Russia's frequent and widespread attacks on Ukraine's power infrastructure have plunged millions of people into darkness, depriving them of heat, power and water just as winter arrives and temperatures drop below zero.

Many Ukrainian and Western leaders quickly condemned the strikes as war crimes because of the harm done to the civilian population. But attacks on energy grids have long been part of warfare - so is Russia's strategy a violation of international law?

With certain limitations, parts of a country's electrical grid can be considered legitimate targets if they are used to power military facilities.

This is true even if the targets have a civilian as well as a military purpose, so long as destroying the object would "offer a definite military advantage".

Iraq's energy infrastructure was attacked by US forces in 1991 - a strategy that has been heavily criticised. Nato forces also targeted the power grid in Serbia in 1999. In both cases, the civilian population was affected by the resulting power outages.

In fact, there may be times when neutralising a military facility by taking out its power supply is preferable to hitting the facility directly with missiles or artillery.

"Would I rather deprive part of the civilian population of electricity for a limited period, rather than risk killing civilians because of the collateral effects of using kinetic weapons? Yeah, I would think so," Michael Schmitt - professor emeritus at the US Naval War College - told the BBC.

Russia denies intentionally targeting civilians, and has sought to justify its attacks on Ukrainian infrastructure as strikes against the "military command system of Ukraine and related energy facilities", according to a defence ministry statement on 18 November.

However, even when an object is a legitimate military target, there are still limits on when and how it can be attacked.

"The state has an obligation under international humanitarian law (IHL) to choose a target or a tactic that will cause less damage to civilians. Less death and less injury, but still fulfilling the military advantage," Dr Maria Varaki from King's College War Studies department told the BBC.

Civilian deaths and injury caused by attacks on military targets are not necessarily violations of international law. But the principle of proportionality must be applied, which says that the harm to civilians should not be excessive in relation to the military advantage gained. Parties must also take "constant care" to spare the civilian population and civilian property.

In Ukraine, President Volodymyr Zelensky said after strikes on cities in November that 10 million people had been left without electricity and that half of the country's power capacity had been knocked out. Six million were still without power by Thursday night, he added.

At a certain point, says Prof Schmitt, "the civilian harm is so severe that you just can't pull the trigger".

The sort of advantage gained by an attack is also a factor when considering whether it is a violation of IHL.

"Demoralising people, terrorising people, is not considered to be an acceptable military advantage," Dr Varaki explains. In fact, she says, the opposite is true: "Terrorising the civilian population is considered to be a war crime."

As well as Russia's insistence that it is targeting only military objects, the Kremlin has hinted that there is another reason for the strikes - persuading Kyiv to talk.

"The unwillingness of the Ukrainian side to settle the problem, to start negotiations, its refusal to seek common ground - this is their consequence," said Kremlin spokesman Dmitry Peskov.

An attacking force may hope that destroying the civilian power grid will lower the morale of the enemy, but that is not enough to justify the attack under international law. There must also be a concrete military advantage before the attack is deemed legal.

The sheer scope and scale of Russia's attacks on Ukrainian infrastructure make it unlikely that they can all be justified in that way, says Prof Schmitt.

"We're at a point now where they're hitting so many targets that I can't imagine they're picking power infrastructure that qualifies as a military objective in every case."

As a former US Air Force targeting officer, Prof Schmitt also doubts that Russia is fully validating every object it attacks - another requirement of IHL.

"You just can't conduct operations of that intensity and that frequency across an entire nation and have done your required verification of targets," he explains.

With that in mind, Prof Schmitt believes it is now "pretty clear" that Russia's main motivation, at least in some attacks, is to "terrorise the civilian population".

Whatever Russia's exact reason for targeting the power grid, Dr Varaki says it has not previously shown a commitment to minimising civilian harm.

"You can identify a general pattern that the Russian army has not been fully concerned by civilian deaths," she argues.

By 28 November, Russia had hit more than 200 separate targets relating to Ukraine's energy infrastructure, according to the defence minister. Millions were without power, and electricity usage was restricted in over a dozen regions.

But despite that, Prof Schmitt says that if Russia hopes to demoralise the population, the tactic is unlikely to work.

"Historically there is no reason to believe the Ukrainian morale will break... [Putin] is hardening the resolve against Russia to stay the fight. This is a strategic miscalculation."

So has Russia violated international law? Any future legal process would have to first consider if the huge number of targets could all be considered legitimate military objects.

Even if they are, the harm done to the civilian population in attacking them should not be excessive in relation to the concrete advantage gained. And that advantage must be military in nature - terrorising the population is not a legitimate reason to launch an attack.

Russia and Ukraine are both parties to Additional Protocol I of the Geneva Conventions, where many of these rules are defined. It remains to be seen whether Russia will ever have to explain how its actions comply with those rules.