Pumped-hydro duty and recharge screen

Define the service boundary, then check every constraint. Built-in values are resettable fictional teaching examples; results prepare further review.

Efficiencies must be greater than 0 and at most 100%. Heads, usable volume, requested hydro power and duty duration must be positive. Machine/interface powers may be zero; a zero recharge window explicitly fails recharge.

Mean effective generating head (m)Net head at the turbine; not elevation difference alone.Mean total pumping head (m)Same returned volume and cycle; include hydraulic loss. Must be at least the generating head in this model.Usable transferred volume (m³)Already exclude dead storage, protected reserve and unavailable water.Generation conversion efficiency (%)Pumping conversion efficiency (%)Validated gross generator limit (MW)Pump electrical input limit excluding auxiliaries (MW)Net service/export interface limit (MW)Net charging import headroom including these auxiliaries (MW)Constant generation auxiliary load (MW)Constant pumping auxiliary load (MW)Required net service (MW)Required continuous duration (h)Window to restore all usable volume (h)

Boundary, states and evidence reference (optional; never independently verified here)

Formulas, assumptions and limits

Fixed freshwater density 1,000 kg/m³ and g = 9.81 m/s². Usable volume already excludes protected water. Mean generating head is effective; pumping head includes hydraulic loss. The same volume is restored.

Stored potential E = ρgH_gen V / 3.6×10⁹ MWh; gross generation = Eη_gen. Net energy at requested duration = gross generation − generation auxiliaries × duration.

Net power limit = max(0, min(generator limit − generation auxiliaries, net interface limit)). Duration is zero if this power limit fails; otherwise gross generation/(net demand + generation auxiliaries).

Pump conversion input = ρgH_pump V/(3.6×10⁹η_pump). Available pump power excludes pumping auxiliaries from import headroom. Minimum recharge time uses maximum available pumping power.

Window charging energy assumes uniform pumping throughout the entire stated window, including constant auxiliaries during that window. It is distinct from minimum-time pumping. Zero window or no pumping path cannot pass recharge.

Gross conversion round-trip ratio excludes auxiliaries. Constant-head/power arithmetic does not validate reservoir curves, hydraulic transients, civil feasibility, permissions, startup, reactive power, reliability or islanding.

Prepare evidence for review

Bring head–volume curves, pump/generator maps, seasonal usable water, auxiliary meters, interface limits and charging windows. Survey, civil, environmental, transient and control studies remain necessary.

DOE / Sandia Energy Storage Handbook

Reviewed 26 October 2026. Equations and examples are original teaching calculations; sources provide technical background, not equipment performance or project approval.

Study the calculation background Data request and evidence check

Sources and review date

Reviewed 26 October 2026. Text, diagrams and exercises are original. All numerical cases use stated teaching assumptions, rather than site measurements or manufacturer commitments. These primary sources support the technical background; verify their applicability to each project.

[S1] DOE FEMP · BESS Procurement Checklist ↗
Early procurement questions and scope.

[S2] DOE FEMP · Lithium-ion BESS Technical Specifications ↗
Customisable procurement template, not a local approval.

[S3] DOE · Energy Storage Safety Strategic Plan ↗
Lifecycle safety research and deployment context.

[S4] Sandia · Energy Storage Safety and Reliability ↗
Testing, failure and degradation background.