1. AC Machine CHAPTER 4 EKT 103

2. AC Machine  Alternating current (ac) is the primary source of electrical energy.  It is less expensive to produce and transmit alternating current (ac) than direct current (dc).  For this reason, and because ac voltage is induced into the armature of all generators, ac machines are generally more practical.  May function as a generator (mechanical to electrical) or a motor (electrical to mechanical)

3. AC Generator This process can be described in terms of Faraday's law when you see that the rotation of the coil continually changes the magnetic flux through the coil and therefore generates a voltageFaraday's lawmagnetic flux

4. AC Motor a current is passed through the coil, generating a torque on the coil. Since the current is alternating, the motor will run smoothly only at the frequency of the sine wave.

5. Generator and Motor

6. How Does an Electric Generator Work?

7. i) Synchronous Machines: Synchronous Generators: A primary source of electrical energy. Synchronous Motors: Used as motors as well as power factor compensators (synchronous condensers). ii) Asynchronous (Induction) Machines: Induction Motors: Most widely used electrical motors in both domestic and industrial applications. Induction Generators: Due to lack of a separate field excitation, these machines are rarely used as generators. Classification of AC Machines  Two major classes of machines;

8. Synchronous Machine

9.  Origin of name: syn = equal, chronos = time  Synchronous machines are called ‘synchronous’ because their mechanical shaft speed is directly related to the power system’s line frequency.  the rotating air gap field and the rotor rotate at the same speed, called the synchronous speed.  Synchronous machines are ac machine that have a field circuit supplied by an external dc source. –DC field winding on the rotor, –AC armature winding on the stator Synchronous Machine

10.  Synchronous machines are used primarily as generators of electrical power, called synchronous generators or alternators.  They are usually large machines generating electrical power at hydro, nuclear, or thermal power stations.  Synchronous motors are built in large units compare to induction motors (Induction motors are cheaper for smaller ratings) and used for constant speed industrial drives  Application as a motor: pumps in generating stations, electric clocks, timers, and so forth where constant speed is desired. Synchronous Machine

11. where P is the number of magnetic poles f e is the power line frequency. Typical machines have two-poles, four-poles, and six-poles The frequency of the induced voltage is related to the rotor speed by:

12. Construction Energy is stored in the inductance As the rotor moves, there is a change in the energy stored Either energy is extracted from the magnetic field (and becomes mechanical energy – motor) Or energy is stored in the magnetic field and eventually flows into the electrical circuit that powers the stator – generator Synchronous Machine

13. Construction DC field windings are mounted on the (rotating) rotor - which is thus a rotating electromagnet AC windings are mounted on the (stationary) stator resulting in three-phase AC stator voltages and currents  The main part in the synchronous machines are i) Rotor ii) Stator Synchronous Machine

14. Rotor  There are two types of rotors used in synchronous machines: i) cylindrical (or round) rotors ii) salient pole rotors  Machines with cylindrical rotors are typically found in higher speed higher power applications such as turbogenerators. Using 2 or 4 poles, these machines rotate at 3600 or 1800 rpm (with 60hz systems).  Salient pole machines are typically found in large (many MW), low mechanical speed applications, including hydrogenerators, or smaller higher speed machines (up to 1-2 MW).  Salient pole rotors are less expensive than round rotors.

15. L  10 m D 1 mD 1 m Turbine Steam Stator Uniform air-gap Stator winding Rotor Rotor winding N S  High speed  3600 r/min    -pole  1800 r/min    -pole  Direct-conductor cooling (using hydrogen or water as coolant)  Rating up to 2000 MVA Turbogenerator d-axis q-axis Synchronous Machine – Cylindrical rotor

16. Stator Cylindrical rotor Synchronous Machine – Cylindrical rotor

17. 1.Most hydraulic turbines have to turn at low speeds (between 50 and 300 r/min) 2.A large number of poles are required on the rotor Hydrogenerator Turbine Hydro (water) D   10 m Non-uniform air-gap N S S N d-axis q-axis Synchronous Machine – Salient Pole

18. Stator Salient-pole rotor Synchronous Machine – Salient Pole

19.  Synchronous machine rotors are simply rotating electromagnets built to have as many poles as are produced by the stator windings.  Dc currents flowing in the field coils surrounding each pole magnetize the rotor poles.  The magnetic field produced by the rotor poles locks in with a rotating stator field, so that the shaft and the stator field rotate in synchronism.  Salient poles are too weak mechanically and develop too much wind resistance and noise to be used in large, high-speed generators driven by steam or gas turbines. For these big machines, the rotor must be a solid, cylindrical steel forging to provide the necessary strength.

20.  Axial slots are cut in the surface of the cylinder to accommodate the field windings.  Since the rotor poles have constant polarity they must be supplied with direct current.  This current may be provided by an external dc generator or by a rectifier.  In this case the leads from the field winding are connected to insulated rings mounted concentrically on the shaft.  Stationary contacts called brushes ride on these slip rings to carry current to the rotating field windings from the dc supply.  The brushes are made of a carbon compound to provide a good contact with low mechanical friction.  An external dc generator used to provide current is called a “ brushless exciter “.

21. Synchronous Machine Stator  The stator of a synchronous machine carries the armature or load winding which is a three-phase winding.  The armature winding is formed by interconnecting various conductors in slots spread over the periphery of the machine’s stator. Often, more than one independent three phase winding is on the stator. An arrangement of a three-phase stator winding is shown in Figure below. Notice that the windings of the three-phases are displaced from each other in space.

22. Construction  Stator Synchronous Machine

23. Magnetomotive Forces (MMF’s) and Fluxes Due to Armature and Field Windings Synchronous Machine Flux produced by a stator winding

24. Magnetomotive Forces (MMF’s) and Fluxes Due to Armature and Field Windings Synchronous Machine

25. Magnetomotive Forces (MMF’s) and Fluxes Due to Armature and Field Windings Synchronous Machine Two Cycles of mmf around the Stator

26. Synchronous Generator Equivalent circuit model – synchronous generator

27.  If the generator operates at a terminal voltage V T while supplying a load corresponding to an armature current Ia, then;  In an actual synchronous machine, the reactance is much greater than the armature resistance, in which case;  Among the steady-state characteristics of a synchronous generator, its voltage regulation and power-angle characteristics are the most important ones. As for transformers, the voltage regulation of a synchronous generator is defined at a given load as;

28. Synchronous Generator Phasor diagram of a synchronous generator The phasor diagram is to shows the relationship among the voltages within a phase (E φ,V φ, jX S I A and R A I A ) and the current I A in the phase. Unity P.F (1.0)

29. Synchronous Generator Leading P.F. Lagging P.F

30. Synchronous Generator Power and Torque In generators, not all the mechanical power going into a synchronous generator becomes electric power out of the machine The power losses in generator are represented by difference between output power and input power shown in power flow diagram below

31. Synchronous Generator Losses Rotor - resistance; iron parts moving in a magnetic field causing currents to be generated in the rotor body - resistance of connections to the rotor (slip rings) Stator - resistance; magnetic losses (e.g., hysteresis) Mechanical - friction at bearings, friction at slip rings Stray load losses - due to non-uniform current distribution

32. Synchronous Generator The input mechanical power is the shaft power in the generator given by equation: The power converted from mechanical to electrical form internally is given by The real electric output power of the synchronous generator can be expressed in line and phase quantities as and reactive output power

33. Synchronous Generator In real synchronous machines of any size, the armature resistance R A is more than 10 times smaller than the synchronous reactance X S (X s >> R A ). Therefore, R A can be ignored

34. Synchronous Motor

35. Power Flow

36. Example : Synchronous Generator.  A three-phase, wye-connected 2500 kVA and 6.6 kV generator operates at full-load. The per-phase armature resistance R a and the synchronous reactance, X d, are (0.07+j10.4) . Calculate the percent voltage regulation at (a)0.8 power-factor lagging, and (b)0.8 power-factor leading.

37. Solution.

38.  The machines are called induction machines because of the rotor voltage which produces the rotor current and the rotor magnetic field is induced in the rotor windings.  Induction generator has many disadvantages and low efficiency. Therefore induction machines are usually referred to as induction motors. Induction Machine

39. Three-phase induction motors are the most common and frequently encountered machines in industry –simple design, rugged, low-price, easy maintenance –wide range of power ratings: fractional horsepower to 10 MW –run essentially as constant speed from no-load to full load –Its speed depends on the frequency of the power source not easy to have variable speed control requires a variable-frequency power-electronic drive for optimal speed control Induction Machine

40. Construction Cutaway in a typical wound- rotor IM. Notice the brushes and the slip rings Brushes Slip rings

41. Construction An induction motor has two main parts i) a stationary stator consisting of a steel frame that supports a hollow, cylindrical core core, constructed from stacked laminations, –having a number of evenly spaced slots, providing the space for the stator winding Stator of IM

42. Construction ii) a revolving rotor composed of punched laminations, stacked to create a series of rotor slots, providing space for the rotor winding conventional 3-phase windings made of insulated wire (wound-rotor) » similar to the winding on the stator aluminum bus bars shorted together at the ends by two aluminum rings, forming a squirrel-cage shaped circuit (squirrel-cage)

43. Construction Two basic design types depending on the rotor design –squirrel-cage: conducting bars laid into slots and shorted at both ends by shorting rings. –wound-rotor: complete set of three-phase windings exactly as the stator. Usually Y-connected, the ends of the three rotor wires are connected to 3 slip rings on the rotor shaft. In this way, the rotor circuit is accessible.

44. 1. Squirrel cage – the conductors would look like one of the exercise wheels that squirrel or hamsters run on. Construction

45. 2. Wound rotor – have a brushes and slip ring at the end of rotor Notice the slip rings Construction

46. Rotating Magnetic Field Balanced three phase windings, i.e. mechanically displaced 120 degrees form each other, fed by balanced three phase source A rotating magnetic field with constant magnitude is produced, rotating with a speed Where f e is the supply frequency and P is the no. of poles and n sync is called the synchronous speed in rpm (revolutions per minute)

47. Synchronous speed P50 Hz60 Hz 230003600 415001800 610001200 8750900 10600720 12500600

48. Principle of operation This rotating magnetic field cuts the rotor windings and produces an induced voltage in the rotor windings Due to the fact that the rotor windings are short circuited, for both squirrel cage and wound-rotor, and induced current flows in the rotor windings The rotor current produces another magnetic field A torque is produced as a result of the interaction of those two magnetic fields Where  ind is the induced torque and B R and B S are the magnetic flux densities of the rotor and the stator respectively

49. Induction motor speed At what speed will the IM run? –Can the IM run at the synchronous speed, why? –If rotor runs at the synchronous speed, which is the same speed of the rotating magnetic field, then the rotor will appear stationary to the rotating magnetic field and the rotating magnetic field will not cut the rotor. So, no induced current will flow in the rotor and no rotor magnetic flux will be produced so no torque is generated and the rotor speed will fall below the synchronous speed –When the speed falls, the rotating magnetic field will cut the rotor windings and a torque is produced

50. Induction motor speed So, the IM will always run at a speed lower than the synchronous speed The difference between the motor speed and the synchronous speed is called the Slip (s) Where n slip = slip speed n sync = speed of the magnetic field n m = mechanical shaft speed of the motor

51. The Slip Where s is the slip Notice that : if the rotor runs at synchronous speed s = 0 if the rotor is stationary s = 1 Slip may be expressed as a percentage by multiplying the above eq. by 100, notice that the slip is a ratio and doesn’t have units

52. Induction Motors and Transformers Both IM and transformer works on the principle of induced voltage –Transformer: voltage applied to the primary windings produce an induced voltage in the secondary windings –Induction motor: voltage applied to the stator windings produce an induced voltage in the rotor windings –The difference is that, in the case of the induction motor, the secondary windings can move –Due to the rotation of the rotor (the secondary winding of the IM), the induced voltage in it does not have the same frequency of the stator (the primary) voltage

53. Frequency The frequency of the voltage induced in the rotor is given by Where f r = the rotor frequency (Hz) P = number of stator poles n = slip speed (rpm)

54. Frequency What would be the frequency of the rotor’s induced voltage at any speed n m ? When the rotor is blocked (s=1), the frequency of the induced voltage is equal to the supply frequency On the other hand, if the rotor runs at synchronous speed (s = 0), the frequency will be zero

55. Torque While the input to the induction motor is electrical power, its output is mechanical power and for that we should know some terms and quantities related to mechanical power Any mechanical load applied to the motor shaft will introduce a Torque on the motor shaft. This torque is related to the motor output power and the rotor speed and

56. Horse power Another unit used to measure mechanical power is the horse power It is used to refer to the mechanical output power of the motor Since we, as an electrical engineers, deal with watts as a unit to measure electrical power, there is a relation between horse power and watts

57. Example A 208-V, 10hp, four pole, 60 Hz, Y-connected induction motor has a full-load slip of 5 percent 1.What is the synchronous speed of this motor? 2.What is the rotor speed of this motor at rated load? 3.What is the rotor frequency of this motor at rated load? 4.What is the shaft torque of this motor at rated load?

58. Solution 1. 2. 3. 4.

59. Equivalent Circuit The induction motor is similar to the transformer with the exception that its secondary windings are free to rotate As we noticed in the transformer, it is easier if we can combine these two circuits in one circuit but there are some difficulties

60. Equivalent Circuit When the rotor is locked (or blocked), i.e. s =1, the largest voltage and rotor frequency are induced in the rotor. On the other side, if the rotor rotates at synchronous speed, i.e. s = 0, the induced voltage and frequency in the rotor will be equal to zero. Where E R0 is the largest value of the rotor’s induced voltage obtained at s = 1(locked rotor)

61. Equivalent Circuit The same is true for the frequency, i.e. It is known that So, as the frequency of the induced voltage in the rotor changes, the reactance of the rotor circuit also changes Where X r0 is the rotor reactance at the supply frequency (at blocked rotor)

62. Equivalent Circuit Then, we can draw the rotor equivalent circuit as follows Where E R is the induced voltage in the rotor and R R is the rotor resistance

63. Equivalent Circuit Now we can calculate the rotor current as Dividing both the numerator and denominator by s so nothing changes we get Where E R0 is the induced voltage and X R0 is the rotor reactance at blocked rotor condition (s = 1)

64. Equivalent Circuit Now we can have the rotor equivalent circuit

65. Equivalent Circuit Now as we managed to solve the induced voltage and different frequency problems, we can combine the stator and rotor circuits in one equivalent circuit Where

66. Power losses in Induction machines Copper losses –Copper loss in the stator (P SCL ) = I 1 2 R 1 –Copper loss in the rotor (P RCL ) = I 2 2 R 2 Core loss (P core ) Mechanical power loss due to friction and windage How this power flow in the motor?

67. Power flow in induction motor

68. Power relations

69. Equivalent Circuit We can rearrange the equivalent circuit as follows Actual rotor resistance Resistance equivalent to mechanical load

70. Power relations

71. 1 s 1-s

72. Example A 480-V, 60 Hz, 50-hp, three phase induction motor is drawing 60A at 0.85 PF lagging. The stator copper losses are 2 kW, and the rotor copper losses are 700 W. The friction and windage losses are 600 W, the core losses are 1800 W, and the stray losses are negligible. Find the following quantities: 1.The air-gap power P AG. 2.The power converted P conv. 3.The output power P out. 4.The efficiency of the motor.

73. Solution 1. 2. 3.

74. Solution 4.

75. Example A 460-V, 25-hp, 60 Hz, four-pole, Y-connected induction motor has the following impedances in ohms per phase referred to the stator circuit: R 1 = 0.641  R 2 = 0.332  X 1 = 1.106  X 2 = 0.464  X M = 26.3  The total rotational losses are 1100 W and are assumed to be constant. The core loss is lumped in with the rotational losses. For a rotor slip of 2.2 percent at the rated voltage and rated frequency, find the motor’s 1.Speed 2.Stator current 3.Power factor 4. P conv and P out 5.  ind and  load 6.Efficiency

76. Solution 1. 2.

77. Solution 3. 4.

78. Solution 5. 6.

79. Induction Motor – Power and Torque The output power can be found as P out = P conv – P F&W – P misc The induced torque or developed torque:

80. Example A two-pole, 50-Hz induction motor supplies 15kW to a load at a speed of 2950 rpm. 1.What is the motor’s slip? 2.What is the induced torque in the motor in N.m under these conditions? 3.What will be the operating speed of the motor if its torque is doubled? 4.How much power will be supplied by the motor when the torque is doubled?

81. Solution 1. 

82. Solution 3.In the low-slip region, the torque-speed curve is linear and the induced torque is direct proportional to slip. So, if the torque is doubled the new slip will be 3.33% and the motor speed will be 4.