Lesson 31 Three Phase Sources and Loads 1

Lesson 31: Three Phase Sources and Loads 1

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. 2

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. http: //www. youtube. com/watch? v=Hq. Ztpt. Hn. C 2 I 3

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: 4

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… Delta ( ) Wye (Y) Has a grounding advantage for varying loads 5 Advantage for dedicated loads where grounding not as important

Y-Connected Generator • If the three phase terminals are connected together at N, the generator is referred to as a Yconnected three-phase 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). 6 Y-Connected Generator

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 7

Y-Connected Load Line Voltages • What are the line voltages? • Let’s look at EAB… (the other line voltages are found similarly) • 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: 8 Y-Connected Generator

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 1. 732 ( ) times the magnitude of the phase voltage. • Line to line voltage leads the phase voltage by 30. + - Y-Connected Generator Phase Voltages Line Voltages 9

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

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 Load Y Generator Phase Voltages: Lines 11 The neutral voltage (Vn. N) in a balanced Y-Y system is zero.

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. 12

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

Diagram of 3 -Phase System 14

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: 15

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 4 th 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 16

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

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

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

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

QUESTIONS? 21