DGUV Information 203-077e - Thermal hazards due to electric fault arcing Guide for selecting Personal protective equipment

4.3.1
General calculation methodology

The assertions that follow apply to low voltage DC installations (LVDC).

Note:

The algorithm applies in particular to direct current circuits, in which a virtual steady-state short-circuit current relationship has set in and/or the short-circuit duration is significantly greater than the DC circuit time constant τ = L/R.

Cases where the time constant is greater and the short-circuit duration is shorter are covered by the calculation base; the results, under certain circumstances, will then encompass safety reserves to a greater degree.

The work environment in DC installations is characterized by the electric parameters

The ohmic resistance of the DC network is comprised of the internal resistance of the DC source (rectifier with an upstream AC network, inverter, battery), the line resistance and the resistance of other elements in the DC circuit (e.g. inductors, etc.).

The short-circuit power in the DC system P_k results from the nominal DC source voltage and the sustained short-circuit current I_kDC (stationary value of the short-circuit direct current with a bolted short-circuit at the fault location):

P_k = U_Nn･I_kDC = U²_Nn / R_N

Note:

The arithmetic mean current value after the transients have subsided is to be considered as the sustained short-circuit current on rectifier-supplied DC systems.

Fig. 4-6
Summary of the estimation process for AC installations

The electric arc short-circuit current I_{k, arc}, the current limiting factor k_B and the electric arc power P_arc are determined iteratively by approximating the current-voltage characteristics

U_arc = (34 + 0.532･d)･I^0.12_{k, arc}

using electrode gap d (the equation applies for the electric arc voltage in V, the electric arc short-circuit current I_{k, arc} in A and the electrode gap d in mm). The recursion rule applies in general for the iteration (i and i+1 are consecutive iteration steps):

This iteration is undertaken up to a designated abort criterion with specification of an initial value I_{k, arc (0)}.

The following applies for electric arc power

P_{arc (i+1)} = U_{arc (i+1)} ･ I_{k, arc (i+1)}

Note:

For expediency, an initial value of I_{k, arc (0)}= 0,5 I_kDCis assumed. The iteration process will be aborted if the results from two consecutive iteration steps fall below a predefined deviation (e.g. 0.5 %).

Normalized arc power can be derived from

The expected value of the electric arc energy is calculated

W_arc = P_arc･t_arc = k_P･P_k･t_arc

on the basis of the electric arc power or normalized arc power. The arc duration t_arc or short-circuit duration t_k is determined by the protection settings or protective device characteristic curve analogous to the AC process on the basis of the electric arc short-circuit current I_{k, arc}.

Note:

When determining the short-circuit duration from the characteristic curves specified by the manufacturer (e.g. circuit protectors), the time constant L/R of the DC system is to be accounted for, if applicable.

The protection level of the PPEaA is determined and evaluated in a manner analogous to the method used for AC installations (Sec. 4.2.3).

4.3.2
Rough estimation based on reference values (worst-case considerations)

For very rough estimations of the electric arc power, the reference value k_{P max} = 0.25 can be used in the DC range:

P_arc = k_{P max}･P_k = 0.25･P_k

Application of the iteration process is no longer necessary.

For the low voltage range, one is usually on the safe side with DC systems if a reference value of k_B = 0.5 is used for the current limiting factor.