# How to apply power flow analysis?

I have an (AC) power grid topology with generators, consumers, power lines, tranformers, etc. I also have a "snapshot" of the system's state, i.e., I know how much real power the generators feed, how much real power is used by the consumers, I know the reactive power values, and voltages. I also know the parameters of the power grid's infrastructure such as the maximum power of the transformers or the impedance of the power lines.

The problem I am facing now is this: Suppose one generator feeds more real power, and one consumer uses more real power. How can I calculate what the load of the power grid's nodes is? I want to ascertain that, e.g., no transformer or power line is loaded beyond its limit.

I basically know that there is something called "power flow analysis," which I've been reading up. The matrices, Newton-Raphson approach to solving the equations, etc., is not the problem: What I do not know is how to apply the matrices to arrive at an answer to my question. I basically need help to formulate the equations: What are my input variables, what are my results?