Environmental Engineering Reference
In-Depth Information
Other elements in the switching circuit may be analysed in a similar manner as
done in the above three subsections. Link capacitors, for example, have losses equal
to the circulating current and capacitor equivalent series resistance (ESR), or
i
2
ESR.
8.3 Distribution system
Losses in the power distribution system comprise harness and cable resistive losses,
connector losses and fuse or contactor or other protective device losses. Fuses are sized
to protect the downstreamwiring from damage due to wire shorts to ground, or to other
circuits, or faults at the load. In a fuse itself a 'weak link' or series of 'weak links' are
regions of the ribbon element that are narrower than the fuse stock. At sufficient
current, Joule heating proportional to
I
2
t
causes the weak link to begin tomelt, at which
point two unstable phenomena contribute to very rapid fuse link metal vaporization.
First, the weak link itself begins tomelt. Melting is followed by a surface tension effect
in which the molten portions tend to form droplets that are still joined. At the napes of
this series of droplets, or unduloids, the cross-sectional area becomes constricted
below that of the original fuse thus further accelerating fuse vaporization. The second
phenomenon that accelerates fuse clearing is the pinch effect whereby current flow
through a liquid conductor reacts with its own magnetic field further constricting the
conductor material into even smaller cross section [14]. The constricting pressure at
the unduloid is proportional to the square of the current flowing in the cross section and
inversely proportional to the diameter squared of the effective cross section. The effect
is that of an Amperean force (as opposed to Lorentz force) that tends to separate the
liquid conductor into individual balls. Fuse elements are made of low melting point
materials such as silver or its alloys. Semiconductor protection fuses such as those used
in each pole of a thyristor inverter, GTO, for example, are made of pure silver to
achieve the fastest clearing time. McCleer [14] develops a concise theory of the fuse
from both an electrical and a thermal model perspective.
Electrical contacts are also analysed by McCleer [14] where he shows that
contact resistance of a relay or contactor can be modelled as a constriction resis-
tance due to a large number of asperities,
N
, having an average radius,
r
a
, at the
points of contact. The contact resistance is calculated as shown in (8.16) where
r
r
is
the contact material resistivity:
r
r
2
P
R
c
¼
ð
8
:
16
Þ
N
a
k
k
Contact voltage drop is nearly self-regulating at 0.1-0.2 V per interface, with
most instances of contact voltage drop in automotive circuits being in the vicinity
of 0.025 V.
Vehicle harness cables are sized to conform with allowable temperature rise
in confined spaces and because of this they tend to follow the industrial practice of
3-5% line drop at rated load from source to point of load. For instance, the circuit
