Consistent Solution for Electric Power System Simulations with inconsistent Initial Values

Consistent initial values, which fulfil the algebraic constraints, are necessary for the simulation of differential-algebraic equations. Inconsistent initial values can lead to permanently false solutions. The calculation of consistent initial values can be more expensive than the simulation itself. In this paper, the options to deal with inconsistent initial values as well as a new approach for electric power system simulations are presented. To show the influence of inconsistent initial values for an electromagnetic transient simulation of an electric power system, formulated with the extended nodal approach, the algebraic constraints are derived and systematically violated. Deduced from this, a circuit theoretical interpretation for the inconsistent values for a linear time-invariant differential-algebraic equation is presented. The discussed solution approaches are carried out by different adaptions of the differential-algebraic equation, which have the consequence that the approximated solution returns to a consistent solution after a transient. Finally, the effects of the interventions on the differential-algebraic equation system are presented and evaluated.