Chapter 12 Three Phase Circuits Chapter Objectives: Be familiar with different three-phase configurations and how to analyze them. Know the difference between balanced and unbalanced circuits Learn about power in a balanced three-phase system Know how to analyze unbalanced three-phase systems Be able to use PSpice to analyze three-phase circuits Apply what is learnt to three-phase measurement and residential wiring Huseyin Bilgekul Eeng224 Circuit Theory II Department of Electrical and Electronic Engineering Eeng 224 1 Eastern Mediterranean University
Three phase Circuits An AC generator designed to develop a single sinusoidal voltage for each rotation of the shaft (rotor) is referred to as a single-phase AC generator. If the number of coils on the rotor is increased in a specified manner, the result is a P olyphase AC generator , which develops more than one AC phase voltage per rotation of the rotor In general, three-phase systems are preferred over single-phase systems for the transmission of power for many reasons. 1. Thinner conductors can be used to transmit the same kVA at the same voltage, which reduces the amount of copper required (typically about 25% less). 2. The lighter lines are easier to install, and the supporting structures can be less massive and farther apart. 3. Three-phase equipment and motors have preferred running and starting characteristics compared to single-phase systems because of a more even flow of power to the transducer than can be delivered with a single-phase supply. 4. In general, most larger motors are three phase because they are essentially self- starting and do not require a special design or additional starting circuitry. Eeng 224 2
Single Phase, Three phase Circuits b) Single phase systems three-wire type. a) Single phase systems two-wire type Allows connection to both 120 V and 240 V. Two-phase three-wire system. The AC sources operate at different phases. Eeng 224 3
Three-phase Generator The three-phase generator has three induction coils placed 120° apart on the stator. The three coils have an equal number of turns, the voltage induced across each coil will have the same peak value, shape and frequency. Eeng 224 4
Balanced Three-phase Voltages Three-phase four-wire system Neutral Wire A Three-phase Generator Voltages having 120 ° phase difference Eeng 224 5
Balanced Three phase Voltages Neutral Wire a) Wye Connected Source b) Delta Connected Source = ∠ ° = ∠ ° V V 0 V V 0 an p an p = ∠ − ° = ∠ + ° V V 120 V V 120 bn p bn p = ∠ − ° = ∠ + ° V V 240 V V 240 cn p cn p a) abc or positive sequence b) acb or negative sequence Eeng 224 6
Balanced Three phase Loads A Balanced load has equal impedances on all the phases a) Wye-connected load b) Delta-connected load Balanced Impedance Conversion: Conversion of Delta circuit to Wye or Wye to Delta. = = = Z Z Z Z Y 1 2 3 = = = Z Z Z Z ∆ a b c 1 = = Z 3 Z Z Z ∆ ∆ Y Y 3 Eeng 224 7
Three phase Connections Both the three phase source and the three phase load can be connected either Wye or DELTA. We have 4 possible connection types. • Y-Y connection • Y-Δ connection • Δ-Δ connection • Δ-Y connection Balanced Δ connected load is more common. Y connected sources are more common. Eeng 224 8
Balanced Wye-wye Connection A balanced Y-Y system, showing the source, line and load impedances. Line Impedance Source Impedance Load Impedance Eeng 224 9
Balanced Wye-wye Connection Line current I n add up to zero. Neutral current is zero : I n = -( I a + I b + I c )= 0 Phase voltages are: V an , V bn and V 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: V ab , V bc and V ca Magnitude of line voltages is √3 times the magnitude of phase voltages. V L = √3 V p Eeng 224 10
Balanced Wye-wye Connection Line current I n add up 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 phase voltages. V L = √3 V p = ∠ ° = ∠ − ° = ∠ + ° V V 0 , V V 120 , V V 120 an p bn p cn p = + = − = ∠ ° V V V V V 3 V 30 ab an nb an bn p = − = ∠− ° V V V 3 V 90 bc bn cn p = − = + = ∠ − ° V V V V V 3 V 21 0 ca cn an an bn p Eeng 224 11
Balanced Wye-wye Connection Phasor diagram of phase and line voltages = = = V V V V L ab bc ca = = = 3 V 3 V 3 V = 3 V an bn cn p = = = V V V V p an bn cn Eeng 224 12
Single Phase Equivalent of Balanced Y-Y Connection Balanced three phase circuits can be analyzed on “per phase “ basis. . We look at one phase, say phase a and analyze the single phase equivalent circuit. Because the circuıit is balanced, we can easily obtain other phase values using their phase relationships. V = I an a Z Y Eeng 224 13
Eeng 224 14
Balanced Wye-delta Connection Three phase sources are usually Wye connected and three phase loads are Delta connected. There is no neutral connection for the Y-∆ system. V = I AB AB Z ∆ V = I BC BC Z ∆ V = CA I CA Z ∆ Line currents are obtained from the phase currents I AB , I BC and I CA = = = = − = ∠ − ° I I I I I I I I 3 30 L a b c a AB CA AB = = = = − = ∠ − ° I I I I I I I I 3 30 b BC AB BC p AB BC CA = − = ∠ − ° I I I I 3 30 = I 3 I c CA BC CA L p Eeng 224 15
Balanced Wye-delta Connection Phasor diagram of phase and line currents = = = I I I I L a b c = = = I I I I p AB BC CA = I 3 I L p Single phase equivalent circuit of the balanced Wye-delta connection Z ∆ 3 Eeng 224 16
Balanced Delta-delta Connection Both the source and load are Delta connected and balanced. V V V = = = I AB , I BC , I CA AB BC CA Z Z Z ∆ ∆ ∆ = − = − = − I I I , I I I , I I I a AB CA b BC AB c CA BC Eeng 224 17
Balanced Delta-wye Connection Transforming a Delta connected source Single phase equivalent of Delta Wye connection to an equivalent Wye connection V ∠ − ° 30 p 3 Eeng 224 18
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