1 ELECTRICAL CIRCUIT ET 201  Become familiar with the operation of a three phase generator and the magnitude and phase relationship.  Be able to calculate the voltages and currents for a three phase Wye and Delta connected generator and load.

2 THREE PHASE SYSTEMS

– Introduction  If the number of coils on the rotor is increased in a specified manner, the result is a polyphase ac generator, which develops more than one ac phase voltage per rotation of the rotor  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  In general, three-phase systems are preferred over single-phase systems for the transmission of power for many reasons, including the following:

4 Introduction 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) and in turn reduces construction and maintenance costs. 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.

5 Introduction  The frequency generated is determined by the number of poles on the rotor (the rotating part of the generator) and the speed with which the shaft is turned.  Throughout the United States the line frequency is 60 Hz, whereas in Europe (incl. Malaysia) the chosen standard is 50 Hz.  On aircraft and ships the demand levels permit the use of a 400 Hz line frequency.  The three-phase system is used by almost all commercial electric generators.

6 Introduction  Most small emergency generators, such as the gasoline type, are one-phased generating systems.  The two-phase system is commonly used in servomechanisms, which are self-correcting control systems capable of detecting and adjusting their own operation.  Servomechanisms are used in ships and aircraft to keep them on course automatically, or, in simpler devices such as a thermostatic circuit, to regulate heat output.  The number of phase voltages that can be produced by a polyphase generator is not limited to three. Any number of phases can be obtained by spacing the windings for each phase at the proper angular position around the stator.

– 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.

8 Three-Phase Generator  At any instant of time, the algebraic sum of the three phase voltages of a three-phase generator is zero.

9 Three-Phase Generator  The sinusoidal expression for each of the induced voltage is:

10 Phase expression In phase expression: Where: E M : peak value E A, E B and E C : rms value

11 Connection in Three Phase System A 3-phase system is equivalent to three single phase circuit Two possible configurations in three phase system: 1.Y-connection (star connection) 2.∆-connection (delta connection)

12 Three-phase Voltages Source Y-connected source ∆-connected source

13 Three-phase Load Y-connected load ∆-connected load

– Y-Connected Generator  If the three terminals denoted N are connected together, the generator is referred to as a Y- connected three-phase generator.

15 Y-Connected Generator  The point at which all the terminals are connected is called the neutral point.  Two type of Y-connected generator: 1.Y-connected, three-phase, three-wire generator (a conductor is not attached from this point to the load) 2.Y-connected, three-phase, four-wire generator (the neutral is connected)  The three conductors connected from A, B and C to the load are called lines.

16 Y-connected, 3-phase, 3-wire generator

17 Y-connected, 3-phase, 4-wire generator

18 Y-Connected Generator  The voltage from one line to another is called a line voltage  The magnitude of the line voltage of a Y-connected generator is:

19 Definition of Phase Voltage In 3-phase system, for Y-connected, the voltage from line to neutral point is called a phase voltage. E AN – phase A voltage E BN – phase B voltage E CN – phase C voltage

20 Definition of Line Voltage In 3-phase system, for Y-connected, the voltage from one line to another is called a line voltage. E AB – voltage between line A and B E BC – voltage between line B and C E CA – voltage between line C and A

21 Y-connected system Line voltage: V AB ; V BC ; V CA Phase voltage: V AN ; V BN ; V CN

22 Voltage in Y-connected system For 3-phase Y-connected system, if the phase voltage V AN is taken as the reference, so

23 Voltage in Y-connected system By applying Kirchhoff’s Voltage Law, the line voltage can be written as

24 Voltage in Y-connected system With the same method, and The relationship between the line voltage and the phase voltage can be represented as V L : line voltage Vφ : phase voltage

25 Current in Y-connected system For the Y-connected system, it should be obvious that the line current equals the phase current for each phase; that is I L : line current I φ : phase current

– Phase Sequence (Y-Connected Generator)  The phase sequence can be determined by the order in which the phasors representing the phase voltages pass through a fixed point on the phasor diagram if the phasors are rotated in a counterclockwise direction.

– Phase Sequence (Y-Connected Generator) In phasor notation, Line voltage: Phase voltage:

– Y-Connected Generator with a Y-Connected Load  Loads connected with three-phase supplies are of two types: the Y and the ∆.  If a Y-connected load is connected to a Y-connected generator, the system is symbolically represented by Y-Y.

29 Y-Connected Generator with a Y- Connected Load  If the load is balanced, the neutral connection can be removed without affecting the circuit in any manner; that is, if Z 1 = Z 2 = Z 3, then I N will be zero, I N = 0.  Since I  L = V  / Z  the magnitude of the current in each phase will be equal for a balanced load and unequal for an unbalanced load. In either case, the line voltage is

30 EXAMPLE 1 Calculate the line currents in the three-wire Y-Y system as shown below.

31 Solution: Single Phase Equivalent Circuit Phase ‘a’ equivalent circuit

32

– Y-Connected Generator with a ∆-Connected Load  There is no neutral connection for the Y-∆ system shown below.  Any variation in the impedance of a phase that produces an unbalanced system will simply vary the line and phase currents of the system.

34 Y-Connected Generator with a ∆-Connected Load  For a balanced load, Z 1 = Z 2 = Z 3.  The voltage across each phase of the load is equal to the line voltage of the generator for a balanced or an unbalanced load: V  = E L.

35 Y-Connected Generator with a ∆-Connected Load  Kirchhoff’s current law is employed instead of Kirchhoff’s voltage law.  The results obtained are:  The phase angle between a line current and the nearest phase current is 30°.

36 EXAMPLE 2 A balanced positive sequence Y- connected source with V AN =100  10  V is connected to a  -connected balanced load (8+j4)  per phase. Calculate the phase and line currents.

37 Solution: Balanced WYE source, V AN = 100  10  V Balanced DELTA load, Z  = 8 + j4  Phase and line currents = ??

38 Phase Currents V ab = voltage across Z  = V AB = source line voltage

39 Phase Currents

40 Line Currents

– ∆ -Connected Generator  In the figure below, if we rearrange the coils of the generator in (a) as shown in (b), the system is referred to as a three-phase, three-wire.

42 ∆ -Connected Generator  ∆-connected ac generator  In this system, the phase and line voltages are equivalent and equal to the voltage induced across each coil of the generator: or E L = E  g  Only one voltage (magnitude) is available instead of the two in the Y-Connected system.

43 ∆ -Connected Generator  Unlike the line current for the Y-connected generator, the line current for the ∆-connected system is not equal to the phase current. The relationship between the two can be found by applying Kirchhoff’s current law at one of the nodes and solving for the line current in terms of the phase current; that is, at node A, I BA = I Aa + I AC or I Aa = I BA - I AC = I BA + I CA

44 ∆ -Connected Generator  The phasor diagram is shown below for a balanced load.  In general, line current is:

45 Definition of Phase Current In 3-phase system, for ∆-connected, the current that flow from one phase to another is called a phase current. I BA – phase A current I CB – phase B current I AC – phase C current

46 Definition of Line Current In 3-phase system, for ∆-connected, the current that flow through the line is called a line current. I Aa – line A current I Bb – line B current I Cc – line C current

47 ∆-connected system (generator) Line current: I Aa ; I Bb ; I Cc Phase current: for generator: I BA ; I AC ; I CB

48 ∆-connected system (load) Line current: I Aa ; I Bb ; I Cc Phase current: for load: I ab ; I bc ; I ca

49 Current in ∆-connected system (Generator side) For 3-phase ∆-connected system (generator), if the phase current I B A is taken as the reference, so

50 Current in ∆-connected system (Generator side) By applying Kirchhoff’s Current Law, the line current can be written as

51 With the same method, and Current in ∆-connected system (Generator side)

52 Current in ∆-connected system (Load side) For 3-phase ∆-connected system (load), if the phase current I ab is taken as the reference, so

53 Current in ∆-connected system (Load side) By applying Kirchhoff’s Current Law, the line current can be written as

54 With the same method, and Current in ∆-connected system (Load side)

55 The relationship between the line current and the phase current can be represented as Where; I L : line current Iφ : phase current Relationship between the phase current and the line current (∆-connected system)

56 Voltage in ∆-connected system For the ∆-connected system, it should be obvious that the line voltage equals the phase voltage for each phase; that is V L : line voltage V  : phase voltage

– Phase Sequence (∆- Connected Generator)  Even though the line and phase voltages of a ∆ - connected system are the same, it is standard practice to describe the phase sequence in terms of the line voltages  In drawing such a diagram, one must take care to have the sequence of the first and second subscripts the same  In phasor notation, V AB = V AB  0 o V BC = V BC  120 o V CA = V CA  120 o

∆-Connected Generator with a ∆-Connected Load

59 EXAMPLE 3 A balanced delta connected load having an impedance 20 - j15  is connected to a delta connected, positive sequence generator having V AB = 330  0  V. Calculate the phase currents of the load and the line currents.

60 Solution:

61 Phase Currents

62 Line Currents

∆-Connected Generator with a Y-Connected Load

64 EXAMPLE 4 A balanced Y-connected load with a phase impedance 40 + j25  is supplied by a balanced, positive-sequence Δ- connected source with a line voltage of 210 V. Calculate the phase currents. Use V AB as reference.

65 Solution: the load impedance, Z Y and the source voltage, V AB are

66 Solution: When the ∆-connected source is transformed to a Y-connected source,

67 Solution: The line currents are

68 Summary of Relationships in Y and ∆-connections Y-connection∆-connection Voltage magnitudes Current magnitudes Phase sequence V L leads V φ by 30° I L lags I φ by 30°