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Induction Machines Introduction Most industrial motors are squirrel cage induction machines because of their simple and robust construction, low cost, minimal maintenance, and inherent overload protection. However, induction generators are much less widely used because the drive speed, electrical frequency, voltage, load, and equivalent terminal capacitance must be juggled to provide both the reactive excitation power to the machine and the varying real power to the load. This type of generator is not widely used outside the wind turbine industry, and in small hydropower units Construction An induction machine has two main parts - a stationary stator • • consisting of a steel frame that supports a hollow, cylindrical core core, constructed from stacked laminations, having a number of evenly spaced slots, providing the space for the stator winding Stator of IM 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. Construction Squirrel cage rotor (copper) Wound rotor Notice the slip rings Construction Slip rings Cutaway in a typical woundrotor IM. Notice the brushes and the slip rings Brushes Principle of operation The stator is usually connected to the grid and, thus, the stator is magnetized A rotating magnetic field with constant magnitude is produced, rotating with a speed nsync 120 f e P rpm Principle of operation contd.. In order to generate power the rotor speed must be slightly above the synchronous speed The harder the rotor is cranked, the more power will be fed into the electrical grid The Slip s nsync nm nsync Where s is the slip. Slip is one of the most important variables in the control and operation of induction machines. s=0 : if the rotor runs at synchronous speed s=1 : if the rotor is stationary s is –ve : if the rotor runs at a speed above the synchronous speed s is +ve : if the rotor runs at a speed below the synchronous speed Frequency The frequency of the voltage induced in the rotor is given by fr Pn 120 Where fr = the rotor current frequency (Hz) P = number of stator poles n = slip speed (rpm) P (ns nm ) fr 120 P sns sf e 120 Alternative Rotor Constructions High efficiency at normal operating conditions requires a low rotor resistance. On the other hand, a high rotor resistance is required to produce a high starting torque and to keep the magnitude of the starting current low and the power factor high. The wound rotor is one way of meeting the above mentioned need for varying the rotor resistance at different operating conditions. Wound-rotor motors are, however, more expensive than squirrel-cage motors. Effect of the rotor resistance the torque-slip curves. Double Squirrel-Cage Rotor Construction Following double squirrel-cage arrangements can also be used to obtained a high value of effective resistance at starting and a low value of the resistance at fullload operation. It consists of two layers of bars, both short-circuited by end rings. The upper bars are small in cross-section and have a high resistance. They are placed near the rotor surface so that the leakage flux sees a path of high reluctance; consequently, they have a low leakage inductance. The lower bars have a large cross-section, a lower resistance and a high leakage inductance. Double squirrel-cage rotor bars Double Squirrel-Cage Rotor Construction (cont’d) At starting, rotor frequency is high and very little current flows through the lower bars; the effective resistance of the rotor is then the high resistance upper bars. At normal low slip operation, leakage reactances are negligible, and the rotor current flows largely through the low resistance lower bars; the effective rotor resistance is equal to that of the two sets of bars in parallel. Double squirrel-cage rotor bars Deep-Bar Rotor Construction The use of deep, narrow rotor bars produces torque-slip characteristics similar to those of a double-cage rotor. Leakage inductance of the top cross-section of the rotor bar is relatively low; the lower sections have progressively higher leakage inductance. At starting, due to the high rotor frequency, the current is concentrated towards the top layers of the rotor bar. At full-load operation, the current distribution becomes uniform and the effective resistance is low. Deep-bar rotor construction Equivalent Circuit with a Double Cage or Deep Bar Rotor Equivalent circuit of a singlecage induction motor (with one rotor winding). Equivalent circuit of a doublecage induction motor (two rotor windings). Equivalent Circuit Single Rotor Circuit Representation For system studies, the rotor should be represented by a single rotor circuit whose parameters vary as a function of slip, s. m 2 ms 2 R1 Rr 0 Rr s Rr 0 m2 s2 Rr 0 mR1 R2 X r s X 1 m2 s2 where, RR Rr 0 1 2 R1 R2 m R1 R2 X2 Modeling Induction Machines In developing the model of induction machines, following aspects will differ from those of synchronous machines: The d- and q-axis equivalent circuits are identical as the rotor has symmetrical structure. The rotor speed is not fixed but varies with load. This has an impact on the selection of the d-q reference frame. There is no excitation source to the rotor windings. Consequently, the dynamics of the rotor circuits are determined by slip. The current induced in the shorted rotor windings produce a field with the same number of poles as that produced by the stator windings. Rotor windings may therefore be modeled by an equivalent threephase winding. Stator and Rotor Circuits r t 1 s s t v a v b v c a R s p b c v A v B vC A R r p B C Rs i a i b R s ic Rr i A i B Rr iC Equivalent Circuit We can rearrange the equivalent circuit as follows Actual rotor resistance Resistance equivalent to mechanical load Power losses in Induction machines Copper losses - Copper loss in the stator (PSCL) = I12R1 Copper loss in the rotor (PRCL) = I22R2 Core loss (Pcore) Mechanical power loss due to friction and windage How this power flow in the motor? Power flow in IM Power relations Pin 3 VL I L cos 3 Vph I ph cos PSCL 3 I12 R1 PAG Pin ( PSCL Pcore ) PRCL 3I 22 R2 Pconv PAG PRCL Pout Pconv ( Pf w Pstray ) Torque, power and Thevenin’s Theorem V1eq jX M V1 R1 j ( X 1 X M ) Req jX eq ( R1 jX 1 ) // jX M Torque, power and Thevenin’s Theorem I2 V1eq ZT V1eq 2 R2 2 R ( X X ) eq eq 2 s Then the power converted to mechanical (Pconv) Pconv R2 (1 s ) I s 2 2 And the internal mechanical torque (Tconv) Tconv Pconv m Pconv (1 s )s R2 I s 2 2 s Torque, power and Thevenin’s Theorem Tconv V1eq 1 2 s R R2 ( X X ) 2 eq 2 eq s R2 s R2 V 1 s 2 s R2 2 R ( X X ) eq eq 2 s 2 1eq Tconv 2 Torque-speed characteristics Typical torque-speed characteristics of induction motor Maximum torque Maximum torque occurs when the power transferred to R2/s is maximum. This condition occurs when R2/s equals the magnitude of the impedance Req + j (Xeq + X2) R2 Req2 ( X eq X 2 )2 sTmax sTmax R2 Req2 ( X eq X 2 )2 Maximum torque The corresponding maximum torque of an induction motor equals Tmax 2 V 1 eq 2s Req Req2 ( X eq X 2 )2 The slip at maximum torque is directly proportional to the rotor resistance R2 The maximum torque is independent of R2 Maximum torque Rotor resistance can be increased by inserting external resistance in the rotor of a wound-rotor induction motor. The value of the maximum torque remains unaffected but the speed at which it occurs can be controlled. Maximum torque Effect of rotor resistance on torque-speed characteristic MATLAB/SIMULINK Simulation d-q Axis Model of IM Model Parameters Simulink Block Configuration d-q Axis Frame Transformations d-q Axis Frame Transformations cont’d.. Simulink Block Parameters Simulink Block Parameters cont’d.. Simulink Block Advanced Properties Input/ Output Parameters Input/ Output Parameters cont’d.. Motor Mode Operation of IM Speed-Torque Characteristics Rotor Current & Stator Current Characteristics PWM Inverter Output Effect of Saturation on IM Saturation Parameters Saturation Model Accuracy