Попри те, що будинок не має електроенергії, резервне живлення працює.

Попри те, що is a conjunction meaning although, even though, or despite the fact that.

So in this sentence, it introduces a contrast:

• the house has no electricity
• but the backup power is still working

A simpler alternative is хоча:

• Хоча будинок не має електроенергії, резервне живлення працює.

Both are correct.
The version with попри те, що sounds a bit more formal or emphatic, like despite the fact that.

Because Попри те, що будинок не має електроенергії is a subordinate clause, and резервне живлення працює is the main clause.

Ukrainian, like English, normally separates this kind of introductory subordinate clause with a comma.

Structure:

• Попри те, що... = subordinate clause
• резервне живлення працює = main clause

So the comma is required.

Here те is in the accusative singular neuter.

That is because попри normally takes the accusative case:

• попри дощ
• попри труднощі
• попри те, що...

In this fixed expression, те is part of the set phrase попри те, що. You do not usually analyze it word-by-word when speaking; it is best learned as one chunk meaning although / despite the fact that.

This is a very common learner question.

The verb мати usually takes the accusative:

• мати час
• мати машину

But with negation, Ukrainian often uses the genitive, especially with abstract or non-count ideas:

• не має часу
• не має можливості
• не має електроенергії

So електроенергії here is genitive singular.

You may also encounter accusative in some contexts, but не має електроенергії sounds very natural and standard.

Yes, absolutely.

That would also be a very natural way to express the idea:

• У будинку немає електроенергії, але резервне живлення працює.

The difference is mainly one of structure:

• Будинок не має електроенергії = literally the house does not have electricity
• У будинку немає електроенергії = there is no electricity in the house

The second version often sounds a bit more idiomatic in everyday speech, but the original sentence is also correct.

Резервне живлення means backup power or backup power supply.

Breakdown:

• резервне = backup, reserve
• живлення = power supply, powering

In technical or everyday contexts involving electricity, живлення often refers to electrical supply or power input.

So this phrase is used for things like:

• a backup power system
• a battery backup
• an emergency power source

Живлення is a neuter noun, so the adjective must also be neuter:

• резервне живлення

That is why it is:

• not резервний
• not резервна
• but резервне

The verb also matches a singular subject:

• резервне живлення працює

Yes. Працювати is used for both people and things.

It can mean:

• to work as in to have a job
• to function / operate for devices, systems, engines, etc.

So here:

• резервне живлення працює = the backup power is working / functioning

This is completely natural Ukrainian.

These words are related, but not identical.

• електроенергія = electrical energy / electricity
  This is more formal and technical, and fits well in this sentence.

• електрика = electricity
  Very common in everyday speech.

• струм = electric current / power
  Often used colloquially when talking about whether the power is on or off.

Examples:

• Немає електроенергії = more formal
• Немає електрики = everyday
• Немає струму = very common colloquial phrasing

So the sentence could be phrased differently in more everyday language, but електроенергії is perfectly correct.

Yes. Ukrainian word order is flexible, although some versions sound more natural than others.

Original:

• Попри те, що будинок не має електроенергії, резервне живлення працює.

Possible variation:

• Резервне живлення працює, попри те, що будинок не має електроенергії.

This version is also correct.
The choice depends on what you want to emphasize:

• starting with Попри те, що... emphasizes the contrast first
• starting with Резервне живлення працює emphasizes the result first

Both будинок and дім can mean house/home, but they are not always identical.

• будинок usually refers more to the physical building
• дім can feel more like home, though it can also mean house in some contexts

In a sentence about electrical power, будинок is a very natural choice because the focus is on the building as a structure.

Yes, in its basic use as a preposition, попри takes the accusative case.

Examples:

• попри труднощі
• попри дощ
• попри це

And in the fixed conjunction:

• попри те, що...

So if you see попри, you should expect accusative after it.

It sounds mostly neutral to slightly formal.

Why?

• попри те, що is a bit more formal than хоча
• електроенергія is more formal/technical than електрика
• резервне живлення sounds technical and precise

A more conversational version might be:

• Хоча в будинку немає електрики, резервне живлення працює.

But the original sentence is completely natural, especially in written or technical contexts.