Rated Average Generating Unit Type (MW) (MBtu/MWh) Problem 1 An existing power system has the following aggregated capacity at the beginning of year 1995: Fuel Cost Escalation Rate (%year) 1996-2015 Average Fuel Cost Capacity Heat Rate Availability in 1995 (S/MBtu) Coal steam 2500 10 80 3 6 Oil steam 2500 10 80 7 11 Gas Turbine 2222 12 90 7 11 Combined-cycle 1176 8 85 7 11 Nuclear steam 1250 10 80 2 6 9648 Reliability studies indicate that the utility requires an additional 600 MW of effective capacity annually between in the year 1995 and 1998. The utility is considering two options: (a) adding new combined-cycle units or (b) converting 2500 MW of oil-steam to 2500 MW of coal-fired generation plus combined-cycle units or plus gas-turbine units. The characteristics of these alternatives are: Heat Rate MW Alternative Oil-to-coal Percent size Availability Capacity MWh) MW Capital Cost in Effective (MBtu/ year 1995 Fuel Cost in Fuel Cost Escalation year 1995 Rate (% year) (S/kW) (S/MBtu) 1996-2015 conversion of 2500 80% N/A 10 750 3 6 steam units New combined-cycle 392 85% 350 8 800 7 11 New gas turbines 50 90% 45 12 400 11 The 1995 annual load duration curve is approximated as: Hours per year Load (MW) 1000 8000 4000 6500 3760 5000 The capital cost for each alternative is forecasted to escalate 5% each year over the next 20 years. The annual load growth is 5%. Use DP to determine the best mix of units to supply the load in each year through 1998. The interest rate is ignored in this case and the capital cost escalation factor is 5% so for each year the capital cost is calculated as Capital Cost in nth year - (Capital Cost in 1st year)-(1+a)* 'where n is the number of years in which the Capital Cost is calculated and a is the escalation factor. In this problem the first year is 1995 and the period is 1995-1998. The same procedure applies to fuel cost which is escalated by the fuel cost escalation rate: Fuel Cost in nth year = (Fuel Cost in 1st year)-(1+a)*