Perform an Online Harmonic Analysis Using the Simscape Spectrum Analyzer Block

Harmonic Distortion

Nonlinear loads create power distortion in the form of harmonics, that is, voltages and currents that are multiples of the fundamental frequency. Harmonic waveforms can result in energy losses through heat dissipation and in reduced power quality. They can also cause equipment to malfunction or to become damaged. Standards development organizations such as the Institute of Electrical and Electronics Engineers (IEEE) and the International Electrotechnical Commission (IEC) define the recommended limits for harmonic content in electric power systems.

This example shows how to examine harmonic distortion in your model using offline, that is after simulation, and online, that is during simulation, analyses. The offline analysis uses the Simscape™ Electrical™ harmonic analysis functions and helps you to determine configuration settings for, and verify the results of, the online analysis. The online analysis uses the Simscape Spectrum Analyzer block.

Prerequisite

This example requires a simulation log variable in your MATLAB^® workspace. The model in this example is configured to log Simscape data for the whole model for the entire simulation time.

To learn how to determine if a model is configured to log simulation data, see Examine the Simulation Data Logging Configuration of a Model.

Perform an Offline Harmonic Analysis

Open the model. At the MATLAB Command Window, enter:
```
openExample("simscapeelectrical/CompositeRectifierExample")
```
The example model contains a three-phase rectifier. The model also contains a Selector block that outputs only the a-phase from three-phase current signal that it receives from the PS-Simulink Converter block.
Simulate the model.
```
sim("CompositeRectifier")
```
View the time-domain results. Open the Scope block.

The time domain analysis shows that the rectifier is converting the voltage, but it does not include any information about the frequencies in the signal.

Determine configuration settings and calculate the expected results for an online harmonic analysis. Perform an offline harmonic analysis.

The Simscape Electrical harmonic analysis functions require that you use a fixed-step solver. Determine the solver type and sample time for the model. To turn on sample-time highlighting, in the Simulink^® editor menu bar, select Debug > Information Overlays > Sample Time > Colors.

The model is running at a discrete rate, therefore it is using a fixed-step solver, with a sample time of 1e-4 s.
Use the ee_getHarmonics function to calculate the harmonic order, the harmonic magnitude, and the fundamental frequency based on the voltage source currents.
```
[harmonicOrder,harmonicMagnitude,fundamentalFrequency] = ...     
ee_getHarmonics(simlog_CompositeRectifier.Voltage_Source.I);
```
Performing an online harmonic analysis using the Spectrum Analyzer block requires that you specify a value for maximum harmonic order and the resolution bandwidth (RBW). The RBW depends on the fundamental frequency.
Extract and display the maximum harmonic order and the fundamental frequency:
```
disp(['Maximum Harmonic Order = ', num2str(max(harmonicOrder))])
disp(['Fundamental Frequency  = ', num2str(fundamentalFrequency)])
```
```
Maximum Harmonic Order = 30
Fundamental Frequency  = 60
```
Determine the peak value of the fundamental frequency. This value is useful for filtering out negligible harmonics and for verifying the results of the offline analyses.
```
fundamentalPeak = harmonicMagnitude(harmonicOrder==1); 
disp(['Peak value of fundamental = ', num2str(fundamentalPeak),' A']);
```
```
Peak value of fundamental = 1945.806 A
```

Filter out small harmonics by identifying and keeping harmonics that are greater than one thousandth of the fundamental peak frequency.

threshold = fundamentalPeak ./ 1e3;
aboveThresold = harmonicMagnitude > threshold;
harmonicOrder = harmonicOrder(aboveThresold)';
harmonicMagnitude = harmonicMagnitude(aboveThresold)';

Display the harmonic data in a MATLAB table.

harmonicRms = harmonicMagnitude./sqrt(2);
harmonicPct = 100.*harmonicMagnitude./harmonicMagnitude(harmonicOrder == 1);
harmonicTable = table(harmonicOrder,...
    harmonicMagnitude,...
    harmonicRms,...
    harmonicPct,...
    'VariableNames',{'Order','Magnitude','RMS','Percentage'});
display(harmonicTable);

harmonicTable =

  10×4 table

    Order    Magnitude     RMS      Percentage
    _____    _________    ______    __________

     1       1945.8       1375.9       100    
     5       218.86       154.75    11.248    
     7       105.83       74.835     5.439    
    11       85.135         60.2    4.3753    
    13       57.599       40.729    2.9602    
    17       50.417        35.65    2.5911    
    19       37.612       26.596     1.933    
    23       33.859       23.942    1.7401    
    25       26.507       18.743    1.3622    
    29       23.979       16.955    1.2323

Calculate the total harmonic distortion (THD) percentage using the ee_calculate_ThdPercent function.

thdPercent = ee_calculateThdPercent(harmonicOrder,harmonicMagnitude);
disp(['Total Harmonic Distortion Percentage = ' num2str(thdPercent),' %']);

Total Harmonic Distortion percentage = 14.1721 %