4.4 Distinguish cogeneration from electricity-only generation | University of Alberta MEC E 340: Applied Thermodynamics

University of Alberta MEC E 340: Applied Thermodynamics

Combined Power and Cogeneration

MEC E 340 Applied Thermodynamics — study topic 4.4

Start with a steady-flow control volume around the plant being classified. A working fluid may pass through a power cycle inside it, but cycle details are not needed to make this distinction. At the plant boundary, identify the energy input and the products delivered for use. Electricity-only generation counts electricity as the useful product in this comparison. Cogeneration, also called combined heat and power, delivers both electricity and useful heat from the same energy supply. The distinction is what the plant delivers for use, not simply whether heat leaves it. Numerical values in this lesson are supplied assumptions, not typical plant data.

What you will learn

Distinguish electricity-only generation from cogeneration by identifying the useful products delivered.
Choose a plant control-volume boundary and identify its energy input, electricity output, and useful heat output.
Calculate electrical efficiency and total useful-energy efficiency from supplied energy rates.
Explain why heat rejected to the surroundings is not automatically a useful product.

1. Define the boundary and identify the products

Choose a control volume around the plant being classified. Treat the supplied energy as an input rate, then identify the energy rates crossing outward. In this lesson, the possible useful products are electricity and heat delivered to a stated user. The boundary and intended use determine what counts.

A heat stream is not a useful heat product just because it exits the plant. Heat rejected to the surroundings without an identified user is not credited as useful heat in this lesson’s accounting. Heat delivered to a building for heating or to a process that uses it is a useful output for that stated purpose.

For steady operation with no net energy accumulation, the first-law balance accounts for the input rate through the rates leaving the control volume. Some outgoing energy may be a useful product and some may not. The balance accounts for energy; the product definitions determine which outputs are counted in an efficiency measure.

The working fluid, plant cycle, and property values need not be specified when the problem supplies the input and output rates directly. Do not infer a particular fuel, cycle, temperature, or performance value from the words electricity-only or cogeneration.

\dot E_{in}=\dot W_{electric}+\dot Q_{useful}+\dot E_{other,out}

Electricity-only generation counts electricity as the useful product being considered.
Cogeneration delivers both electricity and heat for an identified use.
Rejected heat without a stated use is not counted as useful heat in this comparison.

2. Keep the efficiency measures distinct

Electrical efficiency measures the fraction of the supplied energy rate delivered as electricity. Use it when asking how effectively the input produces electricity, whether the plant is electricity-only or cogeneration. It does not credit useful heat.

Total useful-energy efficiency, as defined for this lesson, counts electricity and useful heat in its numerator. State which products are included whenever reporting this value. It is an energy ratio: it does not assign different values to different forms of energy and does not, by itself, measure how suitable the delivered heat is.

Use the same plant boundary and a clearly stated input basis when comparing plants. Do not compare one plant’s electrical efficiency directly with another plant’s total useful-energy efficiency as if they answered the same question. The measures differ because their numerators differ.

When input and output rates are supplied, divide rates in consistent units. For example, megawatts divided by megawatts gives a dimensionless ratio. Convert that ratio to a percentage only after calculating it. No property-table lookup is required unless a problem separately asks for information that depends on working-fluid properties.

Electrical efficiency is defined as

\eta_{\mathrm{electric}}=\frac{\dot W_{\mathrm{electric}}}{\dot E_{\mathrm{in}}}

. Total useful-energy efficiency is defined as

\eta_{\mathrm{useful}}=\frac{\dot W_{\mathrm{electric}}+\dot Q_{\mathrm{useful}}}{\dot E_{\mathrm{in}}}

.

Electrical efficiency credits electricity alone.
Total useful-energy efficiency credits electricity plus heat delivered for an identified use.
Name the measure and state which outputs count.

3. Interpret the comparison and check the accounting

A sound comparison follows a short sequence: state the control-volume boundary, identify the energy input, list electricity and useful heat delivered, then calculate the measure requested. For electrical efficiency, use electricity alone. For the total useful-energy measure used here, include the stated useful heat as well.

The first-law balance checks energy accounting: the input must be accounted for by energy leaving or accumulating. The simplified efficiency measures in this lesson count only the named useful products. Therefore, the total useful-energy efficiency need not account for every energy stream leaving the plant in its numerator.

The second law reminds us that energy in different forms may not have the same practical usefulness. The total useful-energy ratio does not capture that difference. A higher value does not prove that a plant is the best choice for every purpose; the heat must be useful to an actual user, and the purpose of the comparison must be clear.

Classification is based on the stated products, not on an assumed cycle or a label alone. If a problem does not state whether heat is delivered for a use, do not silently count it as useful. State what information is missing or classify only from the products that are identified.

Keep the boundary, product definitions, and efficiency measure consistent.
Do not infer cycle details or performance from a plant’s label.
A total useful-energy ratio does not establish the value of the products or the existence of a heat user.

Worked example

Classify two generation arrangements

Plant A delivers electricity to a grid and rejects its remaining energy to the surroundings. Plant B delivers electricity and supplies hot water to a nearby building for heating. Classify each plant from the stated products.

Set the boundary
Take each plant as the control volume and identify what it delivers across its boundary. The problem states the products directly, so no cycle details or property data are needed.
Classify from useful outputs
Plant A has electricity as its stated useful product. Its remaining energy is rejected, not supplied for an identified use. Plant B supplies hot water for building heating as well as electricity, so it delivers both useful products.

Answer: Plant A is electricity-only generation. Plant B is cogeneration because it delivers electricity and useful heat.

Check: The classification depends on whether heat is delivered for a stated use, not simply on whether heat crosses the plant boundary.

Worked example

Calculate two measures for a cogeneration plant

A steady plant receives energy at

1.00\ \mathrm{MW}

. It delivers

0.32\ \mathrm{MW}

of electricity and

0.48\ \mathrm{MW}

of heat to a process that uses it. Calculate the electrical efficiency and total useful-energy efficiency.

Identify rates and assumptions
Use the plant as a steady-flow control volume. The supplied input rate is $1.00\ \mathrm{MW}$ . Electricity is $0.32\ \mathrm{MW}$ , and the heat is useful because the process uses it. All rates are given, so no property-table data are needed.
Calculate electrical efficiency
Electrical efficiency includes the electricity output alone. Since both quantities are energy rates in megawatts, their ratio is dimensionless.
$\eta_{electric}=\frac{0.32\ \mathrm{MW}}{1.00\ \mathrm{MW}}=0.32=32\%$
Calculate total useful-energy efficiency
This measure includes electricity and the heat delivered to the process. Add those useful output rates before dividing by the same input rate.
$\eta_{useful}=\frac{0.32\ \mathrm{MW}+0.48\ \mathrm{MW}}{1.00\ \mathrm{MW}}=0.80=80\%$

Answer: The electrical efficiency is 32%. The total useful-energy efficiency is 80%.

Check: The counted useful outputs total

0.80\ \mathrm{MW}

, less than the

1.00\ \mathrm{MW}

input. The remaining

0.20\ \mathrm{MW}

is not included among the stated useful products.

Worked example

Compare plants using matching measures

Two plants each receive energy at

2.00\ \mathrm{MW}

. Plant X delivers

0.70\ \mathrm{MW}

of electricity and no useful heat. Plant Y delivers

0.60\ \mathrm{MW}

of electricity and

0.90\ \mathrm{MW}

of useful heat. Calculate both efficiencies for each plant. Identify which plant has the greater electrical efficiency and which has the greater total useful-energy efficiency.

Keep the measures distinct
Both input rates are $2.00\ \mathrm{MW}$ . For electrical efficiency, divide electricity alone by the input. For total useful-energy efficiency, include stated useful heat as well.
Evaluate Plant X
Plant X has no useful heat output in the supplied data, so its counted useful output is electricity alone. The two efficiency measures are therefore equal for this plant.
$\eta_{electric,X}=\frac{0.70}{2.00}=0.35,\qquad \eta_{useful,X}=\frac{0.70+0}{2.00}=0.35$
Evaluate Plant Y
Plant Y delivers useful heat, so its total useful-energy numerator includes both stated output rates. Its electrical efficiency still uses electricity alone.
$\eta_{electric,Y}=\frac{0.60}{2.00}=0.30,\qquad \eta_{useful,Y}=\frac{0.60+0.90}{2.00}=0.75$

Answer: Plant X has the greater electrical efficiency: 35% versus 30%. Plant Y has the greater total useful-energy efficiency: 75% versus 35%. From the stated products, Plant Y is cogeneration and Plant X is electricity-only generation.

Check: Each plant’s counted useful output is below its

2.00\ \mathrm{MW}

input. Plant Y’s total useful-energy efficiency exceeds its electrical efficiency because useful heat is included in the former.

Common mistakes and how to avoid them

Calling any plant that rejects heat a cogeneration plant.

Correction: Cogeneration supplies useful heat alongside electricity. Heat rejected without an identified user is not a useful heat delivery in this comparison.

Including useful heat in electrical efficiency.

Correction: Electrical efficiency counts electricity alone. Include useful heat only in a measure that explicitly counts total useful energy.

Concluding that the plant with the greater total useful-energy efficiency must be the better choice.

Correction: That ratio does not measure the value of the products or establish that a heat user exists. State the purpose and comparison basis.

Lesson summary

Electricity-only generation counts electricity as its useful product; cogeneration delivers electricity and useful heat.
Count heat as useful only when it is delivered for an identified use.
Electrical efficiency and total useful-energy efficiency answer different questions.
Use a consistent control-volume boundary, supplied rates, and clearly stated assumptions.

Check your understanding

Question 1

A plant delivers electricity and rejects warm water that has no stated user. Which classification is supported?

Cogeneration, because warm water leaves the plant
Electricity-only generation, because no useful heat delivery is stated
Cogeneration, because every heat output is useful
Neither classification can use the stated products

Show answer and explanation

Electricity-only generation, because no useful heat delivery is stated

Rejected heat without an identified use is not counted as a useful heat product. On the information given, electricity is the only stated useful product.

Question 2

A plant receives

1.50\ \mathrm{MW}

and delivers

0.45\ \mathrm{MW}

of electricity plus

0.60\ \mathrm{MW}

of useful heat. What is its total useful-energy efficiency?

30%
40%
70%
100%

Show answer and explanation

70%

The useful output is

0.45+0.60=1.05\ \mathrm{MW}

. Dividing by

1.50\ \mathrm{MW}

gives

0.70

, or 70%.

Question 3

A cogeneration plant has an electrical efficiency of 28% and a total useful-energy efficiency of 72%. What does the difference indicate?

The electrical efficiency is 72%
Useful heat is included in the total useful-energy measure but not in electrical efficiency
The plant violates energy conservation because the efficiencies differ
The plant must have higher electrical efficiency than an electricity-only plant

Show answer and explanation

Useful heat is included in the total useful-energy measure but not in electrical efficiency

Electrical efficiency counts electricity alone, while total useful-energy efficiency also counts useful heat. The difference is consistent with an additional useful heat output.

Key terms

Control volume: A selected region in space across whose boundary mass and energy may flow.
Cogeneration: Producing electricity and useful heat from the same energy supply.
Electricity-only generation: Generation in which electricity is the useful product counted for the comparison; rejected heat is not counted as useful heat delivery.
Total useful-energy efficiency: For the stated accounting, the sum of electricity and useful heat output rates divided by the energy input rate.

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Published by DoAssignment. This reviewed lesson follows University of Alberta MEC E 340: Applied Thermodynamics, study topic 4.4. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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4.4 · Distinguish cogeneration from electricity-only generation

University of Alberta MEC E 340: Applied Thermodynamics

MEC E 340 Applied Thermodynamics — study topic 4.4

What you will learn

1. Define the boundary and identify the products

2. Keep the efficiency measures distinct

3. Interpret the comparison and check the accounting

Classify two generation arrangements

Calculate two measures for a cogeneration plant

Compare plants using matching measures

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through MEC E 340

About this lesson and its review