SAN FRANCISCO — The California Public Utilities Commission approved a plan on Thursday allowing providers of high-speed Internet services to test using electricity lines to deliver online access throughout the state. CPUC commissioner Rachelle Chong, who drafted the plan, said broadband over power lines, or BPL, could become a new competitor to Internet services delivered via telephone, cable and satellites and help reduce prices for consumers. BPL uses existing utility lines delivering power to neighborhoods to carry broadband signals into homes. It has been touted by equipment makers and regulators as a possible competitor to cable and telecommunications services, which handle almost all of the roughly 40 million U.S. residential broadband connections. The regulatory commission adopted guidelines for electric utilities and companies that wish to develop and test projects in California. Among the guidelines, electric utility affiliates and other developers can invest in and operate BPL systems. Utility affiliates would have to follow CPUC rules for transactions between a utility and a BPL affiliate to protect against cross-subsidies, the commission said.