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# Demand Factor, Load Factor, and Diversity Factor

## Demand Factor

The demand factor of an electric power station is defined as the ratio of maximum demand on the power station to its connected load, i.e.,

$$\mathrm{Demand \:Factor\:=\:\frac{Maximum\: Demand}{Connected \:Load}}$$

Generally, the value of demand factor is less than 1. It is because the maximum demand on the power station is usually less than the connected load to the power station. The knowledge of demand factor is important in determining the capacity of equipment of the power plant.

## Numerical Example (1)

A generating station has a connected load of 50 MW and a maximum demand of 30 MW. Determine the demand factor of the power station.

**Solution**

Given,

$$\mathrm{Maximum\: Demand\:=\:30\: MW \:and\: Connected\: Load\:=\:50\: MW}$$

$$\mathrm{\because Demand \:Factor\:=\:\frac{Maximum \:Demand}{Connected\: Load}}$$

$$\mathrm{\therefore Demand \:Factor\:=\:\frac{30\:MW}{50\:MW}\:=\:0.6}$$

## Load Factor

The load factor of a power station is defined as the ratio of average load to the maximum demand on the power station during a given period, i.e.,

$$\mathrm{Load\: Factor\:=\:\frac{Average\: Load}{Maximum\: Demand}}$$

If the power station is in operation for T hours, then the load factor is given by,

$$\mathrm{Load\: Factor\:=\:\frac{Average\: Load\:\times \mathit{T}}{Maximum\: Demand\:\mathit{T}}}$$

$$\mathrm{\therefore Load \:Factor\:=\:\frac{Total\: units\: generated\: in\: \mathit{T} \:hours}{Maximum\: Demand\:\times \:\mathit{T}}}$$

The load factor can be *daily load factor, monthly load factor* or annual load factor if the time period (T) considered is a day or a month or a year respectively. The load factor of a power station is always less than 1. It is because the average load on the power station is smaller than the maximum demand. The load factor is very important because it is used to determine the overall cost per unit generated, i.e., if the load factor of the power station is higher, then the cost per unit generated will be lesser.

## Numerical Example (2)

The maximum demand on a power generating plant is 2000 kW. If the number of units (in kWh) generated per year is 50 ☓ 10^{4}. Determine the annual load factor of the plant.

**Solution**

The load factor of the power station is given by,

$$\mathrm{Load\: Factor\:=\:\frac{Average\: Load}{Maximum\: Demand}}$$

$$\mathrm{\because Average\: load\:=\:\frac{Units\: generated\: per\: annum}{Hours\: in\: a\: year}\:=\:\frac{50\:\times 10^{4}}{8760}\:57.078\:kW}$$

$$\mathrm{\therefore Annual\: Load \:Factor\:=\:\frac{57.078}{2000}\:0.0285\:=\:2.85\%}$$

## Diversity Factor

The diversity factor of the power station is defined as the ratio of sum of individual maximum demands to the maximum demand on the power station, i.e.,

$$\mathrm{Diversity \:Factor\:=\:\frac{Sum\: of\: individual \:maximum \:demands}{Maximum \:demand \:on\: the\: power\: station}}$$

The diversity factor of a power station is always greater than 1. The diversity factor plays a vital role in the determination of cost of generation of power. The greater is the diversity factor, the lesser is the cost of generation of power.

## Numerical Example (3)

A diesel power plant supplies the following loads to various consumers −

Domestic light = 500 kW

Domestic power = 100 kW

Industrial consumers = 2000 kW

Commercial establishments = 700 kW

If the maximum demand on the power station is 3000 kW. Determine the diversity factor of the power plant.

**Solution**

The diversity factor of a power station is given by,

$$\mathrm{Diversity \:Factor\:=\:\frac{Sum\: of\: individual \:maximum \:demands}{Maximum \:demand \:on\: the\: power\: station}}$$

$$\mathrm{\Rightarrow Diversity \:Factor\:=\:\frac{\mathrm{\left ( 500\:+\:100\:+\:2000\:+\:700 \right )}kW}{3000\:kW}\:=\:1.1}$$

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