MADRID -- Spain's number one seed, Rafael Nadal began his Mutua Madrid Open campaign with an easy win over fellow countryman, Carlos Alcaraz's 6-1, 6-2 on Wednesday.

Alcaraz was celebrating his 18th birthday but got no presents in what had been billed as a meeting of the generations of Spanish tennis as Nadal completed his progress in an hour and 13 minutes.

Second seed Daniil Medvedev ended a six-game losing streak on clay but had to come back from a set down before taking a hard-fought 4-6, 6-4, 6-2 victory over Spain's Alejandro David in two hours and 13 minutes.

Speaking after the match, the Russian said he felt the fact Madrid is played at altitude meant the balls fly faster, which suits his style of play.

Former Madrid winner and No 5 seed, Alexander Zverev also impressed with a 6-3, 6-2 win over former finalist Kei Nishikori in just 74 minutes.

"Kei is someone who has done well here, reaching the final and he has beaten me on clay before. I'm definitely happy with this performance. I feel comfortable here," commented Zverev after his win.

The German will play current British number one, Dan Evans in the third round after the Brit progressed 6-7(5), 6-2, 6-3 against John Millman in a match that saw him save eight out of nine break points

In the women's tournament, No 1 seed, Ashleigh Barty extended her winning run on clay to 15 matches as she booked a semifinal appearance against Spanish wildcard Paula Badosa, with a 6-1, 3-6, 6-3 defeat of No 9 seed Petra Kvitova.

Barty dominated the first set as Kvitova making too many unforced errors, but her rival recovered in the second with some ferocious serve-volley tennis, before Barty steadied herself and some excellent lobs helped her home in the decisive set.

"It's important not to panic, but everyone emotionally has different ways that they play on the court. I have always been quite calm on the court," the Australian commented afterward.

Badosa continued her excellent form in Madrid and was cheered on by a partisan crowd as she defeated No 8 seed, Belinda Bencic, 6-4, 7-5.

Anastasia Pavlyuchenko won a close quarterfinal against Karolina Muchova 7-6(4), 7-6(2) and will play the winner of the quarter-final between No 7 seed Arnya Sabalenka and 13th seeded Elsie Mertens.