The modeling of dynamical systems often leads to higher index differential-algebraic equations (DAE)$E(x,t)\dot x=f(x,t)$ containing hidden constraints leading to several problems in its direct numerical integration. Therefore, a regularization reducing the index but, in particular, preserving the set of solutions is necessary. Classical regularization approaches often are very technical or lead to DAEs which are enlarged in size or still not suitable for numerical integration due to drift.We discuss an efficient and robust numerical simulation of dynamical systems modeled using the language Modelica. We present an approach combining 1st a derivative array based regularization to obtain an equivalent overdetermined DAE with the same set of solutions and containing no hidden constraints with 2nd the subsequent numerical integration of this overdetermined DAE using adapted methods. Within the Modelica framework, currently there exist no integrator suited for overdetermined systems.