1. Grid system is accomplished by three-phase alternating currents.
Three-phase AC Power
Generation, transmission and distribution of electricity via the National
Grid system is accomplished by three-phase alternating currents.

2. A three-phase a.c. supply is carried by three conductors, called ‘lines’ which are coloured red, yellow and blue. The currents in these conductors are known as line currents (IL) and the p.d.’s between them are known as line voltages (VL). A fourth conductor, called the neutral (coloured black, and connected through protective devices to earth) is often used with a three-phase supply.

3. Difference between line and phase quantities
Line voltage is nothing but the output voltage measured at transformer externally i.e. Voltage available between any 2 wires out of 3 wires. We call it as VL.
But Phase voltage is the output voltage available internally i.e. Voltage available between single phase wire and neutral. We call it as Vph.
And the same definition holds good for current available which shall be called as IL & Iph.

4. Our basic rule is to measure power available at secondary which is nothing but the product of Phase Voltage x Phase Current and summation of all three phases,
   P = 3 x VphIph     ….(1)
But as you see it is very difficult to measure the phase voltages from a transformer which may involve complex connections and may be impossible. Rather it’s easy to measure from the lines present outside.
                                   

5. As we know in a star connected transformer, the line voltage is nothing but the combination of two phase voltages which are out of phase by 120°. But current will be same for both phase and line. And in delta connected transformer, two currents will be out of phase by 120° and voltages will be equal.

6. Here we take the case of star connected transformer,
Since the line voltage is combination of two phase voltages we cannot just add together to make VL  = 2 x Vph which doesn’t make sense since there is a phase shift of 120°.
So,                                        VL  = 2 x Vph x sin(120)
                                              VL  = 2 x Vph x √3/2
                                              VL  = √3 x Vph
                       Vph  = VL  /√3                                  …. (2)
Substituting (2) in (1),

7. We get            P = 3 x VL  /√3 x IL               since Iph  = IL  
P = √3 .VL .IL
This holds good for transformers and for other loads like motors, generators etc. Another factor called power factor gets introduced in the equation and converted as,
  P = √3 .VL .IL.cosθ

8. 4 wires Color Code 3 “active” phases, A, B, C 1 “ground”, or “neutral”
Phase A Red
Phase B Black American system
Phase C Blue
Neutral White or Gray
ECE 441

9. 4 wires Color Code 3 “active” phases, A, B, C 1 “ground”, or “neutral”
Phase A Red
Phase B Yellow British system
Phase C Blue
Neutral Black
ECE 441

10. Basic Three-Phase Circuit
ECE 441

11. What is Three-Phase Power?
Three sinusoidal voltages of equal amplitude and frequency out of phase with each other by 120°. Known as “balanced”.
Phases are labeled A, B, and C.
Phases are sequenced as A, B, C (positive) or A, C, B (negative).
ECE 441

12. Three-Phase Power
ECE 441

13. Typically, transmission lines consist of four wires, rather than two as you might have guessed. One of these wires is the ground; the remaining three are used to transmit three-phase ac power which is a superposition of three ac voltages 120⁰ out of phase with each other:
V₁ = V₀ sinωt
V₂ = V₀ sin(ωt + 2π/3)
V₃ = V₀ sin(ωt + 4π/3).

14. Why is three-phase power used?
Single-phase power—just the voltage V₁ by itself—delivers voltage to a load in pulses. A much smoother flow of power can be delivered if we use three- phase power.
Suppose that each of the three voltages making up the three-phase source is hooked up to a resistor R. Then the power delivered is:
P = 1 𝑅 (V₁² + V₂² + V₃²)
It can be shown that this power is a constant equal to 3V₀²/2R, which is three times the rms power delivered by a single-phase source (V₀/√2 is the rms voltage). This smooth flow of power makes electrical equipment run smoothly. Although houses use single-phase ac power, most industrial- grade machinery is wired for three-phase power.

15. Reasons why three-phase power is superior to single phase power
The horsepower rating of three-phase motors and the KVA (kilo-volt- amp) rating of three-phase transformers is about 150% greater than for single-phase motors or transformers with a similar frame size.
The power delivered by a single-phase system pulsates, The power falls to zero three times during each cycle. The power delivered by a three- phase circuit pulsates also, but it never falls to zero. In a three-phase system, the power delivered to the load is the same at any instant. This produces superior operating characteristics for three-phase motors.
In a balanced three-phase system, the conductors need be only about 75% the size of conductors for a single-phase two-wire system of the same KVA rating. This helps offset the cost of supplying the third conductor required by three-phase systems.

16. Phasor (Vector) Form for abc
Vc=Vm/+120°
Va=Vm/0°
Vb=Vm/-120°
ECE 441

17. Single-phase vs three-phase
With the wave form of single-phase power, when the wave passes through zero, the power supplied at that moment is zero. In the U.S., the wave cycles 60 times per second.
3-phase power has 3 distinct wave cycles that overlap. Each phase reaches its peak 120 degrees apart from the others so the level of power supplied remains consistent.

18. THREE-PHASE POWER
Students sometimes become confused when computing power in three phase circuits. One reason for this confusion is that there are actually two formulas that can be used. If line values of voltage and current are known, the power (watts) of a pure resistive load can be computed using the formula:
VA = √ 3 X ELine X ILine
Likewise, if the phase values of voltage and current are known, then power (watts) can be computed using the formula:
VA = 3 X EPhase X IPhase

19. Notice that in the first formula, the line values of voltage and current are multiplied by the square root of 3. In the second formula, the phase values of voltage and current are multiplied by 3. The first formula is used more often because it is generally more convenient to obtain line values of voltage and current, which can be measured with a voltmeter and clamp-on ammeter.

20. THREE PHASE CIRCUITS

22. Delta Source
Vab = | Vab |  0
Vbc = Vab  -120
Vca = Vab  -240

23. Wye – Wye System

24. Delta – Delta System

25. Delta – Wye System

26. Wye – Delta System
The voltage given for a three-phase system is always the line voltage unless it is stated otherwise.

27. Problem 1. Three loads, each of resistance 30 Ω , are connected in star to a 415 V, 3-phase supply. Determine (a) the system phase voltage, (b) the phase current and (c) the line current.
A ‘415 V, 3-phase supply’ means that 415 V is the line voltage, VL
(a) For a star connection, VL = √3 Vp
Hence phase voltage, Vp = VL √3 = 𝟒𝟏𝟓 √3 = V or 240 V
correct to 3 significant figures
(b) Phase current, Ip = Vp Rp = 𝟐𝟒𝟎 𝟑𝟎 = 8 A
(c) For a star connection, Ip = IL
Hence the line current, IL = 8 A