Sections: Intro | Positive | Negative | Zero

Power System: Introduction

Introduction. The line-to-ground voltages at the fault is designated as V_A, V_B and V_C. Before the fault occurs, the line-to-neutral voltage of phase a is called V_f, which is a positive-sequence voltage since the system is assumed to be balanced.

Since linearity is assumed in drawing the sequence entworks, each of the networks can be replaced by its Thévenin equivalent between the two terminals composed of its reference bus and the point of application of the fault.

The current components, I_A1, I_A2, and I_A0 flow out of their respective sequence networks and out of the equivalent circuits of the networks at the point of application of the fault.

The matrix equations for the symmetrical components of voltages at the fault is the same as in unloaded generators except that V_f replaces E_A.

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Sections: Intro | Positive | Negative | Zero

Power System: Positive-Sequence

The internal voltage of the single generator of the equivalent circuit for the positive sequence is V_f, the prefault voltage to neutral at the point of application of the fault.

The impedance Z₁ of the equivalent circuit is the impedance measued between point of application of the fault and the refernce bus with all the internal emfs short-circuited.

The values of Z₁ is dependent on the reactances used in the network. The subtransient reactances of generators and 1.5 times the subtransient reactances of synchronous motors or the transient reactances of the motors are the values used to calculate the symmetrical fault to be interrupted.

The equation for the positive component of the voltage drop from point of application of the fault to the reference bus (or ground) is:

V_A1 = V_f - I_A1 Z₁

Where:
V_f = the positive -sequence, prefault voltage to neutral
Z₁ = the Thévenin equivalent of the impedances in the positive-sequence network.

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Sections: Intro | Positive | Negative | Zero

Power System: Negative-Sequence

Since no negative-sequence currents are flowing before the fault occurs, the prefault voltage between the point of application of the fault and the reference bus is zero. Therefore, no emfs appear in the equivalent circuits of the negative-sequence network.

The impedance Z₂ is measured between the point of application of the fault and the reference bus in the network and depend on the location of the fault.

The equation for the negative component of the voltage drop from point of application of the fault to the reference bus (or ground) is:

V_A2 = - I_A1 Z₁

Where:
Z₂ = the Thévenin equivalent of the impedances in the negative-sequence network.

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Sections: Intro | Positive | Negative | Zero

Power System: Zero-Sequence

Since no zero-sequence currents are flowing before the fault occurs, the prefault voltage between the point of application of the fault and the reference bus is zero. Therefore, no emfs appear in the equivalent circuits of the zero-sequence network.

The impedance Z₀ is measured between the point of application of the fault and the reference bus in the network and depend on the location of the fault.

The voltage drop of zero-sequence impedance from point a to ground is

-3I_A0Z_N - I_A0Z_g0

Thus the total zero-sequnce impedance through which I_A0 flows is

Z_A0 = 3Z_N + Z_g0

The equation for the zero component of the voltage drop from point of application of the fault to the reference bus (or ground) is:

V_A0 = - I_A0 Z₀

Where:
Z₀ = the Thévenin equivalent of the impedances in the zero-sequence network.

Zero-Sequence Network Equivalent

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Sections: Intro | Positive | Negative | Zero

Power System: Matrix

In matrix form, the three formulas given above would be:

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