GridPACK Application Concept (Steady State Powerflow)

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Steady state powerflow analysis is method of solving a general power system problem where the currents and voltages on the busses (nodes) and branches (lines) of an electric network are computed based on the impedances, current and power injections at nodes (if any), the boundary voltages (if any) and topology of the network.

Power system applications provide this information to a solver in the form of a matrix of bus admittance (called Y), bus injections (called S) and boundary conditions (e.g., V).

Because the problem is essentially non-linear, various iterative solution methods are employed to obtain the solution to this flow problem. The include

Gauss-Seidel (GS) 
This method is the simplest to describe and implement, is guaranteed to converge for any network for which a solution exists, but converges quite slowly. It is sometimes used to initialize other faster solution methods that sometimes can converge reliably (such as Newton-Raphson). The method is implicitly parallel.
Newton-Raphson (NR) 
This method requires the a Jacobian be computed and maintained for the current system. It is not guaranteed to converge but when it does converge it is quite fast. The method is not readily parallelized.
Forward-Backsweep (FBS) 
This method works only on radial flow models but is extremely fast and can be readily parallelized for more networks.
Conjugate-Gradient (CG) 
Yousu Chen TODO.