  We consider linear magneto-quasistatic field equations which arise in
simulation of low-frequency electromagnetic devices coupled to electrical
circuits. A finite element discretization of such equations on 3D domains leads
to a singular system of differential-algebraic equations. First, we study the
structural properties of such a system and present a new regularization
approach based on projecting out the singular state components. Furthermore, we
present a Lyapunov-based balanced truncation model reduction method which
preserves stability and passivity. By making use of the underlying structure of
the problem, we develop an efficient model reduction algorithm. Numerical
experiments demonstrate its performance on a test example.
