Sections: Intro | Positive | Negative | Zero

Unloaded Generator: Introduction

Introduction. The impedance of a circuit when positive-sequence currents alone are flowing is called the impedance to positive-sequence current. When only negative-sequence currents are flowing, the impedance is called the impedance to negative-sequence current. When only zero-sequence currents are present, the impedance is called the impedance to negative-sequence current. The analysis of an unsymmetrical fault on a symmetrical system consists in finding the symmetrical components of thee unbalanced currents that are flowing.

Consider the following schematic:

Circuit diagram of an unloaded generator grounded through a reactance. The emfs of each phase are E_a, E_b and E_c.

Sections: Intro | Positive | Negative | Zero

Unloaded Generator: Positive

The generated voltage are of positive sequence only, since the generator is designed to supply balanced three-phase voltages. Thus, the positive-sequence network is composed of an emf in series with the positive-sequence impedance of the genreator.

The generated emf is the no-load terminal voltage to neutral, which is also equal to the transient, and subtransient internal voltages since the generator is not loaded.

The reactance in the positive-sequence network is the subtransient, transient, or synchronous reactance, depending on whether subtransient, transient, or steady-state conditions are being studied.

The reference bus for the positive-sequence network is the neutral of the generator. The neutral of the generator is at ground potential if there is a connection between neutral and ground having a finite or zero impednace since the connection will carry no positive-sequence current.

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

V_a1 = E_a - I_a1 Z₁

Where:
E_a = the positive -sequence no-load voltage to neutral
Z₁ = the positive -sequence impedance of the generator.

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Sections: Intro | Positive | Negative | Zero

Unloaded Generator: Negative

The negative sequence contains no emfs but include the impedances of the generator to negative-sequence currents.

The reactance in the negative-sequence network is the subtransient, transient, or synchronous reactance, depending on whether subtransient, transient, or steady-state conditions are being studied.

The reference bus for the negative-sequence network is the neutral of the generator. The neutral of the generator is at ground potential if there is a connection between neutral and ground having a finite or zero impednace since the connection will carry no negative-sequence current.

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

V_a2 = - I_a2 Z₂

Where:
Z₂ = the negative -sequence impedance of the generator.

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Sections: Intro | Positive | Negative | Zero

Unloaded Generator: Zero

The negative sequence contains no emfs but include the impedances of the generator to zero-sequence currents.

The reactance in the zero-sequence network is the subtransient, transient, or synchronous reactance, depending on whether subtransient, transient, or steady-state conditions are being studied.

The current flowing in the impedance Z_n between neutral and ground is 3I_a0.

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 a of phase a to the reference bus (or ground) is:

V_a0 = - I_a0 Z₀

Where:
Z₀ = the zero-sequence impedance of the generator, as defined above.

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Sections: Intro | Positive | Negative | Zero

Unloaded Generator: Matrix

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