DC IR-Drop Analysis of Multilayered Power Distribution Network by Discontinuous Galerkin Method With Thermal Effects Incorporated

Abstract

Due to the temperature dependent resistivity of power delivery network (PDN) interconnects, a wiser and necessary strategy is to proceed the electrical-thermal co-simulation in order to include the thermal effects caused by Joule Heating. As a natural domain decomposition method (DDM), in this work, a discontinuous Galerkin (DG) method is proposed to facilitate the steady-state electrical and thermal co-analysis. With the intention to avoid solving a globally coupled steady-state matrix system equations resulted by the implicit numerical flux in DG, the block Thomas method is deployed to solve the entire domain in a subdomain by subdomain scheme. As a direct solver, the block Thomas method is free of convergence problem frequently occurring in iterative methods such as block Gauss-Seidel method. The capability of the proposed DG method in handling multiscale and complex 3D PDNs is validated by several representative examples.

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

“…The traditional DG method [13]- [15] solves (1) by introducing an intermediate variable J, then ( 1) is able to be reduced into two first-order PDEs defined by…”

“…In the traditional DG methods such as the works in [13]- [15], the auxiliary equation is obtained via transforming the second-order PDE in (1) into two first-order PDEs, but which makes J as a volume unknown, i.e., it has to be solved in the whole computational domain. As a result, the number of DoFs increases dramatically, resulting in excessively computational cost.…”

“…It is noted that the numerical flux introduces new variable named as thermal flux q, thus to solve it, another auxiliary equation is needed. In traditional DG method, the PDE defined as ∇ • q = Q is utilized as the auxiliary equation [13]- [15]. As a consequence, the unknown q has to be evaluated in the entire computational region, which no doubt increases the computational burden considerably.…”

“…Algorithm 1 Electrical-Thermal Co-simulation [15] 1: Initializing: Let T = T 0 , ρ = ρ 0 , and define the stop criterion δ 0 as well as the number of iterations N 2: for i = 1 : N do Update the resistivity according to (39) 7:…”

“…With similar methodology, in [14], the DG method is extended to conduct the transient electromagnetic-thermal co-simulation for dispersive media. A further step is made in [15],…”