Presentation on Synchronous Machine.pptx

This Presentation is about synchronous machine.

1. 1 Synchronous Machines ELEN 3441 Fundamentals of Power Engineering Spring 2008

2. 2 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Construction of Synchronous Machines Synchronous machines are AC machines that have a field circuit supplied by an external DC source. In a synchronous generator , a DC current is applied to the rotor winding producing a rotor magnetic field. The rotor is then turned by external means producing a rotating magnetic field, which induces a 3-phase voltage within the stator winding. In a synchronous motor , a 3-phase set of stator currents produces a rotating magnetic field causing the rotor magnetic field to align with it. The rotor magnetic field is produced by a DC current applied to the rotor winding. Field windings are the windings producing the main magnetic field ( rotor windings for synchronous machines); armature windings are the windings where the main voltage is induced ( stator windings for synchronous machines).

3. 3 Construction of Synchronous Machines The rotor of a synchronous machine is a large electromagnet. The magnetic poles can be either salient (sticking out of rotor surface) or non- salient construction. Non-salient- pole rotor: usually two- and four- pole rotors. ELEN 3441 Fundamentals of Power Engineering Spring 2008 Salient- pole rotor: four and more poles. Rotors are made laminated to reduce eddy current losses.

4. 4 Construction of Synchronous Machines Salient pole with field windings Salient pole without field windings – observe laminations A synchronous rotor with 8 salient poles ELEN 3441 Fundamentals of Power Engineering Spring 2008

5. 5 Construction of Synchronous Machines Two common approaches are used to supply a DC current to the field circuits on the rotating rotor: Supply the DC power from an external DC source to the rotor by means of slip rings and brushes; Supply the DC power from a special DC power source mounted directly on the shaft of the machine. Slip rings are metal rings completely encircling the shaft of a machine but insulated from it. One end of a DC rotor winding is connected to each of the two slip rings on the machine’s shaft. Graphite- like carbon brushes connected to DC terminals ride on each slip ring supplying DC voltage to field windings regardless the position or speed of the rotor. ELEN 3441 Fundamentals of Power Engineering Spring 2008

6. 6 Construction of Synchronous Machines Slip rings Brush ELEN 3441 Fundamentals of Power Engineering Spring 2008

7. 7 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Construction of Synchronous Machines Slip rings and brushes have certain disadvantages: increased friction and wear (therefore, needed maintenance), brush voltage drop can introduce significant power losses. Still this approach is used in most small synchronous machines. On large generators and motors, brushless exciters are used. A brushless exciter is a small AC generator whose field circuits are mounted on the stator and armature circuits are mounted on the rotor shaft. The exciter generator’s 3- phase output is rectified to DC by a 3- phase rectifier (mounted on the shaft) and fed into the main DC field circuit. It is possible to adjust the field current on the main machine by controlling the small DC field current of the exciter generator (located on the stator). Since no mechanical contact occurs between the rotor and the stator, exciters of this type require much less maintenance.

8. 8 Construction of Synchronous Machines A brushless exciter: a low 3-phase current is rectified and used to supply the field circuit of the exciter (located on the stator). The output of the exciter’s armature circuit (on the ELEN 3441 Fundamentals of Power Engineering Spring 2008 rotor) is rectified and used current as the field of the main machine.

9. 9 Construction of Synchronous Machines To make ELEN 3441 Fundamentals of Power Engineering Spring 2008 of the a excitation generator completely independent external of any power source, a small pilot exciter is often added to the circuit. The pilot exciter is an AC with a generator permanent magnet mounted on the rotor shaft and a 3- phase winding on the stator producing the power for the field circuit of the exciter.

10. 10 Construction of Synchronous Machines A rotor ELEN 3441 Fundamentals of Power Engineering Spring 2008 of large synchronous machine with a brushless exciter mounted on the same shaft. Many generators synchronous having brushless exciters also include slip rings and provide brushes to emergency source of the field DC current.

11. 11 Construction of Synchronous Machines A large synchronous machine with the exciter and salient poles. ELEN 3441 Fundamentals of Power Engineering Spring 2008

12. 12 Rotation speed of Synchronous Generator 120 e By the definition, synchronous generators produce electricity whose frequency is synchronized with the mechanical rotational speed. f  n m P (7.11.1) ELEN 3441 Fundamentals of Power Engineering Spring 2008 Where f e is the electrical frequency, Hz; n m is mechanical speed of magnetic field (rotor speed for synchronous machine), rpm; P is the number of poles. Steam turbines are most efficient when rotating at high speed; therefore, to generate 60 Hz, they are usually rotating at 3600 rpm and turn 2- pole generators. Water turbines are most efficient when rotating at low speeds (200- 300 rpm); therefore, they usually turn generators with many poles.

13. 13 Internal generated voltage of a Synchronous Generator The magnitude of internal generated voltage induced in a given stator is E A  2  N C  f  K  where K is a constant representing the construction of the machine,  is flux in it and  is its rotation speed. Since flux in the machine depends on the field current it, the generated through internal voltage function is a of the rotor field current. Magnetization curve (open- circuit characteristic) of a synchronous machine ELEN 3441 Fundamentals of Power Engineering Spring 2008

14. 14 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Equivalent circuit of a Synchronous Generator The internally generated voltage in a single phase of a synchronous machine E A is not usually the voltage appearing at its terminals. It equals to the output voltage V  only when there is no armature current in the machine. The reasons that the armature voltage E A is not equal to the output voltage V  are: Distortion of the air- gap magnetic field caused by the current flowing in the stator ( armature reaction ); Self- inductance of the armature coils; Resistance of the armature coils; Effect of salient- pole rotor shapes.

15. 17 Equivalent circuit of a Synchronous Generator Assuming that the load reactance is X , the armature reaction voltage is E stat   jXI A (7.17.1) The phase voltage is then V   E A  jXI A (7.17.2) Armature reactance can be modeled by the following circuit… However, in addition to armature reactance effect, the stator coil has a self- inductance L A ( X A is the corresponding reactance) and the stator has resistance R A . The phase voltage is thus ELEN 3441 Fundamentals of Power Engineering Spring 2008 V   E A  jXI A  jX A I A  RI A (7.17.3)

16. 18 Equivalent circuit of a Synchronous Generator Often, armature reactance and self- inductance are combined into the synchronous reactance of the machine: (7.18.1) V   E A  jX S I A  RI A ELEN 3441 Fundamentals of Power Engineering Spring 2008 X S  X  X A Therefore, the phase voltage is (7.18.2) The equivalent circuit of a 3-phase synchronous generator is shown. The adjustable resistor R adj controls the field current and, therefore, the rotor magnetic field.

17. 19 Equivalent circuit of a Synchronous Generator A synchronous generator can be Y- or  -connected: The terminal voltage will be V T  3 V   for Y ELEN 3441 Fundamentals of Power Engineering Spring 2008 V T  V   for  (7.19.1) (7.19.2)

18. 20 Equivalent circuit of a synchronous generator Note: the discussion above assumed a balanced load on the generator! Since – for balanced loads – the three phases of a synchronous generator are identical except for phase angles, per- phase equivalent circuits are often used. ELEN 3441 Fundamentals of Power Engineering Spring 2008

19. 21 Phasor diagram of a Synchronous Generator Since the voltages in a synchronous generator are AC voltages, they are usually one phase is expressed as phasors. A vector plot of voltages and currents within called a phasor diagram . A phasor diagram of a synchronous generator with a unity power factor (resistive load) Lagging power factor (inductive load): a larger than for leading PF internal generated voltage E A is needed to form the same phase voltage. Leading power factor (capacitive load). For a given field current and magnitude of load current, the terminal voltage is lower for lagging loads and higher for leading loads. ELEN 3441 Fundamentals of Power Engineering Spring 2008

20. 22 torque in Synchronous Power & Generators A synchronous generator needs to be connected to a prime mover whose speed is reasonably constant (to ensure constant frequency of the generated voltage) for various loads. The applied mechanical power P in   app  m (7.22.1) (7.22.2) is partially converted to electricity P conv   ind  m  3 E A I A cos  Where  is the angle between E A and I A . The power- flow diagram of a synchronous generator. ELEN 3441 Fundamentals of Power Engineering Spring 2008

21. 23 torque in Synchronous Power & Generators The real output power of the synchronous generator is P ou t  3 V T I L cos   3 V  I A cos  The reactive output power of the synchronous generator is Q out  3 V T I L sin   3 V  I A sin  (7.23.1) (7.23.2) Recall that the power factor angle  is the angle between V  and I A and not the angle between V T and I L . In real synchronous machines of any size, the armature resistance R A << X S and, therefore, the armature resistance can be ignored. Thus, a simplified phasor diagram indicates that S X ELEN 3441 Fundamentals of Power Engineering Spring 2008 E A sin  I A cos   (7.23.3)

22. 24 torque in Synchronous Power & Generators Then the real output power of the synchronous generator can be approximated as out S P X  3 V  E A sin  (7.24.1) We observe that electrical losses are assumed to be zero since the resistance is neglected. Therefore: (7.24.2) P conv  P out Here  is the torque angle of the machine – the angle between V  and E A . The maximum power can be supplied by the generator when  = 90 : S ELEN 3441 Fundamentals of Power Engineering Spring 2008 X 3 V  E A P max  (7.24.3)

23. 25 torque in synchronous Power & generators The maximum power specified by (7.24.3) is called the static stability limit of the generator. Normally, real generators do not approach this limit: full- load torque angles are usually between 15 and 20 . The induced torque is  ind  kB R  B S  kB R  B net  kB R B net sin  (7.25.1) Notice that the torque angle  is also the angle between the rotor magnetic field B R and the net magnetic field B net . Alternatively, the induced torque is ind m S   X  3 V  E A sin  (7.25.2) ELEN 3441 Fundamentals of Power Engineering Spring 2008

24. 26 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Measuring parameters of Synchronous Generator Model The three quantities must be determined in order to describe the generator model: The relationship between field current and flux (and therefore between the field current I F and the internal generated voltage E A ); The synchronous reactance; The armature resistance. We conduct first the open- circuit test on the synchronous generator: the generator is rotated at the rated speed, all the terminals are disconnected from loads, the field current is set to zero first. Next, the field current is increased in steps and the phase voltage (whish is equal to the internal generated voltage E A since the armature current is zero) is measured. Therefore, it is possible to plot the dependence of the internal generated voltage on the field current – the open- circuit characteristic (OCC) of the generator.

25. 27 Measuring parameters of Synchronous Generator model Since the unsaturated core of the machine has a reluctance thousands times lower than the reluctance of the air- gap, the resulting flux increases linearly first. When the saturation is reached, the core reluctance greatly increases causing the flux to increase much slower with the increase of the mmf. ELEN 3441 Fundamentals of Power Engineering Spring 2008 We conduct next the short- circuit test on the synchronous generator: the generator is rotated at the rated speed, all the terminals are short- circuited through ammeters, the field current is set to zero first. Next, the field current is increased in steps and the armature current I A is measured as the field current is increased. The plot of armature current (or line current) vs. the field current is the short-circuit characteristic (SCC) of the generator.

26. 28 Measuring parameters of Synchronous Generator model The SCC is a straight line since, for the short- circuited terminals, the magnitude of the armature current is A S E A R 2 I A   X 2 (7.28.1) The equivalent generator’s circuit during SC The resulting phasor diagram ELEN 3441 Fundamentals of Power Engineering Spring 2008 The magnetic fields during short- circuit test Since B S almost cancels B R , the net field B net is very small .

27. 29 Measuring parameters of Synchronous Generator model An approximate method to determine the synchronous reactance X S at a given field current: Get the internal generated voltage E A from the OCC at that field current. Get the short- circuit current I A,SC at that field current from the SCC. Find X S from E A X S  I A , SC Since the internal machine impedance is 2 2 ELEN 3441 Fundamentals of Power Engineering Spring 2008 S E A I A , SC Z S  R A  X   X S  since X S ? R A  (7.29.1) (7.29.2)

28. 30 Measuring parameters of Synchronous Generator model A drawback of this method is that the internal generated voltage E A is measured during the OCC, where the machine can be saturated for large field currents, while the armature current is measured in SCC, where the core is unsaturated. Therefore, this approach is accurate for unsaturated cores only. The approximate value of synchronous reactance varies with the degree of saturation of the OCC. Therefore, the value of the synchronous reactance for a given problem should be estimated at the approximate load of the machine. The winding’s resistance can be approximated by applying a DC voltage to a stationary machine’s winding and measuring the current. However, AC resistance is slightly larger than DC resistance (skin effect). ELEN 3441 Fundamentals of Power Engineering Spring 2008

29. 31 Measuring parameters of Synchronous Generator model: Ex Example 7.1 : A 200 kVA, 480 V, 50 Hz, Y- connected synchronous generator with a rated field current of 5 A was tested and the following data were obtained: V T,OC = 540 V at the rated I F . I L,SC = 300 A at the rated I F . When a DC voltage of 10 V was applied to two of the terminals, a current of 25 A was measured. Find the generator’s model at the rated conditions (i.e., the armature resistance and the approximate synchronous reactance). Since the generator is Y- connected, a DC voltage was applied between its two phases. Therefore: 10 ELEN 3441 Fundamentals of Power Engineering Spring 2008 A DC A DC 2 R I R 2 I  V DC  V DC   0.2  2  25

30. 32 Measuring parameters of Synchronous Generator model: Ex The internal generated voltage at the rated field current is 3 3 A  , OC E  V  V T  540  311.8 V The synchronous reactance at the rated field current is precisely 2 2 2 2 311.8 2 300 2 A A A A , SC E 2 I 2 X S  Z S  R   R   0.2  1.02  We observe that if X S was estimated via the approximate formula, the result would be: S ELEN 3441 Fundamentals of Power Engineering Spring 2008 A , SC E A I 300 X   311.8  1.04  Which is close to the previous result. The error ignoring R A is much smaller than the error due to core saturation. The equivalent circuit

31. 33 ELEN 3441 Fundamentals of Power Engineering Spring 2008 The Synchronous Generator operating alone The behavior of a synchronous generator varies greatly under load depending on the power factor of the load and on whether the generator is working alone or in parallel with other synchronous generators. Although most of the synchronous generators in the world operate as parts of large power systems, we start our discussion assuming that the synchronous generator works alone. Unless otherwise stated, the speed of the generator is assumed constant.

32. 34 The Synchronous Generator operating alone Effects of load changes A increase in the load is an increase in the real and/or ELEN 3441 Fundamentals of Power Engineering Spring 2008 reactive power drawn from the generator. Since the field resistor is unaffected, the field current is constant and, therefore, the flux  is constant too. Since the speed is assumed as constant, the magnitude of the internal generated voltage is constant also. Assuming the same power factor of the load, change in load will change the magnitude of the armature current I A . However, the angle will be the same (for a constant PF). Thus, the armature reaction voltage jX S I A will be larger for the increased load. Since the magnitude of the internal generated voltage is constant (7.34.1) E A  V   jX S I A Armature reaction voltage vector will “move parallel” to its initial position.

33. 35 The Synchronous Generator operating alone Increase load effect on generators with ELEN 3441 Fundamentals of Power Engineering Spring 2008 Lagging PF Leading PF Unity PF

34. 36 The Synchronous Generator operating alone Generally, when a load on a synchronous generator is added, the following changes can be observed: For lagging (inductive) loads, the phase (and terminal) voltage decreases significantly. For unity power factor (purely resistive) loads, the phase (and terminal) voltage decreases slightly. For leading (capacitive) loads, the phase (and terminal) voltage rises. Effects of adding loads can be described by the voltage regulation: VR  V nl  V fl 100% V fl ELEN 3441 Fundamentals of Power Engineering Spring 2008 (7.36.1) Where V nl is the no- load voltage of the generator and V fl is its full- load voltage.

35. 37 ELEN 3441 Fundamentals of Power Engineering Spring 2008 The Synchronous Generator operating alone A synchronous generator operating at a lagging power factor has a fairly large positive voltage regulation. A synchronous generator operating at a unity power factor has a small positive voltage regulation. A synchronous generator operating at a leading power factor often has a negative voltage regulation. Normally, a constant terminal voltage supplied by a generator is desired. Since the armature reactance cannot be controlled, an obvious approach to adjust the terminal voltage is by controlling the internal generated voltage E A = K  . This may be done by changing flux in the machine while varying the value of the field resistance R F , which is summarized: Decreasing the field resistance increases the field current in the generator. An increase in the field current increases the flux in the machine. An increased flux leads to the increase in the internal generated voltage. An increase in the internal generated voltage increases the terminal voltage of the generator. Therefore, the terminal voltage of the generator can be changed by adjusting the field resistance.

36. 49 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Parallel operation of Synchronous Generators Most of synchronous generators are operating in parallel with other synchronous generators to supply power to the same power system. Obvious advantages of this arrangement are: Several generators can supply a bigger load; A failure of a single generator does not result in a total power loss to the load increasing reliability of the power system; Individual generators may be removed from the power system for maintenance without shutting down the load; A single generator not operating at near full load might be quite inefficient. While having several generators in parallel, it is possible to turn off some of them when operating the rest at near full- load condition.

37. 50 Conditions required for paralleling A diagram shows that Generator 2 ( oncoming generator ) will be connected in parallel when the switch S 1 is closed. However, closing the switch at an arbitrary moment can severely damage both generators! If voltages are not exactly the same in both lines (i.e. in a and a’ , b and b’ etc.), a very large current will flow when the switch is closed. Therefore, to avoid this, voltages coming from both generators must be exactly the same. Therefore, the following conditions must be met: The rms line voltages of the two generators must be equal. The two generators must have the same phase sequence . The phase angles of both generators must be equal. The frequency of the oncoming generator must be slightly higher than the frequency of the running system. ELEN 3441 Fundamentals of Power Engineering Spring 2008

38. 52 General procedure for paralleling generators When connecting the generator G 2 to the running system, the following steps should be taken: Adjust the field current of the oncoming generator to make its terminal voltage equal to the line voltage of the system (use a voltmeter). Compare the phase sequences of the oncoming generator and the running system. This can be done by different ways: Connect a small induction motor to the terminals of the oncoming generator and then to the terminals of the running system. If the motor rotates in the same direction, the phase sequence is the same; Connect three light bulbs across the open terminals of the switch. As the phase changes between the two generators, light bulbs get brighter (large phase difference) or dimmer (small phase difference). If all three bulbs get bright and dark together, both generators have the same phase sequences. ELEN 3441 Fundamentals of Power Engineering Spring 2008

39. 59 Generators in parallel with other generators of the same size When a generator is working alone, its real and reactive power are fixed and determined by the load. When a generator is connected to an infinite bus, its frequency and the terminal voltage are constant and determined by a bus. When two generators of the same size are connected to the same load, the sum of the real and reactive powers supplied by the two generators must equal the real and reactive powers demanded by the load: ELEN 3441 Fundamentals of Power Engineering Spring 2008 P t o t  P l oa d Q tot  Q load  P G 1  P G 2  Q G 1  Q G 2 (7.59.1) (7.59.2)

40. 68 Synchronous motors The field current produces ELEN 3441 Fundamentals of Power Engineering Spring 2008 a steady-state I F of the motor rotor magnetic field B R . A 3- phase set of voltages applied to the stator produces a 3- phase current flow in the windings. A 3- phase set of currents in an armature winding produces a uniform rotating magnetic field B s . Two magnetic fields are present in the machine, and the rotor field tends to align with the stator magnetic field. Since the stator magnetic field is rotating, the rotor magnetic field will try to catch up pulling the rotor. The larger the angle between two magnetic fields (up to a certain maximum), the greater the torque on the rotor of the machine.

41. 69 Synchronous motor equivalent circuit A synchronous motor has the same equivalent circuit as synchronous generator, except that the direction of power flow (and the direction of I A ) is reversed. Per- phase circuit is shown: A change in direction of I A changes the Kirchhoff’s voltage law equation: ELEN 3441 Fundamentals of Power Engineering Spring 2008 E A  V   jX S I A  R A I A V   E A  jX S I A  R A I A Therefore, the internal generated voltage is We observe that this is exactly the same equation as the equation for the generator, except that the sign on the current terms is reversed. (7.69.1) (7.69.2)

42. 70 Synchronous motor vs. synchronous generator Let us diagram ELEN 3441 Fundamentals of Power Engineering Spring 2008 suppose that a phasor of synchronous generator is shown. B R produces B net E A , produces V  , and B S E stat = -jX S I A . The produces rotation on both counterclockwise induced torque is diagrams is and the  ind  kB R  B net (7.70.1) clockwise, opposing the direction of rotation. In other words, the induced torque in generators is a counter- torque that opposes the rotation caused by external torque. If the prime mover loses power, the rotor will slow down and the rotor field B R will fall behind the magnetic field in the machine B net . Therefore, the operation of the machine changes…

43. 72 Steady- state operation of motor: Torque- speed curve Usually, synchronous motors are connected to large power systems (infinite bus); therefore, their terminal voltage and system frequency are constant regardless the motor load. Since the motor speed is locked to the electrical frequency, the speed should be constant regardless the load. The steady- state speed of the motor is constant from no- load to the maximum torque that motor can supply ( pullout torque ). Therefore, the speed regulation of synchronous motor is 0%. The induced torque is  ind  kB R B net sin  or ind m S  X   3 V  E A sin  (7.72.1) ELEN 3441 Fundamentals of Power Engineering Spring 2008 (7.72.2)

44. 73 Steady- state operation of motor: Torque- speed curve The maximum pullout torque occurs when  = 90 : Normal full- load torques are much less than that (usually, about 3 times smaller). When the torque on the shaft of a synchronous motor exceeds the pullout torque, the rotor can no longer remain locked to the stator and net magnetic fields. It starts to slip behind them. As the motor slows down, the stator magnetic field “laps” it repeatedly, and the direction of the induced torque in the rotor reverses with each pass. As a result, huge torque surges of alternating direction cause the motor vibrate severely. The loss of synchronization after the pullout torque is exceeded is known as slipping poles . max ELEN 3441 Fundamentals of Power Engineering Spring 2008 m S 3 V  E A  X   kB R B net  (7.73.1)

45. 74 Steady- state operation of motor: Effect of torque changes Assuming that a synchronous motor operates initially with a leading PF. If the load on the motor increases, the rotor initially slows down increasing the torque angle  . As a result, the induced torque increases speeding up the rotor up to the synchronous speed with a larger torque angle  . Since the terminal voltage and frequency supplied to the motor are constant, the magnitude of internal generated voltage must be constant at the load changes ( E A = K  and field current is constant). ELEN 3441 Fundamentals of Power Engineering Spring 2008

46. 75 Steady- state operation of motor: Effect of torque changes Assuming that the armature resistance is negligible, the power converted from electrical to mechanical form in the motor will be the same as its input power: S X 3 V  E A sin  P  3 V  I A cos   (7.73.1) Since the phase voltage is constant, the quantities I A cos  and E A sin  are directly proportional to the power supplied by (and to) the motor. When the power supplied by the motor increases, the distance proportional to power increases. Since the internal generated voltage is constant, its phasor “swings down” as load increases. The quantity jX S I A has to increase; therefore, the armature current I A increases too. Also, the PF angle changes too moving from leading to lagging. ELEN 3441 Fundamentals of Power Engineering Spring 2008

47. 76 Steady- state operation of motor: Effect of field current changes Assuming that a synchronous motor operates initially with a lagging PF. If, for the constant load, the field current on the motor increases, the magnitude of the internal generated voltage E A increases. Since changes in I A do not affect the shaft speed and the motor load is constant, the real power supplied by the motor is unchanged. Therefore, the distances proportional to power on the phasor diagram ( E A sin  and I A cos  ) must be constant. Notice that as E A increases, the magnitude of the armature current I A first decreases and then increases again. At low E A , the armature current is lagging and the motor is an inductive load that consumes reactive power Q . As the field current increases , I A eventually lines up with V  , and the motor is purely resistive. As the field current further increases, I A becomes leading and the motor is a capacitive load that supplies reactive power Q to the system (consumes –Q ) . ELEN 3441 Fundamentals of Power Engineering Spring 2008

48. 77 Steady- state operation of motor: Effect of field current changes A plot of armature current vs. field current is called a synchronous motor V curve . V curves for different levels of real power have their minimum at unity PF, when only real power is supplied to the motor. For field currents less than the one giving the minimum I A , the armature current is lagging and the motor consumes reactive power. For field currents greater than the one giving the minimum I A , the armature current is leading and the motor supplies reactive power to the system. Therefore, by controlling the field current of a synchronous motor, the reactive power consumed or supplied to the power system can be controlled. ELEN 3441 Fundamentals of Power Engineering Spring 2008

49. 78 Steady- state operation of motor: Effect of field current changes When the projection of the phasor E A onto V  ( E A cos  ) is shorter than V  , a synchronous motor has a lagging current and consumes Q . Since the field current is small in this situation, the motor is sais to be under-excited . ELEN 3441 Fundamentals of Power Engineering Spring 2008 When the projection of the phasor E A onto V  ( E A cos  ) is longer than V  , a synchronous motor has a leading current and supplies Q to the system. Since the field current is large in this situation, the motor is sais to be over- excited .

50. 79 Steady- state operation of motor: power factor correction Assuming that a load contains a synchronous motor (whose PF can be adjusted) in addition to motors of other types. What does the ability to set the PF of one of the loads do for the power system? ELEN 3441 Fundamentals of Power Engineering Spring 2008 Let us consider a large power system operating at 480 V. Load 1 is an induction motor consuming 100 kW at 0.78 PF lagging, and load 2 is an induction motor consuming 200 kW at 0.8 PF lagging. Load 3 is a synchronous motor whose real power consumption is 150 kW. If the synchronous motor is adjusted to 0.85 PF lagging, what is the line current? If the synchronous motor is adjusted to 0.85 PF leading, what is the line current? Assuming that the line losses are P LL = 3I L 2 R L , how du these losses compare in the two cases?

51. 80 Steady- state operation of motor: power factor correction a. The real power of load 1 is 100 kW, and the reactive power of load 1 is   1 1  1 Q  P tan   100 tan cos 0.78  80.2 kVAR The real power of load 2 is 200 kW, and the reactive power of load 2 is   2 2  1 Q  P tan   200 tan cos 0.8  150 kVAR The real power of load 3 is 150 kW, and the reactive power of load 3 is    1 Q  P tan   150 tan cos 0.85  93 kVAR 3 3 The total real load is P tot  P 1  P 2  P 3  100  200  150  450 kW The total reactive load is Q tot  Q 1  Q 2  Q 3  80.2  150  93   kVAR The equivalent system PF is   Q  323.2  PF  cos   cos  tan  1   cos  tan  1   0.812 lagging   450  The line current is P  450 000 ELEN 3441 Fundamentals of Power Engineering Spring 2008 L L I P 3 V cos   667 A 3  480  0.812  tot 

52. 81 Steady- state operation of motor: power factor correction b. The real and reactive powers of loads 1 and 2 are the same. The reactive power of load 3 is   3 3 93 kVAR  1 Q  P tan   150 tan  cos 0.85   The total real load is P tot  P 1  P 2  P 3  100  200  150  450 kW The total reactive load is Q tot  Q 1  Q 2  Q 3  80.2  150  93  kVAR The equivalent system PF is 137.2 Q  1  1     PF  cos   cos tan  cos tan  0.957 lagging  P   450      The line current is 450 000 ELEN 3441 Fundamentals of Power Engineering Spring 2008 L L I P 3 V cos   566 A 3  480  0.957  tot 

53. 82 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Steady- state operation of motor: power factor correction c. The transmission line losses in the first case are P  3 I 2 R  1344 700 R LL L L L The transmission line losses in the second case are P  3 I 2 R  961  70 R LL L L L We notice that the transmission power losses are 28% less in the second case, while the real power supplied to the loads is the same.

54. 83 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Steady- state operation of motor: power factor correction The ability to adjust the power factor of one or more loads in a power system can significantly affect the efficiency of the power system: the lower the PF, the greater the losses in the power lines. Since most loads in a typical power system are induction motors, having one or more over- excided synchronous motors (leading loads) in the system is useful for the following reasons: A leading load supplies some reactive power to lagging loads in the system. Since this reactive power does not travel along the transmission line, transmission line current is reduced reducing power losses. Since the transmission line carries less current, the line can be smaller for a given power flow reducing system cost. The over- excited mode of synchronous motor increases the motor’s maximum torque. Usage of synchronous motors or other equipment increasing the overall system’s PF is called power- factor correction . Since a synchronous motor can provide PF correction, many loads that can accept constant speed are driven by over-excited synchronous motors.

55. 84 Starting synchronous motors Consider a 60 Hz synchronous motor. When the power is applied to the stator windings, the rotor (and, therefore its magnetic field B R ) is stationary. The stator magnetic field B S starts sweeping around the motor at synchronous speed. Note that the induced torque on the shaft ELEN 3441 Fundamentals of Power Engineering Spring 2008  ind  kB R  B S (7.84.1) is zero at t = since both magnetic fields are aligned. At t = 1/240 s the rotor has barely moved but the stator magnetic field B S has rotated by 90 . Therefore, the torque on the shaft is non- zero and counter-clockwise .

56. 85 Starting synchronous motors At t = 1/120 s the rotor and stator magnetic fields point in opposite directions, and the induced torque on the shaft is zero again. At t = 3/240 s the stator magnetic fields point to the right, and the induced torque on the shaft is non- zero but clockwise . ELEN 3441 Fundamentals of Power Engineering Spring 2008 Finally, at t = 1/60 s the rotor and stator magnetic fields are aligned again, and the induced torque on the shaft is zero . During one electrical cycle, the torque was counter-clockwise and then clockwise, and the average torque is zero. The motor will vibrate heavily and finally overheats!

57. 86 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Starting synchronous motors Three basic approaches can be used to safely start a synchronous motor: Reduce the speed of the stator magnetic field to a low enough value that the rotor can accelerate and two magnetic fields lock in during one half- cycle of field rotation. This can be achieved by reducing the frequency of the applied electric power (which used to be difficult but can be done now). Use an external prime mover to accelerate the synchronous motor up to synchronous speed, go through the paralleling procedure, and bring the machine on the line as a generator. Next, turning off the prime mover will make the synchronous machine a motor. Use damper windings or amortisseur windings – the most popular.

58. 87 Motor starting by amortisseur or damper windings Amortisseur (damper) windings are special bars laid into notches carved in the rotor face and then shorted out on each end by a large shorting ring . ELEN 3441 Fundamentals of Power Engineering Spring 2008

59. 91 ELEN 3441 Fundamentals of Power Engineering Spring 2008 Motor starting by amortisseur or damper windings We observe that the torque is either counter- clockwise or zero, but it is always unidirectional . Since the net torque is nonzero, the motor will speed up. However, the rotor will never reach the synchronous speed! If a rotor was running at the synchronous speed, the speed of stator magnetic field B S would be the same as the speed of the rotor and, therefore, no relative motion between the rotor and the stator magnetic field. If there is no relative motion, no voltage is induced and, therefore, the torque will be zero. Instead, when the rotor’s speed is close to synchronous, the regular field current can be turned on and the motor will operate normally. In real machines, field circuit are shorted during starting. Therefore, if a machine has damper winding: Disconnect the field windings from their DC power source and short them out; Apply a 3- phase voltage to the stator and let the rotor to accelerate up to near- synchronous speed. The motor should have no load on its shaft to enable motor speed to approach the synchronous speed as closely as possible; Connect the DC field circuit to its power source: the motor will lock at synchronous speed and loads may be added to the shaft.

60. 92 Relationship between synchronous generators and motors Synchronous generator and synchronous motor are physically the same machines! A synchronous machine can supply real power to (generator) or consume real power (motor) from a power system. It can also either consume or supply reactive power to the system. The distinguishing characteristic of a synchronous generator (supplying P ) is that E A lies ahead of V  while for a motor E A lies behind V  . The distinguishing characteristic of a machine supplying reactive power Q is that E a cos  > V  (regardless whether it is a motor or generator). The machine consuming reactive power Q has E a cos  < V  . ELEN 3441 Fundamentals of Power Engineering Spring 2008