## Errors in Potential Transformer :

#### The potential transformer also introduces the ratio error and phase angle error just like the current transformer.

### Ratio Error :

Due to a change in load conditions in the distribution system. In a potential transformer, the actual transformation ratio (R) (i.e., the ratio of primary to the secondary terminal voltage V_{p}/V_{s}) differs from its turns ratio (n) and is given by,

From the above equation, it is clear that the voltage across the secondary winding is not a constant fraction of the voltage across the primary winding and hence, an error called 'Ratio Error' is introduced in the measurement of voltage. It is also known as voltage error and it is defined as the deviation of the actual transformation ratio (R) from the nominal ratio (K_{n}).

#### Where,- K
_{n} = Nominal ratio (i.e., rated primary voltage/rated secondary voltage).

_{n}= Nominal ratio (i.e., rated primary voltage/rated secondary voltage).### Phase Angle Error :

When the potential transformer is used in the measurement of power or energy, in order to obtain an accurate reading, the phase of secondary voltage should be exactly 180° out of phase with the primary voltage. But, in P.T.'s these voltages will not be displaced exactly by 180° in-phase and differs by an angle called a phase angle.

This phase angle represents the phase angle error. The phase angle error in a potential transformer is given as,

#### Where,- R
_{p}' = Equivalent resistance of the transformer referred to the primary side. - X
_{p}' = Equivalent reactance of the transformer referred to the primary side. - I
_{w} = Iron loss component. - I
_{m} = Magnetizing component. - I
_{s} = Secondary winding current. - V
_{s} = Secondary terminal voltage. - n = Turns ratio.
- δ = Secondary burden phase angle.

_{p}' = Equivalent resistance of the transformer referred to the primary side._{p}' = Equivalent reactance of the transformer referred to the primary side._{w}= Iron loss component._{m}= Magnetizing component._{s}= Secondary winding current._{s}= Secondary terminal voltage.From the above two errors, it can be seen that the ratio and phase angle errors depend upon the no-load current (i.e., magnetizing and loss component of exciting or no-load current), impedance (i.e., resistance and reactance) of the windings, and secondary burden power factor.

## Characteristics of Potential Transformer :

#### The characteristics of a potential transformer are as follows,

### Effect of Change in Secondary Burden (or Current) :

With the increase in secondary burden, the secondary, as well as primary currents, are increased, increasing the voltage drops in both the windings. As the increase in the primary is more than that of the secondary (since the primary turns are much higher than the secondary turns), their ratio increases with load.

Hence the ratio error increases (i.e., becoming more negative) with the load on secondary. Due to an increase in secondary voltage drop with load, the primary voltage advances and increases the phase angle.

### Effect of Secondary Burden Power Factor :

If the power factor of the secondary burden is reduced (i.e., made more lagging) the phase angle of the secondary load circuit increases which shifts the phase of the primary current, primary voltage, and secondary voltage towards the no-load current, primary and secondary induced EMFs respectively.

Hence, the primary induced emf and secondary terminal voltage decreases. Therefore, the decrease in the secondary power factor increases the transformation ratio and decreases the phase angle.

### Effect of Frequency :

If the frequency of the potential transformers is varied, then it not only affects the ratio error but also the phase angle error.

The effect of frequency on ratio error is that, if the frequency is increased then flux and flux density decreases, due to which magnetizing component I_{m} and core loss component I_{w} also decreases. As a result, the voltage ratio also decreases. Also. if the frequency is increased, then the leakage reactance and hence the drop due to the leakage reactance increases. As a result, the voltage ratio increases.

Hence, it can be concluded that the two effects due to the change in frequency are opposite to each other. Hence, based on the effect that is predominant (i.e., depending on I_{w}, I_{m}, and leakage reactance), the voltage ratio will increase or decrease.

The effect of frequency on phase angle error is that, if the frequency is increased, then apart from the above two mentioned effects, there is another effect. The two effects advance the primary winding terminal voltage V_{p}, whereas the third effect which is due to the secondary leakage reactance, retards the secondary winding terminal voltage V_{s}. Hence, the phase angle 'θ' between V_{p} and V_{s} increases due to which the phase angle error increases.

### Effect of Primary Voltage :

As the primary voltage i.e., supply voltage does not vary widely, the study of variations in errors, in this case, is not of much importance.

## Reduction of Errors in Potential Transformer :

These errors can however be reduced by making some modifications to the design and the construction features of the potential transformer. They are,

### Reduction of Components of No-load Current :

From the expressions of ratio and phase angle error, it is clear that both the errors depend on the value of _{w} and I_{m} i.e., the energy and the magnetizing component of no-load current. Hence, in order to reduce the two errors, the value of I_{w} and I_{m} must be reduced.

### Reduction of Winding Resistance and Leakage Reactance :

We know that the resistance of any material is directly proportional to its length and inversely proportional to the area of the cross-section. Hence, in order to have a low value of winding resistance, a thin conductor with a minimum value of the mean length of the coil should be used.

Also, the resistance of the windings can be reduced by having a high value of flux density. If the flux density is high, then the area will be less (∴ B ∝ 1/A) and hence the mean length of the coil will be reduced. The leakage reactance of the coil can be reduced by reducing the leakage of flux.

The leakage of flux can be reduced by reducing the spacing between the primary and the secondary coils or by winding the primary and the secondary coils on the same limb.

### Turn Compensation :

The transformation ratio is always greater than the turns ratio and it increases with the burden on secondary, as the voltage drop due to resistance and leakage reactance increases with load.

To reduce these errors, either the primary turns are increased or the secondary turns are decreased by which, the transformation ratio is made equal to the nominal ratio and the ratio errors are minimized. As the change in the number of turns is very small, the phase angle error is unaffected.

### Design of Core :

Just like a power transformer, the core of the potential transformer can be either core type or shell type. However, shell type is usually preferred for low voltage transformers. Also, in order to reduce the ratio and phase angle errors, a potential transformer has a larger core and conductor size, when compared to a power transformer. In order to reduce the effect of air gaps at the joints, special care must be taken while assembling and interleaving the core.

### Windings :

The special constructional feature of a potential transformer in order to reduce the ratio and phase angle errors is that the primary winding and the secondary winding must be coaxial i.e., they must have the same axis. In order to reduce the insulation required between the coil layers, the primary winding should have only one coil when used in a low voltage transformer, but it must have multiple short coils in case of a high voltage transformer.

### Insulation :

Sufficient insulation must be provided in order to ensure the safety of low voltage equipment. For high voltage applications, oil-immersed potential transformers are used along with porcelain bushings on the primary terminals. Cotton tape and varnished cambric should be used for coil construction.