# Heat Rate Formula

## What is the Heat Rate Formula?

Heat rate is explained as the total amount of energy that is required to produce one kilowatt-hour (kWh) of electricity using a power plant (plant heat rate formula) or electric generator.

It is defined as the input rate needed for generating unit power. Heat rate may also be defined as the ratio of thermal inputs to electrical output—the lower the heat rate, the higher the efficiency. In a thermal generating system, both incoming and outgoing energy typically exist in a similar unit or value. The heat amount is always proportional to the input of the chemical energy, which is divided by the liberated electrical energy.

### Total Heat Input

The chemical energy that is available in the fuel (biomass, coal, oil, gas, and so on) is converted into heat energy in Boilers. This process is known as oxidation. The heat available in the fuel can be measured in terms of KJ/kg, Kcal/kg or BTU units. The part of this fuel can be used as useful heat and the remaining is lost as moisture loss, dry flue gas loss, unburnt loss, convection/radiation losses, and so on. Based on the Boiler efficiency, this heat energy from the fuel can be utilized (boiler heat rate formula); generally, fuel heat utilization exists in the range of 60 - 90%.

This heat that is generated in the boilers because of fuel oxidation is used to generate high-pressure Et temperature steam. Therefore, the generated steam is fed into the steam Turbine, where this heat energy, also referred to as thermal energy, gets converted into Kinetic energy. And then into Mechanical energy in steam turbines.

Finally, mechanical energy turns into electrical energy in the Generator.

Therefore,

Total heat input to power plant = Thermal energy + Chemical energy + Kinetic energy + Mechanical energy Output

= Electrical power in Kwh Heat rate

= Heat input / Power generation

### Formula of Heat Rate

The formula of heat rate is given as,

R$_{h}$ = W$_{s}$ × c × ΔT

Where,

W$_{s}$ is steam flow in lb/hr,

R$_{h}$ is heat rate in btu/hr,

ΔT is the temperature difference in $^{0}$F,

c is the specific heat capacity in btu/lb $^{0}$F.

### Solved Example

Example 1

Find the heat rate if steam enters a turbine at 400 $^{0}$F at atmospheric pressure and leaves the turbine at 200 $^{0}$F? Steam at 500 lb flows via turbine every hour during the normal operation.

Solution

Given parameters are,

c = 0.48,

W$_{s}$ = 500 lbs/hr,

T$_{out}$ = 200 $^{0}$F,

T$_{in}$ = 400 $^{0}$F,

ΔT = 400 – 200

ΔT = 200 $^{0}$F

We have the Formula,

R$_{h}$ = W$_{s}$ × c ×ΔT

R$_{h}$ = 500 × 0.48 × 200

Thus, R$_{h}$ = 48000 btu/hr.

Q1. Explain the Heat Rate in a Power Plant?

Answer: The word heat rate can be used in the context of thermal power plants. As we may know, these power plants convert heat energy stored in the fuel (such as gas, coal, oil and so on) into electricity (with the unit - kWh).

The amount of heat needed to obtain 1 kWh (which is also known as Unit) of electricity is referred to as heat rate. Its unit is given as kCal/kWh (where in some contexts, it is kJ/kWh). The United States Energy Information Administration (EIA) expresses the heat rates in British thermal units (Btu) per net kWh generated (net heat rate formula).

Q2. Differentiate Turbine Heat Rate and the Gross Turbine Heat Rate?

Answer: In the calculation of any power plant’s output, Gross Heat Rate is defined as an expression of the total energy that is produced by the plant per one unit of mass of fuel. This is before all the parasitic loads are accounted for, the effect of either a calculation of Net Heat Rate or the power, which actually goes out the door, per unit of mass of fuel.

The gross heat rate considers the efficiency losses and power associated with the entire power generation cycle, involving the feed water circulation system, the boiler, condensate recovery system, fuel delivery and water treatment.