Any Abnormal Conditions Which Causes Flow of Huge Current in the Conductors Or Cable Through

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INTRODUCTION

Any abnormal conditions which causes flow of huge current in the conductors or cable through inappropriate paths in the circuit can be defined as a fault. In normal operating conditions all the circuit elements of an electrical system carry currents whose magnitude depends upon the value of the generator voltage and the effective impedances of all the power transmission and distribution system elements including the impedances of the loads usually relatively larger than other impedances.

Modern electric systems may be of great complexity and spread over large geographical area. An electric power system consists of generators, transformers, transmission lines and consumer equipment. The system must be protected against flow of heavy short-circuit currents, which can cause permanent damage to major equipments, by disconnecting the faulty section of system by means of circuit breaker and protective relaying. Such conditions are caused in the system accidentally through insulation failure of equipment or flashover of lines initiated by a lightning stroke or through accidental faulty operation.

The safe disconnection can only be guaranteed if the current does not exceed the capability of the circuit breaker. Therefore, the short circuit currents in the network must be computed and compared with the ratings of the circuit breakers at regular intervals as part of the normal operation planning.

The short circuit currents in an AC system are determined mainly by the reactance of the alternators, transformers and lines upto the point of the fault in the case of phase to phase faults. When the fault is between phase and earth, the resistance of the earth path play an important role in limiting the currents.

Balanced three phase faults may be analyzed using an equivalent single phase circuit. With asymmetrical three phase faults, the use of symmetrical components help to reduce the complexity of the calculations as transmission lines and components are by and large symmetrical, although the fault may be asymmetrical. Fault analysis is usually carried out in per-unit quantities as they give solutions which are somewhat consistent over different voltage and power ratings, and operate on values of the order of unity.

In case of circuit breakers, their rupturing capacities are based on the symmetrical short circuit current which is most easy to calculate among all types of circuit currents. But for the determination of relay settings, it is absolutely necessary to know fault current due to unsymmetrical condition too for which knowledge of symmetrical components is required.

Depending on the location, the type, the duration, and the system grounding, short circuits may lead to

• electromagnetic interference with conductors in the vicinity (disturbance of communication lines),

• stability problems,

• mechanical and thermal stress (i.e. damage of equipment, personal danger)

• danger for personnel

In high voltage networks, short circuits are the most frequent type of faults. Short circuits may be solid or may involve an arc impedance. Figure 1 illustrates different types of short circuits.

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FIGURE 1- Examples for different types of short circuits

A power network comprises synchronous generators, transformers, lines,and loads. Though the operating conditions at the time of fault are important, the loads can usually be neglected during short circuits, as voltages dip very low so that currents drawn by loads can be neglected in comparison with short circuit currents.

The synchronous generator during short circuit has a characteristic time varying behavior. In the event of a short circuit, the flux per pole undergoes dynamic change with associated transients in damper and field windings.

The reactance of the circuit model of the machine changes in the first few cycles from a low subtransient reactance to a higher transient value, finally settling at a still higher synchronous (steady state) value. Depending upon the arc interruption time of the circuit breakers, an appropriate reactance value is used for the circuit model of synchronous generators for the short circuit analysis.

In a modern large interconnected power system, heavy currents flowing during a short circuit must be interrupted much before the steady state conditions are established. Furthermore, from the considerations of mechanical forces that act on the circuit breaker components, the maximum current that a breaker has to carry momentarily must also be determined. Therefore, for selecting a circuit breaker, the initial current that flows on occurrence of a short circuit and also the current in the transient that flows at the time of circuit interruption must be determined.

There are two different approaches to calculate the short circuits in a power system:

• Calculation of transient currents

• Calculation of stationary currents

TRANSIENTS ON A TRANSMISSION LINE

Let us consider the short circuit transient on a transmission line. Certain simplifying assumptions are made at this stage:

1. The line is fed from a constant voltage source.

2. Short circuit takes place when the line is unloaded.

3. Line capacitance is negligible and the line can be represented by a

lumped RL series circuit.

FIGURE 2 –Transmission line model

With the above assumptions the line can be represented by the circuit model shown above. The short circuit is assumed to take place at t = 0. The parameter α controls the instant on the voltage wave when short circuit occurs. It is known from circuit theory that the current after short circuit is composed of two parts, i.e.

where is represents the steady state alternating current

and it represents the transient direct current

With

A plot of i = is + it is shown in figure 3. In power system terminology, the sinusoidal steady state current is called the symmetrical short circuit current and the unidirectional transient component is called the DC off-set current, which causes the total short circuit current to be unsymmetrical till the transient decays.

FIGURE 3 - Waveform of a short circuit current on a transmission line

It follows easily from figure 3 that the maximum momentary short circuit current imm corresponds to the first peak. If the decay of transient current in this short time is neglected, then:

Since transmission line resistance is small, θis nearly 90◦.

This has the maximum possible value for α = 0, i.e. short circuit occurring when the voltage wave is going through zero. Thus imm may be a high as twice the maximum of the symmetrical short circuit current:

For the selection of circuit breakers, momentary short circuit current is taken

corresponding to its maximum possible value.

Modern circuit breakers are designed to interrupt the current in the first few cycles (five cycles or less). With reference to Figure, it means that when the current is interrupted, the DC off-set it has not yet died out and contributes thus to the current to be interrupted. Rather than computing the value of the DC off-set at the time of interruption (this would be highly complex in a network of even moderately large size),

the symmetrical short circuit current alone is calculated. This current is then increased by an empirical multiplying factor to account for the DC off-set current.

SHORT CIRCUIT OF A SYNCHRONOUS MACHINE

Under steady state short circuit conditions, the armature reaction of a synchronous generator produces a demagnetizing flux. In terms of a circuit this effect is modelled as a reactance Xa in series with the induced emf. This reactance when combined with the leakage reactance Xl of the machine is called synchronous reactance Xd. The index d denotes the direct axis. Since the armature reactance is small, it can be neglected. The steady state short circuit model of a synchronous machine is shown in figure shown below.

FIGURE 4- Steady state short circuit model of a synchronous machine

Consider now the sudden short circuit of a synchronous generator that has initially been operating under open circuit conditions. The machine undergoes a transient in all the three phases finally ending up in the steady state condition described above. The circuit breaker must interrupt the current long before the steady condition is reached. Immediately upon short circuit, the DC off-set currents appear in all three phases, each with a different magnitude since the point on the voltage wave at which short circuit occurs is different for each phase. These DC off-set currents are accounted for separately on an empirical basis.

Therefore, for short circuit studies, we need to concentrate our attention on the symmetrical short circuit current only. In the event of a short circuit, the symmetrical short circuit current is limited initially only by the leakage reactance of the machine. Since the air gap flux cannot change instantaneously, to counter the demagnetization of the armature short circuit current, currents appear in the field winding as well as in the damper winding in a direction to help the main flux. These currents decay in accordance with the winding time constants. The time constant of the damper winding which has low X/R-ratio is much less than the one of the field winding, which has high leakage inductance with low resistance. Thus, during the initial part of the short circuit, the damper and field windings have transformer currents induced in them. In the circuit model their reactances—Xf of field winding and Xdw of damper winding—appear in parallel with Xa as shown in figure below.

FIGURE 5 - Approximate circuit model during subtransient period of short circuit

FIGURE 6 - Approximate circuit model during transient period of short circuit

As the damper winding currents are first to die out, Xdw effectively becomes open circuited and at a later stage Xf becomes open circuited. The machine reactance thus changes from the parallel combination of Xa, Xf , and Xdw during the initial period of the short circuit to Xa and Xf in parallel (Figure ) during the middle period. The machine reactance finally becomes Xa in steady state (Figure 7.8). The reactance presented by

the machine in the initial period of the short circuit, i.e.

is called the subtransient reactance of the machine; while the reactance effective

after the damper winding currents have died out, i.e.

is called the transient reactance. Of course, the reactance under steady conditions is the synchronous reactance. Obviously X′′d < X′d < Xd. The machine thus offers a time-varying reactance which changes from X′′d to X′d and finally to Xd.

FIGURE 7 -Symmetrical short circuit armature current in synchronous machine.

SYMMETRICAL THREE PHASE FAULT ANALYSIS

In normal operating conditions, a three-phase power system can be treated as a single-phase system when the loads, voltages, and currents are balanced. If we postulate plane-wave propagation along the conductors (it is, however, known from the Maxwell equations that in the presence of losses this is not strictly true), a network representation with lumped elements can be made when the physical dimensions of the power system, or a part of it, are small as compared with the wavelength of the voltage

and current signals. When this is the case, one can successfully use a single line lumped-element representation of the three-phase power system for calculation. A fault brings the system to an abnormal condition. Short-circuit faults are especially of concern because they result in a switching action, which often results in transient overvoltages. In the case of a symmetrical three-phase fault in a symmetrical system, one can still use a single-phase representation for the short-circuit and transient analysis.

A three phase fault is a condition where either (a) all three phases of the system are short circuited to each other, or (b) all three phase of the system are earthed.

FIGURE 8 – (a) Balanced three phase fault (b) Balanced three phase to earth fault

This is in general a balanced condition, and we need to only know the positive-sequence network to analyze faults. Further, the single line diagram can be used, as all three phases carry equal currents displaced by 120◦.

Typically, only 5% of the initial faults in a power system, are three phase faults with or without earth. Of the unbalanced faults, 80 % are line-earth and 15% are double line faults with or without earth and which can often deteriorate to 3 phase fault. Broken conductor faults account for the rest.

Fault Level Calculations

In a power system, the maximum the fault current (or fault MVA) that can flow into a zero impedance fault is necessary to be known for switch gear solution. This can either be the balanced three phase value or the value at an asymmetrical condition. The Fault Level defines the value for the symmetrical condition. The fault level is usually expressed in MVA (or corresponding per-unit value), with the maximum fault current value being converted using the nominal voltage rating.

MVAbase =√ 3 . Nominal Voltage(kV) . Ibase (kA)

MVAfault =√ 3 . Nominal Voltage(kV) . Isc (kA)

where

MVAfault – Fault Level at a given point in MVA

Ibase – Rated or base line current

Isc – Short circuit line current flowing in to a fault

The per unit value of the fault Level may thus be written as

The per unit voltage for nominal value is unity, so that

The Short circuit capacity (SCC) of a busbar is the fault level of the busbar. The strength of a busbar (or the ability to maintain its voltage) is directly proportional to its SCC. An infinitely strong bus (or Infinite bus bar) has an infinite SCC, with a zero equivalent impedance and will maintain its voltage under all conditions.

Magnitude of short circuit current is time dependant due to synchronous generators. It is initially at its largest value and decreasing to steady value. These higher fault levels tax Circuit Breakers adversely so that current limiting reactors are sometimes used.

The Short circuit MVA is a better indicator of the stress on CBs than the short circuit current as CB has to withstand recovery voltage across breaker following arc interruption.

The currents flowing during a fault is determined by the internal emfs of machines in the network, by the impedances of the machines, and by the impedances between the machines and the fault.

The following figure shows a part of a power system, where the rest of the system at two points of coupling have been represented by their Thevenin’s equivalent circuit (or by a voltage source of 1 pu together its fault level which corresponds to the per unit value of the effective Thevenin’s impedance).

FIGURE 9 – CIRCUIT FOR FAULT CALCULATION

With CB1 and CB2 open, short circuit capacities are

SCC at bus 1 = 8 p.u. gives Zg1 = 1/8 = 0.125 pu

SCC at bus 2 = 5 p.u. gives Zg2 = 1/5 = 0.20 pu

Each of the lines are given to have a per unit impedance of 0.3 pu.

Z1 = Z2 = 0.3 p.u.

Suppose with CB1 and CB2 closed,the SCCs (or Fault Levels) of the busbars in the system is to be determined.

FIGURE 10 – Determination of short circuit capacities

The circuit can be reduced and analysed as shown in the figure 11.

FIGURE 11 – Determination of short circuit capacity at bus 3

Thus, the equivalent input impedance is given by Zin=0.23 pu at bus 3, so that the short circuit capacity at busbar 3 is given as

| SCC3 |= 1/0.23 = 4.35 p.u

The network may also be reduced keeping the identity of Bus 1 as in the following figure.

FIGURE 12 – Determination of short circuit capacity at bus 1

Thus, the equivalent input impedance is given by Zin=0.108 pu at bus 1, so that the short circuit capacity at busbar 1 is given as

| SCC1 |= 1/0.108 = 9.25 p.u

This is a 16% increase on the short circuit capacity of bus 1 with the circuit breakers open. The network may also be reduced keeping the identity of Bus 2. This would yield a value of Zin as 0.157 pu, giving the short circuit capacity at busbar 2 as

| SCC2 |= 1/0.157 = 6.37 p.u

This is a 28% increase on the short circuit capacity of bus 2 with the circuit breakers open.

SYMMETRICAL COMPONENT ANALYSIS (FOR UNSYMMETRICAL SYSTEMS)

For the majority of the fault situations, the power system has become unsymmetrical. Symmetrical components and, especially, the sequence networks are an elegant way to analyse faults in unsymmetrical three-phase power systems because in many cases the unbalanced portion of the physical system can be isolated for a study, the rest of the system being considered to be in balance. This is, for instance, the case for an unbalanced load or fault. In such cases, we attempt to find the symmetrical components of the voltages and the currents at the point of unbalance and connect the sequence networks, which are, in fact, copies of the balanced system at the point of unbalance (the fault point).

The method of symmetrical components is a very powerful approach and has simplified the procedure for solving problems on the unbalanced polyphase systems. The method of symmetrical components was suggested by C.L. Fortesque in the year 1918. This method can be applied to any number of phases but three phase system is of main interest.

According to Fortesque theorem, any unbalanced three phase system of currents, voltages or other sinusoidal quantities can be resolved into there balanced systems of phasors which are called symmetrical components of the original unbalanced system. Such three phase unbalanced systems constitute three sequence networks which are solved separately on a singe phase basis. Once the problem is solved in terms of the symmetrical components, it can be transferred back to the actual circuit condition by superposition or phasor additions of these quantities (currents or voltages) easily.

Symmetrical components of three phase systems

The symmetrical components differ in the phase sequence ,that is, the order in which the phase quantities go through a maximum. There may be a positive phase sequence, negative phase sequence and a zero phase sequence. Thus the balanced set of components can be given as positive sequence component, negative sequence component and zero sequence component. These are shown below in the figure:

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