Three-phase electric power and load

Three-phase electric power is a common method of alternating-current electric power generation, transmission, and distribution. A three-phase system is generally more economical than others because it uses less conductor material to transmit electric power than equivalent single-phase or two-phase systems at the same voltage.
In a three-phase system, three circuit conductors carry three alternating currents (of the same frequency) which reach their instantaneous peak values at different times. Taking one conductor as the reference, the other two currents are delayed in time by one-third and two-thirds of one cycle of the electric current. This delay between phases has the effect of giving constant power transfer over each cycle of the current and also makes it possible to produce a rotating magnetic field in an electric motor.
* $V_a(t)=V_p \sin(\omega\,t-\tfrac{2}{3}\pi)=V_p (-\tfrac{1}{2}\sin \omega t-\tfrac{\sqrt{3}}{2}\cos\omega t)$
* $V_b(t)=V_p \sin(\omega\,t)$
* $V_c(t)=V_p \sin(\omega\,t+\tfrac{2}{3}\pi)=V_p (-\tfrac{1}{2}\sin \omega t+\tfrac{\sqrt{3}}{2}\cos\omega t)$

And you will find $V_a(t)+V_b(t)+V_c(t)=0$ .

Three-phase systems may have a neutral wire. A neutral wire allows the three-phase system to use a higher voltage while still supporting lower-voltage single-phase appliances.

The phase currents tend to cancel out one another, summing to zero in the case of a linear balanced load. This makes it possible to eliminate or reduce the size of the neutral conductor; all the phase conductors carry the same current and so can be the same size, for a balanced load.

Power transfer into a linear balanced load is constant, which helps to reduce generator and motor vibrations.

Three-phase systems can produce a magnetic field that rotates in a specified direction, which simplifies the design of electric motors.

The following simulation let you play with such 3 phase electric power system, power source and load either in Y or $\Delta$ connection mode.
Use checkbox to select AC Y mode (AC $\Delta$ mode) or R Y mode (R $\Delta$ mode)
For AC Y mode:
Phase voltage referer to V_RN=V_a,V_SN=V_b,V_TN=V_c,
Line voltage referer to V_RS=V_a-V_b,V_ST=V_b-V_c,V_TR=V_c-V_a.

Y-connected sources and loads always have line voltages greater than phase voltages, and line currents equal to phase currents. If the Y-connected source or load is balanced, the line voltage will be equal to the phase voltage times the square root of 3.

$V_a-V_b=V_p (-\tfrac{3}{2}\sin \omega t-\tfrac{\sqrt{3}}{2}\cos\omega t)=\sqrt{3}\,V_p (-\tfrac{\sqrt{3}}{2}\sin \omega t-\tfrac{1}{2}\cos\omega t)=\sqrt{3} V_p \sin(\omega\,t-\tfrac{5}{6}\pi)$

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

Please feel free to post your ideas about how to use the simulation for better teaching and learning.
Post questions to be asked to help students to think, to explore.
Upload worksheets as attached files to share with more users.

Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

Related Topics
	Subject	Started by	Replies	Views	Last post
	Transformer without load Electromagnetism	Fu-Kwun Hwang	0	14483	June 08, 2008, 11:06:10 am by Fu-Kwun Hwang
	A loop rotating in a magnetic field (How electric power generator works!) Electromagnetism	Fu-Kwun Hwang	5	52289	December 12, 2009, 11:46:40 am by Fu-Kwun Hwang
	Power Loss in electric power transmission network .. V^2/R OR I^2*R?/board:37-100- Question related to Physics or physics related simulation	hengleng	2	62550	October 14, 2016, 06:41:10 pm by Shahin1990
	A loop rotating in a magnetic field (How electric power generator works! electromagnetism	ahmedelshfie	7	7345	April 22, 2010, 05:19:06 pm by ahmedelshfie
	Pendula in-phase and out-of-phase Collaborative Community of EJS	LeeTl	1	6217	May 23, 2013, 09:26:41 am by lookang

	Author	Topic: Three-phase electric power and load (Read 18263 times)
0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).