Redox Flow Battery (RFB) systems are promising technologies for the multi-hour electrical energy storage that will be necessary for on-demand electricity supply based on wind and solar power. Deriving maximum value from a RFB requires optimisation of both the system design and its operation. In this work three novel algebraic modelling approaches are introduced to represent RFB operation more accurately while maintaining quick optimisation times. First the typical linear programming (LP) optimisation problem is re-posed in terms of current-density rather than power, allowing voltaic losses to be expressed as a quadratic function (QP). Secondly, it is then shown that the current-density framework supports a novel constraint for the avoidance of high cell voltage that may damage the stack. Thirdly, for the first time a binary variable (MIQP) to describe active/idle states is introduced. This allows coulombic leakage and pumping losses to be modelled as fixed terms without constantly draining the RFB, and it allows for the optimisation of pump rating in a VRFB. In a day-ahead energy management case study, it is found that the QP optimisation predicts an additional 19% annual revenue when compared to the LP optimisation. This capture of the true flexibility of the RFB operation allows its full value to be assessed, and therefore advances the case for their deployment within the energy system. Furthermore, the formulations developed are not only applicable to RFBs but to the scheduling of other battery systems, particularly Li–ion, and balance of plant optimisation, such as the sizing of inverters and climate control systems in the context of parasitic losses.