Why do we need 3 phase?
For the reason that voltage will never be zero in 3 phase? OR we need high voltage?
Power Supply – Why Three-Phase Power Supply is Needed
power supplythree phasevoltage
Related Solutions
No need for a complicated formula.
If you have balanced three-phase power, where all three phase voltages are equal in magnitude and 120° apart in phase, then:
$$ V_{L-L} = \sqrt{3} \times V_{L-N} $$
To see why, consider the phasor diagram:
Applying some basic trig:
You are using \$I_{LINE}\$ in both.
There is no dot, so the current that flows in phase must flow in transmission line. So in a star or wye, \$I_{LINE}\ =\ I_{PHASE}\$ (and \$V_{LINE}\ =\ √ (3)\ V_{PHASE}\$). You show this in your answer.
In a delta, \$I_{LINE}\ =\ √ (3)\ I_{PHASE}\$ (and \$V_{LINE}\ =\ V_{PHASE}\$). A component of two phase currents make up the line current. There is a dot.
$$P_T = √ (3)\ V_{LINE}\ I_{LINE}\ cos\ θ $$ $$P_T = 3\ V_{PHASE}\ I_{PHASE}\ cos\ θ $$
So in your first answer, \$V_{L-L}\$ which is line voltage \$V_{LINE}\ =\ 415V\$, which means a \$V_{PHASE}\ =\ 415V / √ (3)\ =\ 239.6V\$. $$ I_{PHASE}\ =\ V_{PHASE} / Z\ = 239.6V / 10Ω = 24.0A$$ $$ P\ = I_{PHASE}^2\ R = (24.0A)^2\ x\ 8Ω\ =\ 4.59kW$$ $$ P_T\ = 3\ P = 3\ x\ 4.59kW\ =\ 13.8kW$$
Related Topic
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- 3 Phase AC to 5V 50mA Power Supply – Design Guide
- Electronic – Why aren’t there any 3-phase domestic power-outlets, or any interest in 3-phase for household (mains) power or anything relatively low-power
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Best Answer
There are several reasons 3-phase is desirable over 1-phase power. One advantage of 3-ph over 1-ph has to do with instantaneous power (i.e. power generated or consumed at any instant in time within the power cycle).
For example, consider a heating element (power resistor) in a 1-phase circuit. Voltage and current are in phase. Both cross zero twice during a cycle as they go positive and then negative.
Their product is power which is a sinusoid at 2x the fundamental frequency (multiply two sine waves and you get a new sine wave with twice the frequency). The power dissipated by the heating element has a sinusoidal waveshape that sits above the zero line (because the two V & I sinusoids, when multiplied together, always give a positive value).
The power sinusoid also reaches zero twice during the fundamental cycle at the same time V or I cross zero. The resistor doesn't produce heat (consume power) at these zero-crossing instants in time (resistor remains hot due to its thermal mass). Now replace the resistor with a 1-ph induction motor.
For similar reasons, despite V & I being out of phase, there are times in its power cycle when the motor doesn't produce mechanical power (it remains spinning due to its own and its load's inertia). In a 3-ph system, the phases are staggered by 120 electrical degrees. If a 3-ph heating element is connected (Y or delta; doesn't matter for the purpose of this discussion), each individual resistor "sees" a zero crossing but collectively the three are producing heat at all times. There is no instant in time when heat is not being produced.
Similarly, with a running 3-ph motor, there is no instant in time when it isn't producing mechanical power. The result is a simplified motor (no starting winding needed as is the case with a 1-phase motor), smaller frame for same horse-power because instantaneous power is never zero. Unlike the 1-ph motor, the 3-ph motor doesn't need the larger bulk to "coast through" a zero crossing.