Foundations checkpoint: estimate an unfamiliar situation

Nine tasks on situations you have not seen, the last an estimate with units, a range and a check

The Foundations checkpoint (CK-F) of Energy Systems, Step by Step: nine tasks on situations you have not seen, from reading a chart and explaining a mechanism to spotting an error in a headline, the last one an estimate with units, a range, the main uncertainty and a check, marked against a published rubric. Answers and times stay in your browser.

1. Learn
2. CK-F

• Foundations · L1
• Checkpoint
• 40 min
• After lesson 6 and N1

1. 1Task
2. 2Worked solution
3. 3Rubric
4. 4Sources

The nine tasks

Answer each task on paper first, then open its worked solution. Task 9 is the main estimate; its worked solution and the rubric are further down this page.

1. Why balance every moment? Explain a mechanism · draws on T0, T3

   In one or two sentences: why must supply equal demand at every moment on a power grid, and what tells the operator when it does not?

   Worked solution, task 1

   Power is made as it is used; only the spinning machines' stored energy covers a gap, for seconds. A shortfall makes the frequency fall, a surplus makes it rise, and controls then restore the balance and 60 Hz.

   A full answer makes two points:

   • The grid stores almost no energy, so power is made as it is used; only the spinning machines' stored energy covers a gap, for seconds.
   • The frequency shows a gap: a shortfall makes it fall below 60 Hz and a surplus makes it rise; controls then restore the balance and bring it back to 60 Hz.

2. Phone charges in a day Estimate with units · draws on T1

   A U.S. home uses about 10,800 kWh of electricity a year. A phone takes about 15 Wh for a full charge (illustrative). About how many full charges equal one day of the home's use?

   • a. 2
   • b. 80
   • c. 2,000
   • d. 720,000
   Worked solution, task 2

   Answer: c. 2,000.

   One day: 10,800 kWh ÷ 365 ≈ 30 kWh = 30,000 Wh, and 30,000 Wh ÷ 15 Wh ≈ 2,000 charges. The trap is the k: kWh and Wh differ by a factor of 1,000.

3. A December day's demand Read a chart · draws on T2

   The chart shows Prairie Town's demand on a real December weekday. When is demand highest, and how much above the day's lowest hour?

   Chart data: Monday 15 December 2025, MW by hour

   Hour	Demand (MW)
   00:00	306
   01:00	304
   02:00	304
   03:00	306
   04:00	311
   05:00	321
   06:00	338
   07:00	347
   08:00	344
   09:00	335
   10:00	326
   11:00	318
   12:00	311
   13:00	288
   14:00	282
   15:00	282
   16:00	286
   17:00	296
   18:00	301
   19:00	303
   20:00	303
   21:00	302
   22:00	294
   23:00	287

   • a. 07:00, about a quarter above the lowest hour
   • b. 07:00, about 4 times the lowest hour
   • c. 19:00, about a quarter above the lowest hour
   • d. 14:00, about a quarter above the lowest hour
   Worked solution, task 3

   Answer: a. 07:00, about a quarter above the lowest hour.

   Peak 347 MW at 07:00, low 282 MW at 14:00 and 15:00: 347 ÷ 282 ≈ 1.23, about a quarter higher. Always read where the axis starts, here at 260 MW, not zero.

4. After a plant trips Explain a mechanism · draws on T3

   A 60 MW gas unit in Prairie Town's region trips (shuts down suddenly). Put what happens next in order, first at the top.

   As shuffled:

   • Within minutes, the operator's control system orders reserve plants (spare capacity kept ready) up to replace the lost 60 MW.
   • The frequency starts to fall below 60 Hz; the spinning machines' stored energy covers the gap for a moment.
   • The frequency is back at 60 Hz, and the operator restores its reserves for the next trip.
   • Within seconds, governors (automatic speed controls on running plants) raise output and the fall stops.
   Worked solution, task 4

   1. The frequency starts to fall below 60 Hz; the spinning machines' stored energy covers the gap for a moment.
   2. Within seconds, governors (automatic speed controls on running plants) raise output and the fall stops.
   3. Within minutes, the operator's control system orders reserve plants (spare capacity kept ready) up to replace the lost 60 MW.
   4. The frequency is back at 60 Hz, and the operator restores its reserves for the next trip.

   The frequency falls first; governors stop the fall within seconds but leave it below 60 Hz. Reserves replace the lost power over minutes and bring 60 Hz back; only then are the reserves rebuilt.

5. Forecast against actual Read a chart · draws on T4

   The chart shows the day-ahead forecast and the actual demand of a real spring day, scaled to Prairie Town. Over the day, the forecast was mostly…

   Chart data: Thursday 17 April 2025, MW by hour

   Hour	Actual demand (MW)	Day-ahead forecast (MW)
   00:00	228	225
   01:00	221	220
   02:00	217	216
   03:00	216	215
   04:00	216	217
   05:00	224	225
   06:00	238	239
   07:00	248	248
   08:00	253	251
   09:00	257	254
   10:00	263	259
   11:00	268	264
   12:00	275	270
   13:00	284	278
   14:00	290	284
   15:00	295	290
   16:00	299	297
   17:00	300	298
   18:00	298	297
   19:00	292	291
   20:00	288	288
   21:00	280	279
   22:00	266	265
   23:00	252	250

   • a. too low, by at most about 2% of demand
   • b. too high, by at most about 2% of demand
   • c. too low, by up to about 20% of demand
   • d. exactly right
   Worked solution, task 5

   Answer: a. too low, by at most about 2% of demand.

   Actual demand is above the forecast in 19 of 24 hours; the largest miss is 6 MW at 13:00 and 14:00, about 2% of demand. Operators hold reserves to cover misses like these.

6. A wind farm's year Estimate with units · draws on T5

   A 50 MW wind farm runs at the 2025 U.S. average capacity factor for wind, 33.8%. About how much energy does it make in a year?

   Answer with a number and a unit.

   Worked solution, task 6

   Answer: about 148 GWh.

   50 MW × 8,760 h × 0.338 ≈ 148,000 MWh, or 148 GWh. Without the capacity factor you would get 438,000 MWh: the farm at full output every hour, which no wind farm does.

7. A windless winter evening Explain a mechanism · draws on T6

   A windless winter evening at 18:00, with demand near its peak. Assume every plant is available and has fuel. Which pair can Prairie Town count on?

   • a. The solar farm and the wind farm
   • b. The gas peaker and the nuclear plant
   • c. The wind farm and the nuclear plant
   • d. Rooftop solar and the gas peaker
   Worked solution, task 7

   Answer: b. The gas peaker and the nuclear plant.

   Firm capacity is output you can count on when it is needed. At a calm winter dusk, with plants available and fuelled, that is the gas peaker and the nuclear plant; wind and solar do other jobs.

8. Spot the error in a headline Spot an error · draws on N1

   Made-up headline: “New 100 MW solar farm will power 100,000 homes.” At the 2025 U.S. solar capacity factor (24.0%) and 10,800 kWh per home a year, about how many homes' yearly use does it make?

   • a. 4,000
   • b. 20,000
   • c. 100,000
   • d. 200,000
   Worked solution, task 8

   Answer: b. 20,000.

   100 MW × 8,760 h × 0.240 ≈ 210,000 MWh a year, or about 19,500 homes at 10.8 MWh each. Even nameplate (maximum rated) output every hour would make only about 81,000: the headline fails the physics question.

9. The school-bus estimate Estimate (main task) · draws on T1, T5, N1

   Prairie Town's 20 diesel school buses go electric. Estimate the electricity they will use in a year, stating your assumptions. The fields below ask for a range with units, the main uncertainty and one way to check.

   On paper: a low and a high value with units, your inputs and steps, the main uncertainty and one way to check.

With JavaScript on, this page gives you nine tasks one at a time, with instant feedback and a worked solution after each first answer, and keeps your times in this browser.

Prairie Town is fictional; its buses and plants are illustrative. The two charts use real 2025 Southwest Power Pool shapes (EIA-930) scaled to the town as in lesson 0. Draws on lessons 0, 1–6 and the news lens N1. Nothing you type leaves this browser unless you copy it; the copied summary includes what you typed in tasks 1 and 9.

Worked solution: the school-bus estimate

Two routes to the mileage, one range for energy per mile

Step	Route A: per school day	Route B: per year
Miles	20 buses × 50 miles a day (a 25-mile morning and a 25-mile afternoon route) × 180 school days (assumed) = 180,000 miles	20 buses × 14,084 miles a year (U.S. average for a school bus) = 281,680 miles
Energy per mile	1.3 kWh per mile (large buses as rated by makers, 1.26–1.58) to 2.3 kWh per mile (a planning worst case: cold, heating, hills)
Year	234,000 to 414,000 kWh: about 230 to 410 MWh	366,000 to 648,000 kWh: about 370 to 650 MWh

• Answer: about 230 to 650 MWh a year, near 440 MWh in the middle.
• Mileage boundary: Route A counts school runs only, not field trips, sports or summer use, so it runs low.
• Electricity boundary: energy at the bus; charging losses add a little more at the meter.
• Shared input: both routes use the same energy per mile, so their overlap does not check it.

Uncertainty and checks

• Main uncertainty: energy per mile. It spans nearly a factor of two, from 1.3 to 2.3 kWh per mile, with cold weather and cabin heat at the high end.
• Next: miles per bus. Route B's 14,084 miles is about 1.6 times Route A's 9,000.
• Check with homes. 440 MWh = 440,000 kWh; 440,000 ÷ 10,791 kWh per home ≈ 41 average U.S. homes' yearly electricity purchases.
• Check with the town. Prairie Town uses about 2,470 GWh a year, so the buses add about 0.02%.
• Check with a battery. 50 miles × 2.3 kWh per mile = 115 kWh per bus per day: plausible next to the battery sizes in EPA's October 2024 webinar (under 100 to over 300 kWh). A real bus needs that much usable energy, plus a reserve.
• Check with records. The district's yearly mileage replaces Route B's national average. A comparable electric fleet's measured charging energy also checks the energy per mile, the input both routes share.

Marking guide in one line each

• Units: energy per year (kWh, MWh or GWh a year), never kW or MW.
• Range: a low and a high from stated inputs (buses, miles, kWh per mile) that meets 230–650 MWh a year, or argues for a different one.
• Uncertainty: names the input that moves the answer most, and why.
• Check: one check that brings in a different input (a comparison, a record or a measured fleet), not “look it up”.

Rubric

The estimate, criterion by criterion

Criterion	Not yet	Developing	Proficient	Strong
Units	A unit of power (kW, MW), or none.	Energy, but no time basis, or units mixed in the steps.	Energy per year, with every conversion right.	Also put in a familiar comparison: homes, or a share of the town.
Range and reasoning	One number, or more than ten times off the worked solution's range.	A range without stated inputs, or far from the worked solution's range with no argument.	Low and high from stated inputs with consistent units, meeting the worked solution's range or arguing for another.	Two routes that differ in at least one main input and agree within their ranges.
Main uncertainty	None named.	A list of factors, not ranked.	The input that moves the answer most, and why.	Also how far it moves the answer.
Check	None.	“Look it up”, without saying what or where.	One concrete independent check: a second route, a comparison or a record.	The check done, with whether it agrees.

The checkpoint's level

• Proficient: at least 5 of the 7 auto-marked tasks right on the first try, Proficient or better on all four estimate criteria, and both points of task 1.
• Strong: at least 6 of 7, Proficient or better on all four criteria with Strong on at least two, and both points of task 1.
• Developing: at least 3 of 7, and Developing or better on every estimate criterion.
• Not yet: anything else. The checkpoint shows readiness for the Analyst tier; it certifies nothing.

Task 1 and the estimate are self-rated. A teacher or mentor can rate them again with the same rubric from the copied summary.

Numbers, sources and what’s next

Numbers used in the tasks

Number	What it means	Source
10,791 kWh	Electricity bought by an average U.S. home in a year (tasks 2, 8 and 9 round it to 10,800).	EIA, Frequently Asked Questions · data for 2022
33.8% and 24.0%	Capacity factors of the U.S. utility-scale wind and solar fleets in 2025.	EIA, Electric Power Monthly, Table 6.07.B · 2025 annual values
14,084 miles	Average miles a U.S. school bus travels in a year.	U.S. DOE Alternative Fuels Data Center · accessed 2 Nov 2026
1.26–1.58 and 2.3 kWh/mile	Energy per mile of large electric school buses as rated by makers, and a planning worst case.	EPA Clean School Bus webinar (PDF), slides 21–25 · 8 Oct 2024
under 100 to over 300 kWh	Battery sizes of electric school buses; usable energy is less, after wear and a minimum charge.	EPA Clean School Bus webinar (PDF), slides 16 and 26 · 8 Oct 2024

Keep going

Back to the course map

Sources and further reading

• EIA. Hourly Electric Grid Monitor (Form EIA-930): the Southwest Power Pool data behind the two charts (15 December and 17 April 2025).
• U.S. EPA Clean School Bus Program and the Joint Office of Energy and Transportation (2024). Fleet Planning and Route Analysis (PDF): bus efficiency, route energy and battery sizes.
• U.S. DOE Alternative Fuels Data Center. Average Annual Vehicle Miles Traveled by Major Vehicle Category.

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.