Hi Bikerbob,
I have an Altura Arran 'Transit' rack bag (the one with smaller, optional 'fold-out' mini-panniers/side pockets) and the internal dimensions of the rackbag/box are oddly almost exactly 32cm long by 14cm wide, although the rear of the 'box' part curves in and the width tapers to less than 14cm for the rearmost 7 or 8 cm. The internal box height is 13cm at the minimum (front) and 17cm at the maximum (back). The panniers are smaller capacity, around 25cm vertical height, max 12cm horizontal 'width' (outward from bike side) and about 22cm max length (along bike axis). The diagonal internal distance is ~28cm and they are not square, wider at top the bottom: I think will not accommodate the size you state, by either width or height, but a larger pannier would.
I've never used the box part to carry an Ezee battery, which I
think would be to big too fit (I think Ian has the same rackbag, but uses another pannier when he carries his spare battery?): I think a pannier would be the better place to carry the weight anyway, for bike stability, and more secure: although the velcro fittings hold the box fairly securely to the rack for moderate loads, a battery (if it fits the box) would be quite heavy and possibly unstable, the weight risking pulling the whole bag from its velcro attachments (depends on the weight though, but a typical NiMH 36V 9Ah would be a bit heavy). It may be
more secure if you bungee either just the battery or box containing battery, but a pannier would be both more secure & stable solution
.
Hope thats useful Bob,
Stuart.