The same company that builds the battery for GM’s upcoming Bolt electric car now wants to put one in your basement — and plug it into solar panels on your roof. LG Chem and San Francisco’s Sunrun announced a partnership Wednesday to offer solar arrays paired with in-home batteries — a combination that many analysts consider the future of the solar industry. LG Chem, based in Korea, will supply lithium-ion batteries for Sunrun’s BrightBox system, which gives homeowners the ability to store solar energy generated during the day for use in the evening. Combining solar panels with batteries at a price consumers can afford has become a holy grail for the industry and is one of the driving forces behind Tesla’s proposed $2.6 billion acquisition of SolarCity. According to Hawaiian Electric Co., the cheapest residential utility rate on the islands last year was 28 cents per kilowatt hour. Under changes already approved by the California Public Utilities Commission, state residents will soon start paying different prices for electricity at different times of day, with the highest prices hitting when demand on the state’s power grid reaches its daily peak. Since Sunrun plans to own the BrightBox systems, the company may be able to sell electricity from the batteries to the utilities during peak hours, when prices are high.