BEIJING — For $104,000, Yu Hangmei expected a car that could, at the very least, be driven. What Ms. Yu said she got instead was a new electric Tesla Model S sedan and a malfunctioning charging station.

While driving through her town in coastal Zhejiang Province recently, Ms. Yu, 45, realized that even though she had plugged in the vehicle, the battery was almost dead. “I thought after a day of charging it was fully charged, but turns out it wasn’t charged at all,” said Ms. Yu, an artifact exporter. Tesla owners need an electric charger specifically calibrated to the vehicle’s voltage and current requirements, still something of a rarity near her home. “Luckily I bumped into a fellow Tesla owner online who let me charge at his place. It took three hours.”

Tesla owners in China are a well-connected bunch. Not only do they tend to be wealthy, but their avid use of social media means word of such car problems can spread in minutes. And finding charging stations is a regular complaint.

It is proving to be a major issue for Tesla’s grand designs in the world’s largest auto market.

China would seem to have all the right ingredients for Tesla, which is based in Palo Alto, Calif. The country has the second-highest number of millionaires worldwide, after the United States. And the government sees electric vehicles as a tool for fixing the nation’s notorious smog problem.