1. Create a MATLAB script for parameters.
Power rating |
3.7kW |
Rated speed |
855 rpm |
Rated voltage |
220V |
Rated frequency |
60Hz |
Rated current |
17A |
Rated torque |
41.3Nm |
Poles |
8 |
Stator resistance |
0.4 ohm |
Rotor resistance |
0.4 ohm |
Magnetizing inductance |
29.4mH |
Stator leakage inductance |
2.1mH |
Rotor leakage inductance |
2.5mH |
2. Implement the model shown in Fig. 1 using Simulink. For this, first we have to put all differential equations under state-space form 𝑥̇ = (𝑥, 𝑢). From Eqs. (1) and (3), there are four differential equations. Once they are built, each equation has to be numerically solved using the block “integrator” in Simulink. To complete the model, Park and alpha- beta transformations have to be implemented (see Fig. 1).
3. Add a three-phase voltage source (three sinus blocks from “Sources” in Simulink library) with:
o Voltage amplitude: 100 V
o Voltage frequency: 20 Hz
4. Set the solver as “Fixed-step” and pick “ode4” in the list of the solvers. Select the step- size and the simulation time.
5. Run the Simulink model and comment the following results:
cψ, cT S(θ) |
So |
S1 |
S2 |
S3 |
S4 |
S5 |
|
cψ = 1 |
cT = 1 |
1,1,0 |
0,1,0 |
0,1,1 |
0,0,1 |
1,0,1 |
1,0,0 |
cT = 0 |
1,1,1 |
0,0,0 |
1,1,1 |
0,0,0 |
1,1,1 |
0,0,0 |
|
cT = -1 |
1,0,1 |
1,0,0 |
1,1,0 |
0,1,0 |
0,1,1 |
0,0,1 |
|
cψ = 0 |
cT = 1 |
0,1,0 |
0,1,1 |
0,0,1 |
1,0,1 |
1,0,0 |
1,1,0 |
cT = 0 |
0,0,0 |
1,1,1 |
0,0,0 |
1,1,1 |
0,0,0 |
1,1,1 |
|
cT = -1 |
0,0,1 |
1,0,1 |
1,0,0 |
1,1,0 |
0,1,0 |
0,1,1 |
• Rotor speed
• Phase currents
• Motor torque
1. Develop a dynamic model of induction machine using electrical and mechanical equations. The parameters of the machine are given below.
2. DC bus voltage is 330V, switching frequency is 5 kHz. Assume a load torque which is proportional to speed. Verify the model by running the machine model in open loop V/f scheme and observe the three phase currents and machine speed for different excitation voltages and frequencies, maintaining V/f ratio constant
3. Implement the direct torque control strategy using stator flux estimation
Assume the reference value of flux to be at the rated value, ѱs* of 0.8Wb, and flux error band of ±10% for the hysteresis comparator of flux.
5. Implement the look up table for switching voltage vectors based on the outputs of flux and torque hysteresis comparators, and sector location of stator flux:
6. Consider a torque error band of ±10% for the hysteresis comparator of torque. Run the machine under Direct Torque Control with fixed torque reference of Te* = 20Nm. Observe
(a) reference and estimated torque, (b) actual and estimated stator flux, and (c) three phase currents.
7. Implement the speed control loop. Perform ramping of reference speed from 0 to 800 rpm in 10 seconds, and observe the actual speed, torque and flux waveforms.
8. Perform step change in load from 0 to 30Nm, at a speed of 500 rpm operation, and observe the speed tracking accuracy of machine speed. Observe the same set of waveforms for load removal in steps of 10Nm from 30Nm to 0 torque over 10 seconds.
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