Hybrid Symbolic-Numeric Library for Power System Modeling and Analysis

With the recent booming of open-source packages for scientific computing, power system simulation is being revisited to reduce the programming efforts for modeling and analysis. Existing open-source tools require manual efforts to develop code for numerical equations and sparse Jacobians. Such work would become repeated, tedious and error-prone when a researcher needs to implement complex models with a large number of equations. This paper proposes a two-layer hybrid library consisted of a symbolic layer for descriptive modeling and a numeric layer for vector-based numerical computation. The open-source library allows to implement differential-algebraic equation (DAE)-based models with descriptive equation strings, which will be transparently generated into robust and fast numerical simulation code and high-quality documentation. Thus, complex models and systems can be easily prototyped and simulated. These two layers are decoupled so that the symbolic layer is case-independent, and existing numerical programs can be reused. Implementation details in indexing, equation evaluation, and Jacobian evaluation are discussed. Case studies present a) implementation of turbine governor model TGOV1, b) the power flow calculation for MATPOWER test systems, c) the validation against commercial software using Kundur's two-area system with GENROU, EXDC2 and TGOV1 models, and d) the full eigenvalue analysis for Kundur's system.