# Relationship heat rate with capacity

I am an economist, so please keep replies simple ;) I am searching for the relationship between heat rate and capacity for gas-fired power plants. Here is what I refer to as heat rate, i.e. the inverse of efficiency: http://en.wikipedia.org/wiki/Heat_rate_(efficiency)

From an IEA publication I got the following approximate relationship (for a CCGT plant):

maximum heat rate = 1.1 * minimum heat rate


Maximum heat rate holds whenever the power plant is operated at minimum capacity, and

minimum capacity = 0.4*maximum capacity


I'd like to know what the heat rate is when I run the power plant at a medium capacity of let's say:

medium capacity = minimum capacity + (maximum capacity-minimum capacity)/2


So

medium heat rate = ?


Is the relationship linear (i.e. = minimum hr+ (maximum hr-minimum hr)/2) or how would you estimate the heat rate here?

• Capacity is the maximum rated continuous power output - measured in Watts (kW, MW etc). But not sure what you mean by heatrate - :energy is delivered through a temperature difference. Commented Aug 21, 2018 at 9:59
• This answer may help : engineering.stackexchange.com/a/15766/10902 Commented Aug 21, 2018 at 10:01
• Here is what I refer to as heat rate: en.wikipedia.org/wiki/Heat_rate_(efficiency). The link you sent is about ramping times and not heat rate and capacity, but maybe @SF does have an idea??? Commented Aug 21, 2018 at 12:44
• Then you should explain exactly what you mean by heat rate by editing your original question as some will assume rate of energy movement through a material ie insulation. Commented Aug 21, 2018 at 12:48
• I'm not sure you're going to find a simple answer- most large CCGT plants are custom designed for the exact application. Some may have more consistent efficiency across the whole load range, others may have better high end efficiency, others may be tuned to have better peformance on hot days vs cold, etc. Commented Aug 21, 2018 at 18:43

I will take a stab at an answer in what I hope might be simple and general terms.

What is defined as heat rate is akin to a relative inefficiency or relative loss rather than heat rate. The value itself has no units. Multiple by 100 and you get a percentage.

You first statement says, the greatest relative loss we expect in a plant is 10% over its minimum. The minimum relative loss occurs when the plant is operating at it greatest efficiency. So, a plant that is 85% efficient in the best case has a heat rate (relative loss) of $1/0.85 = 1.2$ or 120% in the best case. We expect this plant to have a heat rate (relative loss) of $1.1 * 1.2 = 1.3$ or 130% at its worst case operation.

Your next statements say, the worst case (130% heat rate) happens when the plant operates at its lowest capacity. Capacity is akin to the actual amount of electricity that is produced. So, a plant will be least efficient (have the highest heat rate) when it produces the lowest amount of actual electrical energy.

Your next statement says, the lowest capacity of a plant is 40% of its maximum capacity. Basically, this says, we do not operate power plants to produce less than 40% of their maximum rated output of electricity. Let's suppose the maximum capacity of the example power plant from above is $C_{max} = 100$ (with whatever units). The lowest capacity is $C_{min} = 0.4C_{max} = 40$. At 40, the plant operates with a heat rate of 130%. Now for the tricky part ... We apparently have no information about the relationship between increasing capacity and decreasing heat rate. We do not know whether the minimum heat rate of 120% is at maximum capacity ($C = 100$) or perhaps even before. All we know is, as we increase capacity, we can expect that heat rate decreases.

The finding leaves us with this conclusion. Absent any further information, we are free to assume any model we want for a relationship between increasing capacity and decreasing heat rate.

In real life, power plants are not operated continuously at their physical maximum capacity. They are operated below this physical maximum limit, by example continuing from above perhaps at $C_{operation} = 80 - 90$. In real life, inefficiencies also kick in above this operational design "set point".

My instinct to tackle this absent any other information would be to do the following:

• Set the maximum heat rate at the lowest capacity. This is defined by reference.
• Set the minimum heat rate somewhere at 80% - 90% of maximum capacity. This can be defined by further research (i.e. look up typical operating capacities of power plants relative to their rated maximum capacity).
• Define the relationship between increasing capacity and decreasing heat rate as linear over the above range. This is your model. Publish it.
• Do not model the behavior of systems below their minimum capacity.
• Do not model the behavior of systems above the 80% - 90% their rated maximum capacity.
• Thanks. That is exactly what I tried to get at. How realistic is it, however, that the relationship is linear? Commented Aug 22, 2018 at 7:49
• I honestly do not know. An opposite extreme to linear is to assume an exponential behavior one way or the other. In one case, allow heat rate to decrease rapidly from its initial high value and then slowly approach its lowest. In another, allow heat rate to decrease slowly from its high value and then rapidly reach its lowest value as capacity gets close to maximum. Again, absent any other references, this is your model to explore. Someone from the power plant industry may chime in with a more informative reference. Commented Aug 22, 2018 at 13:10