Load flow studies and applications

A load flow study is the steady-state solution of a power network: for given loads and generator outputs, it finds the voltage magnitude and phase angle at every bus, and from them the real and reactive power flow in every line and the total losses.

The inputs are the network data (the $Y_{bus}$) and the bus specifications: $V$ and $\delta$ at the slack bus, $P$ and $|V|$ at PV buses, and $P$ and $Q$ at PQ buses. The equations are non-linear, so they are solved by iteration (Gauss-Seidel, Newton-Raphson or fast decoupled).

Applications

1. System planning and expansion: testing new lines, substations and generators before they are built.
2. Operation and control: keeping bus voltages within limits by setting generator voltages, transformer taps and shunt capacitors/reactors.
3. Finding line loading: checking that lines and transformers stay below their thermal limits.
4. Loss calculation: finding total $I^2R$ losses and the best way to reduce them.
5. Economic dispatch and optimal power flow: sharing load among generators at minimum cost, including losses.
6. Contingency (security) analysis: effect of line or generator outages.
7. Reactive power planning: sizing and placing compensation.
8. Starting point for other studies: pre-fault voltages for short-circuit studies and initial conditions for stability studies.