Load Flow Analysis

Each bus is classified as:

• Slack bus — fixes $|V|$ and angle; balances losses.
• PV (generator) bus — specified $P$ and $|V|$.
• PQ (load) bus — specified $P$ and $Q$.

The power-flow equations are non-linear:

$P_i = \sum_k |V_i||V_k|\left(G_{ik}\cos\theta_{ik} + B_{ik}\sin\theta_{ik}\right)$

and similarly for $Q_i$, built from the bus admittance matrix $Y_{bus}$. They are solved iteratively with Gauss–Seidel, Newton–Raphson (fast, standard) or fast-decoupled methods. Load-flow studies are used for planning, contingency analysis and setting operating limits.