Graham Smith

Working at the interface of electricity and chemistry


Author: Graham

  • RFB Analysis For Tom

    Took about 20 min, cost ~ £0.54.

    Vanadium Flow Battery — Technoeconomic Analysis
    Long-duration storage · Energy arbitrage · GB day-ahead market

    Vanadium flow battery technoeconomics

    A live discounted-cash-flow model for a grid-connected vanadium redox flow battery (VRFB) run on daily price arbitrage — charge at the cheapest hours, discharge at the dearest. Costs follow the standard power-and-energy decomposition; revenue uses 2024-calibrated GB day-ahead spreads. Every assumption below is editable.

    Net present value
    Internal rate of return
    vs 8% discount rate
    Discounted payback
    over 20-yr life
    Levelised cost of storage
    vs spread captured
    Total CAPEX
    CAPEX intensity
    Power rating
    Year-1 net cash
    Energy traded / yr
    System size
    Capital cost (CAPEX)
    Operation & market
    Financial
    Advanced & scaling

    Where the capital goes

    Energy-scaling vs power-scaling components

    A typical trading day

    Cheapest hours charge · dearest hours discharge

    Cumulative discounted cash flow

    Where the line crosses zero is the payback point; its end value is the NPV

    NPV across system size

    Soft costs scale sub-linearly, so £/MWh improves with scale

    Annual economics (Year 1)

    The operating engine behind each year’s cash flow

    Method & assumptions

    How this model is built, and where the defaults come from

    Defaults & sources. CAPEX uses the standard power (£/kW) + energy (£/kWh) split from grid-storage cost studies (PNNL / Viswanathan et al. 2022 list ~$350/kW power and ~$178/kWh energy for VRFB; Minke & Roznyatovskaya techno-economic breakdowns). Arbitrage revenue is calibrated to the 2024 GB day-ahead market — average daily price spread ≈ £54/MWh, annual baseload ≈ £72/MWh (gridcog; Modo Energy; Ofgem/Elexon). LCOS, NPV, IRR and discounted-payback follow conventional DCF practice. The hourly price series is a deterministic, seeded representation tuned to those two published statistics — it captures realistic intraday and seasonal shape but is not the literal historical dataset; swap in your own price file for a hard number.

    Not investment advice   A screening tool for comparison and sensitivity, not a bankable model. Real projects layer in balancing-mechanism, ancillary and capacity-market revenue, degradation testing, financing structure and site-specific civil costs.

  • AI Fuel Cell Calculator

    I’ve been exploring the capabilities of LLMs for supporting my technical work. I’ve been meaning to make a utility calculator for fuel cell testing for a number of years, so I’m defining the problem and letting Claude (Opus 4.8) do the physics and coding with me doing a final quality check.

    Psychrometrics · humidified gas streams

    Humidity ↔ Dew Point

    Convert between relative humidity and dew point for a humidified hydrogen or air stream, 25–90 °C and 0–300 kPa(g).

    2590 °C
    0300 kPa(g)
    0100 %
    Dew point
    40.0°C
    at 60.0 °C, 150 kPa(g)
    Saturation pressure psat(T)
    Water vapour pressure pw
    Absolute pressure
    Water mole fraction
    Molar ratio (mol H₂O / mol dry)
    Humidity ratio (mass) H₂

    Method & assumptions

    Saturation vapour pressure uses the Arden Buck (1996) equation over liquid water, accurate across 0–100 °C. The relative-humidity ↔ dew-point conversion (RH = psat(Tdew) / psat(T)) depends only on temperature and is independent of total pressure.

    Total pressure and gas choice set the amount of water: the mole fraction (pw / Pabs) and the mass humidity ratio ((Mw/Mgas) · pw/(Pabs−pw)). Because hydrogen (2.016 g/mol) is ~14× lighter than air (28.96 g/mol), the same dew point carries ~14× more water per unit mass of gas — a key driver of fuel-cell water management.

    Ideal-gas behaviour is assumed; the vapour-pressure enhancement factor (~0.3–1% at these pressures) is neglected. Atmospheric pressure taken as 101.325 kPa.

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