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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This is an economics of energy transmission assignmnet. It must be all done in Excel and the excel must be neat and organized and the final answers to each questions must be clearly marked.


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 territory 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 $35/MWh, the same as the contracted price in problem 1. All random variables are assumed to be independent. (a) In Excel, draw 1,000 samples of the 4 random variables and compute the annual electricity revenue for the plant under each draw. What is the average electricity revenue across the 1,000 samples? How does it compare to the p-50 revenue in problem 1? (b) Compute the p-50 and p-99 CFADS under these assumptions, i.e., the 500th and 990th ranked outcomes in your sample. (c) Given the increased uncertainty, suppose the debt provider insists on a debt service coverage ratio of 2.25x at the p-50 level. What is the total debt capacity of the project? (d) Assuming the project developers use the debt size calculated in (c), what percent of the project will be funded by the equity investors? How does this compare to the contracted case we considered in problem 1? Note that since Excel will recalculate every time a new sample is drawn, it is okay if output values fluctuate slightly upon recalculation. Problem 1 Assumptions Unit Plant Capacity100MW Capital Cost1,400$/kW P-50 Capacity Factor44.0%% P-99 Capacity Factor36.0%% Operating Expenses$40.00per KW-Year PPA Price$35.00per MWh Sizing DSCR p-991.00x Ratio Sizing DSCR p-501.30x Ratio Interest Rate4.5%% Length25Years Hours in Year8,760Hours Conversion to USD 0001,000USD Debt Sizing p-50p-99 Electricity Production (MWh)385,440315,360 PPA Rate (/MWh)$35.00$35.00 Electricity Revenue$ 13,490,400$ 11,037,600 Operating Expense4,000,0004,000,000 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 Cost140,000,000 Equity share25.5% Demand HourDemand_MW 11615 21553 31518 41562 51733 61976 72274 82597 92838 103023 113125 122963 132743 142666 152578 162482 172422 182374 192378 202501 212506 222258 231988 241760 Resources R_IDResourceExisting_Cap_MWVar_OM_cost_per_MWhFuelHeat_rate_MMBTU_per_MWh 1biomass21.45.234None12.76 2natural_gas_fired_combined_cycle1928.53.4pacific_naturalgas7.52 3natural_gas_fired_combustion_turbine788.410.8pacific_naturalgas10.69 4onshore_wind_turbine217.60None0 5small_hydroelectric7.320None0 6solar_photovoltaic5000None0 Availability 123456789101112131415161718192021222324 onshore_wind_turbine0.75050.78030.5290.46210.37030.63960.34090.22690.76910.60460.5110.42330.23940.29730.22620.30060.26280.36130.24180.28230.33050.44140.58120.6637 small_hydroelectric0.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.43510.4351 solar_photovoltaic0000000.05530.22110.47760.57570.60390.61390.64460.64550.62410.56950.46780.32360.047700000 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 FinalReducedObjectiveAllowableAllowable CellNameValueCostCoefficientIncreaseDecrease $C$13biomass Hour121.4-24.4865.23424.4861E+30 $D$13biomass Hour221.4-24.4865.23424.4861E+30 $E$13biomass Hour321.4-24.4865.23424.4861E+30 $F$13biomass Hour421.4-24.4865.23424.4861E+30 $G$13biomass Hour521.4-24.4865.23424.4861E+30 $H$13biomass Hour621.4-24.4865.23424.4861E+30 $I$13biomass Hour721.4-42.9815.23442.9811E+30 $J$13biomass Hour821.4-42.9815.23442.9811E+30 $K$13biomass Hour921.4-42.9815.23442.9811E+30 $L$13biomass Hour1021.4-42.9815.23442.9811E+30 $M$13biomass Hour1121.4-42.9815.23442.9811E+30 $N$13biomass Hour1221.4-42.9815.23442.9811E+30 $O$13biomass Hour1321.4-42.9815.23442.9811E+30 $P$13biomass Hour1421.4-42.9815.23442.9811E+30 $Q$13biomass Hour1521.4-42.9815.23442.9811E+30 $R$13biomass Hour1621.4-42.9815.23442.9811E+30 $S$13biomass Hour1721.4-42.9815.23442.9811E+30 $T$13biomass Hour1821.4-42.9815.23442.9811E+30 $U$13biomass Hour1921.4-42.9815.23442.9811E+30 $V$13biomass Hour2021.4-42.9815.23442.9811E+30 $W$13biomass Hour2121.4-42.9815.23442.9811E+30 $X$13biomass Hour2221.4-42.9815.23442.9811E+30 $Y$13biomass Hour2321.4-24.4865.23424.4861E+30 $Z$13biomass Hour2421.4-24.4865.23424.4861E+30 $C$14natural_gas_fired_combined_cycle Hour11427.106268029.7218.49524.486 $D$14natural_gas_fired_combined_cycle Hour21358.621788029.7218.49524.486 $E$14natural_gas_fired_combined_cycle Hour31378.304668029.7218.49524.486 $F$14natural_gas_fired_combined_cycle Hour41436.862108029.7218.49524.486 $G$14natural_gas_fired_combined_cycle Hour51627.837788029.7218.49524.486 $H$14natural_gas_fired_combined_cycle Hour61812.238108029.7218.49524.486 $I$14natural_gas_fired_combined_cycle Hour71928.5-18.49529.7218.4951E+30 $J$14natural_gas_fired_combined_cycle Hour81928.5-18.49529.7218.4951E+30 $K$14natural_gas_fired_combined_cycle Hour91928.5-18.49529.7218.4951E+30 $L$14natural_gas_fired_combined_cycle Hour101928.5-18.49529.7218.4951E+30 $M$14natural_gas_fired_combined_cycle Hour111928.5-18.49529.7218.4951E+30 $N$14natural_gas_fired_combined_cycle Hour121928.5-18.49529.7218.4951E+30 $O$14natural_gas_fired_combined_cycle Hour131928.5-18.49529.7218.4951E+30 $P$14natural_gas_fired_combined_cycle Hour141928.5-18.49529.7218.4951E+30 $Q$14natural_gas_fired_combined_cycle Hour151928.5-18.49529.7218.4951E+30 $R$14natural_gas_fired_combined_cycle Hour161928.5-18.49529.7218.4951E+30 $S$14natural_gas_fired_combined_cycle Hour171928.5-18.49529.7218.4951E+30 $T$14natural_gas_fired_combined_cycle Hour181928.5-18.49529.7218.4951E+30 $U$14natural_gas_fired_combined_cycle Hour191928.5-18.49529.7218.4951E+30 $V$14natural_gas_fired_combined_cycle Hour201928.5-18.49529.7218.4951E+30 $W$14natural_gas_fired_combined_cycle Hour211928.5-18.49529.7218.4951E+30 $X$14natural_gas_fired_combined_cycle Hour221928.5-18.49529.7218.4951E+30 $Y$14natural_gas_fired_combined_cycle Hour231836.945948029.7218.49524.486 $Z$14natural_gas_fired_combined_cycle Hour241590.993948029.7218.49524.486 $C$15natural_gas_fired_combustion_turbine Hour1018.49548.2151E+3018.495 $D$15natural_gas_fired_combustion_turbine Hour2018.49548.2151E+3018.495 $E$15natural_gas_fired_combustion_turbine Hour3018.49548.2151E+3018.495 $F$15natural_gas_fired_combustion_turbine Hour4018.49548.2151E+3018.495 $G$15natural_gas_fired_combustion_turbine Hour5018.49548.2151E+3018.495 $H$15natural_gas_fired_combustion_turbine Hour6018.49548.2151E+3018.495 $I$15natural_gas_fired_combustion_turbine Hour7219.085228048.2151E+3018.495 $J$15natural_gas_fired_combustion_turbine Hour8483.991628048.2151E+3018.495 $K$15natural_gas_fired_combustion_turbine Hour9478.758908048.2151E+3018.495 $L$15natural_gas_fired_combustion_turbine Hour10650.504108048.2151E+3018.495 $M$15natural_gas_fired_combustion_turbine Hour11758.771468048.2151E+3018.495 $N$15natural_gas_fired_combustion_turbine Hour12610.854988048.2151E+3018.495 $O$15natural_gas_fired_combustion_turbine Hour13415.521628048.2151E+3018.495 $P$15natural_gas_fired_combustion_turbine Hour14325.472588048.2151E+3018.495 $Q$15natural_gas_fired_combustion_turbine Hour15263.643948048.2151E+3018.495 $R$15natural_gas_fired_combustion_turbine Hour16178.754508048.2151E+3018.495 $S$15natural_gas_fired_combustion_turbine Hour17177.829788048.2151E+3018.495 $T$15natural_gas_fired_combustion_turbine Hour18180.496188048.2151E+3018.495 $U$15natural_gas_fired_combustion_turbine Hour19348.449388048.2151E+3018.495 $V$15natural_gas_fired_combustion_turbine Hour20486.486588048.21548.21518.495 $W$15natural_gas_fired_combustion_turbine Hour21480.998268048.21548.21518.495 $X$15natural_gas_fired_combustion_turbine Hour22208.866428048.21548.21518.495 $Y$15natural_gas_fired_combustion_turbine Hour23018.49548.2151E+3018.495 $Z$15natural_gas_fired_combustion_turbine Hour24018.49548.2151E+3018.495 $C$16onshore_wind_turbine Hour1163.3088-29.72029.721E+30 $D$16onshore_wind_turbine Hour2169.79328-29.72029.721E+30 $E$16onshore_wind_turbine Hour3115.1104-29.72029.721E+30 $F$16onshore_wind_turbine Hour4100.55296-29.72029.721E+30 $G$16onshore_wind_turbine Hour580.57728-29.72029.721E+30 $H$16onshore_wind_turbine Hour6139.17696-29.72029.721E+30 $I$16onshore_wind_turbine Hour774.17984-48.215048.2151E+30 $J$16onshore_wind_turbine Hour849.37344-48.215048.2151E+30 $K$16onshore_wind_turbine Hour9167.35616-48.215048.2151E+30 $L$16onshore_wind_turbine Hour10131.56096-48.215048.2151E+30 $M$16onshore_wind_turbine Hour11111.1936-48.215048.2151E+30 $N$16onshore_wind_turbine Hour1292.11008-48.215048.2151E+30 $O$16onshore_wind_turbine Hour1352.09344-48.215048.2151E+30 $P$16onshore_wind_turbine Hour1464.69248-48.215048.2151E+30 $Q$16onshore_wind_turbine Hour1549.22112-48.215048.2151E+30 $R$16onshore_wind_turbine Hour1665.41056-48.215048.2151E+30 $S$16onshore_wind_turbine Hour1757.18528-48.215048.2151E+30 $T$16onshore_wind_turbine Hour1878.61888-48.215048.2151E+30 $U$16onshore_wind_turbine Hour1952.61568-48.215048.2151E+30 $V$16onshore_wind_turbine Hour2061.42848-48.215048.2151E+30 $W$16onshore_wind_turbine Hour2171.9168-48.215048.2151E+30 $X$16onshore_wind_turbine Hour2296.04864-48.215048.2151E+30 $Y$16onshore_wind_turbine Hour23126.46912-29.72029.721E+30 $Z$16onshore_wind_turbine Hour24144.42112-29.72029.721E+30 $C$17small_hydroelectric Hour13.184932-29.72029.721E+30 $D$17small_hydroelectric Hour23.184932-29.72029.721E+30 $E$17small_hydroelectric Hour33.184932-29.72029.721E+30 $F$17small_hydroelectric Hour43.184932-29.72029.721E+30 $G$17small_hydroelectric Hour53.184932-29.72029.721E+30 $H$17small_hydroelectric Hour63.184932-29.72029.721E+30 $I$17small_hydroelectric Hour73.184932-48.215048.2151E+30 $J$17small_hydroelectric Hour83.184932-48.215048.2151E+30 $K$17small_hydroelectric Hour93.184932-48.215048.2151E+30 $L$17small_hydroelectric Hour103.184932-48.215048.2151E+30 $M$17small_hydroelectric Hour113.184932-48.215048.2151E+30 $N$17small_hydroelectric Hour123.184932-48.215048.2151E+30 $O$17small_hydroelectric Hour133.184932-48.215048.2151E+30 $P$17small_hydroelectric Hour143.184932-48.215048.2151E+30 $Q$17small_hydroelectric Hour153.184932-48.215048.2151E+30 $R$17small_hydroelectric Hour163.184932-48.215048.2151E+30 $S$17small_hydroelectric Hour173.184932-48.215048.2151E+30 $T$17small_hydroelectric Hour183.184932-48.215048.2151E+30 $U$17small_hydroelectric Hour193.184932-48.215048.2151E+30 $V$17small_hydroelectric Hour203.184932-48.215048.2151E+30 $W$17small_hydroelectric Hour213.184932-48.215048.2151E+30 $X$17small_hydroelectric Hour223.184932-48.215048.2151E+30 $Y$17small_hydroelectric Hour233.184932-29.72029.721E+30 $Z$17small_hydroelectric Hour243.184932-29.72029.721E+30 $C$18solar_photovoltaic Hour10-29.7201E+3029.72 $D$18solar_photovoltaic Hour20-29.7201E+3029.72 $E$18solar_photovoltaic Hour30-29.7201E+3029.72 $F$18solar_photovoltaic Hour40-29.7201E+3029.72 $G$18solar_photovoltaic Hour50-29.7201E+3029.72 $H$18solar_photovoltaic Hour60-29.7201E+3029.72 $I$18solar_photovoltaic Hour727.65-48.215048.2151E+30 $J$18solar_photovoltaic Hour8110.55-48.215048.2151E+30 $K$18solar_photovoltaic Hour9238.8-48.215048.2151E+30 $L$18solar_photovoltaic Hour10287.85-48.215048.2151E+30 $M$18solar_photovoltaic Hour11301.95-48.215048.2151E+30 $N$18solar_photovoltaic Hour12306.95-48.215048.2151E+30 $O$18solar_photovoltaic Hour13322.3-48.215048.2151E+30 $P$18solar_photovoltaic Hour14322.75-48.215048.2151E+30 $Q$18solar_photovoltaic Hour15312.05-48.215048.2151E+30 $R$18solar_photovoltaic Hour16284.75-48.215048.2151E+30 $S$18solar_photovoltaic Hour17233.9-48.215048.2151E+30 $T$18solar_photovoltaic Hour18161.8-48.215048.2151E+30 $U$18solar_photovoltaic Hour1923.85-48.215048.2151E+30 $V$18solar_photovoltaic Hour200-48.21501E+3048.215 $W$18solar_photovoltaic Hour210-48
hw4-xpdvdukr.docx problem1-2-solutions-zpq3ksq2.xlsx hw4-iw12nrv5-hv5qynec.docx
Answered 2 days AfterNov 06, 2022

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

Komalavalli answered on Nov 07 2022
49 Votes
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...
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