Power transfer question 2

[veritas]

The classical power transfer equation reads P = [VR*VS*sin(delta)]/X. Here R of the transmission system is neglected. Suppose power is transferred from a generator connected at Bus A to a load Bus B. Let voltage at Bus B = sending voltage, VS. Similarly voltage at Bus B = receiving voltage VR.

The equation states that the power transfer can be increased by increasing angle delta. To me this corresponds to increased steam flow (governor output) in the generator. However, the equation also states that P may be increased by increasing VS. This means raising the machine terminal voltage using the AVR.

I was, however, always under the impression that raising the output voltage affects REACTIVE powerflow whilst real powerflow was influenced by the governor output only.

How does one reconcile these apparently conflicting statements?

Thanks.

 

[waross]

Remembering a related issue with transformers in parallel with different tap settings. I understand the power flow increase with a voltage difference is a second order effect related to the internal voltage drop of the transformers. The flow of reactive current and the related KVARs is much greater than the increased power transfer or kW.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[davidbeach]

Perhaps the P and Q equations are not fully independent of each other. Raising Vs will increase power flow, but if you don't also up the real power you'll find that the increase in Vs doesn't last very long.

 

[waross]

I'll deffer to your answer David.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[xnuke]

Each variable delta and VS can adjust both P and Q, but control looks at the sensitivity of P and Q to each variable. P is more sensitive to delta than VS, therefore adjustment of delta is used to control P. Q is more sensitive to VS than delta, therefore adjustment of VS is used to control Q. I've attached an example calculation sheet here that shows this, but you can determine the sensitivities of each equation by taking partial derivatives of P to both delta and VS, then doing the same for Q.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[veritas]

I like xnuke's explanation. And David is correct, these parameters are not totally independent of each other. The attached Word doc captures the essence of the discussion.

Considering Fig. 3, perhaps xnuke will allow me to rephrase that the angle delta is much more sensitive to P than Q, i.e. delta is a measure of the real powerflow whilst voltage magnitude difference is a measure of reactive powerflow.

 

[ScottyUK]

The influence of V upon reactive power flow assumes that the machine is connected to a much larger system - the classical 'infinite bus'. Changing V when connected to an infinite bus is 'impossible' - although obviously a real system doesn't behave like a perfect infinite bus. Increasing power flow results in an increase in the load angle, and a reduction in the stability margin. A more powerful AVR can allow operation a larger load angle because it can maintain machine stability during a fault.

 

[crshears]

I was, however, always under the impression that raising the output voltage affects REACTIVE powerflow whilst real powerflow was influenced by the governor output only.

In the scenario described in the OP, it must be remembered [although it is true as noted that slight changes in reactive demand will occur with changes in voltage levels] that reactive power is drawn from the system by the load, and cannot arbitrarily be adjusted by means of an AVR in a single-source system. As such, increasing VS will have no material effect on powerflow.

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

 

[waross]

Laws applying to load sharing and load transfer between transformers may not be applicable to generators.

, but if you don't also up the real power you'll find that the increase in Vs doesn't last very long

Increasing the power out without increasing the power in may result in a serious violation of the law of conservation of energy. If the equation seems to justify an over unity event, then possibly the equation is not applicable to generators.



Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[veritas]

In the scenario described in the OP, it must be remembered [although it is true as noted that slight changes in reactive demand will occur with changes in voltage levels] that reactive power is drawn from the system by the load, and cannot arbitrarily be adjusted by means of an AVR in a single-source system. As such, increasing VS will have no material effect on powerflow.

Actually, I would think that V does have an effect on the system voltage, the effect depending on the relative size of the generator to the system. Suppose a generator is connected to a system bus. I deliberately did not say infinite bus as the concept of the infinite bus is not quite compatible with the discussion at hand. Raising V via the AVR in effect increases the emf, E, behind the machine's synchronous reactance, Xs. If E > VS (VS = system volts) will have a volt drop across Xs with a resulting current flow. Fig. 2 shows that if R is neglected that we are looking at an increase in var flow into the system. Current from the generator has to flow somewhere which is into the system, thus affecting it's voltage profile. Bigger the generator and or change in V, bigger the effect on the system. Even with an 'infinite bus', the theory dictates that there has to be a change in the voltage profile even if it is so small it's hardly measurable. Which I suppose flies in the face of the definition of an infinite bus - thus my statement that it is incompatible.

 

[crshears]

Hi veritas,

You'll note that I did not in fact state that voltage would not change at the sending end upon AVR setpoint adjustment change; you are quite correct in stating that V would in fact change.

That notwithstanding, I hold to my original contention.

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

 

[waross]

Without changing the mechanical power input, you can't increase the power out. Possibly some other factor in the equation is reducing to keep the equation balanced.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[crshears]

Fair enough, Bill; nevertheless, after re-reading the OP I'm not as certain as I was of what I thought was being asked...so I'm going to ignore the equation for the moment and simply relate what I would expect to see happen in the actual situation described.

The scenario seems to imply that power is flowing EXCLUSIVELY from A to B, and that there are no alternate paths away from source A into other parts of the system in question. That being the case, for a given power flow from A to B, the load angle between points A and B will be fixed by the composite impedance of all parallel paths between A and B, whilst the load division between the available circuits will vary inversely as the impedances of the individual circuits.

If the scenario is as I grasp it, increasing the amount of real power delivered from source A to B by raising governor speeder gear settings will result in an increase in the I over Z drop between A and B, resulting in a lower terminal voltage at B; the AVRs at A, ASSuming they are controlling for generator terminal voltage, will alter the units' excitations either not at all or minimally. If the independent system operator wishes to correct for the lowered bus voltage at B, they will request the generator operators at A to raise the setpoints of the generator AVRs in increments [typically sharing the required reactive output proportionally] until the voltage at B is returned to its pre-transfer-increase value.

Does the equation under consideration address these dynamics? I believe it does...but I will leave that discussion for those more mathematically erudite than I.

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

 

[waross]

The points that I think that I was trying to make are:
Power flows between two transformers fed from grid systems will vary slightly as the terminal voltage of one transformer is raised by changing tap settings, but the real power increase will not be as great as the reactive power increase.
If a generator is paralleled with a bus, the generator can not draw on an almost infinite grid but power out is limited by power in.

I was, however, always under the impression that raising the output voltage affects REACTIVE power flow whilst real power flow was influenced by the governor output only.

How does one reconcile these apparently conflicting statements?

From this I inferred that the governor was not expected to increase the power in.
HOWEVER,
If an increase in the terminal voltage results in an increased load on the generator, and the governor responds by increasing the power input, then the equation is also satisfied.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[mgtrp]

I was just catching up with this thread, and apologies if I've missed it being said above, but increasing Vs will result in the angle delta decreasing as the generator is now more tightly coupled to the system. Therefore, adjusting Vs will change the reactive power flow without affecting the real power flow, at least in steady state and neglecting losses.

 

[mard57]

To increase Vs or terminal voltage at the generator, you must increase the generated voltage (ie: Field) however with a constant power input from the prime mover, this increase in excitation voltage will decrease the torque angle and therefore the real power output of the generator will remain constant. The reactive power output will increase.

 

[mard57]

A way to visualize this is to consider that the torque angle of a generator, which determines the real and reactive power generated in the stator, is determined by the advance in degrees of the field poles relative to the stator poles. If you increase power input with generated voltage constant, the angle increases. If you keep the power input constant and increase the generated voltage (vie: increasing field current), the rotor poles are pulled back more in phase with the stator poles. (ie: torque angle decreases).

Therefore, sine (torque angle) decreases by the same amount that Vs increases and they balance with no net increase or decrease in real power with just an increase in field current. However, cosine (torque angle) increases and therefore reactive power increases.