Energibesparelsen øker med effektfaktoren.

In Norwegian, the definite article is usually added to the end of the noun instead of appearing as a separate word before it.

• energibesparelse = energy saving / energy conservation
• energibesparelsen = the energy saving
• effektfaktor = power factor
• effektfaktoren = the power factor

So both nouns are in the definite singular form.

It is a compound noun, which is very common in Norwegian.

It breaks down as:

• energi = energy
• besparelse = saving, reduction, economy
• energibesparelse = energy saving / energy conservation
• energibesparelsen = the energy saving

Norwegian often combines words into one long noun where English might use two or more words.

Grammatically, energibesparelsen is singular.

However, English often uses savings where Norwegian uses a singular noun. So a singular Norwegian word can sometimes be translated by an English plural if that sounds more natural.

For example:

• en besparelse = a saving
• besparelsen = the saving

But in context, English may prefer the energy savings even though Norwegian uses singular form.

Øker is the present tense of å øke, which means to increase.

So:

• å øke = to increase
• øker = increases / is increasing

In this sentence, it means increases.

Because in technical Norwegian, effekt often means power in the engineering or physics sense, not effect in the everyday English sense.

So:

• effekt = power
• faktor = factor
• effektfaktor = power factor

This is a common false friend for English speakers, because the word looks like effect.

Here med means something like with or as ... increases.

So the sentence suggests a relationship:

• The energy savings increase with the power factor
• in other words, as the power factor goes up, the energy savings go up

This is not necessarily the same as by in the sense of an exact numerical amount.

A useful distinction:

• øker med 10 % = increases by 10%
• øker med temperaturen = increases with the temperature

In your sentence, med effektfaktoren is most naturally understood as with the power factor.

This is normal Norwegian main-clause word order:

• subject: Energibesparelsen
• verb: øker
• prepositional phrase: med effektfaktoren

So it follows the basic pattern:

Subject + Verb + Rest

That is very similar to ordinary English word order here.

Yes, indefinite forms are possible in other contexts, but the definite forms here suggest that the speaker is talking about a specific energy saving and a specific power factor, or about these concepts as known quantities in the discussion.

Compare:

• Energibesparelsen øker med effektfaktoren.
  = The energy saving increases with the power factor.

• En energibesparelse øker med en effektfaktor.
  This sounds odd and unnatural in most contexts, because it suggests an energy saving and a power factor in a very unspecific way.

In technical or explanatory writing, definite forms are often used when the concept is already established.

The letter ø is a vowel that does not exist in standard English.

A rough guide:

• it is somewhat similar to the vowel in French deux or German schön
• your lips are rounded, but the tongue is placed more toward the front of the mouth

In this sentence:

• øker sounds roughly like UR-ker, but that is only an approximation
• the first sound should be a true Norwegian ø, not an English o or u

Yes.

It breaks down as:

• effekt = power
• faktor = factor
• effektfaktor = power factor
• effektfaktoren = the power factor

Just like energibesparelsen, this is a compound noun plus the definite ending.

It could look that way at first, especially to an English speaker, but in most contexts the more natural meaning is:

The energy savings increase with the power factor.

That is because øker med can mean two different things depending on what follows:

• øker med 5 = increases by 5
• øker med temperaturen = increases with the temperature

Since effektfaktoren is a variable or condition, not a numerical increment, the second interpretation is the more likely one here.