Concept of AC Three Phase Generation.

    3 phase AC Sinusoidal 

In single phase AC circuit one rectangular coil placed in uniform magnetic field but in case of three phases AC circuit three rectangular coils placed in uniform magnetic field an angle of 120 degree phase difference each other rotate with uniform angular velocity ω rad/sec.  rotates such that R- phase wave form started at 0 degree, Y-phase 120 degree and B-phase 240 degree displaced each other’s shown in figure below.In three phase the value of emf induced in the phases  Red(R), Yellow(Y) and Blue(B)

R is E_R =V_M sin ωt,

Y is E_Y = V_M sin (ωt-120 degree) and

B is E_B= V_M sin (ωt-240 degree) = V_M sin (ωt+240 degree)

   3 phases waveform

We can say the phase Y lags 120 degree and B 240 degree lags behind to the R phase. The sums of three phases induced emfs is zero i.e. E_R +E_Y +E_B =0. First the R phase reached the maximum than Y-phase after that B-phase we can say the phase sequences is R-Y-B shown in figure below;Two type of balance supply and load arrangement in three phase circuit one is the star connection and another delta connection. The circuit will be balance when the value of voltage and current is equal magnitude.  Three phase AC system mainly used in industrial applications. When the value of in each phase voltage RY, YB and BR are in equal magnitude displaced 120 degree each other the supply is balanced. In case of balance load in three phase circuit the value of Impedance (Z) is equal magnitude in each phase i.e. RY, YB and BR.

Star connected load:

Star connected balance load

In star connected balanced load shown in above figure E_R, E_Y and E_B is the voltage in R, Y and B phase is phase voltage and E_RY,E_YB and E_BR is voltage between two lines RY,YB and BR called line voltage. The line current I_R,I_Y and I_B flow in each line which is equal to the phase current. According to Kirchhoff’s voltage law the value of the relation between phase voltage and line voltage is

E_RY= E_R- E_Y

E_YB = E_Y- E_B

E_BR= E_B - E_R,Where E_R, E_Y and E_B phase voltages and  E_RY,E_YB and E_BR  line voltages. Also, in case of star connection balance load the value of quantities given below:

E_l= √3 E_ph     

I_l= Iph

P=3 E_ph I_ph cosφ

P=√3 E_l I_l cosφ ,Where E_ph- phase voltage, E_l- line voltage, I_ph- phase current, I_l- line current, cosφ power factor.

Delta connected load:

Delta connected balance load

In delta connected balanced load shown in figure I_R, I_Y and I_B is the line current in R, Y and B phases and I_RY, I_YB and I_BR is phase current. In delta connected load phase voltage is equal to the line voltage.  According to Kirchhoff’s current law the value of the relation between phase current and line current is

I_R= I_RY -I_BR

I_Y = I_YB -I_RY

I_B = I_BR -I_YB,Where I_R, I_Y and I_B is the line current. Also, in case of delta connection balance load the value of quantities given below:

I_l= √3 I_ph     

E_l= Eph
P=3 E_ph I_ph cosφ

P=√3 E_l I_l cosφ,Where E_ph- phase voltage, E_l- line voltage, I_ph- phase current, I_l- line current, cosφ power factor.

Mathematical summery AC single phase

1. E=E_m sin ωt            Sinusoidal EMF
2. I= I_m sin ωt             Sinusoidal current
3. ω =2πf                     Angular frequency
4. I_av=2I_m/π                Average value of sinusoidal current
5. I_rms= I_m/√2             RMS value of sinusoidal current
6. FF= I_rms/ I_av              Form factor
7. PF= I_m/ I_rms               Peak factor
8. P=VI cosφ               Active power (Watt)
9. Q=VI sineφ             Reactive power (VAR)
10. S= √ P²+Q²            Apparent power (VA)
11. Cosφ=R/Z               Angle between resistance and impedance

Mathematical summery AC three phase

1. E_R =V_M sin ωt                            Sinusoidal EMF R phase
2. E_Y = V_M sin (ωt-120 degree)     Sinusoidal EMF Y phase  
3. E_B = V_M sin (ωt+240 degree)    Sinusoidal EMF B phase
4. P=3 E_ph I_ph cosφ                         Power three times the single phase

Differences between AC single phase and three phase

1. Flow of power in AC single phase through single conductor and three phase through three conductors.
2. The voltage in single phase is 230Volt and three phase 440 Volt measured through voltmeter.
3. Single phase supply mostly used in domestic appliances and three phase supply used in industrial heavy load.
4. The single phase power loss more, efficiency less compare to three phases. 
5. AC single phase power transmission less economical compare to three phases.
6. AC single phase known single phase 2-wire system but  AC three phase known as 3-phase 4-wire system.