# Voltage and Reactive Power Relationship

• OliskaP
In summary, the grid-centric approach is explained in the PF Insights article mentioned. VAR flow is proportional to voltage differences, and raising field voltage raises terminal voltage. Park's equations relate field voltage to terminal voltage. The generator-centric view is explained with diagrams of phasor diagrams. The armature reaction and synchronous impedance are explained.

#### OliskaP

Hi,

I have some trouble regarding the relationship between voltage and reactive power. From what I've read you control the amount of reactive power the generator is producing or absorbing by increasing or lowering the excitation of the generator.

I have some trouble getting my head around this, so I was wondering if someone could show me the equation that shows me when I increase the excitation I increase the amount of reactive power into the grid and vice versa.

I need to see the equation to see how this relates, that's how my brain is put togheter, or if someone could attempt to explain this to me I would be glad.Thank you for any help, best regards.

There are two approaches to answering your question. Grid centric or generator centric.

The grid centric approach is explained in the PF Insights article https://www.physicsforums.com/insights/ac-power-analysis-part-2-network-analysis/. VAR flow is proportional to voltage differences. Raising field voltage raises terminal voltage, thus sending more positive VARS to the grid.

In the generator centric view, how does field voltage relate to terminal voltage? Those are called Park's Equations. See http://electrical-riddles.com/topic.php?lang=en&cat=5&topic=390

cnh1995 and OliskaP
the key is to understand the machine is mostly inductive
and it sums mmf's

drawing phasor diagrams will help...
assume machine is tied directly to infinite bus so terminal voltage is fixed

we have control of the torque applied to the shaft
and control of the field current
let's vary them one at a time

next i'll raise excitation just enough to bring power factor back to 1.0

I am equation challenged so think in pictures,
sorry if above seems over-simplistic but it's how i figure out the formulas.

Think of the generator as an ideal voltage source with voltage in proportion to field current,
and an inductance in series equal to Zsynchronous which is a physical characteristic of the machine..Some old threads that might help you conceptualize..https://www.physicsforums.com/threads/synchronous-generator-excitation.829603/#post-5214090

i hope above helps you accept the math.

OliskaP
Both of you, thanks, and jim for taking the time creating the drawings.

jim hardy said:
...

By the way jim hardy, will the total MMF be constant? From what I see from the pictures, you adjust the field MMF by adjusting the field current, so will the armature MMF "adjust automatically" to maintain constant total MMF?

OliskaP said:
so will the armature MMF "adjust automatically" to maintain constant total MMF?

Remember i postulated connection to infinite bus.
Yes is the answer, with that qualification. Ohm's law dictates it.
Armature current will flow and remember that mmf is current X number of turns.

I further simplified by omitting non-liearity of iron, i used mmf and flux interchangeably.
Voltage is proportional to flux
Omitting the nonlinearity of BH curve simplifies the explanation. I think that's necessary to get that "intuitive feel" for the synchronous machine.
Sans that nonlinearity voltage would be linear with total MMF . You'll see something called "Potier Triangles" that helps adjust calculations for nonlinearity.

The effect is called "Armature Reaction" and "Synchronous Impedance" ..
You'll study both soon in your coursework I'm sure.

If you add impedance between machine terminals and infinite bus , then of course terminal volts will change.

OliskaP
jim hardy said:
In that phasor diagram observe that total mmf must be perpendicular to terminal volts, and must have same radius..

Why must the terminal volts and total MMF have the same radius? I understand that terminal volt should be of a constant value if connected directly to infinite bus, but I do not fully understand why the total MMF should be of the same magnitude/radius as terminal voltage?

OliskaP said:
Why must the terminal volts and total MMF have the same radius? I understand that terminal volt should be of a constant value if connected directly to infinite bus, but I do not fully understand why the total MMF should be of the same magnitude/radius as terminal voltage?

two ways to explain what i did
1.
I used MMF and Fux interchangeably , ignoring nonlinearity of iron. That's a simplification.
If you allow that departure from rigorous math
then mmf NI and flux Φ are linearly proportional
because Φ = μμ0NIArea/Length
only non-constant in that formula is current I

Now since voltage is proportional to flux* , it is also proportional to MMF
(* Faraday's law, e = ndΦ/dt and since d(sinωt )= ωcosωt they're proportional by ratio ω)
choice of radii is up to the presentor and i chose to keep the presentation as simple as i could.

2.
Power engineering uses "Per Unit" notation where everything is calculated as a ratio to some base,
usually machine ratings for an individual machine or 100mva for power system problems.

So i , without explaining it first,
I started with terminal voltage at 1.0 of nominal rating, so set radius = 1.0 , 1 per unit volts
field amps at 1.0 of whatever is required to make 1.0 nominal rated volts at rated rpm and unloaded , 1 per unit field amps
field mmf then is 1.0 of whatever are field amps X number of turns on field, for simplicity i set turns = 1 and used same radius = 1.0 per unit field mmf
(though you'll never find field mmf on a machine's nameplate)

then i rotated field mmf some arbitrary amount ccw to represent power angle at some applied torque
drew the phasor that completed the isoscles triangle

for armature amps i just lifted that phasor, changed its color and pasted ot at the origin because that's what armature amps do, flow as necessary to make total flux match terminal volts..

What's set by physics is that terminal volts and total flux must be perpendicular late edit- and in proportion
if you want to redraw the pictures with different radii for mmf and terminal volts go ahead , I drew mine using plain old windows "Paint"
but i don't see a need for that when you're just trying to get the mental models working in your head.

...............

all that said,
they don't have to have the same radii, it just makes it a lot easier to demonstrate what's happening if you draw them that way.

old jim

Last edited:
OliskaP
Ok, thank you, I think I finally got to understand my initial question a whole lot more, I really appreciate your help.

jim hardy

## 1. What is the relationship between voltage and reactive power?

The relationship between voltage and reactive power is that as voltage increases, reactive power also increases. This is because reactive power is a measure of the power that is needed to maintain the electric and magnetic fields in a circuit, and higher voltage means a stronger electric field.

## 2. How does reactive power affect power system efficiency?

Reactive power can decrease the efficiency of a power system by causing voltage drops and increasing line losses. This is because reactive power does not contribute to the power consumed by the load, but it still needs to be supplied by the power system. This can lead to wasted energy and higher operating costs.

## 3. Can reactive power be measured directly?

No, reactive power cannot be measured directly. It is a calculated value based on the voltage and current in a circuit. However, it can be indirectly measured using instruments such as power factor meters or power analyzers.

## 4. How does voltage control affect reactive power?

Voltage control is important in managing reactive power in a power system. If the voltage is too low, it can lead to voltage drops and an increase in reactive power. On the other hand, if the voltage is too high, it can cause excessive reactive power and lead to overvoltage issues. Proper voltage control can help maintain a balance between voltage and reactive power.

## 5. What are some methods for controlling reactive power in a power system?

There are various methods for controlling reactive power in a power system. These include capacitor banks, synchronous condensers, and static var compensators. These devices can be used to supply or absorb reactive power as needed to maintain voltage and improve power system efficiency. Other methods include power factor correction, voltage regulation, and load management.