The vanadium redox flow battery (VRFB) is a promising grid-scale energy storage technology, but future widespread commercialization requires a considerable reduction in capital costs. Determining the appropriate battery size for the intended power range can help minimize the amount of materials needed, thereby reducing capital costs. A physics-based model is an essential tool for predicting the power range of large scale VRFB systems to aid in the design optimization process. This paper presents a modeling framework that accounts for the effects of flow rate on the pumping losses, local mass transfer rate, and nonuniform vanadium concentration in the cell. The resulting low-order model captures battery performance accurately even at high power densities and remains computationally practical for stack-level optimization and control purposes. We first use the model to devise an optimal control strategy that maximizes battery life during discharge. Assuming optimal control is implemented, we then determine the upper efficiency limits of a given VRFB system and compare the net power and associated overpotential and pumping losses at different operating points. We also investigate the effects of varying the electrode porosity, stack temperature, and total vanadium concentration on the peak power.