Numerical integration solution of stationary power systems induced by the port-based approach

This paper proposes the application of phasor bond graphs (PhBG) as a tool for a numerical integration solution of the power flow problem. PhBG’s are multiport elements with two-dimensional multibond as representation of the real and imaginary part of a phasor. The methodology suggested consist in inserting dynamic C-elements into the PhBG model. A C-element is connected to each 0-junction where the voltage is unknown. Therefore, they act as a kind of controller by integrating the current error in a node until the voltage has reached the equilibrium point. In other words: they introduce a relaxation process by breaking the algebraic loops in the implicit algebraic model