How can a harmonic voltage spectrum be converted to a harmonic current injection?

Power Quality

An equivalent voltage distortion of a voltage source can be achieved by a current source by defining a harmonic current type that matches the phase currents of the voltage source. This can be useful in case that an expansion of a grid where harmonic sources already exist need to be analyzed and the only information regarding the existing harmonics is a voltage measurement. 


Assuming a harmonic voltage measurement is present and needs to be converted into current injections, the following steps need to be taken:

1. Convert the measurement data from phase voltage distortions (and angles) to positive, negative and zero sequence voltage injections (and angles). This step may be skipped if the measurement data is already in the appropriate format. This needs to be done because the AC voltage source requires this format to define harmonic voltage injections. An example measurement file with conversion can be found in the attached Excel file "Harmonic_Distortion_Measurement".

The measurement point in the exemplary network model is connected to the slack (external grid) through a YNd5-transformer, which causes a phase shift in the voltage at the measurement point. In order to consider this angle and result in exactly the measured values, the angle for positive and negative sequence has to be corrected. The phase shift can be determined through a load flow calculation evaluating the initial phase shift "b:phiini" (found in the Calculation Parameter Varaible Set on the Basic Data page in the variable selection dialog). The -2.618 radians correspond to -150 degrees. For the positive sequence the angles have to be increased in order to result together with the -150 degrees in the desired measured angle values. For the negative sequence, the angle has to be subtracted.

2. Connect a voltage source to the busbar at which the measurement was recorded. Set the voltage source type to "Ideal RC-Source" under the "Basic Data" page. Enter the converted sequence voltage distortion data under the "Harmonic/Power Quality" page of the voltage source. Make sure to select a phase correct input type to consider the phase angles. In the attached PowerFactory project, the sample measurement data was entered in the study case "2. Added voltage source from measurement" for the AC voltage source "Measurement Source".

3. Calculate an unbalanced harmonic load flow and record the phase currents (m:I:bus1:{A,B,C}) as well as the absolute current angles (m:phii:bus1:{A,B,C}) of the AC voltage source which is responsible for the harmonic voltage injection. This data is the result of the harmonic voltage spectrum at that specific node impedance and serves as input data for the current source in the next step.

4. Connect an AC current source to the same busbar as the AC voltage source. Disable the AC voltage source. Set the current setpoint to 0 p.u. under the "Load Flow" page to avoid interference with the fundamental frequency load flow. Under the "harmonics/Power Quality" page, set the conductances and susceptances of all sequences to 0 S. This is models the current source as an ideal current source and mimics the behaviour of the ideal harmonic voltage source defined in step 2.

5. Create a harmonic current source type (phase correct) in the project library and enter the resulting phase currents that have been extracted from the AC voltage source. Link this current source type to the AC current source. Mind the rated current of the AC current source. It is thus recommended to set a rated current of 100 A in the current source if the measured currents of the voltage source are in A. This will not require any conversion multiplier for the harmonic current source type, as it requires an input of the harmonic phase current to be in % of the nominal current. Leave the phase angles at 0 for now.

6. Execute an unbalanced harmonic load flow and record the phase currents (m:I:bus1:{A,B,C}) and their absolute angles (m:phii:bus1:{A,B,C}) of the AC current source, preferably in a bar graph. The current magnitudes should now match with those resulting from the AC voltage source in an earlier calculation. Compare the current phase angles of AC current source and AC voltage source (from previous calculation in step 3) and use an external tool (Spreadsheet software of your choice works well) to determine the harmonic phase angles for the current source type. The formula used should be: phase angle of current source - phase angle voltage source.

7. Check that the correct phase angles of the current source currents are reached when the correction phase angles are entered into the harmonic current source type.

The result of all steps is a phase correct behaviour of the harmonic voltage distortion by the current source as caused by the original voltage source. This is only true if the impedance of the system does not change. The attached PowerFactory project contains two study cases where steps 3 to 7 are executed and bar plots have been added to visualise the results. The project uses a sample measurement that is also attached.