[FEATURE] Use more numerically stable method to calculate source injection in power flow

[TonyXiang8787]

Background

The current implementation of power flow treats each source as a Thévenin's equivalence with an ideal voltage source and an internal impedance. The size of the impedance depends on the short circuit power of the source. In this way, we can cope with multiple sources within one interconnected grid. The contribution of each source is determined by their reference voltage and internal impedance.

Problem

You do not get the same voltage at the node as the reference voltage of the source, due to the voltage drop in the internal impedance. Users who wish to match the reference voltage exactly need to specify a large short circuit power (sk). However, this might cause numerical stability issue.

Experiment

We have conducted an experiment to see the effect of large sk for source. We have drawn the following conclusions.

• A high short circuit power sk in sources will force the node voltage to approach to the source u_ref. The calculation itself will not have numerical stability issue.
• The current way of calculating source injection power does suffer from numerical instability. The votlage difference between source node and source u_ref is too close.
• We need to use the node admittance matrix to help with calculation of source injection.

Proposal

As the conclusion of the experiment, we need to use node admittance matrix to calculation source injection, as described below in the conclusion chapter of the experiment.