Lecture
Positive-sequence impedances are the same impedances that characterize the individual elements of a power supply system under normal, symmetrical operating conditions.
For elements whose magnetically coupled circuits are stationary relative to one another, the positive- and negative-sequence impedances are equal, since reversing the phase-rotation order of a symmetrical three-phase current system does not change the mutual inductance between the phases of the element. Such elements include transformers and autotransformers, overhead and cable transmission lines, and reactors. For these, r1 = r2 , x1 = x2 .
The negative-sequence reactances of elements with rotating electromagnetic fields (synchronous generators, synchronous compensators, motors) are, in general, not equal to the positive-sequence impedances. In electrical machines, negative-sequence currents likewise produce magnetic fluxes that move relative to the stator in the reverse direction. As it moves, the reverse-direction magnetic flux, rotating relative to the rotor at twice the speed, encounters a continuously varying magnetic reluctance along its path. This is caused by the magnetic asymmetry of the rotor and by the fact that the currents induced in the rotor's direct- and quadrature-axis circuits produce different response reactions.
The negative-sequence flux at synchronous frequency generally induces odd harmonics in the stator, which distort the sinusoidal shape of the stator magnetic field. This circumstance significantly complicates the determination of the reactance of a synchronous machine.
Values of negative-sequence reactance are given in catalogs and reference books as machine parameters. In the absence of such data, for machines with damper windings one can take
x2 = 1.22 x”d ;
for salient-pole machines without damper windings –
x2 = 1.45 x”d .
In approximate practical calculations for turbogenerators, one can assume
x2 ≈ x”d .
For induction motors, the negative-sequence impedance is taken equal to their subtransient impedance x2 = x”d =1/ I p ,
where I p – the starting-current ratio of the motor.
+For an aggregate (composite) load, the negative-sequence reactance is practically the same as at the instant a disturbance suddenly occurs, i.e.
x1 = x2 = 0.35 .
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