Pathway Explorer
Plan Prairieland’s five regions to 2050 within a carbon budget and an import cap, run the pathway as one linear program, and test it against shocks and full years of hours
Sandbox SB4 of Energy Systems, Step by Step: plan a fictional nation’s electricity and fuels to 2050, run its five regions as one linear program within a cumulative carbon budget and an import cap, and test the pathway against shocks, decade-by-decade decisions and full years of hours.
- Modeler · L3
- Sandbox
- 30 min
- After M3
- Completed
The brief
- The nation
- Prairieland (fictional): 20 million people in five regions joined by seven links; oil imported through one strait; all its coal mined in Ridge County.
- You decide
- How fast buildings, transport and industry switch to electricity; a cumulative carbon budget; an import cap; what the model may build or retire; a shock; the costs, within fixed ranges.
- The engine works out
- One linear program (LP) picks what to build, run and retire in each region for 2030, 2035, 2040, 2045 and 2050 at the least present value of cost, on twelve time slices of 2025's weather.
- It leaves out
- Power-flow physics, outages, end-use equipment costs, fuels other than electricity for the oil that remains, and who decides: a teaching model, not a forecast.
- Units
- Power in MW and GW; energy in TWh and PJ (1 TWh = 3.6 PJ); CO₂ in Mt, million tonnes. Fuel prices per GJ on net calorific values.
- Short forms
- O&M: operation and maintenance. LNG: liquefied natural gas, imported by ship. t per TJ: tonnes of CO₂ per terajoule of fuel.
Open-ended: start from a preset, change one thing at a time, and copy the plan link to keep a plan. Prairieland is fictional; its numbers are illustrative.
The bench
| Control | Default plan | Range |
|---|---|---|
| Demand growth | Central | one of: Low growth, Central, High growth |
| Buildings: electricity's share of useful energy in 2050 | 80 % | 54 to 100 %, in steps of 1 % |
| Transport: electricity's share of useful energy in 2050 | 50 % | 3 to 78 %, in steps of 1 % |
| Industry: electricity's share of useful energy in 2050 | 55 % | 40 to 60 %, in steps of 1 % |
| Carbon budget, 2026-2050 | 3,600 Mt | 500 to 5,400 Mt, in steps of 100 Mt |
| Counting the years between | Straight lines between model years | one of: Straight lines between model years, Each model year for its five years |
| Import share cap, each model year | 40 % | 10 to 60 %, in steps of 5 % |
| Foresight | Perfect foresight (2030-2050 at once) | one of: Perfect foresight (2030-2050 at once), Decade by decade |
| Peak-hour reserve rule | Stress hours + 10% | one of: No peak-hour rule, Meet the stress hours, Stress hours + 10%, Stress hours + 20% |
| Generic firm clean option allowed | 1 | 0 to 1, in steps of 1 |
| New transmission allowed | 1 | 0 to 1, in steps of 1 |
| Early retirement of fossil plants allowed | 1 | 0 to 1, in steps of 1 |
| Shock | No shock | one of: No shock, Gas-price spike, Drought, Mineral export restriction, Demand surprise |
| Wind farm, capital | 1,712 $/kW | 1,500 to 2,400 $/kW, in steps of 1 $/kW |
| Solar farm, capital | 1,484 $/kW | 1,350 to 1,900 $/kW, in steps of 1 $/kW |
| Battery (4 hours), capital | 1,521 $/kW | 1,380 to 1,690 $/kW, in steps of 1 $/kW |
| Gas combined cycle, capital | 1,032 $/kW | 850 to 1,400 $/kW, in steps of 1 $/kW |
| Gas turbine, capital | 1,158 $/kW | 950 to 1,580 $/kW, in steps of 1 $/kW |
| Generic firm clean plant, capital | 7,000 $/kW | 3,000 to 11,000 $/kW, in steps of 10 $/kW |
| New transmission | 1,500 $/MW-km | 800 to 3,000 $/MW-km, in steps of 50 $/MW-km |
| Domestic gas | 4.05 $/GJ | 2 to 9 $/GJ, in steps of 0.01 $/GJ |
| LNG imports | 10 $/GJ | 6 to 30 $/GJ, in steps of 0.5 $/GJ |
| Coal | 2.41 $/GJ | 1.5 to 4 $/GJ, in steps of 0.01 $/GJ |
| Crude oil | 12 $/GJ | 7 to 22 $/GJ, in steps of 0.5 $/GJ |
| Discount rate (real) | 5 % | 2 to 8 %, in steps of 0.5 % |
With JavaScript on, you change these, run the pathway in your browser and copy a link to your plan. Prairieland is fictional; its numbers are illustrative.
- Illustrative: Prairieland, its regions, fleet, links, demand and shocks (prairieland.json); the existing plants' operating costs, the penalties and the peak-hour rule are set for teaching (e4-pathways.json).
- Based on public data: new plants' costs from EIA's 2026 assumptions, fuel prices from EIA's 2025 data, CO₂ factors from the IPCC, hourly shapes from SPP's 2025 and 2024 grid.
- Left out of the cost: heat pumps, cars and boilers (end-use equipment), so a plan that electrifies more looks cheaper here than it would be.
- Precomputed: the presets, perfect and decade by decade, with their shocks and full-year checks, come from a library made with this engine; any other plan runs in your browser.
- Against lesson A20: no pathway here gets below about 2,700 Mt (straight-line counting, central demand). A20 meets 2,600 Mt because its fastest path electrifies buildings and industry years sooner.
Results
| Result: the default plan (Central: electrify, budget 3,600 Mt) | Value |
|---|---|
| Cost 2026–2050, present value in 2025 (2025 dollars; supply side and every fuel bought) | $401.6 billion |
| CO₂ 2026–2050 against the budget | 3,600 of 3,600 Mt |
| CO₂ a year, 2030, 2035, 2040, 2045, 2050 | 171, 142, 130, 123, 115 Mt |
| Imports, share of primary energy, 2030, 2035, 2040, 2045, 2050 | 32%, 32%, 30%, 27%, 24% (cap 40%) |
| Clean share of electricity, 2030 and 2050 | 83% and 90% |
| Built 2026–2050: wind, solar, gas, batteries, firm clean (generic) | 72.0 GW, 32.5 GW, 35.5 GW, 0.0 GW, 3.3 GW |
| New transmission | 8.9 GW |
| The budget's marginal value (the LP's dual: what one more tonne allowed would save) | $48 a tonne, present value in 2025 |
| Ridge Station (2,400 MW of coal) | closed by 2040 |
Precomputed with this engine on 7 November 2026: one linear program over 2030–2050 on twelve time slices. Prairieland is fictional; its numbers are illustrative. With JavaScript on, the bench runs your own plan.
How the engine works, as diagrams
- Decisions
- What to build in each region and model year, what to retire early, which links to widen, how to run every slice, and which fuels to buy.
- Goal
- The least present value of cost 2026–2050, with each plant paying only for the years it runs up to 2050 (its residual value is not charged).
- Rules
- Each region-slice balances; plants within their limits; links within theirs; CO₂ summed over the years within the budget; imports within the cap; the stress hours met.
- It holds when
- Twelve slices of 2025's weather stand for every year; costs stay the same whatever is built; electrification follows the plan.
Go deeper · ModelerThe linear program behind the bench
Go deeperWhen two answers cost the same: the tie rule and penalties
Small stated costs, left out of every reported number, pick one plan when several cost the same:
- $0.05 per MWh carried on any link, so power does not wander between regions;
- $0.50 per MWh out of a battery, so it does not cycle for nothing;
- $0.01 per GJ more for imported crude than domestic crude, so domestic crude is used first.
Penalties keep every run solvable and are never part of a reported cost:
| Rule broken | Unit | Penalty |
|---|---|---|
| Electricity not served | MWh | $10,000 |
| Short at a stress hour | MW for a year | $750,000 |
| CO₂ over the budget | tonne | $1,000 |
| Imports over the cap | GJ | $100 |
The budget and the cap are limits, not prices. A run that misses either is solved twice more: first for the least overshoot, serving no less demand; then for the least cost at that overshoot.
So "out of reach" means no plan within your levers meets the limit; the run shown is the closest.
A check on the default plan: plans within $1,000 of its best cost build the same national wind, solar, gas and firm capacity in 2030, 2040 and 2050, within 10 MW (the engine's test). That covers those totals only, not regions or links.
The tie rule picks one answer; it does not make it the only one. Within a millionth of the cost, 2046–2050's new solar can move by a gigawatt or more (M13, step 11).
Numbers, sources and what’s next
Inputs the engine uses
| Input (2025 dollars) | Default | Range you can set (set for teaching) | Source, and the source's own range |
|---|---|---|---|
| Wind farm, capital | $1,712/kW (EIA Table 3) | $1,500/kW to $2,400/kW | EIA AEO2026 Table 4, its regions: $1,478/kW to $4,335/kW |
| Solar farm, capital | $1,484/kW (EIA Table 3) | $1,350/kW to $1,900/kW | EIA AEO2026 Table 4, its regions: $1,342/kW to $1,949/kW |
| Battery (4 hours, 85% round trip), capital | $1,521/kW (EIA Table 3) | $1,380/kW to $1,690/kW | NREL's 2025 battery update (low) and EIA AEO2026 Table 4 (high): $1,371/kW to $1,698/kW |
| Gas combined cycle, capital | $1,032/kW (EIA Table 3) | $850/kW to $1,400/kW | EIA AEO2026 Table 4, its regions: $830/kW to $1,445/kW |
| Gas turbine, capital | $1,158/kW (EIA Table 3) | $950/kW to $1,580/kW | EIA AEO2026 Table 4, its regions: $946/kW to $1,585/kW |
| Generic firm clean plant, capital | $7,000/kW (set for teaching) | $3,000/kW to $11,000/kW | EIA AEO2026 Table 4, firm low-carbon plants that burn no fuel: $2,685/kW to $11,568/kW |
| New transmission | $1,500 per MW-km (set for teaching) | $800 per MW-km to $3,000 per MW-km | set for teaching |
| Domestic gas | $4.05/GJ (EIA, 2025: $3.85 per MMBtu, on net calorific values) | $2.00/GJ to $9.00/GJ | EIA Electric Power Annual, Table 7.4 |
| LNG imports | $10.00/GJ (set for teaching) | $6.00/GJ to $30.00/GJ | set for teaching |
| Coal (Ridge County) | $2.41/GJ (EIA, 2025: $2.42 per MMBtu, on net calorific values) | $1.50/GJ to $4.00/GJ | EIA Electric Power Annual, Table 7.4 |
| Crude oil | $12.00/GJ (set for teaching: about $70 a barrel) | $7.00/GJ to $22.00/GJ | set for teaching |
| CO₂ factors: crude oil, gas, coal | 73.3, 56.1, 94.6 t per TJ | fixed | IPCC 2006 Guidelines, Volume 2, net calorific values |
| Build limits, a region a period | wind 6, solar 8, batteries 6, gas 4 + 4, firm 2 GW | fixed | set for teaching: one generic rule, no technology's own timeline |
| Discount rate (real) | 5% (set for teaching) | 2% to 8% | set for teaching |
| Hourly shapes | SPP's 2025 grid (slices); 2024 for the independent year | fixed | EIA Hourly Electric Grid Monitor (Form EIA-930) |
Keep going
Sources and further reading
- U.S. Energy Information Administration (April 2026). Assumptions to the Annual Energy Outlook 2026: Electricity Market Module, Tables 3 and 4 (read 7 Nov 2026).
- U.S. Energy Information Administration. Electric Power Annual, Table 7.4: weighted average cost of fossil fuels for the electric power industry, 2015 through 2025 (2025: gas $3.85, coal $2.42 per MMBtu; read 7 Nov 2026).
- Cole, W., Ramasamy, V. and Turan, M. (2025). Cost Projections for Utility-Scale Battery Storage: 2025 Update (PDF). NREL/TP-6A40-93281. Only its 2024 cost, in 2025 dollars, as the low end of the battery range.
- Intergovernmental Panel on Climate Change (2006). 2006 IPCC Guidelines for National Greenhouse Gas Inventories, Volume 2: Energy, chapters 1 and 2.
- U.S. Energy Information Administration. Hourly Electric Grid Monitor (Form EIA-930), Southwest Power Pool, 2025 and 2024 (accessed 2 and 3 Nov 2026).
- International Energy Agency. Statistics questionnaires FAQ: the physical energy content method (read 7 Nov 2026).
- DeCarolis, J., et al. (2017). Formalizing best practice for energy system optimization modelling. Applied Energy, 194, 184–198.
- Huangfu, Q., and Hall, J. A. J. (2018). Parallelizing the dual revised simplex method. Mathematical Programming Computation, 10, 119–142 (the HiGHS solver).
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.