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Sahithyan's S1
Sahithyan's S1 -- Electrical Fundamentals

3-Phased System

Why 3-phase?

  • The current can be distributed into 3 wires instead of just 1.
    There is a maximum limit of how much current a wire can carry.
  • Economical as less amount of wires.
    3-phase system requires wires ( if balanced) while single phase system requires .

The phases are denoted by in that order.

Balanced 3-phase

A 3-phase system is said to be balanced iff:

  • Supply is balanced
  • Loads are the same in each phase

Power source

A 3-phase power source which produces 3 phase voltages of equal rms value, but with phase difference.

Phasor diagram

Balanced 3-phase system

Phase voltage

Voltage between a phase wire and the neutral wire.

, , are the phase voltages.

Line-to-line voltage

Voltage between any 2 phase wires. Line-to-line voltages also have a phase difference.

, , are the line-to-line voltages or line voltages.

Analysis

Analysis of 3-phase circuit

When the loads are balanced: ,
In this case, neutral wire is optional and can be eliminated. have to be maintained so that the voltage is equal to ground voltage in neutral wire. This makes sure there are no power losses in neutral wire.

Real-life Usage

Most domestic loads are single-phase. In case of 3-phase domestic wiring, the single-phase loads are distributed among the 3 phases at the main distribution board.

Devices that have a 3-phase power input, doesn’t require a neutral line.

Per-phase Equivalent Circuit

Power, voltage, current, power factor are same for all phases.

When a 3-phase system is balanced, it is sufficient to consider only a single phase. The diagram showing the single-phase equivalent of the power system using standard symbols.

Per-phase equivalent circuit

Here:

  • - voltage across the source
  • - voltage across the load

Here:

  • - phase voltage
  • - line voltage
  • - line current
  • - power factor
  • The power can either be source power, load power, or transmission power losses.

Unbalanced 3-phase system

A 3-phase system becomes unbalanced, when load distribution is not equal among the phases. . Highly undesirable. Neutral wire is the return path for the line currents and is compulsory.

Large currents in the neutral wire could cause:

  • If neutral wire have significant impedance, different points of the neutral wire will have different voltage
  • Series voltage unbalances can happen if the neutral wire is broken

Each phase will be different. Complete system has to be considered when analyzing the circuit.