DC IR-Drop Analysis of Power Distribution Networks by a Robin Transmission Condition-Enhanced Discontinuous Galerkin Method

Abstract

In this work, a novel Robin transmission condition (RTC)-enhanced discontinuous Galerkin (DG) method is proposed for the dc IR-drop analysis of power distribution networks with Joule heating effects included. Unlike the conventional DG method, the proposed DG method straightforwardly applied to discretize the second-order spatial partial differential governing equations for the electrostatic potential <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> and the steady-state temperature <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> . The numerical flux in DG used to facilitate the information exchange among neighboring subdomains introduces two additional variables: the current density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$J$ </tex-math></inline-formula> for the electrical potential equation and the thermal flux <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> for the thermal equation. To solve them, at the interface of neighboring subdomains, an RTC is presented as the second equation to establish another connection for solutions in neighboring subdomains. With this strategy, the number of degrees of freedom (DoFs) involved in the proposed RTC-DG method is dramatically reduced compared with the traditional DG method. The finalized matrix system is solved in an finite-element tearing and interconnecting (FETI)-like procedure, namely the unknowns are obtained in a subdomain-by-subdomain scheme. Finally, the accuracy and the efficiency of the proposed RTC-DG method are validated by several representative examples.