ELEC3565 Electric Machines
Appendix to Part 1 of Course Assignment - DC Machines Lab
Deriving the parameters from measurements:
1) Once you have your measurements as obtained forthe DC machine labs, follow the steps below to assist you with completing part 1 of the course assignment.
2) Open MS Excel. As shown in Figure 2, type out the above measurements.
Figure 1: Excel entry for speed-current measurements
3) You should enter the value of armature voltage next to VAN. Now you have a set of speed-current measurements for one voltage case.
4) Repeat the above for two other voltages.
5) Now you should have three tables similar to that shown in Figure 1.
6) To derive the circuit parameters, y-intercept of the characteristics must be calculated first by typing the following function in MS Excel’s formula (i.e. next to fx): =INDEX(LINEST(Range of speed values, Range of current values),1,2). An example is shown in Figure 2 where the value of the y-intercept (i) is estimated in Cell E4. The range of speed values is denoted as A3:A5 and the range of current values is B3:B5.
Note that these are just example values.
Figure 2: Example of estimating the y-intercept a linear line.
7) The gradient is also needed and can be found by typing the following function: =INDEX(LINEST(Range of speed values, Range of current values),1) in the formula box. The example shown in Figure 3 estimates the gradient in Cell F4 based on the speed values in A3:A5 and the current values in B3:B5.
Figure 3: Example of estimating the gradient of a linear line.
8) For each VAN case and the expressions you derived in Section 1, estimate the machine constant, kE and armature resistance, RA. You will have three different values for kE and RA but their averages are taken as the final values of kE and RA.
Plotting Speed-Current Characteristic using y-intercept and gradient
To plot the characteristics, you must create another column in the table as shown in Figure 4 to estimate the speed using the y-intercept and gradient through the following formula:
Speed = Current *Gradient + y-intercept
where in this example, current is in Cell B3, Gradient in F4 and y-intercept in E4 so the estimated speed is calculated which is acceptably close to the measured value you have.
Figure 4: Example of estimating the speed.
Repeat the above for other motor speed-speed cases. Please note that you may need to manually type the formula for the other cases.
You can then plot speed-current characteristics in MATLAB or MS Excel. To do that in MS Excel, you could use the feature Scatter with Smooth Lines and Markers in MS Excel as shown in the following image:
File Home Insert Draw Page Layout Formulas Data Review View Help
Right click on the white box and select Select Data.
Click on Add.
Click on under Series X values
And select the data related to x-axis. For speed-current characteristics, this will be the numerical values under Current (A) column - make sure you have not selected any other text. Once you have done that, the excel data should look like the following. Make sure you have pressed Enter before you continue.
For Series Y values, repeat the above but now you need to select all the data under Motor Speed (rad/s). You should also have a meaningful name for the plot by entering some text under Series name. If you have not done this, you can right-click any empty space, select the relevant series and click edit. You could also just select the VAN voltage for a series name. There are other features to add onto your characteristics:
- Add current axis labels and meaningful chart titles by clicking on the Chart Elements and ticking on Axis Titles.
- Add minor and major lines too by right clicking the axis scale (i.e. the numbers along the axis) and selecting Add major and minor lines. Do this for both x and y axes. You finally can add more characteristics onto the same graph by right clicking on any white space of the graph and selecting Add and repeating above for different sets of speed- current data.