Site Bench

Size a home’s or a wind farm’s equipment, run every hour of 2025, and see the cash flow

Sandbox SB0 of Energy Systems, Step by Step: one site behind one meter, a Prairie Town home or the ridge wind farm; you size the equipment, a linear program runs every hour of 2025, and you read the bills, the CO₂ and the cash flow.
  • Analyst to Modeler · L2–L3
  • Sandbox
  • 20 min
  • After lesson 9

The brief

The site
A Prairie Town home or the ridge wind farm, behind one meter, through every hour of 2025.
Its hours
The hourly patterns of the Southwest Power Pool (SPP) grid in 2025, reshaped to EIA's monthly capacity factors: modelled sites, not measured ones.
You decide
Home: solar (kW), a battery (kWh), a heat pump, the tariff. Farm: wind, a battery, an electrolyzer, a hydrogen tank.
The engine works out
The cheapest way to run all 8,760 hours, a linear program; then the bills, the CO₂ and the NPV.
It leaves out
Outages, taxes and incentives, storage from one week to the next, and costs that change over time.

Open-ended: start from a preset, change one thing at a time, and copy the plan link to keep a plan.

The bench

Control Default plan Range
Site Prairie Town home one of: Prairie Town home, Ridge wind farm
Rooftop solar 6 kW 0 to 15 kW, in steps of 0.5 kW
Home battery 0 kWh 0 to 30 kWh, in steps of 0.5 kWh
Heat pump none (keep the gas furnace) one of: none (keep the gas furnace), standard heat pump, high-efficiency heat pump
Tariff flat price one of: flat price, time-of-use
Export credit 4 ¢/kWh 0 to 8 ¢/kWh, in steps of 0.5 ¢/kWh
Wind farm 150 MW 0 to 300 MW, in steps of 10 MW
Line to the grid 100 MW 10 to 300 MW, in steps of 10 MW
Battery (4 hours) 0 MWh 0 to 1,000 MWh, in steps of 10 MWh
Electrolyzer 0 MW 0 to 200 MW, in steps of 5 MW
Hydrogen tank 0 t 0 to 200 t, in steps of 1 t
Buyer takes at most 1,000 kg/h 0 to 5,000 kg/h, in steps of 100 kg/h
Hydrogen price 4 $/kg 1 to 8 $/kg, in steps of 0.25 $/kg
Power contract fixed $50/MWh one of: fixed $50/MWh, time-of-use
Discount rate (real) 4 % 0 to 10 %, in steps of 0.5 %
Equipment cost 100 % of sourced 50 to 150 % of sourced, in steps of 5 % of sourced

With JavaScript on, you change these, run the year in your browser, and copy a link to your plan.

Hourly patterns: SPP's 2025 demand, wind and solar (EIA-930), reshaped to EIA's 2025 capacity factors. The home's use and heat are illustrative. Costs: EIA, DOE and NLR, in 2025 dollars; sources below.

Results

Result for the default plan Value
Net present value, 25 years (against the same home with nothing new, at 4.0% real) −$17,813
Saved on bills and gas, a year ($2,114 a year before, $1,314 with the plan) $800
Equipment, up front (upkeep $120 a year) $28,430
CO₂ a year, bought power and gas (down 1.3 t from 5.9 t; net of power sent back, credited at the same factor: 3.1 t) 4.6 t
Own solar covers (of the home's electricity use, at once or through the battery) 48%
Hours that need the grid (of 8,760; the busiest hour draws 1.5 kWh) 5,240 h

Run on every hour of 2025, as 52 weeks and 31 December, with this engine on 2026-11-05.

How the engine works, as diagrams

Decisions
Every hour: how much to buy and send back (home) or sell and spill (farm), what goes into and out of the battery, and what the electrolyzer and tank do.
Goal
The lowest yearly cost for the home, or the highest yearly revenue for the farm, with the sizes you set.
Rules
Each hour balances; nothing runs above its size; the battery loses 15% of what it stores; the line and the buyer's take are limits.
Time
All 8,760 hours of 2025, as 52 weeks and 31 December, one small linear program each.
Tie rule
A tiny wear charge on battery use and, on the farm, a hair's preference for selling earlier in the week. Both are left out of every number shown.
Ties
Every total shown is the same on every least-cost schedule. With storage, the hour-by-hour schedule, and the hour counts read from it, can differ.
It holds when
  • the weather and prices of 2025 are a fair guide to the next 25 or 30 years;
  • the sourced costs, converted to 2025 dollars, hold for the whole horizon;
  • the grid is always there to buy from (home) or to sell to, up to the line (farm).
It leaves out
  • storage carried from one week to the next (the check below measures what that changes);
  • outages, taxes, tax credits, incentives and financing;
  • how other plants respond to the site: the CO₂ uses one average factor (CF6 explains the difference).

Checked on one full-year LP

The test runs each preset again as one LP over all 8,760 hours, with storage free to carry across weeks.

Preset NPV, 52 weeks and 31 December NPV, one full-year LP Difference
Home: solar only −$17,813 −$17,813 +$0 (0.00% of the equipment cost)
Home: solar and a battery −$37,790 −$37,789 +$1 (0.00% of the equipment cost)
Home: heat pump only −$9,924 −$9,924 +$0 (0.00% of the equipment cost)
Home: all three −$51,033 −$51,035 −$2 (0.00% of the equipment cost)
Wind farm: wind farm alone $27.9M $27.9M +$0 (0.00% of the equipment cost)
Wind farm: add a battery −$54.1M −$54.3M −$258,298 (0.08% of the equipment cost)
Wind farm: add an electrolyzer −$94.1M −$94.1M +$0 (0.00% of the equipment cost)
Wind farm: electrolyzer and tank −$119M −$119M −$39,802 (0.01% of the equipment cost)

Solved on 2026-11-05 with HiGHS by the bench's test.

Go deeper · ModelerThe linear program behind the bench
  • Each hour adds a balance row. For the home: bought − sent back + battery out − battery in = the home’s use − solar.
  • For the farm: sold + spilled + into the battery + into the electrolyzer − battery out = wind.
  • The battery’s state of charge is one more variable per hour: this hour’s level = last hour’s + 0.85 × charge − discharge.
  • “Size it for me” makes the sizes decisions too, each charged its yearly cost through the capital recovery factor. It runs on a few representative weeks, as lesson 13 and M3 do.
  • Storage and coupled carriers, modelling power, hydrogen and heat together (M4, in the Modeler tier), writes this model in Python.

Numbers, sources and what’s next

Inputs the engine uses

Input Value Source
Price index $1 of 2022 = $1.093 of 2025; $1 of 2024 = $1.028 EIA STEO, Table 9a
Discount rate 4% real (you can change it) NLR 2025 ATB, financial cases
Home: household use 9,000 kWh a year, the town's 2025 demand shape (illustrative) EIA-930, SPP 2025
Home: heating need 14,000 kWh of heat a year, from a smooth made-up temperature (illustrative) illustrative
Home: rooftop solar $4,336/kW in 2022 dollars = $4,738/kW; 25 years; upkeep $20/kW a year (illustrative). Output: SPP's 2025 hourly solar pattern, scaled month by month to EIA's 2025 capacity factors and to a 17.6% year EIA AEO2026, residential assumptions, Tables 2-3; EIA, distributed generation costs (2024), Table 2-2; EIA Electric Power Monthly, Table 6.07.B
Home: battery $1,000/kWh (illustrative); 2.5 hours; 85% round trip; 15 years; upkeep 4% a year NLR 2025 ATB, residential battery
Home: heat pumps standard: about 2.4 kWh of heat for each kWh of electricity over a season (HSPF 8.2, the heating seasonal performance factor), $6,730 in 2022 dollars = $7,355; high efficiency: about 3.6 (HSPF 12.4), $8,620 = $9,420. HSPF ÷ 3.412 = the season's heat over electricity EIA AEO2026, residential assumptions, Tables 2-3
Home: gas furnace and gas 80% efficient; $14.81 per thousand cubic feet = $14.30 per MMBtu (a million British thermal units, about 293 kWh of heat); 52.91 kg CO₂ per MMBtu burned EIA, Kansas residential gas price; EIA, British thermal units; EIA, CO₂ emissions coefficients
Home: tariffs 14¢/kWh flat; time-of-use 9.66¢ and 28.98¢ (16:00–21:00), illustrative EIA Electric Power Monthly, Table 5.6.B
Home: export credit what the utility pays for each kWh the panels send to the grid (net billing): 4¢ by default, 0 to 8¢ on the bench (illustrative) illustrative
Home: grid CO₂ 680 lb/MWh = 0.308 kg CO₂/kWh (Kansas, 2024) EIA, Kansas Electricity Profile 2024
Farm: wind $1,712/kW and $34.57/kW a year (2025 dollars); 30 years: $133,575 a year per MW at 4%. Output: SPP's 2025 hourly wind pattern, reshaped month by month to EIA's 2025 capacity factors and to a 33.8% year, the best hours at full size EIA AEO2026, electricity assumptions, Table 3; EIA Electric Power Monthly, Table 6.07.B
Farm: battery $1,521/kW for 4 hours = $380.25/kWh; $41.84/kW a year; 85% round trip; 15 years EIA AEO2026, electricity assumptions, Table 3; NREL battery cost projections, 2025
Farm: electrolyzer $2,000/kW in 2022 dollars = $2,186/kW; upkeep 5% a year; 57.5 kWh/kg. Stack wear $6.01/MWh used: an illustrative allowance per MWh, based on DOE's stack replacement (11% of the cost after 40,000 operating hours) as if every hour ran at full power DOE Hydrogen Program Record 24005
Farm: hydrogen tank $800 per kg held (illustrative); 30 years illustrative
Farm: prices power $50/MWh fixed, or $40 and $100/MWh (16:00–21:00); hydrogen $4.00/kg by default (all illustrative) illustrative
Farm: potential CO₂ avoided 0.18 MMBtu of gas per kg of hydrogen made from natural gas × 52.91 kg CO₂ per MMBtu = 9.52 kg CO₂ per kg, if the farm's hydrogen replaces it EIA AEO2026, hydrogen assumptions, Table 2; EIA, CO₂ emissions coefficients

Next

C0 · Behind one meter: what should one home or one plant install?

Sources and further reading

Spotted an error, or stuck? Write to hlli@ksu.edu. Corrections are made in place and dated here.

Text licensed CC BY 4.0, code MIT: teachers and students may reuse and adapt it, with credit to Honglin Li.