Short Circuit Ratio of a Synchronous Machine (SCR)

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Short Circuit Ratio of a Synchronous Machine

Short Circuit Ratio is defined as –

The ratio of the field current needed to produce the rated voltage on an open circuit to the field current needed to Circulate the rated armature current on a short circuit is known as the short circuit ratio (SCR) of a Synchronous machine. The SCR can be Calculated from the open-circuit characteristic (O.C.C) at rated speed and the short circuit characteristic (S.C.C) of a Three-phase synchronous machine as shown in the figure below:

From the above figure, the SCR is given by the Equation shown below.

Short Circuit Ratio of a Synchronous Machine

Since the triangles Oab and Ode are similar. Therefore,

The ratio of the armature short circuit current for a given field current to the open-circuit voltage is known as the direct axis synchronous reactance, or Xd.

For the field current equal to Oa, the direct axis Synchronous reactance in ohms is given by the equation shown below:

The per-unit value of X_dis given as:

But, the base Impedance is:

Therefore,

From equation (1) and equation (6), we get

From equation (7) it is clear that the short circuit ratio is equal to the reciprocal of the Per-unit value of the direct axis Synchronous reactance.

In a Saturated Magnetic circuit, the value of X_d depends upon the degree of Saturation.

Importance of Short Circuit Ratio (SCR)

The short circuit ratio (SCR) is crucial to the operation of the Synchronous machine. The machine’s cost, physical size, and operating characteristics are impacted. A synchronous generator’s lower short circuit ratio causes a significant change in the terminal voltage with a change in load. The field current (If) needs to be adjusted over a wide range in order to maintain the terminal voltage constant.

For the small value of the short circuit ratio (SCR), the synchronizing power is small. As the synchronizing power keeps the machine in synchronism, a lower value of the SCR has a low stability limit. In other words, a machine with a low SCR is less stable when operating in parallel with the other generators.

The steady-state stability limit and voltage regulation of a synchronous machine with a high SCR value were both improved, but the short circuit fault current in the armature was high. It also has an impact on the machine’s size and price.

The excitation voltage of the synchronous machine is given by the equation:

For the same value of Tph Excitation voltage is directly proportional to the field flux per pole.

The synchronous inductance is given as:

Therefore,

Hence, the short circuit ratio is directly proportional to the air gap reluctance or air gap length.

The SCR can be raised by extending the air gap’s length. For a given value of excitation voltage, the field MMF must be increased as the air gap length increases (Ef). Therefore, either field current or the number of field turns must be increased to increase the value of the field MMF. All of this necessitates a higher field pole height, which increases the machine’s overall diameter.

Thus, a conclusion is that the large value of SCR will increase the size, weight, and cost of the machine.

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