What should Prairie Town build? Plan its power system

Choose what to build, run a year of real weather, and ask the optimizer

Lesson 13 of Energy Systems, Step by Step: choose how much wind, solar, gas, nuclear and battery a small fictional town builds, run its year on real 2025 weather in a linear program, ask the optimizer for the cheapest plan under a CO₂ cap, and place your plan on the cost and CO₂ frontier.
  • Analyst to Modeler · L2–L3
  • Lesson 13 of 14
  • 15 min
  • After lesson 9 and lesson 12

The cheapest plan for Prairie Town at each CO₂ cap (seven weeks of 2025, EIA and NREL costs)

CO₂ cap a year Cost a year Wind Solar Gas (CC + peaker) Nuclear Battery (MW / MWh)
none (792 kt) $102.9M 0 MW 33 MW 425 MW 0 MW 0 / 0
600 kt $108.8M 181 MW 54 MW 367 MW 0 MW 0 / 0
400 kt $117.3M 389 MW 50 MW 341 MW 0 MW 0 / 0
200 kt $129.3M 576 MW 100 MW 302 MW 0 MW 15 / 15
100 kt $143.1M 649 MW 216 MW 280 MW 0 MW 28 / 40
0 kt $288.9M 220 MW 59 MW 0 MW 330 MW 62 / 447

kt: thousand tonnes. A battery has two sizes: power (MW, how fast it charges or discharges) and energy (MWh, how much it holds).

With JavaScript on, you choose the plants yourself, run the year in a solver and ask it for the cheapest plan under a CO₂ cap.

Weather and demand: real 2025 hourly shapes of the Southwest Power Pool grid (EIA-930), scaled to a 450 MW peak.
Wind and solar: output matched to EIA's 2025 U.S. capacity factors.
Costs: EIA's and NREL's, dated under Sources; constant within a scenario.
Price year: 2025 dollars throughout; NREL's 2024 battery costs are converted with BEA's GDP implicit price deflator (×1.0263).
Prairie Town: fictional.

About 15 guided minutes. Practice, about 20 more: by hand, earn all nine stars with a plan under 100 kt, or try a gas price of $6/MMBtu.

What you just did, as diagrams

What to build
Seven numbers: MW of five plants and the battery's MW and MWh; each costs money every year.
Hourly operation
Given what is built, the solver runs the plants and the battery at least cost each hour.
Seven weeks
Four typical weeks and three extreme ones stand for the 52 weeks of 2025.
Storage link
The battery's charge carries from each calendar week to the next.
CO₂ cap
An extra rule; its shadow price is the cost of the last tonne cut.
Frontier
The cheapest plan at each CO₂ level; no plan is both cheaper and cleaner.
Go deeper · ModelerThe capstone as a linear program

The model decides what to build (\(K_i\)) and how to run it every modelled hour \(t\), at least yearly cost:

\[\min \; \sum_i f_i K_i + \sum_t w_t \big(r_\mathrm{cc}\, g_t + r_\mathrm{pk}\, q_t + V u_t\big)\]

\[ \begin{aligned} a^{w}_t K_\mathrm{wind} + a^{s}_t K_\mathrm{solar} + 0.911\,K_\mathrm{nuc} + g_t + q_t + d_t - c_t + u_t &\ge D_t && \text{(demand)}\\ g_t \le K_\mathrm{cc}, \quad q_t \le K_\mathrm{pk}, \quad c_t + d_t &\le K_\mathrm{bp} && \text{(sizes)}\\ s_t = s_{t-1} + 0.85\,c_t - d_t, \qquad 0 \le s_t &\le K_\mathrm{be} && \text{(battery)}\\ \textstyle\sum_t w_t\,(0.329\, g_t + 0.484\, q_t) &\le \text{cap} && \text{(CO}_2\text{)} \end{aligned} \]

Symbol Meaning Unit
\(K_i\) size built: wind, solar, gas CC, peaker, nuclear; battery power \(K_\mathrm{bp}\) MW
\(K_\mathrm{be}\) battery energy MWh
\(f_i\) yearly cost of one unit built; for nuclear it also holds fuel and O&M, as its output is constant $ per MW-year (per MWh-year)
\(g_t, q_t\) output of the gas CC plant and the peaker MW
\(r_\mathrm{cc}, r_\mathrm{pk}\) running cost of gas $/MWh
\(c_t, d_t, s_t\) battery charge, discharge and level MW, MW, MWh
\(u_t\) demand left unserved MW
\(V\) $10,000 per unserved MWh: a weight that steers a fixed plan to keep the lights on, never counted in its cost $/MWh
\(a^w_t, a^s_t\) wind and solar output per MW built MW per MW
\(D_t\) demand MW
\(w_t\) hours of the year that modelled hour \(t\) stands for h
\(0.911\) nuclear output per MW built, the same every hour: a simplification MW per MW
  • Yearly cost of a plant: overnight capital cost × capital recovery factor + fixed O&M (operation and maintenance). At a 4% real (after-inflation) cost of capital over 30 years, the factor is 0.05783.
  • Running cost of gas: heat rate × gas price + variable O&M. MMBtu is a million Btu of fuel energy.

\[ \begin{aligned} \text{wind, per kW-year:}\;\; & 1{,}712 \times 0.05783 + 34.57 = \$133.6\\ \text{combined-cycle, per MWh:}\;\; & 6.226 \times \$3.85 + \$3.49 = \$27.46\\ \text{its CO}_2\text{, t per MWh:}\;\; & 6.226 \times 0.05291 = 0.329 \end{aligned} \]

Need a refresher? Toolbox K3 (discounting and the capital recovery factor).

Every term is linear, so this is a linear program. Your plan fixes the \(K_i\); the optimizer chooses them too, with \(u_t = 0\). M3 (capacity expansion) writes the same model in code, on representative weeks checked against the full year.

Go deeper · ModelerSeven weeks for a year: how, and how well
  • Seasons. Each season’s representative week is its medoid: the real week closest, hour by hour, to the season’s other weeks. Scaled to keep the season’s demand, wind and solar energy, it stands for 11 (winter), 14 (spring), 11 (summer) or 13 (fall) weeks.
  • Extremes. Three weeks are kept as they were: the year’s peak demand, the peak of demand minus wind and sun, and the least wind.
  • Storage across weeks (after Kotzur and co-authors, 2018). Calendar week \(i\) starts at level \(S_i\), and its representative week \(k\) adds its net change: \(S_{i+1} = S_i + \Delta_k\).
  • Within each week. Its lowest and highest swing, \(\ell_k\) and \(h_k\), keep \(0 \le S_i + \ell_k\) and \(S_i + h_k \le K_\mathrm{be}\). The year ends where it began.

The check: the optimizer’s plans, rounded up to the sliders’ steps, re-run hour by hour on all 8,760 hours.

Plan Cost, 7 weeks Cost, full year CO₂, 7 weeks CO₂, full year Unserved, full year
Optimizer at 400 kt $118.6M $118.7M 392 kt 393 kt 43 MWh
Optimizer at 200 kt $130.5M $132.1M 197 kt 215 kt 33 MWh
Optimizer at 100 kt $144.4M $147.2M 98 kt 131 kt 0 MWh
  • Cost. Each plan costs at most 2% more on the full year.
  • CO₂. Deeper cuts overshoot their caps: 215 kt against 200 kt (7% over) and 131 kt against 100 kt (31% over). Seven weeks miss some still, hot evenings when gas must run.
  • Unserved energy. Tiny: at most 43 MWh, under 0.002% of the year’s demand.
  • Re-optimized on all 8,760 hours. The cheapest 200 kt plan costs $133.2M, 3% more, and its last tonne $139 instead of $85: seven weeks underestimate the cost of deep cuts.

Planners respond with more or longer periods, extreme weeks and adequacy tests over many weather years (A5).

Check yourself

Myth or fact? “If wind is the cheapest way to cut CO₂, the cheapest clean plan is all wind.”

  • Myth
  • Fact
Answer

Myth. On still evenings the town still needs firm plants or storage; at 100 kt the optimizer keeps 280 MW of gas and adds solar and a battery.

Myth or fact? “The cheapest plan never spills any wind or sun.”

  • Myth
  • Fact
Answer

Myth. At a 100 kt cap the optimizer spills 9% on purpose: extra wind is cheaper than storing every last MWh.

Myth or fact? “Seven well-chosen weeks give exactly the same answer as the whole year.”

  • Myth
  • Fact
Answer

Myth. Re-run on all 8,760 hours, the optimizer's 200 kt plan emits 215 kt and leaves 33 MWh unserved.

Your plan costs $140.0M a year and emits 150 kt. The cheapest plan at 150 kt costs $134.5M. How far above the frontier are you?

  • 5.5%
  • 4.1%
  • $5.5M
  • 150 kt
Answer

4.1%: 140.0 ÷ 134.5 − 1 = 0.041. You could cut cost by $5.5M a year with the same CO₂.

Numbers, sources and what’s next

Numbers to remember

Number What it means Source
$1,712/kW Overnight capital cost (the building cost, as if paid at once) of a new onshore wind farm; solar with tracking: $1,484/kW. EIA, AEO2026 assumptions, Table 3 (PDF) · 2025 dollars, April 2026
$1,086/kW A new gas combined-cycle plant; a combustion-turbine peaker: $1,158/kW. EIA, AEO2026 assumptions, Table 3 (PDF) · 2025 dollars, April 2026
$8,255/kW EIA's overnight cost for a large light-water nuclear plant: the lesson's default, which you can change. EIA, AEO2026 assumptions, Table 3 (PDF) · 2025 dollars, April 2026
$247/kWh + $382/kW A lithium-ion battery's energy and power costs in 2025 dollars (NREL's $241 and $372 in 2024 dollars, converted); a 4-hour battery: $343/kWh. NREL, battery cost projections, 2025 update (PDF) · 2024 costs, June 2025; BEA, NIPA Table 1.1.9 · revised 29 Oct 2026
$3.85/MMBtu Average cost of natural gas to U.S. power plants in 2025. MMBtu: a million Btu of fuel energy. EIA, Electric Power Annual, Table 7.4 · 2025 data
91.1% Capacity factor of the U.S. nuclear fleet in 2025. For simplicity, the lesson's plant makes a constant 91.1% of its size every hour; real output varies, with refuelling outages, so this cannot show reliability. EIA, Electric Power Monthly, Table 6.07.B · 2025 data

End of the starter path

Choose a tier to go deeper

In the real world

Real planning studies solve this problem with many regions, transmission and decades of investment. Two open examples: NLR's ReEDS model for the contiguous U.S., and PyPSA, a Python framework.

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.