Power angles are generally caused due to voltage drop due to impedance in transmission line. Power factor is caused due to phase angle between reactive and active power. How are these phase angles created in an inverter?
As you know the inverter convert DC to highly distorted AC. However, filter on the inverter output will make the signal as much close as to sinusoidal waveform. The inductance and capacitance of the filter plus that of the load will specify the phase shift. If it is more inductive than lag PF and if it is more capacitive lead PF.
An inverter produces a current waveform that is shaped by a feedback loop to be sinusoidal at the same frequency as the grid. Depending on the power topology of the inverter, some can only push power into the grid (2 quadrant) -- others can either push or pull power (4 quadrant). In a 4-quadrant inverter, the feedback loop compares the generated output current to a reference sine wave that is out-of-phase with respect to the grid voltage. The phase of that reference signal determines the power factor -- leading or lagging.
It depends where you measure the angle. At the output bornes of the inverter the angle dependes on the load. Circuits theory can be used to find the angle in lag or advance,
However, if the output of the inverter is a signal with harmonics, the angle is different for each harmonic. These angles can be calculated with circuit theory, to measure in the field is not easy,, the voltage and current of each harmonic should be measured by separating each one and by filtering each signal. Other way to obtain the angle for each harmonic is to measirung both signal: voltage and current with some instrument that make a dighital outpu of the measured signals, and later to apply FFT.