1. Suppose we are planning a 100 MW wind farm with a 1-year p-50 capacity factor of 44% and a 1-year...

Question

1. Suppose we are planning a 100 MW wind farm with a 1-year p-50 capacity factor of 44% and a 1-year p-99 capacity factor of 36%. The total cost to build the plant is $1,400/kW, and all power will be sold on a long-term power purchase agreement for $35/MWh. The plant has fixed operating costs of $40/kW-yr. A lender is willing to offer a 25-year loan at an interest rate of 4.5%.
(a) What is the wind farm’s Cash Flow Available for Debt Service (CFADS) if the lender sizes the debt based on a debt service coverage ratio of 1.30x at the p-50 level?
(b) What would the CFADS be if the lender instead used a DSCR of 1.00x at the p-99 level?
(c) Suppose the lender uses the smaller of the annual payments implied by parts (a) and
(b). What is the total debt capacity (i.e., maximum loan size) for the project?
(d) Assuming the project developers use the maximum amount of debt on offer, what percent of the project will be funded by the equity investors?
Answers to this question have been provided in the Excel file. Use the information in this question and the answer provided to answer the next questions.
2. Suppose we are planning power system operations for 24 hours. Data for a typical spring day in the San Diego Gas & Electric te
itory has been uploaded to an Excel workbook on Canvas (with generators aggregated to avoid exceeding Excel Solver’s limit of 200 decision variables). Data includes the resources, the availability of renewable resources in each of the 24 hours, and demand. Note that demand is recorded at the level of the transmission-distribution interface, and accordingly does not include any load served by distribution-level photovoltaics.
Construct a model in Excel describing this system and solve to determine an optimal production schedule for the six resources. Assume a gas price of $3.50/MMBtu, but leave in the capability to modify this assumption for future problem sets.
(a) What is the total cost to operate the system for the day?
(b) In what hours is the combined cycle gas plant on the margin? What is the price during these hours?
Answers to this question have been provided in the Excel file. Use the information in this question and the answer provided to answer the next questions.
2. Consider the linear program from Problem 2. If you did not produce a sensitivity report that yielded prices in each of the 24 hours, do so now (or consult the posted answers). Instead of the system problem, consider the optimization problem faced by the CCGT, which wants to maximize profit. Suppose that the system operator sets prices equal to the shadow prices calculated in the sensitivity report. The operator of the CCGT then determines a production schedule that maximizes revenue (quantity times price) minus its production cost. Note that we assume that the CCGT is a price taker, i.e., it cannot change the price by changing its production.
(a) For this optimization problem, what is the objective function?
(b) For this optimization problem, what are the decision variables?
(c) Construct a model describing the CCGT’s problem in Excel and solve to determine a profit-maximizing production schedule. How does the profit-maximizing schedule compare to the socially optimal schedule determined in problem 2?
3. Consider a modification to the 100 MW wind farm from problem 2. Suppose the annual capacity factor from the plant is normally distributed with mean of 44% and standard deviation of 4%. The total cost to build the plant is $1,400/kW, and the plant has fixed operating costs of $40/kW-yr. A lender is willing to offer a 25-year loan at an interest rate of 4.5%. However, unlike in problem 1, the plant does not sell its power on a long-term contract. Instead, it operates on a merchant basis, selling in the spot market. Spot market prices for the wind farm are a product of the natural gas price, the average market heat rate for the year, and a nodal scalar, each of which (we assume) follows a normal distribution. The natural gas price has mean $3.50/MMBtu and standard deviation $0.35/MMBtu. The average market heat rate has mean 10 MMBtu/MWh and standard deviation 0.5 MMBtu/MWh. The nodal scalar has mean 1.0 and standard deviation .03. This means that the expected price is $35/MWh, the same as the contracted price in problem 1. All random variables are assumed to be independent.
(a) In Excel, draw 1,000 samples of the 4 random variables and compute the annual electricity revenue for the plant under each draw. What is the average electricity revenue across the 1,000 samples? How does it compare to the p-50 revenue in problem 1?
(b) Compute the p-50 and p-99 CFADS under these assumptions, i.e., the 500th and 990th ranked outcomes in your sample.
(c) Given the increased uncertainty, suppose the debt provider insists on a debt service coverage ratio of 2.25x at the p-50 level. What is the total debt capacity of the project?
(d) Assuming the project developers use the debt size calculated in (c), what percent of the project will be funded by the equity investors? How does this compare to the contracted case we considered in problem 1? Note that since Excel will recalculate every time a new sample is drawn, it is okay if output values fluctuate slightly upon recalculation.

Problem 1
        Assumptions
                Unit
        Plant Capacity    100    MW
        Capital Cost    1,400    $/kW
        P-50 Capacity Factor    44.0%    %
        P-99 Capacity Factor    36.0%    %
        Operating Expenses    $40.00    per KW-Yea
        PPA Price    $35.00    per MWh
        Sizing DSCR p-99    1.00x     Ratio
        Sizing DSCR p-50    1.30x     Ratio
        Interest Rate    4.5%    %
        Length    25    Years
        Hours in Year    8,760    Hours
        Conversion to USD 000    1,000    USD
        Debt Sizing
                p-50    p-99
        Electricity Production (MWh)        385,440    315,360
        PPA Rate (/MWh)        $35.00    $35.00
        Electricity Revenue        $ 13,490,400    $ 11,037,600
        Operating Expense        4,000,000    4,000,000
        EBITDA        $ 9,490,400    $ 7,037,600
        Cash Flow Available for Debt Service (CFADS)        $ 9,490,400.00    $ 7,037,600.00
        Maximum debt service        $ 7,037,600.00
        Debt Capacity        ($104,355,003.40)
        Capital Cost        140,000,000
        Equity share        25.5%
Demand
    Hour    Demand_MW
    1    1615
    2    1553
    3    1518
    4    1562
    5    1733
    6    1976
    7    2274
    8    2597
    9    2838
    10    3023
    11    3125
    12    2963
    13    2743
    14    2666
    15    2578
    16    2482
    17    2422
    18    2374
    19    2378
    20    2501
    21    2506
    22    2258
    23    1988
    24    1760
Resources
    R_ID    Resource    Existing_Cap_MW    Var_OM_cost_per_MWh    Fuel    Heat_rate_MMBTU_per_MWh
    1    biomass    21.4    5.234    None    12.76
    2    natural_gas_fired_combined_cycle    1928.5    3.4    pacific_naturalgas    7.52
    3    natural_gas_fired_combustion_tu
ine    788.4    10.8    pacific_naturalgas    10.69
    4    onshore_wind_tu
ine    217.6    0    None    0
    5    small_hydroelectric    7.32    0    None    0
    6    solar_photovoltaic    500    0    None    0
Availability
        1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24
    onshore_wind_tu
ine    0.7505    0.7803    0.529    0.4621    0.3703    0.6396    0.3409    0.2269    0.7691    0.6046    0.511    0.4233    0.2394    0.2973    0.2262    0.3006    0.2628    0.3613    0.2418    0.2823    0.3305    0.4414    0.5812    0.6637
    small_hydroelectric    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351    0.4351
    solar_photovoltaic    0    0    0    0    0    0    0.0553    0.2211    0.4776    0.5757    0.6039    0.6139    0.6446    0.6455    0.6241    0.5695    0.4678    0.3236    0.0477    0    0    0    0    0
Sensitivity Report 1
    Microsoft Excel 16.0 Sensitivity Report
    Worksheet: [ps3_answers.xlsx]Model
    Report Created: 10/28/2022 11:51:55 AM
    Variable Cells
                Final    Reduced    Objective    Allowable    Allowable
        Cell    Name    Value    Cost    Coefficient    Increase    Decrease
        $C$13    biomass Hour1    21.4    -24.486    5.234    24.486    1E+30
        $D$13    biomass Hour2    21.4    -24.486    5.234    24.486    1E+30
        $E$13    biomass Hour3    21.4    -24.486    5.234    24.486    1E+30
        $F$13    biomass Hour4    21.4    -24.486    5.234    24.486    1E+30
        $G$13    biomass Hour5    21.4    -24.486    5.234    24.486    1E+30
        $H$13    biomass Hour6    21.4    -24.486    5.234    24.486    1E+30
        $I$13    biomass Hour7    21.4    -42.981    5.234    42.981    1E+30
        $J$13    biomass Hour8    21.4    -42.981    5.234    42.981    1E+30
        $K$13    biomass Hour9    21.4    -42.981    5.234    42.981    1E+30
        $L$13    biomass Hour10    21.4    -42.981    5.234    42.981    1E+30
        $M$13    biomass Hour11    21.4    -42.981    5.234    42.981    1E+30
        $N$13    biomass Hour12    21.4    -42.981    5.234    42.981    1E+30
        $O$13    biomass Hour13    21.4    -42.981    5.234    42.981    1E+30
        $P$13    biomass Hour14    21.4    -42.981    5.234    42.981    1E+30
        $Q$13    biomass Hour15    21.4    -42.981    5.234    42.981    1E+30
        $R$13    biomass Hour16    21.4    -42.981    5.234    42.981    1E+30
        $S$13    biomass Hour17    21.4    -42.981    5.234    42.981    1E+30
        $T$13    biomass Hour18    21.4    -42.981    5.234    42.981    1E+30
        $U$13    biomass Hour19    21.4    -42.981    5.234    42.981    1E+30
        $V$13    biomass Hour20    21.4    -42.981    5.234    42.981    1E+30
        $W$13    biomass Hour21    21.4    -42.981    5.234    42.981    1E+30
        $X$13    biomass Hour22    21.4    -42.981    5.234    42.981    1E+30
        $Y$13    biomass Hour23    21.4    -24.486    5.234    24.486    1E+30
        $Z$13    biomass Hour24    21.4    -24.486    5.234    24.486    1E+30
        $C$14    natural_gas_fired_combined_cycle Hour1     XXXXXXXXXX    0    29.72    18.495    24.486
        $D$14    natural_gas_fired_combined_cycle Hour2     XXXXXXXXXX    0    29.72    18.495    24.486
        $E$14    natural_gas_fired_combined_cycle Hour3     XXXXXXXXXX    0    29.72    18.495    24.486
        $F$14    natural_gas_fired_combined_cycle Hour4     XXXXXXXXXX    0    29.72    18.495    24.486
        $G$14    natural_gas_fired_combined_cycle Hour5     XXXXXXXXXX    0    29.72    18.495    24.486
        $H$14    natural_gas_fired_combined_cycle Hour6     XXXXXXXXXX    0    29.72    18.495    24.486
        $I$14    natural_gas_fired_combined_cycle Hour7    1928.5    -18.495    29.72    18.495    1E+30
        $J$14    natural_gas_fired_combined_cycle Hour8    1928.5    -18.495    29.72    18.495    1E+30
        $K$14    natural_gas_fired_combined_cycle Hour9    1928.5    -18.495    29.72    18.495    1E+30
        $L$14    natural_gas_fired_combined_cycle Hour10    1928.5    -18.495    29.72    18.495    1E+30
        $M$14    natural_gas_fired_combined_cycle Hour11    1928.5    -18.495    29.72    18.495    1E+30
        $N$14    natural_gas_fired_combined_cycle Hour12    1928.5    -18.495    29.72    18.495    1E+30
        $O$14    natural_gas_fired_combined_cycle Hour13    1928.5    -18.495    29.72    18.495    1E+30
        $P$14    natural_gas_fired_combined_cycle Hour14    1928.5    -18.495    29.72    18.495    1E+30
        $Q$14    natural_gas_fired_combined_cycle Hour15    1928.5    -18.495    29.72    18.495    1E+30
        $R$14    natural_gas_fired_combined_cycle Hour16    1928.5    -18.495    29.72    18.495    1E+30
        $S$14    natural_gas_fired_combined_cycle Hour17    1928.5    -18.495    29.72    18.495    1E+30
        $T$14    natural_gas_fired_combined_cycle Hour18    1928.5    -18.495    29.72    18.495    1E+30
        $U$14    natural_gas_fired_combined_cycle Hour19    1928.5    -18.495    29.72    18.495    1E+30
        $V$14    natural_gas_fired_combined_cycle Hour20    1928.5    -18.495    29.72    18.495    1E+30
        $W$14    natural_gas_fired_combined_cycle Hour21    1928.5    -18.495    29.72    18.495    1E+30
        $X$14    natural_gas_fired_combined_cycle Hour22    1928.5    -18.495    29.72    18.495    1E+30
        $Y$14    natural_gas_fired_combined_cycle Hour23     XXXXXXXXXX    0    29.72    18.495    24.486
        $Z$14    natural_gas_fired_combined_cycle Hour24     XXXXXXXXXX    0    29.72    18.495    24.486
        $C$15    natural_gas_fired_combustion_tu
ine Hour1    0    18.495    48.215    1E+30    18.495
        $D$15    natural_gas_fired_combustion_tu
ine Hour2    0    18.495    48.215    1E+30    18.495
        $E$15    natural_gas_fired_combustion_tu
ine Hour3    0    18.495    48.215    1E+30    18.495
        $F$15    natural_gas_fired_combustion_tu
ine Hour4    0    18.495    48.215    1E+30    18.495
        $G$15    natural_gas_fired_combustion_tu
ine Hour5    0    18.495    48.215    1E+30    18.495
        $H$15    natural_gas_fired_combustion_tu
ine Hour6    0    18.495    48.215    1E+30    18.495
        $I$15    natural_gas_fired_combustion_tu
ine Hour7     XXXXXXXXXX    0    48.215    1E+30    18.495
        $J$15    natural_gas_fired_combustion_tu
ine Hour8     XXXXXXXXXX    0    48.215    1E+30    18.495
        $K$15    natural_gas_fired_combustion_tu
ine Hour9     XXXXXXXXXX    0    48.215    1E+30    18.495
        $L$15    natural_gas_fired_combustion_tu
ine Hour10     XXXXXXXXXX    0    48.215    1E+30    18.495
        $M$15    natural_gas_fired_combustion_tu
ine Hour11     XXXXXXXXXX    0    48.215    1E+30    18.495
        $N$15    natural_gas_fired_combustion_tu
ine Hour12     XXXXXXXXXX    0    48.215    1E+30    18.495
        $O$15    natural_gas_fired_combustion_tu
ine Hour13     XXXXXXXXXX    0    48.215    1E+30    18.495
        $P$15    natural_gas_fired_combustion_tu
ine Hour14     XXXXXXXXXX    0    48.215    1E+30    18.495
        $Q$15    natural_gas_fired_combustion_tu
ine Hour15     XXXXXXXXXX    0    48.215    1E+30    18.495
        $R$15    natural_gas_fired_combustion_tu
ine Hour16     XXXXXXXXXX    0    48.215    1E+30    18.495
        $S$15    natural_gas_fired_combustion_tu
ine Hour17     XXXXXXXXXX    0    48.215    1E+30    18.495
        $T$15    natural_gas_fired_combustion_tu
ine Hour18     XXXXXXXXXX    0    48.215    1E+30    18.495
        $U$15    natural_gas_fired_combustion_tu
ine Hour19     XXXXXXXXXX    0    48.215    1E+30    18.495
        $V$15    natural_gas_fired_combustion_tu
ine Hour20     XXXXXXXXXX    0    48.215    48.215    18.495
        $W$15    natural_gas_fired_combustion_tu
ine Hour21     XXXXXXXXXX    0    48.215    48.215    18.495
        $X$15    natural_gas_fired_combustion_tu
ine Hour22     XXXXXXXXXX    0    48.215    48.215    18.495
        $Y$15    natural_gas_fired_combustion_tu
ine Hour23    0    18.495    48.215    1E+30    18.495
        $Z$15    natural_gas_fired_combustion_tu
ine Hour24    0    18.495    48.215    1E+30    18.495
        $C$16    onshore_wind_tu
ine Hour1     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $D$16    onshore_wind_tu
ine Hour2     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $E$16    onshore_wind_tu
ine Hour3     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $F$16    onshore_wind_tu
ine Hour4     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $G$16    onshore_wind_tu
ine Hour5     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $H$16    onshore_wind_tu
ine Hour6     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $I$16    onshore_wind_tu
ine Hour7     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $J$16    onshore_wind_tu
ine Hour8     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $K$16    onshore_wind_tu
ine Hour9     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $L$16    onshore_wind_tu
ine Hour10     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $M$16    onshore_wind_tu
ine Hour11     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $N$16    onshore_wind_tu
ine Hour12     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $O$16    onshore_wind_tu
ine Hour13     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $P$16    onshore_wind_tu
ine Hour14     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $Q$16    onshore_wind_tu
ine Hour15     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $R$16    onshore_wind_tu
ine Hour16     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $S$16    onshore_wind_tu
ine Hour17     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $T$16    onshore_wind_tu
ine Hour18     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $U$16    onshore_wind_tu
ine Hour19     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $V$16    onshore_wind_tu
ine Hour20     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $W$16    onshore_wind_tu
ine Hour21    71.9168    -48.215    0    48.215    1E+30
        $X$16    onshore_wind_tu
ine Hour22     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $Y$16    onshore_wind_tu
ine Hour23     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $Z$16    onshore_wind_tu
ine Hour24     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $C$17    small_hydroelectric Hour1     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $D$17    small_hydroelectric Hour2     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $E$17    small_hydroelectric Hour3     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $F$17    small_hydroelectric Hour4     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $G$17    small_hydroelectric Hour5     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $H$17    small_hydroelectric Hour6     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $I$17    small_hydroelectric Hour7     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $J$17    small_hydroelectric Hour8     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $K$17    small_hydroelectric Hour9     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $L$17    small_hydroelectric Hour10     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $M$17    small_hydroelectric Hour11     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $N$17    small_hydroelectric Hour12     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $O$17    small_hydroelectric Hour13     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $P$17    small_hydroelectric Hour14     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $Q$17    small_hydroelectric Hour15     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $R$17    small_hydroelectric Hour16     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $S$17    small_hydroelectric Hour17     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $T$17    small_hydroelectric Hour18     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $U$17    small_hydroelectric Hour19     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $V$17    small_hydroelectric Hour20     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $W$17    small_hydroelectric Hour21     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $X$17    small_hydroelectric Hour22     XXXXXXXXXX    -48.215    0    48.215    1E+30
        $Y$17    small_hydroelectric Hour23     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $Z$17    small_hydroelectric Hour24     XXXXXXXXXX    -29.72    0    29.72    1E+30
        $C$18    solar_photovoltaic Hour1    0    -29.72    0    1E+30    29.72
        $D$18    solar_photovoltaic Hour2    0    -29.72    0    1E+30    29.72
        $E$18    solar_photovoltaic Hour3    0    -29.72    0    1E+30    29.72
        $F$18    solar_photovoltaic Hour4    0    -29.72    0    1E+30    29.72
        $G$18    solar_photovoltaic Hour5    0    -29.72    0    1E+30    29.72
        $H$18    solar_photovoltaic Hour6    0    -29.72    0    1E+30    29.72
        $I$18    solar_photovoltaic Hour7    27.65    -48.215    0    48.215    1E+30
        $J$18    solar_photovoltaic Hour8    110.55    -48.215    0    48.215    1E+30
        $K$18    solar_photovoltaic Hour9    238.8    -48.215    0    48.215    1E+30
        $L$18    solar_photovoltaic Hour10    287.85    -48.215    0    48.215    1E+30
        $M$18    solar_photovoltaic Hour11    301.95    -48.215    0    48.215    1E+30
        $N$18    solar_photovoltaic Hour12    306.95    -48.215    0    48.215    1E+30
        $O$18    solar_photovoltaic Hour13    322.3    -48.215    0    48.215    1E+30
        $P$18    solar_photovoltaic Hour14    322.75    -48.215    0    48.215    1E+30
        $Q$18    solar_photovoltaic Hour15    312.05    -48.215    0    48.215    1E+30
        $R$18    solar_photovoltaic Hour16    284.75    -48.215    0    48.215    1E+30
        $S$18    solar_photovoltaic Hour17    233.9    -48.215    0    48.215    1E+30
        $T$18    solar_photovoltaic Hour18    161.8    -48.215    0    48.215    1E+30
        $U$18    solar_photovoltaic Hour19    23.85    -48.215    0    48.215    1E+30
        $V$18    solar_photovoltaic Hour20    0    -48.215    0    1E+30    48.215
        $W$18    solar_photovoltaic Hour21    0    -48

hw4-xpdvdukr.docx problem1-2-solutions-zpq3ksq2.xlsx hw4-iw12nrv5-hv5qynec.docx

Komalavalli · Accepted Answer

Problem 1
		Assumptions
				Unit
		Plant Capacity	100	MW
		Capital Cost	1,400	$/kW
		P-50 Capacity Factor	44.0%	%
		P-99 Capacity Factor	36.0%	%
		Operating Expenses	$40.00	per KW-Year
		PPA Price	$35.00	per MWh
		Sizing DSCR p-99	1.00x 	Ratio
		Sizing DSCR p-50	1.30x 	Ratio
		Interest Rate	4.5%	%
		Length	25	Years
		Hours in Year	8,760	Hours
		Conversion to USD 000	1,000	USD
		Debt Sizing
				p-50	p-99
		Electricity Production (MWh)		385,440	315,360
		PPA Rate (/MWh)		$35.00	$35.00
		Electricity Revenue		$   13,490,400	$   11,037,600
		Operating Expense		4,000,000	4,000,000
		EBITDA		$   9,490,400	$   7,037,600
		Cash Flow Available for Debt Service (CFADS)		$   9,490,400.00	$   7,037,600.00
		Maximum debt service		$   7,037,600.00
		Debt Capacity		($104,355,003.40)
		Capital Cost		140,000,000
		Equity share		25.5%
Demand
	Hour	Demand_MW
	1	1615
	2	1553
	3	1518
	4	1562
	5	1733
	6	1976
	7	2274
	8	2597
	9	2838
	10	3023
	11	3125
	12	2963
	13	2743
	14	2666
	15	2578
	16	2482
	17	2422
	18	2374
	19	2378
	20	2501
	21	2506
	22	2258
	23	1988
	24	1760
Resources
	R_ID	Resource	Existing_Cap_MW	Var_OM_cost_per_MWh	Fuel	Heat_rate_MMBTU_per_MWh
	1	biomass	21.4	5.234	None	12.76
	2	natural_gas_fired_combined_cycle	1928.5	3.4	pacific_naturalgas	7.52
	3	natural_gas_fired_combustion_turbine	788.4	10.8	pacific_naturalgas	10.69
	4	onshore_wind_turbine	217.6	0	None	0
	5	small_hydroelectric	7.32	0	None	0
	6	solar_photovoltaic	500	0	None	0
Availability
		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
	onshore_wind_turbine	0.7505	0.7803	0.529	0.4621	0.3703	0.6396	0.3409	0.2269	0.7691	0.6046	0.511	0.4233	0.2394	0.2973	0.2262	0.3006	0.2628	0.3613	0.2418	0.2823	0.3305	0.4414	0.5812	0.6637
	small_hydroelectric	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351	0.4351
	solar_photovoltaic	0	0	0	0	0	0	0.0553	0.2211	0.4776	0.5757	0.6039	0.6139	0.6446	0.6455	0.6241	0.5695	0.4678	0.3236	0.0477	0	0	0	0	0
Sensitivity Report 1
	Microsoft Excel 16.0 Sensitivity Report
	Worksheet: [ps3_answers.xlsx]Model
	Report Created: 10/28/2022 11:51:55 AM
	Variable Cells
				Final	Reduced	Objective	Allowable	Allowable
		Cell	Name	Value	Cost	Coefficient	Increase	Decrease
		$C$13	biomass Hour1	21.4	-24.486	5.234	24.486	1E+30
		$D$13	biomass Hour2	21.4	-24.486	5.234	24.486	1E+30
		$E$13	biomass Hour3	21.4	-24.486	5.234	24.486	1E+30
		$F$13	biomass Hour4	21.4	-24.486	5.234	24.486	1E+30
		$G$13	biomass Hour5	21.4	-24.486	5.234	24.486	1E+30
		$H$13	biomass Hour6	21.4	-24.486	5.234	24.486	1E+30
		$I$13	biomass Hour7	21.4	-42.981	5.234	42.981	1E+30
		$J$13	biomass Hour8	21.4	-42.981	5.234	42.981	1E+30
		$K$13	biomass Hour9	21.4	-42.981	5.234	42.981	1E+30
		$L$13	biomass Hour10	21.4	-42.981	5.234	42.981	1E+30
		$M$13	biomass Hour11	21.4	-42.981	5.234	42.981	1E+30
		$N$13	biomass Hour12	21.4	-42.981	5.234	42.981	1E+30
		$O$13	biomass Hour13	21.4	-42.981	5.234	42.981	1E+30
		$P$13	biomass Hour14	21.4	-42.981	5.234	42.981	1E+30
		$Q$13	biomass Hour15	21.4	-42.981	5.234	42.981	1E+30
		$R$13	biomass Hour16	21.4	-42.981	5.234	42.981	1E+30
		$S$13	biomass Hour17	21.4	-42.981	5.234	42.981	1E+30
		$T$13	biomass Hour18	21.4	-42.981	5.234	42.981	1E+30
		$U$13	biomass Hour19	21.4	-42.981	5.234	42.981	1E+30
		$V$13	biomass Hour20	21.4	-42.981	5.234	42.981	1E+30
		$W$13	biomass Hour21	21.4	-42.981	5.234	42.981	1E+30
		$X$13	biomass Hour22	21.4	-42.981	5.234	42.981	1E+30
		$Y$13	biomass Hour23	21.4	-24.486	5.234	24.486	1E+30
		$Z$13	biomass Hour24	21.4	-24.486	5.234	24.486	1E+30
		$C$14	natural_gas_fired_combined_cycle Hour1	1427.106268	0	29.72	18.495	24.486
		$D$14	natural_gas_fired_combined_cycle Hour2	1358.621788	0	29.72	18.495	24.486
		$E$14	natural_gas_fired_combined_cycle Hour3	1378.304668	0	29.72	18.495	24.486
		$F$14	natural_gas_fired_combined_cycle Hour4	1436.862108	0	29.72	18.495	24.486
		$G$14	natural_gas_fired_combined_cycle Hour5	1627.837788	0	29.72	18.495	24.486
		$H$14	natural_gas_fired_combined_cycle Hour6	1812.238108	0	29.72	18.495	24.486
		$I$14	natural_gas_fired_combined_cycle Hour7	1928.5	-18.495	29.72	18.495	1E+30
		$J$14	natural_gas_fired_combined_cycle Hour8	1928.5	-18.495	29.72	18.495	1E+30
		$K$14	natural_gas_fired_combined_cycle Hour9	1928.5	-18.495	29.72	18.495	1E+30
		$L$14	natural_gas_fired_combined_cycle Hour10	1928.5	-18.495	29.72	18.495	1E+30
		$M$14	natural_gas_fired_combined_cycle Hour11	1928.5	-18.495	29.72	18.495	1E+30
		$N$14	natural_gas_fired_combined_cycle Hour12	1928.5	-18.495	29.72	18.495	1E+30
		$O$14	natural_gas_fired_combined_cycle Hour13	1928.5	-18.495	29.72	18.495	1E+30
		$P$14	natural_gas_fired_combined_cycle Hour14	1928.5	-18.495	29.72	18.495	1E+30
		$Q$14	natural_gas_fired_combined_cycle Hour15	1928.5	-18.495	29.72	18.495	1E+30
		$R$14	natural_gas_fired_combined_cycle Hour16	1928.5	-18.495	29.72	18.495	1E+30
		$S$14	natural_gas_fired_combined_cycle Hour17	1928.5	-18.495	29.72	18.495	1E+30
		$T$14	natural_gas_fired_combined_cycle Hour18	1928.5	-18.495	29.72	18.495	1E+30
		$U$14	natural_gas_fired_combined_cycle Hour19	1928.5	-18.495	29.72	18.495	1E+30
		$V$14	natural_gas_fired_combined_cycle Hour20	1928.5	-18.495	29.72	18.495	1E+30
		$W$14	natural_gas_fired_combined_cycle Hour21	1928.5	-18.495	29.72	18.495	1E+30
		$X$14	natural_gas_fired_combined_cycle Hour22	1928.5	-18.495	29.72	18.495	1E+30
		$Y$14	natural_gas_fired_combined_cycle Hour23	1836.945948	0	29.72	18.495	24.486
		$Z$14	natural_gas_fired_combined_cycle Hour24	1590.993948	0	29.72	18.495	24.486
		$C$15	natural_gas_fired_combustion_turbine Hour1	0	18.495	48.215	1E+30	18.495
		$D$15	natural_gas_fired_combustion_turbine Hour2	0	18.495	48.215	1E+30	18.495
		$E$15	natural_gas_fired_combustion_turbine Hour3	0	18.495	48.215	1E+30	18.495
		$F$15	natural_gas_fired_combustion_turbine Hour4	0	18.495	48.215	1E+30	18.495
		$G$15	natural_gas_fired_combustion_turbine Hour5	0	18.495	48.215	1E+30	18.495
		$H$15	natural_gas_fired_combustion_turbine Hour6	0	18.495	48.215	1E+30	18.495
		$I$15	natural_gas_fired_combustion_turbine Hour7	219.085228	0	48.215	1E+30	18.495
		$J$15	natural_gas_fired_combustion_turbine Hour8	483.991628	0	48.215	1E+30	18.495
		$K$15	natural_gas_fired_combustion_turbine Hour9	478.758908	0	48.215	1E+30	18.495
		$L$15	natural_gas_fired_combustion_turbine Hour10	650.504108	0	48.215	1E+30	18.495
		$M$15	natural_gas_fired_combustion_turbine Hour11	758.771468	0	48.215	1E+30	18.495
		$N$15	natural_gas_fired_combustion_turbine Hour12	610.854988	0	48.215	1E+30	18.495
		$O$15	natural_gas_fired_combustion_turbine Hour13	415.521628	0	48.215	1E+30	18.495
		$P$15	natural_gas_fired_combustion_turbine Hour14	325.472588	0	48.215	1E+30	18.495
		$Q$15	natural_gas_fired_combustion_turbine Hour15	263.643948	0	48.215	1E+30	18.495
		$R$15	natural_gas_fired_combustion_turbine Hour16	178.754508	0	48.215	1E+30	18.495
		$S$15	natural_gas_fired_combustion_turbine Hour17	177.829788	0	48.215	1E+30	18.495
		$T$15	natural_gas_fired_combustion_turbine Hour18	180.496188	0	48.215	1E+30	18.495
		$U$15	natural_gas_fired_combustion_turbine Hour19	348.449388	0	48.215	1E+30	18.495
		$V$15	natural_gas_fired_combustion_turbine Hour20	486.486588	0	48.215	48.215	18.495
		$W$15	natural_gas_fired_combustion_turbine Hour21	480.998268	0	48.215	48.215	18.495
		$X$15	natural_gas_fired_combustion_turbine Hour22	208.866428	0	48.215	48.215	18.495
		$Y$15	natural_gas_fired_combustion_turbine Hour23	0	18.495	48.215	1E+30	18.495
		$Z$15	natural_gas_fired_combustion_turbine Hour24	0	18.495	48.215	1E+30	18.495
		$C$16	onshore_wind_turbine Hour1	163.3088	-29.72	0	29.72	1E+30
		$D$16	onshore_wind_turbine Hour2	169.79328	-29.72	0	29.72	1E+30
		$E$16	onshore_wind_turbine Hour3	115.1104	-29.72	0	29.72	1E+30
		$F$16	onshore_wind_turbine Hour4	100.55296	-29.72	0	29.72	1E+30
		$G$16	onshore_wind_turbine Hour5	80.57728	-29.72	0	29.72	1E+30
		$H$16	onshore_wind_turbine Hour6	139.17696	-29.72	0	29.72	1E+30
		$I$16	onshore_wind_turbine Hour7	74.17984	-48.215	0	48.215	1E+30
		$J$16	onshore_wind_turbine Hour8	49.37344	-48.215	0	48.215	1E+30
		$K$16	onshore_wind_turbine Hour9	167.35616	-48.215	0	48.215	1E+30
		$L$16	onshore_wind_turbine Hour10	131.56096	-48.215	0	48.215	1E+30
		$M$16	onshore_wind_turbine Hour11	111.1936	-48.215	0	48.215	1E+30
		$N$16	onshore_wind_turbine Hour12	92.11008	-48.215	0	48.215	1E+30
		$O$16	onshore_wind_turbine Hour13	52.09344	-48.215	0	48.215	1E+30
		$P$16	onshore_wind_turbine Hour14	64.69248	-48.215	0	48.215	1E+30
		$Q$16	onshore_wind_turbine Hour15	49.22112	-48.215	0	48.215	1E+30
		$R$16	onshore_wind_turbine Hour16	65.41056	-48.215	0	48.215	1E+30
		$S$16	onshore_wind_turbine Hour17	57.18528	-48.215	0	48.215	1E+30
		$T$16	onshore_wind_turbine Hour18	78.61888	-48.215	0	48.215	1E+30
		$U$16	onshore_wind_turbine Hour19	52.61568	-48.215	0	48.215	1E+30
		$V$16	onshore_wind_turbine Hour20	61.42848	-48.215	0	48.215	1E+30
		$W$16	onshore_wind_turbine Hour21	71.9168	-48.215	0	48.215	1E+30
		$X$16	onshore_wind_turbine Hour22	96.04864	-48.215	0	48.215	1E+30
		$Y$16	onshore_wind_turbine Hour23	126.46912	-29.72	0	29.72	1E+30
		$Z$16	onshore_wind_turbine Hour24	144.42112	-29.72	0	29.72	1E+30
		$C$17	small_hydroelectric Hour1	3.184932	-29.72	0	29.72	1E+30
		$D$17	small_hydroelectric Hour2	3.184932	-29.72	0	29.72	1E+30
		$E$17	small_hydroelectric Hour3	3.184932	-29.72	0	29.72	1E+30
		$F$17	small_hydroelectric Hour4	3.184932	-29.72	0	29.72	1E+30
		$G$17	small_hydroelectric Hour5	3.184932	-29.72	0	29.72	1E+30
		$H$17	small_hydroelectric Hour6	3.184932	-29.72	0	29.72	1E+30
		$I$17	small_hydroelectric Hour7	3.184932	-48.215	0	48.215	1E+30
		$J$17	small_hydroelectric Hour8	3.184932	-48.215	0	48.215	1E+30
		$K$17	small_hydroelectric Hour9	3.184932	-48.215	0	48.215	1E+30
		$L$17	small_hydroelectric Hour10	3.184932	-48.215	0	48.215	1E+30
		$M$17	small_hydroelectric Hour11	3.184932	-48.215	0	48.215	1E+30
		$N$17	small_hydroelectric Hour12	3.184932	-48.215	0	48.215	1E+30
		$O$17	small_hydroelectric Hour13	3.184932	-48.215	0	48.215	1E+30
		$P$17	small_hydroelectric Hour14	3.184932	-48.215	0	48.215	1E+30
		$Q$17	small_hydroelectric Hour15	3.184932	-48.215	0	48.215	1E+30
		$R$17	small_hydroelectric Hour16	3.184932	-48.215	0	48.215	1E+30
		$S$17	small_hydroelectric Hour17	3.184932	-48.215	0	48.215	1E+30
		$T$17	small_hydroelectric Hour18	3.184932	-48.215	0	48.215	1E+30
		$U$17	small_hydroelectric Hour19	3.184932	-48.215	0	48.215	1E+30
		$V$17	small_hydroelectric Hour20	3.184932	-48.215	0	48.215	1E+30
		$W$17	small_hydroelectric Hour21	3.184932	-48.215	0	48.215	1E+30
		$X$17	small_hydroelectric Hour22	3.184932	-48.215	0	48.215	1E+30
		$Y$17	small_hydroelectric Hour23	3.184932	-29.72	0	29.72	1E+30
		$Z$17	small_hydroelectric Hour24	3.184932	-29.72	0	29.72	1E+30
		$C$18	solar_photovoltaic Hour1	0	-29.72	0	1E+30	29.72
		$D$18	solar_photovoltaic Hour2	0	-29.72	0	1E+30	29.72
		$E$18	solar_photovoltaic Hour3	0	-29.72	0	1E+30	29.72
		$F$18	solar_photovoltaic Hour4	0	-29.72	0	1E+30	29.72
		$G$18	solar_photovoltaic Hour5	0	-29.72	0	1E+30	29.72
		$H$18	solar_photovoltaic Hour6	0	-29.72	0	1E+30	29.72
		$I$18	solar_photovoltaic Hour7	27.65	-48.215	0	48.215	1E+30
		$J$18	solar_photovoltaic Hour8	110.55	-48.215	0	48.215	1E+30
		$K$18	solar_photovoltaic Hour9	238.8	-48.215	0	48.215	1E+30
		$L$18	solar_photovoltaic Hour10	287.85	-48.215	0	48.215	1E+30
		$M$18	solar_photovoltaic Hour11	301.95	-48.215	0	48.215	1E+30
		$N$18	solar_photovoltaic Hour12	306.95	-48.215	0	48.215	1E+30
		$O$18	solar_photovoltaic Hour13	322.3	-48.215	0	48.215	1E+30
		$P$18	solar_photovoltaic Hour14	322.75	-48.215	0	48.215	1E+30
		$Q$18	solar_photovoltaic Hour15	312.05	-48.215	0	48.215	1E+30
		$R$18	solar_photovoltaic Hour16	284.75	-48.215	0	48.215	1E+30
		$S$18	solar_photovoltaic Hour17	233.9	-48.215	0	48.215	1E+30
		$T$18	solar_photovoltaic Hour18	161.8	-48.215	0	48.215	1E+30
		$U$18	solar_photovoltaic Hour19	23.85	-48.215	0	48.215	1E+30
		$V$18	solar_photovoltaic Hour20	0	-48.215	0	1E+30	48.215
		$W$18	solar_photovoltaic Hour21	0	-48.215	0	1E+30	48.215
		$X$18	solar_photovoltaic Hour22	0	-48.215	0	1E+30	48.215
		$Y$18	solar_photovoltaic Hour23	0	-29.72	0	1E+30	29.72
		$Z$18	solar_photovoltaic Hour24	0	-29.72	0	1E+30	29.72
	Constraints
				Final	Shadow	Constraint	Allowable	Allowable
		Cell	Name	Value	Price	R.H. Side	Increase	Decrease
		$C$35	Power Balance1	1615	29.72	1615	501.393732	1427.106268
		$D$35	Power Balance2	1553	29.72	1553	569.878212	1358.621788
		$E$35	Power Balance3	1518	29.72	1518	550.195332	1378.304668
		$F$35	Power Balance4	1562	29.72	1562	491.637892	1436.862108
		$G$35	Power Balance5	1733	29.72	1733	300.662212	1627.837788
		$H$35	Power Balance6	1976	29.72	1976	116.261892	1812.238108
		$I$35	Power Balance7	2274	48.215	2274	569.314772	219.085228
		$J$35	Power Balance8	2597	48.215	2597	304.408372	483.991628
		$K$35	Power Balance9	2838	48.215	2838	309.641092	478.758908
		$L$35	Power Balance10	3023	48.215	3023	137.895892	650.504108
		$M$35	Power Balance11	3125	48.215	3125	29.628532	758.771468
		$N$35	Power Balance12	2963	48.215	2963	177.545012	610.854988
		$O$35	Power Balance13	2743	48.215	2743	372.878372	415.521628
		$P$35	Power Balance14	2666	48.215	2666	462.927412	325.472588
		$Q$35	Power Balance15	2578	48.215	2578	524.756052	263.643948
		$R$35	Power Balance16	2482	48.215	2482	609.645492	178.754508
		$S$35	Power Balance17	2422	48.215	2422	610.570212	177.829788
		$T$35	Power Balance18	2374	48.215	2374	607.903812	180.496188
		$U$35	Power Balance19	2378	48.215	2378	439.950612	348.449388
		$V$35	Power Balance20	2501	48.215	2501	301.913412	486.486588
		$W$35	Power Balance21	2506	48.215	2506	307.401732	480.998268
		$X$35	Power Balance22	2258	48.215	2258	579.533572	208.866428
		$Y$35	Power Balance23	1988	29.72	1988	91.554052	1836.945948
		$Z$35	Power Balance24	1760	29.72	1760	337.506052	1590.993948
Model
		Assumptions
		Natural Gas Price	3.5
		Objective Function
		Total Cost	$   1,592,539.56
		Decision Variables
			Hour1	Hour2	Hour3	Hour4	Hour5	Hour6	Hour7	Hour8	Hour9	Hour10	Hour11	Hour12	Hour13	Hour14	Hour15	Hour16	Hour17	Hour18	Hour19	Hour20	Hour21	Hour22	Hour23	Hour24
			1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
	biomass	1	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4
	natural_gas_fired_combined_cycle	2	1427.106268	1358.621788	1378.304668	1436.862108	1627.837788	1812.238108	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1836.945948	1590.993948
	natural_gas_fired_combustion_turbine	3	0	0	0	0	0	0	219.085228	483.991628	478.758908	650.504108	758.771468	610.854988	415.521628	325.472588	263.643948	178.754508	177.829788	180.496188	348.449388	486.486588	480.998268	208.866428	0	0
	onshore_wind_turbine	4	163.3088	169.79328	115.1104	100.55296	80.57728	139.17696	74.17984	49.37344	167.35616	131.56096	111.1936	92.11008	52.09344	64.69248	49.22112	65.41056	57.18528	78.61888	52.61568	61.42848	71.9168	96.04864	126.46912	144.42112
	small_hydroelectric	5	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932
	solar_photovoltaic	6	0	0	0	0	0	0	27.65	110.55	238.8	287.85	301.95	306.95	322.3	322.75	312.05	284.75	233.9	161.8	23.85	0	0	0	0	0
		Cost Parameters
			1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
		1	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234	5.234
		2	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72	29.72
		3	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215	48.215
		4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
		5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
		6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
		Structural Constraints
			Power Balance1	Power Balance2	Power Balance3	Power Balance4	Power Balance5	Power Balance6	Power Balance7	Power Balance8	Power Balance9	Power Balance10	Power Balance11	Power Balance12	Power Balance13	Power Balance14	Power Balance15	Power Balance16	Power Balance17	Power Balance18	Power Balance19	Power Balance20	Power Balance21	Power Balance22	Power Balance23	Power Balance24
		Power Balance	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
			1615	1553	1518	1562	1733	1976	2274	2597	2838	3023	3125	2963	2743	2666	2578	2482	2422	2374	2378	2501	2506	2258	1988	1760
			1615	1553	1518	1562	1733	1976	2274	2597	2838	3023	3125	2963	2743	2666	2578	2482	2422	2374	2378	2501	2506	2258	1988	1760
		Capacity
			1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
		1	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4
		2	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5
		3	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4	788.4
		4	163.3088	169.79328	115.1104	100.55296	80.57728	139.17696	74.17984	49.37344	167.35616	131.56096	111.1936	92.11008	52.09344	64.69248	49.22112	65.41056	57.18528	78.61888	52.61568	61.42848	71.9168	96.04864	126.46912	144.42112
		5	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932
		6	0	0	0	0	0	0	27.65	110.55	238.8	287.85	301.95	306.95	322.3	322.75	312.05	284.75	233.9	161.8	23.85	0	0	0	0	0
Problem3 a &b
		Assumptions
		Natural Gas Price	3.5
		Objective Function
		Profit maximisation	-104356737.439444
		Decision Variables
			Hour1	Hour2	Hour3	Hour4	Hour5	Hour6	Hour7	Hour8	Hour9	Hour10	Hour11	Hour12	Hour13	Hour14	Hour15	Hour16	Hour17	Hour18	Hour19	Hour20	Hour21	Hour22	Hour23	Hour24
			1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
	biomass	1	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4	21.4
	natural_gas_fired_combined_cycle	2	1427.106268	1358.621788	1378.304668	1436.862108	1627.837788	1812.238108	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1928.5	1836.945948	1590.993948
	natural_gas_fired_combustion_turbine	3	0	0	0	0	0	0	219.085228	483.991628	478.758908	650.504108	758.771468	610.854988	415.521628	325.472588	263.643948	178.754508	177.829788	180.496188	348.449388	486.486588	480.998268	208.866428	0	0
	onshore_wind_turbine	4	163.3088	169.79328	115.1104	100.55296	80.57728	139.17696	74.17984	49.37344	167.35616	131.56096	111.1936	92.11008	52.09344	64.69248	49.22112	65.41056	57.18528	78.61888	52.61568	61.42848	71.9168	96.04864	126.46912	144.42112
	small_hydroelectric	5	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932	3.184932
	solar_photovoltaic	6	0	0	0	0	0	0	27.65	110.55	238.8	287.85	301.95	306.95	322.3	322.75	312.05	284.75	233.9	161.8	23.85	0	0	0	0	0	0
Problem3 c
		Assumptions
				Unit
		Plant Capacity	100	MW
		Capital Cost	1,400	$/kW
		P-50 Capacity Factor	44.0%	%
		P-99 Capacity Factor	36.0%	%
		Operating Expenses	$40.00	per KW-Year
		PPA Price	$35.00	per MWh
		Sizing DSCR p-99	1.00x 	Ratio
		Sizing DSCR p-50	1.30x 	Ratio
		Interest Rate	4.5%	%
		Length	25	Years
		Hours in Year	8,760	Hours
		Conversion to USD 000	1,000	USD
		Debt Sizing
				p-50	p-99
		Electricity Production (MWh)		385,440	315,360
		PPA Rate (/MWh)		$1.00	$1.00
		Electricity Revenue		$   385,440	$   315,360
		Operating Expense		- 0	- 0
		EBITDA		$   385,440	$   315,360
		Cash Flow Available for Debt Service (CFADS)		$   385,440.00	$   315,360.00
		Maximum debt service		$   296,492.31
		Debt Capacity		($4,396,449.89)
		Capital Cost		140,000,000
		Equity share		96.9%
Sheet3
	R_ID	Resource	Existing_Cap_MW	Var_OM_cost_per_MWh	Fuel	Heat_rate_MMBTU_per_MWh
	1	biomass	21.4	5.234	None	12.76
	2	natural_gas_fired_combined_cycle	1928.5	3.4	pacific_naturalgas	7.52
	3	natural_gas_fired_combustion_turbine	788.4	10.8	pacific_naturalgas	10.69
	4	onshore_wind_turbine	217.6	0	None	0
	5	small_hydroelectric	7.32	0	None	0
	6	solar_photovoltaic	500	0	None	0
problem 4 a
		Electricity Production (MWh)	Electricity Revenue	Operating Expense	EBITDA	Cash Flow Available for Debt Service (CFADS)
	1	0.0835655971	2.9247958975	0.0683340626	0.6684907464	0.3798199363
	2	0.5209634988	18.2337224578	0.8075242298	0.7811720046	0.3134352417
	3	0.2746905087	9.6141678048	0.0296774681	0.6854164903	0.9259538101
	4	0.4069481992	14.2431869713	0.2293828621	0.3283544254	0.8358109965
	5	0.9119588371	31.9185592973	0.674232427	0.0356863707	0.7749336631
	6	0.958503162	33.5476106684	0.0364150628	0.6780404834	0.0302272647
	7	0.811510764	28.4028767401	0.6171283793	0.807002604	0.8343900766
	8	0.9467758062	33.137153216	0.0881796716	0.8691458463	0.1466956581
	9	0.9497013551	33.2395474287	0.1790958945	0.703096618	0.0934085265
	10	0.7144436666	25.0055283297	0.9239582375	0.0600910841	0.8438574899
	11	0.4783219234	16.7412673194	0.6250740982	0.5594802229	0.0042532076
	12	0.5174992597	18.112474091	0.7488393498	0.172954894	0.7985123738
	13	0.9358728804	32.7555508136	0.4102602385	0.7876631005	0.477499539
	14	0.0672785122	2.3547479267	0.5604444886	0.1929845742	0.3166647048
	15	0.8365062225	29.2777177892	0.2146511197	0.7771617779	0.8625548643
	16	0.9794259568	34.2799084873	0.8149164488	0.1575953674	0.1436584775
	17	0.0562307126	1.968074941	0.3161540587	0.5798468008	0.2025019784
	18	0.6465193175	22.6281761111	0.3775776473	0.7840445957	0.8179213728
	19	0.4330739864	15.157589524	0.5195059544	0.314548674	0.8240104796
	20	0.4576687682	16.0184068858	0.9428659339	0.9325308597	0.1162416622
	21	0.0991772636	3.471204225	0.4817076723	0.1762071416	0.2202414606
	22	0.4448097596	15.5683415847	0.361368417	0.3222333161	0.7513123406
	23	0.0475224177	1.6632846202	0.522410527	0.3123601284	0.8583996468
	24	0.6690878753	23.4180756367	0.1789470292	0.4663635003	0.1001642932
	25	0.6202766699	21.7096834471	0.0696350916	0.8939329322	0.6298604367
	26	0.8775343245	30.7137013592	0.9635037361	0.87477484	0.0542577645
	27	0.6708968443	23.4813895516	0.2136569347	0.9637284816	0.725516634
	28	0.2468815374	8.64085381	0.1064187473	0.4970940524	0.1375385055
	29	0.7988757281	27.960650483	0.8796177944	0.3639439402	0.4824133051
	30	0.8113253356	28.396386745	0.4014809488	0.7914432544	0.2331855934
	31	0.6051348533	21.1797198645	0.0087949769	0.4273726396	0.7576667046
	32	0.5220331306	18.2711595727	0.1888382315	0.2027272492	0.3057506524
	33	0.6844690481	23.9564166836	0.2037644418	0.3098596838	0.9422071808
	34	0.7794587496	27.2810562345	0.6088434802	0.6364614698	0.7182082081
	35	0.7552401097	26.4334038378	0.1305626644	0.0265437209	0.6400668836
	36	0.144666678	5.0633337284	0.9296299199	0.1875849291	0.8861840343
	37	0.1257216298	4.4002570413	0.8296408979	0.8726952082	0.8015401848
	38	0.3078310168	10.7740855865	0.2625166001	0.8910815676	0.1482537115
	39	0.5225544073	18.2894042549	0.2004277088	0.5392917857	0.1602048475
	40	0.291949054	10.2182168893	0.5690965705	0.9142329729	0.4784100811
	41	0.1270649807	4.4472743241	0.9494501334	0.0167574593	0.6106689563
	42	0.2466799735	8.6337990717	0.5179381031	0.8215842578	0.7041633237
	43	0.6396951871	22.3893315479	0.6712816474	0.1391010094	0.0209625484
	44	0.1948952488	6.8213337091	0.4198040493	0.3792927659	0.325182544
	45	0.6906483548	24.1726924173	0.0599151442	0.8950911682	0.3263680705
	46	0.6936673303	24.2783565605	0.0589829181	0.6329492469	0.6047939598
	47	0.0544463478	1.9056221728	0.7892296877	0.8303964577	0.5950676476
	48	0.6940831305	24.2929095688	0.1966135911	0.4820200086	0.507077525
	49	0.4566424788	15.9824867595	0.4935063534	0.9558468775	0.123161429
	50	0.0891292597	3.1195240904	0.702222688	0.3147776005	0.4048769498
	51	0.3507053356	12.2746867454	0.2100001898	0.6795157961	0.9740464181
	52	0.1502349938	5.2582247838	0.0704616567	0.6625290928	0.798777289
	53	0.3084771896	10.7967016353	0.3690703383	0.2760246447	0.1841132952
	54	0.542282917	18.9799020964	0.4806469757	0.9232127031	0.6367058495
	55	0.9288714835	32.5105019232	0.1776470853	0.3952327885	0.4921749798
	56	0.0748326494	2.6191427273	0.8836196686	0.2667083886	0.4281244514
	57	0.091263879	3.1942357648	0.3975346754	0.9917377788	0.5689731142
	58	0.1170721529	4.0975253513	0.7269560991	0.9380581475	0.2635052978
	59	0.8463688734	29.6229105689	0.6103263846	0.0400454531	0.8646544662
	60	0.4189060663	14.6617123222	0.7684295625	0.2095226087	0.8475934622
	61	0.39232638	13.731423301	0.1278944542	0.0636537375	0.2980926631
	62	0.3251965558	11.3818794535	0.9034644167	0.7842539163	0.7401305327
	63	0.6205164476	21.718075666	0.0731863966	0.4544616207	0.8496969138
	64	0.4627838376	16.1974343175	0.0367098667	0.0055190758	0.0561168187
	65	0.8408635719	29.4302250164	0.9042490734	0.0250472698	0.2375652066
	66	0.4644916054	16.2572061896	0.0221785426	0.5278361285	0.2486790005
	67	0.9364540494	32.7758917303	0.3148224077	0.3732370162	0.9810587304
	68	0.0478027439	1.6730960367	0.886050647	0.2506977908	0.5014632268
	69	0.4555150051	15.9430251778	0.5566024725	0.2058028159	0.4949798514
	70	0.0632278165	2.2129735773	0.2515192418	0.0615535723	0.113021546
	71	0.6870620724	24.0471725325	0.000763835	0.1502716017	0.4740706834
	72	0.7298780232	25.5457308136	0.2831360924	0.4350480122	0.5735265439
	73	0.7910103297	27.6853615394	0.0423014695	0.818018511	0.5573524622
	74	0.0244244992	0.8548574712	0.3479066936	0.7815221917	0.9733277827
	75	0.3871698062	13.5509432161	0.0636767327	0.905494049	0.5713692976
	76	0.5327067954	18.6447378381	0.7808778015	0.3102695649	0.505209553
	77	0.8219558056	28.7684531974	0.6067631762	0.7910945545	0.8980153992
	78	0.0591914898	2.0717021439	0.9261492935	0.2408611393	0.1471687
	79	0.7855134354	27.4929702404	0.6296454476	0.8165877852	0.4232775489
	80	0.3505471547	12.2691504133	0.9309499175	0.0664544101	0.2470452019
	81	0.1889167459	6.6120861065	0.4561190928	0.0828989149	0.5706395837
	82	0.8485513401	29.699296904	0.4757516737	0.6728190188	0.521961829
	83	0.2896620508	10.1381717766	0.2006824075	0.8430967689	0.60276339
	84	0.4664738028	16.3265830983	0.3358778541	0.1746019633	0.685305517
	85	0.992330162	34.7315556692	0.7486406515	0.1541317708	0.0033752215
	86	0.3392248963	11.8728713692	0.7273172309	0.217970687	0.2768766168
	87	0.2620131211	9.170459238	0.7265035754	0.8741491894	0.2347038125
	88	0.2360207892	8.2607276223	0.0988922383	0.5126581577	0.1962799126
	89	0.6644189828	23.2546643991	0.5537686584	0.6290061621	0.6668215543
	90	0.7676010017	26.8660350594	0.2487299775	0.1365489242	0.5399288129
	91	0.2285083685	7.9977928977	0.5915536201	0.9365352698	0.6260449312
	92	0.517462351	18.1111822843	0.8755396678	0.0283443982	0.365910514
	93	0.5035070672	17.6227473519	0.4685834303	0.1702932008	0.9106331855
	94	0.2599207087	9.0972248036	0.5017729349	0.0171259187	0.4985681215
	95	0.7813163828	27.3460733968	0.5574698003	0.4256670851	0.9591866599
	96	0.5538482873	19.384690056	0.7544227993	0.6938180585	0.9233340218
	97	0.9781102243	34.2338578521	0.068612666	0.9086389057	0.9008291315
	98	0.8341684336	29.1958951769	0.7651162167	0.4082724179	0.8076146636
	99	0.559158304	19.5705406385	0.589715591	0.3942689886	0.5056811496
	100	0.9493381067	33.2268337328	0.7143320789	0.9537800032	0.1641727611
	101	0.2520304922	8.8210672266	45.9969671191	49.6979551754	50.9065244231
	102	0.7685987109	26.9009548799	91.9256001756	98.7274196043	101.4332289098
	103	0.3426553334	11.9929366676	183.0436761213	196.673667204	202.5530225779
	104	0.6736935668	23.5792748395	366.0576747746	392.6619179177	404.1800913458
	105	0.9580555583	33.5319445404	731.8859666871	784.9954814099	807.5243716951
	106	0.730831753	25.5791113559	1463.0977009471	1569.9552764491	1614.2738097271
	107	0.7776855588	27.2189945576	2926.1589868314	3139.2325124149	3228.5173921895
	108	0.2072656952	7.2542993336	5851.7008452835	6277.6580222257	6456.2003943024
	109	0.9127063563	31.9447224718	11703.3135108953	12554.4468986051	12912.2540929467
	110	0.0000638805	0.0022358187	23406.4479258962	25108.1907005922	25824.414777367
	111	0.0034831839	0.1219114369	46811.9718935548	50216.3213101003	51647.9856972441
	112	0.783881398	27.4358489297	93623.3187130114	100432.083139978	103295.967141281
	113	0.7749627432	27.1236960114	187245.888586673	200863.993325062	206591.135770187
	114	0.1860813864	6.512848524	374491.366913108	401727.198987023	413181.794040836
	115	0.7546870089	26.4140453131	748982.173381727	803454.204989471	826363.271416966
	116	0.4929441378	17.2530448217	1497964.13211233	1606907.63281716	1652725.68027907
	117	0.0003014304	0.0105500649	2995927.44930822	3213815.10803896	3305451.21689966
	118	0.6269097651	21.9418417793	5991854.58246238	6427629.63623112	6610902.23129734
	119	0.2583620822	9.0426728787	11983708.7873471	12855258.4884176	13221803.6446733
	120	0.8440810737	29.5428375797	23967417.0551883	25710516.6622866	26443606.4653361
	121	0.2948119728	10.3184190475	47934833.1675106	51421032.3920424	52887212.8144306
	122	0.4111433045	14.3900156584	95869665.8533135	102842064.607878	105774425.40862
	123	0.8179035391	28.6266238688	191739331.345259	205684128.893522	211548850.065927
	124	0.5528164992	19.3485774713	383478662.168107	411368257.474684	423097699.273455
	125	0.3900381138	13.6513339842	766957324.157266	822736514.483004	846195398.446745
	126	0.9532674791	33.3643617678	1533914648.2449	1645473028.07207	1692390796.26363
	127	0.5371151221	18.7990292737	3067829295.52629	3290946055.26937	3384781592.473
	128	0.3342341936	11.698196776	6135658590.83893	6581892109.57502	6769563184.22049
	129	0.2336157803	8.1765523094	12271317181.5714	13163784218.6529	13539126368.3034
	130	0.3645666248	12.759831868	24542634362.2633	26327568436.9419	27078252736.1245
	131	0.4536474231	15.8776598078	49085268724.125	52655136873.0925	54156505472.0157
	132	0.443689712	15.5291399207	98170537448.2412	105310273745.758	108313010943.274
	133	0.0376136063	1.3164762189	196341074896.294	210620547491.312	216626021886.242
	134	0.1560382803	5.4613398119	392682149792.384	421241094982.315	433252043771.542
	135	0.9262502312	32.4187580913	785364299584.158	842482189963.993	866504087542.365
	136	0.8952267809	31.33293733	1570728599168.19	1684964379927.96	1733008175084.09
	137	0.1320389162	4.6213620687	3141457198335.44	3369928759855.73	3466016350167.29
	138	0.0457033698	1.5996179432	6282914396670.05	6739857519710.59	6932032700333.78
	139	0.3569315642	12.4926047458	12565828793339.8	13479715039420.3	13864065400667.4
	140	0.0520882725	1.8230895366	25131657586679.5	26959430078840	27728130801334.7
	141	0.9982424404	34.9384854138	50263315173358.4	53918860157679.2	55456261602668.9
	142	0.4987177717	17.4551220103	100526630346716	107837720315358	110912523205337
	143	0.4845865391	16.9605288697	201053260693431	215675440630716	221825046410674
	144	0.0486422133	1.7024774647	402106521386862	431350881261432	443650092821347
	145	0.9864860092	34.5270103219	804213042773723	862701762522863	887300185642694
	146	0.0059639287	0.2087375037	1.60842608554745E+15	1.72540352504573E+15	1.77460037128539E+15
	147	0.0477720187	1.6720206543	3.21685217109489E+15	3.45080705009145E+15	3.54920074257077E+15
	148	0.7582416986	26.5384594496	6.43370434218979E+15	6.9016141001829E+15	7.09840148514155E+15
	149	0.440434312	15.4152009185	1.28674086843796E+16	1.38032282003658E+16	1.41968029702831E+16
	150	0.7096138714	24.8364854982	2.57348173687591E+16	2.76064564007316E+16	2.83936059405662E+16
	151	0.4805075662	16.817764817	5.14696347375183E+16	5.52129128014632E+16	5.67872118811324E+16
	152	0.9462880887	33.1200831062	1.02939269475037E+17	1.10425825602926E+17	1.13574423762265E+17
	153	0.0305482027	1.0691870938	2.05878538950073E+17	2.20851651205853E+17	2.2714884752453E+17
	154	0.3643259319	12.7514076175	4.11757077900146E+17	4.41703302411705E+17	4.54297695049059E+17
	155	0.6497211209	22.7402392307	8.23514155800292E+17	8.83406604823411E+17	9.08595390098118E+17
	156	0.9213603314	32.247611598	1.64702831160058E+18	1.76681320964682E+18	1.81719078019624E+18
	157	0.305498996	10.6924648601	3.29405662320117E+18	3.53362641929364E+18	3.63438156039247E+18
	158	0.602285803	21.0800031039	6.58811324640234E+18	7.06725283858729E+18	7.26876312078495E+18
	159	0.7208486296	25.2297020351	1.31762264928047E+19	1.41345056771746E+19	1.45375262415699E+19
	160	0.2060244816	7.2108568568	2.63524529856094E+19	2.82690113543492E+19	2.90750524831398E+19
	161	0.6817734969	23.8620723909	5.27049059712187E+19	5.65380227086983E+19	5.81501049662796E+19
	162	0.5516657166	19.3083000804	1.05409811942437E+20	1.13076045417397E+20	1.16300209932559E+20
	163	0.2921955952	10.2268458317	2.10819623884875E+20	2.26152090834793E+20	2.32600419865118E+20
	164	0.0688658855	2.4103059912	4.2163924776975E+20	4.52304181669586E+20	4.65200839730236E+20
	165	0.7235916341	25.3257071923	8.43278495539499E+20	9.04608363339173E+20	9.30401679460473E+20
	166	0.8580068273	30.0302389551	1.686556991079E+21	1.80921672667835E+21	1.86080335892095E+21
	167	0.7510801265	26.2878044266	3.373113982158E+21	3.61843345335669E+21	3.72160671784189E+21
	168	0.2665191256	9.3281693944	6.74622796431599E+21	7.23686690671338E+21	7.44321343568378E+21
	169	0.0167525776	0.5863402173	1.3492455928632E+22	1.44737338134268E+22	1.48864268713676E+22
	170	0.0406501662	1.4227558166	2.6984911857264E+22	2.89474676268535E+22	2.97728537427351E+22
	171	0.852735355	29.8457374265	5.3969823714528E+22	5.78949352537071E+22	5.95457074854703E+22
	172	0.7720769069	27.02269174	1.07939647429056E+23	1.15789870507414E+23	1.19091414970941E+23
	173	0.1252968102	4.3853883577	2.15879294858112E+23	2.31579741014828E+23	2.38182829941881E+23
	174	0.1758103643	6.1533627512	4.31758589716224E+23	4.63159482029656E+23	4.76365659883762E+23
	175	0.0928850665	3.2509773284	8.63517179432447E+23	9.26318964059313E+23	9.52731319767524E+23
	176	0.4368970072	15.2913952513	1.72703435886489E+24	1.85263792811863E+24	1.90546263953505E+24
	177	0.5571951496	19.5018302363	3.45406871772979E+24	3.70527585623725E+24	3.8109252790701E+24
	178	0.2331733099	8.161065848	6.90813743545958E+24	7.4105517124745E+24	7.62185055814019E+24
	179	0.922397431	32.2839100833	1.38162748709192E+25	1.4821103424949E+25	1.52437011162804E+25
	180	0.

1. Suppose we are planning a 100 MW wind farm with a 1-year p-50 capacity factor of 44% and a 1-year p-99 capacity factor of 36%. The total cost to build the plant is $1,400/kW, and all power will be...

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