8.9:
Power Distribution in Three-phase and Single Phase Circuits
Consider a two-wire single-phase system providing electricity to homes and a three-wire balanced three-phase system powering a factory with heavy machinery.
Both systems use wires of the same material and length with resistive loads and have the same line voltage and absorbed power.
In the single-phase system, the current equals the ratio of the absorbed power to the line voltage, with the power loss proportional to the square of the absorbed power divided by the square of the line voltage.
For the three-phase system, the current is divided into three wires, and the total power loss is calculated differently.
In the ratio of the power losses of the two systems, resistances are substituted in terms of the wire radii.
If power loss is equal in both systems, the wire's radius in the single-phase system is twice that of the three-phase system.
Comparing the material required for the two systems, the single-phase system uses 33% more material than the three-phase system.
So, for the same power output, a three-phase system substantially minimizes material consumption, enhancing its power distribution efficiency.
8.9:
Power Distribution in Three-phase and Single Phase Circuits
Power distribution within electrical circuits is a foundational aspect of residential and industrial energy systems. While single-phase power is common in residential settings, three-phase power is the standard for industrial environments with heavy machinery. Each system is different and has advantages, and it's crucial to understand the underlying principles of power distribution and material efficiency.
Single-Phase Power Distribution:
Single-phase circuits are typical in household settings; a two-wire system is used. The current in this system is determined by the power absorbed by the load and the line voltage :
The power loss in the wires due to resistance is proportional to the square of the current:
where R is the resistance of the wires.
Three-Phase Power Distribution:
A balanced three-phase system, most widely used in an industrial setting. In this system, the current is divided among the three wires, reducing the current in each wire compared to a single-phase system with the same power level. Assuming the same current and resistance in each phase, the total power loss is the sum of the losses in each phase.
Wire Size and Material Consumption:
When comparing wire sizes for equal power loss in both systems, the cross-sectional area of the wires in a single-phase system must be larger than that in a three-phase system to carry the increased current without increasing power loss. Specifically, the single-phase system requires wires with a cross-sectional area twice that of each phase wire in the three-phase system. This means that the single-phase system would require wires with a greater cross-sectional area to handle the same power load as the three-phase system, translating to an increase of approximately 33% more conducting material.