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# Short circuit phenomenon you should properly understand

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## Why short circuit is so important?

A short circuit in an electrical circuit is a part of the circuit that for some reasons has become “shorter” than it should be. The current in an electrical circuit flows the easiest way and if two points in a circuit with different potentials are connected with low electrical impedance the current is taking a shortcut between the two points.

The consequences of an short circuit can be everything from just a minor malfunction to a disaster. The consequences are dependent of the system´s capacity for driving current in an short circuit situation and how long time the short circuit current is allowed to flow. In almost every electric circuit there has to be some kind of protection against short circuit currents.

When circuits are analyzed mathematically, the short circuit is usually described by zero impedance between two nodes in the circuit.

In reality it is impossible that the impedance should be zero and therefore the calculations will not give the “real” value but in most cases the highest possible value. To get right results of a calculation it is also important to know all parameters of the circuit.

Especially in short circuit situations the behavior of the circuits are “strange” and there is no linearity between the voltage of the system and the current flowing.

Contents:

### 1. The need for transformer short-circuit current calculation

Today more than ever before, the electricity grid is developing so quickly — the power plant capacity, the substation capacity and electricity loads, as well as load density, sustainably grow.

Take China as an example. The number of 500 kV substations in the North China power grid is almost 2 times higher than in the past decade. The number has grown from 48 to 97; the substation capacity has increased from 52,069,000 kVA to 157,960,000 kVA.

As a result, the short-circuit currents in the power grid increase year by year. Based on the statistical analysis of the State Grid Corporation of China (SGCC), the short current current accidents of power transformers (Size ≥ 110 kV) happened 125 times. The total power capacity influenced by the short circuit accidents is 7,996 MVA in 1995~1999. The number represents 37.5% of all power accidents and 44% of the transformers accidents.

The short circuit current is an important specification and standard for equipment and conductors in the power industry, and short circuit current withstand capability of the main devices decides whether the grid could run more safely or not. So it’s significant to calculate the short circuit current and offer some possible solutions.

The correct calculation can help us to:

1. Specify fault ratings for electrical equipment (e.g. short circuit withstand ratings)
2. Help identify potential problems and weaknesses in the system and assist in system planning
3. Form the basis for protection coordination studies

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### 2. Symmetrical components

In the practical work, engineers often use “symmetrical components” to analyze the three-phase power system. It was invented by a Canadian electrical engineer Charles L.Fortescue in 1913. Mr Fortescue’s original purpose was to analyze the operation of the electrical motors.

The theory was not used for the power system until 1937. The analytical technique was adopted and advanced by engineers at General Electric and Westinghouse and after World War II it was an accepted method for asymmetric fault analysis.

Now it’s a common tool used to analyze the faults of three-phase power system.

The basic setting for the theory is that any unbalanced system quantities (current or voltage) could be decomposed into 3 symmetrical sets of balanced vectors:

1. Positive sequence components,
2. Negative sequence components and
3. Zero sequence components.

The positive sequence component of the current shown in Figure 1 above is balanced in magnitude with a 120 degree phase separation and counter-clockwise rotation, just like the original balanced system.

The negative sequence component of the current is balanced in magnitude with a 120 degree phase separation, but has the opposite rotation, in this case, clockwise.

The zero sequence components have equal magnitudes, but zero phase separation.

Here, we denote the positive sequence with the subscript “1”. Likewise, the negative sequence is denoted with the subscript “2” and the zero sequence is denoted with the subscript “0”.

Under a no fault condition, the power system is considered to be essentially a symmetrical system and therefore only positive sequence currents and voltages exist. At the time of a fault, positive, negative and possibly zero sequence currents and voltages exist.

Using real world phase voltages and currents along with Fortescue’s formulas, all positive, negative and zero sequence currents can be calculated. Protective relays use these sequence components along with phase current and/or voltage data as the input to protective elements.

#### Principles of Symmetrical Components (VIDEO)

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## 3. Two kinds of short circuit

### 3.1 DC circuits

What circuit information is needed to do an short circuit calculation for a DC circuit? In an electrical circuit the current is dependent of the electromotive force (emf), the electromagnetic field, and the total impedance of the circuit.

In a battery the emf-value is dependent of the charge of the battery. The internal impedance of the battery is also a changing parameter and dependent of the charge, the temperature, and the age of the battery and so on.

In a DC circuit the resistance is the current limiting factor together with the emf in steady-state which means “after a while”.

In the beginning of a transient, like an short circuit situation, also the inductance of the circuit is limiting. Any inductance in the circuit will smooth up the rise of the current. The current is increasing exponentially due to the relation between the inductance and the resistance of the circuit.

Direct current causes different problems from AC when trying to interrupt high value currents since the arc extinction is more difficult. AC passes through zero every half period thus helping the breaking of current.

A circuit breaker for a certain AC current is usually not able to break the same magnitude of DC current. The difficulties of breaking a DC circuit increases with the ratio of inductance versus resistance in the circuit. Inductances are always in opposition to changes of current.

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### 3.2 AC circuits

Alternating current circuits (AC) are more complex to solve than direct current circuits (DC). There are more parameters affecting the results and in fast changing situations the first values of current are strongly dependent of the phase of the active voltage source.

#### 3.2.1 Single-phase circuits

Most large power networks are three-phase but especially in low voltage systems most of the connected circuits are single-phase. When calculating short circuit currents the situation is dependent on how near the generator or transformer the fault occurs.

Not only due to the increasing impedance in the end of the network but also to the fact that generators and transformers are acting “strange” when they are not loaded symmetrically in all phases.

In some cases the circuit may be fed from a single-phase transformer with a current carrying capacity that is not enough to make the three-phase system behave “strange”.

The fact that the short circuit current is easier to calculate far from a transformer or a generator is because the line impedances are playing an important role in the process and the impedances are often easier to know than the voltage in the beginning of the circuit.

With longer lines the currents decreases and the voltage from the source will not change very much.

In single-phase low voltage circuits that are commonly used in households the short circuit currents must be disconnected for different reasons. One reason is because of the touch voltage that may occur during a contact between phase and protective earth.

The protective earth in a circuit is used to prevent exposed conductive parts from getting a dangerous potential referred to earth. When a direct contact between phase and exposed conductive parts is established by a fault situation the potential will rise to a dangerous level for persons to touch and therefore the circuit must be disconnected by protection devices like fuses and circuit breakers.

In household situations the maximum time for disconnection is normally 0.4 seconds. To access the clearance time under fault conditions the prospective fault current must be determined by measurement or calculation. It is the prospective current that will flow when the end of the cable being protected is connected to the protective earth conductor that is of concern.

With long cable runs this prospective current can be found to be comparatively low.

It should be remembered however that the first problem with long cable runs is the possibility of excessive voltage drop, and cables should be selected first for current rating, and then checked for voltage drop before determining the fault prospective.

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#### 3.2.2 Three-phase circuits

Three-phase electric power is a common method of AC electric power generation, transmission, and distribution. It is a type of polyphase system and is the most common method used by electrical grids worldwide to transfer power.

It is also used to power large motors and heavy loads. A three-phase system is usually more economical than an equivalent single-phase or two-phase system at the same voltage because it uses less conductor material to transmit electrical power.

The three-phase system was independently invented by Galileo Ferraris, Mikhail Dolivo-Dobrovolsky and Nikola Tesla in the late 1880s.

Most single-phase circuits are just a part of a three-phase network. In a three-phase system various types of short circuit can occur.

For example, short circuit current can be phase-to-earth (80% of faults), phase-to-phase (15% of faults — this type of fault often degenerates into a three-phase fault) and three-phase (only 5% of initial faults). These different short-circuit currents are shown in Figure 4.

In China, there is another rough classification which is based on the number of the fault phase: three-phase fault, double-phase fault and single phase fault due to phase-to-earth fault which may happen for two phases.

The primary characteristics of short-circuit currents are:

1. Duration – The current can be self-extinguishing, transient or steady-state
2. Origin – it may be caused by mechanical reasons (break in a conductor, accidental electrical contact between two conductors via a foreign conducting body such as a tool or an animal), internal or atmospheric overvoltage, and insulation breakdown due to heat, humidity or a corrosive environment
3. Location (inside or outside a machine or an electrical switchboard)

The consequences of short circuit are depending on the type and duration of the fault and the short-circuit power available. Locally at the fault point there may occur electrical arcs causing damage to insulation, welding of conductors and fire.

On the faulty circuit, electro dynamic forces may result in deformation of busbars and cables and the excessive temperature rise may damage insulation. Other circuits in the network or in nearby networks are also affected by the short-circuit situation.

Voltage drops occur in other networks during the time of short circuit and shutdown of a part of a network may include also “healthy” parts of the network depending on the design of the whole network.

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#### 3.3 Development of short-circuit current

A simplified AC network can be represented by a source of AC power, some kind of switching device, a total impedance ZN that represents all the impedances upstream of the switching point and a load, represented by its impedance (see Figure 5).

In a real network the total impedance ZN is made up of the impedances of all components upstream. The components are for example generators, transformers, wires, circuit-breakers and metering systems.

When a fault with negligible impedance occurs between A and B a short-circuit current limited only by ZN flows in the circuit. The short-circuit current Isc develops under transient conditions depending on the relation between inductances and resistances in the whole circuit.

If the circuit is mostly resistive the waveform of the current is following the waveform of the voltage but if there are inductances in the circuit the waveform of the current will differ from the waveform of the voltage during a transient time of the process.

In an inductive circuit the current cannot begin with any value but zero. The influence of inductances is described by reactance X in AC circuits with a fixed frequency of the voltage.

In low voltage systems where cables and conductors represent most of the impedance it can be regarded as mostly resistive. In power distribution networks the reactance is normally much greater than the resistances.

Generally the total impedance Z in steady-state in an AC circuit is made up of the total resistance R and the total reactance X as the following relation shows.

In the simplified circuit above the voltage is constant and so is the total impedance. In faults far from generators and transformers where most of the impedance consists of impedances from wires the calculations can be done with a good result and the transient current is almost the same as if the current would flow for a longer time.

The meaning of far from is not necessarily physical but means that generator or transformer impedances are less than the impedance of the elements from wires.

The impedance elements from wires are constant at a constant temperature but the impedances of generators vary during a short-circuit and the impedances of transformers change if the transformers are asymmetrically loaded with high currents.

Figure 6 shows the current in beginning of a short-circuit far from the generator. The short-circuit starts at a moment when the current normally is zero and continues symmetrically.

Figure 7 shows the current when the short-circuit starts at a moment when the voltage is zero and the current is also starting from zero but asymmetrically during a transient time.

### IEC 61439 – Short-circuit withstand tests (VIDEO)

Short-circuit withstand testing, examples of rated conditional short-circuit (Icc) tests on functional units of a low-voltage assembly (Protective device trip units are enabled)

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Reference // Transformer Short Circuit Current Calculation and Solutions by Ling Song

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### Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.

1. yunana Zachariah
Feb 04, 2022

2. Saeed Hammam
Nov 18, 2019

very nice .. thank you

3. NguyenCao Ky
Nov 17, 2019

thank you

4. Sayed taha
Sep 13, 2019

Please can you explain different between DC component and ac component fault current especially if we need to design CB and switchgear.

5. MOHAMMED IFTAQUAR AHMED
Oct 07, 2018

i need your support to learn short circuit calculation from the beginning or basic.
if you have any data or document please send.

6. Jose Domingo Maglatang
Oct 07, 2018

Very good presentation and explanation, thanks a lot.

7. Isaac Santillán
Oct 04, 2018

Me podrías enviar el documento es muy bueno

8. Biobele Alexander Wokoma
Oct 04, 2018

Nice one

9. Graham Ison
Oct 03, 2018

In 3.2.2 you reference in China a classification: “single phase fault due to phase-to-earth fault which may happen for two phases”. I am unclear on the interpretation, however, if flags with me as cross country faults that occur on impedance grounded networks in which a phase to earth fault at one point of the network in causing the other phase potentials to rise to L-L potentials relative to earth stress the associated phase insulation which if weak – typically due to insulator contamination – can result in a phase to earth fault in another part of the network. This results in a L-G-L fault, with the L-G currents now at L-L values in excess of the impedance restriction. Typically these account for <5% of such network faults, but can result in ground potential rises at the fault location greater than intended and present a hazard. If the earthing conductors have not been sized for these higher fault currents then greater damage can occur. Such faults are more common in coastal areas where salt contamination of insulators is more prevalent.