again produces in the stator windings double frequency or second harmonic currents. Thus the waveform of transient current consists of fundamental, a.c. and second harmonic components of currents.

Thus whenever short circuit occurs in three phase generator then the stator currents are distorted from pure sine wave and are similar to those obtained when an alternating voltage is suddenly applied to series R-L circuit.

4. Stator Currents During Short Circuit

If a generator having negligible resistance, excited and running on no load is suddenly undergoing short circuit at its terminals, then the e.m.f. induced in the stator winding is used to circulate short circuit current through it. Initially the reactance to be taken into consideration is not the synchronous reactance but only the leakage reactance of the machine. The effect of armature flux (reaction) is to reduce the main field flux. But the flux linking with stator and rotor can not change instantaneously because of the induction associated with the windings. Thus at the short circuit instant, the armature reaction is ineffective. It will not reduce the main flux. Thus the synchronous reactance will not come into picture at the moment of short circuit. The only limiting factor for short circuit current at this instant is the leakage reactance.

After some time from the instant of short circuit, the armature reaction slowly shows its effect and the alternator then reaches to steady state. Thus the short circuit current reaches to high value for some time and then settles to steady value.

It can be seen that during the initial instant of short circuit is dependent on induced emf and leakage reactance which is similar to the case which we have considered previously of voltage source suddenly applied to series R-L circuit. The instant in the cycle at which short circuit occurs also affects the short circuit current. Near zero e.m.f. (or voltage) it has doubling effect. The expressions that we have derived are applicable only during initial conditions of short circuit as the induced e.m.f. also reduces after some time because of increased armature reaction. 

The short circuit currents in the three phases during short circuit are as shown in the Fig. 3.18.5.

5. Single Phase Short Circuit

Consider a single phase alternator operating under no load condition. This alternator is suddenly short circuited. As discussed earlier during initial moment of short circuit only leakage reactance of the machine limits the short circuit current. Under steady state, the armature reaction produces a demagnetizing flux which we take as synchronous reactance. Let the resistance of armature winding be small and can be neglected.

Immediately after the short circuit, the D.C. offset currents appear in the armature winding which can be computed separately on an emperical basis. Thus symmetrical short circuit currents are to be considered only. Due to theorem of constant flux linkages, the air gap flux cannot change instantaneously for counterbalancing the demagnetizing effect of armature short circuit current, the current is initially limited by leakage reactance only. The currents are thus induced in the field winding and the damper winding in a direction to help the main flux. Thus reactances X_f,X_d are in parallel with X_a during initial period. The equivalent circuit is shown in Fig. 3.18.6. and the equivalent reactance in this case is called subtransient reactance.

These currents appearing in the damper winding and the field winding decay depending upon winding time constants. The damper winding has inductance less than that of field winding and hence current in it dies out first and afterwards X_d is said to be effectively open circuited. The machine reactance changes from its value of subtransient to transient consisting of parallel combination of X_f and X_a. This is shown in the Fig. 3.18.7.

The current in the field winding also dies out and we say that the machine is operating in the combination of X_i and X_a. The equivalent circuit at steady state is shown in Fig. 3.18.8.

The subtransient and transient reactances are respectively given by,

It can be seen that X”_d < X’_d < X _d. Thus the machine offers variable reactance. As X”_d is smallest initially current is very large which is reduced subsequently when currents in damper winding and field winding die out.

The currents are given by,

I” = E_g / X”_d

I’ = E_g / X’_d

I'

The oscillogram of current neglecting d.c. offset currents is shown in the Fig. 3.18.9.

Review Questions

1. Discuss the short circuit transients in three phase alternator.

2. Explain the short circuit behaviour of single phase alternator.