Economic of power generation 11

 Question= A power station having a maximum demand of 100 mw has a load factor of 30% and is to be supplied by one of the following schemes.

(1) A steam station in conjunction with a hydro - electric station, the latter supplying 100×10⁶ kwh per annum with a maximum output of 40 mw. 

(2) a steam station capable of supplying the whole load . 

(3) a hydro station capable of supplying the whole load. Compare the overall cost per kwh generated,??  assuming the following data .

Solution= overall cost/kwh= (total annual charges for both steam and hydro station)÷ ( unit generated per annum) , 

» Total annual charges steam station = 

• so, steam station, total annual cost= operating cost+annual interest and depreciation, 

» operating cost= operating cost/kwh 5 paise × unit supplied by station, 

» unit supplied by station = unit generated per annum - unit supplied by hydro station , 

» unit generated per annum = maximum demand × L F. × hours in a year, = 100 mw × 30% × 8760 hours , = 262.8×10⁶ kwh , 

» unit supplied by hydro station = 100 ×10⁶ kwh, 

» so, unit supplied by station = 262.8×10⁶ kwh - 100×10⁶ kwh  = 162.8 × 10⁶ kWh, 

» so, operating cost = 5 paise × 162.8 × 10⁶ kwh , = 8.14 ×10⁶ RS , (add)

» annual interest and depreciation = interest and depreciation on capital investment 12% × capital cost, 

» capital cost = power station maximum demand (100 kw) - hydro station maximum output 40 mw, = 60 mw (balance demand) , × capital cost per kw installed(RS 1250), 

» capital cost = 60×10³ kw ×rs 1250 = 75×10⁶ RS , 

» annual interest and depreciation = 12% × 75 × 10⁶ = 9 × 10⁶ RS , (add)

» total annual cost =( 8.14 ×10⁶ RS) + ( 9 × 10⁶ RS ) , = 17.14 × 10⁶ RS , 

• Total annual charges hydro station station = 

» total annual cost= annual interest and depreciation+operating cost+transmission cost , 

» annual interest and depreciation = capital cost × interest and depreciation on capital cost 10% , 

» capital cost = capital cost per kw installed × hydro maximum output

» capital cost = RS 2500 × 40 × 10³ kw =100×10⁶ RS , 

» annual interest and depreciation = 10% × 100×10⁶ RS , = 10 × 10⁶ RS , (add) 

» operating cost= operating cost per kwh × capital cost= 1.5 paise × =100×10⁶ RS = 1.5 ×10⁶ RS , (add) 

» transmission cost= transmission cost per kwh × capital cost, = 0.002 RS ×100×10⁶ RS = RS 0.2 ×10⁶ (add) 

» Total annual cost= RS (10+1.5+0.2)×10⁶ ,= 11.7 ×10⁶ RS (add)

» total annual charges for both steam and hydro station = RS (17.14 + 11.7)× 10⁶ = RS 28.84 × 10⁶ , 

» overall cost per kwh = 28.84×10⁶÷262.8×10⁶ =RS 0.1097 or , 10.97 paise , answer ✓

(2) overall cost per kwh= fixed charges per kwh+ operating cost per unit , 

• A steam station whole load 

» maximum load = 100 mw , 

» fixed charges/kwh = annual interest and depreciation ÷ unit generated per annum, 

» annual interest and depreciation =interest and depreciation on capital cost 12% × capital cost, 

» capital cost = capital cost per kw installed × maximum demand,  = RS 1250 × 100 mw, = 125×10⁶ RS, 

»annual interest and depreciation = 12% ×125×10⁶ RS = 15×10⁶ RS, 

» unit generated per annum = maximum demand × L F. × hours in a year, = 100 mw × 30% × 8760 hours , = 262.8×10⁶ kwh , 

» fixed charges per kwh= 15×10⁶ RS ÷ 262.8 ×10⁶ = RS 0.0571 or , 5.71 paise, 

» operating cost per kwh= 5 paise. ( is given)

» transmission cost/kwh= negligible.

» So, overall cost per kwh = 5.71+5= 10.71 paise, answer ✓

(3) • hydro station maximum demand= 100 mw , 

 » overall cost per kwh= fixed charges per kwh+operating cost per kwh (1.5 paise) +transmission cost per kwh ( 0.2 paise) , 

» fixed charges per kwh = annual interest and depreciation ÷ unit generated per annum, 

» annual interest and depreciation= interest and depreciation on capital investment 10% × capital cost , 

» capital cost = capital cost per kw installed (RS 2500 ) × maximum demand, = RS 2500 × 100 ×10³ kw , = 250 × 10⁶ RS , 

»annual interest and depreciation= 10% × 250 × 10⁶ RS , = 25×10⁶ RS, 

» fixed charges per kwh= 25×10⁶ RS ÷ 262.8×10⁶ = RS 0.0951 or, 9.51 paise (add) 

» adding the operating cost per unit and transmission cost per unit, 

» we get = overall cost per kwh = 9.51 + 1.5 + 0.2 = 11.21 paise , answer ✓