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Run-of-river low-head hydropower plant (Kaplan / bulb)

Low-head run-of-river plant (6-30 m) with Kaplan or bulb turbines: site flow-duration curve, residual flow and part-load efficiency give energy and capacity factor; ORNL capital, licensing and O&M costs in EUR2014 give the LCOE.

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Open Jack

Founder · OpenJack

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  • CurrencyEUR 2014
  • Battery limitinstalled
  • 105 documented assumptions
  • Updated27 Oct 2026

Mass and energy balance

What the asset draws and delivers for the case and load you choose.

Reference case

Percent of the year during which the available flow (river flow minus residual flow) reaches the design flow: the sizing decision against the river, and the lever that sets the capacity factor (Q20 about 37 %, Q50 about 61 % on the default curve). 30 % (Q30) is the ORNL/Reclamation rule of thumb for the best installed capacity per dollar. At a fixed installed capacity, moving it changes the river the plant needs: the implied median flow Q50 goes from about 45 m3/s at Q20 to about 157 m3/s at Q50 (10 MW, 10 m).

Flows

    Asset

    Run-of-river low-head hydropower plant

    • Out: Electricity (busbar)—

    Annual quantities at the current usage.

    Electrical capacity at the plant busbar after generator and transformer losses. It sets the design flow through the head and the water-to-wire efficiency. The ORNL cost equations are refused below 3 MW (NSD and O&M validity floor); for an existing-weir (NPD) site the ORNL equation stops at 105 MW.

    Design flow
    — m3/s
    Implied median river flow (Q50)
    — m3/s
    Annual energy
    — MWh/year
    Average electrical output
    — MW

    CAPEX

    Specific cost at this size, what backs it, and how it behaves with scale.

    Specific CAPEX at this size

    —

    Reference size 10 MW

    ORNL Eq. 2

    Model value = the ORNL equation of the selected case, scaled with capacity and head. Customized = your own quote per kW, used as entered at every capacity and head (no capacity law, no head term, no clamp). The figure is then no longer sourced.

    Retained ICC per kW by installed capacity

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    1. Ex-factory
    2. Installed· this figure
    3. Fully financed
    CAPEX at the battery limit—
    Working capital, contingencyproject level

    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.

    Concept sketch, not to scale · drag to rotate

    Electricity (busbar) outMain product
    —
    CAPEX to the battery limit
    —
    Fixed O&M
    —
    Variable O&M, excluding feedstocks
    0 EUR/year
    Asset lifetime
    40 years

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    Levelised cost of electricity

    A standalone indicator for a quick read. Project mode recomputes it for the whole system.

    —

    • LCOE: ICC component—
    • LCOE: licensing component—
    • LCOE: O&M component—

    Linked to the balance above

    Percent of the year during which the available flow (river flow minus residual flow) reaches the design flow: the sizing decision against the river, and the lever that sets the capacity factor (Q20 about 37 %, Q50 about 61 % on the default curve). 30 % (Q30) is the ORNL/Reclamation rule of thumb for the best installed capacity per dollar. At a fixed installed capacity, moving it changes the river the plant needs: the implied median flow Q50 goes from about 45 m3/s at Q20 to about 157 m3/s at Q50 (10 MW, 10 m).

    Headwater minus tailwater level at design conditions. The slider starts at 6 m because the ORNL new-development cost equation is fitted on 19.3 ft (5.9 m) and above; the tailwater rise during floods is not modelled.

    Flow left in the river and never turbined, as a multiple of the flow exceeded 95 % of the time. 1 x Q95 is the UK starting point quoted by ESHA. The French/Portuguese rule (10 % of the mean flow) cannot be computed from a flow-duration curve whose top is open.

    Sets the peak turbine efficiency (ESHA Table 6.7). The part-load curve shape is RETScreen's Kaplan curve in both cases; a single-regulated machine in practice also has a narrower operating range, which is not modelled.

    ORNL licensing equations (INL 2003 escalated to 2014$), which ORNL calls order-of-magnitude estimates. They are a development cost outside the ICC. When included, they are part of the total capital cost exported to the project CAPEX field.

    Real weighted average cost of capital applied to constant 2014 EUR. 0.062 is the ORNL LCOE basis. Costs are not escalated, so a nominal rate would be inconsistent.

    Annuity period for the capital cost in this calculator. 20 years is the ORNL LCOE basis; civil works physically last much longer, so a longer period lowers the LCOE. The project mode receives a 40-year service life instead (IRENA: 40 years or more for electro-mechanical equipment, 50-100 years for civil works).

    Flow exceeded 20 % of the time, divided by the median flow Q50. The turbine is assumed to run at design flow for at least the wettest 20 % of the year. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 25 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 30 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 35 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 40 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 45 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 55 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 60 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 65 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 70 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 75 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 80 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 85 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 90 % of the time, divided by the median flow Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Flow exceeded 95 % of the time (Q95) divided by Q50. It also sets the residual flow. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Lowest flow of the curve (exceeded 100 % of the time) divided by Q50. Enter the site flow-duration curve (5 % steps, as in RETScreen). The default is the ESHA example curve, a flashy small stream: illustrative only. The curve must not increase with duration; the slider band is the ESHA shape raised to the power 0.75 (flatter) to 1.2 (flashier).

    Levelised cost of electricity by design flow exceedance

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    Benchmarks

    This model's figures against published references and reference cases.

    Retained ICC per kW, EUR/kW

    1,882 ORNL section 3.1

    3,011 ORNL section 3.1

    4,140 ORNL section 3.1

    4,893 ORNL section 3.1

    LCOE in USD2014, USD/MWh

    80 ORNL §6.2

    100 ORNL §6.2

    200 ORNL §6.2

    210 ORNL §6.2

    Reference cases at this size and usage

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    All results

    Every model output at the current settings, grouped, with the sensitivity charts.

    57 outputs · 5 groups · 13 also shown above, dimmed

    Hydrology and design flow

    9
    Design flow
    Computingm3/s
    Implied median river flow (Q50)
    Computingm3/s
    Implied Q95 flow
    Computingm3/s
    Residual (ecological) flow
    Computingm3/s
    Minimum technical flow
    Computingm3/s
    Best-efficiency flow
    Computingm3/s
    Design flow / median flow
    Computingratio
    Net head at design flow
    Computingm
    Gross head in feet
    Computingft

    Turbine and efficiency

    5
    Peak turbine efficiency
    Computing%
    Turbine efficiency at design flow
    Computing%
    Water-to-wire efficiency at design
    Computing%
    Part-load and head-loss penalty
    Computingratio
    Energy lost to part load and head loss
    Computing%

    Energy

    9
    Annual energy
    ComputingMWh/year
    Capacity factor
    Computing%
    Equivalent full-load hours
    Computingh/year
    Average electrical output
    ComputingMW
    Power-duration integral (before availability)
    Computing%
    Turbined flow integral
    Computing%
    Annual turbined volume
    Computinghm3/year
    Specific water use
    Computingm3/kWh
    Hydraulic and conversion losses
    ComputingMWh/year

    Costs

    26
    Levelised cost of electricity
    ComputingEUR/MWh
    LCOE: ICC component
    ComputingEUR/MWh
    LCOE: licensing component
    ComputingEUR/MWh
    LCOE: O&M component
    ComputingEUR/MWh
    Retained ICC per kW
    ComputingEUR/kW
    Model ICC per kW
    ComputingEUR/kW
    Case ICC per kW at the reference size
    ComputingEUR/kW
    Capacity scale factor
    Computingratio
    Initial capital cost per kW
    ComputingEUR/kW
    Retained ICC per kW (USD2014)
    ComputingUSD/kW
    Initial capital cost (ICC)
    ComputingEUR
    Civil works
    ComputingEUR
    Electro-mechanical equipment
    ComputingEUR
    Electrical infrastructure
    ComputingEUR
    Engineering and construction management
    ComputingEUR
    Civil works per kW
    ComputingEUR/kW
    Electro-mechanical per kW
    ComputingEUR/kW
    Licensing and permitting
    ComputingEUR
    Total capital cost (ICC + licensing)
    ComputingEUR
    Total capital cost per kW
    ComputingEUR/kW
    Capital recovery factor
    Computing1/year
    Annualised capital cost
    ComputingEUR/year
    Annual O&M
    ComputingEUR/year
    O&M as share of ICC
    Computing%
    O&M per kW-year
    ComputingEUR/kW/year
    Total annual cost
    ComputingEUR/year

    ORNL references

    8
    LCOE in USD2014
    ComputingUSD/MWh
    ORNL low-head LCOE band, low end
    ComputingUSD/MWh
    ORNL low-head LCOE band, high end
    ComputingUSD/MWh
    Position of the LCOE in the ORNL band
    Computing%
    Historical ICC reference, low
    ComputingEUR/kW
    Historical ICC reference, high
    ComputingEUR/kW
    Model ICC per kW, ORNL low uncertainty
    ComputingEUR/kW
    Model ICC per kW, ORNL high uncertainty
    ComputingEUR/kW

    Sensitivities

    5 charts
    LCOE and ICC per kW vs gross head

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    Scale effect vs installed capacity

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    Sizing: design flow exceedance

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    Residual flow vs energy and cost

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    LCOE vs real discount rate

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    Sources

    105 documented assumptions · 8 sources

    About

    Calculator context

    Screening techno-economics of a run-of-river hydropower plant at low head (6-30 m) with Kaplan or bulb turbines, no storage. The installed capacity is the input; the calculator returns the design flow, the river flow the plant needs, annual energy, capacity factor, capital cost with its civil / electro-mechanical split, O&M and the LCOE.

    Energy follows the RETScreen Small Hydro method (eq. 3, 7, 8, 10-12, 19) and the ESHA strip method. The site flow-duration curve (FDC) is entered at 5 % steps as multiples of the median flow. The design flow is the flow available at the design exceedance (default Q30, the ORNL/Reclamation rule of thumb) after the residual flow (default 1 x Q95, the UK starting point quoted by ESHA). At each point the turbine takes the available flow up to the design flow and stops below 15 % of it. The RETScreen Kaplan curve (best efficiency at 75 % of design flow) is scaled to a 93 % peak (ESHA, double regulated). Hydraulic losses grow with the square of the flow (5 % at design), and the generator (97 %) and transformer (99 %) losses are applied. The power-duration curve is integrated with the trapezoidal rule and multiplied by 93 % availability (ORNL from NERC GADS).

    At 10 MW and 10 m the design flow is 120.7 m3/s and the implied median river flow 65.0 m3/s. On the default curve the capacity factor is 44.9 %. The default curve is the ESHA example, a one-year record from a small, flashy stream. Large lowland rivers have flatter curves and reach 0.62-0.67 (NREL ATB bulb-Kaplan plants). Enter the site curve. The tailwater rise during floods and parasitic loads are not modelled, and the plant is treated as one equivalent unit.

    Costs are the ORNL Baseline Cost Model v2 (ORNL/TM-2015/471) in 2014$: initial capital cost (construction, equipment, engineering and construction management) for two reference cases, a new weir (NSD) or an existing weir whose dam cost is not included (NPD), scaled with capacity as (P / 10 MW)^(e - 1) around the case value; a Customized quote per kW can replace the model value, licensing (optional, order-of-magnitude), and O&M as the lesser of 225,417 P^0.547 and 2.5 % of ICC. All figures are converted to EUR2014 at the ECB 2014 average of 1.3285 USD/EUR. This is a currency conversion only, with no US-to-Europe location factor. At the default the ICC is 4,417 EUR2014/kW. ORNL states that site costs can fall between -50 % and +100 % of the parametric prediction, and the calculator shows that band. The LCOE uses a real annuity (default 6.2 % real, 20 years, the ORNL basis) on constant 2014 EUR. It comes to 123.0 EUR2014/MWh, or 163.4 USD2014/MWh, which sits inside ORNL's low-head NSD band of 100-210 USD2014/MWh at the default; a Customized CAPEX or other corners can leave the band. The project receives the total capital cost (ICC plus licensing per the selected option) as an installed CAPEX, the fixed O&M, an hourly electricity outlet in MW and a 40-year service life (IRENA: 40 years or more for electro-mechanical equipment).

    Model

    209 variables — inputs, calculations and outputs, with their dependencies.

    209 variables shown of 209
    VariableValueUnitDepends on
    10MW—
    10m—
    30%—
    1x Q95—
    1——
    1——
    0——
    4417EUR/kW—
    2——
    0.062ratio—
    20years—
    2.93ratio—
    2.47ratio—
    2.087ratio—
    1.761ratio—
    1.455ratio—
    1.227ratio—
    0.86ratio—
    0.725ratio—
    0.613ratio—
    0.5ratio—
    0.446ratio—
    0.392ratio—
    0.338ratio—
    0.283ratio—
    0.229ratio—
    0.175ratio—
    VariableFormulaUnitDepends on
    if((<)+(>)*(==)+(<=0)+(/<)*(==)+(/<)*(==)+(<)+(>)+(<0)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<)+(<0)+(if(<=,+(-)*(-)/,if(<=,+(-)*(-)/,if(<=,+(-)*(-)/,if(<=,+(-)*(-)/,if(<=,+(-)*(-)/,+(-)*(-)/)))))-*<=)+(<)+(>)+(<)+(>)+(<)+(>)+(<0)+(>=)+(<)+(<0)+(>)+(>=)*((<)+(>))>0,1,0)bool
    -*((-)/)^ratio
    *ratio
    if(<=,+(-)*(-)/,if(<=,+(-)*(-)/,if(<=,+(-)*(-)/,if(<=,+(-)*(-)/,if(<=,+(-)*(-)/,+(-)*(-)/)))))ratio
    *ratio
    *ratio
    (-)*ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(-<*,0,min((-)/max(,),))ratio
    *(-*^2)*(-*((-)/)^)/max(,)ratio
    if(==,,)USD2014
    if(==,,)—
    if(==,,)—
    VariableFormulaUnitDepends on
    if(==,,)%
    *%
    *(-)m
    *****(-)%
    */max(****,)m3/s
    *m3/s
    **m3/s
    -ratio
    /max(,)m3/s
    *m3/s
    *m3/s
    +*(*++++++++++++++++*)%
    +*(*++++++++++++++++*)%
    **%
    **h/year
    *MWh/year
    /MW
    ******/hm3/year
    ****/-MWh/year
    */max(*,)m3/kWh
    /max(*,)ratio
    (-/max(,))*%
    /ft
    *^(-)*^//EUR/kW
    (/)^(-)ratio
    clamp(*,/,/)EUR/kW
    if(>=,,)EUR/kW
    *USD/kW
    EUR/kW
    **EUR
    *if(==,,)*EUR
    *if(==,,)*EUR
    *if(==,,)*EUR
    *if(==,,)*EUR
    /(*)EUR/kW
    /(*)EUR/kW
    (>)*if(==,,)*^*if(==,+*,)/EUR
    +EUR
    /(*)EUR/kW
    *(+*)EUR/kW
    *(+*)EUR/kW
    if(==,,)/EUR/kW
    if(==,,)/EUR/kW
    if(<,/,(*(+)^)/max((+)^-,))1/year
    *EUR/year
    min(*^,****)/EUR/year
    /max(,)*%
    /(*)EUR/kW/year
    +EUR/year
    /max(,)EUR/MWh
    */max(,)EUR/MWh
    */max(,)EUR/MWh
    /max(,)EUR/MWh
    *USD/MWh
    if(==,,)USD/MWh
    if(==,,)USD/MWh
    (-)/max(-,)*%

    Assumptions

    105 assumptions used in the calculations

    • Protects divisions.

      Market range Not applicable.

      0
      OpenJack DSL convention

    • Annualisation of power into energy.

      8760h/year
      Calendar

    • Converts m3/s into m3 per hour.

      Market range Exact.

      3600s/h
      SI

    • Specific water use per kWh.

      Market range Exact.

      1000kWh/MWh
      SI

    • Unit term in the efficiency curve, the CRF and the uplift factors.

      Market range Exact.

      1
      Numerical constant

    • End-point weight of the trapezoidal integration.

      Market range Exact.

      0.5
      Numerical constant

    • Converts percent inputs and constants to fractions.

      Market range Exact.

      0.01
      Numerical constant

    • Converts fractions to percent outputs.

      Market range Exact.

      100
      Numerical constant

    • MW to kW for the per-kW costs.

      Market range Exact.

      1000kW/MW
      SI

    • MW to W in the power equation rho g Q H eta.

      Market range Exact.

      1000000W/MW
      SI

    • Turbined volume reported in hm3.

      Market range Exact.

      1000000m3/hm3
      SI

    • Power equation P = rho g Q H eta.

      1000kg/m3
      RETScreen eq. 7

    • Power equation.

      9.81m/s2
      RETScreen eq. 7

    • The ORNL cost equations take the head in feet.

      Market range Exact.

      0.3048m/ft
      International foot

    • Flow of best efficiency as a fraction of design flow.

      Market range No independent range cited.

      0.75ratio
      RETScreen App. A

    • Shape of the part-load efficiency curve.

      Market range No independent range cited.

      3.5
      RETScreen App. A

    • Flatness of the Kaplan curve around its peak.

      Market range No independent range cited.

      6
      RETScreen App. A

    • Peak efficiency of a double-regulated Kaplan or bulb.

      Market range ESHA Table 6.7 gives 0.91 (single regulated) to 0.93 (double regulated).

      93%
      ESHA Table 6.7

    • Peak efficiency when the single-regulated option is selected.

      Market range See the double-regulated entry.

      91%
      ESHA Table 6.7

    • Turbine flow below which the unit is stopped and the water spilled.

      Market range No independent range cited.

      15%
      ESHA Table 3-2

    • Generator loss, held constant over load.

      Market range ESHA Table 6.8 lists 0.95-0.98 across sizes.

      97%
      ESHA Table 6.8

    • Step-up transformer loss.

      Market range No independent range cited.

      99%
      GRASS r.green

    • Head loss at design flow; scales with (Q/Qd)^2 at part flow (RETScreen eq. 8).

      Market range No independent range cited.

      5%
      RETScreen Fig. 15

    • Applied to the FDC energy to give annual energy.

      Market range No independent range cited.

      93%
      ORNL from NERC GADS

    • Integration step of the trapezoidal rule and spacing of the FDC inputs.

      Market range Not applicable.

      5%
      ESHA §3.6

    • Below 20 % duration the turbine is assumed at design flow; this holds because t_d >= 20 % and the curve does not increase with duration.

      Market range Not applicable.

      20%
      Model grid

    • Interpolation of the FDC at the design exceedance.

      Market range Not applicable.

      25%
      Model grid

    • Interpolation of the FDC at the design exceedance.

      Market range Not applicable.

      30%
      Model grid

    • Interpolation of the FDC at the design exceedance.

      Market range Not applicable.

      35%
      Model grid

    • Interpolation of the FDC at the design exceedance.

      Market range Not applicable.

      40%
      Model grid

    • Interpolation of the FDC at the design exceedance.

      Market range Not applicable.

      45%
      Model grid

    • Upper limit of the design exceedance.

      Market range Not applicable.

      50%
      Model grid

    • Double-regulated Kaplan / bulb.

      Market range Not applicable.

      1
      Selector

    • Single-regulated Kaplan.

      Market range Not applicable.

      2
      Selector

    • Reference case 1 (default): ORNL new stream-reach development, new weir and powerhouse. ICC Eq. 2, licensing, Figure 3 split and O&M all from ORNL/TM-2015/471 (2014$). Efficiency from ESHA / RETScreen (ORNL prints none).

      Market range Not applicable.

      1
      OpenJack case selector

    • Reference case 2: ORNL non-powered dam, existing weir whose cost is not paid and not included. ICC Eq. 1, licensing, Figure 3 split and O&M all from ORNL/TM-2015/471 (2014$). Efficiency from ESHA / RETScreen (ORNL prints none). 3,540.7 EUR2014/kW and 99.22 EUR2014/MWh at the default.

      Market range Not applicable.

      2
      OpenJack case selector

    • Licensing not counted.

      Market range Not applicable.

      1
      Selector

    • Licensing at the ORNL point estimate.

      Market range Not applicable.

      2
      Selector

    • Licensing with the ORNL +20 % present-value uplift.

      Market range Not applicable.

      3
      Selector

    • New-weir ICC coefficient.

      Market range ORNL: -50 % to +100 % around any parametric prediction.

      9605710USD2014
      ORNL Eq. 2

    • Capacity exponent of the specific-ICC law: specific_capex_scaled = case ICC at 10 MW x (P / 10 MW)^(0.977 - 1), x1.028 at 3 MW and x0.964 at 50 MW. The 3-50 MW slider is inside both ORNL application ranges (NSD 3-824 MW, NPD 66 kW-105 MW), so the domain is not reduced. Low-head class: 6-30 m is 19.7-98 ft, at the bottom of the NSD sample. ORNL itself applies these equations to low-head resources (section 6.2, p. 30: 100 to 210 $/MWh for low-head NSD, 80 to 200 $/MWh for low-head NPD at 33 ft or less), and the NPD sample (31 projects, 14-356 ft) covers low head (Low Head NPDs below 32.8 ft, p. 6). The head term stays in the model. Limit: the capacity-class sub-regressions of Table A.8 (1 to <10 MW: P^1.06, R2 0.67; 10 to <30 MW: P^1.49, R2 0.46) are not the model ORNL recommends and are not used.

      Market range ORNL Table A.8 alternative NSD models: P^0.24 to P^1.49 by capacity class; no independent range cited.

      0.977
      ORNL Eq. 2

    • Head elasticity of the cost per kW. Empirical: it comes from the regression on built projects, not from physics.

      Market range No independent range cited.

      -0.126
      ORNL Eq. 2

    • Below 3 MW the input is refused rather than extrapolated.

      Market range Not applicable.

      3MW
      ORNL §4.2.3

    • Below 5.9 m a new-weir case is refused.

      Market range Not applicable.

      19.3ft
      ORNL §4.2.3

    • Existing-weir ICC coefficient.

      Market range ORNL: -50 % to +100 %.

      11489245USD2014
      ORNL Eq. 1

    • Power economy of scale, NPD.

      Market range No independent range cited.

      0.976
      ORNL Eq. 1

    • Head elasticity of NPD cost per kW (empirical).

      Market range No independent range cited.

      -0.24
      ORNL Eq. 1

    • Existing-weir cases above 105 MW are refused.

      Market range Not applicable.

      105MW
      ORNL Eq. 1

    • Existing-weir cases below 4.3 m are refused.

      Market range Not applicable.

      14ft
      ORNL Eq. 1

    • Lower guard of the model ICC per kW; never binds inside the slider box (model 2,617-4,843 EUR2014/kW). Also sets the Customized floor, 753 EUR2014/kW.

      1000USD/kW
      ORNL §3.1

    • Upper guard of the model ICC per kW; never binds inside the slider box. Also sets the Customized ceiling, 6,775 EUR2014/kW.

      9000USD/kW
      ORNL §3.1

    • New-weir licensing and permitting.

      Market range No independent range cited.

      969613USD2014
      ORNL Table 5

    • Existing-weir licensing and permitting.

      Market range No independent range cited.

      492754USD2014
      ORNL Table 5

    • Licensing scale effect.

      Market range No independent range cited.

      0.7
      ORNL Table 5

    • Optional uplift (third licensing option).

      Market range No independent range cited.

      20%
      ORNL §6.1

    • Power-law O&M.

      Market range No independent range cited.

      225417USD2014/year
      ORNL Eq. 6

    • Strong economy of scale of O&M.

      Market range No independent range cited.

      0.547
      ORNL Eq. 6

    • Cap on O&M for cheap plants.

      Market range No independent range cited.

      2.5%
      ORNL Table 9

    • Civil share of a new weir. Fixed share: civil and E-M scale identically with power and head, a stated limitation.

      Market range No independent range cited.

      50%
      ORNL Fig. 3

    • Electro-mechanical share, NSD.

      Market range No independent range cited.

      26%
      ORNL Fig. 3

    • Electrical infrastructure share, NSD.

      Market range No independent range cited.

      8%
      ORNL Fig. 3

    • Engineering and CM share, NSD.

      Market range No independent range cited.

      16%
      ORNL Fig. 3

    • Civil share, existing weir.

      Market range No independent range cited.

      49%
      ORNL Fig. 3

    • Electro-mechanical share, existing weir.

      Market range No independent range cited.

      37%
      ORNL Fig. 3

    • Electrical share, existing weir.

      Market range No independent range cited.

      5%
      ORNL Fig. 3

    • Engineering and CM share, existing weir.

      Market range No independent range cited.

      9%
      ORNL Fig. 3

    • Converts the ORNL 2014$ figures to EUR2014. Currency conversion only: no US-to-Europe location factor is applied.

      Market range No independent range cited.

      1.3285USD/EUR
      ECB 2014 average

    • Reference band for the new-weir option, compared in USD2014.

      100USD/MWh
      ORNL §6.2

    • Upper end of the new-weir band.

      210USD/MWh
      ORNL §6.2

    • Reference band for the existing-weir option.

      80USD/MWh
      ORNL §6.2

    • Upper end of the existing-weir band.

      200USD/MWh
      ORNL §6.2

    • Low end of the ICC uncertainty band.

      Market range -50 % to +100 %.

      -50%
      ORNL §6.2

    • High end of the ICC uncertainty band.

      Market range -50 % to +100 %.

      100%
      ORNL §6.2

    • Low end of the new-weir reference.

      4000USD/kW
      ORNL §3.1

    • High end of the new-weir reference.

      6500USD/kW
      ORNL §3.1

    • Low end of the existing-weir reference.

      2500USD/kW
      ORNL §3.1

    • High end of the existing-weir reference.

      5500USD/kW
      ORNL §3.1

    • Default design exceedance (input).

      Market range Slider 20-50 %.

      30%
      Kao et al. 2014

    • Default residual flow (input).

      Market range Slider 0.5-2 x Q95.

      1x Q95
      ESHA Part 2 §9

    • Not usable here: the mean flow cannot be computed from an FDC whose top 20 % is open. Convert it to a Q95 multiple by hand.

      Market range No independent range cited.

      10%
      ESHA Part 2 §9

    • Default discount rate (input 0.062).

      Market range Slider 5-10 % real.

      6.2%
      ORNL §6.1

    • Default annuity period of the calculator LCOE (input). It is not the service life exported to the project mode, which is 40 years (asset_service_life_years).

      Market range Slider 20-40 years.

      20years
      ORNL §6.1

    • Lower reference for the capacity factor.

      Market range ATB representative plants 0.333-0.665.

      0.333ratio
      NREL ATB 2024

    • Shows that flat lowland FDCs give higher CF than the ESHA default.

      Market range NSD 1-4: 0.624-0.665.

      0.665ratio
      NREL ATB 2024

    • Reference range for run-of-river capacity factor.

      53%
      Kao et al. 2014

    • Upper reference for the capacity factor.

      71%
      Kao et al. 2014

    • ENERGY MODEL. Design flow from the installed capacity (eq. 10). At each 5 % point of the FDC: available flow = river flow - residual flow (eq. 3), turbine flow = min(available, design flow) (eq. 11), zero below 15 % of design flow; net head = Hg (1 - 5 % (Q/Qd)^2) (eq. 8); power = rho g Q h_net eta_t eta_gen eta_tr (eq. 7). Annual energy = 8760 x availability x trapezoidal integral (eq. 12); CF = E / (8760 P) (eq. 19).

      Market range Not applicable.

      —
      RETScreen + ESHA

    • FDC INPUT. The site flow-duration curve is entered at 5 % steps from Q20 to Q100 as multiples of the median flow Q50. The default is the ESHA example curve, linearly interpolated and divided by its median (2.0 m3/s). The curve is scaled to the plant: the available flow at the design exceedance equals the design flow, which gives the implied median flow (65.0 m3/s at the default). The ESHA curve is a one-year example from a small, flashy stream: large lowland low-head rivers have flatter curves and higher CF (NREL ATB bulb-Kaplan NSD plants 0.62-0.67). Enter the site curve.

      Market range Slider band: ESHA shape to the power 0.75 (flatter) to 1.2 (flashier).

      —
      ESHA example FDC

    • OMISSIONS. (1) The tailwater rise at high flows (RETScreen eq. 9) is not modelled: at low head this overstates energy during floods. (2) One equivalent unit: RETScreen's multi-unit rule (flow split between identical units) would raise part-load efficiency. (3) No parasitic consumption. (4) Single-regulated turbines keep the Kaplan curve shape. (5) No seasonal or interannual variability beyond the entered FDC.

      Market range Not applicable.

      —
      Model limits

    • COST MODEL. ICC from the ORNL regressions on built US projects (construction and equipment including engineering and construction management; excludes licensing, development and financing). The head elasticity of the cost per kW (-0.126 NSD, -0.240 NPD) is empirical: it comes from the regression on built projects. It is far weaker than the growth of the design flow as head falls (Qd ~ 1/H), so the model does not claim that civil quantities were derived from the flow. The civil / E-M / electrical / engineering split uses fixed historical shares, so every line scales like the ICC.

      Market range ORNL: -50 % to +100 % around the parametric prediction.

      —
      ORNL 2015

    • CURRENCY. Every money figure is EUR2014 obtained from ORNL 2014$ at 1.3285 USD/EUR (currency conversion only, no location factor, no escalation to a later year). LCOE uses constant EUR2014 and a real discount rate, so no cost line is escalated. The meta declares EUR, currency year 2014.

      Market range Not applicable.

      —
      EUR2014

    • PROJECT EXPORT. The meta exports the total capital cost, ICC plus licensing per the selected option, as an installed CAPEX (battery_limit 'installed'). The ICC already includes engineering and construction management, so 'installed' is the right level, not 'fully_financed' (financing is excluded). In 'installed' the project cashflow adds only working capital and contingency; it adds no licensing, so licensing travels inside the exported CAPEX. O&M is exported as fixed O&M; there is no variable O&M and no fuel inlet. The asset lifetime exported is the 40-year service life, not the 20-year ORNL annuity.

      Market range Not applicable.

      —
      Meta boundary

    • BATCH ALIGNMENT. Same economic basis as the other hydro calculators of the batch: EUR2014 from ORNL 2014$ at 1.3285 USD/EUR, real discount rate (default 6.2 %) and economic lifetime (default 20 years) as user inputs.

      Market range Not applicable.

      —
      Batch convention

    • CROSS-CHECK, at the default only. At 10 MW, 10 m, Q30, 1 x Q95, new weir, licensing included, 6.2 % and 20 years, the model gives 163.4 USD2014/MWh (123.0 EUR2014/MWh), inside ORNL's low-head NSD band of 100-210 USD2014/MWh. This is a plausibility check, not a validation: ORNL's band comes from the same cost equations applied to US resource data. The existing-weir case gives 131.8 USD2014/MWh against ORNL's 80-200 band. The model ICC per kW (5,868 USD2014/kW at the default) sits inside the 4,000-6,500 $/kW of NSD C-stage projects (same currency and year). Away from the default the LCOE leaves the band: a Customized 753 EUR2014/kW quote at 50 MW and Q50 (other inputs at default) gives 26.1 USD2014/MWh, far below it.

      Market range 100-210 USD2014/MWh (NSD), 80-200 (NPD).

      —
      ORNL §6.2

    • CORNERS. Model value, default FDC: LCOE 31.7-247.0 EUR2014/MWh, CF 34.5-65.2 %, ICC 2,617-4,843 EUR2014/kW. Model value, flattest and flashiest smooth FDC of the slider band: LCOE 30.0-254.8, CF 33.4-69.0 %. With the Customized option the ICC spans 753-6,775 EUR2014/kW and the LCOE 10.4-332.3 EUR2014/MWh (753 EUR2014/kW, 50 MW, 6 m, Q50, 5 %, 40 years, licensing excluded; and 6,775 EUR2014/kW, 3 MW, Q20, 2 x Q95, 10 %, 20 years, licensing + 20 %). Irregular site curves (steep above the design point, flat at low flow) combined with a high residual flow can push CF below 30 %: that is the site signalling an oversized plant, not a model fault.

      Market range Not applicable.

      —
      Corner scan

    • Reference size Pref of specific_capex_scaled = case ICC at Pref x (P/Pref)^(e-1). 10 MW is an OpenJack convention (the default capacity), not the size of a cited cost anchor.

      Market range No independent range cited.

      10MW
      OpenJack convention

    • Lowest Customized ICC accepted (slider min and guard), EUR2014.

      Market range 1,000 to nearly 9,000 $/kW, historical extremes of built US projects.

      753EUR/kW
      ORNL section 3.1 / ECB 2014

    • Highest Customized ICC accepted (slider max and guard), EUR2014.

      Market range 1,000 to nearly 9,000 $/kW, historical extremes of built US projects.

      6775EUR/kW
      ORNL section 3.1 / ECB 2014

    • Converts the gross hydraulic energy rho g H V to MWh for the loss balance.

      Market range Not applicable.

      3600000000J/MWh
      SI

    • Benchmark for the retained ICC per kW, new weir, low end. Same ICC scope as the model (licensing and financing excluded).

      3011EUR/kW
      ORNL section 3.1

    • Benchmark for the retained ICC per kW, new weir, high end.

      4893EUR/kW
      ORNL section 3.1

    • Benchmark for the retained ICC per kW, existing weir, 25th percentile.

      1882EUR/kW
      ORNL section 3.1

    • Benchmark for the retained ICC per kW, existing weir, 75th percentile.

      4140EUR/kW
      ORNL section 3.1

    • Service life exported as meta.asset.lifetime_years: the shortest design life of a major component (electro-mechanical, 40 years or more), so the project does not buy the plant again after the 20-year ORNL annuity. Civil works last longer; the project treats the whole plant as one asset.

      Market range 40 years or more (E-M), 50-100 years (civil).

      40years
      IRENA RPGC 2023

    • LIMITS OF THE SCALE LAW. O&M at scale: the power law gives 103.2 EUR2014/kW-year at 3 MW and 28.8 at 50 MW, i.e. 0.68 % of the model ICC at 50 MW, below the 1-4 % range the same source quotes. The 'lesser of' rule is ORNL's and is kept, so large plants carry an O&M at the low end of the published range. The ICC law itself is a US regression on 18 (NSD) and 31 (NPD) built projects; no European data enter it.

      Market range Not applicable.

      —
      Model limits