Short-Circuit Currents | 3-Phase VS 1-Phase

Introduction

Short-circuit calculations are performed because of several reasons. In short-circuit studies, generally, different characteristic values of short-circuit current e.g. peak short-circuit current (i_p), equivalent thermal short-circuit current (I_th), etc. are calculated. There is also often a need to calculate various types of short-circuit currents e.g. symmetrical or unsymmetrical. Each application uses a different value of short-circuit current as input. For example, in grounding calculations, it is clear that input value is single-line-to-ground short-circuit current. On the contrary, generator circuit breaker selection and harmonic propagation analysis demands three-phase short-circuit values as input. 

From these considerations, it can be quite challenging to dimension electrical devices from the thermal and dynamic effects of fault currents. An electrical designer needs to use the maximum values of short-circuit currents for these purposes. Generally, the value of three-phase short-circuit current is the highest value. But this is not always the case.  It is rather important that the electrical designer has to understand which value of short-circuit current should be taken for dimensioning of electrical devices. The main aim of this article is to point out the subtle dilemma of choosing the correct value of short-circuit current for dimensioning of electrical equipment. The theoretical derivation is done on a very simple circuit example.

Three-phase short-circuit current

Let us assume a simple network according to Figure 1. Transformer impedance in per unit was calculated on following base values: S_base = 100 MVA and V_base = 110 kV.

Transformer T1 is supplying the distribution load. Let us assume further that the 110 kV network is operated as solidly grounded. Figure 2 shows the equivalent diagram for the case of a three-phase fault in point F:

A three-phase short-circuit is symmetrical, therefore negative and zero sequence components are not present. The equivalent sequence network consists only of a positive sequence network. Solving for the short-circuit current,

where index 1 is used to indicate positive sequence

Calculating the short-circuit current will yield,

Single Phase Short-Circuit Current

Now, let´s assume the occurrence of single-phase (single-line-to-ground) short-circuit at point F. The value of short-circuit current is dependent on the zero-sequence connection of transformer T1 (which is given by the type of transformer and its winding connection).

Consider a shell-type transformer. According to [2], [3]  shell-type transformers have a zero sequence to positive sequence ratio in the range of X₀/X₁ = 1:10 depending on the winding connection of the transformer. Let us consider for example a zero sequence to positive sequence ratio, X₀/X₁ = 1. What this means is that the zero-sequence impedance of the transformer is equal to its positive sequence impedance, Z_T0 = Z_T1. The equivalent diagram is shown in the following figure.

Because all three sequence impedances are equal, Z_T1 = Z_T2 = Z_T0, we can calculate the short-circuit current as shown below.

The value of single-phase short-circuit current, in this case, is equal to the three-phase short circuit current.

In the second case, let us consider a core type transformer (T1), with a zero sequence impedance, Z_T0 = 0.85Z_T1. Solving for the short-circuit current,

In this case, the value of single-phase short-circuit is bigger than three-phase short-circuit current. This situation can occur in case of ‘near’ faults on solidly grounded transformers or grounding transformers. This is especially true for transformers with following winding connections:

where y or z are grounded on the low voltage side.

In technical literature, it can be found that single-phase short-circuit currents can be as high as 1.5 times the three-phase short-circuit currents.

In solidly grounded networks, the electrical devices should be rated on the higher value of short-circuit current.

In ungrounded networks (isolated) or in resonant, resistance/reactance grounded networks, single-phase short-circuit fault can’t occur (instead earth-fault occurs in these networks). Therefore, in this type of network, the value of three-phase short-circuit current is always the highest.

References

[1] IEC 60909 – 0: Short-circuit currents in three-phase a.c. systems. Part 0: Calculation of currents. Valid from 1.10.2016.

[2] IEC 60909 – 2: Electrical equipment. Data for short-circuit current calculations in accordance with IEC 60909. Valid from 1.8.2000.

[3] Schlabbach, J.: Short-circuit currents. The institution of Electrical Engineering and Technology. London, United Kingdom, 2005.