What engineering lies beneath the system?

Tap a component to meet the discipline that designs it, the questions it answers and the numbers system models borrow from it

X1 of Energy Systems, Step by Step: eight components, from an inverter and a relay to a turbine blade, a combustor, a reactor core, an electrolyzer stack, a battery cell and a control room; the discipline behind each, and the ratings, efficiencies, ramp limits, outlet temperatures and failure rates a system model borrows.
  • Foundations · L1
  • 12 min
  • After F4

Eight components, the discipline behind each, and what system models borrow

Inverter · Power electronics
Asks
  • How does it turn the direct current of solar panels and batteries into alternating current?
  • How fast can it respond, and does it hold on through a voltage dip?
Models borrow
Its AC rating, its conversion losses, how fast it can change output and, in A17, whether it forms or follows the grid.
In this course
  • DC to AC (what it does): Solar cells make direct current; an inverter turns it into the grid's alternating current.
Read next
Erickson and Maksimović, Fundamentals of Power Electronics (Springer)
Protective relay · Power system protection
Asks
  • Which breaker should open, and how fast, when a line has a fault?
  • How are its settings chosen so that healthy lines stay in service?
Models borrow
Not the relay settings: equipment ratings, such as a line's thermal rating, and how often equipment is forced out of service.
In this course
  • Thermal rating (a line's limit): The most current a line or transformer can carry before it overheats; models keep flows under it. A relay is different: it detects a fault and tells a breaker to open.
Read next
Horowitz and Phadke, Power System Relaying (Wiley)
Turbine blade · Aerodynamics and structural engineering
Asks
  • How much of the wind's power can the rotor catch?
  • Will the blade survive repeated gusts over its intended life?
Models borrow
A power curve with its rated power, and how often the turbines are available.
In this course
  • 59.3% (the Betz limit): The most of the wind's power any rotor can take, the Betz limit (physics).
  • 0.52 (best measured power coefficient): The best measured power coefficient of DOE's 1.5 MW test turbine: the share of the wind's power it turned into electricity.
Read next
Burton, Jenkins, Sharpe and Bossanyi, Wind Energy Handbook (Wiley)
Gas-turbine combustor · Combustion and thermodynamics
Asks
  • How hot can the flame burn before metal or emission limits are reached?
  • How low can the turbine run and still burn steadily?
Models borrow
A heat rate, a ramp limit, a minimum load and a start time.
In this course
  • 7,535 Btu/kWh (full-load tested heat rate, 2025): EIA's 2025 average full-load tested heat rate for U.S. natural-gas combined-cycle plants: 3,412 ÷ 7,535 = 45.3% of the fuel's energy becomes electricity at full load.
  • 40 MW per hour (ramp limit, Prairie Town): The ramp limit of Prairie Town's combined-cycle plant (illustrative).
Read next
Turns, An Introduction to Combustion (McGraw-Hill)
Reactor core · Reactor physics, thermal hydraulics and nuclear materials
Asks
  • How does the core hold its chain reaction steady?
  • How is heat carried away so that the fuel and the metal tubes that hold it stay within their limits?
Models borrow
A thermal and an electric rating, an outlet temperature and a heat rate.
In this course
  • about 300 °C (outlet temperature): The outlet temperature of large water-cooled reactors.
  • 10,443 Btu/kWh (fleet heat rate, 2025): The U.S. nuclear fleet's 2025 heat rate: 3,412 ÷ 10,443 = 32.7% of the heat becomes electricity.
Read next
Lamarsh and Baratta, Introduction to Nuclear Engineering (Pearson)
Electrolyzer stack · Electrochemistry, catalysis and materials
Asks
  • How much electricity does a kilogram of hydrogen take?
  • How fast do the cells wear, and how low can the stack run?
Models borrow
Electricity per kilogram of hydrogen for the whole system (stack, power supply, pumps and dryers), a minimum load and a stack life.
In this course
  • 57 kWh/kg (whole-system electricity use): A16 assumes about 57 kWh per kilogram of hydrogen for the complete PEM electrolyzer system; stack design helps set that system value.
  • PEM 5%, alkaline 15% (minimum loads): The lowest steady load of PEM and of alkaline electrolyzers, as a share of their size.
Read next
U.S. Department of Energy, Hydrogen and Fuel Cell Technologies Office, Hydrogen Production: Electrolysis (energy.gov)
Battery cell · Electrochemistry and materials science
Asks
  • How much energy does a cell hold, and how fast can it charge?
  • How do heat and cycling age it?
Models borrow
A round-trip efficiency for the whole battery system, a duration (energy over power) and a life.
In this course
  • 85% (round trip of the battery system): The course assumes 85% of the electricity sent into its utility-scale battery system comes back out: charging and discharging losses together, for the whole system, not one cell.
  • 15 years (life): The life the course gives that battery system.
Read next
Linden's Handbook of Batteries (McGraw-Hill)
Control room · Control engineering, operations and cybersecurity
Asks
  • How do operators see the grid every few seconds and send each plant its target output?
  • How are those systems kept safe from cyberattack?
Models borrow
Operating rules: how often dispatch runs, how much reserve is held and which limits are watched.
In this course
  • CIP (cybersecurity standards): The mandatory Critical Infrastructure Protection (CIP) standards of the North American Electric Reliability Corporation (NERC) cover the bulk power system's cyber systems, in general not those on the distribution grid.
Read next
Wood, Wollenberg and Sheblé, Power Generation, Operation, and Control (Wiley)

The kinds of number a model borrows

  • Rating: How much it can make, carry or store: MW, MWh, a line's limit.
  • Efficiency: How much of what goes in comes out: a heat rate, a round trip, kWh per kilogram.
  • Ramp limit: How fast its output can change, in MW per hour.
  • Minimum load: The lowest output it can hold steadily, as a share of its size; below that it must stop.
  • Outlet temperature: How hot the heat it gives is, which sets the uses that heat can serve.
  • Reliability and life: Three separate numbers: how often it fails, how long each outage lasts, and how many years it serves before replacement.
  • Operating rule: How the people and software running the grid decide: time steps, reserves, limits.

With JavaScript on, you tap each component, sort what models borrow, and light the components by the kind of number they supply.

Read from the lessons that teach them. Every number here comes from F4, F5, A16, lesson 13 or Prairie Town (fictional, illustrative), with the source each lesson cites.

Need a refresher? F4 on how power plants turn heat, water, wind and sunlight into electricity.

What you just did, as diagrams

Disciplines
Power electronics, protection, aerodynamics, combustion, reactor physics, electrochemistry and control each design a part of the system.
What crosses over
A system model borrows ratings, efficiencies, ramp limits, minimum loads, outlet temperatures, and reliability and life, plus the control room's operating rules.
What stays
Designs, materials and calculations stay with each discipline; the model sees them only through the numbers they lead to.
Cybersecurity
NERC's mandatory standards protect the bulk power system's cyber systems; distribution-grid devices are in general outside them.

Where we stop

This side topic stops at the nameplate

Devices enter the course only as numbers: ratings, efficiencies, ramp limits and minimum loads, outlet temperatures, failure rates and lifetimes. Designing them belongs to each discipline.

This side topic covers

  • What each discipline designs and which questions it answers.
  • Which numbers a system model borrows from it, and where this course uses them.
  • Where cybersecurity sits: standards for the bulk power system's control systems.

Left to specialists

  • Design methods, physics and calculations for any device.
  • Testing, certification and equipment standards.
  • Running or securing a control room.

Read next, three rungs

  1. Start here. A short tour of turbines, generators and inverters, and how each makes electricity. EIA, Electricity explained: How electricity is generated, read 3 November 2026
  2. Go further. Pick one discipline and read its textbook: each component card above names one, in any recent edition. The reading line on each component card, list of 7 November 2026
  3. Go deep. For control systems: how the mandatory cybersecurity standards reach the bulk power system, and where distributed resources stand. NERC, Cyber Security for Distributed Energy Resources and DER Aggregators (white paper), December 2022
Go deeper · ModelerWhere each borrowed number enters a model
  • Efficiency. A heat rate times a fuel price becomes a running cost per MWh in a dispatch model (M1).
  • Ramp limit. It becomes a rule linking one hour's output to the next (M2).
  • Minimum load. It becomes a lower bound on output while a unit runs, paired with an on or off choice (M2).
  • Round trip. It becomes the loss in a storage balance, hour by hour (M4).
  • Reliability. A forced outage rate, the share of time a unit is unexpectedly out, becomes the chance it is unavailable in each hour an adequacy simulation draws (A5).

Check yourself

Two quick checks.

Myth or fact? “To plan a grid, a modeller needs the full design of every turbine and inverter.”

  • Myth
  • Fact
Answer

Myth. A system model borrows a few numbers from each design (ratings, efficiencies, ramp limits, minimum loads, outlet temperatures, and reliability and life); the design itself stays with the engineers.

EIA reports an average full-load tested heat rate of 7,535 Btu per kWh for U.S. natural-gas combined-cycle plants in 2025; one kWh holds 3,412 Btu. About what share of the fuel's energy becomes electricity at full load?

  • About 23%
  • About 45%
  • About 68%
Answer

3,412 ÷ 7,535 = 0.453, about 45%: the full-load efficiency a model borrows as a heat rate (lesson F4).

Numbers, sources and what’s next

Numbers to remember

Number What it means Source
59.3% The most of the wind's power any rotor can take, the Betz limit (physics). Physics: 16/27 of the wind's power · lesson 5
7,535 Btu/kWh EIA's 2025 average full-load tested heat rate for U.S. natural-gas combined-cycle plants: 3,412 ÷ 7,535 = 45.3% of the fuel's energy becomes electricity at full load. U.S. Energy Information Administration, Electric Power Annual, Table 8.2: Average Tested Heat Rates by Prime Mover and Energy Source, 2015-2025 · 2025 data
about 300 °C The outlet temperature of large water-cooled reactors. U.S. Department of Energy, Quadrennial Technology Review 2015, Technology Assessment 4.M: Light Water Reactors · 2015
57 kWh/kg A16 assumes about 57 kWh per kilogram of hydrogen for the complete PEM electrolyzer system; stack design helps set that system value. DOE Hydrogen Program Record 24005, Clean Hydrogen Production Cost Scenarios with PEM Electrolyzer Technology, Table 1 and p. 1 (2022 dollars) · 2024-05-20
85% The course assumes 85% of the electricity sent into its utility-scale battery system comes back out: charging and discharging losses together, for the whole system, not one cell. Cole, Ramasamy and Turan, Cost Projections for Utility-Scale Battery Storage: 2025 Update, NREL/TP-6A40-93281 · June 2025

Keep going

Back to the course map

Sources and further reading

The numbers, read from the lessons that teach them, and the cybersecurity paper:

  • U.S. Energy Information Administration, Solar explained: Photovoltaics and electricity. Link. read 3 November 2026.
  • National Renewable Energy Laboratory, Power Performance Test Report for the U.S. Department of Energy 1.5-Megawatt Wind Turbine (NREL/TP-5000-63684). Link. 2015; test February to June 2011.
  • U.S. Energy Information Administration, Electric Power Annual, Table 8.2: Average Tested Heat Rates by Prime Mover and Energy Source, 2015-2025. Link. 2025 data.
  • U.S. Department of Energy, Quadrennial Technology Review 2015, Technology Assessment 4.M: Light Water Reactors. Link. 2015.
  • U.S. Energy Information Administration, Electric Power Annual, Table 8.1: Average Operating Heat Rate for Selected Energy Sources, 2015 through 2025. Link. 2025 data, read 3 November 2026.
  • DOE Hydrogen Program Record 24005, Clean Hydrogen Production Cost Scenarios with PEM Electrolyzer Technology, Table 1 and p. 1 (2022 dollars). Link. 2024-05-20.
  • IRENA, Green Hydrogen Cost Reduction (2020), Table 6: load range of PEM 5%–120%, of alkaline 15%–100%. Link. 2020-12.
  • Cole, Ramasamy and Turan, Cost Projections for Utility-Scale Battery Storage: 2025 Update, NREL/TP-6A40-93281. Link. June 2025.
  • NERC Security Integration and Technology Enablement Subcommittee, Cyber Security for Distributed Energy Resources and DER Aggregators. Link. December 2022.
  • EIA, Electricity explained: How electricity is generated: most electricity comes from turbines driving generators. Link. Page undated; read 3 November 2026 (lesson F4).

One book per discipline (cited by name; any recent edition):

  • Power electronics: Erickson and Maksimović, Fundamentals of Power Electronics (Springer).
  • Power system protection: Horowitz and Phadke, Power System Relaying (Wiley).
  • Aerodynamics and structural engineering: Burton, Jenkins, Sharpe and Bossanyi, Wind Energy Handbook (Wiley).
  • Combustion and thermodynamics: Turns, An Introduction to Combustion (McGraw-Hill).
  • Reactor physics, thermal hydraulics and nuclear materials: Lamarsh and Baratta, Introduction to Nuclear Engineering (Pearson).
  • Electrochemistry, catalysis and materials: U.S. Department of Energy, Hydrogen and Fuel Cell Technologies Office, Hydrogen Production: Electrolysis (energy.gov).
  • Electrochemistry and materials science: Linden's Handbook of Batteries (McGraw-Hill).
  • Control engineering, operations and cybersecurity: Wood, Wollenberg and Sheblé, Power Generation, Operation, and Control (Wiley).

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.