This problem concerns a hypothetical no-storage wind/diesel system on a remote i

Question

This problem concerns a hypothetical no-storage wind/diesel system on a remote island.  Wind and load data for the island for ten hours are shown below.  Assume that the wind turbine has the following power curve:

P = 0 for U < 4 m/s

P = 30*U - 120 for U > 4m/s

   

Where P = power (kW) and U = wind speed (m/s)

The diesel to be considered is one rated at 100 kW, with no load fuel consumption of 2 fuel units per hour and full load fuel consumption of 10 units per hour.

For the first 10 hours of the find the following:

(1) the average wind power, kW ---> I found this to be 46.8 kW

(2) the useful wind power, kW

(3) the average dumped power, kW

(4) the average fuel consumption, units/hr

Wind         Load m/s kW 4.3 36.6 5.4 35 5.6 36.1 5.1 37.4 6.3 37.7 6.9 39.8 6 52.7 5.8 56 5 60.1 5.2 63.2

Explanation / Answer

1) avg wind power =3*(4.3+5.4+..+5.2) -120 =46.8

2) useful wind power is calculated by adding power ouput from wind (where rquirment is greater) or adding requirment (where wind energy is greater) =373.3 kw.hr

3)dumped =7+11.9+21.3+47.2+7.3 =94.7 kw.hr

4)here for no load 2 units and ful koad 10 units hence for 100kw 8 units variable

2 is aded to avg as for no power 2 uints are used

avg fuel comsumption is =(27.6+4.4+2+30.1+37.2)/80 +2 = 3.266 uints per hour

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