Hydro, Geothermal, Nuclear, and Renewable Plants

Beyond fossil-fired steam and gas plants, the MELE covers the plants that need little or no fuel: hydro, geothermal, nuclear, solar, and wind. The Philippines is a major user of hydro and geothermal, so this is high-yield, locally relevant material. Most items reduce to one power equation per plant type, plus a set of definitions. Work in SI: power in watts or MW, head in meters, flow in m3/s.

Hydroelectric power

A hydro plant converts the potential energy of stored water into electricity. The power available is:

P = rho x g x Q x H x efficiency

where rho = 1,000 kg/m3 is the density of water, g = 9.81 m/s2, Q is the volume flow in m3/s, H is the net head in meters, and efficiency accounts for turbine and generator losses.

Worked example: a plant passes Q = 20 m3/s through a net head of H = 50 m at an overall efficiency of 0.90. Then P = 1,000 x 9.81 x 20 x 50 x 0.90 = 8,829,000 W, or about 8.83 MW. With no losses (efficiency = 1) and Q = 10 m3/s at H = 30 m, the ideal power would be 1,000 x 9.81 x 10 x 30 = 2,943,000 W, about 2.94 MW.

You can also solve for the flow needed. To produce 5 MW at a net head of 40 m with an efficiency of 0.85:

Q = P / (rho x g x H x efficiency) = 5,000,000 / (1,000 x 9.81 x 40 x 0.85) = about 15 m3/s

Heads and pumped storage

The gross head is the total vertical drop from the water surface to the turbine. The net (effective) head is the gross head minus friction and other losses in the penstock:

net head = gross head minus losses

A gross head of 120 m with 5 m of losses gives a net head of 115 m. Always use the net head in the power equation.

A pumped-storage plant is a giant battery. During off-peak hours, cheap surplus electricity pumps water from a lower reservoir to an upper one; during peak hours, that water flows back down through the turbines to generate power. It consumes more energy pumping up than it recovers coming down, but it earns money by shifting cheap off-peak energy to valuable peak hours, and it provides fast reserve.

Geothermal power

Geothermal plants tap the earth's heat. There are three main types:

• Dry-steam: the well delivers steam directly to the turbine.
• Flash-steam: high-pressure hot water is flashed to steam by dropping its pressure; the steam drives the turbine.
• Binary-cycle: moderate-temperature water heats a secondary working fluid with a low boiling point, which vaporizes and drives the turbine, so the geothermal water never contacts it.

The Philippines is one of the world's largest geothermal producers, making this a favorite MELE topic.

Nuclear power

A nuclear plant is a steam plant whose boiler is a reactor: the heat comes from nuclear fission of uranium-235 rather than from burning fuel. Three components define the reactor:

• The moderator (water or graphite) slows the fast neutrons so they can sustain the chain reaction.
• The control rods (boron or cadmium) absorb neutrons to control or stop the reaction.
• The coolant carries the heat away to raise steam.

The energy released comes from a tiny loss of mass, per Einstein's relation:

E = m x c^2

with c = 3 x 10^8 m/s. Converting just 1 gram of mass would release E = 0.001 x (3 x 10^8)^2 = 9 x 10^13 J, an enormous quantity that shows why nuclear fuel is so energy-dense. In practice only a small fraction of the fuel's mass is actually converted.

Solar power

Solar plants use sunlight two ways:

• Photovoltaic (PV) cells convert sunlight directly into electricity. Panel output is P = area x irradiance x efficiency. A 10 m2 array under 1,000 W/m2 of sunlight at 18% efficiency delivers 10 x 1,000 x 0.18 = 1,800 W.
• Solar-thermal plants concentrate sunlight to raise steam for a conventional turbine.

The sunlight reaching the top of the atmosphere, the solar constant, is about 1,360 W/m2; less reaches the ground after atmospheric losses.

Wind power

A wind turbine extracts kinetic energy from moving air. The power in the wind through a swept area A is:

P = 0.5 x rho x A x V^3 x Cp

with rho = 1.225 kg/m3 for air, V the wind speed, and Cp the power coefficient. Because power grows with the cube of wind speed, doubling the wind gives eight times the power. No turbine can capture all of it: the Betz limit caps Cp at 16/27, about 59.3%, since the air must keep some speed to flow out of the way.

Exam-day strategy

• Hydro power is P = rho x g x Q x H x efficiency; always use the net head, not the gross head.
• Net head = gross head minus losses; you can rearrange the power equation to solve for Q, H, or efficiency.
• Pumped storage is a net energy consumer that shifts cheap off-peak energy to the peak.
• Know the three geothermal types (dry-steam, flash, binary) and the reactor trio (moderator slows, control rods absorb, coolant carries heat).
• Wind power scales with V^3 and is capped by the Betz limit of about 59.3%; PV output is area times irradiance times efficiency.