Energy · simulation and game
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”?
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
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.
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.
* Fusion in the game is a future scenario: no fusion power plant feeds electricity into the grid yet. We assumed a 2,000 MW unit that — like nuclear — changes output slowly and emits no CO₂ from a smokestack. Key 0 selects fusion.
* Poland’s generation mix, approximate data (around 2024), on average about 600–700 g CO₂/kWh.
| Source | Power in game | Ramp rate | CO₂ from stack g/kWh | Life-cycle CO₂* g/kWh | Variable cost PLN/MWh |
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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.
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.
Electricity generation in Poland by source over a year. approximate data
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.
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.
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.
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.
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.
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.
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.
A charged particle in a magnetic field circles around a field line (the Larmor radius — a few millimeters for ions in ITER) and glides freely along it. Close the lines into a ring and the problem of the ends disappears.
But in a torus the field is stronger on the inner side than on the outer side. Because of that, ions drift up and electrons drift down, an electric field appears, and it pushes the whole plasma outward — into the wall.
The fix: twist the field lines. In a tokamak this is done by a current flowing in the plasma itself (on the order of megaamperes, driven by the central solenoid); in a stellarator — by complicated, contorted coils. A particle traveling along the spiral is sometimes at the top, sometimes at the bottom, and the drifts cancel out.
A disruption is a sudden loss of confinement in a tokamak: the plasma’s energy hits the wall in a fraction of a second. That’s dangerous for the walls and magnets, but the reaction dies out instantly — there are at most a few grams of fuel in the chamber, and no chain reaction. A stellarator has no plasma current, so it practically has no disruptions; on the other hand, it’s harder to build.
Another approach is inertial confinement: a capsule of frozen D–T, smaller than a peppercorn, is compressed so fast that it reacts before it has time to fly apart. At NIF (USA), 192 laser beams heat a tiny gold cylinder, which then bathes the capsule in X-rays.
Status based on information available in 2025–2026. Future dates are plans — in fusion they often slip.
This joke has been going around among physicists for decades — and there’s something to it: old forecasts promised fusion power plants back in the 20th century.
But the progress is real. The product n·T·τ in tokamaks has grown by several orders of magnitude since the 1960s, JET and TFTR burned real D–T fuel, and in 2022 NIF became the first to get more energy out of fusion than the lasers delivered to the target. Today the main obstacles are engineering and cost: neutron-resistant materials, breeding tritium, reliable magnets and running nonstop for years.
Net electricity (as a fraction of fusion power) versus plasma gain Q = Pfusion/Pheating, with the other settings as alongside.
There is almost no tritium in nature (it decays with a half-life of 12.3 years). The world’s stockpile is on the order of 20–30 kg, mostly from Canadian CANDU reactors. A power plant must make its own in the blanket: ⁶Li + n → T + ⁴He. The tritium breeding ratio (TBR) tells you how many tritium atoms are made for each one burned.
With the current settings (the plant runs all year at a net output of 1,000 MW):
D + ³He → ⁴He (3.6 MeV) + p (14.7 MeV). Both products are charged, so in principle they could be turned into electricity directly, without a boiler or turbine, and the reaction itself produces no neutrons. But D–D reactions always happen in the mix too, so a few percent of the energy (depending on conditions) is carried off by neutrons anyway.
The catch: at the same temperature D–³He reacts much more slowly than D–T. You need a plasma several times hotter and much better confined — check the chart in tab 1 and the calculator in tab 4.
On Earth helium-3 is very rare. It comes mainly from tritium decay, in amounts on the order of kilograms per year. It’s needed for neutron detectors and for dilution refrigerators, which cool things like quantum computers to thousandths of a kelvin.
On the Moon, the solar wind has been “implanting” helium-3 into the regolith — the loose rock on the surface — for billions of years. Estimates put it at a few to a dozen or so ppb (parts per billion by mass), in places up to about 20 ppb. More about our satellite: Moon.
The energy is fusion heat (before conversion to electricity). The regolith has to be dug up and heated to a few hundred °C to release the gas — a gigantic mining undertaking.
The physics behind every wall socket — in nine steps.
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 = PusefulPsuppliedCoal units typically reach 35–46%, combined-cycle gas about 55–62%, nuclear about 33–37%, and hydro as much as about 90%.
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.
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 minuteFor 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.
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 − PloadWithin 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.
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-section10 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.
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.
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.
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.
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