Transformer PF Compensation – Load & No-load Condition

Where: V_P is the source voltage, V_S is the load voltage, I_O is the no load current, I_W is the no load watt Loss current, I_M is the magnetizing current, R_NL is the no load resistance, L_mag is the magnetizing inductance, L_leakage is the leakage inductance, R_T is the winding resistance. T As can be seen from the equivalent circuit, the inductive elements, namely L_mag and L_leakage contribute to the VAR consumption of the transformer

The magnetizing kVAr consumption is a function of the rated voltage and the magnetizing current of the transformer. The no load current of a transformer varies between 0.5 % and 2.5% of the full load current depending on the design of the transformer and the operating flux level. The magnetizing current is around 80% of the no load current and thus varies between 0.4% and 2%. It is safe to assume a value of 1-1.2% for distribution transformers. Thus, the kVAr required to compensate for the magnetizing current of the transformer is around 1- 1.2% of the transformer kVA rating. 

The kVAr requirement due to leakage reactance is a function of the square of the current and the leakage reactance. At full load the voltage drop across the leakage reactance is equal to the impedance voltage (%Z impedance). The reactive kVAr consumption is equal to the product of impedance voltage and load current.

Q_x = IL₂ × X_leakage

Where I_L is the load current and X_leakage is the leakage reactance; Q_X is the kVAr

Power Requirement

Typically, for a 3-phase transformer,

X_leakage = V₂ 2kVA × (%Z);

Where V₂ is the secondary voltage.

Q_x = (%Z) × (kVA) × (%load)²

%Loading is assumed to be 50% to 75%. Thus for % Z=5%, Q_X works out to 5% × (75%)² i.e. 3%.

Thus, the kVAr requirement to compensate for the leakage reactance of the transformer is around 3% of the kVA rating of the transformer. The total kVAr required to compensate for the reactive power consumed by the transformer is around 4% to 4.25% of the kVA rating of the transformer

During no-load/fractional load conditions, reactive power consumption by transformer is contributed by magnetizing branch in the circuit shown in fig 1. Approximately the reactive power consumed by the distribution transformer would be around 1.2% of the power rating (kVA).

Let us assume 1000 kVA transformer operating at fractional load. As per above data, the magnetizing kVAr consumed by transformer would be 12 kVAr (1.2% of 1000 kVA). Let us assume 5 kW as active power is consumed.

At this condition below would be the HT meter readings:

Active power consumed (kW) = 5 kW

Reactive power consumed (kVAr lag) = 12 kVAr

Apparent power (kVA) = √ (5²+12²) = 13 kVA

Power Factor = kW ÷ kVA = 0.385

Let us calculate expected energy bill, with assumption of Rs. 7 per unit. Other fixed charges are not considered for the sake of simplicity. 

Active energy (kWh) per month = 5 kW x 24 x 30 = 3600 units.

PF penalty is typically 2% active energy charges for every reduction of 0.01 in PF from 0.9. In the above case, the energy charges (kWh) will be Rs. 25200 and PF penalty would be Rs. 25975 per month.

Total bill value based on kWh + PF penalty will be Rs. 51175.

By compensating for transformer kVAr, the same bill can be reduced up to Rs. 25200. 

kVAh consumed per month = 13 kVA x 24 x 30 = 9360 units! The electricity bill based on kVAh would be Rs. 65520 per month.

By compensating for transformer kVAr, the same bill can be reduced up to Rs. 25200.

Capacitors need to be added at the LT side of the transformer and always remain in circuit (call as Fixed Capacitors). Some consumers are aware of this issue and have provided some fixed capacitors as solution. But many are not aware of this serious issue and end up paying hefty penalty. Capacitor rating for no-load transformer compensation can be calculated as:

Capacitor kVAr = 1.2% of Transformer kVA rating

These are the minimum required capacitor value to improve PF to healthier levels during no-load conditions. It may not be possible to achieve exact unity power factor, but enough to reduce electricity bill due to very low PF. When the transformer loading increases, the capacitor required for transformer compensation also increases. Capacitor kVAr rating can go up to 5% of transformer kVA rating, depending upon transformer loading and its impedance value.