## Definitions

The term ‘residual current I_{Δ} (in a residual current device)’ is officially defined within the IEC 60050-442 as:

RMS value of the vector sum of the instantaneous values of the currents flowing through the main circuit of the residual current device.

IEC 60050-442

**Note 1 to entry**: Since at least two conductors pass through the main circuit of any residual current device (RCD), at least two electrical currents are flowing in the main circuit of the RCD.

The term ‘residual current I_{Δ} (in an electrical installation))’ is officially defined within the IEC 60050-826-2022 as:

Algebraic sum of the values of the electric currents in all live conductors, at the same time at a given point of an electric circuit in an electrical installation.

IEC 60050-826-2022

**Note 2 to entry**: The definition of “residual current ” in IEC 60050-826 is formulated for an electric circuit. Through the main circuit of the residual current device protecting the electric circuit, all its live conductors pass so that the residual current appearing in the electric circuit will be equal to the residual current determined by the residual current device.

This note establishes equivalence between the residual currents for the RCD and the circuit it protects. The declared equality of residual currents is only possible in AC circuits which include a phase conductor and a neutral conductor. However, given the prohibition on the use of PEN conductors in the electrical installations of residential and public buildings, commercial establishments and medical facilities, this equivalence will apply to most newly installed and reconstructed electrical installations of buildings.

Since the vast majority of electrical circuits in existing building installations are made by conductors with a cross-section smaller than the minimum allowable cross-section of a PEN conductor – 10 mm^{2} for copper and 16 mm^{2} for aluminum, these electrical circuits consist only of phase and neutral conductors.

The IEC standards for surge protectors and thermistors refer to specific electrical currents flowing through these devices under certain conditions as residual currents.

The British Standard BS 7671 defined the term “residual current” as follows:

Algebraic sum of the currents in the live conductors of a circuit at a point in the electrical installation.

BS 7671

**The residual current is not an electric current. Therefore, it cannot pose any danger to humans.**

## Features for Electrical Circuits

Let’s look at examples of what the residual current can be, as applied to electrical circuits:

- In a 3-phase 4-wire electrical circuit consisting of 3-phase conductors and a neutral conductor, the algebraic sum of the electric currents in these four live conductors will be equal to the protective conductor current (leakage current).
- In a 3-phase 4-wire electrical circuit consisting of three phase conductors and a PEN conductor, the algebraic sum of the electric currents in the three live conductors, that is, the phase conductors, will be equal to the current flowing in the PEN conductor.
- The electric current in a PEN conductor is usually equal to the sum of the currents in the neutral and protective conductors. The current in the neutral conductor is several orders of magnitude greater than the protective conductor current.
- Under single fault conditions, when a earth fault has occurred, representing a phase conductor short circuit to a protective conductor in the first electrical system or to a PEN conductor in the second, the algebraic sum of the electrical currents is equal to the earth-fault current.
- Under normal conditions in a 1-phase 2-wire electrical circuit consisting of a phase conductor and a neutral conductor, the algebraic sum of the electric currents in the two live conductors will also be equal to the protective conductor current. If a 1-phase 2-wire electrical circuit is made with a phase conductor and a PEN conductor, it will be impossible to determine the residual current for it, since there is only one live conductor.

## Features for Residual Current Device

The main factor affecting the residual current device and initiating its operation is the residual current, which is defined in the regulatory documentation as the effective value of the vector sum of the currents flowing in the main circuit of the RCD. To determine the residual current the RCD is equipped with a differential transformer (DTR), the principle of operation of which is illustrated in Fig. 1.

The differential transformer of a 2-pole residual current device has two primary windings made by the two conductors of the main circuit RCD, and one secondary winding to which the residual current release is connected.

**Note 3 **– A residual current release is a release that triggers an RCD, with or without time delay, when the residual current exceeds a predetermined value.

**Consider normal circuit operating conditions when there is no fault in the basic insulation of hazardous-live-parts. **

There is no earth-fault current flowing through the main circuit of the RCD because there is no earth fault in the circuit.

In both conductors of the main circuit of the residual current device electrical currents equal in their absolute value to the load current I_{H} (see note 4 below) are flowing. That is, the electric currents I_{1} and I_{2} flowing in the primary windings of the differential transformer are equal to each other in absolute value:

│I_{1}│ = │I_{2}│.

**Note 4 **– If there is no leakage current. If there is leakage current in the circuit, the electrical currents flowing in the phase and neutral conductors of the RCD main circuit differ from each other by approximately the amount of leakage current.

Since the electric currents flowing in the main circuit RCD are towards each other, their vector sum is zero.

The magnetic fluxes Ф_{1} and Ф_{2}, created by the electrical currents I_{1} and I_{2} in the core of the differential transformer, are also directed towards each other and are equal to each other in absolute value. Since these magnetic fluxes cancel each other out, the total magnetic flux in the core of the differential transformer is zero.

Consequently, the absolute value of the electric current that can flow in the electric circuit connected to the secondary of the differential transformer will also be zero:

| I_{p} | = 0

Therefore, under normal conditions, the residual current release cannot trip the RCD which, in turn, does not trip the external circuits connected to it.

**Consider the operation of an electric circuit under conditions of a fault in the basic insulation of a hazardous live part and its earth-fault, when the earth-fault current flows through the main circuit RCD.**

Under fault conditions, in addition to the load current I_{H}, a earth fault current I_{EF} flows through one of the conductors of the main circuit RCD. Therefore the absolute value of the electric current flowing in one of the primary windings of the differential transformer exceeds the absolute value of the electric current flowing in its other primary winding:

│I_{1}│ > │I_{2}│.

Consequently, the vector sum of the electric currents flowing in the main circuit RCD will be non-zero.

The magnetic fluxes Ф_{1} and Ф_{2} in the core of the differential transformer, directly proportional to the electric currents I_{1} and I_{2}, are not equal to each other in absolute value. They cannot compensate each other. Therefore the total magnetic flux in the core of the differential transformer is different from zero.

Consequently, the absolute value of the electric current that flows in the circuit connected to the secondary winding of the differential transformer is also not equal to zero:

│I_{р}│ > 0.

Therefore, under these conditions, the residual current release will be triggered by the electric current I_{p}, causing the residual current device to open its main contacts and disconnect the external electric circuits connected to it.

3-pole residual current devices are used in 3-phase 3-wire electrical circuits and 4-pole RCDs in 3-phase 4-wire electrical circuits, which are equipped with differential transformers with three and four primary windings, respectively. These differential transformers function in the same way as a 2-pole RCD differential transformer. The vector sums of the electric currents flowing in the main circuits of the RCD are determined by taking into account the lag and phase advance of the electric currents in the conductors of the different phases connected to the RCD.

Thus, by determining the residual current the earth fault current is detected and evaluated. When a live part is shorted to earth the residual current is almost equal to the earth fault current. Under normal conditions, the residual current is approximately equal to the leakage current flowing in the circuit.

## Types of Residual Currents

The variety of residual currents that can occur in the main circuit of a household residual current device are reduced in IEC 61008-1 and IEC 61009-1 to the following two types: **sinusoidal residual alternating current** and **residual pulsating direct current**.

Sinusoidal residual current occurs when AC circuits which are connected to a residual current device do not use rectifiers, dimmers, variable speed drives or similar devices which significantly change the sinusoidal current waveform. Leakage current and earth-fault current in such circuits are sinusoidal in shape. The residual current is also sinusoidal in shape (Fig. 2).

When rectifiers, dimmers, variable speed drives and similar devices are used in the electrical installation of buildings, the shape of the sinusoidal current in electrical circuits can change significantly.

If a diode is used as a discrete regulator in any electrical appliance, if the basic insulation of the live part connected downstream of the diode is faulted, an earth-fault current may occur which will only flow for half a period (180° or 10 ms). Such an electric current is called a pulsating direct current in IEC 61008-1 and IEC 61009-1. The flow of pulsating direct current in the main circuit of a residual current device significantly changes its characteristics compared to sinusoidal current.

In the electrical installations of residential buildings, there are a large number of current-using equipments that have built-in rectifiers. All of them are characterized by small direct leakage currents, which can create a total (background) direct leakage current flowing through the main circuit of the residual current device. Even a small direct current flowing through the primary circuit of an RCD differential transformer significantly changes (degrades) its characteristics. For this reason, IEC 61008-1 and IEC 61009-1 take into account the possibility of a small direct current flowing through the main circuit of a residual current device.

Pulsating direct current is defined in international standards as follows:

current of pulsating wave form which assumes, in each period of the rated power frequency, the value 0 or a value not exceeding 0,006 A d.c. during one single interval of time, expressed in angular measure, of at least 150°.

IEC 61009-1

Pulsating direct current is also characterized by the current delay angle (α), which is the time, expressed in angular measure, by which the starting instant of current conduction is delayed by phase control. Fig. 3 and 4 shows a pulsating direct current at current delay angles α, equal to 0°, 90° and 135°.

The appearance of a pulsating direct current in the main circuit of a residual current device significantly changes the characteristics of the RCD. AC-type residual current devices, which are designed to operate only with sinusoidal current, cannot function correctly with pulsating direct current. Therefore, in some countries, their use in electrical installations of buildings is prohibited or significantly restricted. AC-type residual current devices are being replaced by the more modern RCD type A, which are designed for use with both sinusoidal and pulsating direct currents.

In 2009, IEC 62423-2009 was enacted, which applies to Type F and Type B RCDs for household uses. Type F RCDs are designed to protect electrical circuits to which frequency converters are connected.

**They operate in the same way as type A RCDs and in addition:**

- for composite residual currents, whether suddenly applied or slowly rising intended for circuit supplied between phase and neutral or phase and earthed middle conductor
- and for residual pulsating direct currents superimposed on smooth direct current of 0,01 A.

**Type B residual current devices operate in the same way as Type F RCDs, and in addition:**

- for residual sinusoidal alternating currents up to 1 000 Hz (see 8.2.1.1),
- for residual alternating currents superimposed on a smooth direct current of 0,4 times the rated residual current (I
_{Δn}), - for residual pulsating direct currents superimposed on a smooth direct current of 0,4 times the rated residual current (IΔn) or 10 mA, whichever is the highest value,
- for residual smooth direct currents,
- for residual direct currents which may result from rectifying circuits, i.e.,

– two-pulse bridge connection line to line for 2-, 3- and 4-pole devices,

– three-pulse star connection or six-pulse bridge connection for 3- and 4-pole devices.

The above specified residual currents may be suddenly applied or slowly increased independent of polarity.

Thus, the most modern RCDs of type B operate correctly in AC electrical circuits with earth-fault currents of various forms, ranging from 50 Hz sinusoidal current to direct current.

## List of References

- IEC 60050-442
- IEC 60050-826-2022
- BS 7671
- IEC 61008-1
- IEC 61009-1