Network Fault Level: Converting Fault Current, MVA and Impedance

The network fault level, sometimes called the external fault level, is the fault contribution available at the source side of a cable from all upstream network elements. It may be specified as apparent power, impedance, or fault current with a power factor.

These quantities are different ways of describing the same upstream source strength. Converting between them is useful when entering source data for fault current calculations, IEC 60909 calculations or earth fault loop impedance checks.

Three-phase AC system

Quantity required	Using apparent power	Using impedance
Fault current	$$I_k=\frac{S_k}{\sqrt{3}{U}_n}$$	$$I_k=\frac{U_n}{\sqrt{3}{Z}_e}$$
Apparent power	$$S_k=\sqrt{3}{I}_k{U}_n$$	$$S_k=\frac{{U_n}^2}{Z_e}$$
External impedance	$$Z_e=\frac{U_n}{\sqrt{3}{I}_k}$$	$$Z_e=\frac{{U_n}^2}{S_k}$$

Single-phase AC system

Quantity required	Using line-line voltage	Using line-neutral voltage	Using impedance
Fault current	$$I_k=\frac{\sqrt{3}{S}_k}{U_n}$$	$$I_k=\frac{S_k}{U_{\mathrm{LN}}}$$	$$I_k=\frac{U_n}{\sqrt{3}{Z}_e}$$
Apparent power	$$S_k=\frac{I_k{U}_n}{\sqrt{3}}$$	$$S_k=I_k{U}_{\mathrm{LN}}$$	$$S_k=\frac{{U_n}^2}{3Z_e}$$
External impedance	$$Z_e=\frac{U_n}{\sqrt{3}{I}_k}$$	$$Z_e=\frac{U_{\mathrm{LN}}}{I_k}$$	$$Z_e=\frac{{U_n}^2}{3S_k}$$

DC system

Quantity required	Using apparent power or current	Using impedance
Fault current	$$I_k=\frac{S_k}{U_n}$$	$$I_k=\frac{U_n}{Z_e}$$
Power	$$S_k=I_k{U}_n$$	$$S_k=\frac{{U_n}^2}{Z_e}$$
External impedance	$$Z_e=\frac{U_n}{I_k}$$	$$Z_e=\frac{{U_n}^2}{S_k}$$

For AC systems, current, voltage and impedance are phasor quantities. Using only absolute values can introduce error, particularly where the source fault power factor is important. The most robust approach is to carry out the calculations in complex form so resistance and reactance are both represented.

Symbols

Ik	Network or external fault current, A
Sk	Network or external fault apparent power, VA or MVA. Multiply MVA by 106 to convert to VA.
pf	Network or external fault power factor
ULN	Nominal line-neutral voltage for a single-phase circuit, V
Un	Nominal line-line voltage, or absolute voltage for d.c. systems, V
Ze	Network or external fault impedance, ohm

For transformer-derived source fault data, see Transformer Secondary Fault Level.

Source impedance: resistance, reactance and X/R ratio

For an AC system, source impedance is a complex quantity comprising resistance and reactance:

$$Z_e=R_e+j{X}_e$$

where:

• R_e is the resistive component of the source impedance, Ω;
• X_e is the reactive component, normally inductive, Ω;
• j represents a 90° phase displacement.

The magnitude of the source impedance is:

$$\left|Z_e\right|=\sqrt{{R_e}^2+{X_e}^2}$$

The magnitude determines the symmetrical RMS fault current. However, resistance and reactance should normally be retained separately when combining the source impedance with transformer, cable or other network impedances:

$$R_{\mathrm{total}}=\sum _{}^{}R$$ $$X_{\mathrm{total}}=\sum _{}^{}X$$ $$\left|Z_{\mathrm{total}}\right|=\sqrt{{R_{\mathrm{total}}}^2+{X_{\mathrm{total}}}^2}$$

Adding impedance magnitudes directly can give an incorrect result where the individual X/R ratios differ. Network components are therefore normally combined by adding their resistance and reactance separately. This approach is consistent with conventional short-circuit calculation practice. Schneider Electric’s Electrical Installation Guide provides the same treatment.

X/R ratio

The X/R ratio describes the relationship between the reactive and resistive parts of the source impedance:

$$\frac{X}{R}=\frac{X_e}{R_e}$$

If the impedance magnitude and X/R ratio are known, let:

$$k=\frac{X}{R}$$

The resistance and reactance are then:

$$R_e=\frac{\left|Z_e\right|}{\sqrt{1+k^2}}$$ $$X_e=\frac{\left|k\right|\left|Z_e\right|}{\sqrt{1+k^2}}$$

A high X/R ratio indicates a predominantly inductive source. This matters because it affects the DC offset, peak fault current, and the rate at which the asymmetrical component of the fault current decays. A higher X/R ratio generally produces a larger and more persistent asymmetrical component, which can affect equipment making duties and short-circuit ratings. Schneider Electric’s Electrical Distribution Fundamentals Design Guide discusses this relationship.

Indicative X/R ratios for preliminary estimates

Source or component	Indicative X/R
Small LV distribution transformer	1–3
Larger LV distribution transformer	3–6
Remote distribution-network source	5–15
Power transformer up to approximately 30 MVA	7–30
Large transformer or source close to generation	30–60
Directly connected synchronous machines or reactors	40–120

Do not average these ranges when combining several network components. Calculate the overall ratio from X_total/R_total.

Relationship to fault power factor

For an inductive source:

$$\mathrm{pf}=\cos \phi =\frac{R_e}{\left|Z_e\right|}$$

The X/R ratio can therefore be calculated from the fault power factor:

$$\frac{X}{R}=\tan \phi$$

or:

$$\frac{X}{R}=\sqrt{\frac{1}{{\mathrm{pf}}^2}-1}$$

If |Z_e| and the fault power factor are known:

$$R_e=\left|Z_e\right|\mathrm{pf}$$ $$X_e=\left|Z_e\right|\sqrt{1-{\mathrm{pf}}^2}$$

The “fault power factor” is the power factor associated with the equivalent source impedance during the fault. Do not confuse it with the normal operating power factor of the connected load.

The tabulated equations use RMS magnitudes. For AC calculations, the source impedance is more completely represented as Z_e = R_e + jX_e. Where fault power factor or X/R data is available, calculate resistance and reactance separately and retain them when combining the source with transformer, cable, and other network impedances.