SCIENCE · INVESTIGATE AND EXPLAIN

Trace storage limits and dispatch losses

Distinguish capacity, power, internal energy and delivered output.

Learning outcome: Explain an unmet request even when energy remains stored.

Starting recap

Initial storage is zero; local supply precedes storage and grid support.

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Try

A full lossy-fast store withdraws 4 internal kWh to deliver 3 kWh and lose 1.

Open the experiment

Predict

Can later charging serve the first empty-store deficit?

Your prediction and reason

Experiment

Compare middle generation with ideal fast, lossy fast and ideal slow profiles; audit the historical EIA panel separately.

Match generation timing, storage and electrical service

Original four-hour electrical service scenario · separate lifecycle evidence · Original four-hour scenario: four one-hour bins each request 4 kW. All generation packets offer 16 kWh; initial storage is zero. Local supply, surplus charging, deficit discharge and at most 1 kW grid support follow a fixed greedy rule. Curtailed potential is not generated bus input. No forecast, emissions, prices, degradation or reliability certification is calculated.

Available local generation timing: Middle-period availability Storage capacity, power and efficiency profile: Ideal fast storage

Reset keeps your prediction, captures and practice history.

Same requested service, different timing and limits

Middle-period availability; Ideal fast storage. Every case requests 4 kW for four one-hour bins: 16 kWh over a four-hour window, not a whole day. Available local generation also totals 16 kWh. Initial storage is zero. Predict whether equal totals are sufficient before comparing the timing and storage controls.

Storage capacity is 4 kWh internal energy. Charge input power is limited to 4 kW; useful discharge output is limited to 4 kW. Charge efficiency is 100% and discharge efficiency is 100%. These are supplied reference profiles, not measured device ratings.

Grid import follows storage discharge and cannot exceed 1 kW. There is no grid charging or grid export. Surplus and deficit cannot coexist in a bin, so charging and discharge never occur together. This stipulated greedy rule is not scheduling optimization. Curtailed potential is unused availability, not generated energy dissipated inside the bus.

Close two distinct accounts

Physical account (kWh): 12 used local generation + 1 grid + 0 initial store = 13 served + 0 charge loss + 0 discharge loss + 0 final store. Residual: 0.

Availability allocation (kWh): 16 available generation + 1 grid + 0 initial store = 13 served + 4 curtailed potential + 0 conversion losses + 0 final store. Residual: 0. This second account allocates potential generation; it does not imply all availability entered the physical bus.

Served 13 + unserved 3 = 16 kWh requested. Do not add unserved demand to either energy balance, or count battery output a second time as a new primary source.

Each bin lasts 1 h. Energy columns are kWh; the first two numerical columns are kW.
Bin	Demand kW	Available kW	Demand kWh	Available kWh	Direct	Charge input	Used generation	Curtailed potential	Storage output	Grid	Served	Unserved
1	4	0	4	0	0	0	0	0	0	1	1	3
2	4	8	4	8	4	4	8	0	0	0	4	0
3	4	8	4	8	4	0	4	4	0	0	4	0
4	4	0	4	0	0	0	0	0	4	0	4	0

Internal storage and energy accounts, all in kWh; start + stored charge − internal withdrawal = end.
Bin	Start store	Stored charge	Internal withdrawal	End store
1	0	0	0	0
2	0	4	0	4
3	4	0	0	4
4	4	0	4	0

Reserve and service are different indicators

The illustrative end-reserve target is 1 kWh internal energy. Final store: 0 kWh; reserve shortfall: 1 kWh; target not met. This comparison did not constrain dispatch and does not guarantee future service. It is not another course requirement. Stored internal energy is not identical to deliverable energy for the lossy profile.

The 75% discharge case assigns all modeled loss to discharge for clarity: 4 kWh withdrawn delivers 3 kWh and loses 1 kWh to conversion. It is not a measured battery rating. No self-discharge, aging, thermal constraints, within-bin fluctuations, costs or emissions are calculated.

Check timing, capacity and an unfamiliar duration

Middle-period availability with ideal fast storage ends each bin at [0,4,4,0] kWh. The first bin still has 3 kWh unmet demand: later generation cannot serve an earlier request. With ideal slow storage the stores are [0,1,2,1]; 5 kWh remains unserved across the window despite meeting the final reserve target.

For a separate paper case, an ideal full 4 kWh store limited to 1 kW output can deliver at most 0.5 kWh in half an hour. Multiply power by duration; the numerical equality of kW and kWh in the live one-hour bins is a convenience, not a unit identity.

Served 13 of 16 kWh requested; unserved 3 kWh; final internal store 0 kWh.

Physical account: 12 used local generation + 1 grid = 13 served + 0 losses + 0 final store (kWh). Curtailed available potential 4 kWh is separate. Illustrative reserve shortfall 1 kWh; this does not establish future service.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Predict which deficit storage can actually serve

Choose middle-period generation and ideal fast storage. The store begins empty, has 4 kWh capacity and can accept or deliver at most 4 kW. Predict whether it can supply the first bin’s 4 kWh request before any generation arrives. Write your prediction before following the daily-looking graph: these are four hourly bins, not four days.

In the first bin, local generation is zero and storage is empty. The grid supplies 1 kWh and 3 remains unserved. In bin two, 8 kWh is available: 4 goes directly to demand and 4 charges storage. In bin three, the store is already full, so 4 serves demand and the other 4 is curtailed potential. In bin four, storage supplies all 4 requested.

Read capacity and power as different constraints

The ideal fast store’s end-bin sequence is [0,4,4,0] kWh. Total grid import is 1, served demand 13 and unserved demand 3. A storage capacity does not allow energy to travel backward from a later charging interval into the first deficit.

Now choose ideal slow storage. Its energy capacity remains 4 kWh, but charge and delivered-discharge limits are only 1 kW. End stores become [0,1,2,1]. The store charges only 1 kWh during each middle bin and delivers only 1 in the final bin. Grid import totals 2, served demand 11 and unserved demand 5.

Capture fast and slow cases at the same generation setting. Explain why the slow store finishes with 1 kWh even though demand went unmet. Its remaining energy satisfies the separate illustrative reserve objective; its power limit prevents meeting present service. Reserve and unserved demand must not be merged into a single success badge.

Account for loss on the correct side

Choose lossy fast storage. It accepts up to 4 kWh and has 4 kW output capability, but discharge efficiency is 0.75. A full internal store therefore delivers 3 kWh and loses 1 during discharge. All loss is placed on discharge for this teaching profile; this is not a measured battery rating.

For middle-period generation, final-bin grid import supplies the remaining 1 kWh. Total served demand is again 13 and total unserved is 3, but grid import is now 2 rather than 1. Equal served totals do not establish identical energy inputs or losses.

The physical account is 12 kWh used local generation + 2 grid = 13 served + 1 loss. The availability account instead reads 16 available + 2 grid = 13 served + 1 loss + 4 curtailed potential. The curtailed 4 is not an additional physical input or conversion loss.

Compare with an actual historical summary

A dated agency summary, not a universal efficiency

The EIA article published February 12, 2021 reports these 2019 U.S. fleet average monthly round-trip efficiencies, using finalized 2019 Power Plant Operations Report data:

Historical reported summary values
Storage group	Round-trip efficiency
Utility-scale batteries	82%
Pumped-storage facilities	79%

Round-trip efficiency compares electricity retrieved with electricity put into storage. Calculate the percentage-point difference. Then explain why these fleet summaries do not prove that every battery plant outperforms every pumped-storage plant.

Check the historical comparison

82 − 79 = 3 percentage points. For an illustrative 100 kWh input, applying the reported factors yields 82 or 79 kWh output. Those products are arithmetic examples, not additional observed plant records. Aggregate round-trip figures do not identify separate charge and discharge efficiencies, calibrate the lab’s 75% discharge-only assumption or establish current technology limits.

Source: EIA, Utility-scale batteries and pumped storage return about 80% of the electricity they store, February 12, 2021; primary record independently checked October 26, 2026. This fixed panel preserves the agency’s summary, not a locally reproduced raw-data analysis. Efficiency is not power capacity, and these values establish no current national storage shares.

The EIA article published February 12, 2021 reports 2019 U.S. fleet average monthly round-trip efficiencies of 82% for utility-scale batteries and 79% for pumped storage. Their difference is three percentage points. These are historical agency summaries, not current limits or evidence that every battery exceeds every pumped-storage plant.

Multiplying an illustrative 100 kWh input by those percentages gives 82 or 79 kWh output, but those products are not additional plant observations. A round-trip summary cannot identify separate charging and discharging efficiencies or calibrate our discharge-only 75% case.

Transfer: test a short service window

An ideal full 4 kWh store has a 1 kW output limit. A fictional load asks for 4 kWh during half an hour. With no other supply, what can the store deliver and what remains internally? Use duration explicitly.

Check the storage-dispatch transfer

The power limit permits 1 × 0.5 = 0.5 kWh output. An ideal store retains 3.5 kWh while 3.5 kWh of the request remains unserved. Available internal energy alone does not establish deliverable service within a specified time. No real equipment performance or reliability guarantee follows.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Separate round-trip historical averages from the supplied discharge-only efficiency.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Match power, energy and service timing Next: Separate efficiency from service demand

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