ES1.2 · Pumped hydro and hydraulic design
Reservoir hydro uses natural inflow; pumped storage consumes electricity to restore water elevation. A combined plant may do both, but its natural-inflow generation is not energy recovered from charging. Define upper and lower operating levels, usable volume, pumping intake and generation outlet before calculating storage.
Learning objectives
- Calculate potential and electrical energy.
- Can it supply 5 MW for six hours?
- What average charging power is needed?
Allow 30–45 minutes including derivations and exercises. All numerical values are teaching assumptions.
1. Distinguish natural inflow and pumping
Reservoir hydro uses natural inflow; pumped storage consumes electricity to restore water elevation. A combined plant may do both, but its natural-inflow generation is not energy recovered from charging. Define upper and lower operating levels, usable volume, pumping intake and generation outlet before calculating storage.
2. Derive energy from elevation
At approximately constant head, potential energy is ρgHV. Divide joules by 3.6×10^9 for MWh. Use the volume that can actually move between permitted reservoir levels. Dead storage and environmental commitments cannot automatically be counted. Integrate changing head for a more detailed reservoir model.
Lesson service and evidence flow
3. Derive power from flow
Electrical generation is approximately ρgHQη, with Q in cubic metres per second. Turbine rating, waterways, losses and allowed operating regions limit flow. Generation power does not establish pumping power or variable-speed capability. Check startup, ramp and minimum stable output independently.
4. Close the recharge and civil scope
Charging energy is potential energy divided by pumping efficiency; delivered electricity is potential energy multiplied by generation efficiency. Add auxiliaries only where not already included. Geology, slopes, waterways, evaporation, leakage, access and water/land permissions can dominate feasibility, particularly for island projects.
5. Specify measurements and studies
A defensible pre-feasibility sheet identifies survey quality, head-volume curves, seasonal water balance, machine curves and preliminary civil scope. The simplified example below is not a hydraulic transient study, dam safety assessment or confirmation of islanding capability. Assign those studies before design approval.
Case and independent exercises
Teaching assumptions: H=100 m, V=100,000 m³, ρ=1000 kg/m³, g=9.81 m/s², generation efficiency 85%, pumping efficiency 90%, output limit 5 MW and a four-hour recharge window.
- Calculate potential and electrical energy.
- Can it supply 5 MW for six hours?
- What average charging power is needed?
Worked answers and reasoning
Attempt the exercises before opening each answer.
Answer 1
Potential energy is 27.25 MWh; generated energy is 23.1625 MWh_e. Charging needs 30.2778 MWh_e before additional excluded auxiliaries. The simplified round-trip ratio is 76.5%.
Answer 2
No: six hours needs 30 MWh_e. The energy-limited duration at 5 MW is 4.6325 hours. A larger reservoir may change energy but cannot by itself increase machine power.
Answer 3
30.2778/4 = 7.5694 MW average. Verify the pumping machine, import headroom and waterway constraints; the 5 MW generating rating does not establish this capability.
Decision method to take away
A defensible pre-feasibility sheet identifies survey quality, head-volume curves, seasonal water balance, machine curves and preliminary civil scope. The simplified example below is not a hydraulic transient study, dam safety assessment or confirmation of islanding capability. Assign those studies before design approval.
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.