Australian Open: Serena Williams in emphatic second round victory over Su-Wei Hsieh as Maria Sharapova wins

“A long time” clearly means different things to different people. Two weeks ago Serena Williams was struggling with a knee problem which forced her to withdraw halfway through her only match at the Hopman Cup, her warm-up tournament before the Australian Open.

After the world No 1 won her second-round match here in emphatic fashion, beating Taiwan’s Su-Wei Hsieh 6-1, 6-2, Williams was asked whether her knee was still bothering her. “No, it hasn't been bothering me in a long time,” the American said. “It’s been OK. It’s totally fine.”

Hsieh, the world No 90, did her best to get Williams running around the court, even throwing in the odd drop-shot return of serve, but it was to no avail. The match lasted just an hour as Williams coasted into the third round. It proved less of a test than her first-round meeting with Italy’s Camila Giorgi.

“I think I was really focused,” Williams said. “That first round really helped me because I was just fighting. I really gave a big effort there. Today again I just wanted to stay focused for the whole time.”

Williams, who hit 26 winners, was pleased above all with the consistency of her game. “I don't think I made that many errors today,” she said. “That’s something I was hopefully trying to get back into. I also moved much better today, so slowly but surely I’m feeling a little bit better.”

In the third round Williams will face Russia’s Daria Kasatkina, who beat the world No 1’s sister Venus in the first round in Auckland a fortnight ago.

“I don't think it's going to be easy,” Serena said. “Any time someone is beating Venus they are more than likely playing really good. So I definitely will be ready for that. I obviously will ask Venus what she thought of the match, and I'm sure [my coach] will know everything about her match.”

Venus, meanwhile, was fined $5,000 for missing her post-match press conference following her first-round defeat at the hands of Britain's Johanna Konta. The fine is Williams' second in a year – she was fined $3,000 for the same offence at the French Open - and the biggest ever handed to a woman for missing a press conference at a Grand Slam tournament. All players are obliged to attend press conferences after matches.

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Serena, meanwhile, is on course for a quarter-final with one of her oldest rivals, Maria Sharapova, in what would be a rematch of their final here last year. Sharapova was one of those who played under a closed roof after rain in the morning. The Russian took everything in her stride, beating Aliaksandra Sasnovich, of Belarus, 6-2, 6-1.

Sharapova has had her own problems in the build-up to the year’s opening Grand Slam event, having had to withdraw from the Brisbane International because of an arm injury. However, there was little sign of any problem as Sharapova secured a third-round meeting with Lauren Davis, of the United States.

“I felt I was more confident with my left hand today,” Sharapova said afterwards. “That's always something - especially when it's like in the hand-wrist area – that is in the back of your mind even though you're feeling it. I felt really good and confident today about it.”

Sharapova was confident enough to test her opponent with some well-judged drop shots. “When I'm aggressive and I have depth on my shots, it's just good to have that variety to bring players in, to move forward myself,” Sharapova said.

“It's actually something that I had to add, because I was getting really frustrated losing to my hitting partner all the time. He just stood so far back behind the baseline.”

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Konta and Heather Watson won their opening match in the women’s doubles, beating Gabriela Dabrowski and Alicja Rosolska 6-1, 7-6. Another British pair, Jocelyn Rae and Anna Smith, beat China’s Chen Liang and Peng Shuai 3-6, 6-2, 7-6.