Heat rate is a measure of the efficiency of the turbine in turning fuel into energy. There is no simple correlation between heat rate and power factor.
Power factor is a means of representing the ratio of active power (MW) to apparent power (MVA). The difference between active power and apparent power is due to reactive power (MVAr); apparent power is the square root of the sum of the squares of reactive and active power. Changes in reactive power do not directly affect power input to the generator from the turbine except in an indirect way due to variation in power required for the generator field and to supply the losses within the generator.
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If we learn from our mistakes I'm getting a great education!
Heat rate is the measure of the conversion fuel into sellable energy-power you can put on the grid and get paid for. Plant auxiliary losses and turbne and generator losses count against heat rate - fuel you bought and burned but that you can't sell as electricity to a customer.
Reactive power causes higher heat losses in the generator core which are rejected to your heat sink (as well as in transformers and in transmission lines but that is beyond the scope of the OP.) It takes fuel to generate the heat that is rejected to the atmosphere because of the heat generated due to reactive power. That counts against heat rate. Power companies (mostly) want to sell MW. If you are selling only real power, your best heat rate is when MVA = MW or PF = unity. That is when generator heat losses are at a minimum. Even if you are paid for reactive power, the generator heat losses caused by generating it reduces your heat rate.
To answer your second question, based on the above heat rate is affected by PF but not in any way proportional to it.
rmw
PD: I predict that this post will get my EE buddies stirred up so have at me.
I agree with rmw, but keep in mind that losses associated with increased var output are small when compared with even the normal generator losses, which in turn are miniscule in comparison with the huge losses on the steam side.
