Chapter 12 Three Phase Circuits. Chapter Objectives:

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1 Chater 12 Three Phase Circuits Chater Objectives: Be familiar with different three-hase configurations and how to analyze them. Know the difference between balanced and unbalanced circuits Learn about ower in a balanced three-hase system Know how to analyze unbalanced three-hase systems Be able to use PSice to analyze three-hase circuits Aly what is learnt to three-hase measurement and residential wiring Huseyin Bilgekul Eeng224 Circuit Theory II Deartment of Electrical and Electronic Engineering Eastern Mediterranean University

2 Three hase Circuits An AC generator designed to develo a single sinusoidal voltage for each rotation of the shaft (rotor) is referred to as a single-hase AC generator. If the number of coils on the rotor is increased in a secified manner, the result is a Polyhase AC generator, which develos more than one AC hase voltage er rotation of the rotor In general, three-hase systems are referred over single-hase systems for the transmission of ower for many reasons. 1. Thinner conductors can be used to transmit the same ka at the same voltage, which reduces the amount of coer required (tyically about 25% less). 2. The lighter lines are easier to install, and the suorting structures can be less massive and farther aart. 3. Three-hase equiment and motors have referred running and starting characteristics comared to single-hase systems because of a more even flow of ower to the transducer than can be delivered with a single-hase suly. 4. In general, most larger motors are three hase because they are essentially selfstarting and do not require a secial design or additional starting circuitry.

3 Single Phase, Three hase Circuits a) Single hase systems two-wire tye b) Single hase systems three-wire tye. Allows connection to both 120 and 240. Two-hase three-wire system. The AC sources oerate at different hases.

4 Three-hase Generator The three-hase generator has three induction coils laced 120 aart on the stator. The three coils have an equal number of turns, the voltage induced across each coil will have the same eak value, shae and frequency.

5 Balanced Three-hase oltages Three-hase four-wire system Neutral Wire A Three-hase Generator oltages having 120 hase difference

6 Balanced Three hase oltages Neutral Wire a) Wye Connected Source b) Delta Connected Source an = 0 an = 0 bn = 120 bn = cn = 240 cn = a) abc or ositive sequence b) acb or negative sequence

7 Balanced Three hase Loads A Balanced load has equal imedances on all the hases a) Wye-connected load b) Delta-connected load Balanced Imedance Conversion: Conversion of Delta circuit to Wye or Wye to Delta. Z = Z = Z = Z Y Z = Z = Z = Z a b c Z = 3Z Z = Y Y 1 Z 3

8 Three hase Connections Both the three hase source and the three hase load can be connected either Wye or DELTA. We have 4 ossible connection tyes. Y-Y connection Y- connection - connection -Y connection Balanced connected load is more common. Y connected sources are more common.

9 Balanced Wye-wye Connection A balanced Y-Y system, showing the source, line and load imedances. Source Imedance Line Imedance Load Imedance

10 Balanced Wye-wye Connection Line current I n add u to zero. Neutral current is zero: I n = -(I a + I b + I c )= 0 Phase voltages are: an, bn and cn. The three conductors connected from a to A, b to B and c to C are called LINES. The voltage from one line to another is called a LINE voltage Line voltages are: ab, bc and ca Magnitude of line voltages is 3 times the magnitude of hase voltages. L = 3

11 Balanced Wye-wye Connection Line current I n add u to zero. Neutral current is zero: I n = -(I a + I b + I c )= 0 Magnitude of line voltages is 3 times the magnitude of hase voltages. L = 3 = 0, = 120, = an bn cn = + = = ab an nb an bn = = bc bn cn = = + = ca cn an an bn

12 Balanced Wye-wye Connection Phasor diagram of hase and line voltages = = = L ab bc ca = 3 = 3 = 3 = 3 an bn cn = = = an bn cn

13 Single Phase Equivalent of Balanced Y-Y Connection Balanced three hase circuits can be analyzed on er hase basis.. We look at one hase, say hase a and analyze the single hase equivalent circuit. Because the circuıit is balanced, we can easily obtain other hase values using their hase relationshis. I a = Z an Y

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15 Balanced Wye-delta Connection Three hase sources are usually Wye connected and three hase loads are Delta connected. There is no neutral connection for the Y- system. Line currents are obtained from the hase currents I AB, I BC and I CA I = I I = I a AB CA I = I I = I I b BC AB = I I = ICA 3 30 I = 3I c CA BC AB BC I I I AB BC CA I = I = I = I L a b c I = I = I = I = Z AB = Z = Z AB BC CA L BC CA

16 Balanced Wye-delta Connection Phasor diagram of hase and line currents I = I = I = I L a b c I = I = I = I AB BC CA I L = 3I Single hase equivalent circuit of the balanced Wye-delta connection Z 3

17 Balanced Delta-delta Connection Both the source and load are Delta connected and balanced. AB BC I AB =, I BC =, ICA= Z Z Z I = I I, I = I I, I = I I a AB CA b BC AB c CA BC CA

18 Balanced Delta-wye Connection Transforming a Delta connected source to an equivalent Wye connection Single hase equivalent of Delta Wye connection 30 3