Where should a cogeneration study’s boundary be drawn?

Follow one study’s boundary through six parts, then move the line yourself around a toy steam plant and its load

Case file CF5 of Energy Systems, Step by Step. Where should an hourly cogeneration study draw its boundary: which plant streams, which loads and which alternatives must it include to price the steam sent to cooling?
  • Analyst · L2
  • Case file
  • 10 min
  • After lesson 7

1 · The puzzle

Reactor steam can either drive the turbine or feed an absorption chiller that makes chilled water.

Steam sent to the absorption chiller is steam the low-pressure turbine does not convert.

So is the cooling free?

2 · The question in one sentence

Where should an hourly cogeneration study draw its boundary: which plant streams, which loads and which alternatives must it include to price the steam sent to cooling?

The case's method question.

3 · Scale and boundary

Inside
  • one plant with high- and low-pressure turbines,
  • one large load that needs power and cooling,
  • an absorption chiller and an electric chiller,
  • and power bought from and sold to the grid,

every hour of a year (8,760 hours).

Left out
  • demand charges and ancillary-service revenues;
  • reliability compared on a common basis across options;
  • marginal emission factors, because emissions are counted at hourly averages;
  • other load profiles and sites;
  • the choice of plant size, because the plant is one fixed unit.

The plant produces much more power than the load uses, so it is partly a merchant generator that sells power to the grid.

4 · Decisions, goal and rules, in words

Decisions

in every hour,

  • the reactor's output,
  • the steam extracted at the turbine crossover,
  • how the absorption and electric chillers share the cooling,
  • and the power bought from or sold to the grid.
Goal

the lowest annualized cost of meeting the load's power and cooling, counting what the power sold to the grid earns.

Rules
  • the load's power and cooling are met in every hour;
  • every unit of steam sent to the chiller lowers turbine output;
  • the absorption chiller has no steam during refueling.

5 · Data and method

  • The value of steam cooling depends on hourly physics: wet-bulb derating, crystallization risk, part-load chiller efficiency and the turbine work lost to extraction.
  • A mixed-integer linear program co-optimizes, for every hour of a year, reactor output, steam extraction at the turbine crossover, absorption and electric cooling, and grid exchange.
  • The plant, with and without steam cooling, is compared with grid supply and an on-site gas combined cycle, all evaluated on the same hourly basis.
DetailHow the hourly physics is modeled
  • Absorption performance follows hourly wet-bulb temperature with a crystallization cutoff;
  • the electric chiller's part-load curve uses SOS2 constraints;
  • extraction carries a Willans-line penalty from a steam-table heat balance.
DetailTwo design choices
  • Steam is extracted at the high- to low-pressure turbine crossover rather than from a parallel tap on main steam:
    • crossover steam has already expanded through the high-pressure turbine, so it costs about half as much turbine work, and a sweep of the penalty tests this assumption.
  • A full-size electric chiller stays beside the absorption chiller, and the optimizer chooses between the chillers hour by hour.
DetailScenario runs and how results are reported
  • Scenario runs vary the market year (2022 to 2024), the carbon price, the cost of capital, cooling efficiency, battery storage and the size of the load.
  • The load's size is swept with the plant fixed, and the grid connection is enlarged only for loads above the baseline size.
  • Margins measured against grid cost are distorted across market years, because the grid cost itself falls in low-price years, so cross-year results are also reported in absolute annualized cost.

6 · What came out, and where it holds

Pricing diverted steam matters: treating it as a free by-product can by itself decide the sign of a cogeneration result.

Approved excerpt of: Li et al. (2026), accepted paper, Energy Conversion and Management; DOI pending.

Holds when: steam sent to cooling would otherwise turn the low-pressure turbine; the study used one load profile, ERCOT's hourly prices for 2022 to 2024, and one fixed plant.

Leaves out: demand charges, ancillary-service revenues, and reliability on a common basis across options.

The study in time

  1. 2026 · Paper accepted. An hourly model prices the steam sent to cooling by the turbine work it gives up, and compares the plant, with and without steam cooling, with grid supply and an on-site gas combined cycle. Source: Li et al. (2026), accepted paper, Energy Conversion and Management; DOI pending

The toy below is the course's own, with illustrative numbers you set; it holds none of the study's inputs or results.

Move the boundary yourself, then where the result holds

One hour at a steam plant beside a large load (illustrative)

Illustrative round numbers you set: a generic steam plant and one load that needs power and cooling, not the study's inputs or results. Average power during one hour, in MW; auxiliary electricity for pumps and fans is left out.

  • Electric chiller: 4.0 MW of electricity for 20 MW of cooling.
  • Steam cooling: 25.0 MW of steam heat, which costs the turbine 5.0 MW of electricity.
  • The grid: in the reference the site sends 56.0 MW to the grid; with steam cooling the site sends 55.0 MW to the grid.
Switching the cooling from the electric chiller to steam: the change in average power during the hour, as each view counts it. + means less electricity used or more sent to the grid; − means the opposite. An ordinary hour, at the defaults.
View Change What it says
Plant only, steam priced −5.0 MW steam cooling looks worse
Plant and load, steam priced −1.0 MW steam cooling looks worse
Plant only, turbine loss ignored (incomplete) 0.0 MW no difference shows
Plant and load, turbine loss ignored (incomplete) +4.0 MW steam cooling looks better
The toy's assumptions
  • Illustrative: the turbine makes 100 MW of electricity from all its steam; the load needs 40 MW of power.
  • The reference is the same plant and load, using electric cooling; the grid takes what the site does not use, or supplies what it lacks.
  • A hot, humid hour: the absorption chiller makes 25% less cooling per MW of steam. The toy changes its efficiency only; it has no capacity limit.
  • A planned outage: no steam, so the turbine makes nothing and the absorption chiller cannot run.

Where the result holds

It holds when
  • steam sent to cooling is steam the low-pressure turbine does not convert, so it costs the turbine work it gives up;
  • one load profile;
  • ERCOT's hourly prices for the market years 2022 to 2024;
  • hourly average, not marginal, emission factors;
  • the plant is one fixed unit;
  • steam is taken at the turbine crossover, and a sweep of the penalty tests that choice.
It leaves out
  • demand charges and ancillary-service revenues;
  • reliability on a common basis across options;
  • other load profiles and sites.

Approved excerpt of: Li et al. (2026), accepted paper, Energy Conversion and Management; DOI pending.

Go deeper · ModelerThe toy's four views, as arithmetic

The toy’s symbols, all average power over one hour, in MW:

  • \(C\): the cooling the load needs.
  • \(\mathit{COP}_e\): the electric chiller’s MW of cooling per MW of electricity; it uses \(C / \mathit{COP}_e\) MW of electricity.
  • \(\mathit{COP}_a\): the absorption chiller’s MW of cooling per MW of steam heat; it takes \(C / \mathit{COP}_a\) MW of steam heat.
  • \(w\): the turbine electricity lost per MW of steam heat taken; the steam costs the turbine \(w\,C / \mathit{COP}_a\) MW.
  • Left out: auxiliary electricity, such as the pumps and fans that both chillers need.
View Change from switching to steam cooling
Plant only, steam priced \(-\,w\,C / \mathit{COP}_a\)
Plant and load, steam priced \(C / \mathit{COP}_e - w\,C / \mathit{COP}_a\)
Plant only, turbine loss ignored \(0\)
Plant and load, turbine loss ignored \(+\,C / \mathit{COP}_e\)
  • Both views that ignore the turbine loss are incomplete; only the plant-and-load views include the electric chiller’s saving.
  • Only the plant-and-load view with the steam priced holds both sides of the switch.
  • A model that runs every hour, as in M11, adds what the toy leaves out: the hours, prices, a chiller that derates in hot weather, and the choice to switch at all.

Check yourself, then try it

Myth or fact? “Steam that would otherwise go to the turbine is free cooling.”

  • Myth
  • Fact
Answer

Myth. In the toy's defaults, 20 MW of cooling takes 25.0 MW of steam heat, which costs the turbine 5.0 MW of electricity: more than the electric chiller's 4.0 MW.

Myth or fact? “Drawing the line around the plant alone can make steam cooling look like a pure loss.”

  • Myth
  • Fact
Answer

Fact. The plant sees the turbine work it gives up (−5.0 MW in the toy) but not the electric chiller's 4.0 MW saved, which sits outside its line.

Try it yourself

About 5 minutes, in the toy above.

  • Set the turbine work lost per MW of steam heat taken to 0.14 MW, then to 0.30 MW. Which views change their verdict, and which never can?
  • Switch to a hot, humid hour, then to a planned outage. What happens to the steam, and to the electric chiller?
  • Draw the line around the plant only, then around the plant and load. Which costs and savings cross the line?
  • Now ignore the turbine loss. Which view changes sign, and what did it leave out?
Worked answers, at the toy's defaults
  • At 0.14 MW of turbine work per MW of steam heat: plant and load, steam priced, +0.5 MW (steam cooling looks better); plant only, steam priced, −3.5 MW (steam cooling looks worse).
  • At 0.30 MW: plant and load, steam priced, −3.5 MW; plant only, −7.5 MW; both worse. The two views that ignore the turbine loss stay at 0.0 MW and +4.0 MW at any setting of the turbine work: they never change.
  • A hot, humid hour: 0.60 MW of cooling per MW of steam, so 20 MW of cooling takes 33.3 MW of steam heat and 6.7 MW of turbine work; plant and load, steam priced, −2.7 MW.
  • A planned outage: no steam, so the electric chiller carries all 20 MW of cooling with 4.0 MW of electricity; there is no switch to make.
  • Plant only: the 5.0 MW of turbine work is inside the line and the electric chiller's 4.0 MW saving is outside, so −5.0 MW. Plant and load: both are inside, so −1.0 MW.
  • Turbine loss ignored: plant and load goes from −1.0 MW to +4.0 MW, so the sign flips, because the 5.0 MW of turbine work is no longer counted; plant only goes from −5.0 MW to 0.0 MW.

Sources and what’s next

Keep going

Back to the course map

Sources and further reading

  • Li et al. (2026). Accepted paper on a techno-economic analysis of reactor cogeneration for power and cooling loads. Energy Conversion and Management (2026), accepted; DOI pending.
  • Earlier lessons: lesson 7 (what a cost counts), F4 (how a steam plant works), A16 (where a by-product is worth using).

Spotted an error, or stuck? Write to hlli@ksu.edu. Corrections are made in place and dated here.

Text licensed CC BY 4.0, code MIT: teachers and students may reuse and adapt it, with credit to Honglin Li.