Electrical Machines and Energy Systems: Operating Principles (Part 3) SYED A RIZVI

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1 Electrical Machines and Energy Systems: Operating Principles (Part 3) SYED A RIZVI

2 Missing piece: The induced voltage in the stator windings, E S. The rotor s rotating magnetic field induces a voltage in the stator windings of the motor in the same way that the rotating magnetic did in the armature windings in the case of the synchronous generator. Note that the rotor s magnetic field is rotating in synchronism with the rotating magnetic field of the stator. Therefore, the frequency of the induced voltage E S is the same as that of the applied voltage V P at the terminals of the motor. However, E S lags V P by an angle α. We now have enough information to develop the equivalent circuit of the synchronous motor, which is essentially the same as that of the synchronous generator except that the current now flows from machine s terminals to the stator windings. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 2

3 The figure below shows the equivalent circuit of the synchronous motor (per phase). Syed A Rizvi ENS 436, Department of Engineering and Environment Science 3

4 In the following analysis, we will assume the motor is operating with a lagging power factor and use the phase voltage as the reference with a phase angle of 0 o. That is, V P = V P 0 o E A = E A α o I A = I A ɵ o and EE AA = VV PP II AA (R A + jjx A ) (26) or VV PP = EE AA + II AA (R A + jjx A ) (27) Syed A Rizvi ENS 436, Department of Engineering and Environment Science 4

5 Accordingly, total power delivered to the motor can be expressed by Eq. (25). That is, noting we get P total = 3VV PPEE AA sin αα XX AA (28) P total = ττ iiiiiiiiiiiiii ωω mm (29) ττ iiiiiiiiiiiiii = 3VV PPEE AA sin αα XX AA ωω mm (30) Syed A Rizvi ENS 436, Department of Engineering and Environment Science 5

6 Accordingly, the pull out torque can be expresses as ττ pppppppppppppp = 3VV PPEE AA XX AA ωω mm (33) Syed A Rizvi ENS 436, Department of Engineering and Environment Science 6

7 The figure below shows the phaser diagram of a synchronous motor with a unity power factor. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 7

8 The figure below shows the phaser diagram of a motor with a leading power factor. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 8

9 Start up issues: Let s assume that the magnetic fields of the stator and rotor are as shown in the figure on the right with the stator s magnetic field rotating CCW. The rotor will experience an induced torque in CCW direction. So far, everything seems to be in order: the rotor should start rotating CCW under the induced torque and chase the rotating magnetic field of the stator. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 9

10 In a half cycle of electrical frequency (1/120 of a second or about 2.7 ms), the stator s magnetic field would rotate such that its orientation becomes exactly opposite to the one at the start (see figure on the right). However, the rotor would barely move from its initial position in that amount of time due to inertia. So the rotor s magnet field would remain at the same orientation as it was at the beginning of the process. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 10

11 However, the induced torque on the rotor is now CW. In this way, the induced torque on the rotor would keep reversing direction twice in every electrical cycle, making it practically impossible for the rotor to rotate. In fact, we would need a separate process to put the rotor in motion without powering up its field windings. Once the rotor gains close to the synchronous speed, the rotor s field windings can be powered up to run the synchronous motor normally. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 11

12 AC Machines Operating Principles: Induction Motor An Induction motor also uses a rotating magnet field generated by the stator. The rotor of the induction motor, however, does not require a separate source to establish rotor s magnetic field. The rotor s magnetic field is established through the voltage in the rotor s windings induced by the stator s rotating magnetic field. Induction motors use two kind of rotors: (1) squirrel-cage rotor and (2) wound rotor. The squirrel-cage rotor has slots carved into the face of the rotor, which carry metal bars. Those bars are short circuited at either end. A wound rotor has three-phase windings in the rotor, which are the mirror image of the stator s windings. The windings are available through brush and slip ring mechanism to add extra resistance in the windings if desired. Otherwise, they are shorted at the brushes. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 12

13 AC Machines Operating Principles: Induction Motor The induced voltage in the rotor windings of an induction motor s is given by Eq. (14) (fundamentals). E = vv BB. ll (34) where, BB = is the flux density (in AA Weber/meter2 : Wb/m 2 or Telsa: T) l = active length of the conductor in the magnetic field (m) v = relative speed of the conductor (m/s) w.r.t. the stator s magnetic field Syed A Rizvi ENS 436, Department of Engineering and Environment Science 13

14 AC Machines Operating Principles: Induction Motor The figure on the right shows the orientation of the stator s magnetic field along with that of the rotor s magnetic field. The rotor s magnetic field is created by the induced voltage (the dot and cross represent the current out of the paper and in the paper, respectively). The direction of the induced torque is CCW. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 14

15 AC Machines Operating Principles: Induction Motor The figure on the right shows the orientation of the stator s magnetic field along with that of the rotor s magnetic field after half of the electrical cycle. Note that as B s reverses so do the induced voltage, current causing B r to reverse its orientation as well. The direction of the induced torque is still CCW. Syed A Rizvi ENS 436, Department of Engineering and Environment Science 15

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