Alternating current (AC) power flow analysis in an electrical power network

A computer-implemented method for alternating current (AC) power flow management in an electrical power network, the method comprising:

• (a) based on information relating to loads, buses connecting the loads, and transmission lines connecting the buses in the electrical power network, determining a convex approximation of AC power flows in the electrical power network, comprising convex approximation of nonlinear cosine terms associated with active power components and reactive power components of the AC power flows the cosine terms having arguments based on a phase angle difference;
• (b) using the convex approximation of the nonlinear cosine terms with arguments based on the phase angle difference to optimize a convex objective function with load variables associated with the loads of the electrical power network, the convex objective function comprising a linear constraint including an inequality that represents a relaxation of quadratic approximation of the nonlinear cosine terms, the linear constraint applied to a non-negative artificial variable {circumflex over (t)}nm∈(0,∞) of active loses and reactive loses to be greater than or equal to a square of the phase angle difference;
• and
• (c) shedding one or more of the loads based on the load values of the optimized convex objective function.