We have seen in this series of turorials about the transformer, that when the primary winding of a transformer is energised, it produces a secondary voltage and current at an amount determined by the transformers turns ratio, (TR). So if a single-phase transformer has a step down turns ratio of 2:1 and 240V is applied to the high voltage primary winding, we would expect to see an output terminal voltage on the secondary winding of 120 VAC because we have assumed it to be an ideal transformer.

However in the real world this is not always true as being a wound magnetic circuit, all transformers suffer from losses consisting of I^{2}R copper losses and magnetic core losses which would reduce this ideal secondary value by a few precent to say 117 VAC, and this is normal. But there is also another value related to transformers (and electrical machines) which also has an affect on this secondary voltage value when the transformer is supplying full power, and this is called “regulation”.

## Transformer Voltage Regulation

**Voltage Regulation** of single-phase transformers is the percentage (or per unit value) change in its secondary terminal voltage compared to its original no-load voltage under varying secondary load conditions. In other words, regulation determines the variation in secondary terminal voltage which occurs inside the transformer as a result of variations in the transformers connected load thereby affecting its performance and efficiency if these losses are high and the secondary voltage becomes too low.

When there is no-load connected to the transformers secondary winding, that is its output terminals are open-circuited, there is no closed-loop condition, so there is no output load current (I_{L} = 0) and the transformer acts as one single winding of high self-inductance. Note that the no-load secondary voltage is a result of the fixed primary voltage and the turns ratio of the transformer.

Loading the secondary winding with a simple load impedance causes a secondary current to flow, at any power factor, through the internal winding of the transformer. Thus voltage drops due to the windings internal resistance and its leakage reactance causes the output terminal voltage to change.

A transformers voltage regulation change between its secondary terminal voltage from a no-load condition when I_{L} = 0, (open circuit) to a fully-loaded condition when I_{L} = I_{MAX} (maximum current) for a constant primary voltage is given as:

### Transformer Voltage Regulation as a Fractional Change

Note that this voltage regulation when expressed as a fraction or unit-change of the no-load terminal voltage can be defined in one of two ways, *voltage regulation-down*, (Reg_{down}) and *voltage regulation-up*, (Reg_{up}). That is when the load is connected to the secondary output terminal, the terminal voltage goes down, or when the load is removed, the secondary terminal voltage goes up. Thus the regulation of the transformer will depend on which voltage value is used as the reference voltage, load or non-load value.

We can also express transformer voltage regulation as a percentage change between the no-load condition and the full-load conditions as follows:

### Transformer Voltage Regulation as a Percentage Change

So for example, if a single-phase transformer has an open-circuit no-load terminal voltage of 100 volts and the same terminal voltage drops to 95 volts on the application of a connected load, the transformers voltage regulation would therefore be 0.05 or 5%, ((100 – 95)/100)*100%). Therfore a transformers voltage regulation can be expressed as either a unit change value or as a percentage change value of the no-load voltage.

## Transformer Voltage Regulation Example No1

The primary winding of a 500VA, 10:1 single-phase step-down transformer is fed from a constant 240Vrms supply. Calculate the percentage regulation of the transformer when connected to an impedance of 1.1Ω

Data given: VA = 500, TR = 10:1, V_{P} = 240V, Z_{S} = 1.1Ω, find %Reg.

Therefore, V_{S(no-load)} = 24 Volts

Therefore, V_{S(full-load)} = 23.45 Volts

Then the percentage down regulation calculated for the transformer is given as: 2.29%, or 2.3% rounded-off

## Transformer Voltage Regulation Example No2

A single-phase transformer with a voltage regulation of 4% has a secondary terminal voltage of 115.4 volts at full load current. Calculate its no-load terminal voltage when the load is removed.

Then we can see that a change in the connected load creates a change in the transformers terminal voltage between its “no-load” voltage and its “full-load” voltage therby making transformer voltage regulation a function external to the transformer. Thus the lower the percentage voltage regulation the more stable the transformers secondary terminal voltage will be no matter what the load current value is. If the connected load is purely resistive, then the voltage drop would be smaller. Thus an ideal transformer would have zero voltage regulation, that is V_{S(full-load)} is equal to V_{S(no-load)} as there would be zero losses.

So we now know that a transformers voltage regulation is the difference between its full-load voltage and no-load voltage to its maximum rated secondary current which can be expressed as a ratio or as a percentage (%) value. But why does the secondary voltage change or drop with changes in load current.

## Transformers on-load

When a transformers secondary winding is supplying a load, there are magnetic iron losses within the laminated core and copper losses due to the resistivity of its windings, and this is true for both the primary and secondary windings.

These losses produce a reactance and resistance in the transformers winding providing an impedance path through which the secondary output current, (I_{S}) must flow as shown.

As the secondary winding consists of both resistance and reactance, it follows that an internal voltage drop must occur in the windings of the transformer by an amount depending on the effective impedance and the load current being supplied as Ohm’s Law states: V = I*Z.

Then we can see that as the secondary load current increases, the voltage dropped within the transformers windings must also increase, and for a constant primary supply voltage, the secondary output voltage must therefore fall.

The impedance (Z) of the secondary winding is the phasor sum of both its resistance (R) and the leakage reactance (X) with a different voltage drop produced across each component. Then we can define the secondary impedance as well as the no-load and full-load voltages as being:

Thus the secondary windings no-load voltage is defined as:

V_{S(no-load)} = E_{S}

and its full-load voltage is defined as:

V_{S(full-load)} = E_{S} – I_{S}R – I_{S}X

or V_{S(full-load)} = E_{S} – I_{S}(R+jX)

∴ V_{S(full-load)} = E_{S} – I_{S}*Z

Clearly then we can see that the transformers winding consists of a reactance in series with a resistance with the load current being common to both. Since voltage and current are in-phase for a resistance, the voltage drop across the resistor given as I_{S}R must therefore be “in-phase” with the secondary current, I_{S}.

However, in a pure inductor having inductive reactance, X_{L} the current lags by 90^{o} so the voltage drop across the reactance given as I_{S}X leads the current by an angle Φ_{L} as its an inductive load.

Since the impedance, Z of the secondary winding is the phasor sum of the resistance and reactance, their individual phase angles are given as:

As V = I*Z, the voltage drop across the secondary impedance is therefore given as:

V_{drop} = I_{S}(RcosΦ + XcosΦ)

and as V_{S(full-load)} = V_{S(no-load)} – V_{drop}, the percentage regulation can be given as:

### Lagging Power Factor Expression

For a positive regulation expression between cos(Φ) and sin(Φ) the transfomers secondary terminal voltage will decrease (fall) indicating a lagging power factor (inductive load). For a negative regulation expression between cos(Φ) and sin(Φ), the transfomers secondary terminal voltage will increase (rise) indicating a leading power factor (capacitive load). Thus a transformers regulation expression is the same for both leading and lagging loads, its just the sign that changes to indicate a voltage rise or fall.

### Leading Power Factor Expression

Therefore a positive regulation condition produces a voltage decrease (drop) within the secondary winding while a negative regulation condition produces a voltage increase (rise) in the winding. While leading power factor loads are not as common as inductive loads (coils, solenoids or chokes), a transformer feeding a light load with low currents may experience a capacitive condition causing the terminal voltage to rise.

## Transformer Voltage Regulation Example No3

A 10KVA single-phase transformer provides a no-load secondary voltage of 110 volts. If the equivalent secondary winding resistance is 0.015Ω and its total reactance is 0.04Ω, determine its voltage regulation when supplying a load at 0.85 power factor lagging.

Data given: VA = 10000, V_{S(no-load)} = 110V, R = 0.015Ω, X = 0.04Ω, find %Reg.

if cosΦ = 0.85, Φ = cos^{-1}(0.85) = 31.8^{o} ∴ sinΦ = 0.527

Secondary current is defined as:

I_{S} = VA/V = 10000/110 = 90.9 Amps

Percentage voltage regulation is given as:

## Transformer Voltage Regulation Summary

We have seen here in this tutorial about **Transformer Voltage Regulation** that when a transformers secondary winding is loaded its output voltage can change and that this voltage change can be expressed either as a ratio, or more commonly as a percentage value. With no-load connected there is no secondary current which means that the secondary voltage is at its maximum value.

However when fully-loaded, secondary currents flow producing core losses and copper losses within the winding. The core loss is a fixed loss due to the transformers magnetic circuit produced by the primary winding voltage, while the secondaries copper loss is a variable loss that is related to the load current demand connected to the secondary winding.

Then variations in load current will cause variations in the losses affecting regulation. The smaller the transformers voltage regulation, the less the variation in secondary terminal voltage with changes in the load, and this is very useful to have in regulated power supply circuits.

We also said that for a lagging power factor (inductive load), the secondary terminal voltage will decrease. If the transformer supplies a very low lagging power factor, large secondary currents will flow resulting in poor voltage regulation due to greater voltage drops in the winding.

A leading power factor (capacitive load), the output terminal voltage will rise. Therefore positive regulation produces a voltage drop in the winding while a negative regulation produces a voltage rise in the winding. While it is not possible to have a zero-voltage regulation condition (only ideal transformers), minimum regulation and therefore maximum efficiency generally occurs when when the windings core losses and the copper losses are approximately equal.