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Highlights • Methodology for optimal power sharing between fuel cell stacks. • Solution approach broken down into off-line and on-line computations. • On-line computations reduced to simple equation solving. • Identification of globally optimal solution. Abstract In power networks, where multiple fuel cell stacks are employed in a series-parallel configuration to deliver the required power, optimal sharing of the power demand between different stacks is an important problem. This is because the total current collectively produced by all the stacks is directly proportional to the fuel utilization, through stoichiometry. As a result, one would like to produce the required power while minimizing the total current produced. In this paper, an optimization formulation is proposed for this power distribution control problem. An algorithm that identifies the globally optimal solution for this problem is developed. Through an analysis of the KKT conditions, the solution to the optimization problem is decomposed into off-line and on-line computations. The on-line computations reduce to solving a nonlinear equation. For an application with a specific V–I function derived from data, we show that analytical solutions exist for on-line computations. We also discuss the wider applicability of the proposed approach for similar problems in other domains. [ABSTRACT FROM AUTHOR]