D. Energy and Society · Work, Energy and Power

Generating Electrical Energy: Comparing Input, Output and Efficiency

D2.7 D1.1 D1.2 D3.1 D3.4 A2.1About 75 minutes

Learning goals

I can describe the input energy, the energy transformations and the useful output of hydroelectric, thermal, nuclear, wind and solar generation.
I can calculate and compare the per cent efficiency of different methods of generating electrical energy.
I can analyse how a thermal generating station works and how combined-cycle and cogeneration designs improve its efficiency.
I can assess social and environmental impacts of thermal generation, using efficiency as part of the evidence.

Words to know

generating station
A facility that transforms another form of energy into electrical energy, usually by spinning a turbine connected to a generator.

input energy
The energy fed into a generating station: the Eg of water, the chemical energy of fuel, the nuclear energy of uranium, the Ek of wind, or the radiant energy of sunlight.

useful output energy
For a generating station, the electrical energy it delivers to the grid.

thermal generating station
A station that produces thermal energy (by burning fuel or by nuclear fission) to make steam or hot gas that spins a turbine.

combined-cycle station
A natural gas station where hot exhaust from a gas turbine is used to make steam for a second turbine, so more of the fuel's energy becomes electrical energy.

cogeneration (combined heat and power)
Producing electrical energy and using the station's waste thermal energy for heating buildings or industrial processes.

power engineer
A certified professional who operates and maintains boilers, turbines and other equipment in generating stations, hospitals and factories.

Which station gets the most out of its input?

In Grade 9 you compared Ontario's sources of electrical energy by their benefits and challenges. Now you have the tools to put numbers on them. For each method we can ask three questions: What is the input energy? How much becomes useful electrical energy? What happens to the rest? The answers explain why a hydroelectric station turns most of its input into electrical energy while a nuclear or natural gas station turns only about a third to just over half of it.

Input, output and efficiency of each method

Hydroelectric. Input: gravitational potential energy of water stored behind a dam. Water falls, spins a turbine and generator. Losses are mostly friction and turbulence in the water and electrical resistance. Large stations are about 90% efficient.
Thermal (natural gas, and coal in the past). Input: chemical energy of the fuel. Burning it makes hot gas or steam, which spins turbines. As heat engines, these stations must release much of their input as thermal energy to cooling water or the air. Typical: about 30% to 40% for a simple design; about 50% to 60% for a combined-cycle station.
Nuclear. Input: nuclear energy in uranium fuel. Fission releases thermal energy, which makes steam for a turbine. This is also a heat engine; Ontario's CANDU stations turn roughly one-third of the thermal energy into electrical energy. (How fission releases this energy is explained in the Thermal and Nuclear Energy unit.)
Wind. Input: kinetic energy of moving air. No turbine can capture more than about 59% of the wind's kinetic energy passing through its blades (capturing all of it would mean the air stopping dead behind the blades, so no new air could flow through). Modern turbines capture very roughly 35% to 45% at good wind speeds.
Solar photovoltaic (PV). Input: radiant energy of sunlight. Panels transform it directly into electrical energy with no moving parts. Typical rooftop panels are about 15% to 22% efficient.

Approximate, typical efficiencies. Real stations vary with design, age and operating conditions. Note that the inputs are different forms of energy, so efficiency is only one part of comparing methods.

Worked example

Example 1: A hydroelectric station

Water flows through a hydroelectric station at 300 m³/s (300 000 kg each second) and falls 50 m to the turbines. The station is 90% efficient. Find (a) the rate at which the water loses Eg (the input power), (b) the electrical power output.

(a) Each second, ΔEg = mgΔh = (300 000 kg)(9.8 N/kg)(50 m) = 1.47 × 10⁸ J. So the input power is 1.47 × 10⁸ W ≈ 147 MW.
(b) Output = 0.90 × 147 MW ≈ 132 MW.
The other 15 MW becomes thermal energy and sound (water turbulence, bearing friction, resistance in the generator).

Input about 147 MW; electrical output about 1.3 × 10² MW.

Worked example

Example 2: A nuclear generating unit

A nuclear reactor produces thermal energy at a rate of 2700 MW. Its generator delivers 880 MW of electrical power. (a) Find the efficiency. (b) At what rate is thermal energy released to the cooling water? (c) How much electrical energy is produced in one day, in MWh and in joules?

(a) Efficiency = 880 ÷ 2700 × 100% ≈ 33%.
(b) Waste = 2700 − 880 = 1820 MW, released through the condenser to lake water.
(c) ΔE = PΔt = 880 MW × 24 h = 21 120 MWh ≈ 2.1 × 10⁴ MWh.
In joules: 880 × 10⁶ W × 86 400 s ≈ 7.6 × 10¹³ J.

About 33% efficient, releasing about 1.8 × 10³ MW of thermal energy to the cooling water and producing 2.1 × 10⁴ MWh (7.6 × 10¹³ J) per day.

Worked example

Example 3: Wind and solar

(a) In 1 s, 12 000 kg of air moving at 10 m/s passes through a wind turbine's blades. The turbine delivers 240 kW. What is its efficiency? (b) A 1.7 m² solar panel receives sunlight at 1000 W/m² and delivers 340 W. What is its efficiency?

(a) Ek of the air each second: ½(12 000)(10)² = 600 000 J, so the input power is 600 kW. Efficiency = 240 ÷ 600 = 40%.
(b) Input power = 1.7 m² × 1000 W/m² = 1700 W. Efficiency = 340 ÷ 1700 = 20%.

The wind turbine is 40% efficient and the solar panel is 20% efficient.

Analysing a thermal generating station

A thermal station is a long energy chain, and each step loses some energy, but the biggest loss is unavoidable for a heat engine: after the steam has pushed the turbine, it must be cooled and condensed back into water so it can be pumped back to the boiler. The condenser transfers a huge amount of thermal energy to a lake, river or cooling tower. Ontario's nuclear stations are built on the shores of the Great Lakes and use lake water for cooling.

The energy chain in a thermal generating station. For a nuclear station, the input is nuclear energy in the fuel instead of chemical energy. The condenser must release a large share of the input as waste thermal energy.

Getting more from the fuel

Engineers improve thermal stations by making use of thermal energy that would otherwise be wasted:

Combined cycle. A gas turbine burns natural gas and spins a generator. Its exhaust is still very hot, so instead of releasing it, the station uses it to boil water and run a second (steam) turbine. Two turbines from one fuel raise the efficiency from roughly 35% to roughly 55%.
Cogeneration (combined heat and power). The station's waste thermal energy is piped to nearby buildings, greenhouses or factories for heating. The electrical efficiency stays the same, but a much larger share of the fuel's energy is put to use. Some university campuses and hospitals in Canada run their own cogeneration plants.

Higher efficiency means less fuel for the same electrical energy, which means lower fuel costs and lower carbon dioxide emissions.

Worked example

Example 4: Why efficiency matters for emissions

Two natural gas stations each must deliver 1000 MWh of electrical energy. Station A is a simple-cycle station (35% efficient); Station B is combined-cycle (55% efficient). How much fuel energy does each need? By what percentage does B reduce fuel use (and so CO₂ emissions)?

Input = output ÷ efficiency.
A: 1000 ÷ 0.35 ≈ 2857 MWh of fuel energy.
B: 1000 ÷ 0.55 ≈ 1818 MWh of fuel energy.
Reduction = (2857 − 1818) ÷ 2857 × 100% ≈ 36%.

A needs about 2.9 × 10³ MWh and B about 1.8 × 10³ MWh of fuel energy. B burns about 36% less gas, and so releases about 36% less CO₂, for the same electrical energy.

Efficiency is not the whole story

A 20% efficient solar panel is not "worse" than a 55% efficient gas station in every way. Sunlight and wind cost nothing and release no CO₂ while generating, but they are intermittent. Gas can be turned up when demand peaks, but burns a fossil fuel. Hydro is very efficient but needs suitable rivers and floods land. When you assess a technology, weigh efficiency together with fuel cost, emissions, reliability, land and water use, and the effects on nearby communities, including First Nations whose lands and waters may be affected.

Just for fun

Why can't a wind turbine catch all of the wind's kinetic energy? Because the air would have to stop completely behind it, and then no new wind could get through. Even turbines have to let some of their lunch go by.

Hands-on activity

Station analyst

You need: a notebook, a calculator and internet access with a grown-up's help.

Choose one thermal generating station in Ontario or elsewhere in Canada (natural gas or nuclear). Find, from a reliable source such as the operator's website or a government site, its electrical output (MW) and the type of station.
Draw its energy chain, like the diagram in this lesson. Label input energy, useful output and the main waste.
Using a typical efficiency for its type (from this lesson), estimate its rate of fuel or thermal energy input, and its rate of waste thermal energy.
Find one way this station (or stations like it) reduces waste or uses waste thermal energy, or could do so.
Write a short assessment (about 150 words): one environmental impact, one social or economic impact, and whether you think efficiency improvements are worth the cost. Cite your sources.

What to look for: sample: a 500 MW combined-cycle gas station at 55% needs about 500 ÷ 0.55 ≈ 910 MW of fuel input and releases about 410 MW of waste thermal energy. A strong assessment uses numbers, names a specific impact (for example CO₂ emissions, warm water returned to a lake, local jobs, reliable supply on cold winter evenings) and considers more than one point of view.

Careers in energy

Generating stations need many skilled people. Power engineers operate boilers, turbines and related equipment; in Ontario they are certified by class, and many train through college power engineering programs. Electrical, mechanical and nuclear engineers design and improve stations. Technicians maintain wind turbines, hydro stations and transmission lines, and environmental scientists monitor effects on air, water and wildlife. Physics, math and chemistry in high school are the starting point for all of these paths.

Your turn

Name the input form of energy for (a) a hydroelectric station, (b) a natural gas station, (c) a wind turbine, (d) a solar panel.

A station takes in 500 MW of fuel energy and produces 175 MW of electrical power. Find its efficiency and its waste power.

Each second, 1.0 × 10⁵ kg of water falls 80 m through a hydroelectric station that is 88% efficient. Find the electrical power output.

A 2.0 m² solar panel in bright sunlight (1000 W/m²) is 18% efficient. Find its power output.

Why must thermal and nuclear stations release so much thermal energy to the surroundings?

Explain how a combined-cycle station is more efficient than a simple-cycle one.

More practice: warm-up

Which method in this lesson typically has the highest efficiency?

Write the formula for the efficiency of a generating station.

What does a condenser do in a thermal station?

What is cogeneration?

Name one career in electricity generation.

More practice: on your own

A gas station delivers 400 MW at 50% efficiency. How much thermal energy does it release to the surroundings in one hour, in joules?

A wind turbine is 40% efficient when 15 000 kg of air passes through it each second at 12 m/s. Find its electrical power output.

A nuclear unit must deliver 800 MW at 32% efficiency. Find the reactor's thermal power and the waste power.

A town is choosing between a 35% efficient simple-cycle gas station and a 55% efficient combined-cycle one that costs more to build. Give one argument for each choice.

Explain why comparing only efficiencies could be misleading when choosing between solar panels and a gas station.

Challenge

A cogeneration plant takes in 100 MW of fuel energy. It delivers 35 MW of electrical power and supplies 40 MW of thermal energy to heat buildings. (a) What is its electrical efficiency? (b) What percentage of the fuel's energy is put to use? (c) Where does the rest go?

A pumped-storage station pumps water up 100 m at night and lets it flow back through turbines by day. The pumps are 90% efficient and the turbines are 88% efficient. (a) What is the overall efficiency? (b) Why might it still be worth building?

A coal station that is 35% efficient is replaced by a combined-cycle gas station that is 55% efficient. Burning coal releases about 0.34 t of CO₂ per MWh of fuel energy and gas about 0.20 t per MWh of fuel energy (approximate). Compare the CO₂ released per MWh of electrical energy.

Check your understanding

Quiz

Which typically has the highest efficiency for generating electrical energy?

A station takes in 900 MW and produces 300 MW of electrical power. Its efficiency is about:

The main reason nuclear stations and simple-cycle natural gas stations have efficiencies well under 50% is that:

What is the input form of energy for a wind turbine?

A combined-cycle gas station is more efficient than a simple-cycle station because it:

Station B (55% efficient) and station A (35% efficient) produce the same electrical energy from the same fuel. Compared with A, B:

Cogeneration improves the overall use of fuel by:

For parents and teachers

Big idea: This lesson covers D2.7 (comparing input energy, useful output and per cent efficiency of generation methods), D1.1 (analysing a thermal technology, a generating station, and how its efficiency can be improved) and D1.2 (assessing impacts of thermal generation). Careers (A2.1) are included. Detailed nuclear physics (fission, isotopes, radiation) is in the Thermal and Nuclear Energy unit.

How to help: Look up where your electricity comes from on a cold winter evening versus a sunny summer afternoon (Ontario's grid operator publishes this). Discuss trade-offs: efficiency, cost, emissions, reliability.

Common difficulties:

Thinking low efficiency means a method is useless; inputs like sunlight and wind are free.
Mixing MW (power) and MWh (energy).
Forgetting that per cent efficiency must use the same units on top and bottom.

Note on numbers: efficiencies in this lesson are approximate, typical values. Real stations vary, and teens should use sources such as operators' websites or government data for any specific station.