ライン損失の削減

Transformers reduce line loss by stepping up voltage at the source, which decreases current in transmission lines. Since power loss is proportional to the square of current, this reduction significantly minimizes energy dissipation as heat in the lines. A step-down transformer at the load restores voltage to usable levels while maintaining consistent load voltage and current through inverse turn ratios.

Line current is calculated by dividing the impedance-reflected load by the secondary voltage of the step-up transformer. The reflected load impedance is the actual load impedance multiplied by the square of the transformer's turns ratio. This calculation accounts for how the transformer's turns ratio affects the apparent impedance seen from the primary side.

Phase voltage at the load is determined by multiplying the primary phase voltage by the transformer's turns ratio. In a Y-to-Y configuration, the line-to-line voltage at the load is found by multiplying the phase voltage by √3 due to the phase shift between line voltages. This ensures the load receives the correct voltage despite the step-up and step-down transformations.

With step-up and step-down transformers properly configured, approximately 99.5 percent of the power supplied by the source reaches the load, with only 0.5 percent lost in the transmission lines. This dramatic reduction in line loss demonstrates the effectiveness of voltage transformation in minimizing energy dissipation during power transmission.

Real power delivered by the source is calculated using P = √3 × VL × IL × cos(θ), where VL is the line-to-line voltage, IL is the line current, and cos(θ) is the power factor. This formula accounts for the three-phase nature of the system and the phase relationship between voltage and current, providing the total real power supplied.

The step-up transformer increases voltage while decreasing current by a factor equal to its turns ratio. The step-down transformer reverses this process with an inverse turns ratio, restoring voltage to original levels while increasing current proportionally. This complementary relationship ensures the load receives stable voltage and current despite the intermediate transmission at high voltage and low current.

Impedance connected to the secondary of a step-up transformer appears multiplied by the square of the turns ratio when viewed from the primary side. For example, if the turns ratio is 10:1, the reflected impedance is 100 times the actual load impedance. This impedance transformation is critical for calculating line current and analyzing the overall circuit behavior.