The invention provides a non-aqueous redox flow battery comprising a negative electrode immersed in a non-aqueous liquid negative electrolyte, a positive electrode immersed in a non-aqueous liquid positive electrolyte, and a cation-permeable separator (e.g., a porous membrane, film, sheet, or panel) between the negative electrolyte from the positive electrolyte. During charging and discharging, the electrolytes are circulated over their respective electrodes. The electrolytes each comprise an electrolyte salt (e.g., a lithium or sodium salt), a transition-metal free redox reactant, and optionally an electrochemically stable organic solvent. Each redox reactant is selected from an organic compound comprising a conjugated unsaturated moiety, a boron cluster compound, and a combination thereof. The organic redox reactant of the positive electrolyte is selected to have a higher redox potential than the redox reactant of the negative electrolyte.

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