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------------------- Credit : Dr.Muhammad Adil ----------------------
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Sequence Impedances And Sequence Networks
Sequence impedances and sequence networks are the fault analyzing and calculating parameters in power system networks. Sequence impedances are of three types. They are positive, negative and zero sequence impedances.

The sequence impedances in positive and negative sequences are equal in magnitude in case of transformers and transmission lines. Whereas these are not equals in case of rotating machines such as synchronous machines (alternators, synchronous motors).

Consider the sequences networks for a synchronous machine.

Positive sequence network:

Figure 1 is the Positive sequence network for three phase system and its equivalent for single phase system.
If the fault involves ground, a current In (equal to phasor sum of line currents Ia, Ib and Ic.) flows to neutral from ground via reactor Zn. Depending on the type of fault one or more of the line currents may be zero. Unbalanced line currents can be resolved into their symmetrical components.

Three-Phase Unloaded Synchronous Generator

1. Positive-Sequence Impedance and Network:

Since a synchronous machine is designed with symmetrical windings, it has induced emfs of positive sequence only, i.e., no negative-or zero-sequence voltages are induced in it. The armature reaction field set up by positive-sequence currents rotates at synchronous speed in the same direction as the rotor, i.e., it is stationary with respect to field excitation.

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The machine equivalently offers a direct-axis reactance whose value increases from subtransient reactance X”d to transient reactance X’d and finally to steady- state (synchronous) reactance Xd as the short circuit transient progresses in time. Subtransient reactance is used in a circuit where a sudden value of current under switching of fault condition is to be obtained.

Where current after a few cycles (3 or 4) is desired, transient reactances are used, and for steady-state condition, the steady-state or synchronous reactances are used. Positive-sequence reactances together with the negligible resistance make up the positive sequence subtransient, transient or steady-state positive sequence impedances, respectively.

The positive-sequence network for a synchronous machine can be represented by the source emf on no load and the positive sequence impedance Z1 in series with it, as shown in Fig. 3.10(a). The neutral impedance Zn does not appear in the circuit because the phasor sum of Ia1, Ib1 and Ic1 is zero and no positive sequence current can flow through Zn. Since it is a balanced network, it can be drawn on single phase basis, as shown in Fig 3.10( b), for purpose of analysis.

Positive-Sequence Network of a Synchronous Machine

The reference bus for a positive-sequence network is at neutral potential. Further, since no curr



2. Negative-Sequence Impedance and Network:


The synchronous machine does not generate any negative-sequence voltage. Flow of negative sequence currents in the stator winding produces an mmf rotating synchronously in a direction opposite to that of the rotor. Thus the negative sequence field rotates at a speed twice the synchronous speed with respect to rotor. Currents at double the stator frequency are, therefore, induced in rotor field and damper winding.

In sweeping over the rotor surface, the negative sequence mmf is alternately presented with reluctances of direct and quadrature axes. Thus the negative-sequence reactance X2 is found to oscillate between Xd” and Xq” and the value taken is usually the average.

Thus the negative-sequence reactance –

X2 = Xd” + Xq”/2 ….(3.8)

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The negative-sequence networks of a synchronous machine, on a three-phase and single phase basis are shown in Figs. 3.11 (a) and 3.11 (b) respectively. The reference bus for the negative- sequence network is also the neutral of the machine.

The negative-sequence voltage of terminal a with respect to reference b

Negative-Sequence Network of a Synchronous Machine

3. Zero-Sequence Impedance and Network:

No zero-sequence voltage is induced in synchronous machine. The flow of zero-sequence currents in the stator windings produces three mmfs which are in time phase but are distributed in space by 120°. The resultant air gap field produced by zero-sequence currents is therefore zero. Hence, the rotor windings present leakage reactance only to the flow of zero-sequence currents.

Zero-Sequence Network of a Synchronous Machine

As the current flowing in the reactor impedance Zn is the sum of the zero sequence currents in all the three phases, hence voltage drop caused by it will be 3 Ia0 Zn.