Generalized Power Flow Analysis of Electrical Power Systems Modeled as Mixed Single-Phase/Three-Phase Sub-Systems

Electrical power generation, transmission and distribution systems are often simulated through the single-phase equivalent model by assuming the presence of only the positive sequence in the real system. The well known power flow (pf) analysis is typically used to determine the steady state solution of these single-phase models. After the pf solution was determined, other elements, such as for example synchronous generators and controllers, are initialised. This provides the initial conditions to subsequent transient stability analyses. Nowadays, this simulation approach may be no longer feasible due to the large penetration of unbalanced and/or electronic elements in the power systems. In this paper we present a novel numerical method that allows to freely compute the steady state solution of complex power systems made up of a 'mixing' of conventional single-phase models and more complex, detailed three-phase models, for example of some portions of the transmission system and of the distribution ones. This steady state solution can be viewed as a generalization and/or an extension of the conventional pf.