How long should storage last? From batteries to seasonal stores

Put four stores through a calm winter week, then see what each MWh it delivers costs

Analyst lesson A8 of Energy Systems, Step by Step: shelve storage technologies on a duration ladder from seconds to seasons, run a battery, pumped hydro, a heat store and hydrogen through a calm winter week on the Plains Grid with a linear program, and price each MWh a store delivers against how often it cycles.
  • Analyst · L2
  • 30 min guided · about 30 min practice
  • After lesson 9 and lesson 13

2–8 January 2025 on the Plains Grid: four stores of 1,000 MW, each full at the start

Store Energy held Round trip Unserved left Shortfall covered
Lithium-ion battery, 4 h 4,000 MWh 83% 37,710 MWh 21%
Pumped storage hydro, 10 h 10,000 MWh 80% 30,495 MWh 36%
Heat store, 24 h 24,000 MWh 50% 17,066 MWh 64%
Hydrogen in a salt cavern, 168 h 168,000 MWh 31% 4,009 MWh 92%

Without storage the week is 47,733 MWh short, in 72 hours. The hydrogen store's 4,009 MWh left are the hours when the gap tops firm output plus its 1,000 MW.

With JavaScript on, you place stores on a duration ladder, run each through the week with a solver, and price what each MWh delivered costs.

Illustrative grid. The Plains Grid (a 4,000 MW peak, as in lesson 3) with 5,000 MW of wind, 2,000 MW of solar and 1,000 MW of firm gas: a mix chosen so that a calm week leaves a gap.

Real shapes. Demand, wind and sun follow the Southwest Power Pool's hours of 2–8 January 2025 (EIA-930); wind and solar scaled to EIA's monthly capacity factors.

Stores and costs. Round trips and 2021 installed costs from DOE's 2022 storage assessment. The heat store's 2% a day is an illustrative assumption, borrowed from a 2020 NREL tank design target.

About 30 guided minutes in eight steps. Solver: HiGHS (open source), loaded on your first solve (about 3.5 MB, once).

What you just did, as diagrams

Duration
Energy ÷ power: how long a store gives full power. 4,000 MWh at 1,000 MW is 4 hours.
Round trip
What comes back of 1 MWh put in: 83% for the battery, 31% for hydrogen.
Heat losses
A hot store cools whether or not it is used, a standing loss: 2% a day here.
Endurance
In the calm week the battery covers 21% of the shortfall, the hydrogen store 92%.
Power still matters
In 23 hours the gap tops firm output plus 1,000 MW: no 1,000 MW store can close it.
Cost per MWh delivered
Yearly cost ÷ MWh delivered a year: the fewer the full cycles, the more each MWh carries.
Go deeper · AnalystWhy the cost per MWh delivered depends on cycles
  • The formula. Cost per MWh delivered = 1,000 × capital recovery × installed cost ($ per kW) ÷ (cycles a year × duration in hours), plus the charging price ÷ round trip. The 1,000 turns kW into MW.
  • Capital recovery is the share of the installed cost to recover each year, with interest: 4% real (inflation taken out) over the store’s life (lesson 7).
  • The battery. At 250 cycles a year and $20/MWh charging, 4 hours at $1,540 per kW over 16 years: 1,000 × 0.0858 × 1,540 ÷ (250 × 4) = $132 of capital, plus $24 of charging: $156 per MWh.
  • Hydrogen. A 24-hour hydrogen store at 31% needs 24 + 24 ÷ 0.31 = 101 hours a cycle, so at most 86 cycles a year: $149 per MWh at best, $65 of it charging.
  • Left out. Fixed upkeep adds under a quarter to the capital for pumped hydro and hydrogen ($28.19 and $23.90 per kW-year); the report gives no battery figure at this size.
  • Longer hydrogen stores add mostly cavern, at $5.82 per kWh in the report: energy capacity is cheap, the converters are not.
Go deeper · ModelerThe week as a linear program

For each hour \(t = 0 \dots 167\) (one hour each, so MW over the hour is MWh), with a store of power \(P\), energy \(E\), round trip \(\eta\) and standing loss \(\lambda\) per hour:

\[\min \sum_t \big(V + \tau\,(168 - t)\big)\,u_t + \delta \sum_t d_t\]

\[ \begin{aligned} f_t + u_t - s_t - c_t + d_t &= g_t && \text{(balance)}\\ e_t = (1-\lambda)\,e_{t-1} + \eta\,c_t - d_t, \quad e_{-1} &= E && \text{(level; starts full)}\\ 0 \le f_t \le 1{,}000, \quad 0 \le s_t \le w_t + \sigma_t, \quad 0 \le c_t, d_t \le P, \quad 0 \le e_t &\le E, \quad u_t \ge 0 && \text{(limits)} \end{aligned} \]

Symbol Meaning Unit
\(g_t\) the gap: demand minus wind and sun MW
\(w_t\), \(\sigma_t\) wind and sun available in hour \(t\) MW
\(f_t\) firm (gas) output MW
\(u_t\), \(s_t\) unserved demand, spilled wind and sun MW
\(c_t\), \(d_t\) charging and discharging MW
\(e_t\) energy held at the end of hour \(t\) MWh
\(P\), \(E\) the store’s power and energy (1,000 MW; 1,000 MW × its hours) MW, MWh
\(\eta\) round trip, all of its loss on charging share
\(\lambda\) standing loss: \(1 - 0.98^{1/24}\) for 2% a day per hour
\(V\) value of a MWh unserved: $10,000 $/MWh
\(\tau\) tie rule: $0.01 more per MWh unserved for each hour before the week’s end $/MWh per hour
\(\delta\) tie rule: $0.001 per MWh discharged $/MWh
  • Tie rule, stated in advance. Many schedules leave the same MWh unserved. \(\tau\) pushes shortfalls late and \(\delta\) uses firm output before the store; neither changes the least unserved energy, the only number the page reads.
  • One of the best schedules. The dashed line in step 5 is the one this tie rule picks; others leave the same MWh unserved.
  • Next. M4 adds conversion between carriers; M3 links a store across representative weeks of a whole year.
Go deeperWhat this lesson leaves out
  • The rest of the year: whether a store refills before the next calm spell needs the whole year in order (M3).
  • Adequacy: many weather years and plant outages, judged by a criterion such as a loss-of-load expectation (A5).
  • Building the stores: here each is given, at 1,000 MW; choosing sizes is capacity expansion (lesson 13, M3).
  • Wires: the Plains Grid is one node with no limits on its lines.
  • Wear, fixed upkeep and replacements in the costs; costs differ by site and change over time.

Check yourself

Myth or fact? “A store that holds more energy than the week's shortfall can always cover the week.”

  • Myth
  • Fact
Answer

Myth. The hydrogen store holds 168,000 MWh against a 47,733 MWh shortfall, yet leaves 4,009 MWh unserved: in 23 hours the gap tops firm output plus its 1,000 MW.

Myth or fact? “If a store gets a grid through its calmest week, the grid is adequate.”

  • Myth
  • Fact
Answer

Myth. A week shows endurance. Adequacy needs many weather years and plant outages, and the store must also refill in time for the next calm spell.

Myth or fact? “The store with the lowest installed cost per kWh delivers the cheapest MWh.”

  • Myth
  • Fact
Answer

Myth. Hydrogen has the lowest installed cost per kWh ($126, against $263 for pumped hydro and $385 for the battery).

At 250 cycles a year pumped hydro delivers the cheapest MWh, $71; hydrogen, capped at 86 cycles, $149 (DOE's 24-hour cost case).

A pumped storage plant is rated 400 MW and 3,200 MWh. What is its duration?

  • 0.125 hours
  • 3,600 hours
  • 8 hours
  • 2,800 hours
Answer

8 hours: 3,200 MWh ÷ 400 MW. 0.125 is the ratio upside down; 3,600 and 2,800 add or subtract MW and MWh, which have different units.

You put 10 MWh into the lesson's heat store (50% round trip, 2% a day) and take it out 5 days later. About how much comes back?

  • 5.0 MWh
  • 4.5 MWh
  • 9.0 MWh
  • 4.0 MWh
Answer

About 4.5 MWh: 10 × 0.50 × 0.985 = 4.52.

5.0 forgets the heat losses; 9.0 forgets the round trip; 4.0 takes 2% of the original 10 MWh off each day, not 2% of what is left.

Numbers, sources and what’s next

Numbers to remember

Number What it means Source
82% and 79% Average monthly round-trip efficiency of U.S. utility-scale batteries and of pumped storage plants in 2019. EIA, Today in Energy · published 12 Feb 2021; data for 2019
about 23,156 MW U.S. pumped storage hydro capacity in 2025, in 18 states. EIA, Energy Explained: where hydropower is generated · accessed 3 Nov 2026
10 hours and more DOE's Long Duration Storage Shot (2021): 90% lower cost by 2030, against a 2020 lithium-ion baseline, for storage of 10 or more hours. DOE Office of Electricity, Achieving the Promise of Low-Cost Long Duration Energy Storage, p. iii · August 2024
less than one a day Full cycles of 24- and 100-hour stores: their yearly output, and so their cost per MWh, is limited by how often they can cycle. DOE, 2022 Grid Energy Storage Technology Cost and Performance Assessment, p. viii · August 2022

Next

A16 · Where does hydrogen make sense? From renewables to electrolysis, storage and use

In the real world

Compared with wind and a battery alone, adding an electrolyzer reduced total system cost by about 7%, and using hydrogen as the storage medium for fuel cells reduced it by about 26%.

Battery, hydrogen and hybrid storage were compared, each set to deliver the largest stabilized output in every hour at the lowest life-cycle cost.

Holds when: one planned West Texas wind farm, ERCOT prices, costs from 2020 to 2023. Leaves out: final federal hydrogen credit rules.

Case file CF2 tells that study in full.

Sources and further reading

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.