The relationship is exactly between real power with frequency and reactive power with voltage. If you want to know that, just take an essay example of two power supplies connected through Z impedance, we found that the frequency or delta angle is related to the active power, and voltage is related to reactive power. Furthermore, we see the curve characteristics of P/f and Q/V droop control in any power system books.

I hope that this answer guidance to know more information about this issue.

i thought of typing frequency only but mistakenly i typed as load angle. But I am unable to get your answer.

Consider a two bus system connected through a lossless line. Then the voltage at bus 2 can be shown as

V2 = V1 - jX (P-jQ) / V1

= {V1 – QX/V1} -jPX/V1 (1)

= V2

where V1 is the reference phasor.

Bus 1 – generator bus

Bus 2 – load bus

Assumption: V1 is kept constant by changing Synchronous Generator SG’s excitation. Transmission line resistance is negligible. P and Q are the real and reactive powers transmitted to the load bus.

Observations: The following points can be observed by analyzing (1).

V2 is affected mainly by changes in Q and less affected by changes in P as QX /V1is directly subtracted from V2 and P is in quadrature with V1. This leads to

Q – V control.

If Q is positive (Inductive load), V2< V1 (Voltage Sag)

If Q is negative (capacitive load) V2 > V1 (Voltage Swell - Ferranti effect ).

If P increases (decreases) then  increases (decreases). Its affect on V2 is minimal. But torque angle  depends on frequency (speed) of SG. P -  control becomes P-f control as f depends on 

Practically when P increases (decreases) speed decreases (increases) and so does frequency. Then the KE stored in rotor tries to supply that extra power by increasing  , as P = V1V2 sin /X. This leads to P – f control or load frequency control (LFC).

thank you sir. Now i have understood.

Dear Arun,

You can easily see this relationship just by running a power flow program and analyzing its Jacobian Matrix. This fact is the basis of Fast-decoupled Load Flow method and you can find it in the related books especially Prof. Hadi Saadat's book.

Regards,

Morteza Shabanzadeh

http://mortezash.blogfa.com/

A very simple concept is to think of a steam turbine generator combination.To get more power open the steam governor which tends to make the turbine generator spin faster that is a change in frequency. If you vary the voltage on the generator excitation system the voltage and Var output changes but not the power. 

 Read book power system stability and control for P. Kundur, chapter 11 , you will find a lot of detail about that 

Critically restudy the Jacobian matrix when it has not been decoupled ,and then follow step-by-step process in decoupling it to get the final real&reactive powerflow equation. it will become clearer, also read power system stability and control by P. Kundur, chapter 11 and ..

All the generators have two loops one for controlling frequency and another one for controlling voltage. Control of frequency is a mechanical process which can be done with the help of governor and gate operation and so its response time is more and control of voltage is an electrical process which can be done with the help of excitation system and so its response time is less. Therefore, for changing frequency we control gate and governor i.e. we control load. While for changing voltage we change current flow in exciting winding i.e. change in reactive power.

It is also important to know that response time for both the loops are different so they assume as decoupled with each other in preliminary stage studies.

I totally agree with Dr. (Prof.) Nitin Kumar Saxena; Further I would like to add,

• The real power of the generator/Alternator is governed by the real work acting on it as the action of the prime mover/Turbine which drives the rotor to create some power angle, Which causes the generation of Real/Active power because of the Real/Active work performed by the prime mover/turbine in rotating the rotor and maintaining some power angle. This is a part of the ALFC loop. So the Real/Active power is related to mechanical(Real) input/rotation/Frequency..
• The next part is reactive power/magnetizing power/Virtual power which is by name not real, so no real work/Mechanical work is required for the production of this power. Instead, this power is governed by the excitation/magnetizing current supplied to the field winding via Exciter and AVR loop. Now as we know the voltage depends on the flux and the flux is produced by the reactive/magnetizing current (Isinɸ) or reactive/magnetizing power (VIsinɸ) supplied to the field winding via Exciter and controlled by the AVR loop. So this power is actually responsible for producing air gap flux which interns responsible for generating the armature voltage and this is how the Reactive power is closely related to the voltage.

Dear Hamza Shakil the load angle is not the angle between P and Q rather it is a angle between induce EMF and terminal voltage it is totally different from Power Factor.