Basic Calculations for a Power Plant- Calculating the Coal Quantity

Very often, the Power engineer is required to perform some basic calculations regarding the key parameters of a power plant. Most important is the quantity and cost of fuel that is required.This article gives the simple calculation method. (A detailed calculation required in the context of a contract, tender, performance repor,t or a legal document may require more accurate input data.)

We take the example of a 100 MW Coal Fired Power Plant.

The basic function of the power plant is to convert energy in coal to electricity. Therefore, the first thing we should know is how much energy there is in coal. Energy content of coal is given in terms of KiloJoules (kJ) per Kilogram (kg) of coal as the Gross calorific value (GCV) or the Higher Heating value (HHV) of coal. This value can vary from 10500 kJ/kg to 25000 kJ/kg depending on the quality and type of the coal.

You should have an idea of the type of coal, or the source or mine from where the the plant gets the coal. Published data about the sources, mines, regions or the procurement data gives an idea about the HHV of coal. For this example we use a HHV of 20,000 kJ/kg.

Energy conversion takes place in two stages.

• The first part of the conversion is efficiency of the boiler and combustion. For this example we take 88 % on an HHV basis that is the normal range for a well-optimized power plant.

• Second part is the steam cycle efficiency. Modern Rankine cycle, adopted in coal fired power plants, have efficiencies that vary from 32 % to 42 %. This depends mainly on the steam parameters. Higher steam perssure and temperatures in the range of 600 ° C and 230 bar have efficiencies around 42 %. We assume a value of 38 % for our case.

• The overall conversion efficiency then is (38% x 88%) 33.44 %.

Heat rate is the heat input required to produce one unit of electricity. (1 kw hr)

• One Kw is 3600 kJ/hr. If the energy conversion is 100 % efficient then to produce one unit of electricity we require 3600 kJ.
  
• After considering the conversion efficiency in a power plant we require an heat input of (3600 / 33.44% ) 10765 kJ/ kw hr.

• Since coal has a heat value of 20,000 kJ/kg, for producing one kw.hr we require (10765 / 20000) 0.538 kg of coal. This translates to (0.538 x 100 x 1,000) 53800 kg/hr (53.8 T/hr) of coal for an output of 100 MW.

Basic cost of coal depends on the market conditions. Transportation costs, regional influences and government taxes are also part of the cost. Coal trader’s web sites give base prices in the international market.

• We take a coal price of around 65 $ / Ton.
• The cost of coal consumed by 100 MW power plant is (53.8 x 65) 3497 $ /hr
• A 100 MW unit produces 100,000 units of electricity. So the cost of coal per unit of electricity is (3497/100,000) 3.5 cents per unit.