Calculation of minimum levels of short-circuit current

If a protective device in a circuit is intended only to protect against short-circuit faults, it is essential that it will operate with certainty at the lowest possible level of short-circuit current that can occur on the circuit

In general, on LV circuits, a single protective device protects against all levels of current, from the overload threshold through the maximum rated short-circuit current breaking capability of the device. The protection device should be able to operate in a maximum time to ensure people and circuit safety, for all short-circuit current or fault current that may occur. To check that behavior, calculation of minimal short-circuit current or fault current is mandatory.

In addition, in certain cases overload protective devices and separate short-circuit protective devices are used.

Examples of such arrangements

Figures G40 to G42 show some common arrangements where overload and short-circuit protections are achieved by separate devices.

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Fig. G40: Circuit protected by aM fuses

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Fig. G41: Circuit protected by circuit-breaker without thermal overload relay

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Fig. G42a: Circuit-breaker D provides protection against short-circuit faults as far as and including the load

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As shown in Figures G40 and G41, the most common circuits using separate devices control and protect motors.
Figure G42a constitutes a derogation in the basic protection rules, and is generally used on circuits of prefabricated bustrunking, lighting rails, etc.
Variable speed drive
Figure G42b shows the functions provided by the variable speed drive, and if necessary some additional functions provided by devices such as circuit-breaker, thermal relay, RCD.

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Protection to be provided	Protection generally provided by the variable speed drive	Additional protection if not provided by the variable speed drive
Cable overload	Yes	CB / Thermal relay
Motor overload	Yes	CB / Thermal relay
Downstream short-circuit	Yes
Variable speed drive overload	Yes
Overvoltage	Yes
Undervoltage	Yes
Loss of phase	Yes
Upstream short-circuit		Circuit-breaker (short-circuit tripping)
Internal fault		Circuit-breaker (short-circuit and overload tripping)
Downstream earth fault (indirect contact)	(self protection)	RCD ≥ 300 mA or CB in TN earthing system
Direct contact fault		RCD ≤ 30 mA

Fig. G42b: Protection to be provided for variable speeed drive applications

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Conditions to be fulfilled

The protective device must fulfill:

• instantaneous trip setting Im < Isc_min for a circuit-breaker
• fusion current Ia < Isc_min for a fuse

The protective device must therefore satisfy the two following conditions:

• Its breaking capacity must be greater than Isc, the 3-phase short-circuit current at its point of installation
• Elimination of the minimum short-circuit current possible in the circuit, in a time tc compatible with the thermal constraints of the circuit conductors, where:[math]\displaystyle{ tc \ge \frac{k^2S^2}{Isc_{min}\, ^2} }[/math]

(valid for tc < 5 seconds)

where S is the cross section area of the cable, k is a factor depending of the cable conductor material, the insulation material and initial temperature.

Example: for copper XLPE, initial temperature 90 °C, k = 143 (see IEC60364-4-43 §434.3.2 table 43A).

Comparison of the tripping or fusing performance curve of protective devices, with the limit curves of thermal constraint for a conductor shows that this condition is satisfied if:

• Isc (min) > Im (instantaneous or short timedelay circuit-breaker trip setting current level), (see Fig. G43)
• Isc (min) > Ia for protection by fuses. The value of the current Ia corresponds to the crossing point of the fuse curve and the cable thermal withstand curve (see Fig. G44 and G45)

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Fig. G43: Protection by circuit-breaker

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Fig. G44: Protection by aM-type fuses

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Fig. G45: Protection by gG-type fuses

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Practical method of calculating Lmax

In practice this means that the length of circuit downstream of the protective device must not exceed a calculated maximum length: [math]\displaystyle{ \definecolor{bggrey}{RGB}{234,234,234}\pagecolor{bggrey}L_{max}=\frac{0.8\ U\ Sph}{2 \rho Im} }[/math]

The limiting effect of the impedance of long circuit conductors on the value of short-circuit currents must be checked and the length of a circuit must be restricted accordingly.
The method of calculating the maximum permitted length has already been demonstrated in TN- and IT- earthed schemes for single and double earth faults, respectively. Two cases are considered below:
1 - Calculation of L_max for a 3-phase 3-wire circuit
The minimum short-circuit current will occur when two phase wires are short-circuited at the remote end of the circuit (see Fig. G46).

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Fig G46: Definition of L for a 3-phase 3-wire circuit

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Using the “conventional method”, the voltage at the point of protection P is assumed to be 80% of the nominal voltage during a short-circuit fault, so that 0.8 U = Isc Zd, where:
Zd = impedance of the fault loop
Isc = short-circuit current (ph/ph)
U = phase-to-phase nominal voltage
For cables ≤ 120 mm², reactance may be neglected, so that  [math]\displaystyle{ Zd=\rho \frac{2L}{Sph}\ ^{(1)} }[/math]
where:
ρ = resistivity of conductor material at the average temperature during a short-circuit,
Sph = c.s.a. of a phase conductor in mm²
L = length in metres
The condition for the cable protection is Im ≤ Isc with Im = magnetic trip current setting of the CB.
This leads to [math]\displaystyle{ Im \ge \frac{0.8 U}{Zd} }[/math]  which gives with U = 400 V
ρ = 1.25 x 0.018 = 0.023 Ω.mm²/m⁽²⁾ (Cu)
Lmax = maximum circuit length in metres [math]\displaystyle{ L_{max}=\frac {k\ Sph}{Im} }[/math]

2 - Calculation of L_max for a 3-phase 4-wire 230/400 V circuit
The minimum Isc will occur when the short-circuit is between a phase conductor and the neutral.
A calculation similar to that of example 1 above is required, but using the following formulae (for cable ≤ 120 mm^{2 (1)} ).

• Where Sn for the neutral conductor = Sph for the phase conductor [math]\displaystyle{ L_{max}=\frac {3,333 Sph}{Im} }[/math]
•  If Sn for the neutral conductor < Sph, then [math]\displaystyle{ L_{max}= 6,666 \frac{Sph}{Im}\frac{1}{1+m} }[/math]  where [math]\displaystyle{ m=\frac{Sph}{Sn} }[/math]

For larger c.s.a.’s than those listed, reactance values must be combined with those of resistance to give an impedance. Reactance may be taken as 0.08 mΩ/m for cables (at 50 Hz). At 60 Hz the value is 0.096 mΩ/m.

(1) For larger c.s.a.’s, the resistance calculated for the conductors must be increased to account for the non-uniform current density in the conductor (due to “skin” and “proximity” effects) Suitable values are as follows: 150 mm2: R + 15% 185 mm2: R + 20% 240 mm2: R + 25% 300 mm2: R + 30% (2) The factor 1.25 applied to the copper resistivity is due to the elevated temperature of the conductor when passing short-circuit current. This value of 1.25 corresponds to the max temperature of EPR or XLPE cables.

Tabulated values for Lmax

Figure G47 below gives maximum circuit lengths (Lmax) in metres, for:

• 3-phase 4-wire 400 V circuits (i.e. with neutral) and
• 1-phase 2-wire 230 V circuits

protected by general-purpose circuit-breakers. In other cases, apply correction factors (given in Figure G53) to the lengths obtained. The calculations are based on the above methods, and a short-circuit trip level within ± 20% of the adjusted value Im. For the 50 mm² c.s.a., calculation are based on a 47.5 mm² real c.s.a.

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Operating current level Im of the instantaneous magnetic tripping element (in A)	c.s.a. (nominal cross-sectional-area) of conductors (in mm2)
	1.5	2.5	4	6	10	16	25	35	50	70	95	120	150	185	240
50	100	167	267	400
63	79	133	212	317
80	63	104	167	250	417
100	50	83	133	200	333
125	40	67	107	160	267	427
160	31	52	83	125	208	333
200	25	42	67	100	167	267	417
250	20	33	53	80	133	213	333	467
320	16	26	42	63	104	167	260	365	495
400	13	21	33	50	83	133	208	292	396
500	10	17	27	40	67	107	167	233	317
560	9	15	24	36	60	95	149	208	283	417
630	8	13	21	32	63	85	132	185	251	370
700	7	12	19	29	48	76	119	167	226	333	452
800	6	10	17	25	42	67	104	146	198	292	396
875	6	10	15	23	38	61	95	133	181	267	362	457
1000	5	8	13	20	33	53	83	117	158	233	317	400	435
1120	4	7	12	18	30	48	74	104	141	208	283	357	388	459
1250	4	7	11	16	27	43	67	93	127	187	253	320	348	411
1600		5	8	13	21	33	52	73	99	146	198	250	272	321	400
2000		4	7	10	17	27	42	58	79	117	158	200	217	257	320
2500			5	8	13	21	33	47	63	93	127	160	174	206	256
3200			4	6	10	17	26	36	49	73	99	125	136	161	200
4000				5	8	13	21	29	40	58	79	100	109	128	160
5000				4	7	11	17	23	32	47	63	80	87	103	128
6300					5	8	13	19	25	37	50	63	69	82	102
8000					4	7	10	15	20	29	40	50	54	64	80
10000						5	8	12	16	23	32	40	43	51	64
12500						4	7	9	13	19	25	32	35	41	51

Fig. G47: Maximum circuit lengths in metres for copper conductors (for aluminium, the lengths must be multiplied by 0.62)

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Figures G48 to G50 give maximum circuit length (Lmax) in metres for:

• 3-phase 4-wire 400 V circuits (i.e. with neutral) and
• 1-phase 2-wire 230 V circuits

protected in both cases by domestic-type circuit-breakers or with circuit-breakers having similar tripping/current characteristics. In other cases, apply correction factors to the lengths indicated. These factors are given in Figure G51.

Circuit-breaker rating (A)	c.s.a. (nominal cross-sectional-area) of conductors (in mm2)
	1.5	2.5	4	6	10	16	25	35	50
6	200	333	533	800
10	120	200	320	480	800
16	75	125	200	300	500	800
20	60	100	160	240	400	640
25	48	80	128	192	320	512	800
32	37	62	100	150	250	400	625	875
40	30	50	80	120	200	320	500	700
50	24	40	64	96	160	256	400	560	760
63	19	32	51	76	127	203	317	444	603
80	15	25	40	60	100	160	250	350	475
100	12	20	32	48	80	128	200	280	380
125	10	16	26	38	64	102	160	224	304

Fig. G48: Maximum length of copper-conductor circuits in metres protected by B-type circuit-breakers

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Circuit-breaker rating (A)	c.s.a. (nominal cross-sectional-area) of conductors (in mm2)
	1.5	2.5	4	6	10	16	25	35	50
6	100	167	267	400	667
10	60	100	160	240	400	640
16	37	62	100	150	250	400	625	875
20	30	50	80	120	200	320	500	700
25	24	40	64	96	160	256	400	560	760
32	18.0	31	50	75	125	200	313	438	594
40	15.0	25	40	60	100	160	250	350	475
50	12.0	20	32	48	80	128	200	280	380
63	9.5	16.0	26	38	64	102	159	222	302
80	7.5	12.5	20	30	50	80	125	175	238
100	6.0	10.0	16.0	24	40	64	100	140	190
125	5.0	8.0	13.0	19.0	32	51	80	112	152

Fig. G49: Maximum length of copper-conductor circuits in metres protected by C-type circuit-breakers

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Circuit-breaker rating (A)	c.s.a. (nominal cross-sectional-area) of conductors (in mm2)
	1.5	2.5	4	6	10	16	25	35	50
1	429	714
2	214	357	571	857
3	143	238	381	571	952
4	107	179	286	429	714
6	71	119	190	286	476	762
10	43	71	114	171	286	457	714
16	27	45	71	107	179	286	446	625	848
20	21	36	57	86	143	229	357	500	679
25	17.0	29	46	69	114	183	286	400	543
32	13.0	22	36	54	89	143	223	313	424
40	11.0	18.0	29	43	71	114	179	250	339
50	9.0	14.0	23	34	57	91	143	200	271
63	7.0	11.0	18.0	27	45	73	113	159	215
80	5.0	9.0	14.0	21	36	57	89	125	170
100	4.0	7.0	11.0	17.0	29	46	71	100	136
125	3.0	6.0	9.0	14.0	23	37	57	80	109

Fig. G50: Maximum length of copper-conductor circuits in metres protected by D-type circuit-breakers

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Circuit detail
3-phase 3-wire 400 V circuit or 1-phase 2-wire 400 V circuit (no neutral)		1.73
1-phase 2-wire (phase and neutral) 230 V circuit		1
3-phase 4-wire 230/400 V circuit or 2-phase 3-wire 230/400 V circuit (i.e with neutral)	Sph / S neutral = 1	1
	Sph / S neutral = 2	0.67

Fig. G51: Correction factor to apply to lengths obtained from Figures G47 to G50

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Note: IEC 60898 accepts an upper short-circuit-current tripping range of 10-50 In for type D circuit-breakers. European standards, and Figure G50 however, are based on a range of 10-20 In, a range which covers the vast majority of domestic and similar installations.

Examples

Example 1

In a 3-phase 3-wire 400 V installation the protection is provided by a 50 A circuit-breaker type NS80HMA, the instantaneous short-circuit current trip, is set at 500 A (accuracy of ± 20%), i.e. in the worst case would require 500 x 1,2 = 600 A to trip. The cable c.s.a. = 10 mm² and the conductor material is copper.
In Figure G47, the row Im = 500 A crosses the column c.s.a. = 10 mm² at the value for Lmax of 67 m. The circuit-breaker protects the cable against short-circuit faults, therefore, provided that its length does not exceed 67 metres.
Example 2
In a 3-phase 3-wire 400 V circuit (without neutral), the protection is provided by a 220 A circuit-breaker type NSX250N with an instantaneous short-circuit current trip unit type MA set at 2,000 A (± 20%), i.e. a worst case of 2,400 A to be certain of tripping. The cable c.s.a. = 120 mm² and the conductor material is copper.
In Figure G47 the row Im = 2,000 A crosses the column c.s.a. = 120 mm² at the value for Lmax of 200 m. Being a 3-phase 3-wire 400 V circuit (without neutral), a correction factor from Figure G51 must be applied. This factor is seen to be 1.73.
The circuit-breaker will therefore protect the cable against short-circuit current, provided that its length does not exceed 200 x 1.73= 346 metres.