How to Calculate Pumped Thermal Energy Storage Efficiency
Pumped thermal energy storage (PTES) systems decouple electricity supply and demand by converting electrical energy into high-grade heat during charge and returning electricity via heat engines on discharge. Decision-makers therefore need a repeatable way to express round-trip efficiency (RTE) that captures the full cycle, from charge through dwell to discharge. This walkthrough formalises the calculation, clarifies mandatory variables, and documents validation controls so engineers and financial analysts can interpret PTES projections on equal footing.
The methodology enumerates charge and discharge energies, isolates leakage and auxiliary losses, and reconciles the resulting ratios with grid services revenue models. It also references complementary analytics such as the thermal storage sizing calculator so PTES studies integrate smoothly with existing long-duration storage portfolios.
Definition and boundary conditions
Round-trip efficiency for PTES is the ratio of usable electrical energy returned during discharge to electrical energy consumed during charge once all same-cycle losses are included. Count the heat-pump charge phase, the storage dwell period, and the heat-engine discharge phase, and include auxiliary loads such as circulation pumps, compressors, recuperator fans, and control systems when they are dedicated to the PTES plant. Exclude balance-of-plant losses (for example, shared transformers) unless the project finance model allocates them explicitly.
Track one complete cycle from the start of charging until the discharge window closes. Attribute standby leakage between those events to the same cycle, and when PTES units stack services, isolate the energy windows that belong to the RTE under review to avoid double counting.
Variables, symbols, and units
Use megawatt-hours (MWh) for all energy terms and percentages for dimensionless ratios. Consistent SI units simplify reconciliation with other decarbonisation metrics such as energy reuse effectiveness, explained in the energy reuse effectiveness walkthrough. The following variables underpin the calculation:
- Ec – Electrical energy absorbed during charging (MWh).
- Ed – Electrical energy exported during discharge before auxiliary deductions (MWh).
- Eaux – Auxiliary electrical energy drawn by pumps, controls, or fans (MWh).
- fleak – Fraction of stored thermal energy lost during dwell (percentage of Ec).
- Eleak – Leakage loss, computed as Ec × fleak (MWh).
- Enet – Net electrical energy delivered after losses, max(Ed − Eaux − Eleak, 0) (MWh).
- ηgross – Gross round-trip efficiency = Ed ÷ Ec.
- ηnet – Net round-trip efficiency = Enet ÷ Ec.
Auxiliary consumption may come from AC or DC sources. Convert all telemetry to MWh referenced to the same voltage boundary as Ec and Ed. This alignment prevents reporting inflated efficiencies that quietly exclude internal consumption.
Governing equations and derived metrics
The efficiency workflow rests on a concise set of deterministic equations. Present them consistently in engineering notebooks and investment memos to maintain traceability:
1. Eleak = Ec × fleak
2. Enet = max(Ed − Eaux − Eleak, 0)
3. ηgross = Ed ÷ Ec
4. ηnet = Enet ÷ Ec
Report ηgross and ηnet together. The gross metric reveals the combined effectiveness of the heat pump and heat engine, while the net metric captures auxiliary penalties. Confirm whether vendor datasheets cite gross or net values before reconciling with your models.
Step-by-step calculation workflow
1. Establish metering boundaries
Confirm the electrical meters or SCADA tags that capture charge and discharge energy, align timestamps to the same cycle, and create virtual meters when PTES shares infrastructure with other assets.
2. Aggregate charge energy
Sum electrical energy drawn by the heat-pump stage during charge, include any pre-heating or defrost cycles needed to reach target temperature, and record the total as Ec.
3. Capture discharge output
Measure generator-side electrical energy exported during discharge to determine Ed, filtering out parasitic recirculation within the plant to avoid overstating useful output.
4. Quantify auxiliary consumption
Track pump drives, valve controllers, and thermal management subsystems through the cycle, convert kilowatt traces into MWh to obtain Eaux, and document any nameplate-based estimates when telemetry is missing.
5. Model leakage and publish results
Determine fleak from laboratory calorimetry, computational fluid dynamics, or historical field data, apply it to Ec to compute Eleak, scale the coefficient for longer dwell periods using the storage medium’s decay constant, and then derive ηgross and ηnet while recording cycle context—date, ambient conditions, durations, and operational mode.
Validation and quality assurance
Validate telemetry by reconciling energy balances. The sum of Ed, Eaux, and Eleak should sit within ±3% of Ec; larger gaps point to metering drift or untracked loads. Compare ηgross with design-point coefficients of performance for the heat pump and heat engine, and cross-check leakage rates against thermal imagery or storage medium temperature decay.
Complement the balance check with temporal validation by plotting efficiency versus ambient temperature, dwell duration, and state-of-charge; light-touch Monte Carlo perturbations on Eaux and fleak provide confidence bands for merchant revenue stacks.
Limits, sensitivities, and communication
The efficiency model assumes a single-cycle perspective. Extend the leakage term when dispatch involves multi-day dwell periods, and track degradation effects such as heat exchanger fouling or compressor wear through periodic re-baselining.
Communicate results with transparent caveats. Decision-makers should see sensitivity tables that vary leakage and auxiliary loads alongside dispatch profiles, similar to scenario work in the battery energy arbitrage margin study. When reporting to regulators, pair ηnet with meter calibration certificates and notes on any estimation procedures.
Embed: Pumped thermal energy storage efficiency calculator
Use the embedded calculator to combine measured or modelled charge energy, discharge output, and optional loss terms to obtain gross and net round-trip efficiency instantly.