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# Heat Rate Formula

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Last updated date: 19th Sep 2024
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## What is the Heat Rate Formula?

The heat rate is the entire amount of energy required by an electric generator or power plant to create one kilowatt-hour (kWh) of electricity.

It is the rate of input necessary to generate unit power. The ratio of thermal inputs to electrical output is also known as the heat rate. The better the efficiency, the lower the heat rate. In a thermal power supply, input and output energy are usually measured in the same unit. The amount of heat produced is proportional to the chemical energy supplied divided by the electrical energy freed.

The term efficiency is a non-dimensional measure (often expressed as a percentage), and specifically, heat rate is also non-dimensional but is frequently expressed as energy per energy in appropriate quantities. It's joule per joule in SI units, but it's also known as joule/kilowatt hour or British thermal units/kWh. Because kilowatt-hour is typically used to refer to electrical current and joule or Btu is generally used to refer to thermal energy, this is the case.

In the context of power plants, heat rate can be thought of as the amount of energy required to generate one unit of output. It refers to the amount of fuel needed to produce one unit of power. Effectiveness, fuel prices, plant load factor, pollutants level, and other performance indicators tracked for any thermal power station are all a result of the station heat rate and can be directly linked.

### How to calculate Heat Rate?

Heat rate is a measurement of a power plant's or generator's thermal efficiency, usually expressed in British thermal units (Btu) per kilowatt-hour (kWh). It's computed by multiplying the energy output of the fuel used to generate electricity by the quantity of electrical energy produced.

### Input of Total Heat:

In boilers, the chemical energy present in the fuel (coal, biomass, oil, gas, etc.) is turned into heat energy, a process known as oxidation. The heat capacity of a fuel is expressed in Kcal/kg, KJ/kg, or BTU units. The remainder of this fuel is lost as dry flue gas loss, water loss, unburnt loss, radiation/convection losses, and so on. This excess heat from the fuel is used based on boiler efficiency; normally, fuel heat usage is in the range of approximately to 90%.

The heat created in the boilers as a result of fuel oxidation is used to produce high-pressure, high-temperature steam. Thus, the created vapor is fed into the gas turbine, where the heat energy, also known as thermal energy, is turned into kinetic energy, then mechanical energy in the steam turbine, and finally electrical energy in the generator. Chemical energy + Thermal energy + Kinetic energy + Mechanical energy = total heat input to the power plant

Electrical power in kilowatt-hours = output

Heat rate is the product of heat input and power generated.

### Formula of Heat Rate

Rh = Ws × c × ΔT

Where,

Ws  represents the steam flow

Rh  represents rate of heat

c stands for specific heat capacity

### Solved Example

1. Determine the heat rate if vapor enters a rotor at 400°F and departs at 200°F at atmospheric pressure. During a typical operation, 500 lb of steam passes through the rotor every hour.

ΔT = 400 – 200

ΔT = 200°F

We have the Formula,

Rh = Ws × c × ΔT

Rh = 500 × 0.48 × 200

That equals,  Rh  = 48000 btu/hr

1. Compute the Gross station heat rate of a 100 MW thermal power plant that runs on 100% PLF and uses roughly 55 MT of coal with a GCV of 4500 kcal/kg per hour.

We've done so.

Heat input to the plant/gross station heat rate generating electricity

GCV (kcal/kg) of fuel/Power generation/MWH =Fuel spent (MT)X GCV (kcal/kg) of fuel

100 = (55 X 4500)

= 2475 calories per kilowatt-hour

By converting fuel consumption in kilogrammes per hour and power generation in kilowatt-hours, the heat rate can be computed as follows:

=2475 calories per kilowatt-hour

=55 X 1000 X 4500/(100 X 1000 X 4500)

=0.55

## FAQs on Heat Rate Formula

1. Explain the Heat Rate in a Power Plant?

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 a 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).

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

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.