Arcing behaviour of cartridge fuselinks
3.1 Basic conditions during the arcing period
During the pre-arcing period the current will have varied with time in a manner determined by the source EMF and the impedances in the circuit up to the point of
current
time
Figure 3.1 Prospective and actual currents – – – – – – – prospective current
———— actual current
es
Rc
Lc
vf
i
Figure 3.2 Equivalent circuit
fault. It will be slightly lower at the end of the period because of the fuse resistance than it would have been had the fuse not been present. The current which would have flowed in these circumstances is known as the prospective current and typical variations are shown in Figure 3.1. The lower the circuit impedance, the greater is the reduction of current caused by the presence of the fuse, and the degree of current limiting is thus greatest at very high prospective currents. This in itself is a very advantageous feature, as the energy let-through to the circuit protected by the fuselink is thereby considerably reduced during the most severe fault conditions.
At the instant when arcs are initiated in a fuselink, there is a significant increase in the voltage drop across it. This voltage then rises as the arcs lengthen owing to more metal being eroded from the element, because of the high arc temperature.
Consideration of the simple circuit shown in Figure 3.2, which is assumed to apply for a fault condition, shows that the basic voltage/current relationship is:
es = iRc+ d
dt(Lci)+ vf (3.1)
in which
es= source EMF
Rc= resistance of circuit except for fuselink Lc= inductance of circuit
currentvoltage
a b time
c d
Figure 3.3 Electrical conditions during short circuit Where
a pre-arcing period b arcing period c fuselink voltage d source EMF
vf = voltage across the fuselink including the resistance drop within it i= circuit current.
For the condition in which the current is positive at the commencement of arcing, it is necessary for the rate of change of current (di/dt) to become negative so that the current will fall to zero, allowing the arcs to extinguish. This occurs, when (es− iRc− vf) is negative. Clearly although this condition may not be met at the start of arcing and the current may continue to rise, it will eventually be met and the current will then fall. To achieve rapid extinction it is necessary that the voltage across the fuse should be large, as this causes the current to begin to fall earlier and to reach zero more quickly. These conditions are illustrated in Figure 3.3.
Fuselinks containing notched-strip elements may be made to reduce the current more rapidly during the arcing period by increasing the number of restrictions, because this leads to the establishment of several arcs in series and consequently a greater voltage across the fuselink. This must, however, be limited to a level which will not cause such a large rate of change of current that excessive voltages may be induced in inductive components, and upper limits for fuselinks voltages are quoted in specifications. Although it cannot be achieved, the ideal situation would be for the fuselink voltage to rise to the limiting value at the commencement of arcing and to remain there until current interruption is achieved. This would give the fastest possible fault clearance and thus reduce to a minimum the amount of energy supplied to the protected circuit.
It should be appreciated that the situation is much less controlled in fuselinks with cylindrical-wire elements. Theoretically the whole of such an element should have uniform conditions in it, but in practice element distortion occurs during the pre-arcing period, as a result of which the cross-sectional area does not remain constant and there are variations along the length, producing bulges, i.e. thinner and fatter sections, known as unduloids. Gaps ultimately form at the centres of the thin sections and their number is not fixed, as with notched-strip elements. In some cases, the number of arcs may be great enough to cause excessive fuselink voltages to be produced.
Because of the insignificant heat movements which occur during the clearance of very high currents, the thermal properties of the body, end caps and terminals of a fuselink have no significant effect on the performance or arcing, provided that they are not affected by thermal or mechanical shock. It is the element material and configuration, particularly its restrictions, and the characteristics of the filling material which are of prime importance.
Empirical relationships of fuselink voltage and current during arcing have been produced to enable eqn. 3.1 to be solved to determine the current variations for various applications. A relationship developed by Gnanalingam and Wilkins [21] enabled them to predict the performances of certain fuses with reasonable accuracy and they claimed that the simulation technique is useful for screening preliminary designs and for investigating the effects of various system parameters such as frequency.
Such methods do not, however, deal with the underlying phenomena and are not of much assistance in explaining behaviour, developing fuses or considering the suitability of materials different to those which are presently used. It must be recognised that the arcing process is very complex and it is therefore unlikely that a completely accurate model can be constructed. Nevertheless, Wright and Beaumont [10] did develop a mathematical model, admittedly based on a number of simplifying assumptions, which they considered to be superior to earlier models in that it did attempt to deal with the detailed processes involved during arcing. It was therefore felt to be more general than other models and apart from aiding understanding it was hoped that it would enable the effects of changes in materials and parameters to be predicted and thus enable designs to be optimised. It probably must be accepted that it will always be necessary to determine fuselink characteristics by experimental means.
The development of the modelling technique of Wright and Beaumont is outlined in the following sections.