INSTITUTE OF AERONAUTICAL ENGINEERING

Transcription

1 POWER POINT PRESENTATION ON ELECTRICAL MACHINES - II II B. Tech II semester (JNTUH-R15) Mr. K DEVENDER REDDY, Assistant Professor ELECTRICAL AND ELECTRONICS ENGINEERING INSTITUTE OF AERONAUTICAL ENGINEERING DUNDIGAL, HYDERABAD

2 UNIT -I Single-Phase Transformers

3 Single-Phase Transformers Objectives: Discuss the different types of transformers. List transformer symbols and formulas. Discuss polarity markings.

4 Single-Phase Transformers A transformer is a magnetically operated machine. All values of a transformer are proportional to its turns ratio.

5 Single-Phase Transformers The primary winding is connected to the incoming power supply. The secondary winding is connected to the driven load.

6 Single-Phase Transformers This is an isolation transformer. The secondary winding is physically and electrically isolated from the primary winding.

7 Single-Phase Transformers The two windings of an isolation transformer are linked together by the magnetic field.

8 Single-Phase Transformers The isolation transformer greatly reduces voltage spikes.

9 Single-Phase Transformers Basic construction of an isolation transformer.

10 Single-Phase Transformers Each set of windings (primary and secondary) is formed from loops of wire wrapped around the core. Each loop of wire is called a turn. The ratio of the primary and secondary voltages is determined by the ratio of the number of turns in the primary and secondary windings. The volts-per-turn ratio is the same on both the primary and secondary windings.

11 Single-Phase Transformers Transformer Symbols N P = number of turns in the primary N S = number of turns in the secondary E P = voltage of the primary E S = voltage of the secondary I P = current in the primary I S = current in the secondary

12 Single-Phase Transformers Transformer Formulas E P / E S = N P / N S E P x N S = E S x N P E P x I P = E S x I S N P x I P = N S x I S

13 Single-Phase Transformers The distribution transformer is a common type of isolation transformer. This transformer changes the high voltage from the power company to the common 40/10 V.

14 Single-Phase Transformers The control transformer is another common type of isolation transformer. This transformer reduces high voltage to the value needed by control circuits.

15 Single-Phase Transformers Polarity dots are placed on transformer schematics to indicate points that have the same polarity at the same time.

16 Single-Phase Transformers Review: 1. All values of voltage, current, and impedance in a transformer are proportional to the turns ratio.. The primary winding of a transformer is connected to the source voltage. 3. The secondary winding is connected to the load.

17 Single-Phase Transformers Review: 4. An isolation transformer has its primary and secondary voltage electrically and mechanically separated. 5. Isolation transformers help filter voltage and current spikes. 6. Polarity dots are often added to schematic diagrams to indicate transformer polarity.

18 Transformer Regulation Loading changes the output voltage of a transformer. Definition of % Regulation V noload V V load load *100 V no-load =RMS voltage across the load terminals without load V load = RMS voltage across the load terminals with a specified load

19 ' 0 ' 1 0; max. 0 eq eq eq eq or imum when is V Clearly Z I V V Maximum Transformer Regulation

20 Transformer Losses and Efficiency Transformer Losses Core/Iron Loss =V 1 / R c1 Copper Loss = I 1 R 1 + I R Definition of % efficiency V VI Cos Losses V I Cos V I Cos *100 1 / Rc1 I1 R1 I R VI Cos V V 1 / Rc1 I Req VI Cos Cos I Cos = load power factor *100 *100 Transformer 0

21 Maximum Transformer Efficiency The efficiency varies as with respect to independent quantities namely, current and power factor Thus at any particular power factor, the efficiency is maximum if core loss = copper loss.this can be obtained by differentiating the expression of efficiency with respect to I assuming power factor, and all the voltages constant. At any particular I maximum efficiency happens at unity power factor. This can be obtained by differentiating the expression of efficiency with respect to power factor, and assuming I and all the voltages constant. Maximum efficiency happens when both these conditions are satisfied. Transformer 1

22 Maximum efficiency point 100 pf=1 pf= 0.8 pf= At this load current core loss = copper loss % full load current Transformer

23 Transformer Equivalent circuit (1) I1 INL E1 E I Transformer 3

24 Transformer Equivalent circuit () I I1 INL Transformer 4

25 Transformer Equivalent circuit (3) I1 I INL Transformer 5

26 Transformer Equivalent circuit (4) I1 INL I' Transformer 6

27 PARTS OF TRANSFORMER MAIN TANK RADIATORS CONSERVATOR EXPLOSION VENT LIFTING LUGS AIR RELEASE PLUG OIL LEVEL INDICATOR TAP CHANGER WHEELS HV/LV BUSHINGS FILTER VALVES OIL FILLING PLUG DRAIN PLUG CABLE BOX

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38 UNIT TESTING OF TRANSFORMERS

39 TESTING OF TRANSFORMER Testing of single phase Transformers OC Test SC test Sumpner s Test or Back to Back Test

40 Open circuit Test It is used to determine L m1 (X m1 )and R c1 Usually performed on the low voltage side The test is performed at rated voltage and frequency under no load This test gives the values of core losses in a transformer Transformer 40

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42 Woc= Core loss of the transformer From the data Cosø= Woc/(Voc*Ioc) Iw=IocCosø Ių = Ioc Sinø Rcl=Voc/Iw Xml=Voc/I ų

43 Short circuit Test It is used to determine Ll p (X eq ) and R p (R eq ) Usually performed on the high voltage side This test is performed at reduced voltage and rated frequency with the output of the low voltage winding short circuited such that rated current flows on the high voltage side. This test gives copper loss of the transformer. Transformer 43

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45 Wsc= copper losses of the transformer. Zeq=Vsc/Isc Req=Wsc/Isc² Xeq=sqrt(Zeq²-Req²)

46 Efficiency of the transformer Ŋ = output Power/ Input power Ŋ = XVICosø/(XVICosø + Pc +x²pcu)

47 Sumpner s test or back to back test on set of transformers From this test Losses and Efficiency of the two transformers can be determined

48 Parallel operation of transformers Wrong connections give circulating between the windings that can destroy transformers. Transformer 48

49 To connect the transformers in parallel the following conditions must be satisfied i. Transformers must be of same rating. ii. Transformers should have the same phase sequence. iii. voltage ratio must be same. iv. Per unit impedence of the transformers must be same.

50 UNIT-III AUTO AND POLY PHASE TRANSFORMERS

51 Autotransformer Primary and secondary on the same winding. Therefore there is no galvanic isolation. Transformer 51

52 Features of Autotransformer Lower leakage Lower losses Lower magnetizing current Increase kva rating No galvanic Isolation Transformer 5

53 Review of balanced three phase circui Two possible configurations: Star (Y) and delta () Star has neutral, delta does not Transformer 53

54 Star (Y) connection Line current is same as phase current Line-Line voltage is 3 phase-neutral voltage Power is given by 3 V L-L I L cos or 3V ph I ph cos Transformer 54

55 Delta () connection Line-Line voltage is same as phase voltage Line current is 3 phase current Power is given by 3 V L-L I L cos or 3V ph I ph cos Transformer 55

56 Typical three phase transformer connections Transformer 56

57 Other possible three phase transformer Connections Y- zigzag - zigzag Open Delta or V Scott or T Transformer 57

58 How are three phase transformers made? Either by having three single phase transformers connected as three phase banks. Or by having coils mounted on a single core with multiple limbs The bank configuration is better from repair perspective, whereas the single three phase unit will cost less,occupy less space, weighs less and is more efficient Transformer 58

59 Phase-shift between line-line voltages in transformers Transformer 59

60 Vector grouping of transformers Depending upon the phase shift of line-neutral voltages between primary and secondary; transformers are grouped. This is done for ease of paralleling. Usually transformers between two different groups should not be paralleled. Group 1 :zero phase displacement (Yy0, Dd0,Dz0) Group :180 0 phase displacement (Yy6, Dd6,Dz6) Group 3 : 30 0 lag phase displacement (Dy1, Yd1,Yz1) Group 4 : 30 0 lead phase displacement (Dy11, Yd11,Yz11) (Y=Y; D= ; z=zigzag) Transformer 60

61 Calculation involving 3-ph transformers Transformer 61

62 An example involving 3-ph transformers Transformer 6

63 Open delta or V connection Transformer 63

64 Open delta or V connection Power from winding ab is P ab =V ab I a cos(30 0 +) Power from winding bc is P cb =V cb I c cos(30 0 -) Therefore total power is =V L-L I L cos30 0 cos or 57.7% of total power from 3 phases Transformer 64

65 Harmonics in 3- Transformer Banks In absence of neutral connection in a Y-Y transformers 3 rd harmonic current cannot flow This causes 3 rd harmonic distortion in the phase voltages (both primary and secondary) but not line-line voltages, as 3 rd harmonic voltages get cancelled out in line-line connections Remedy is either of the following : a) Neutral connections, b) Tertiary winding c) Use zigzag secondary d) Use stardelta or delta-delta type of transformers. a) The phenomenon is explained using a star-delta transformer. Transformer 65

66 Harmonics in 3- Transformer Banks() Transformer 66

67 Harmonics in 3- Transformer Banks(3) Transformer 67

68 Three-Phase Transformers Sine wave distortion caused by harmonics.

69 UNIT-4 POLY-PHASE INDUCTION MOTORS

70 Introduction 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

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

72 Construction a revolving rotor composed of punched laminations, stacked to create a series of rotor slots, providing space for the rotor winding one of two types of rotor windings 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) 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.

73 Construction Squirrel cage rotor Wound rotor Notice the slip rings

74 Construction Slip rings Cutaway in a typical woundrotor IM. Notice the brushes and the slip rings Brushe s

75 Rotating Magnetic Field Balanced three phase windings, i.e. mechanically displaced 10 degrees form each other, fed by balanced three phase source A rotating magnetic field with constant magnitude is produced, rotating with a speed n sync 10 f e P rpm 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)

76 Synchronous speed P 50 Hz 60 Hz

77 Rotating Magnetic Field

78 Rotating Magnetic Field

79 Rotating Magnetic Field B ( t) B ( t) B ( t) B ( t) net a b c B sin( t) 0 B sin( t 10 ) 10 B sin( t 40) 40 B M M M M sin( t)ˆ x 3 [0.5B sin( 10 )] ˆ M t x[ BM sin( t 10 )] yˆ 3 [0.5B sin( 40 )] ˆ M t x[ BM sin( t 40 )] yˆ

80 Rotating Magnetic Field Bnet ( t) [ BM sin( t) BM sin( t) BM cos( t) BM sin( t) BM cos( t)]ˆ x [ BM sin( t) BM cos( t) BM sin( t) BM cos( t)]ˆ y [1.5 B sin( t)] xˆ[1.5 B cos( t)] yˆ M M

81 Rotating Magnetic Field

82 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 kb B ind R s Where ind is the induced torque and B R and B S are the magnetic flux densities of the rotor and the stator respectively

83 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

84 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 n n n slip sync m Where n slip = slip speed n sync = speed of the magnetic field n m = mechanical shaft speed of the motor

85 The Slip Where s is the slip s n sync n sync Notice that : if the rotor runs at synchronous speed s = 0 n 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 m

86 Frequency The frequency of the voltage induced in the rotor is given by P n fr 10 Where f r = the rotor frequency (Hz) P = number of stator poles n = slip speed (rpm) P( ns nm) fr 10 P sns sfe 10

87 Frequency What would be the frequency of the rotor s induced voltage at any speed n m? f r s f e 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

88 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 load Pout Nm. n m m 60 and m rad / s

89 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 hp 746 watts

90 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

91 Equivalent Circuit When the rotor is locked (or blocked), i.e. s =1, the largest voltage and rotor frequency are induced in the rotor, Why? 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, Why? E se R R0 Where E R0 is the largest value of the rotor s induced voltage obtained at s = 1(loacked rotor)

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

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

94 Equivalent Circuit Now we can calculate the rotor current as I R ER ( R jx ) R Dividing both the numerator and denominator by s so nothing changes we get I R R0 ( R jsx ) R se Where E R0 is the induced voltage and X R0 is the rotor reactance at blocked rotor condition (s = 1) R R0 ER0 RR ( jx R0) s

95 Equivalent Circuit Now we can have the rotor equivalent circuit

96 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 X a X eff R0 R a R I eff R eff E a E a R 1 eff R0 eff I a N N S R

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

98 Power flow in induction motor

99 Power relations P 3 V I cos 3V I cos in L L ph ph PSCL 3 I R 1 1 P P ( P P ) AG in SCL core PRCL 3I R P P P conv AG RCL P P ( P P ) out conv f w stray ind P conv m

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

101 Power relations P 3 V I cos 3V I cos in L L ph ph PSCL 3 I R 1 1 P P ( P P ) AG in SCL core PRCL 3I R P P P P conv AG RCL conv (1 s) P AG 3I P P ( P P ) out conv f w stray R P conv (1 s) s ind P RCL P 3I R s P (1 ) RCL s s conv m (1 sp ) AG (1 s) s P RCL s

102 Power relations P AG 1 P conv 1- s P : P : P AG RCL conv 1 : s : 1-s P RCL s

103 Torque, power and Thevenin s Theorem Thevenin s theorem can be used to transform the network to the left of points a and b into an equivalent voltage source V TH in series with equivalent impedance R TH +jx TH

104 Torque, power and Thevenin s Theorem jx M VTH V R j ( X X ) 1 1 R jx ( R jx ) // jx TH TH 1 1 M M V V TH X M R ( X X ) 1 1 M

105 Torque, power and Thevenin s Theorem Since X M >>X 1 and X M >>R 1 X M VTH V X 1 X M Because X M >>X 1 and X M +X 1 >>R 1 X X X M RTH R1 X 1 X M TH 1

106 Torque, power and Thevenin s Theorem I V Z TH T V TH R RTH XTH X s ( ) Then the power converted to mechanical (P conv ) R (1 s) P conv 3I s And the internal mechanical torque (T conv ) ind P conv m P conv (1 s) s R 3I s s PAG s

107 Torque, power and Thevenin s Theorem ind 3 V R TH s s R RTH ( XTH X ) s ind 1 s 3V TH R RTH XTH X s R s ( )

108 Torque-speed characteristics Typical torque-speed characteristics of induction motor

109 Comments 1. The induced torque is zero at synchronous speed. Discussed earlier.. The curve is nearly linear between no-load and full load. In this range, the rotor resistance is much greater than the reactance, so the rotor current, torque increase linearly with the slip. 3. There is a maximum possible torque that can t be exceeded. This torque is called pullout torque and is to 3 times the rated full-load torque.

110 Comments 4. The starting torque of the motor is slightly higher than its full-load torque, so the motor will start carrying any load it can supply at full load. 5. The torque of the motor for a given slip varies as the square of the applied voltage. 6. If the rotor is driven faster than synchronous speed it will run as a generator, converting mechanical power to electric power.

111 Complete Speed-torque c/c

112 Maximum torque Maximum torque occurs when the power transferred to R /s is maximum. This condition occurs when R /s equals the magnitude of the impedance R TH + j (X TH + X ) R s T max R ( X X ) TH TH s T max R R ( X X ) TH TH

113 Maximum torque The corresponding maximum torque of an induction motor equals max 1 3V TH R R ( X X ) s TH TH TH The slip at maximum torque is directly proportional to the rotor resistance R The maximum torque is independent of R

114 Maximum torque Rotor resistance can be increased by inserting external resistance in the rotor of a woundrotor induction motor. The value of the maximum torque remains unaffected but the speed at which it occurs can be controlled.

115 Maximum torque Effect of rotor resistance on torque-speed characteristic

116 Determination of motor parameters Due to the similarity between the induction motor equivalent circuit and the transformer equivalent circuit, same tests are used to determine the values of the motor parameters. No-load test: determine the rotational losses and magnetization current (similar to no-load test in Transformers). Locked-rotor test: determine the rotor and stator impedances (similar to short-circuit test in Transformers).

117 UNIT-5 CIRCLE DIAGRAM AND SPEED CONTROL OF INDUCTION MOTORS

118 No-load test 1. The motor is allowed to spin freely. The only load on the motor is the friction and windage losses, so all P conv is consumed by mechanical losses 3. The slip is very small

119 No-load test 4. At this small slip R (1 s) R (1 s) R & s s X The equivalent circuit reduces to

120 No-load test 5. Combining R c & R F+W we get

121 No-load test 6. At the no-load conditions, the input power measured by meters must equal the losses in the motor. 7. The P RCL is negligible because I is extremely small because R (1-s)/s is very large. 8. The input power equals P P P P in SCL core F & W 3I R 1 1 P rot Where P P P rot core F& W

122 No-load test 9. The equivalent input impedance is thus approximately V Zeq X1 X I 1, nl M If X 1 can be found, in some other fashion, the magnetizing impedance X M will be known

123 Blocked-rotor test In this test, the rotor is locked or blocked so that it cannot move, a voltage is applied to the motor, and the resulting voltage, current and power are measured.

124 Blocked-rotor test The AC voltage applied to the stator is adjusted so that the current flow is approximately full-load value. The locked-rotor power factor can be found as PF cos 3VI The magnitude of the total impedance Z LR V I P in l l

125 Blocked-rotor test Z R jx ' LR LR LR Z LR cos j Z LR sin R R R LR 1 X X X ' ' ' LR 1 Where X 1 and X are the stator and rotor reactances at the test frequency respectively R R R LR 1 f rated ' X LR X LR X1 X ftest

126 Blocked-rotor test X 1 and X as function of X LR Rotor Design X 1 X Wound rotor 0.5 X LR 0.5 X LR Design A 0.5 X LR 0.5 X LR Design B 0.4 X LR 0.6 X LR Design C 0.3 X LR 0.7 X LR Design D 0.5 X LR 0.5 X LR

127 Speed Control of Induction Motor 1- Variable Terminal Voltage Control - Variable Frequency Control 3- Rotor Resistance Control 4- Injecting Voltage in Rotor Circuit

128 ms 1- Variable Terminal Voltage Control m T L V decreasing T variable terminal voltage control Low speed range Lower rated speed variable frequency control Wide speed range Lower & higher rated speed

129 a f / f rated - Variable Frequency Control Per-Unit Frequency I I 1- Operation Below the Rated Frequency a <1 m m E X E ax rated m m a * E f rated rated E f rated 1 * L m 1 * L m At rated frequency At any frequency, f Comparing of the above equations, value if E a E rated f f rated E rated I m will stay constant at a value equal to its rated E f E f rated rated The above equation suggests that the flux will remain constant if the back emf changes in the same ratio as the frequency, in other ward, when E/f ratio is maintained constant.

130 The rotor current at any frequency f can be obtained from the following equation: r r rated r r rated r X as R E ax s R ae I ms sl ms m ms a a a s ms m Angular Speed at frequency f Synchronous Speed at rated frequency rated f / * 3 3 r r r rated ms r r ms X as R as R E s R I a T Torque at frequency f At a given f and E r r m ax R s m ms sl a ms sl ms m ms a sa r rated ms X E T max 3

131 T 3 a ms I R r s E rated * Rr as R r X r as 3 / r ms R as r X r T 3E rated ms R r as consta nt sl (6-51)

132 m ms a ms T Braking Motoring

133 R s X s V/f Control X r R r / s I s I m Ir V X m E R s X s X r R r / s I m I s I r V X m E

134 V/f Control / / * 3 3 r s r s r rated ms r r ms X X s R R s R V s R I T max 3 r s s s rated ms X X R R V T At rated frequency / / / * 3 r s r s r rated ms X X as R a R as R V T max / / 3 r s s s rated ms X X a R a R V T At any frequency, f, 1 a

135 V/f Control m ms a ms T

136 Operation above the rated frequency a>1 The terminal voltage has to be constant = Rated Volatge= V consta nt T 3 Flux * R when a rated r ms V Rs Rr / s a X s X r / as V rated At any frequency, f, a 1 T max 3 ms a R s V rated R s a X s X r

137 m Constant torque locus ms f rated a ms Constant torque locus T

138 THANK U.