Does it Cost More to Generate at Leading or at Unity Power Factor

The losses in the cabling increase with lower-than-unity power factor. As utility companies incur additional costs for this that don't appear as kWh, the temptation is to impose a tariff that encourages the power user to operate close to unity power factor.

Power factor correction is one of CR4's more common topics, which has been covered ad nauseam before. Try entering "power factor correction" into the "Search all of CR4" box on the right→.

DF is asking about fuel savings not power factor correction. I agree with his overall premise which I'll simplify as "...all other things being equal, since the rotor draws less excitation current when the generator operates underexcited, the losses are lower than operation at the same load and with the numerically identical but overexcited power factor ...".

Sure, but it ignores the typical operational constraints about operating underexcited, which can lead to machine damage, system instability, loss of voltage control, and loss of synchronization.

So while technically correct, operationally it is fraught with problems that can cause a lot more additional costs than the potential fuel savings.

Ooops! I must need new glasses, the title of the question has to do with going from unity pf to underexcited but the post said that it was a comparison between same pf over/underexcited.

The answer is a bit different under when going from unity to over/underexcited primarily because the for constant MVA the MW are greatest at unity, therefore more fuel is consumed to supply the higher MW. Conversely as we move the pf away from unity the MW goes down so less fuel is consumed.

The magnitude of the current, and therefore the losses, does not change, except for the DC power consumed in the field which does go down as the machine gets more underexcited.

In theory the changes in reactive power have no effect on the real power, and changes in the fuel consumption have no effect on the reactive power. In real life they are slightly interrelated since these are not ideal machines, and the changes have to do with the fact that as the excitation changes so does the terminal voltage and its effect on load current.

You discuss cost of generation.

When the power factor goes leading, the watts that a synchronous generator can absorb drops like a stone. With zero excitation current, the power to push it out of sync is only about 30% rated - and there is zero stability margin for sudden load changes.

It is not economic to operate a plant at 30% rating. In fact, system operators have to pay generators a premium to operate part load, because they would get less kW earning less at higher unit cost otherwise.

Part-load operation is kept to the minimum needed to cover sudden loss of a generator or generating station without too much frequency drop. Grid Systems are managed mostly by skillful adjustment of number /size of generators (on-line, at full rating) at 15 minute intervals according to predicted load, modified by reality.

You have forgotten the "engine". Diesels lose ~10% efficiency at 75% load. Gas turbines lose efficiency seriously below full load, say 20% drop at 80% load for free turbine type, worse for single shaft. I have little knowledge on steam turbines, but I think they may be similar to diesel figure. Any serious Grid electric generator, 30MW up has >=98.5% efficiency, so its loss variations are minor compared to engine efficiency.

Finally, systems must have that lagging generator output to magnetise all the transformers and motors in the system.

The OP had Cost in the title, Fuel in the middle and Economical at the end. He seemed to me to have already convinced himself, correctly, that between equal leading and lagging power factors at the same real power, generator losses are least for leading.

So I tried to briefly mention the constraints that require synchronous generators to operate off the loss optimum, without "ifs, buts and depends" , and thank you for the erudite additions, for which I give you a Good Answer.

The "30% load" was a clumsy attempt to bring in stability limits. But I note the OP's "In m(a)y opinion, the MW output and the torque angle are constant for a given output of a prime mover." which seems an error because rotor angle/torque increases with weakening field, but was not commented upon.

I take issue with your comment on "skillful adjustment", I never meant "not automated". Are you really saying that skill is in hardware and silicon integrated circuits, not in designers, programmers, consultants, weather forecasters, market analysts etc. who have a hand in prediction and procedures?

67model

RAMconsult said:

""...Finally, systems must have that lagging generator output to magnetise all the transformers and motors in the system..." This is only true when the load is only inductive, most likely in small isolated systems. As an example, very long transmission overhead lines appear capacitive (the Ferranti Effect), as do systems that have large underground cable installations, plus many systems now have switchable reactors and capacitor banks as part of their overall VAR/voltage control strategies."

Ferranti effect is a long transmission line effect, I have never seen it is distribution systems, where the loads are almost always inductive.

My guess is that you're more familiar with small local generation and that you've never been to any built up city like NY, LA, Boston, etc. where most of the subtransmission/distribution is underground cable which is highly capacitive, but you're right, on the customer side of the meter the loads tend to be net inductive.

It Costs more at leading P.F.

That is if you want to generate the same kW or MW ! But the issue is how do you do that? At leading P.F., there will be problems of stability. usually, you use this method to produce compensating kVARs on a grid and not kWatts. Tricky business if you are not in the business...

Logically, 1 kVA = 1kW is the minimum cost at P.F.=1. At leading or Lagging P.F. you are producing kW but consuming (or producing) something else in addition.How much more, ...?

The "something else" is the reactive current, but that does not come out of the fuel, it comes out of the magnetic field. No additional fuel is used except for the power to run the excitation system.

As long as you hold the real power constant you add VARs by adjusting the excitation level, so if you measure the current at 0.9 pf overexcited it will be exactly the same as 0.9pf underexcited, therefore the I²R losses are identical, except for the the losses in the excitation system. This assumes that the terminal voltage doesn't change, an unrealistic assumption in the real world, but in theory that's how it works.

Point Taken.

Since the P.F. depends on the load connected to the Generator, and since the reactive power is supplied to the load, and then there are losses on the transmission lines if the P.F. is lagging at the consumer point, surely, that is going to cost the generating utility.

Now, I think that the OP is trying to say that maybe if the generator is made to produce under a leading P.F. setting, in order to still supply the same Kw power, will this be cheaper for the generating unit than just correcting the load end to unity P.F. only?

Well, it's really a theoretical "what-if" question, but it has validity since the excitation system is a parasitic loss and someone has to pay for that DC power consumption, and it's not small.

A midsize 500 MVA generator uses about 0.5% of its output power to provide the full load field current, that's 2.5 MW!!! 1,000Vdc x 2,500Adc is a nontrivial amount of power that has to be produced from somewhere and controlled by the excitation system.

So OP's question takes on a new meaning, after all if we can cut that 2.5MW down to 1.25MW by running underexcited, why not do it? Let's see, 1,250kW x 1 hr = 1,250kWh, at 0.30 $/kWh that's 375 bucks per hour x 24hrs = $9,000/day saved. The difference in fuel cost adds up quickly.

In reality we can't get a 2:1 turndown or we'd likely slip poles so the number is somewhat less, and it does go down kind of linearly with the MVA load on the generator. So yes, if the pf at the machine's terminal goes from overexcited towards unity the amount of energy going into the field goes down too.

Here I give a typical capability diagram of Turbo-generator. On under excited oparating conditions the limit could be minimum excitation (or in other terms load angle) which affects its steady state stability (with modern solid state voltage regulators the theoretical transient limit shifts from delta equal to 90 degrees to 135 degrees. But there is another aspect which needs to be consider. This is end zone heating of the generator. Under leading power factor operation of the generator, the flux distribution changes (the armature reaction is magnetizing) and it results in over heating of the end structure (generator casing, core clamping plate etc.). Therefore generator manufactures put a limit on the MVA that is permitted at different leading .power factor. So one should not assume that any amount of MVA could be drawn under leading power factor condition. In most of the cases, this end zone heating limit is more critical than stability limit