Reducing Line Loss

In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.

With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss in transmission lines is proportional to the square of the current, this reduction in current leads to a decrease in line losses.

Calculation of Line Current:

The line current is calculated by dividing the impedance-reflected load (considering the transformer's turns ratio) by the secondary voltage of the transformer.

The line current is:

Where n is the transformer's turns ratio and Z_load is the actual load impedance on the secondary side

Calculation of Phase Voltage at the Load:

If the primary to secondary turns ratio of the transformer is given as N_p:N_s, then the phase voltage at the load can be found by:

where:

V_phase is the phase voltage at the load,

V_primary is the phase voltage at the primary side of the transformer

In a Y-to-Y (star-to-star) three-phase system with transformers on both sides, the full line-to-line voltage at the load can be found by multiplying the phase voltage by sqrt 3, due to the phase shift between line voltages in a Y configuration:

The real power P delivered by the source in a three-phase system is:

Where:

P is the total real power delivered by the source.

V_L is the line-to-line voltage.

I_L is the line current.

cos(θ) is the power factor.