Session 4: Basic Operation of an Asynchronous Induction Machine
4.1 Aims and Objectives
The aim of this task is to develop simple models showing the basic control of an asynchronous induction machine in Matlab / Simulink, while the objective is a better understanding of how machines can be controlled using Simscape: Power Systems. The general principles used developing this model can be applied to any combined power electronic converter and machine system used for your project.
4.2 Introduction to the Asynchronous Induction Machine
Asynchronous induction machines use the principle of induction to operate. The rotor speed is different to that expected from the applied stator frequency and pole number due to its inherent operating principles. Lots of information concerning asynchronous induction machines will have been given to you in your undergraduate studies and earlier MSc Semester One courses; you will also learn more about the advanced control of this machine in Dr Atkinson’s Electric Drives Course EEE8014 (if you are taking it).
4.3 Task 1: Developing the Grid Connected Asynchronous Induction Machine Model using Simulink.
With the help of the ‘Simscape: Power Systems’ library, construct an asynchronous induction machine model in Simulink. On completion, the model should look like Fig. 1. Hint: do not forget the powergui block!
Page 1 of 33
The asynchronous induction machine we are going to simulate is a 7.5kW, 4 pole, star connected induction machine with the following parameters:
Parameter
Value
Rated Stator Voltage (line-line)
415Vrms
Rated Stator Current (line)
15Arms
Rated Stator Frequency (Hz)
50
Stator Resistance (Ω)
0.7767
Rotor Resistance (Ω)
0.703
Stator/ Rotor Leakage Inductance (mH)
4.51
Magnetising / Mutual Inductance (mH)
103.22
Inertia (Kg/m2)
0.19
Friction (B or F) (Nm/s)
0.014
Due to the earlier information given in Sessions 2 and 3 you should be familiar with the software and should easily be able to implement the following models in Simulink and Simscape: Power Systems
The asynchronous induction machine is in the ‘Simscape: Power Systems: Specialized Technology: Fundamental Blocks: Machines’ library; choose ‘Asynchronous Machine SI Units’. Set the machines ‘Configuration’ as shown below, while its ‘Parameters’ are shown in the above table.
Rotor type: Squirrel-cage
Squirrel cage preset model: No
Mechanical Input: Torque Tm
Reference frame: Stationary
Make sure the Initial Conditions in the ‘Parameters’ are specified as: [10000000]
Page 2 of 33
The Three Phase Programmable Voltage Source is found in ‘Simscape: Power Systems: Specialized Technology: Fundamental Blocks: Electrical Sources’, set the parameters as specified below:
Amplitude (Vrms Ph-Ph): 415
Phase (deg): 0
Freq. (Hz): 50
Up to 28 signals for the asynchronous machine can be obtained via the ‘m’ port on the block; to choose which ones you want to view use the ‘Bus Selector’ block, from ‘Simulink: Signal Routing’. Double clicking on this block allows you to choose which signals you want to view. The ‘Tm’ input on the block allow you to apply load to the machine, a positive load means the machine is operating as a motor, a negative input means a generator. Set it to 0.1 Nm.
Figure 1: Grid Connected Asynchronous Machine
Set the simulation time to 5 seconds, the ‘Solver Type’ to ‘Variable-step’ and the ‘Solver’ to ‘ode45 (Dormand-Prince)’. If your simulation is working correctly the results for the rotor speed and one phase of the stator current should look like Figs. 2 & 3.
Page 3 of 33
Figure 2: Rotor Speed (rad/s)
Figure 3: Phase A Stator Current (A)
Page 4 of 33
If you look at ‘close ups’ of the stator current between 3 and 3.1 seconds, how sinusoidal does the current waveform actually look? Try altering the ‘Relative tolerance’ in the ‘Model Configuration Parameters’ from ‘1e-3’, to ‘1e-4’ and ‘1e-5’ and re-simulate, are better results obtained?
……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………..
Run the simulations again but using the ‘ode23tb (stiff/TR-BDF2) Solver’. How do the results compare with those of the ‘ode45’ solver?
……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………..
Figure 4: Variable Step Type, ode45 (Dormand-Prince) Solver, relative tolerance 1e-3
Page 5 of 33
Figure 5: Variable Step Type, ode45 (Dormand-Prince) Solver, relative tolerance 1e-4
Figure 6: Variable Step Type, ode45 (Dormand-Prince) Solver, relative tolerance 1e-5
Page 6 of 33
Figure 7: Variable Step Type, ode23tb (stiff/TR-BDF2) Solver, relative tolerance 1e-3
Figure 8: Variable Step Type, ode23tb (stiff/TR-BDF2) Solver, relative tolerance 1e-4
Page 7 of 33
Figure 9: Variable Step Type, ode23tb (stiff/TR-BDF2) Solver, relative tolerance 1e-5
Carry out some further experiments of your own to see the effect of the different parameters options for the variable step solver, and the different solvers options on the accuracy of the waveforms and the time it takes to run the simulations.
4.4 Alternative Three Phase Signal Measurement Option
A method of looking at the Simscape: Power Systems signals was mentioned in Session 3 using the voltage and current measurement blocks; there is an alternative way of measuring three phase signals, this is the ‘Three Phase V-I Measurement block’ (I will let you find this one). Place this block as shown in Fig. 10 and compare the signals it measures with those available from the ‘Asynchronous Machine’ block, are there any differences? For this simulation use ‘ode45’ and a ‘Relative tolerance’ of ‘1e-6’. To obtain the 3 phase voltage signals from the machine you will need to obtain the vs_d and vs_q signals and transform them into three phase signals. This is a process that you will learn about in Dr Atkinson’s Electric Drives Course. For this simulation, implement the system shown in Fig. 10 using the ‘Alpha-Beta-Zero to abc’ block available in ‘Simscape: Power Systems: Specialized Technology: Control & Measurements: Transformations’.
Page 8 of 33
Figure 10: Placement of Three Phase V-I Measurment Block
……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………..
Figure 11: Three phase measurement block current
Page 9 of 33
Figure 12: Asynchronous Machine three phase current
Figure 13: Three phase measurement block voltage
Page 10 of 33
Figure 14: Asynchronous Machine three phase voltage
These quick tests have shown you how important it is to choose your Solver and tolerances wisely if using Variable Step Solvers.
Page 11 of 33
4.5 Task 2: Open Loop V/Hz Control
Open loop V/Hz is a popular simple method of scalar control of asynchronous machines. In this, the scalar quantities controlled are the magnitudes of the applied stator voltages and the excitation frequency (𝜔𝑒), these are usually controlled in a fixed (V/Hz or V/ 𝜔𝑒) ratio to maintain a constant air gap flux and to maximise the torque available. This scalar method is used where accuracy in the machines dynamic response to rotor speed demands and applied loads is not essential. The desired rotor speed is used to determine the excitation frequency with the assumption that is will run at synchronous speed, and that any error between the desired and actual rotor speeds due to the motor slip is acceptable for the application.
With a high excitation frequency the voltage drop associated with the stator impedance can be assumed to be small, therefore the following ratio can be used:
𝜓 ≈ 𝑣𝑠 𝜔𝑒
If the ratio is kept constant, a constant air gap flux is obtained.
(1)
However, at lower values of 𝜔𝑒, the stator resistance of the machine cannot be ignored, therefore a boost voltage needs to be applied ensure the air gap flux is at its rated value. There are many different methods for calculating this boost voltage, but this is beyond the scope of this simple introductory exercise. We will concentrate only on generating a variable frequency three phase sine wave and its connection via an inverter to the asynchronous machine.
4.6 Implementation
The variable frequency supply system is shown in Fig. 15, with its frequency to angle conversion system in Fig. 16. The excitation frequency is in rad/s (Hint: remember the relationship between 𝑓 and 𝜔𝑒). The angle calculator generates the angle for the three phase sinusoidal waveforms generated, remember, 1 revolution = 360 degrees = 2π radians.
For the sinusoidal waveform generators as shown in Fig. 15 use the ‘Fcn’ block. In the expressions for the three blocks, insert:
Page 12 of 33
Sin (u[1])
Sin (u[1]-(2*pi/3))
Sin (u[1]+(2*pi/3))
Whilst for the V/𝜔𝑒 ratio remember to use the per phase voltage.
For the angle calculator you will need to use a continuous time ‘Integrator’ with an external
reset, and the ‘Switch’ block, their properties are shown below: Integrator
External reset: rising
Initial condition source: internal
Initial condition: 0
Absolute tolerance: auto
Switch
Criteria for passing first input: u2 > Threshold
Threshold: 2*pi
For the simulation use the following ‘Model Configuration Parameters’ to get the best accuracy:
Type: Variable Step
Solver: ode23tb (stiff/TR-BDF2)
Max step size: 10e-6
Relative Tolerance: 1e-6
You will also need to double click on the ‘Diagnostics’ option, select ‘Connectivity’, and change ‘Mux blocks used to create bus signals’ to ‘error’.
Page 13 of 33
Look at the demanded voltage graph, for a standard mains input frequency of 50Hz, (𝜔𝑒=314.159 rad/s) what should the V/𝜔𝑒 ratio and peak of the voltages be? (Hint: remember you are looking at the phase voltages!). Are you getting what you expected?
……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………..
Figure 15: Variable Frequency Supply Simualtion Blocks
Figure 16: Excitation Frequency to Angle Converter Simualtion Blocks
Page 14 of 33
Figure 17: Angle with constant excitation frequency of 50Hz
Figure 18: Close up of angle showing reset at 2π
Page 15 of 33
Figure 19: Demanded phase voltages for constant 50Hz excitation
Figure 20: Closeup of demanded phase voltages
Page 16 of 33
4.7 Ramped Frequency Source
Replace the constant block you have used for the excitation frequency with a ‘Ramp’ block; use the following parameters. This will show the variable frequency capability of the three phase sine wave generator.
Slope: 2*pi*10
Start time: 1
Initial output: 0
Add a “Saturation” block after the “Ramp” block with an upper limit of 2*pi*50, and a lower limit of 0. This will limit the signal to 50Hz. Run the simulation for 10 seconds and look at the demanded voltages and the angle. Do the results you achieve make sense? Are you getting a stable variable frequency sine wave up to 50Hz?
……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………..
Figure 21: Excitation frequency (𝝎𝒆) (rad/s)
Page 17 of 33
Figure 22: Ramped excitation frequency angle
Figure 23: Ramped excitation frequency demanded phase voltage
Page 18 of 33
4.8 Controlling the Machine via an Inverter
For the inverter we will utilise the ‘Universal Bridge’ block which implements universal power converters with selectable topologies and power electronic devices. Look at the different options for this block, but we will only consider a device with 3 bridge arms, and use either the ‘IGBT/Diode’, ‘Average-model based VSC’, or ‘Switching-function based VSC’. Information on these can be found by clicking on the help button. The main difference we are initially concerned about is that both the ‘IGBT/Diode’ and ‘Switching-function based VSC’ options require PWM pulses to be applied, while the ‘Average-model based VSC’ just requires the voltage reference signals. This will be shown in more detail during the following simulations.
The overall simulation diagrams for the ‘Average-model based VSC’, and one for the ‘Switching-function based VSC’ and ‘IGBT/Diode’ can be seen in Figs. 24 and 25 respectively. For the ‘DC Voltage Sources’, set the voltage to ‘360V’, and for the gain block ‘1/(Vdc/2)’, set the value to ‘1/360’. In Fig. 25 the PWM in generated by the ‘PWM Generator (2-Level)’ with the following parameters:
Generator type: Three-phase bridge (6 pulses)
Mode of operation: Unsynchronized
Carrier frequency (Hz): 10000
Initial phase(degrees): 90
Sampling technique: Natural
Minimum and maximum values: [-1 1]
Sample time: 0
For the simulation use the following ‘Model Configuration Parameters’ to get the best accuracy:
Type: Variable Step
Solver: ode23tb (stiff/TR-BDF2)
Max step size: 10e-6
Relative Tolerance: 1e-6
Page 19 of 33
Make sure the 3 phase measurement block is measuring the phase to phase voltage, and for each of the different inverter options mentioned run the simulation for 5 seconds looking closely at the stator currents; how are these affected by the different inverter options? Also check how long each simulation takes for the different inverters. To check the simulation time type the following code in Matlab, where ‘vhz_3’ is the filename you have chosen. Hint: these simulations might take some time – do not start these simulations just before you have to leave!
tic,[t]=sim(‘vhz_3’);toc
……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………….. ……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………..
You will need to remember and take into account the difference in simulation times when you are carrying out the simulations for your project!
Page 20 of 33
Figure 24: Average-model based VSC Simulink Implementation
Page 21 of 33
Figure 25: Switching-function based VSC and IGBT/Diode Simulink implementation
Page 22 of 33
Figure 26: Average-model based VSC Voltage
Figure 27: Average-model based VSC current
Page 23 of 33
Figure 28: Switching-function based VSC voltage
Figure 29: Switching-function based VSC current
Page 24 of 33
Figure 30: IGBT/Diode model voltage
Figure 31: IGBT/Diode model current
Page 25 of 33
4.9 Torque / Speed and Torque / Slip Curves
To show that variation of the speed with load you should create some electromagnetic torque / rotor speed curves. To do this, decide on which inverter configuration you want to use (this should be easy after the previous testing). Set the excitation frequency to 40Hz (𝜔𝑒 = 251.3274) then run the simulation with varying loads; how does the rotor speed change?
……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………..
You can use the ‘Signal Builder’ function and Excel to help you change the load torque. For ‘Signal Builder’ initially create a set of load torque and time steps in Excel, an example of which is shown in Fig. 32. Hint: you have to start the data in A1 as shown with the time in the first column; it is also advisable to only have one sheet in your Excel document. Import the data into ‘Signal Builder’ using:
‘File: Import from File’
Browse to the correct file
On the ‘Data to Import’ section make sure you have selected the right set of data as
shown in Fig. 33.
For the ‘Placement for Selected Data’ option use ‘Replace existing dataset’, press
‘Confirm Selection’, and then ‘OK’. If you get an Import Filter warning, choose ‘No, import without saving’.
If it has worked correctly you should get a load profile as shown in Fig. 34. You may want to change the load profile to different loads and / or use an amended simulation time to get the full extent of the torque / speed curve. Hint: for your result graphs ignore the oscillatory start up conditions shown in red on the following results. For example, the 50Hz torque / speed curve is shown in Fig. 35, while the torque / slip curve is shown in Fig. 36.
For information, the slip can be calculated using the following equation:
Page 26 of 33
Where 𝑝𝑝 = number of pole pairs
Figure 32: Excel Loads
𝜔𝑠𝑙𝑖𝑝 (%) = (𝜔𝑒⁄𝑝𝑝) − 𝜔𝑟 ∗ 100 (𝜔𝑒⁄𝑝𝑝)
(2)
Figure 33: Signal Builder Import
Figure 34: Signal Builder Load Function Graph
Page 27 of 33
You can save different data to the Matlab workspace using the ‘To Workspace’ block. Its parameters are mostly self-explanatory, for the ‘Decimation’ use ‘10’, and for the ‘Save Format’, use ‘Array’.
Save the electromagnetic torque (𝑇𝑒) and the rotor speed (𝜔𝑟) from the ‘Asynchronous Machine’. Plot 𝜔𝑟 against 𝑇𝑒, the following code is for the 50Hz waveform. After you change the x and y axes properties on your graph to sensible values, a plot similar to Fig. 35 should be obtained.
plot(wr(1:35000),Te(1:35000), ‘color’, [1 0 0]);
hold on;
plot(wr(35001:end),Te(35001:end), ‘color’, [0 0 0]);
The red line shows the dynamic behaviour of the machine due to the direct online starting (the simulation was started assuming that 50Hz was instantaneously applied to the stator), while the black line is the torque / speed curve expected with load applied.
Figure 35: 50Hz Torque/Speed Curve
Page 28 of 33
For the torque / slip curve amend the following code which is for the 50Hz waveform and was used to produce Fig. 36.
slip=((((2*pi*50)/2)-wr)/((2*pi*50)/2))*100;
plot(slip(1:35000),Te(1:35000), ‘color’, [1 0 0]);
hold on;
plot(slip(35001:end),Te(35001:end), ‘color’, [0 0 0]);
Figure 36: 50Hz Torque / Slip Curve
Page 29 of 33
4.10 40Hz Torque / Speed and Torque / Slip Results
Figure 37: 40Hz Torque / Speed Curve
Figure 38: 40Hz Torque / Slip Curve
Page 30 of 33
4.11 Multiple Torque / Speed and Torque / Slip Results
Once you have worked out how to do the 40Hz simulation, see if you can plot the data for the 50Hz, 40Hz, 30Hz, 20Hz and 10Hz results on the same graphs (ignore the plotting of the initial direct online start up oscillations) to show how the torque available from the asynchronous machine changes with frequency.
Figure 39: Multiple Torque / Speed Curves with Start-up Oscillations
Page 31 of 33
Figure 40: Multiple Torque / Speed Curves without Start-up Oscillations
Figure 41: Multiple Torque / Slip Curves with Start-up Oscillations
Page 32 of 33
Figure 42: Multiple Torque / Slip Curves without Start-up Oscillations
Page 33 of 33