### How do you model a harmonic current injection based on IEC as an unbalanced source?

The injection of harmonic currents is modeled in PowerFactory using the "Harmonic Sources" object (class "TypHmcur"). Various PowerFactory elements can be configured as harmonic current sources, such as the General Load (ElmLod), Static Generator (ElmGenstat) and the AC Current Source (ElmIac). The current injections are defined for each harmonic order, based on the corresponding harmonic current spectrum.

The harmonic current injection spectrum can be configured within the Harmonic Source as follows:

- IEC spectrum (input data is based on the maximum magnitude of all phases)
- Balanced spectrum (input data is based on the maximum magnitude of all phase currents along with the phase angle of the current)
- Unbalanced spectrum (input data is based on per phase current magnitude and angle)

Due to the lack of phase angle information, the IEC harmonic current spectrum (i.e. the IEC compliant measurement report) does not specify which sequence component (or sequence components) a particular harmonic order injects currents into. Although less typical, it may also be that at any of these harmonic orders, there will exist non-characteristic harmonic currents that are injected either in positive, negative, zero sequence or any combination of these. Each equipment type may have a different behaviour in terms of harmonic injections and their typical harmonic spectrum. Further information is readily available in external literature e.g. J.C.Das - Power System Harmonics and Passive Filter Designs, ISBN 978-1-118-86162-2.

As stated in the PowerFactory User Manual, if an IEC Harmonic Source is included in a simulation then:

- the orders 2,5,8,11, .. are computed in the NEGATIVE sequence (using negative sequence impedances, currents and voltages) by employing the IEC 61000-3-6 specific summation laws irrespective if the harmonic load flow calculation is set to balanced or unbalanced.

- the orders 3,6,9,12, .. are computed in the POSITIVE sequence (using POSITIVE sequence impedances, currents and voltages) by employing the fore mentioned summation laws irrespective if the harmonic load flow calculation is set to balanced or unbalanced. This consideration is taken due to the fact that normally, triplen harmonics are not existing within a high-voltage power system, due to the existence of a delta winding at the interface between transmission system and load/generation centres. As such, if any triplen harmonics would exist, then they must be of a non-zero sequence nature. PowerFactory assumes that these harmonics are in the positive sequence (in reality, this may or may not be true).

- the orders 4,7,10,13, .. are computed in the POSITIVE sequence (using POSITIVE sequence impedances, currents and voltages) by employing the fore mentioned summation laws irrespective if the harmonic load flow calculation is set to balanced or unbalanced.

As stated in the PowerFactory User Manual, if no IEC Harmonic Source is included in a simulation then:

- the calculation will not be using the IEC 61000-3-6 summation law. This is of particular advantage to employ when the model developer defines a highly detailed network containing accurate modelling of harmonic sources throughout the entire network. If, by chance, the user has information for a limited number of devices based on IEC harmonic measurement reports, then the inclusion of these injections using IEC harmonic injections will force the harmonic load flow to consider the IEC specific summation laws - thus losing much of the gained accuracy via the accurate, phase correct, modelling of all other harmonic injections. Out of this reason, it is sometimes of advantage to avoid using any IEC Harmonic Sources within a calculation.

- in order to take advantage of availability of IEC measurements but still avoid that the harmonic load flow calculation uses the IEC summation law, it should be possible to translate an IEC measurement data set into an "unbalanced, phase correct" compliant data entry.

For the purpose of translating an IEC measurement data set into an "unbalanced, phase correct" compliant data entry, then the information within the phase angle fields should follow these guidelines:

- For orders 2,5,8,11,.. one should set a phase angle of [0 0 0] if the intention is to keep the harmonic injection in its typical sequence (for these orders, typical means negative sequence)

- For orders 3,6,9,12,.. one should set a phase angle of [0 0 0] if the intention is to keep the harmonic injection in its typical sequence (for these orders, typical means zero sequence)

- For orders 3,6,9,12,.. one should set a phase angle of [0 -120 120] if the intention is to set the harmonic injection in the positive sequence, as per the assumption made within the PowerFactory harmonic load flow calculation when an IEC harmonic current source is used.

- For orders 4,7,10,13,.. one should set a phase angle of [0 0 0] if the intention is to keep the harmonic injection in its typical sequence (here typical means positive sequence)

The attached Excel-sheet contains an example on how to create an unbalanced, phase correct Harmonic Source based on the information available in an IEC report. Particular to this example is the obvious intention to maintain similar behaviour of each harmonic order as per the considerations taken for IEC sources (specifically, the triplen harmonic current orders are injected in the positive sequence). If the intention would be in fact to represent the triplen harmonics in the zero sequence (as per their typical case), then the corresponding phase angles need to be adjusted as per the guidance above.