# Plant Load Factor and its Calculation

### What is Plant Load Factor?

Plant Load Factor (PLF) is the ratio of average power generated by the plant to the maximum power that could have been generated for a given time period. Thus mathematically it can be written as,

PLF = P_{avg} / P_{max}…………….(1)

As it is the ratio of same quantity, hence it is a unit less quantity.

Note that maximum power P_{max} is dependent on load. During peak load period a power plant is supposed to operate at its maximum capacity. Plant Load Factor may either be calculated on daily basis, weekly, monthly or early basis. It is clear from the mathematical representation of PLF that value of Plant Load Factor is less than one since P_{avg} < P_{max}. But when a plant is operated above its rating for a certain period of time, then obviously for that period average power supplied by the Plant i.e. P_{avg} will be more than the P_{max}. Therefore for such case value of PLF become more than unity. But it is usually not the practice to operate a Generator beyond its rating. Thus, normally PLF is less than 1.

PLF can also be defined in terms of energy supplied by the plant for a given period of time. Let us suppose that we are only interested in calculating PLF for a period of T. Then plant load factor PLF from (1),

PLF = (P_{avg}xT) / (P_{max}xT)

= Average Energy Supplied / Energy Supplied at maximum demand ……..(2)

Thus in terms of energy, Plant Load Factor is the ratio of average energy supplied for a given time period to the energy that could have been supplied at maximum loading condition for the same time period.

Plant Load Factor is one of the performance parameter of a power plant. It is a degree of plant capacity utilization for a period of time. More the PLF, more will be the revenue of the plant. Alternatively, higher the PLF, lesser will be cost of per unit (kWh) energy generated.

**Calculation of Plant Load Factor:**

We already discussed the mathematical representation of PLF. It is calculated for a certain time period as per the definition. Therefore it may either be calculated from Load Curve or Load Duration Curve. If we have the load curve, then Plant Load Factor can be calculated using (1). But for calculation from load duration curve, it is calculated by using energy interpretation i.e. (2). Let us consider a load curve as shown below and try to calculate the Plant Load Factor.

As per the definition,

Plant Load Factor, PLF = P_{avg} / P_{max}

From the load curve, P_{max} = 200 MW but we need to calculate the average power P_{avg}.

Average power Pavg can be calculated as below.

Pavg = Units (kWh) Generated per day / 24 hrs

But units (kWh) generated per day is the area under the curve i.e. area of ABCFILM.

Area under the curve = Area of (rectangle ABLM + Trapezoid BCFI)

= [(100×16) + (1/2)(12+4)x100]

= 1600 + 800

= 2400 MWh = 2400×10^{3} kWh

= 2400×10^{3} Units

= 2.4 Million Units (MUs)

Thus the average power P_{avg }= 2400 MWh / 24 h

= 100 MW

Hence,

PLF = 100 / 200 = 0.5

**Second Method:**

Let us assume that the plant is operated through the day at its maximum loading i.e. 200 MW. Then the total energy that could have been generated will be equal to the 24×200 MWh = 4800 MWh (This is simple multiplication as the power output is assumed constant and time period is known).

But the actual energy generated by the plant in 24 hours is equal to the area under the curve ABCFILM. Thus by using energy interpretation of plant load factor i.e. (2),

PLF = area under the curve ABCFILM / 4800

= 2400 / 4800 = 0.5

Thus the second method is not different from the first method but actually both are same.