Unit systems

Formulas for per unit systems:-

For each system parameter, per-unit value is equal to the actual value divided by a base value:

Epu = E / Ebase

Ipu = I / Ibase

Zpu = Z / Zbase

Select rated values as base values, usually rated power in MVA and rated phase voltage in kV:

Sbase = Srated = Ö3ElineIline

Ebase = Ephase = Eline/ Ö3

The base values for line current in kA and per-phase star impedance in ohms/phase are:

Ibase = Sbase / 3Ebase ( = Sbase / Ö3Eline)

Zbase = Ebase / Ibase = 3Ebase2 / Sbase ( = Eline2 / Sbase)

Note that selecting the base values for any two of Sbase, Ebase, Ibase or Zbase fixes the base values of all four. Note also that Ohm’s Law is satisfied by each of the sets of actual, base and per-unit values for voltage, current and impedance.

Transformers

The primary and secondary MVA ratings of a transformer are equal, but the voltages and currents in the primary (subscript 1) and the secondary (subscript 2) are usually different:

Ö3E1lineI1line = S = Ö3E2lineI2line

Converting to base (per-phase star) values:

3E1baseI1base = Sbase = 3E2baseI2base

E1base / E2base = I2base / I1base

Z1base / Z2base = (E1base / E2base)2

The impedance Z21pu referred to the primary side, equivalent to an impedance Z2pu on the secondary side, is:

Z21pu = Z2pu(E1base / E2base)2

The impedance Z12pu referred to the secondary side, equivalent to an impedance Z1pu on the primary side, is:

Z12pu = Z1pu(E2base / E1base)2

Note that per-unit and percentage values are related by:

Zpu = Z% / 100

Detailed details of the Vector Surge relay :

The Vector Surge Relay

The vector surge relay is used to decouple synchronous generators from the grid utility in case of gridfailure.

Synchronous generators are generally operated in parallel with the grid utility. This ensures greater reliability and enables the generator to export power to the grid. In this condition, there is a chance, of a momentary interruption of the grid supply which may result for a few milliseconds. Such temporary interruptions can be caused to mal-operation of the circuit breakers on the grid transformerside.

For a synchronous generator, running in parallel with the grid utility, such a temporary interruption and restoration of the supply can be dangerous. As the restoration of the supply can be asynchronous i.e. the generator and the grid are now not in a synchronised condition. The can lead to the consequences of wrong synchronization such as damage to the generator or the prime mover.

The vector surge relay prevents this condition by decoupling the generator from the grid as soon as the grid supply fails. This is an extremely fast acting relay with an operating time of less than 300ms fromrelayoperationtobreakeropening.

Principle:

The vector surge relay functions by monitoring the rate of change of the rotor displacement angle of the generator. During parallel operation there is an angular difference between the terminal phase voltage (Up) and the internal synchronous voltage of the generator (Ui). This is due to the fact that the generator rotor is magnetically coupled to the generator stator and is forced to rotate at the grid frequency. The angle between the vector of the mains voltage Up and synchronous electro-motive force is known as the rotor displacement angle.

This angle is constantly varying and is dependent on the torque produced by the generator rotor. In the case of the grid failure, there is sudden change in the rotor displacement angle.

This causes a surge in the generator voltage shown in the figure. The relay works by monitoring the time taken between the zero-crossings in the waveform. Under normal operation, the time interval between two consecutive zero-crossings is almost constant. During the grid failure, the vector surge which occurs causes a delay in the zero-crossing. This delay is detected by a highly sensitive timer inside the relay and the relay operates.

The relays are usually set to operate for a change in the rotor displacement angle of 0 to 20 degrees