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.

But the company has stumbled in China as it tries to attract customers. Worries about charging infrastructure and an official bias toward bolstering homegrown competition may have contributed to the company’s lackluster Chinese performance last year, which ended with the resignation of Tesla’s China president.

China is expected to be a trouble spot in Tesla’s earnings, which the company is set to report on Wednesday. Speaking in Detroit last month, Elon Musk, Tesla’s chief executive, acknowledged that sales in China were “unexpectedly weak” at the end of 2014. He blamed a “misperception about charging,” saying owners worried they would not be able to charge up at home.

Tesla is racing to get on Chinese maps. Since the carmaker began delivering its Model S sedans to China last April, it has built 52 free rapid Supercharger stations in 20 cities and set up about 800 other charging stations at malls, hotels and restaurants in over 70 cities. The Supercharger stations fully charge a car in about an hour.

There are now nine stores and service centers in metropolises like Beijing, Shanghai and Shenzhen, which is already one of Tesla’s highest-grossing stores worldwide, the company reported in its third-quarter 2014 shareholder letter. The United States has over 60 Tesla stores and more than 40 service centers.

“In the past few months, Tesla has made great progress in China,” the company’s China office said in an email.

But the results have been tepid. So far, Tesla has exported around 3,500 cars to China, missing the company’s sales goal of 5,000 in the country, which accounts for 30 percent of its global target. Over all, some 80,000 electric and hybrid vehicles were sold in the country last year, according to Yale Zhang, the managing director of Automotive Foresight, a consulting firm in Shanghai.

The Chinese government aims to put half a million electric cars or plug-in hybrids on the roads by this year and five million by 2020. To encourage drivers to go green, domestic electric cars receive a combined subsidy from the central and local governments of 120,000 renminbi, or about $19,000. While Tesla owners are not eligible for those subsidies because the cars are foreign-made, the city of Shanghai offers free license plates for all electric car brands, saving drivers around $12,000 in fees. These include 400 Tesla owners who received the plates in October.

However, given the six-figure price tag — compared with $70,000 in the United States — the lack of subsidies is not a deal breaker for Chinese Tesla owners. “Frankly, it really makes no difference to the people who can afford a Tesla,” Mr. Zhang said. “Tesla has succeeded not as a popular model but by being perceived as a rich person’s toy.”

A bigger concern for them is where to charge. While many American car owners live in houses with a garage, the majority of Chinese urban housing consists of low-rise multifamily units. Thus, installing residential charging facilities means negotiating with property managers or neighbors.

Xie Yujian, 39, the owner of an international trading company in coastal Hangzhou, parks four of his cars at his apartment garage but had the Tesla charger installed at his factory. “I heard you have to apply with the property company to get that type of wiring so I just couldn’t be bothered,” he said.

Mr. Xie enjoys taking his Tesla on short trips, though not the wait that comes with recharging. In Hangzhou, it takes him two to three hours total for supercharging, including the journey, he said. “I think this is probably one of the biggest challenges Tesla has to overcome.”

Tesla is hampered by concerns over its relatively tiny charging network compared with traditional gas stations or charging stations in overseas markets. While China has 52 free Supercharger stations, it trails Europe, which has over 120, as well as the United States, home to over 150.

“It will take time to build out a comprehensive charging infrastructure across the whole country,” Tesla’s China office said.

In addition to building more Supercharger stations, Tesla plans to deliver to China high-power wall chargers for home use in the first half of this year. These will reduce the time it takes to achieve a full charge — which lasts 310 miles — to five hours, from 10.

But current drivers have already found a workaround of sorts for their charging needs. Hundreds of Tesla owners are members of group chats on the popular social messaging platforms QQ and Weixin, which they use to talk shop, share complaints with upper management and arrange to charge their cars at one another’s homes. They call it “stealing electricity.”

Xiao Zufu, 44, who works in brand sales, needed to do just that on a recent trip from his home in Zhejiang Province to Shanghai, about 380 kilometers or 236 miles away. In an unfamiliar town and his battery down to about 60 kilometers of charge left, he used QQ to find a fellow Tesla owner nearby who let him charge his battery.

“It was a bit embarrassing,” he said. “If I’m driving a diesel car, even if the light has turned yellow I’m confident there’s still about 50 kilometers left in the car. But with electric cars I don’t really know for sure.”

Still, most Tesla drivers appear to be forgiving of the company’s growing pains, particularly those among China’s equivalent of Silicon Valley. “We chose to be lab rats,” said Chen Zhong, 32, the chief marketing officer of an online media company in Beijing who bought a Tesla Model S last year. For these early adopters with money to spend, the car symbolizes the high-tech culture they adore. “The first time I drove it I thought I was driving an iPad.” Owning a Tesla, he added, “makes us Internet technology people feel superior.”

Wei Jianguo, 40, an angel investor in Hangzhou, owns a Tesla in addition to a Mercedes-Benz S350 and a BMW 3 Series Gran Turismo. He does not mind the headache of finding charging stations, a problem he expects will disappear as China expands its electric vehicle infrastructure.

“It’s just like when cars first came out and affected the businesses of horse rides,” he said.