The bombardment on Wednesday blasted targets in seven Ukrainian regions, including the Kyiv area and parts of the south and west, damaging homes and the country's rail network, authorities said.
Three people, including an eight-year-old girl, were injured, according to officials.
By taking out the power, the Kremlin's forces aim to rob Ukrainian manufacturing of its energy supply, especially military plants, and crush public morale.
The mass barrages also drain Ukrainian air defences of ammunition as Kyiv's depleted forces await delivery of the latest batch of promised Western military support.
Ukrainian officials have been pleading for more Nato-standard air defence systems, such as Patriots.
Russia pummelled Ukraine's energy infrastructure during the "blackout winter" of 2022-23.
In March, it launched a new wave of attacks, one of which completely destroyed the Trypilska power plant near Kyiv, one of the country's biggest.
Russian President Vladimir Putin has framed the attacks as retaliation for Ukrainian long-range strikes on Russian oil refineries.
On Wednesday, a Ukrainian attack hit an oil terminal, injuring five workers and starting a fire, Russia-appointed authorities in the partially occupied Luhansk region said.
Russian bombardments, though frequent, have become less regular in recent weeks, and Ukrainian officials suspect Moscow is stockpiling resources ahead of a major battlefield offensive that could come within weeks.
The 1,000-kilometre (600 mile) front line has changed little since the early months of the war, but Russia has recently made small but steady gains in some areas as Ukraine battles with a lack of manpower and a shortage of weapons.
In a social media post, Mr Zelensky noted that Wednesday's attacks occurred on the day that Ukraine observes the end of European fighting in World War Two and equated Ukraine's current struggle with that conflict.
National electrical grid operator Ukrenergo said facilities were hit in the Vinnytsia, Zaporizhzhia, Kirovohrad, Poltava and Ivano-Frankivsk regions.
Two energy facilities were hit in the Lviv region, which is in the country's far west and distant from the fighting's front lines, according to regional Governor Maksym Kozytskyi.
DTEK, Ukraine's biggest private energy supplier, said the attack "seriously damaged" equipment at three of its thermal power plants.
The attack was the fifth in the last six weeks targeting the company's facilities, DTEK said.
Overall, since the beginning of Russia's full-scale invasion in February 2022, the company's assets have come under attack nearly 180 times, injuring 51 workers and killing three, it said.
Russia launched 55 missiles and 21 Shahed drones overnight, the Ukrainian air force said.
Air defences downed 39 of the missiles and 20 of the drones, Ukrainian air force commander Mykola Oleshchuk said.
Russian forces also damaged the railway station building and train tracks in Kherson, national railway operator Ukrzaliznytsia said.