Electrical Power Systems

406 Electrical Power Systems
In ig. 16.1, (MW) min is the minimum loading limit of generator below which it is uneconomical
or technically infeasible and (MW) max is the output limit.
The shape of the fuel cost curve (concave upward) may be understood in terms of the heat
rate curve. The approximate shape of this curve is shown in ig. 16.2.
ig. 16.2: Heat-rate curve.
The curve gives Hi(Pgi), the MKCal of heat energy supplied by burning the fuel per MWhr
of electric energy. The generating unit is most efficient at the minimum point of this curve. This
curve reflects the drop in efficiency of most energy conversion machines at the low and high
ends. At peak efficiency, the heat rates of modern fossil-fuel unit is around 2.40 MKCal /MWhr,
3600 ´ 100
giving a peak efficiency of
= 35.7%. Typical maximum overall efficiencies vary
2. 4 ´ 4. 2 ´ 1000
in the range of 34 to 39%. or 100% conversion, the heat rate is approximately 0.86 MKCal/
MWhr. Note that 1 MKCal = 1.164 MWhr is the equivalent of heat. or example, suppose that
ig. 16.2, Pgi = 100 MW. rom the ig. 16.2, we see that Hi (Pgi ), the corresponding heat rate is
0.86 MKCal. In an hour, the electrical energy output would be 100 MWhr while the heat energy
required would be 100 × 0.86 = 86 MKCal. Thus, a heat input energy rate of 86 MKCal/hr is
required to sustain a power output of 100 MW. we get this figure by multiplying Pgi (three-phase
power) by the corresponding heat rate Hi (Pgi ). Generally, the heat input energy rate, i (Pgi ), is
found by the formula
i (Pgi ) = Pgi Hi (Pgi ) ...(16.1)
where Pgi = three-phase power (MW)
Hi (Pgi ) = heat-rate (MKCal/MWhr)
i(Pgi) = input energy rate (MKCal/hr)
Let the cost of the fuel be K Rs/MKCal.
Then the input fuel cost, Ci (Pgi ) is
Ci (Pgi ) = Ki (Pgi ) = KPgiHi (Pgi ) ...(16.2)
The heat-rate curve of ig. 16.2, may be approximated in the form,
H i(P gi) =
a¢ i
P gi
+ b´ i + g´ i Pgi ...(16.3)