An alternating current (AC) power flow analysis in an electrical power network. Based on information relating to buses and transmission lines connecting the buses in the electrical power network, a convex approximation of AC power flows in the electrical power network is determined. The convex approximation of the AC power flows comprises convex approximation of nonlinear cosine terms associated with active power components and reactive power components of the AC power flows. A convex objective function associated with the electrical power network is optimised using the convex approximation of the AC power flows.