Cheap, clean, reliable, fair, secure: can you have them all?
Watch five goals move at once, find the plans nothing beats, and see whose priorities choose
Nine plans for Prairie Town, each run through all 8,760 hours of 2025
| Plan | Cheap: cost a year | Clean: CO₂ a year | Reliable: unserved energy | Fair: low-income share of home bills | Secure: gas share | Verdict |
|---|---|---|---|---|---|---|
| A · Gas only | $103.9M | 815 kt | 0 MWh | 31.3% | 100% | unbeaten |
| B · Gas + wind | $119.5M | 521 kt | 0 MWh | 32.8% | 64% | unbeaten |
| C · Wind, sun and battery, full gas backup | $161.7M | 146 kt | 0 MWh | 34.3% | 18% | beaten by D |
| D · Wind, sun and battery, lean gas backup | $155.8M | 146 kt | 0 MWh | 34.3% | 18% | unbeaten |
| E · Sun and battery, gas backup | $166.6M | 428 kt | 0 MWh | 33.6% | 52% | unbeaten |
| F · Nuclear and gas | $233.7M | 66 kt | 0 MWh | 34.1% | 8% | unbeaten |
| G · Even mix | $176.2M | 164 kt | 0 MWh | 34.0% | 20% | unbeaten |
| H · Wind with thin gas backup | $116.2M | 424 kt | 1,605 MWh | 33.1% | 52% | unbeaten |
| I · Deep clean | $221.6M | 27 kt | 0 MWh | 34.6% | 3% | unbeaten |
Verdicts compare values as shown: two values that round to the same number count as a tie.
Fair assumes a fixed charge per home: each home pays an equal share of the plants' fixed costs, and running costs per kWh. Secure assumes all gas is piped in and none is stored.
Five illustrative sets of priorities pick three plans: Bills first picks A, Climate first and Supply first pick I, Lights first and Equal weights pick D.
Limits of 200 kt CO₂, 25% gas and a 33% low-income share: no plan meets them on seven weeks of 2025 under a fixed charge per home. With the income-graduated charge the seven weeks meet them, but the full year emits 215 kt and leaves 33 MWh unserved.
With JavaScript on, you change the plan yourself, find the unbeaten plans, weigh the goals, switch definitions and ask a solver for a plan that meets your limits, then check it on the full year.
Model: lesson 13's linear program, each plan run hour by hour through 2025; plants never break down.
Data: real 2025 hourly shapes of the Southwest Power Pool grid (EIA-930); costs from EIA and NREL, held fixed at the values dated in lesson 13's sources.
Homes: the U.S. split by income from EIA RECS 2020 (PDF).
Illustrative: the plans, tariffs, priority weights and radar scales; Prairie Town is fictional.
About 25 guided minutes. Practice, about 20 more: the practice set under Check.
What you just did, as diagrams
- Five measures
- One number per goal: cost, CO₂, unserved energy, the low-income share of home bills, the gas share.
- Definitions
- Each measure is a choice of unit, boundary and formula; Fair and Secure most of all.
- Unbeaten plans
- No other plan is at least as good on all five goals and better on one: 8 of the 9 plans here, comparing values as shown.
- Weights
- How much each goal counts; people set them, and different weights pick different plans.
- Limits
- Caps on some goals; the solver finds the cheapest plan that meets them on seven weeks, or reports that none exists. The full year then checks it.
- Who decides, who pays
- Households and businesses pay through the tariff; a regulator or council approves; people downwind bear harm outside the cost.
Go deeper · AnalystReading a radar honestly
- Scales are choices. Rim (best) and centre (worst): cost $100M and $250M a year; CO₂ 0 and 850 kt; unserved energy 0 and 2,000 MWh; low-income share 20% and 35%; gas share 0% and 100%.
- Equal weights carry a price. One spoke of cost ($150M) counts as much as one spoke of CO₂ (850 kt): about $176 a tonne, set by the scales, not by anyone's judgement of harm (lesson 12: weights carry units).
- Squeezed spokes. Under a fixed charge per home, every plan's low-income share lies between 31.3% and 34.6%, so Fair scores span only 0.03 to 0.25: a weight on Fair barely moves a pick.
- Shape, not area. Reordering the spokes changes a polygon's area; compare plans spoke by spoke.
- Ties as shown. Verdicts treat values that round to the same shown number as equal. Under the income-graduated charge, C's share (21.61%) and D's (21.63%) both show 21.6%, so D beats C; at full precision, C is unbeaten.
Go deeper · AnalystOther ways to measure fairness, security and reliability
- Fairness as burden. Energy burden is the share of income spent on home energy: electricity, gas and other fuels, not transport.
- DOE's numbers. DOE's LEAD tool puts it at about 6% for low-income U.S. households and 2% for others (2018–2022 data). DOE uses a different definition here: income up to 80% of the local median.
- Not in this model. Burden needs incomes and whole bills, which this town model does not have.
- Security as diversity. A supply is concentrated when one source makes most of it, and diverse when many sources make similar shares.
- Diversity indices. Shannon's and the Herfindahl index turn every source's share into one number; the Herfindahl index is the sum of the squared shares, 1 when one source makes everything. Stirling (2010) adds how different the sources are.
- Reliability over many years. Loss-of-load expectation counts shortfall hours over many weather years with random plant failures (A5).
Reviews of energy decisions with several criteria (Wang and co-authors, 2009) find cost, emissions, reliability and social measures in most studies, each defined in many ways.
Go deeper · ModelerFive goals as a model
Write each goal as a number to make small, \(f_k(x)\) for \(k = 1, \dots, 5\). The lesson’s tools, in words:
- Dominance. Plan \(x\) beats plan \(y\) when \(f_k(x) \le f_k(y)\) for every \(k\) and \(f_k(x) < f_k(y)\) for at least one.
- Adding a goal. It can rescue a beaten plan. It can beat a plan that was unbeaten only if another plan tied that plan on every earlier goal.
- Weighted sum. Each goal gets a score on its scale and a weight; the pick has the highest weighted total. With every weight above zero, the pick is unbeaten.
- Clipping. A value beyond its scale’s end scores the same as that end, which can hide a difference, so the page weighs only the unbeaten plans.
- Limits. Step 7 asks for the cheapest plan with caps on CO₂, the gas share and the low-income share: the epsilon-constraint method, then a check on the full year.
The low-income share, worked out for a plan whose fixed costs are 95% of its cost:
| Tariff | Low-income homes pay | Their share of home bills |
|---|---|---|
| Fixed charge per home | 34.7% of the fixed costs, 29.6% of the running costs | 34.7% × 0.95 + 29.6% × 0.05 = 34.4% |
| Income-graduated (half the charge) | 21.0% of the fixed costs, 29.6% of the running costs | 21.0% × 0.95 + 29.6% × 0.05 = 21.4% |
| Per kWh only | 29.6% of every cost | 29.6% |
Same plan, same costs: the tariff alone moves the share by 13.0 points.
Mavrotas (2009) shows how to sweep the limits. Next: M6 (carbon in models) and M12 (a city model with screening fairness outputs).
Check yourself
Myth or fact? “With five goals, a good plan can usually win on all of them.”
- Myth
- Fact
Answer
Myth. Here the cheapest plan (A) emits the most, and the cleanest (I) costs more than twice as much; no plan is best on all five.
Myth or fact? “Adding a goal can turn a beaten plan into an unbeaten one.”
- Myth
- Fact
Answer
Fact. Here 4 plans beaten on cost and CO₂ alone are unbeaten on all five. The reverse needs a tie: a new goal can beat an unbeaten plan only if another plan matched it on every earlier goal.
Myth or fact? “A fairness score is measured, just as CO₂ is.”
- Myth
- Fact
Answer
Myth. It rests on a tariff. With an income-graduated fixed charge, plans with more building cost (here the cleaner ones) have the lower low-income share, and E, F and G become beaten.
Plans C and D differ only by 80 MW of gas peakers, which never ran in 2025. Which measure can tell them apart in C's favour?
- A reserve margin
- Unserved energy
- CO₂ a year
- The gas share
Answer
A reserve margin: it counts capacity at the peak, 88% for C against 70% for D. The other three see the same year for both.
Practice · about 20 minutes on your own
Use the nine plans' table at the top (a fixed charge per home; Reliable as unserved energy, Secure as the gas share).
Is plan B beaten? H costs less than B ($116.2M against $119.5M) and emits less (424 kt against 521 kt).
Answer
Unbeaten: H leaves 1,605 MWh unserved and B none, so no plan matches B on all five.
Which plan beats plan C?
Answer
D: it costs $5.9M less and is the same on the other four goals.
Measure Reliable by the reserve margin: is C still beaten? C's margin is 88%, D's 70%.
Answer
No: C is now better on one goal, so D no longer beats it.
Plan D's total under equal weights. Its scores: Cheap 0.63, Clean 0.83, Reliable 1.00, Fair 0.05, Secure 0.82.
Answer
0.666, the average of the five: the highest of the nine, so Equal weights picks D.
Give weights that pick plan D, not plan A. Bills first (cost 40, clean 5, reliable 20, fair 30, secure 5) picks A.
Answer
For example cost 30, clean 30, reliable 20, fair 10, secure 10: D wins. Someone else's weights could still pick A.
A plan's fixed costs are 60% of its cost. What share of home bills do low-income homes pay with a fixed charge per home, and with the income-graduated charge (21.0% of the fixed charges)?
Answer
32.6% and 24.4%: the tariff alone moves the share by 8.2 points.
Numbers, sources and what’s next
Numbers to remember
| Number | What it means | Source |
|---|---|---|
| 34.7% · 29.6% | U.S. homes with income under $40,000 in 2020: their share of homes, and of home electricity use. | EIA, RECS 2020, Table CE2.1 (PDF) · revised March 2024 |
| 6% · 2% | Average energy burden of low-income U.S. households, and of other households (2018–2022 data). Home energy only, not transport; DOE's low-income means income up to 80% of the local median. | U.S. DOE, LEAD tool · checked 3 Nov 2026 |
| 44.2% · 27.3% | Shares of plant outages, derates and failures to start in the February 2021 freeze in Texas and the South Central U.S. caused by freezing, and by gas fuel supply. | FERC, NERC and Regional Entities staff report (PDF), pp. 15–16 · November 2021 |
Next
In the real world
- Fairness: DOE's LEAD tool maps energy burden, with low income as up to 80% of the local median.
- Security: the FERC–NERC report on February 2021 traced plant outages to freezing and to gas supply.
- Choosing: which yardstick to use, and how much each counts, is decided by people.
Sources and further reading
- EIA (2023, revised 2024). 2020 Residential Energy Consumption Survey, Table CE2.1 (PDF): homes and electricity use by household income.
- U.S. DOE. Low-Income Energy Affordability Data (LEAD) Tool.
- FERC, NERC and Regional Entities (November 2021). The February 2021 Cold Weather Outages in Texas and the South Central United States (PDF), pp. 15–16.
- Wang, J.-J., Jing, Y.-Y., Zhang, C.-F. and Zhao, J.-H. (2009). Review on multi-criteria decision analysis aid in sustainable energy decision-making. Renewable and Sustainable Energy Reviews 13(9), 2263–2278.
- Stirling, A. (2010). Multicriteria diversity analysis. Energy Policy 38(4), 1622–1634.
- Mavrotas, G. (2009). Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems. Applied Mathematics and Computation 213.
- Technology costs, fuel prices and the 2025 weather: as listed in lesson 13's sources.
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.