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As part of early system design, one must verify that the power grid provides the underlying logic circuitry with voltage levels that are within specified ranges. In this paper, we describe a vectorless verification approach that can be applied early in the design process. We adopt an RLC model of the grid in the framework of current constraints that capture uncertainty about circuit details and activity. With just a few linear programs and one linear system solve, our proposed approach provides tight conservative bounds on the maximum and minimum worst-case voltage drops at every node of the grid. Results show the accuracy and speed of our technique thus making it practical and scalable.