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Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE) PDF Download

Introduction

The types of faults occurring in power systems are symmetrical and unsymmetrical faults. The unsymmetrical fault is the type of fault in which the three-phase line of the system becomes unbalanced therefore giving rise to unbalanced currents in the different phases.
In brief the types of unsymmetrical faults we will be discussing are:

  • Single line-to-ground fault (SLG)
  • Line-to-line fault (L-L)
  • Double line-to-ground fault (2LG)
  • Balanced three-phase fault

These faults give rise to unsymmetrical currents therefore different fault currents flow in different phases.
Here we will be discussing the types of unsymmetrical faults concerning a synchronous generator operating at no load.

Types of Unsymmetrical Faults

Following are the types of unsymmetrical faults in the power system.

Balanced Three-Phase Unsymmetrical Faults
In balanced three-phase unsymmetrical faults, the fault occurs when all the three phases of the transmission line or the terminals of the machine come in contact with each other.
Here let us consider an unloaded three-phase star-connected alternator. There is balanced three-phase unsymmetrical faults occurring at the terminals of the generator as a result the phase currents (Ia, Ib, and Ic) and voltages to be zero.

Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)

Firstly here,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)

Where Zn is the impedance through which generator neutral is earthed.
Secondly, representing above relations in matrix form

Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)

Further from the above matrix form we have,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Finally, we have,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)In the case of balanced three-phase unsymmetrical faults, only the positive sequence network is present in the solution.

Single Line-To-Ground Fault (L-G)

For single line-to-ground unsymmetrical faults, we consider a synchronous generator where a fault occurs at the ‘a’ phase of the generator with the fault impedance of Zf.
The generator is grounded through an impedance of Zn.

Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)

Under the single line-to-ground unsymmetrical faults condition, firstly we have
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Here we use the symmetrical components and represent the fault currents by substituting the above values. As Ib=0 and Ic=0.
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Secondly, from the above equation
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Further, we have,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)From the sequence network of a synchronous generator, we have the positive, negative, and zero sequence voltages as,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Moreover, substituting the value of equations (i) and (ii) in the above equations we have
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Also, we know that
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)So,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Therefore we have the expression of current as,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Finally, the figure below shows the sequence networks representing the L-G fault.
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)

Line-To-Line Fault (L-L)

For line-to-line unsymmetrical faults, we consider a synchronous generator where a line-to-line fault occurs on the phases ‘b’ and ‘c’ with a fault impedance of Zf.
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)

Firstly, under the condition of line-to-line fault
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Here we use the symmetrical components and represent the fault currents by substituting the above values.
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Secondly, from this relation we have
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Similarly, representing the voltages in terms of symmetrical components.
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Further from this equation we have,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Solving the above two equations for Va1 and Va2.

Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)As Ia2 = – Ia1 and Ia =0 so,
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Moreover from equation (iii) and (iv), we have
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Finally, the figure below shows the sequence network of L-L fault occurring on phases b and c of the generator.
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)In the terms of Thevenin’s equivalent circuit, the currents are
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)

Double Line-to-Ground Fault (L-L-G)

Here, we consider a synchronous generator where a double line-to-ground fault occurs between phases ‘b’, ‘c’, and ground with a fault impedance of Zf.

Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Under the condition of fault
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)The symmetrical components of voltages are
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)From the above equation
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)Now, subtracting Va1 from Va0.
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)The figure below shows the sequence network of the double line-to-line fault of the generator.

Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)

In the terms of Thevenin’s equivalent circuit, the currents are
Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE)In the cases of direct short-circuit for all the above fault cases, take Zf =0.

The document Short Notes: Unsymmetrical Faults | Power Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Power Systems.
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