An analytical model for shunt currents in electrolyser, fuel cell, and flow battery stacks

In a bipolar stack, electrochemical cells are electronically connected in series. If the electrolyte resistance between cells through the manifold is insufficient, some current will leak out of the cells. This reduces overall efficiency, an important loss mechanism to consider when designing a stack. Many works exist in the literature that model these shunt currents through an equivalent circuit with resistances R io into or out of the cells, R mn in the manifold between cells, and a linearised cell voltage with offset V lin and resistance R lin . However, these typically require a numerical solution. We discuss the exact analytical solution, which gives − ( V lin − I R lin ) / ( R mn + R lin + 12 R io / ( N ( N + 1 ) ) ) as a new intuitive, simple approximation for the average manifold shunt current. In an electrolyser, V lin < 0 and shunt currents increase with increasing current I . In a discharging (flow) battery, V lin > 0 and shunt currents are negative, as they run in a direction opposite to the stack current. We use this model to provide clear engineering guidelines for stack design. The exact and approximate solutions are highly practical and insightful results that can be easily used for optimisation and should find widespread use in various industrially relevant applications.