An efficient dual algorithm for vectorless power grid verification under linear current constraints

Abstract

Vectorless power grid verification makes it possible to evaluate worst-case voltage drops without enumerating possible current waveforms. Under linear current constraints, the vectorless power grid verification problem can be formulated and solved as a linear programming (LP) problem. However, previous approaches suffer from long runtime due to the large problem size. In this paper, we design the DualVD algorithm that efficiently computes the worst-case voltage drops in an RC power grid. Our algorithm combines a novel dual approach to solve the LP problem, and a preconditioned conjugate gradient power grid analyzer. Our dual approach exploits the structure of the problem to simplify its dual problem into a convex problem, which is then solved by the cutting-plane method. Experimental results show that our algorithm is extremely efficient -it takes less than an hour to complete the verification of a power grid with more than 50K nodes and it takes less than 1 second to verify one node in a power grid with more than 500K nodes.

A hierarchical matrix inversion algorithm for vectorless power grid verification

“…Therefore, a verification approach, which is not dependent on simulation, is highly desirable. To satisfy this need, vectorless power grid verification under linear current constraints has been proposed in [1], and studied in [2], [3], [4]. All possible current waveforms of the circuit blocks are captured by a group of linear current constraints defining a feasible excitation set of currents.…”

“…Recent works [3], [4] have achieved significant speed-ups by decomposing each LP problem into two steps. In the first step, the affine function that relates the voltage drop and the currents is obtained by solving a power grid analysis problem.…”

“…In the second step, the maximum voltage drop is computed by maximizing the affine function subject to the current constraints, which is also an LP problem but with reduced number of decision variables and constraints. In [4], after an efficient dual algorithm was proposed that greatly reduces the running time for the second step, it was observed that the first step consumes more than 80% of the total running time for large power grids, and thus is the performance bottleneck of the overall approach.…”

“…Therefore, for all the nodes, essentially the whole inverse of the power grid matrix is computed in a row-by-row manner. In comparison to [4] where the rows are computed independently by the preconditioned conjugate-gradient (PCG) method [5], [6], we propose a hierarchical algorithm to speed up the matrix inversion by exploiting the fact that there are dependencies among the rows in the inverse of the matrix.…”

“…We integrate the proposed hierarchical matrix inversion algorithm with the dual algorithm in [4] to solve the vectorless power grid verification problem for RC power grids. Experimental results show that our hierarchical matrix inversion algorithm is more efficient than the approach in [4] that applies the PCG method to each node independently.…”