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Energy · simulation and game

Power Plant from coal to the socket

Before 230 V shows up in your wall socket, energy travels a long way: from fuel to heat, from heat to a spinning turbine, from motion to electricity — and then hundreds of kilometers down a wire. Follow that path, then run the grid of all of Poland for a whole day yourself. Finally, take a peek at the future: how would a fusion power plant* work — a “star in a box”?

50 Hz
the rhythm at which every generator in Europe spins
≈ 35%
of the energy stored in coal reaches your wall socket
P = I²R
which is why power flows through 400,000 V lines
01

From fuel to socket

Choose a kind and type of power plant — there are 23 of them, including 3 marked with an asterisk*: the thorium reactor exists today only as a small experiment, and fusion power plants don’t exist yet. The glowing dots are packets of energy: their color tells you what form the energy is in, and their density shows how much of it flows. Dots drifting off to the sides are losses. Hover over an element to see details. 1–6 quick pick · ↑/↓ power · Space pause

chemical / primary heat steam, water, wind gas, heavy water, ORC fluid sodium, molten salt motion (mechanical) electrical losses (waste heat) heat for the city plasma (fusion*) fuel in molten salt
Diagram elements and energy conversion stages

    Where does the energy go? Sankey diagram

    Sankey diagram · typical, rounded values · 100% = input energy

    02

    Be the dispatcher: hold 50 Hz

    The chart shows the demand forecast for all of Poland over one day. Set the output of your power plants so that production equals consumption at every moment. When there isn’t enough power, the generators slow down and the frequency drops; when there’s too much, it rises. Outside 49.0–51.0 Hz, customers start getting disconnected, and outside 47.5–51.5 Hz the units trip off on their own: blackout.

    00:00

    The day starts at midnight

    The grid is balanced. Demand is about to start changing — watch the dashed forecast line and move the source sliders ahead of time, because coal, nuclear and geothermal change their output slowly.

    Where do these numbers come from? Emissions, costs and ramp speed of sources
    SourcePower in gameRamp rateCO₂ from stack
    g/kWh
    Life-cycle CO₂*
    g/kWh
    Variable cost
    PLN/MWh

    Direct emissions are the CO₂ coming out of the smokestack during operation (coal: a mix of hard coal and lignite). Life cycle* means the medians from the IPCC report (2014): construction, fuel mining, operation and decommissioning. Variable cost is roughly fuel plus emission allowances (assuming about 300 PLN — Polish złoty, ≈ $75 — per tonne of CO₂), not counting construction. All numbers are approximate and rounded.

    03

    Why high voltage?

    We’re sending power from a plant to a city. The same power can mean a large current at low voltage or a small current at high voltage (P = U·I). A wire heats up the more current flows through it — and with the square of it: Ploss = I²·R.

    Line losses
    –
    Power lost
    –
    Current per phase
    –
    Reaches the city
    –
    deliveredturned into heat in the wires
    04

    Where does Poland get its electricity?

    Electricity generation in Poland by source over a year. approximate data

    Generation mix, around 2024

    share of annual generation, rounded values
      Your day
      play

      The numbers vary a bit between sources and from year to year — coal’s share is falling fast, while solar and wind keep growing. The “Your day” bar shows the mix from the game in section 02.

      In numbers (roughly)

      • Over 20 GW of solar panels, much of it on house roofs, and about 10 GW of onshore wind farms (2025).
      • Demand swings from about 13–14 GW on summer nights to about 27 GW on frosty winter evenings.
      • On average about 600–700 g of CO₂ for every kilowatt-hour — more than twice the European Union average.
      • The 220 and 400 kV transmission grid (over ten thousand kilometers of lines) is run by Polskie Sieci Elektroenergetyczne, Poland’s grid operator.
      • The first nuclear power plant (3 units, about 3.75 GW) is planned in Pomerania, in the municipality of Choczewo on the Baltic coast.
      05

      Fusion power plant*

      The Sun shines because, deep inside it, light nuclei fuse into heavier ones. On Earth we’ve been trying to repeat this for over 70 years: heat the fuel to about 150 million °C, keep it away from the walls, and extract the heat. 1–6 tabs

      * A fusion power plant doesn’t exist yet — it’s a project for the future; below you’ll see how it would work and where the research is happening.

      Deuterium + tritium → helium + neutron

      deuterium (D)1 p + 1 n + tritium (T)1 p + 2 n fuzja helium-4 (α particle)3.5 MeV + neutron14.1 MeV total 17.6 MeV · ≈ 80% of the energy is carried by the neutron

      Helium-4 and the neutron together weigh less than the deuterium and tritium. The missing mass turns into energy according to Einstein’s formula:

      The helium stays in the plasma and heats it. The neutron has no charge, so the magnetic field can’t hold it — it flies out and deposits its energy in the reactor blanket. That’s where the heat for the turbine comes from.

      How much energy in a kilogram?

        Why so hot?

        Nuclei are positively charged and repel each other (the Coulomb barrier, a few hundred keV for D–T). They collide hard enough only in a plasma hotter than 100 million °C — and even then they get close only thanks to quantum tunneling. The curve shows the reaction rate ⟨σv⟩ for different fuels.

        15 keV

        Curves: D–T, D–D and D–³He from the Bosch–Hale parameterization (1992); p–¹¹B computed from a fit of the astrophysical S-factor (after Nevins and Swain, plus newer measurements). Each is shown within its range of validity. 1 keV ≈ 11.6 million K.

        The Lawson criterion: dense, hot and long

        For the plasma to heat itself (ignition), the product of density n, temperature T and energy confinement time τE must exceed about 3·10²¹ keV·s/m³ (for D–T, at about 15 keV). You set the temperature with the slider next to it.

        So how does the Sun do it?

        The Sun’s core is about 15 million K — ten times cooler than a tokamak. The Sun fuses ordinary protons (the p–p chain), and the first step requires turning a proton into a neutron via the weak interaction. That’s why it’s incredibly slow: an average proton waits billions of years for its turn.

        The Sun wins by sheer size: gravity squeezes the gas to about 150 g/cm³ and holds it for free for billions of years. On Earth we have no such “bottle,” so we must use the easiest fuel (D–T) and make the plasma much hotter.

          By estimates, the power density at the center of the Sun is about 280 W/m³ — roughly the same as in a rotting compost heap. The human body: about 100 W in about 0.07 m³.

          06

          How does it work?

          The physics behind every wall socket — in nine steps.

          01

          Energy isn’t created, it only changes form

          In a coal power plant, the fuel’s chemical energy turns into heat, heat into the energy of steam, the steam spins a turbine (mechanical energy), and the generator turns motion into electrical energy. At every stage some energy escapes as heat. The measure of this is efficiency:

          η = PusefulPsupplied

          Coal units typically reach 35–46%, combined-cycle gas about 55–62%, nuclear about 33–37%, and hydro as much as about 90%.

          02

          Why does so much heat go to the cooling tower?

          No heat engine can turn all its heat into work. The upper limit is set by the temperature difference between the steam and the cooling water (the Carnot efficiency, temperatures in kelvins):

          ηmax = 1 − TcoldThotsteam 600 °C = 873 K, condenser 30 °C = 303 K → ηmax ≈ 65%

          Real turbines have friction and eddies, so they achieve less. Waste heat can be put to use: combined heat and power plants use it to heat cities.

          03

          The generator and 50 hertz

          Inside a generator an electromagnet spins, and an alternating voltage is induced in the stationary windings around it — that’s electromagnetic induction, discovered by Faraday. The frequency depends on the speed of rotation:

          f = p · n60p — number of pole pairs, n — revolutions per minute

          For p = 1 and 3000 rpm you get exactly 50 Hz. In nuclear plants the turbine often spins at 1500 rpm and the generator has two pole pairs.

          04

          Water, wind and sun

          P = η·ρ·g·Q·Hwater: flow Q (m³/s) and head H (m) P = ½·ρ·A·v³·Cpwind: 2× faster wind = 8× more power; Cp ≤ 16/27 ≈ 59.3% (Betz limit) P = η·G·Asun: at G ≈ 1000 W/m², a 21%-efficient panel gives about 210 W per 1 m²
          05

          Frequency gives away the balance

          Every second, power plants must produce exactly as much as we consume. When power runs short, the energy comes from the spinning turbines and generators — they slow down and the frequency drops. In simplified form (H — inertia constant, S — power of the rotating machines):

          2HSf0 · dfdt = Pgen − Pload

          Within seconds the units add power on their own (primary control), and within minutes secondary control brings back 50 Hz — in the game, that’s you. Solar panels and wind turbines connect through inverters and add no inertia.

          06

          High voltage = low losses

          Losses in a wire grow with the square of the current. For a three-phase line:

          I = P√3 · U,   Ploss = 3·I²·R = P²·RU² R = ρ · LSρ — resistivity, L — length, S — conductor cross-section

          10 times higher voltage means 10 times less current and a whopping 100 times lower losses. A transformer changes voltage with almost no loss — that’s why the grid has many levels: 400 kV, 110 kV, 15 kV, 230 V.

          07

          Cooling: water or air

          Every steam power plant has to dump the heat from its condenser somewhere. The coldest option is water from a river or the sea (once-through cooling) — it gives the highest efficiency, but needs about 100–200 m³ for every MWh. A wet cooling tower uses about 2–3 m³/MWh, because the water evaporates. A dry cooler uses almost no water, but lowers efficiency by 1–3 points.

          The white cloud above a cooling tower is water vapor, not smoke — smoke goes out the smokestack, and only at plants that burn fuel.

          08

          Reactors differ “on the inside”

          Every reactor needs fuel, a coolant to carry away the heat, and usually a moderator to slow down neutrons (water, heavy water or graphite). Fast reactors have no moderator.

          This choice determines whether uranium has to be enriched, how many loops there are and how hot the steam is. But beyond that, every nuclear power plant has a turbine, a generator and a condenser — just like a coal plant.

          09

          Dispatchable vs. weather-dependent

          Dispatchable power plants (coal, gas, nuclear, hydro with a reservoir, geothermal, biomass) deliver power on demand. Wind, solar and run-of-river plants depend on the weather and the river, and tidal plants — on the Moon.

          That’s why a grid with lots of renewables needs storage, fast gas units and good forecasts. The capacity factor tells you what fraction of the year a plant would be running if it always ran at full power.

          Did you know…?

          1. Half a continent spins to one rhythm. The continental European grid — from Portugal to Poland, Greece and Turkey, and since 2022 also Ukraine and Moldova — is a single synchronous grid. All its generators turn in the same 50 Hz beat.
          2. Turbine blade tips move faster than sound. The last-stage blades of a large steam turbine are over a meter long. At 3000 revolutions per minute their tips race at several hundred meters per second — faster than sound in air (about 340 m/s).
          3. Żarnowiec is a battery made of water. When there’s too much electricity, this pumped-storage plant in northern Poland pumps water from Lake Żarnowiec to a reservoir on a hill, and at peak times releases it through turbines with a combined capacity of about 700 MW. It recovers about 3/4 of the energy put in.
          4. A gram of fusion fuel is worth about 8 tonnes of oil. Fusing 1 g of a deuterium–tritium mix would yield about 3.4·10¹¹ J — as much as burning about 8 tonnes of crude oil or about 15 tonnes of coal.
          5. The Sun heats less than compost. In the Sun’s core there’s only about 280 W per cubic meter — less than in a human body. The Sun shines so brightly because it’s huge, not because its reactions run fast.
          6. A kilogram of thorium holds millions of times more energy than a kilogram of coal. Splitting one nucleus releases about 200 MeV. If all the thorium were turned into uranium-233 and fissioned, 1 kg would give about 8·10¹³ J — almost 4 million times more than a kilogram of coal.

          What did we simplify?

          • Efficiencies and losses are typical values for whole units at full power; at lower output, efficiency usually drops.
          • The power figures in the game are modeled on Poland around 2025 (rounded). Poland doesn’t have a nuclear power plant yet — in the game you can have one.
          • Game time runs about 300 times faster (1 h = 12 s at 1× speed), while frequency changes at its real pace, in seconds.
          • We leave out power exchange with neighboring countries, biomass, combined heat and power plants, line overloads and the long startup of units. Primary control in the model is a single automatic regulator with a ±800 MW reserve.
          • Emissions in the game are direct (from the smokestack). Storage doesn’t emit, but it returns energy taken earlier from other sources.
          • Plant-type efficiencies, the effect of cooling and water use are approximate values; the drawings in the diagram are simplified and building proportions are not to scale.
          • Fusion power plants* are projects: we assumed parameters similar to the planned European DEMO (about 2 GW of fusion power, about 500 MW net). In the power balance, all plasma heating returns as heat, neutrons carry a fixed share of the energy, and the plant’s own needs are a percentage of gross output. The magnetic bottle model shows the drifts qualitatively, magnified. The Lawson criterion is calculated without radiation losses.
          • The molten-salt thorium reactor* is an illustrative drawing based on experiments (MSRE, TMSR-LF1); the efficiency of about 45% is a value assumed in designs, not measured in a power plant.

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