1. PGE fixed and variable costs. Cost and performance parameters of PGE's "candidate" are entered in your spreadsheet (HW1 Template). Assumptions: Use 6.2% as the discount rate, from which to calculate capital recovery factor and levelized capital costs. Assume that fuel prices are $4/MMBtu for natural gas, and $2/MMBtu for biomass. For each of the technologies listed: a. What is the annualized capital cost per kW of capacity ($/kW-y)? Be sure to account for the different lifetimes in your capital recovery factor (CRF) calculation. b. What is the total levelized fixed cost per kW of capacity ($/kW-y)? c. Assuming that each plant's capacity factor is equal to the "expected availability/CF" value in the table (not realistic, FYI), what is the levelized fixed cost per MWh of energy produced ($/MWh)? d. What is the fuel cost per MWh of energy produced ($/MWh)? e. What is the total variable cost per MWh of energy ($/MWh)? f. Using the fuel emission rates intensities in section 12.5.2, estimate the combustion CO2 emissions in metric tonnes CO2 per MWh for each fossil fuel-fired technology? g. Assuming that CO2 emissions incur a cost of $20 per metric tonne (1000 kg, not the same as a 2000 lb. short ton), what is the CO2 emissions cost per MWh of energy ($/MWh) for the fossil plants? h. What is the total levelized cost of energy produced ($/MWh), including the assumed CO2 emission cost? PROBLEM #1 RENEWABLE FOSSIL Small-Scale BFB Binary Geothermal Biomass Central Station Solar PV Wind Plant PNW Wind Plant Montana CCCT-DF a. Annualized capital cost per kW of capacity ($/kW-y) $488.43 $320.76 $132.96 $140.93 $135.47 $78.74 Wartsilla Recip CHP SCCT $105.12 $45.27 Total annualized fixed cost per b. kW of capacity ($/kW-y) $488.69 $322.47 $143.16 $186.83 $191.37 $87.44 $108.55 $48.55 Levelized fixed cost per MWh C. of energy produced ($/MWh) $6.33 $4.27 $6.94 $6.37 $5.26 $1.01 $1.24 $0.54 Fuel cost per MWh of energy d. produced ($/MWh) $0.00 $26.70 $0.00 $0.00 $0.00 $26.01 $15.60 $39.92 Total variable cost per MWh of e. energy ($/MWh) $27.29 $36.19 $0.84 $0.84 $0.84 $28.66 $24.71 $49.40 CO2 emissions intensities f. (metric tons per MWh) 0.00 0.00 0.00 0.00 0.00 0.03 0.02 0.05 CO2 emissions cost per MWh g. of energy ($/MWh) $0.00 $0.00 $0.00 $0.00 $0.00 $0.69 $0.02 $1.06 Total levelized cost of energy h. produced ($/MWh) $33.62 $40.46 $7.78 $7.21 $6.10 $30.36 $26.36 $51.00 DATA: Nameplate (MW) Life (years) Capacity factor Cap Cost ($/kW) Fixed O&M ($/kW-yr) Variable O&M ($/MWh) Heat Rate (Btu/kWh) Fuel cost ($/MMBtu) CO2 Emissions Factor (lb/MMBtu) CO2 Tax ($/tonne) Small-Scale BFB Central Station 35 30 0.87 Solar PV 103 25 338 27 400 Wartsilla 110 30 SCCT 230 30 Wind Plant Wind Plant PNW Montana CCCT-DF 236 27 35 0.42 0.95 0.96 1650 1071 45.9 8.7 1442 3.43 0.98 621 0.84 2.65 9.11 3.28 9.48 6503 3900 9981 mmmm. Binary Geothermal 35 Biomass 30 0.89 0.24 0.34 6700 4400 1500 1600 27.29 1.71 9.49 10.2 45.9 0.84 0.84 13350 2 $0.26 117 20 117 117 20 20 PROBLEM #2 Fixed Cost ($/kW/y) a. Wartsilla Recip CHP Equation 108.55 CCCT Equation 87.44 SCCT Equation 48.55 Variable Cost ($/kWh) 500 1000 1500 910 1213 1516 2000 1819 2122 2500 3000 2. PGE load duration and screening curves. The PGE resource plan lacks a good load duration curve, which is odd, but we can use the one shown below for this exercise. The PGE load is about 3900 MW in the highest hour of the year and 1400 MW in the lowest hour. The annual average load is about 2600 MW. 2018 Load Duration Curve 4000 3500 the delta between the highest 1st and 100th hour is 549 MW, and between the 1st and 10th 299 MW 2425 2728 3031 3334 3637 3940 4243 4546 1910 4849 5152 5455 5758 1909 6364 4999 7576 8182 Hours For this exercise, assume the PGE generation fleet is composed entirely of three types: natural gas-fired reciprocating engine, combined-cycle CCCT and simple-cycle SCGT plants, with the characteristics shown on the spreadsheet template. Assume that the reciprocating engine produces combined heat and power (CHP), with a net heat rate of only 3900 Btu/kWh. a. Write down the equations for annual cost of capacity (ACOC) in $/kW-year as a function of operating hours for each technology (you will already have the needed info-fixed and variable costs - in your solution to problem 1). b. Draw screening curves for each technology and determine the number of annual hours of operation at which each pair of technologies has the same annual cost, i.e., the points of intersection on the screening curve, using either graphical methods or an algebraic solution. c. Estimate the load, from the load duration curve above, that corresponds to the points of intersection on the screening curve, which you can use to select the capacity level for each technology, as demonstrated in class. d. For the simple least-cost portfolio of the three generator types in a single year, estimate (based either on graphical methods or an algebraic solution) the needed generation capacity value for each type of generator and for the portfolio as a whole, assuming a 17% planning reserve margin that is supplied by additional SCCT capacity.