Analytic state-space description of networks including static VAr compensators

In this paper an approach for the calculation of networks, including current converter bridges is generalized to systems including static VAr compensators (SVCs). It utilizes the periodicity of all state variables in steady-state operating mode again. The entire system, consisting of the entire 3-phase network, the thyristor controlled reactor, the optionally switched capacitors and filter circuits is represented in complex space phasor components for each switching status. The resulting state space description considers the eigenvalues and switching sequence of the complete network structure. The respective linear independent circuits are coupled into a linear inhomogeneous boundary value problem which can be solved as a whole. Therefore the time functions of all state variables are obtained analytically. By further signal processing the harmonic load, power flows, reactive compensation factors and stationary resonance conditions can be calculated.