# Direct and indirect measurements using CTs and VTs

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## Direct and indirect measurements

In order to measure electrical quantities, the measuring instruments must be connected to the lines safely, with maximum simplicity and convenience. Generally, the fundamental parameters to be detected are voltage and current, which respectively require a parallel connection and a serial connection to the line on which the measurement is taken.

Generally speaking, there are two approaches when you want to do the measurements:

### Direct measurements

The direct connection to the line defines a direct measurement of the quantity as the instrument is connected in the measuring point without the interposition of adapters.

The direct measurement is possible only when the quantity to be measured has a level that is within the instrument’s capacity!

For example, if 230 V voltage has to be measured, the instrument must have a capacity that is greater than this value (for example 300 V). This also applies to the current measurements: if currents up to 5 A have to be measured, an instrument with at least 5 A capacity and 0-5 A input is required.

Panel and cabinet instruments for direct measurements generally consist of intruments with very limited capacity (measurement of small current and voltage values) with one or several additional resistances inserted inside for the voltmeters and/or one or more shunts for the ammeters.

When the capacity resistances are inserted into the instrument, the instrument can be connected directly to the lines where the measurement is conducted.

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### Indirect measurements

When the quantity to be measured is larger than the capacity of the measuring instrument, a transformer must be interposed that reduces the quantity and supplies the quantity to the instrument with values that are compatible with its capacity. This methodology is defined as indirect measuring.

The measurement conducted via a measuring transformer is defined as an indirect measurement because it does not take place directly on the line under examination.

For example, if a current up to 100 A has to be measured with an current that has a capacity of 5 A, a current transformer (CT) has to be interposed with a transformation ratio of 100/5

If the current transformer is of the wound primary type, it is connected directly serially to the conductor on which the current has to be measured. On the other hand, if it is of the type with a through primary, the insulated or bare conductor is inserted inside the hole of the device.

The current transformer has an outlet that will supply a current that is reduced by 20 times the current that circulates in the conductor being measured, to which the current with 5 A capacity is connected. In current transformers the primary winding is intended to be connected serialy to the circuit traversed by the current to be measured, whilst the secondary winding supplies one or more measuring instruments (all serially connected to each other).

The wiring diagram in Figure 1 shows these transformers.

Compared with the operating principle of a normal transformer, the CT is designed to make the magnetisation current I0 negligeable that is required to produce the flow Φ in the core.

In these conditions, the primary and secondary currents are in exact phase opposition and their respective effective values are in a ratio to one another that is inverse to the number of coils N1 and N2. In other words:

from which:

The coil ratio n between the secondary and primary winding is thus the ideal transformation ratio between the primary and secondary current.

In fact, the magnetic core of the transformer cannot have nil reluctance and IEC 38-1 standards define, for every single transformer, the primary and secondary reference currents, which constitute the nominal currents IPn and ISn of the transformer. The ratio between these two currents is the nominal ratio:

which is indicated by always specifying the numerator and denominator: the current transformer is, for example, said to have a nominal ratio of 75 to 5 A and is written for the sake of brevity as CT 75 A / 5 A.

Table 1 shows the ratio and angle errors (phase difference between the primary and the secondary current) permitted by IEC standards for current transformers.

Table 1 – CT ratio and angle errors permitted by IEC standard.

 Accuracy rating Current as % of nominal value Ratio errors % Angle errors in arc minutes in hundredths or percentages 0.1 10 ± 0.25 ± 10 ± 0.3 10 ± 0.20 ± 8 ± 0.24 100 ± 0.1 ± 5 ± 0.15 120 ± 0.1 ± 5 ± 0.15 0.2 10 ± 0.5 ± 20 ± 0.6 20 ± 0.35 ± 15 ± 0.45 100 ± 0.2 ± 10 ± 0.3 120 ± 0.2 ± 10 ± 0.3 0.5 10 ± 1 ± 60 ± 1.8 20 ± 0.75 ± 45 ± 1.35 100 ± 0.5 ± 30 ± 0.9 120 ± 0.5 ± 30 ± 0.9 1 10 ± 2 ± 120 ± 3.6 10 ± 1.5 ± 90 ± 2.7 100 ± 1 ± 60 ± 1.8 120 ± 1 ± 60 ± 1.8 3 50 ± 3 no prescription 120 ± 3 5 50 ± 5 no prescription 120 ± 5

When there is the problem of measuring high voltages or voltages that are greater than the capacity of the instrument, voltage transformers are used (indicated by the letters VT), the primary of which is supplied with the UP voltage to be measured whilst the transformers use the secondary to supply the measuring instruments (all parallel to one another) at the US voltage.

The wiring diagram in Figure 2 shows these transformers.

Similarly to the current transformers, the theoretical ratio n between the number of coils of the two windings (ideal transformation ratio) is given by the formulas:

However, in practice the falls in ohmic and inductive voltage of the two windings mean that the ratio UP/US differs from the coils n ratio, giving rise to a ratio error ηV%. Accordingly, for every single transformer, the manufacturer sets the nominal primary and secondary voltages, which correspond to a set load condition: the two defined voltages constitute the nominal voltages of the transformer, which must be indicated respectively by the symbols UPn and USn.

The ratio between these two voltages is the nominal ratio of the transformer:

which must be indicated by always specifying the two terms: the voltage transformer is, for example, said to have a nominal ratio of 10,000 to 100 V and is written for the sake of brevity as VT 10,000 V / 100 V. Also for the VTs Table 2 shows the ratio and angle errors specified by the IEC standard.

Table 2 – VT ratio and angle errors permitted by IEC standard.

 Classes Ratio errors % Angle errors in arc minutes in hundredths 0.1 ± 0.1 ± 5 ± 0.15 0.2 ± 0.2 ± 10 ± 0.3 0.5 ± 0.5 ± 20 ± 0.6 1.0 ± 1 ± 40 ± 1.2 3.0 ± 3 no prescription no prescription

To conclude this discussion of voltage and current measuring instruments, we remind the reader that when the margin of error of the measurement is evaluated, the error of the instrument must always be added to the error of the transformer.

For example // If the accuracy rating of the instrument is 1.5 and the accuracy rating of the transformer is 0.5 the margin of error can be ± 2% of the read value (accuracy rating 2).

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Reference // Practical guide to electrical measurements in low voltage switchboards by ABB