I examine the effects of increasing amounts of fluctuating renewable energy on residual load, which is defined as the difference between actual power demand and the feed-in of non-dispatchable and inflexible generators. I draw on policy-relevant scenarios for Germany and make use of extensive sensitivity analyses. Whereas yearly renewable surplus energy is low in most scenarios analyzed, peak surplus power can become very high. Decreasing thermal must-run requirements and increasing biomass flexibility substantially reduce surpluses. I use an optimization model to determine the storage capacities required for taking up renewable surpluses. Allowing curtailment of 1% of the yearly feed-in of non-dispatchable renewables would render storage investments largely obsolete until 2032 under the assumption of a flexible power system. Further restrictions of curtailment as well as lower system flexibility strongly increase storage requirements. By 2050, at least 10 GW of storage are required for surplus integration, of which a sizeable share is seasonal storage. Results suggest that policy makers should work toward avoiding surplus generation, in particular by decreasing the must-run of thermal generators. Concerns about surpluses should not be regarded as an obstacle to further renewable expansion. The findings are also relevant for other countries that shift toward fluctuating renewables.