A hierarchical matrix inversion algorithm for vectorless power grid verification

Abstract

Abstract-Vectorless power grid verification is a powerful technique to validate the robustness of the on-chip power distribution network for all possible current waveforms. Formulated and solved as linear programming problems, vectorless power grid verification demands intensive computational power due to the large number of nodes in modern power grids. Previous work showed that the performance bottleneck of this powerful technique is within the sub-problem of power grid analysis, which essentially computes the inverse of the sparse but large power grid matrix. In this paper, we propose a hierarchical matrix inversion algorithm to compute the rows of the inverse efficiently by exploiting the structure of the power grid. The proposed algorithm is integrated with a previous dual algorithm addressing an orthogonal sub-problem for vectorless power grid verification. Results show that the proposed hierarchical algorithm accelerates the matrix inversion significantly, and thus makes the overall vectorless power grid verification efficient.

Verifying RLC Power Grids With Transient Current Constraints

“…From the circuit perspective, this symmetry is due to the fact that all the R/L/C components are bidirectional and linear. It has been employed to formulate the voltage noise of each node as an affine function of current sources in (12), where c j,k is the vector of voltage noise responses of all the nodes at time t = k t corresponding to the impulse current excitation at node j when t = t. Note that (12) can also be viewed as the convolution of impulse responses and inputs.…”

“…For efficient verification of power grids, [11] uses an approximate inverse technique to generate a reduced-size LP problem for each node, [12] designs a hierarchical matrix inversion algorithm to compute the inverse of the power grid matrix, [13] and [14] propose convex dual algorithms to solve the LP problem fast, [15] exploits the dominance relations among node voltage noises to reduce the number of LP problems, and [16] proposes a fast approach to compute the bounds of voltage noises in an RLC power grid. Moreover, it is proposed in [17] that the VDD network and the GND network of the power grid should be verified together, because their voltage noises have mutual effect through the decoupling capacitors.…”

Smart Grid: Advanced Electricity Distribution Network

“…According to this program the European electricity networks should be flexible to requests of customers, available to network users and renewable power sources, secure and endowed with high quality of power supply. [9] …”

Vectorless verification of RLC power grids with transient current constraints

“…To enable early power grid verification, vectorless verification approaches have been proposed [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. These approaches use linear current constraints to restrict the feasible set of all possible current waveforms, then solve linear programming (LP) problems to evaluate the worst-case voltage noise.…”

“…The initial vectorless approach [7] considers the DC analysis model, and it is extended to handle RC and RLC power grids in [8] and [9], respectively. Reference [10] uses an approximate inverse technique to generate a reduced-size LP problem for each node, [11] designs a hierarchical matrix inversion algorithm to compute the inverse of the power grid matrix, [12] and [13] propose convex dual algorithms to solve the LP problem fast. Besides, wavelet analysis is employed in [14] to characterize current excitations in order to identify the worst-case voltage fluctuations.…”