KILOMETRIC FAULTS: NATURE, AFFECTING PARAMETERS, AND IMPACT ON THE BREAKER STRESSES _____________________________ Mohamed M. Saied Electrical Engineering Department College of Engineering and Petroleum Kuwait University State of Kuwait

Contents _________________________ 1. Introduction 2. Objectives 3. Method of Analysis 4. Results of Parameter Studies 5. Conclusions

Introduction _____________________ In general, the current will be interrupted at the time point of its natural zero crossing, which almost coincides with the voltage peak of the supply. It will result in the known values of (RRRV). There are special situations, in which the circuit breaker will have difficulty in handling the interruption of much smaller currents.

Introduction-2 _______________________ Two known examples are: i)The interruption of small inductive currents (such as the no-load currents of transformers), giving rise to the current chopping phenomenon. ii)The clearing of small capacitive currents (e.g. the charging currents of short cable sections), which can lead to the problem of voltage escalation

Introduction-3 ___________________________ Current chopping The abrupt (almost vertical) interruption of current, especially in air-blast CB. In this breaker type, the arc quenching mechanism is almost independent on the current to be interrupted. This leads to excessive recovery voltage which will be proportional to the value of the chopped current, rather than the supply voltage.

Introduction-4 ___________________________ One more interesting phenomenon is the short-line or kilometric faults. *They occur at considerably short distances from the source. *The natural frequencies of these shorter line sections will be very high. *The shape of the recovery transient will deviate from the usually expected high frequency sinusoidal waveforms, *will instead exhibit several additional high frequency ramp functions of positive and negative slopes.

Introduction-5 ____________________________ With air blast CB, the interruption of the kilometric fault can be completed within the first few microseconds after the zero crossing. This phenomenon is sometimes accompanied by unusual situations in networks where the circuit breaking of faults closer to the line sending end is, unexpectedly, easier than of those farther from the source.

Objectives _______________________ A refined model for analyzing kilometric faults on power lines. Closed-form expressions for the current and voltage transients along the line. Identify the main affecting parameters The model gives also the rate of rise of the recovery voltage transient (r.r.r.v.). The effect of the damping introduced by breaker resistive switching is investigated

Method of Analysis ___________________ Fig. 1: The single-phase equivalent circuit

Applying Superposition The supply voltage is given by e(t) = cos t The total voltage, vtotal(x,t) and total current itotal(x,t) at any point of coordinate x are : vtotal(x,t) = v1(x,t) + v2(x,t) itotal(x,t) = i1(x,t) + i2(x,t)

Case study of a fault at d=300km, on a 500-kV,50-Hz line. The peak phase voltage=408.25kV, and the phase delay of =18degs=0.1. Fig. 2: The instantaneous value of the 50-Hz component of the per unit voltage distribution along the line.

Fig. 3: The transient component of both the per unit voltage and current distributions along the line, at t=0.33ms.

Fig. 4: The total per unit voltage and current distributions along the line, at t=0.33ms.

Fig. 5: The time waveform of the per unit voltage at 2 different locations on the line.

Fig.6: The per unit total voltage as a function of both time t (from zero to 7 times the line delay, with 100 time scale divisions) and location x/d.

Fig. 7: The time waveform of the per unit current at 3 different locations on the line.

Fig.8: A 3-D plot for the per unit total current as a function of both time t (from zero to 10ms, with 100 time scale divisions) and location x/d.

Fig. 9: The per unit circuit breaker recovery voltage over 50ms.

Fig. 10: The breaker recovery voltage transient as affected by the damping effect introduced by connecting a shunt resistor k left:k=infinity (no damping), top:k=,4 bottom:k=2 ____________________________________________________

Conclusions ___________________________ 1.The technical issues and practical implications of the kilometric faults are pointed out. Expressions for the transient voltages and currents along the faulty line are derived in a normalized form. 2.Attention is paid to the stresses on the circuit breaker, in terms of the recovery voltage, its initial rate of rise r.r.r.v., and the damping effect of applying breaker resistive switching.

Conclusions ___________________________ 3.Typical waveforms for the circuit breaker recovery voltage are given. The superimposed transient triangular transient components recognized, and the r.r.r.v. could be calculated. 4. The effect of the distance to fault on the time curve of the breaker recovery voltage is evaluated: *The frequency of oscillations decreases with the length of the line section. *The amplitude of the recovery transient increases with that distance.

Conclusions ___________________________ 5. Results demonstrating the effect of adding a resistor k in parallel with the breaker contacts on the voltage recovery transient are given. The corresponding values for the r.r.r.v. increase with k.

Thank You!