Cable Losses :
|Cable losses can be divided as current dependent and voltage dependent. Voltage dependent losses arise in the di-electric due to change of polarity in the alternating field which di-electric losses.
Di-electric loss per unit length in each phase is given by:
Wd=w C U2o tan (W/m)
Current dependent cable losses comprise of the following:
- Ohmic conductor losses
- Losses due to skin effect
- Losses due to proximity effect
- Losses in metallic sheath
|Ohmic conductor losses: These are dependent on the material and temperature and are calculated as follows:
Wc = 12R (W/m)
R is the a.c resistance of conductor at operating temperature and calculated as
R = R2 ( [1 a(t-20)]
a = 0.00393 for Copper,
a = 0.00403 for Aluminium,
t = temperature in °C
|Losses due to skin effect: These are caused by the displacement of the current into the outer areas of the conductor and increase approximately with the square of the frequency. These can be reduced by special conductor constructions (segmental conductors). The losses can make up to 8 to 17% of the ohmic losses of the conductor for cross-sections between 500 mm2 to 2000 mm2.
|Losses due to proximity effect: These are caused by parallel conductors laid close together Le., by magenetic fields. If the cables are laid far apart, the effect can be reduced to 10% of the ohmic conductor losses even for large conductor cross-sections.
Sheath Losses: Power loss in sheath or screen are caused by eddy currents and induced sheath current
Eddy current losses are produced in all metal parts adjacent to the conductor especially in presence of large conductor currents.
|Induced sheath current: Because the metal sheath of a single core cable is linked much more closely to the alternating magenetic field of its own conductor than to the altrernating current field of the other two phase conductors, the result is an induced voltage along the length of the cable. This amounts to approximately 60 to 150
V/km per kA of the conductor current for practical installation purpose. If the sheath is bonded at both ends, this results in a longitudinal sheath current with correspnding extra losses in the sheath.
|If longitudinal sheath resistance Rm is known, the following formula can be used to determine sheath current Im:
XM = w x 0.2 x Ln x 10-3
Ui = XM I L
ZM = (RM² + XM²)½
XM = Mutual reactance of sheath (W/Km)
S = Space between cable axis (mm).
dM = Mean diameter of sheath (mm).
Ui = Induced voltage on sheath (kV)
ZM = Sheath Impedance (W/Km)
I = Phase current (kA)
Sheath losses are calculated as follows:
Ws = IM² x RM
|Bonding Systems: In addition, extra losses can arise as a result of magnetic reversal on ferrous materials in the vicinity us the cable. Sheath losses may influence the ampacity of the cables considerably. These can be reduced by grounding the sheath at one end only, in which case the free cable end has to be fitted with over voltage protection. The disadvantage of the one side grounding is that the zero sequence impedance rises considerably, possibly leading to interferance problems with nearby tele-communication cables. Another method fo reducing sheath losses is cross-bonding.
|Single point Bonding: In case the actual circuit is too small to accommodate one or two lengths, single point bonding can be adopted where the sheath is directly bonded at one end and is bqnded through an SVL at the other end. In this case there shall be no circulating currents but, there shall be induced voltage at one end, the value of which can be computed. Induced voltage here can be treated in a similar way as for cross-bonding system. In case of fault, the maximum acceptable induced voltage depends on outer sheath characteristics and in such case a ground continuity conductor is required to carry the earth fault and also help in reducing the induced voltage during earth fault conditions.
|Cross bonding system: This can be considered when the circuit length can be sub-divided into major sections and each major section can be divided into three equal minor sections taking into consideration the reduction in number of joints to a minimum as the weakest point in the circuit is the joint.
It is possible to reduce the resultant sheath voltage to low levels. Particularly with larger conductor cross-sections and on cable lengths with joints, by carrying cross bonding at about every 1/3rd of the sheath length of each phase in series, reduces the resultant sheath voltage to zero. Even sheath grounded at both ends, reduces the extra sheath losses drastically. The zero sequence impednace is practically of the same low level as in normal both end grounded system.
|The cyclic permutation of longitudinal sheath connections results in similar sheath over voltage problems at points where the subdivided sheaths are insulated as in single grounded cable sheath. Therefore, these insulated points will have to be provided with suitable over voltage protection (surge arrestors, non-linear silicon-carbide or zinc oxide resistors)
Mixed System: Sometimes mixed system Le., cross-bonding and single point bonding in the same circuit can be used where the number of minor sections cannot be divided over 3 such as 4 or 5 sections. Here cross-bonding system can be considered for the first 3 sections and single point bonding used for the other section(s).