CHAPTER 2

CURRENT AND

SHORT-CIRCUIT KVA CALCULATIONS

FAULT IN A POWER SYSTEM Faults occur when two or more

conductors that normally operate with a potential difference come in contact with each other.

These faults may be caused by sudden failure of a piece of equipment, accidental damage or short-circuit to overhead lines or by insulation failure resulting from lightning surges

The faults in a 3-phase system can be classified into two main categories :-

Symmetrical faultsUnsymmetrical faults

SYMMETRICAL FAULTS That faults which gives rise to

symmetrical faults currents (i.e. equal faults currents with 120º displacement) is called a symmetrical fault.

The most common example of symmetrical fault is when all the three conductors of a 3-phase line are brought together simultaneously into a short-circuit condition.

The following points may be particularly noted:The symmetrical fault rarely occurs in

practice as majority of the faults are of unsymmetrical nature.

The symmetrical fault is the most severe and imposes more heavy duty on the circuit breaker.

 FIGURE 2.1 THE SYMMETRICAL FAULT

UNSYMMETRICAL FAULTS Those faults which give rise to

unsymmetrical currents (i.e. unequal line currents with unequal displacement) are called unsymmetrical faults

The unsymmetrical faults may take one of the following forms:Single phase-to-ground faultPhase-to-phase faultTwo phase-to-ground fault

 FIGURE 2.2 THE UNSYMMETRICAL FAULT

The great majority of faults on the power system are of unsymmetrical nature; the most common type being a short circuit from one phase to ground.

Single phase open circuit and two phase open circuit are unsymmetrical types of faults.

Single phase-to-ground faultA short circuit between any one of the phase conductors and earth is called a single phase to ground faults. It may be due to the failure of the insulation between a phase conductors and the earth or due to a phase conductor breaking and falling to the ground.

Two phase-to-ground faultsA short circuit between any two phases and the earth is called a double line to ground or a two phase to ground fault.

Phase-to-phase faultA short circuit between any two phases is called a line-to-line or phase-to- phase faults.

Open circuited phasesThis type of faults is caused by a break in the conducting path. Such faults occur when one or more phase conductors break or a cable joint or a joint on the overhead lines fails. Such situations may also arise when circuit breakers or isolators open but fail to close one or more phase. Due to the opening of one or two phase, unbalanced currents flow in the system, thereby heating rotating machines. Protective schemes must be provided to deal with such abnormal situations.

Winding faultsAll types of faults discussed above also occur on the alternator, motor and transformer windings. In addition to these types of faults, there is one more type of faults, namely the short circuiting of turns which occurs on machine windings.

SYMMETRICAL COMPONENTS METHOD When unsymmetrical faults occurs, it

gives rise to unsymmetrical currents i.e. the magnitude of faults currents in the three lines are different having unequal phase displacement.

The calculations procedure known as method of symmetrical components is used to determine the current and voltages on the occurrence of an unsymmetrical fault.

THE SYMMETRICAL COMPONENT THEORY

A balances system of 3-phase currents having positive phase sequence (red-yellow-blue) with equal magnitude 120º phase displacement. These are called positive phase sequence components

A balanced system of 3-phase currents having the opposite or negative phase sequence (red-yellow-blue) with equal magnitude 120º phase displacement. These are called negative phase sequence components

A system of three currents equal in magnitude and having zero phase displacement. These are called zero phase sequence components

 FIGURE 2.3 THE SYMMETRICAL COMPONENT THEORY

THE SYMMETRICAL COMPONENT THEORY A balanced system of 3-phased currents ,

and having positive sequence as shown in Figure 2.4(i). These are the positive phase sequence components.

A balanced system of 3-phased currents , and having negative sequence as shown in Figure 2.4(ii). These are the negative phase sequence components.

A system of three currents , and equal in magnitude with zero phase displacement from each other as shown in Figure 2.4 (iii). These are the zero phase sequence components.

FIGURE 2.4 THE SYMMETRICAL COMPONENT THEORY