The advent of low-cost solar photovoltaics (PV) and battery electricity storage has the potential to bring about fundamental shifts in the structure of the power sector in the United States. We analyze how PV-battery systems of various sizes could reduce the dependence of residential customers on the central grid and their impact on CO2 emissions. We further analyze how the costs of such systems change as customers attempt to decrease their dependence on the grid, considering the installed cost of PV-battery systems and the cost of electricity under a net-energy metered rate structure. We analyze these relationships for residential customers in five locations across the U.S. We find that fully disconnecting from the grid with a PV-battery system is impractical for most residential customers without also having dispatchable backup generation. Finally, we estimate how the economics of behind-the-meter PV-battery systems may change if the costs of PV systems continue to fall.