Hydroelectric
Hydropower converts the potential energy of falling water into electricity. Learn the power equation, head and flow, turbine types (Pelton, Francis, Kaplan), run-of-river vs reservoir plants, pumped storage and micro-hydro design.
Hydropower is the largest renewable source of electricity worldwide. Water stored at height has potential energy; releasing it through a turbine converts that energy into rotation and then electricity with efficiencies above 90 %.
Hydro plants are also uniquely flexible: they can ramp from zero to full output in minutes, and pumped-storage plants act as giant batteries for the grid.
An analogy
A hydro plant is a water tank on a hill with a tap at the bottom: the height (head) is the pressure, the flow is how far you open the tap, and the turbine is a water wheel in the stream.
Head and flow
Power depends on both how far water falls (head) and how much flows. A mountain plant may have 1000 m of head and little flow; a river barrage may have 10 m of head and huge flow. Both can produce the same power.
Turbine types
Each turbine type suits a different head and flow range.
- Pelton (impulse): high head, low flow; water jets hit spoon-shaped buckets.
- Francis (reaction): medium head, the most common large turbine.
- Kaplan/propeller: low head, high flow, adjustable blades.
- Cross-flow and Turgo: small/micro hydro.
Plant types
Run-of-river plants use natural flow with little storage and vary with the season. Reservoir plants store water behind a dam and dispatch on demand. Pumped-storage plants pump water uphill when power is cheap and generate when it's valuable.
Control and grid role
Hydro governors adjust wicket gates or needle valves to control power and frequency. Water inertia in long penstocks causes a non-minimum-phase response (opening the gate briefly reduces power), and surge tanks absorb water-hammer pressure waves. Hydro provides inertia, black-start capability and fast reserves.
Environmental and social aspects
Large dams change river ecosystems, sediment transport and fish migration, and can displace communities. Fish ladders, environmental flows and careful siting reduce impacts; reservoirs can also emit methane from decaying vegetation.
Formulas
- Hydraulic power:
P = η · ρ · g · Q · H - Stored energy:
E = ρ · g · V · H - Pumped-storage round trip:
η_rt = η_pump · η_turbine · (other losses)
Worked example: Plant output
Given: Q = 20 m³/s; H = 50 m; η = 0.90
Find: Electrical power.
- P = 0.90 × 1000 × 9.81 × 20 × 50
- = 8.83 × 10⁶ W
Answer: 8.83 MW
Worked example: Energy in an upper reservoir
Given: V = 1 000 000 m³; H = 300 m; Generating efficiency 0.90
Find: Recoverable energy.
- E = 1000 × 9.81 × 10⁶ × 300 = 2.94 × 10¹² J
- = 817.5 MWh → × 0.9 = 736 MWh
Answer: ≈ 736 MWh
Common mistakes
- Wrong: Using gross head in the power equation. — Right: Subtract penstock friction losses to get the net head.
- Wrong: Picking a turbine by power alone. — Right: Choose by head and flow (specific speed) — the same power can need Pelton or Kaplan.
Applications
- Large reservoirs: Plants like Three Gorges (22.5 GW) and Itaipu provide bulk, dispatchable renewable energy.
- Pumped storage: The dominant form of grid-scale storage worldwide, with ~75–80 % round-trip efficiency and many hours of duration.
- Micro-hydro: Small streams power remote villages and farms with 5–100 kW systems.
Key takeaways
- P = ηρgQH — head and flow both matter.
- Pelton for high head, Francis medium, Kaplan low.
- Reservoir and pumped hydro are dispatchable and flexible.
- Use net head; consider water hammer and environmental impacts.
Going further
- Specific speed: N_s = N√P/H^(5/4) characterises turbines independent of size: low N_s → Pelton, medium → Francis, high → Kaplan.
- Variable-speed pumped storage: Doubly-fed or full-converter units let pumped-storage plants vary pumping power and provide fast frequency regulation even in pump mode.
- Hydro-solar hybrids: Floating PV on reservoirs shares grid connections, reduces evaporation, and lets water be saved when the sun shines.