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The reduction in PV prices and interest in energy independence accelerate the adoption of residential battery storage. This storage can support various functions of an energy system undergoing decarbonization. In this work, operative benefits of storage from the system perspective, namely, generation cost reduction and congestion mitigation, are investigated. Germany is chosen as a case study due to its strong reliance on variable renewable energy. For the analysis, an economic dispatch model with a high spatial resolution is coupled with a pan-European transmission grid model. It is shown that the system's generation costs are highest when the assets are used only to maximize PV self-consumption, and the costs are lowest when the storage also reacts to the market dynamics. This amounts to a 6% cost reduction. Both operation strategies result in an equal level of grid congestion and infrastructure loading. This is improved with a strategy that accounts for regional peak reduction as a secondary objective. The high congestion level emphasizes that grid expansion needs to keep pace with the generation and electrification expansion necessary to decarbonize other sectors. Lastly, policymakers should enable multipurpose utilization, e.g., via the introduction of market-oriented retail electricity prices with intervention options for grid operators. [ABSTRACT FROM AUTHOR]