Energy mass balanceCostingHydro
Small and micro hydropower plant (Pelton / Turgo / crossflow)
Run-of-river impulse hydro from 50 kW to 10 MW: flow-duration curve with residual flow, design flow from installed kW, part-load turbine efficiency, annual energy, ORNL CAPEX scaling law, O&M and LCOE in EUR 2014.
Open Jack
Founder · OpenJack
- CurrencyEUR 2014
- Battery limitinstalled
- 88 documented assumptions
- Updated27 Oct 2026
Mass and energy balance
What the asset draws and delivers for the case and load you choose.
Reference case
Long-term mean flow at the intake, from gauging or a regional study. It scales the flow-duration curve below. The 0.45 m3/s default is an illustrative mountain stream, not a site.
Flows
Asset
Small and micro hydropower plant (impulse turbine)
- Out: Electricity (net)—
Annual quantities at the current usage. Band width: share of energy in; non-energy flows are not to scale.
Rated electrical output at the generator terminals (RETScreen eq. 10). Design flow follows from it, the gross head and the design-point losses. 50 kW to 10 MW: below 50 kW (pico and the smallest micro plants) the cost law still applies down to 10 kW but the LCOE leaves any published range. A capacity the stream cannot deliver at its peak flow, even without losses, is refused.
- Design flow
- — m3/s
- Average electrical output
- — MW
- Annual energy delivered
- — MWh/year
- Capacity factor
- — %
CAPEX
Specific cost at this size, what backs it, and how it behaves with scale.
Specific CAPEX at this size
—
Reference size 1,630 kW
ORNL/TM-2015/471 Eq. 3
Model value: the reference case, scaled to the capacity with the ORNL exponent 0.81 from its 1,630 kW sample mean. Customized: the value below is used as entered at every capacity, with no scaling, and is no longer a sourced figure. O&M is then 2.5 % of it per year.
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- Ex-factory
- Installed· this figure
- Fully financed
Included
- Equipment
- Installation, civil works and engineering
Not included
- Working capital
- Contingency
Added at project level
- Working capital layer, from the project settings
- Contingency, from the project settings
Project figures
Values passed to project mode when this asset is added to a project.
Small and micro hydropower plant (impulse turbine)Concept sketch, not to scale · drag to rotate
- Electricity (net) outMain product
- —
- CAPEX to the battery limit
- —
- Fixed O&M
- —
- Variable O&M, excluding feedstocks
- 0 EUR/year
- Asset lifetime
- 30 years
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Levelised cost of electricity
A standalone indicator for a quick read. Project mode recomputes it for the whole system.
—
- Capital component of the LCOE—
- O&M component of the LCOE—
Linked to the balance above
Long-term mean flow at the intake, from gauging or a regional study. It scales the flow-duration curve below. The 0.45 m3/s default is an illustrative mountain stream, not a site.
Impulse turbine family. It sets the best efficiency (ESHA 2004 Table 6.7: Pelton multi-jet 0.90, single jet 0.89, Turgo 0.85; crossflow 0.79 from the RETScreen curve) and the part-load behaviour. The calculator flags a head outside the ESHA range of the selected type; it does not switch type for you.
Level difference between intake water surface and the runner (impulse turbines sit above tailwater, so the tailrace effect of RETScreen eq. 9 is ignored). 20 to 550 m stays inside the ORNL cost-model range (1.5 to 563 m).
Flow-duration curve, flow exceeded 0 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 5 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 10 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 15 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 20 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 25 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 30 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 35 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 40 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 45 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 50 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 55 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 60 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 65 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 70 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 75 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 80 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 85 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 90 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 95 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow-duration curve, flow exceeded 100 % of the time, in % of the mean flow. The 21 points (0 to 100 % in 5 % steps, RETScreen §2.1.1) are rescaled so that their trapezoidal mean is exactly the mean flow above. Must not increase from one point to the next. The default shape is an illustrative snow- and rain-fed mountain stream; replace it with your gauged curve.
Flow left in the stream, in % of the mean flow, subtracted at every point of the curve (RETScreen eq. 3). ESHA 2004 §7.4.3.2.2: 10 % of the average flow is the typical figure. Your permit governs.
Intake, trashrack and penstock head loss at design flow, in % of gross head. Scales with (Q/Qdes)^2 at part load (RETScreen eq. 8). 5 % is the RETScreen worked case; its costing sheet gives 1-5 % intake/misc. and 1-4 % penstock, hence 1-9 %.
RETScreen user input with no grounded default. 0 is optimistic: set your transformer's losses.
Station auxiliaries (controls, cooling, lighting). RETScreen user input with no grounded default; 0 is optimistic.
Share of the year's energy lost to outages and trashrack cleaning (RETScreen eq. 12). No grounded default; 0 is optimistic.
Real discount rate for the capital recovery factor. 8 % over 30 years is the ESHA 2004 Chapter 8 basis. Costs are in constant EUR 2014, so the rate must be real.
Annuity period. ESHA 2004 uses 30 years; civil works last longer, electro-mechanical equipment is usually refurbished within that span. ORNL does not cost that rehabilitation, so it is not modelled.
Share of the energy used on site (valued at the avoided purchase price); the rest is exported. Default 0 = full export.
Value of exported energy. Default 120.3 EUR/MWh = EEG 2023 §40(1) no. 1 reference value for hydropower up to 500 kW (nominal EUR, 2023 law); larger plants fall in lower §40 bands. Replace with your tariff or PPA.
Value of self-consumed energy. Default 194.1 EUR/MWh = Eurostat nrg_pc_205, EU27 2024-S2, non-household band 500-1999 MWh, excluding VAT and recoverable taxes (nominal EUR 2024).
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Benchmarks
This model's figures against published references and reference cases.
Specific CAPEX, scaled or customized, EUR/kW
1,882 ORNL/TM-2015/471 §3.1
3,357 ORNL/TM-2015/471 §3.1
4,140 ORNL/TM-2015/471 §3.1
Reference cases at this size and usage
Log in to compare the reference cases.
All results
Every model output at the current settings, grouped, with the sensitivity charts.
45 outputs · 6 groups · 11 also shown above, dimmed
Stream and sizing
8- Design flow / mean flow
- Computingratio
- Residual flow
- Computingm3/s
- Peak available flow
- Computingm3/s
- Mean turbined flow
- Computingm3/s
- Share of the mean stream flow turbined
- Computing%
- Annual turbined water volume
- Computingm3/year
- Rated output never reached
- Computingflag
Turbine and efficiency
8- Water-to-wire efficiency at design flow
- Computing%
- Turbine best efficiency
- Computing%
- Generator efficiency
- Computing%
- Flow-weighted turbine efficiency
- Computing%
- Part-load efficiency penalty
- Computing%
- Net head at design flow
- Computingm
- Specific water consumption
- Computingm3/kWh
- Head outside the turbine's range
- Computingflag
Energy
6- Full-load hours
- Computingh/year
- Capacity factor outside the IRENA small-hydro range
- Computingflag
Costs
14- Specific installed CAPEX
- ComputingEUR/kW
- Specific CAPEX of the reference case
- ComputingEUR/kW
- Case specific CAPEX at the 1,630 kW reference
- ComputingEUR/kW
- Size factor on the specific CAPEX
- Computingratio
- Annual O&M per kW
- ComputingEUR/kW/year
- Capital recovery factor
- Computing1/year
- Annualised CAPEX
- ComputingEUR/year
- Total annual cost
- ComputingEUR/year
ORNL references and flags
6- ORNL Eq. 3 total (model reference)
- ComputingEUR
- ORNL Eq. 3 in source currency (model reference)
- ComputingUSD
- ORNL Table A.9 E&C row (model reference)
- ComputingEUR
- Spread between ORNL Eq. 3 and its Table A.9 E&C row
- Computing%
- Inside the ORNL cost-model range
- Computingflag
- ORNL Eq. 6 O&M (model reference)
- ComputingEUR/year
Value of output
3- Blended value of output
- ComputingEUR/MWh
- Annual value of output
- ComputingEUR/year
- Indicative net annual margin
- ComputingEUR/year
Sensitivities
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Sources
88 documented assumptions · 7 sources
- msessd.ioe.edu.npRETScreen Engineering & Cases Textbook, Small Hydro Project Analysis (NRCan 2004)FDC energy model eqs. 3, 7-12 and crossflow efficiency (Appendix A)
- canyonhydro.comESHA (2004) Guide on How to Develop a Small Hydropower Plantturbine head ranges, turbine and generator efficiencies, residual flow, 8 %/30-year basis
- info.ornl.govORNL/TM-2015/471 Hydropower Baseline Cost Modeling v2 (2015)canal/conduit ICC law Eq. 3, Table A.9 construction row, application range, -50 %/+100 % site spread, O&M Eq. 6 and 2.5 % of ICC, canal cost quartiles
- data-api.ecb.europa.euECB reference rate USD/EUR, 2014 annual average 1.3285
- irena.orgIRENA (2012) Hydropower cost analysissmall-hydro O&M 1-6 %, capacity factor 20-95 %
- gesetze-im-internet.deEEG 2023 §40reference value for hydropower up to 500 kW, 12.03 ct/kWh
- ec.europa.euEurostat nrg_pc_205, EU27 2024-S2 non-household electricity price, 500-1,999 MWh band, excl. VAT and recoverable taxes
About
Calculator context
About
Calculator context
Screening techno-economics for a small (under 10 MW) or micro (under 100 kW) run-of-river hydropower plant with an impulse turbine: Pelton (multi-jet or single jet), Turgo or crossflow. It is built for mountain streams, rehabilitated mill sites, community and off-grid schemes, where the question is how much energy the stream really gives and what a kWh costs.
Energy follows the RETScreen Small Hydro model (NRCan 2004). The stream is described by its mean flow and a 21-point flow-duration curve (0 to 100 % exceedance in 5 % steps), rescaled to that mean. A residual flow (ESHA default 10 % of mean flow) is left in the stream at every point. The installed capacity in kW sets the design flow through RETScreen eq. 10, with ESHA turbine and generator efficiencies and the design-point hydraulic loss. At each curve point the turbined flow is capped at the design flow, the head loss scales with (Q/Qdes)^2, and the turbine efficiency follows its part-load curve: the RETScreen formula for crossflow, a flat best efficiency inside the ESHA operating band for Pelton and Turgo (zero below 10 % or 30 % of design flow). Power is integrated over the curve (RETScreen eq. 12) into annual energy, capacity factor and full-load hours, and exported to project mode as an hourly electricity flow in MW.
Capital cost uses the ORNL/TM-2015/471 canal/conduit law (Eq. 3): ICC = 9,297,820 x P[MW]^0.810 x H[ft]^-0.102 in 2014 USD, fitted on 62 projects from 10.5 kW to 13 MW (mean 1.63 MW), converted to EUR 2014 at the ECB 2014 average of 1.3285 USD/EUR. It is written as a scaling law: the case cost at the 1,630 kW sample mean times (P/1,630 kW)^(0.81-1). Its P^-0.19 per-kW slope is the strong economy of scale of small hydro: at 100 m head the specific cost falls from about 6,800 EUR/kW at 50 kW to about 2,500 EUR/kW at 10 MW. A second reference case uses ORNL's construction-stage row (Table A.9, 7,188,377 P^0.81 H^-0.10, 20 built projects), about 22 % lower. ORNL's Table A.9 prints a different E&C row for the Eq. 3 coefficient; the calculator shows that row and the spread instead of hiding it. A Customized option takes your own quote in EUR 2014 on the same scope, bounded by ORNL's -50 % / +100 % site spread (825-16,140 EUR/kW), and uses it as entered at every size. O&M is a model value: 2.5 % of the capital cost per year, and from 3 MW the lesser of that and ORNL Eq. 6 (2.5 % of the quote under Customized). The LCOE annualises the capital cost with a real discount rate (default 8 % over 30 years, ESHA) and is in constant EUR 2014. Licensing and development (outside the ORNL scope) and electro-mechanical rehabilitation (not costed by ORNL) are not included.
At the defaults (500 kW, 100 m gross head, multi-jet Pelton, 0.45 m3/s illustrative stream) the plant runs at a 49.3 % capacity factor, delivers 2,161 MWh a year, costs 4,422 EUR 2014/kW and produces at 116.5 EUR 2014/MWh. At a fixed stream, a larger plant lowers the cost per kW but raises the LCOE once it outgrows the flows (capacity factor falls): the sizing chart shows that trade-off. An optional value-of-output block blends an export value (EEG 2023, up to 500 kW) and an avoided purchase price (Eurostat 2024-S2). Those are nominal 2023-2024 figures, so the margin they give is indicative only.
The calculator detects and flags rather than corrects: a head outside the ESHA range of the chosen turbine, a design flow above the peak available flow, a capacity factor outside IRENA's 20-95 % small-hydro range. A capacity the stream could not deliver even without any loss is refused. The default flow-duration curve is illustrative: replace it with gauged data before defending a figure.
Model
258 variables — inputs, calculations and outputs, with their dependencies.
Model
258 variables — inputs, calculations and outputs, with their dependencies.
| Variable | Value | Unit | Depends on |
|---|---|---|---|
| 1 | — | — | |
| 500 | kW | — | |
| 100 | m | — | |
| 0.45 | m3/s | — | |
| 600 | % of mean | — | |
| 300 | % of mean | — | |
| 230 | % of mean | — | |
| 185 | % of mean | — | |
| 155 | % of mean | — | |
| 132 | % of mean | — | |
| 115 | % of mean | — | |
| 101 | % of mean | — | |
| 89 | % of mean | — | |
| 79 | % of mean | — | |
| 70 | % of mean | — | |
| 62 | % of mean | — | |
| 55 | % of mean | — | |
| 48 | % of mean | — | |
| 42 | % of mean | — | |
| 37 | % of mean | — | |
| 32 | % of mean | — | |
| 27 | % of mean | — | |
| 22 | % of mean | — | |
| 17 | % of mean | — | |
| 10 | % of mean | — | |
| 10 | % | — | |
| 5 | % | — | |
| 0 | % | — | |
| 0 | % | — | |
| 0 | % | — | |
| 1 | — | — | |
| 0 | — | — | |
| 4422 | EUR/kW | — | |
| 0.08 | ratio | — | |
| 30 | years | — | |
| 0 | % | — | |
| 120.3 | EUR/MWh | — | |
| 194.1 | EUR/MWh | — |
| Variable | Formula | Unit | Depends on |
|---|---|---|---|
if((<)+(>)+(<=)+(<=)+(<=)+(<=)+(<)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(>)+(<)+(>=)+(<)+(>=)+(<)+(>=)+(<)+(>=)+(<)+(>=)+(<)+(>)+(<)+(>)+(<)+(<=)+(<)+(>)+(<)+(<)+(*>****(/max(**((+)*+++++++++++++++++++),)-*))>,,) | bool | ||
* | MW | ||
/ | ft | ||
* | ratio | ||
if(==,,if(==,,if(==,,))) | ratio | ||
if(==,,if(==,,))* | ratio | ||
if(<=,,if(<=,+(-)*(-)/(-),if(<=,+(-)*(-)/(-),if(<=,+(-)*(-)/(-),if(<=,+(-)*(-)/(-),if(<=,+(-)*(-)/(-),)))))) | ratio | ||
**((+)*+++++++++++++++++++) | % of mean | ||
/max(,) | m3/s per % | ||
(-*)*(-*) | ratio | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
min(max(*-,),) | m3/s | ||
if(==,max(-*(-/max(,))-*(-/max(,))^,),if(/max(,)>=,,)) | ratio | ||
if(>,,) | m3/s | ||
***(-**(/max(,))^2)**** | kW | ||
**((*+*)*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*+*) | m3/s | ||
**((+)*+++++++++++++++++++) | kW | ||
if(==,,) | USD 2014 | ||
if(==,,) | — | ||
** | EUR/year |
| Variable | Formula | Unit | Depends on |
|---|---|---|---|
*(-) | m | ||
*/max(***(-)**,) | m3/s | ||
* | % | ||
* | % | ||
**(-)* | % | ||
** | m3/s | ||
max(*-,) | m3/s | ||
/max(,) | ratio | ||
**((+)*+++++++++++++++++++) | m3/s | ||
*(-*)** | MWh/year | ||
/ | MW | ||
/max(*,)* | % | ||
/max(,) | h/year | ||
/max(,)* | % | ||
max(-/max(*,),)* | % | ||
/max(,)* | % | ||
*(-*)** | m3/year | ||
/max(*,) | m3/kWh | ||
max(***/-,) | MWh/year | ||
if(>,,) | flag | ||
if((==)*((<)+(>))+(==)*((<)+(>))+(<=)*((<)+(>))>,,) | flag | ||
if((<)+(>)>,,) | flag | ||
*^*^ | USD | ||
*(*)^*^// | EUR/kW | ||
(/max(,))^(-) | ratio | ||
* | EUR/kW | ||
clamp(if(>=,,),,) | EUR/kW | ||
/ | EUR | ||
| EUR/kW | ||
* | EUR | ||
*^*^/ | EUR | ||
(/max(,)-)* | % | ||
if((<)+(>)+(<)+(>)>,,) | flag | ||
*^/ | EUR/year | ||
if((<)*(>=)>,min(,),) | EUR/year | ||
/max(,) | EUR/kW/year | ||
if(<,/max(,),(*(+)^)/max((+)^-,)) | 1/year | ||
* | EUR/year | ||
+ | EUR/year | ||
/max(,) | EUR/MWh | ||
/max(,) | EUR/MWh | ||
/max(,) | EUR/MWh | ||
**+(-*)* | EUR/MWh | ||
* | EUR/year | ||
- | EUR/year |
Assumptions
88 assumptions used in the calculations
Assumptions
88 assumptions used in the calculations
Protects divisions; far below any physical value of the model.
Market range Not applicable (numerical guard).
0OpenJack DSL conventionUnit constant for complements such as (1 - losses) and the CRF.
Market range Exact by definition.
1Numerical constantFloor for flows and efficiencies; false value of the flags.
Market range Exact; not a parameter.
0Numerical constantWeight of the two end points in the trapezoidal integration of the flow-duration curve.
Market range Exact for the trapezoid rule.
0.5Trapezoidal ruleTurns percent inputs into fractions.
Market range Exact (1 % = 0.01).
0.011/%Unit conversionTurns fractions into percent outputs; also the upper limit of percent inputs.
Market range Exact (fraction 1 = 100 %).
100%Unit conversionConverts kW to MW for the ORNL law (P in MW) and annual energy.
Market range Exact (1 kW = 0.001 MW).
0.001MW/kWSI prefixesConverts the installed capacity to watts for the hydraulic power equation.
Market range Exact (1 kW = 1,000 W).
1000W/kWSI prefixesConverts rho g Q H (watts) to kW at each curve point.
Market range Exact (1 W = 0.001 kW).
0.001kW/WSI prefixesConverts annual energy to kWh for the specific water consumption.
Market range Exact (1 MWh = 1,000 kWh).
1000kWh/MWhSI prefixesAnnualises power into energy (RETScreen eq. 12 uses 8,760 h).
Market range 8,760 h (8,784 in a leap year).
8760h/yearCalendar conventionConverts the mean turbined flow (m3/s) into an annual volume.
Market range Exact (3,600 s per hour).
3600s/hTime unitsORNL Eq. 3 takes the head in feet: H_ft = H_m / 0.3048.
Market range Exact by definition.
0.3048m/ftInternational foot (1959)Hydraulic power rho g Q H.
Market range1000kg/m3RETScreen eq. 7 valueHydraulic power rho g Q H.
Market range9.81m/s2RETScreen eq. 7 valueSpacing of the 21 flow-duration points (0, 5, ... 100 %).
Market range Fixed by the method (21 points).
5%RETScreen §2.1.1Selector code for Pelton multi-jet in the turbine_type input.
Market range Selector code 1 (Pelton multi-jet), not a physical value.
1OpenJack selector conventionSelector code for Pelton single jet in the turbine_type input.
Market range Selector code 2 (Pelton single jet), not a physical value.
2OpenJack selector conventionSelector code for Turgo in the turbine_type input.
Market range Selector code 3 (Turgo), not a physical value.
3OpenJack selector conventionSelector code for crossflow in the turbine_type input.
Market range Selector code 4 (crossflow), not a physical value.
4OpenJack selector conventionLowest valid turbine code.
Market range Code range 1-4.
1OpenJack selector conventionHighest valid turbine code.
Market range Code range 1-4.
4OpenJack selector conventionBest efficiency of a multi-jet Pelton, flat across its operating band.
Market range ESHA lists 0.89 (1 nozzle) and 0.90 (n nozzles); manufacturer curves of large units reach higher.
0.9ratioESHA 2004 Table 6.7Best efficiency of a single-jet Pelton.
Market range One point below the multi-jet value in the same table.
0.89ratioESHA 2004 Table 6.7Best efficiency of a Turgo runner.
Market range RETScreen models Turgo as Pelton minus 0.03 (0.87 against a 0.90 Pelton); ESHA's 0.85 is the lower and is kept.
0.85ratioESHA 2004 Table 6.7Below 10 % of design flow a multi-jet Pelton is taken as off.
Market range ESHA: good efficiency from 10 % to 100 % of maximum discharge with several jets.
10%ESHA 2004 §6.2Below 30 % of design flow a single-jet Pelton or a Turgo is taken as off.
Market range ESHA: 30 % to 100 % of maximum discharge for one jet. Applied to Turgo too, since ESHA gives no Turgo-specific band.
30%ESHA 2004 §6.2Crossflow efficiency at design flow: e = a - b x - c x^14 with x = (Qd - Q)/Qd.
Market range Crossflow peaks are usually quoted 0.78-0.84 by manufacturers; no independent range cited here.
0.79ratioRETScreen Appendix ALinear part-load term of the crossflow curve.
Market range Formula coefficient; no independent range.
0.15ratioRETScreen Appendix ASteep low-flow term: makes efficiency collapse below about 10 % of design flow.
Market range Formula coefficient; no independent range.
1.37ratioRETScreen Appendix AExponent of the low-flow term.
Market range Formula exponent; no alternative cited.
14RETScreen Appendix AGenerator efficiency at 10 kW; interpolated linearly between table points.
Market range Table point; held at 0.97 above 1 MW and at 0.91 below 10 kW.
0.91ratioESHA 2004 Table 6.8Rated power of the ESHA Table 6.8 point at 10 kW (interpolation abscissa).
Market range Abscissa 10 kW of the table, not a parameter.
10kWESHA 2004 Table 6.8Generator efficiency at 50 kW; interpolated linearly between table points.
Market range ESHA 6.8 point at 50 kW; no independent range cited.
0.94ratioESHA 2004 Table 6.8Rated power of the ESHA Table 6.8 point at 50 kW (interpolation abscissa).
Market range Abscissa 50 kW of the table, not a parameter.
50kWESHA 2004 Table 6.8Generator efficiency at 100 kW; interpolated linearly between table points.
Market range ESHA 6.8 point at 100 kW; no independent range cited.
0.95ratioESHA 2004 Table 6.8Rated power of the ESHA Table 6.8 point at 100 kW (interpolation abscissa).
Market range Abscissa 100 kW of the table, not a parameter.
100kWESHA 2004 Table 6.8Generator efficiency at 250 kW; interpolated linearly between table points.
Market range ESHA 6.8 point at 250 kW; no independent range cited.
0.955ratioESHA 2004 Table 6.8Rated power of the ESHA Table 6.8 point at 250 kW (interpolation abscissa).
Market range Abscissa 250 kW of the table, not a parameter.
250kWESHA 2004 Table 6.8Generator efficiency at 500 kW; interpolated linearly between table points.
Market range ESHA 6.8 point at 500 kW; no independent range cited.
0.96ratioESHA 2004 Table 6.8Rated power of the ESHA Table 6.8 point at 500 kW (interpolation abscissa).
Market range Abscissa 500 kW of the table, not a parameter.
500kWESHA 2004 Table 6.8Generator efficiency at 1000 kW; interpolated linearly between table points.
Market range Table point; held at 0.97 above 1 MW and at 0.91 below 10 kW.
0.97ratioESHA 2004 Table 6.8Rated power of the ESHA Table 6.8 point at 1000 kW (interpolation abscissa).
Market range Abscissa 1000 kW of the table, not a parameter.
1000kWESHA 2004 Table 6.8Lower net head of the pelton range; below it the flag is raised.
Market range ESHA range 50 < Hn < 1300 m.
50mESHA 2004 Table 6.3Upper net head of the pelton range; above it the flag is raised.
Market range ESHA range 50 < Hn < 1300 m.
1300mESHA 2004 Table 6.3Lower net head of the turgo range; below it the flag is raised.
Market range ESHA range 50 < Hn < 250 m.
50mESHA 2004 Table 6.3Upper net head of the turgo range; above it the flag is raised.
Market range ESHA range 50 < Hn < 250 m.
250mESHA 2004 Table 6.3Lower net head of the crossflow range; below it the flag is raised.
Market range ESHA range 5 < Hn < 200 m.
5mESHA 2004 Table 6.3Upper net head of the crossflow range; above it the flag is raised.
Market range ESHA range 5 < Hn < 200 m.
200mESHA 2004 Table 6.3Coefficient of the canal/conduit cost law ICC = a P^0.810 H^-0.102 (P MW, H ft), Eq. 3, printed identically on p.viii, p.14 and in Table 8 p.31. Citation risk, kept visible: Table A.9 p.A-25 prints the E&C row as '9,297,820 P0.76 H-0.13', the same coefficient with other exponents, while 0.81/-0.10 are the exponents of the construction row. The calculator uses Eq. 3 as recommended and shows the Table A.9 E&C row and the spread (13.6 % at 500 kW and 100 m).
Market range Table A.9 prints the same coefficient in the E&C row with 0.76/-0.13; the construction row prints 7,188,377 P0.81 H-0.10.
9297820USD 2014ORNL/TM-2015/471 Eq. 3Capital-cost exponent on installed capacity: specific CAPEX = case cost at 1,630 kW x (P/1,630 kW)^(0.81-1), so the per-kW cost falls as P^-0.19 (x1.252 at 500 kW, x0.708 at 10 MW). The 50 kW-10 MW slider sits inside ORNL's 10 kW-13 MW application range (§4.3.3), so no reduction of the slider. Evidence medium: US sample, canals and conduits reusing existing conveyance.
Market range Table A.9 rows by capacity class print 0.77 (< 1 MW) and 0.58 (>= 1 MW, R2 0.36); not used, they would break a single law.
0.81ORNL/TM-2015/471 Eq. 3Reference size of the scaling law: the printed average capacity of the Eq. 3 sample. At 1,630 kW the size factor is 1 and the case enters unscaled (3,532.4 EUR/kW for Eq. 3 at 100 m).
Market range Sample: 10.5 kW to 13 MW.
1630kWORNL/TM-2015/471 §4.3.2Head exponent: higher head means less flow and smaller works for the same power.
Market range Appendix A rows print -0.13 and -0.10.
-0.102ORNL/TM-2015/471 Eq. 3Lower capacity of the Eq. 3 application range.
Market range 10 kW to 13 MW.
0.01MWORNL/TM-2015/471 §4.3.3Upper capacity of the Eq. 3 application range.
Market range 10 kW to 13 MW.
13MWORNL/TM-2015/471 §4.3.3Lower head of the Eq. 3 application range (1.5 m).
Market range 5 to 1,847 ft.
5ftORNL/TM-2015/471 §4.3.3Upper head of the Eq. 3 application range (563 m).
Market range 5 to 1,847 ft.
1847ftORNL/TM-2015/471 §4.3.3Capacity exponent of ORNL's Table A.9 engineering & construction row, used only for the spread output.
Market range 0.76 here against 0.810 in Eq. 3.
0.76ORNL/TM-2015/471 Table A.9Head exponent of the same Appendix A row.
Market range -0.13 here against -0.102 in Eq. 3.
-0.13ORNL/TM-2015/471 Table A.9Code of the reference cost case 'ORNL 2015 Eq. 3, engineering and construction stage'.
Market range Not applicable.
1OpenJack selector codeCode of the reference cost case 'ORNL 2015 Table A.9, construction stage'.
Market range Not applicable.
2OpenJack selector codeCoefficient of the construction-stage case. Same capacity exponent as Eq. 3, so the scaling law stays the same; about 22 % lower than Eq. 3 at 500 kW and 100 m (3,458.33 against 4,421.65 EUR/kW). O&M of the case: 2.5 % of its ICC, same document.
Market range Eq. 3 (E&C stage, 62 projects) is the other case.
7188377USD 2014ORNL/TM-2015/471 Table A.9Head exponent of the construction-stage case.
Market range -0.102 in Eq. 3.
-0.1ORNL/TM-2015/471 Table A.9Converts ORNL 2014 USD into EUR 2014 (same year, so no price index is needed).
Market range Daily rates in 2014 ran from about 1.21 to 1.39 USD/EUR.
1.3285USD/EURECB reference rate, 2014 annual averageLower bound of the customized specific CAPEX and of the clamp on the specific CAPEX (same number in the slider, the guard, the help and bounds_json). The model never goes below 1,651 EUR/kW on the slider box, so the clamp does not bind.
Market range ORNL: -50 % to +100 % around the modelled cost.
825EUR/kWORNL/TM-2015/471 p.viiiUpper bound of the customized specific CAPEX and of the clamp. It sits above the model everywhere on the slider box (highest model value 8,070 EUR/kW), so a quote twice the model is accepted at any size.
Market range ORNL: -50 % to +100 % around the modelled cost.
16140EUR/kWORNL/TM-2015/471 p.viiiAnnual O&M in % of the initial capital cost, a model value for both cases and for a customized CAPEX.
Market range2.5% of CAPEX/yrORNL/TM-2015/471 §5.5Coefficient of ORNL's capacity-only O&M model, used from 3 MW as a cap on 2.5 % of ICC.
Market range No independent range cited.
225417USD 2014/yrORNL/TM-2015/471 Eq. 6Capacity exponent of ORNL Eq. 6 (P in MW).
Market range No independent range cited.
0.547ORNL/TM-2015/471 Eq. 6Below 3 MW, Eq. 6 is shown but not used; the O&M is 2.5 % of ICC.
Market range3MWORNL/TM-2015/471 §5.6Converts the potential energy of the turbined water into MWh for the losses output.
Market range Not applicable (unit conversion).
3600000000J/MWhSIReference mark on the specific CAPEX: lower quartile of ORNL canal/conduit project costs, 2,500 USD/kW in EUR 2014.
Market range ORNL: 2,500-5,500 USD 2014/kW interquartile; exceptional cases from 1,000 to nearly 9,000.
1,881.82EUR/kWORNL/TM-2015/471 §3.1Reference mark on the specific CAPEX: average ORNL canal/conduit project, 4,460 USD/kW in EUR 2014.
Market range ORNL: 2,500-5,500 USD 2014/kW interquartile.
3,357.17EUR/kWORNL/TM-2015/471 §3.1Reference mark on the specific CAPEX: upper quartile of ORNL canal/conduit project costs, 5,500 USD/kW in EUR 2014.
Market range ORNL: 2,500-5,500 USD 2014/kW interquartile.
4,140.01EUR/kWORNL/TM-2015/471 §3.1Lower end of the small-hydro capacity-factor range, used by the CF flag.
Market range IRENA: 20-95 % for small hydro.
20%IRENA 2012 Table 1Upper end of the same range.
Market range IRENA: 20-95 % for small hydro.
95%IRENA 2012 Table 1SCOPE. One run-of-river impulse plant (Pelton, Turgo or crossflow), 50 kW to 10 MW, from the intake to the generator terminals (transformer and auxiliaries as optional losses). Energy follows the RETScreen Small Hydro model: flow-duration curve at 21 points, residual flow, design flow from installed capacity (eq. 10), head loss in (Q/Qdes)^2 (eq. 8), part-load turbine efficiency, power at each point (eq. 7) and trapezoidal integration (eq. 12). No storage, no pumping, no Kaplan/Francis. Not modelled: electro-mechanical rehabilitation within the lifetime, since ORNL does not cost it.
Market range Not applicable (scope statement).
—RETScreen Small Hydro chapterHYDROLOGY. The default curve (Q0 = 600 % of mean, Q50 = 70 %, Q100 = 10 %) and the 0.45 m3/s mean flow describe an illustrative mountain stream, not a measured site. Energy, capacity factor and LCOE depend on it more than on any other input; replace it with gauged or regionalised data before using a figure.
Market range Real curves vary widely between glacial, snow-fed and rain-fed streams.
—OpenJack illustrative defaultPART LOAD. Pelton and Turgo are modelled at their best efficiency across the whole operating band and at zero below it. RETScreen's full Pelton part-load formula is printed as an image in the source and could not be verified, so it is not used. Real Pelton curves droop by a few points at low flow: energy is slightly optimistic for flashy streams.
Market range Not applicable (modelling choice).
—ESHA 2004 §6.2 and Table 6.7Impulse runners sit above tailwater, so the RETScreen tailrace-backwater reduction (eq. 9) is not applied. It matters for reaction turbines at low head, which are out of scope.
Market range Not applicable (out-of-scope effect).
—RETScreen eq. 9CAPEX BOUNDARY. ORNL's initial capital cost covers civil works, electro-mechanical equipment, electrical infrastructure and engineering/construction management; it excludes licensing, project development and financing (p.11), which weigh heavily in small hydro. costs.capex.isbl exports it with battery_limit 'installed', so project mode adds working capital and contingency (about x1.17 at its defaults). Both reference cases share that scope. A customized value must be a quote on the same scope, in EUR 2014. Money basis: constant EUR 2014 (ORNL 2014 USD / 1.3285).
Market range Not applicable (boundary statement).
—ORNL/TM-2015/471 §4TRANSPOSITION. The ORNL laws are fitted on US canal/conduit projects, which reuse existing water conveyance. A new mountain diversion carries more civil works, and licensing (excluded by ORNL) is heavy for small hydro. ORNL reports averages of 4,460 USD/kW for canals and 4,800 USD/kW for new stream-reach projects, both in 2014 USD. A known site premium goes through the Customized CAPEX option, bounded by ORNL's own -50 % / +100 % site spread.
Market range Project-class averages quoted in 2014 USD; no European range cited.
—ORNL/TM-2015/471O&M is a model value, not an input. Model CAPEX: 2.5 %/yr of the initial capital cost, and from 3 MW the lesser of that and ORNL Eq. 6 (225,417 P^0.547 in 2014 USD, / 1.3285). It does not bind at the defaults (500 kW); at 10 MW and 100 m Eq. 6 gives 794 kUSD against 831 kUSD. Customized CAPEX: 2.5 % of the quote. IRENA 2012 reports 1-6 % of investment for small hydro.
Market range 1-6 % of investment per year (IRENA 2012).
—ORNL/TM-2015/471 §5.5; IRENA 2012Default 8 % real discount rate over 30 years, the ESHA 2004 Chapter 8 basis (CRF 0.08883). Costs are constant EUR 2014, so a real rate is consistent; no tax, no inflation, no debt structure.
Market range Not applicable (financial convention).
—ESHA 2004 Chapter 8VALUE. Export default 120.3 EUR/MWh (EEG 2023 §40 reference value for hydropower up to 500 kW, nominal 2023); self-consumption default 194.1 EUR/MWh (Eurostat nrg_pc_205, EU27 2024-S2, 500-1,999 MWh non-household band, excluding VAT and recoverable taxes). These are nominal 2023-2024 EUR and are not converted to EUR 2014: the net margin output mixes years and is indicative only. The LCOE does not use them.
Market range Germany only for the export value; EU average for the purchase price.
—EEG 2023 §40; Eurostat nrg_pc_205Transformer, parasitic and downtime losses are RETScreen user inputs with no grounded default (checked: RETScreen leaves them to the user). They default to 0, which is optimistic; set them from your equipment and maintenance plan. They stay inputs rather than model values because no sourced typical figure was found; a typical value from ESHA 2004 is a lead still to verify.
Market range No independent range cited.
—RETScreen eqs. 7 and 12DOMAIN. Evaluated with the calculator at the corners of capacity (50 kW, 10 MW), head (20, 550 m), the four turbine types, the two reference cases and the CAPEX source (model value, Customized at 825 and at 16,140 EUR/kW), with the default curve shape, the default sizing (design flow 1.38 x mean flow), 10 % residual flow, the default economics (8 %, 30 years) and no optional losses. The model value alone runs from about 43 EUR/MWh (10 MW, 550 m, multi-jet Pelton, construction case) to about 236 EUR/MWh (50 kW, 20 m, single-jet Pelton, Eq. 3); the Eq. 3 case alone from about 55 to 236. With the Customized extremes the span is about 22-471 EUR/MWh, and the 20-480 EUR/MWh bound covers it. Outside that sub-box the LCOE leaves the bound, and the bundle tests show it: on the boundary stream and site (1.6 m3/s, 30 % residual flow, 550 m, single-jet Pelton, 10 % downtime, 2 % + 2 % electrical losses) at 8 % and 30 years, Customized gives 15.4 EUR/MWh at 50 kW and 825 EUR/kW and 714 EUR/MWh at 10 MW and 16,140 EUR/kW. Sizing from 0.6 to 2.5 x mean flow and residual flow from 0 to 30 % widen the corner span to about 13-1,024 EUR/MWh.
Market range IRENA 2012: 0.02-0.27 USD 2010/kWh for small hydro (10 % cost of capital), more for pico; different currency, year and discount rate, not converted, so no position against it is concluded.
—Corner evaluation of this calculatorPROJECT MODE. The meta exports electricity as an hourly MW flow (annual energy / 8,760), the installed CAPEX as ISBL ('installed'), and the O&M as fixed opex. No inlet: river water is not a purchased commodity. The plant output is set by the stream, so the outlet is manual_only: OpenJack flags a mismatch with a downstream consumer and never resizes the plant.
Market range Not applicable (contract statement).
—OJ_ASSET_META_V1