IEEE 1584 paragraph 1.2 states that Single-phase ac systems and dc systems are not included in the Guide. So what to do?

The resistance load line of the DC circuit is described by V = Vs - I*Rs equation, where Vs stands for open source voltage (V) and Rs is the circuit internal resistance (Ohm). Introducing into the circuit Var - voltage drop across arc, arcing current can be resolved as Iar = (Vs - Var) / Vs * Isc, where Isc is the available fault current at the point of the arc.

Arc voltage is shown to be the function of combination of contact materials (Uc, V), gap between the contacts (L, cm) and the amount of the available short circuit current (Isc, A) [1]:

Var = Uc + Upc * L + 3.6 * 10e-3 * Isc

where,

Uc is the sum of the anodic and cathodic drops. It has been found to be [1]:

• 32 V for Al-Al and Cu-Steel
  
• 36 V for Cu-Cu
  
• 30 V for Steel-Steel

Figure 1 Model of a dc arc. (a) Pictorial. (b) Voltage distribution

DC arcing power Par = Var * Iar and arcing energy Ear = Par * tar,

where tar, sec - arcing time determined using fuse time-current curves (ac) and the circuit time constant [2]. We suggest using Isc instead of Iar in the above equations. Also, similar to the IEEE guide, we suggest using calculated Iar reduced by 15% and the fuse tc-characteristic adjusted for the circuit time constant to determine tar. This will effectively compensate for deviations in arc current due to the condition of contact plates, the SCPD time-current curve margin of error etc.

In case of an open arc assuming all the energy is converted into thermal (arc) energy:

incident energy Einc = Ear / 4piR², joule / cm², R being working distance in cm.

Figure 2 represents volt-ampere characteristic for arcs in air with copper electrodes having 1 to 200mm. gap [4]. Arc voltage versus arc current characteristic curve will shift upward as the gap increases in length.

Figure 2 Current-voltage characteristics for DC arcs in air, with copper electrodes.

The arc operates at the intersection of this curve and the resistance load line of the DC circuit. Therefore, the arcing current will stabilize itself at a fixed point on the curve and the arc will dissipate a relatively constant amount of power. The load line may intercept the characteristic curve in two locations ( a and b ) as shown in figure 3 but only one point b is stable [3]. The stable operating location is the point with the lowest arc voltage.

Figure 3 10mm gap voltage - current relationship and sample dc load line

Calculated Par had been compared to test values reported in [3]. The calculated arc power values are consistently higher (and therefore safer) than the observed when Isc is used to calculate arc power Par = Var * Isc.

Arcing fault data @ 3/8 inch gap 325 VDC system
(data in bold - reported by [3])

Test #	Ri, Ohms	Isc, A	Var, V	calc Var, V	Iar, A	calc. Iar, A	Iar vs calc Iar, %	Par	calc Par	Par vs calc Par, %
B5	0.60	500	75	58	375	411	10%	28125	28900	3%
B6	0.60	500	75	58	375	411	10%	28125	28900	3%
C5	0.30	975	75	60	750	796	6%	56250	58022	3%
C6	0.30	1000	75	60	750	817	9%	56250	59600	6%
C10	0.20	1380	58	61	1200	1121	-7%	69600	84136	21%
C11	0.20	1380	50	61	1200	1121	-7%	60000	84136	40%
F3	0.36	850	55	59	675	696	3%	37125	50201	35%
F4	0.36	840	50	59	650	687	6%	32500	49580	53%
G1	0.31	950	50	59	800	776	-3%	40000	56449	41%
G2	0.51	950	65	59	780	776	0%	50700	56449	11%
H1	0.39	775	50	59	580	635	9%	29000	45562	57%
H2	0.23	1100	60	60	1000	897	-10%	60000	65956	10%
I1	0.23	1100	50	60	1020	897	-12%	51000	65956	29%
I2	0.20	1270	50	61	1200	1033	-14%	60000	76926	28%
I3	0.20	1300	50	61	1200	1057	-12%	60000	78884	31%
I4	0.16	1700	50	62	1400	1375	-2%	70000	105604	51%
I5	0.16	1700	50	62	1500	1375	-8%	75000	105604	41%
J1	0.15	1750	50	62	1400	1415	1%	70000	109025	56%
J2	0.15	1750	50	62	1600	1415	-12%	80000	109025	36%
J3**	0.15	1800	50	58	1500	1476	-2%	75000	105264	40%
K1**	0.15	1800	50	58	1500	1476	-2%	75000	105264	40%
K2**	0.15	1800	50	58	1500	1476	-2%	75000	105264	40%
K3**	0.20	1400	48	57	1200	1154	-4%	57600	79856	39%
K4**	0.20	1400	67.5	57	1150	1154	0%	77625	79856	3%
K5**	0.20	1400	50	57	1200	1154	-4%	60000	79856	33%
L1**	0.20	1400	50	57	1150	1154	0%	57500	79856	39%
L2****	0.20	1400	62.5	55	1200	1163	-3%	75000	77056	3%
M1****	0.20	1380	48	55	1240	1147	-8%	59520	75856	27%
M1****	0.20	1380	48	55	1240	1147	-8%	59520	75856	27%

** = Copper and Steel
**** - both electrodes Steel

Calculation Example: Consider 350VDC, Isc = 3000A, 10mm gap between copper contacts protected by TRS60RDC 60A 600V fuse. Maximum arcing voltage between the contacts will be equal to Var = 36 + 24 * 1 + 0.0036*3000 = 71V. Maximum Var would produce lowest Iar = (350 - 71) * 3000 / 350 = 2390A. We will use the Iar reduces by 15% and equal to 2030A to determine arc duration from the fuse average melt time current characteristic. Figure 4 shows the TR60RDC time current characteristic (ac) as well as the dc curve adjusted for time constants of 10, 50 and 100ms. The adjustment was done according to procedure proposed in [2]. Figure 4 TRS60RDC fuse average melt time-current characteristic. Table below summarises the fuse operation times (arc duration) and associated incident energies at working distance of 20 inches for the three different time constant values: time const, ms tar, sec Einc, joules / cm2 0 0.02 0.12 10 0.04 0.25 50 0.1 0.61 100 0.15 0.91 Incident energy values above are calculated using Var = 71V and Isc = 3000A which corresponds to arcing power of approx. 210kW. The table above shows how much the incident energy depends on the circuit time constant value. Compare dc incident energy above with approx 0.07 joule / cm2 produced by single phase and 0.21 joule / cm2 produced by 3 phase ac arcs in 350VAC, 3000A bolted fault current 10mm gap system. The ac arc incident energy is only a fraction of dc arc energy produced in 100ms time constant dc circuit The higher the circuit inductance the more violent arc appears to be, all other system parameters kept unchanged.

[1] Arcing faults and their effect on the settings of ground fault relays in solidly grounded voltage systems, by Keith Malmedal. North American power symposium, Cleveland state university, Oct.18-20, 1998.
[2] Fuse protection of DC systems, by Cinthia Cline. Ferraz Shawmut.
[3] Arcing faults on direct current trolley systems, by Paul Haul, Kenneth Myers and William Vilcheck. Mine Safety and Health Administration. 1978.
[4] Electric arcs and arc interruption, by Solver. Chalmers university of technology, 2005

Read More: How to resolve single phase arcs

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