A conformable battery wherein the outer casing has an upper face plate, a lower face plate, and at least one perimetric wall, and an interior of the battery comprising a grid of walls extending from the upper face plate to the lower face plate and connecting to the at least one perimetric wall, thereby dividing the interior of the battery into at least two compartments and increasing the battery's structural stiffness and ability to sustain increased internal pressure. Each compartment contains an electrochemically active plate stack, and a network of electrical conductors provides electrical connection between the plate stacks in each of the compartment. The battery may further comprise a reservoir containing an acid additive which, when released into each of the compartments, shifts the battery from a low power mode into a high power mode.