Power transfer question
Power transfer question
(OP)
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.
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.






RE: Power transfer question
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Power transfer question
RE: Power transfer question
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Power transfer question
xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
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RE: Power transfer question
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.
RE: Power transfer question
RE: Power transfer question
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]
RE: Power transfer question
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
RE: Power transfer question
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.
RE: Power transfer question
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]
RE: Power transfer question
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Power transfer question
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]
RE: Power transfer question
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.
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
RE: Power transfer question
RE: Power transfer question
RE: Power transfer question
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.