Table 1 Typical per-unit reactance for three -phase synchronous machines

Type of machine

 

Turbine

2 pole

0.09

0.15

1.20

0.09

0.03

generator

4 pole

0.14

0.22

1.70

0.14

0.07

Salient pole

with dampers

0.20

0.30

1.25

0.20

0.18

generator

without dampers

0.28

0.30

1.20

0.35

0.12

X"= subtransient reactance; X'd =transient reactance; Xd=synchronous reactance X.2=negative sequence reactance; X0=zero sequence reactance

 

The subtransient reactance is the reactance applicable at the onset of the fault occurrence. Within 0.1 sec. the fault level falls to a value determined by the transient reactance and then decays exponentially to a steady-state value determined by the synchronous reactance.

Typical per-unit reactance's for three phase synchronous machines are given in Table 1.

In connecting sequence networks together, the reference busbar for the positive- and negative-sequence networks is the generator neutral which, in these networks, is at earth potential so that only zero-sequence currents flow through the impedances between neutral and earth. The reference busbar for zero-sequence networks is the earth point of the generator. The current which flows in the impedance between the neutral and earth are three times the zero-sequence current. Figure 2.9 illustrates the sequence networks for a generator.

The zero sequence networks carries only zero-sequence current in one phase which has an impedance of Zo = n + Zeo

The voltage and current components for each phase are obtained from the equations given for the sequence networks. The equations for the components of voltage, corresponding to the phase of the system, are obtained from the point an on phase a relative to the reference bus bar, and can be deduced from Figure 2.9 as follows:
 


Where

Εa = no load voltage to earth of the positive-sequence network

Z1 = positive-sequence impedance of the generator

Z2 = negative-sequence impedance of the generator
Zo= zero-sequence impedance of the generator (Zeo) plus three times the impedance to earth

The above equations can be applied to any generator which carries unbalanced currents and are the starting point for calculations for any type of fault. The same approach can be used with equivalent power systems or applied to loaded generators, Ea then being the voltage behind the reactance before the fault occurs.

 

2.2.2 Calculation of asymmetrical faults using symmetrical components

The positive, negative and zero-sequence network, carrying currents I1, I2 and Io respectively, are connected together in a particular arrangement to represent a given unbalanced fault condition. Consequently, in order to calculate fault 1 levels using the method of symmetrical components, it is essential to determine the individual sequence impedances and combine these to make up the correct sequence networks. Then, for each .type of fault, the appropriate combination of sequence networks is formed in order to obtain the relationships between fault currents and voltages.

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