How do power plants turn heat, water, wind and sunlight into electricity?

Open six plants, follow 100 units of energy to the wire, and compare three real days on a solar farm

F4 of Energy Systems, Step by Step: open six power plants, follow 100 units of energy to the wire and to waste heat, turn a heat rate into an efficiency, compare a high-output and a low-output day on a solar farm, and meet the limits of reservoirs and ramp rates.
  • Foundations · L1
  • 20 min guided · about 10 min practice
  • After lesson 5

The idea in one table: 100 units of energy in, how many reach the wire

Plant Energy in What spins Of 100 units, to the wire
Gas combined cycle natural gas, burned a gas turbine, then a steam turbine 45.3 (heat rate 7,535 Btu per kWh)
Gas peaker natural gas, burned a gas turbine 31.1 (heat rate 10,975 Btu per kWh)
Coal steam plant coal, burned in a boiler a steam turbine 34.0 (heat rate 10,040 Btu per kWh)
Geothermal plant (flash steam) hot water or steam from wells, 300 to 700 °F a steam turbine about 16
Hydro dam water falling from a height a water turbine about 90
Wind turbine, at rated wind speed moving air the rotor, then a generator about 26 (no rotor can catch more than 59.3)
Solar panel, today's best modules sunlight nothing nearly 25, as direct current at the module (inverter losses not counted)

Three real September days on Prairie Town's 200 MW solar farm (SPP's 2025 shape, scaled)

Day Energy made Day's capacity factor Peak hour
High output, 11 September 2025 1,666 MWh 34.7% 173 MW
Afternoon dip, 3 September 2025 1,411 MWh 29.4% 161 MW (it fell 37 MW into 14:00)
Low output, 5 September 2025 776 MWh 16.2% 93 MW
  • Hydro: power = 1,000 kg/m³ × 9.81 m/s² × flow × head × 0.9. With a head of 120 m and a flow of 100 m³/s: 105.9 MW. A toy reservoir of 20 million m³, with no inflow and a steady head, lasts 55.6 hours at that flow.
  • Ramp: on lesson 0's evening (3 September 2025), a combined-cycle plant that can add 40 MW per hour falls 10 MWh short at 18:00; a fast peaker, or 50 MW per hour, closes the gap.

With JavaScript on, you try each idea yourself in eight short steps.

Real data, gas and coal. EIA's 2025 tested heat rates at full load (Electric Power Annual, Table 8.2), turned into shares with 3,412 Btu in a kWh. They are test values, not a year's measured fuel use.

Real data, solar days. The Southwest Power Pool's 2025 hourly solar shape (EIA-930), scaled so its highest hour of the year is 200 MW. A regional fleet is smoother than one farm.

Typical, not measured. Geothermal, hydro and wind: EIA's notional equipment efficiencies (Annual Energy Review 2010, Table F1, p. 358). Solar: the best modules approach 25%, as direct current at the module.

Illustrative. Prairie Town's 200 MW solar farm, its combined-cycle plant's 40 MW per hour ramp, the hydro plant and its reservoir. All sources read 3 November 2026.

Need a refresher? Lesson 5 (capacity factor and the wind's cube law) and toolbox K2 (efficiency as a rate).

What you just did, as diagrams

Most plants spin a generator
Gas, steam, hydro, geothermal and wind plants all turn a turbine that turns a generator; solar panels have no moving parts.
Heat plants lose most as waste heat
EIA's 2025 full-load tests imply that U.S. combined-cycle gas plants send about 45.3 of every 100 units of fuel energy to the wire, coal steam plants 34.0; the rest leaves as waste heat.
Heat rate and efficiency are one number
Share to the wire = 3,412 Btu ÷ the heat rate in Btu per kWh: 3,412 ÷ 7,535 = 45.3%.
Wind and solar follow the weather
The 200 MW farm made 776 MWh on 5 September 2025 and 1,666 MWh on 11 September; its output alone cannot show which weather made the gap.
Stored water and ramp rates set limits
A reservoir with no inflow runs dry after so many hours at full flow, and a plant's ramp rate caps how fast it can follow demand.
Go deeper · AnalystHeat rate, efficiency and why hotter heat helps

Two views of one number. Efficiency \(\eta\) (a share, no unit) and heat rate \(HR\) (Btu of fuel per kWh sent out):

\[ \eta = \frac{3{,}412\ \text{Btu per kWh}}{HR}. \]

EIA’s heat rates are net: they divide the fuel by the electricity the plant sends out. EIA typically counts fuel at its gross heat content, which includes the heat in the exhaust’s water vapour (EIA glossary).

Hotter heat helps. A heat engine can turn a larger share of its heat into work when that heat is hotter than its cooling water.

Heat source How hot Of 100 units, to the wire
Geothermal water 300 to 700 °F (EIA) about 16 (EIA, typical)
Gas in a gas turbine above 2,000 °F (DOE) 20 to 35 alone (DOE)

The physics of that ceiling, and how engineers approach it, is device thermodynamics, beyond this lesson (side topic X1).

  • Combined cycle. The gas turbine’s exhaust is still hot enough to boil water for a steam turbine. With that second turbine, EIA’s 2025 full-load tests imply about 45.3% for U.S. combined-cycle plants; DOE reports efficiencies as high as 60 percent for its advanced turbines.
  • Measured against notional. The gas and coal shares come from tested heat rates at full load, not a year’s fuel use; the hydro, wind and geothermal shares are EIA’s typical equipment values. Wind, sunlight, falling water and the earth’s heat are not bought by the unit, so the energy a plant does not catch carries no significant cost (EIA, AER 2010, Appendix F).
Go deeper · ModelerPlant limits as rules in a model

A dispatch model chooses each plant’s output in every hour so that supply meets demand at the lowest cost, within each plant’s rules:

  • Size: output stays between zero and the plant’s size, in MW.
  • Ramp: from one hour to the next, output changes by no more than the ramp limit (MW per hour) times the hour.
  • Fuel: fuel burned is the heat rate times the electricity made.
  • Stored water: the electricity made over the period (MWh) stays within what the usable water can give at its head.
  • Weather: wind and solar output stay within what the wind or the sun allows that hour.

The fuel rule, with output \(p_t\) in MW held for \(\Delta t\) hours, \(HR\) in Btu per kWh and 1,000 kW in a MW:

\[ F_t = 1{,}000 \cdot HR \cdot p_t\,\Delta t \quad \text{(Btu)}. \]

At 150 MW for one hour and 7,535 Btu per kWh, that is about 1.13 billion Btu.

Lesson 0 followed the evening greedily, one hour at a time; a model that sees the whole day can warm the slow plant up early. M1 writes rules like these as a model and solves it, M2 adds start-ups and minimum output, and lesson 9 treats a reservoir like a battery.

Go deeperWhat this lesson leaves out
  • How turbines, boilers and cells are designed, and the thermodynamics of their limits (side topic X1).
  • Output and efficiency at part load: a plant running below its size usually does worse than its full-load heat rate.
  • Emissions and air quality: F11. Costs: lesson 7.
  • Concentrated solar power, which uses mirrors to make steam, biomass plants and pumped-storage hydro (lesson 9 treats storage).
  • A solar farm's inverter, wiring and other losses between the module and the grid.
  • Cooling water, land and the materials each plant needs.
  • Start-up times beyond the four plant types in EIA's 2020 article.

Check yourself

Practice, about 10 minutes: four myths, then four questions.

Myth or fact? “A modern power plant turns nearly all the fuel it burns into electricity.”

  • Myth
  • Fact
Answer

Myth. EIA's 2025 full-load tests imply about 45.3% for U.S. combined-cycle gas plants and 34.0% for coal steam plants; the rest leaves as waste heat.

Myth or fact? “A plant with a low share to the wire is always wasting something it paid for.”

  • Myth
  • Fact
Answer

Myth. A solar panel sends nearly 25 of 100 units to the wire, but sunlight is not bought fuel: the energy it does not catch carries no significant cost (EIA, AER 2010, Appendix F).

Myth or fact? “A hydro dam can run at full power for as long as it likes.”

  • Myth
  • Fact
Answer

Myth. It runs until the reservoir runs low: with no inflow, the lesson's 20 million m³ last 55.6 hours at 100 m³/s. A run-of-river plant has almost no store at all.

Myth or fact? “The fastest gas plant is also the one that gets the most electricity from its gas.”

  • Myth
  • Fact
Answer

Myth. At full load, a peaker (a gas turbine alone) sends about 31.1% of its fuel energy to the wire and a combined cycle about 45.3% (EIA's 2025 tests). Speed and efficiency are different jobs.

A gas peaker has a heat rate of 10,975 Btu per kWh. What share of its fuel energy reaches the wire?

  • 31.1%
  • 68.9%
  • 45.3%
  • 321.7%
Answer

31.1%: 3,412 ÷ 10,975 = 0.311. The other 68.9% leaves as waste heat in the hot exhaust; dividing the other way round gives an impossible 321.7%.

A hydro plant doubles its head and keeps the same flow. What happens to its power?

  • It stays the same
  • It doubles
  • It grows eight times
  • It halves
Answer

It doubles: power = density × gravity × flow × head × efficiency, so it grows in step with the head. The cube law belongs to wind (lesson 5).

On 5 September 2025 the 200 MW solar farm made 776 MWh. What was its capacity factor for that day?

  • 388%
  • 32.3%
  • 16.2%
  • 47%
Answer

16.2%: 776 ÷ (200 × 24). Counting only 12 daylight hours would give 32.3%, but the night counts too; the high-output 11 September reached 34.7%.

Which kind of plant usually goes from cold to full output fastest?

  • A coal steam plant
  • A gas combined-cycle plant
  • A geothermal plant
  • A hydro plant
Answer

Hydro: most hydro turbines reach full output in under 10 minutes; most combined-cycle plants take 1 to 12 hours and coal plants more than half a day (EIA, 2020).

Numbers, sources and what’s next

Numbers to remember

Number What it means Source
45.3% Share of their fuel energy U.S. combined-cycle gas plants send to the wire at full load: 3,412 ÷ a tested heat rate of 7,535 Btu per kWh. EIA, Electric Power Annual, Table 8.2 · 2025 data, read 3 November 2026
34.0% The same full-load share for U.S. coal steam plants: 3,412 ÷ 10,040 Btu per kWh. EIA, Electric Power Annual, Table 8.2 · 2025 data, read 3 November 2026
3,412 Btu The energy in one kWh of electricity; divide it by a heat rate to get an efficiency. EIA, Frequently Asked Questions · read 3 November 2026
59.3% The most any rotor can catch of the wind's power (the Betz limit, 16/27). Physics; lesson 5
under 10 minutes How long most hydro turbines take from a cold start to full output; most combined-cycle plants take 1 to 12 hours. EIA, Today in Energy · 19 November 2020
42% · 34% Shares of U.S. electricity made by steam turbines and by combined-cycle plants in 2022. EIA, Electricity explained · 2022 data, read 3 November 2026

Next

F5 · How does a nuclear reactor make electricity, and heat?

In the real world

  1. Turbines everywhere: in 2022, steam turbines made about 42% of U.S. electricity, combined-cycle plants about 34%, wind turbines about 10%, hydro turbines about 6% and solar panels about 3% (EIA).
  2. Panels keep improving: commercial solar panels averaged less than 10% in the mid-1980s; today's best modules approach 25% (EIA).
  3. A turbine's output is not one number: it depends on the wind speed, through its power curve (lesson 5).

From the course author's research: a wind turbine's real power curve is a band, not a line. Adding the turbine's theoretical curve to about two hundred measurements can narrow that band, but whether it helps depends on how the fit is scored. (Li et al., ASME IDETC 2023)

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.