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Three Phase Circuits

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Three Phase Circuits

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  1. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  P    INTRODUCTION    This chapter has been divided into following topics:  1) Basic concepts of Poly phase Circuits and its advantages  2) Generation of three phase supply  3) Star – Delta Connections (Balanced load)  4) Relationship between phase and line currents and voltages  5) Phasor diagrams  6) Measurement of power by two wattmeter method    POLYPHASE SYSTEMS    1) Poly phase alternators have two or more windings symmetrically spaced                     around the armature. Such alternators produce as many independent                   alternating voltages as the number of windings (Phase).  2) These voltages in the individual windings have the same magnitude and                       frequency but they have definite phase difference. The amount of phase                       difference depends upon the number of windings.  3) Thus, by using appropriate poly phase alternator, it is possible to generate                         two phase and three phase ac and from these to obtain four, six, nine,                             twelve phase AC depending upon the requirements. These systems are                     collectively known as poly phase systems.    ADVANTAGES OF 3- Φ SYSTEM OVER 1- Φ SYSTEM     1) The output of a 3- φ machine is greater than that of 1- φ machine of the                                   same size.   2) The total power output of a 3- φ machine is not fluctuating as in the case                                 of a 1- φ machine. It has a higher efficiency.   1 1 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 1/27

  2. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464      Email : care@ekeeda.com  3) A 3- φ transmission needs less conducting material than a 1- φ                     transmission line. Hence, transmission becomes economical.   4) 3- φ motors are self-starting, whereas 1- φ motors are not self-starting.   5) Power factor of a 1- φ motor is always lower than that of a 3- φ motor of                 the same output and speed.   6) 1- φ supply can be obtained from 3- φ supply but 3- φ supply cannot be                                                     obtained from 1- φ supply.     GENERATION OF THREE PHASE SUPPLY      Waveforms of 3- φ supply    Construction     1) The armature of the alternator consists of three single-turn rectangular                     coils R 1 R 2 , Y 1 Y 2and B 1 B 2fixed to one another at angles of 120˚. The coils               are mounted on a common shaft and have same physical dimensions.                   2) The ends of coil are connected to a pair of slip-rings carried on the shaft.                               The coils are placed in the uniform magnetic field provided by the North                           and South poles of the magnet.   3) The carbon brushes are pressed against the slip-rings to collect the                       induced currents in the coils.     2 2 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 2/27

  3. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  Operation     1) Suppose the three coils are rotating in an anti-clockwise direction at                       uniform speed. Because of this each coil will have its own generated e.m.f.                           and current which will be alternating in nature.   2) As shown in the figure the plane of the coil R 1 R 2is perpendicular to the               magnetic field and hence no e.m.f. is generated in the coil. After 120˚ Y 1 Y 2               will occupy this position and after 120˚ B 1 B 2 will occupy this position.   3) This cycle continues and maximum value attained by every coil has 120˚                                                       phase shift w.r.t e.m.f. in other coil.   4) If the instantaneous value of the e.m.f. generated in the coil R 1 R 2is             represented by,                   then, the instantaneous values of the e.m.f.’s generated in the coil Y 1 Y 2and             B 1 B 2 are,                    5) Thus, we got three independent alternating voltages from 3- φ alternator                       which have phase shift of 120˚. The phasor diagram for 3- φ system is as                               show:    3 3 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 3/27

  4. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464    Email : care@ekeeda.com  6) If we perform vector addition of these three voltages, it can be observed                         that, the sum of three voltages at any instant is zero. Mathematically,                         Important Definitions related to 3-φ System    1) Symmetrical System :-  A 3-φ system in which the three voltages are of same magnitude and frequency                             and displaced by 120¢ª phase angle from each other is defined as                         ‘Symmetrical System’.  2) Phase Sequence :-  4 4 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 4/27

  5. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464    Email : care@ekeeda.com  The sequence in which the voltages in 3-φ               reach their maximum positive         values is called ‘Phase Sequence’.  3) Balanced System :-  A 3-φ system is said to be balanced when,  a) All phase inpedances are identical.   b) Magnitude and phase angle of all phase impedances are identical.  c) All phases have same power factor.    Connections in Three Phase System     In 3- φ system we can have following connections:   a) Star or Wie (Y) connection:    b) Mesh or Delta (Δ) connection:  ➢ ➢ Star Connection :-    1) In this connection, like terminals of the coil i.e. either starting terminals                         R 1 , Y 1 , B 1or finishing terminals R 2, Y 2 , B 2are connected together to form a               common point ‘N’ which is known as neutral point or star point.                  2) This kind of connection is also known as ‘Four wire three phase system’.                           This connection is shown in figure.  3) Assuming phase sequence R-Y-B all the line quantities and phase                     quantities of star connection are shown in figure.  5 5 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 5/27

  6. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  a) Line Voltage (V L ) :   The potential difference between any two lines gives line to line voltage called                           as line voltage.   For above fig. Line voltages are V L = V RY = V YB = V BR  b) Phase Voltage (V ph ) :   The potential difference between any line and neutral point is called as phase                           voltage.   For above fig. Phase voltages are V ph = V RN = V YN = V BN  c) Line Current (I L ):   The current flowing through each line is called as line current.   For above fig. Line currents are I L = I R = I Y = I B    d) Phase Current (I ph ) :   The current flowing through each phase is called as phase current.   For above fig. phase currents are I ph = I RN = I YN = I BN  ✓ Relation Between Line Quantities and phase Quantities for Star                   Connected System  1) Consider a 3- φ star connected balanced system as shown in figure.   From figure,     But,  and    Hence,  …... (1)   2) To get the relation between line voltage and the phase voltage, plot the                           vector diagram. Assuming phase sequence to be R-Y-B with lagging                     power factor.  From fig. voltage across line R and line Y is  6 6 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 6/27

  7. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  …... (2)   3) Vector Diagram for 3- φ star connected balanced system is shown in                         below figure.   4) Consider   In draw   From vector diagram,     But ….... (3)   In         5) Substituting this in equation (3),   7 7 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 7/27

  8. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com    Hence,    6) Thus, for a star connected connection we can conclude following points:  and   a) b) Line voltages are apart.   c) Line voltages are ahead of their respective phase voltages.  d) The angle between line currents and the corresponding line voltages                     is with current lagging.   e) The angle between line currents and the corresponding line voltages                     is with current leading.  ✓ Expression for Power in 3- φ star connected system :   1) Active Power :    We know that for a 1-φ system active power is given by,  ……(1)  Hence for a 3- φ system,   Total active power = 3 × (Power/phase)    Bus for star connected ckt.    8 8 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 8/27

  9. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com    Where φ is the angle between phase voltage and phase current.  2) Reactive Power :  Total reactive power is given by,       3) Apparent Power :  Total apparent Power is given by,                     9 9 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 9/27

  10. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  Delta Connection    1) In this connection finishing terminal of one coil is connected to starting                         terminal of second coil and finishing of that to starting of next and so on                               i.e. In Δ connection coils are connected to form a closed loop as shown in                               fig. (1)   2) This kind of connection is also known as ‘three wire three phase system’.                           This connection is shown in fig. (1)   3) Assuming phase sequence R-Y-B all the line quantities and phase                     quantities of delta connection are shown in fig. (1)  a) Line Voltage (V L ) :   The potential difference between any two lines gives line to line voltage called                           as line voltage.   For above fig. Line voltages are V L = V RY = V YB = V BR  b) Phase Voltage (V ph ) :   The potential difference between any line and neutral point is called as phase                           voltage.   For above fig. Phase voltages are V ph = V R = V Y = V B  c) Line Current (I L ):   The current flowing through each line is called as line current.   For above fig. Line currents are I L = I R = I Y = I B    10 10 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 10/27

  11. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  d) Phase Current (I ph ) :   The current flowing through each phase is called as phase current.   For above fig. phase currents are I ph = I RY = I YB = I BR      ✓ Relation Between Line Quantities and phase Quantities for Delta                   Connected System:-   1. Consider a 3- φ delta connected balanced system as shown in figure.   From figure,     But,    2. To get the relation between line voltage and the phase voltage, plot the                           vector diagram. Assuming phase sequence to be R-Y-B with lagging                     power factor.  From fig.   …… (2)  3. Vector Diagram for 3- φ delta connected balanced system is shown                       below figure.   11 11 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 11/27

  12. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com    4. Consider   In draw   From vector diagram,     But …… (3)  In       5. Substituting this in equation (3),       Hence,   6. Thus, for a delta connected connection we can conclude following                     points :   12 12 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 12/27

  13. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com      a) b) Line currents are 120 ˚ apart.   c) Line currents are 30˚ ahead of their respective phase currents.   d) The angle between line currents and the corresponding line voltages                     is (30+ ) with current lagging.   e) The angle between line currents and the corresponding line voltages                     is (30-φ) with current leading.   ✓ Expression for Power in 3- φ delta connected system :   1) Active Power :      But for delta connected ckt.        Where φ is the angle between phase voltage and phase current.  2) Reactive Power :  Total reactive power is given by,       3) Apparent Power :  Total apparent Power is given by,       13 13 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 13/27

  14. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com    Relationship between Power drawn by Star and Delta Connected Load     1) Let       2) For star connected system,   we have,      But       3) Now,     …..[From (1)]  ….(2)  4) For delta connected system,   we have,  14 14 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 14/27

  15. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com    But         5) Now,     ….[From (3)]  ….(4)  6) Thus, from . (2) and (4), we have     From this     . we can conclude that for the same load, power drawn in delta                           ckt. is three times more than the power drawn in star connected ckt.          15 15 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 15/27

  16. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com                                  MEASUREMENT OF POWER IN THREE PHASE SYSTEM    Wattmeter     1. It is a device which is used to measure power drawn by single phase                             circuit.. It consists of two coils (1) Current Coil (CC) and (2) Potential Coil                             (PC)   2. Current coil senses the current and it is always connected in series with                           the load. The resistance of the coil is very small and hence its cross                             sectional area is large and it has less number of turns.   3. Potential coil is also known as ‘Pressure Coil’. This senses the voltage and                           it is always connected across the supply terminals. The resistance of this                         16 16 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 16/27

  17. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464      Email : care@ekeeda.com  coil is very high and hence its cross sectional area is small and it has more                             number of turns   4. The symbol for wattmeter is as shown in fig. (1)     M Mains, C Common, L Line, V Voltage      5. The circuit connection for measurement of power of a single phase circuit                         is shown in fig.(2)    6. Wattmeter reading is directly proportional to   a) Current (I) through the coil.   b) Voltage (V) across the coil.   c) Cosine of the angle between this voltage and current.   Thus, wattmeter reading is    Hence, wattmeter gives the direct reading of the power absorbed by the single                           phase circuit.  17 17 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 17/27

  18. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  7. It is also used for measurement of power in 3-φ system. There are three                             methods available for measuring power in 3-φ system. They are as follows   a) Three wattmeter method   b) Two wattmeter method   c) One wattmeter method                                               18 18 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 18/27

  19. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com      TWO WATTMETER METHOD     Star Connection     1. The circuit diagram of two wattmeter method for star connected 3-                       system is as shown above.   2. Current coil of each wattmeter is connected in any two lines and the             potential coils of both the wattmeter are connected to third line.                 3. In above fig. current coils of wattmeter               are connected in line-R         and line-Y respectively and their potential coils are shorted to line B.   4. For   current through current coils is           and voltage across potential         coil is . ….(1)  5. Similarly, for       current through current coil is             and voltage across       potential coil is .   19 19 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 19/27

  20. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  6. Hence reading is, = ….(2)  7. Now consider the phasor diagram for star ckt. Assuming phase sequence                       R-Y-B and lagging p.f. we have,       1) From circuit diagram.     and   2) From vector Diagram we have,   Angle between     ….(3)   ….(4)   3) But for star connected balanced system,     20 20 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 20/27

  21. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  Hence from . (3) and (4), we have  ….(5)  ….(6)                4) Adding .’s (5) and (6) we get,           ….(7)  5) But for star connected system,   Thus,    21 21 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 21/27

  22. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464      Email : care@ekeeda.com  i.e. the total power absorbed is equal to algebraic sum of the two wattmeter                         readings.                                    DELTA CONNECTION   22 22 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 22/27

  23. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com    1. The circuit diagram of two wattmeter method for delta connected 3-                       system is as shown above.   2. Current coil of each wattmeter is connected in any two lines and the                           potential coils of both the wattmeter are connected to third line.   3. In above fig. current coils of wattmeter               and     are connected in line-R           and line-Y respectively and their potential coils are shorted to line B.   4. For     current through current coil is           and voltage across potential coil           is . Hence reading is, ….(1)  5. Similarly, for       current through current coil is           and voltage across       potential coil is .   Hence reading is, ….(2)    6. Now consider the phasor diagram for delta ckt. Assuming phase sequence                       R-Y-B and lagging p.f. we have,   23 23 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 23/27

  24. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com      7. From circuit diagram.     and   8. From vector Diagram we have,   Angle between and is and angle between and is (30 + φ)  Thus eqn. (1) and (2) becomes,   W1 = VRB IR cos (30 - φ) W2 = VYB IY cos (30 + φ)  9. But for delta connected balanced system,   VL = VRB = VYB and IL = IR = IY   Hence from eqn. (3) and (4), we have   ….(3)   ….(4)    ….(5)   ….(6)  10. Adding eqn.’s (5) and (6) we get,          24 24 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 24/27

  25. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com    ….(7)  11. But for delta connected system,   Thus,   i.e. the total power absorbed is equal to algebraic sum of the two                           wattmeter readings.  EXPRESSION FOR POWER FACTOR USING TWO WATTMETER METHOD     1. When two wattmeter are used for measurement of power in 3-φ system,             the wattmeter readings are given by,   2. Adding (1) and (2) we get,                           ….(3)  3. Subtracting (2) from (1) we get,     25 25 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 25/27

  26. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com            ….(4)  4. From eqn. (3) and (4),     ….(5)      5. But   ….(6)  6. From the above expressions we can conclude following points   1) If , then the readings of two wattmeter are equal.   2) If , then the readings of both the wattmeter are positive.   26 26 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 26/27

  27. 10/01/2019 4.Three Phase Circuits - Google Docs www.ekeeda.com  Contact : 9029006464  Email : care@ekeeda.com  3) If , then the reading of wattmeter is zero.   4) If , then the reading of wattmeter is negative.     ADVANTAGES OF TWO WATTMETER METHOD      1. Availability of neutral point in star connected system is not compulsory,                       for power measurement using two wattmeter method.   2. This method can be used for balanced as well as unbalanced systems.   3. It is very easy to determine             of a     system using two wattmeter         method.   4. Total volt-amperes can be obtained using two wattmeter readings for                     balanced load.   5. Circuit connections are very simple.     27 27 https://docs.google.com/document/d/17mK5dOQyAGK3QrDoLWXilx4ySZ2eQwGGisE2egwWZ84/edit 27/27

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