Proximity effect coefficient

The proximity effect may be calculated using formulae developed for solid round conductors provided that the resistance of the conductor is divided by a factor $k_p$, which is the ratio of the resistance of the path along the strands to the resistance of the path across the strands. This factor depends on many parameters such as the surface condition of the strands, the lay of the strands, the impregnation of the core and the tightness of the insulation on the core.

Values are according to IEC 60287-1-1 with extensions from Cigre TB 272. Default value is $k_p$ = 1.0 for cases not covered below.

Values for PP are assumed to be identical to PE and for SiR to EPR.

Theoretical explanations by A.H.M. Arnold

When the two conductors of a single-phase system are close to one another the magnetic fields due to each current are superimposed, and the effective resistance of both conductors is increased. A formula which is easy to evaluate numerically and which has negligibly small errors has been developed for the case of two round cylindrical conductors. In the stranded core of a cable, the problem is complicated by the unknown contact resistance between the strands.

The proximity effect is due mainly to an increase of current in the part of the conductor nearest the return conductor and to a diminution of current in the part of the conductor remote from the return conductor. If, therefore, the current followed the strands, the proximity effect would be suppressed entirely, since the strands occupy positions alternately near to remote from the return conductor. Experimental results show, however, that the proximity effect is quite appreciable in stranded conductors and it follows, therefore, that the eddy currents follow a path across the strands. The resistance of the path of the current across the strands is greater than the resistance along the strands and is dependent on factors such as the surface condition of the strands, the lay of the strands, the impregnation of the core, and the tightness of the insulation on the core.

Let the ratio of the resistance of the path along the strands to the resistance of the path across the strands be $k_p$. Then the formula for the proximity effect in solid cylindrical conductors may be used for stranded cables provided that the assumed resistance of the conductor is divided by the factor $k_p$. Experimental results indicate that the value of the factor $k_p$ may vary for different stranded conductors between 0.45 and 0.8.

Symbol

$k_p$

Related

$c_{type}$

Construction of conductor

$k_s$

Skin effect coefficient

$M_c$

Material of conductor

$M_i$

Material of insulation

Used in

$x_p$

Factor for proximity effect of conductors

Choices

Conductor construction	Conductor material	Insulation material	Copper wire type	Value
2	Cu	PPLP		0.8
2	Cu	Mass		0.8
2	Cu	OilP		0.8
2	Al			0.8
2	AL3			0.8
3	Cu	PE	unidirectional	0.37
3	Cu	PE	bidirectional	0.37
3	Cu	PE	insulated	0.2
3	Cu	HDPE	unidirectional	0.37
3	Cu	HDPE	bidirectional	0.37
3	Cu	HDPE	insulated	0.2
3	Cu	XLPE	unidirectional	0.37
3	Cu	XLPE	bidirectional	0.37
3	Cu	XLPE	insulated	0.2
3	Cu	XLPEf	unidirectional	0.37
3	Cu	XLPEf	bidirectional	0.37
3	Cu	XLPEf	insulated	0.2
3	Cu	PVC	unidirectional	0.37
3	Cu	PVC	bidirectional	0.37
3	Cu	PVC	insulated	0.2
3	Cu	EPR	unidirectional	0.37
3	Cu	EPR	bidirectional	0.37
3	Cu	EPR	insulated	0.2
3	Cu	IIR	unidirectional	0.37
3	Cu	IIR	bidirectional	0.37
3	Cu	IIR	insulated	0.2
3	Cu	PP	unidirectional	0.37
3	Cu	PP	bidirectional	0.37
3	Cu	PP	insulated	0.2
3	Cu	SiR	unidirectional	0.37
3	Cu	SiR	bidirectional	0.37
3	Cu	SiR	insulated	0.2
3	Cu	PPLP		0.37
3	Cu	Mass		0.37
3	Cu	OilP		0.37
3	Al			0.15
3	AL3			0.15
4	Cu	PPLP		0.8
4	Cu	Mass		0.8
4	Cu	OilP		0.8
4	Al			0.8
4	AL3			0.8