1. Lesson 31: Three Phase Sources and Loads

2. Learning Objectives
Review the induced AC voltage output for a three phase AC generator as a function of time and as phasors.
Define a three-wire Y-Y three phase circuit and a four-wire Y-Y three phase circuit.
Define the symbols for line to neutral voltages, line to line voltages, line currents, and phase impedances that will be used in three phase circuits.
Analyze Ohm’s law in a three-wire Y-Y three phase circuit and in a four-wire YY three phase circuit using a basic three phase generator that produces three balanced voltages which are connected to balanced loads.
Analyze Kirchhoff’s current law in a three-wire Y-Y three phase circuit and in a four-wire Y-Y three phase circuit using a basic three phase generator that produces three balanced voltages with a Y connected balanced purely resistive loads.

3. Why Three-Phase?
Nearly all power generated and distributed is 3-phase, 60 Hz (or 50 Hz outside the U.S.).
When single phase is needed, it can simply be taken from one of the three phases.
The instantaneous power in 3-phase system can be constant (not pulsating).
Results in less vibration in 3-phase machines.
Three phase systems are more economical than single systems.
Amount of wire needed is less than single phase. 3

4. Three-Phase Generator
A three-phase source generates three separate ac voltage signals, all of the same peak value, same frequency, but differing from each other by a phase separation of
The vector sum of the phase voltages of a three-phase generator is zero
Phasor diagram for a
three-phase generator
Phase voltages of a three-phase generator
For example, if the RMS value of each waveform is, , then the three waveforms shown above are:

5. Wye(Y) and Delta() Connections
AC three-phase generators can be connected in multiple configurations. The first we will discuss is the Y-Connected Generator…
Wye (Y)
Delta ()
Has a grounding advantage
for varying loads
Advantage for dedicated loads
where grounding not as important

6. Y-Connected Generator
If the three phase terminals are connected together at N, the generator is referred to as a Y-connected three-phase generator.
Y-Connected Generator
Note that the negative (-) terminals are connected together at N, which is the neutral.
The three phase Y generator is connected to the load via the three lines labeled with a corresponding phasor current (IA, IB and IC).

7. Y-Connected Load Phase Voltages
Y-Connected Generator
Phase voltages are the voltages across the different phases.
For a Y load, phase voltage is measured from line to neutral (N).
For the generator above , EAN, EBN and ECN are the phase voltages.
KVL holds true:
EAN + EBN + ECN = 0

8. Y-Connected Load Line Voltages
What are the line voltages?
Let’s look at EAB… (the other line voltages are found similarly)
Y-Connected Generator - +
By KVL:
It was previously stated that the RMS phase voltage magnitudes are equal, thus:
So now we can say:
Pressing on and converting to rectangular coordinates and then simplifying further, and then converting back to polar it can be shown that the line voltage are:

9. Y-Connected Generator Phase and Line Voltages
However, the phase for EAN is rarely fixed at zero. So for any Ѳ relationship it can be shown that for a balanced Y-Connected Generator the magnitude of line-to-line voltage is ( ) times the magnitude of the phase voltage.
Line to line voltage leads the phase voltage by 30.
Y-Connected Generator - + 3
Phase Voltages
Line Voltages

10. Example Problem 1 Consider the three phase system shown where
Determine:
Phase voltage EBN
Phase voltage ECN
The three line-to-line voltages (EAB, EBC and ECA) + -

11. Y-Connected Generator with a Y-Connected Load (3-Wire System)
Usually we connect a Y load with a Y generator as shown below.
The below is known as a 3-Wire System.
For all systems, assume that the loads are balanced (Zan=Zbn=Zcn).
Analyzing this type of circuit can be cumbersome.
Y Generator
Y Load
Phase Voltages:
Line Voltages:
The neutral voltage (VnN) in a balanced Y-Y system is zero.
Lines

12. Y-Load Phase and Line Currents
Line currents are the currents in the line conductors.
Phase currents are the currents through phases.
For Y loads, line current and phase current are the same.

13. Currents for a Y Circuit
For Y loads, line current and phase current are the same.
Line current
Phase current

14. Diagram of 3-Phase System

15. Example Problem 2
For the load depicted below, EAB = 2080 V . Find the phase voltages and line voltages and currents (remember that for a Y system, the phase and line currents are the same).
Line Voltages:
Phase Voltages:
Notice the balanced load
Phase/Line Currents:

16. 4-Wire Y-Y System
What if there were a fourth wire added between the points N and n?
The system then becomes a 4-wire Y-Y System.
The system is still balanced.
The 4th wire allows for easier analysis of the system.
Ohms law can easily be used for IA, EAN ,Van or Zan
Since it is a balanced system Zan = Zbn = Zcn

17. Example Problem 3 EAN = 7620-18 V
What are the phase and line voltages ?
Phase Voltages:
Line Voltages:

18. -Connected Load
For  loads, phase voltage and line voltage are the same thing.

19.  Load Definitions
Y-Y
Y-Δ
Line currents are the currents in the line conductors.
Phase currents are the currents through phases .

20. Line/Phase Currents for a Delta Circuit
Line current
Phase current

21. QUESTIONS?