# Harmonic Analysis of the Transformer in Renewable Energy Systems and Microgrids

In renewable energy systems and microgrids, the transformer windings always use a Y connection at the LV side, and Д connection at the distribution network side or high-voltage side, with the voltage around 10-12 kV, as shown in Figure 6.25. Therefore, the harmonic analysis model of the transformer can be considered as either a voltage source-driven or current source-driven HBFEM model from the LV side.

The waveforms of voltage and current in the LV side contain harmonics due to the transformer being connected to the DC/AC inverters or power electronic drives, are illustrated in Figure 6.26.

Figure 6.25 Transformer with Y/Д connected to the grid

Figure 6.26 Waveforms of voltage and current in the LV side due to power electronic devices

Based on Maxwell equations and a quasi-static magnetic field expressed in Equation (6-2), the magnetic vector potential *A* on the arbitrary node *i* in the HBFEM descretized system and the source current density *J _{s}* can be respectively expressed as:

where harmonic *k* includes all kinds of harmonics generated by power electronic devices, but only a finite number is required in the real system.