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Mode Inverso — Per-Site Design Optimisation

Since 0.4.0 OTEX exposes a second mode of operation that flips the question OTEX answers:

Mode Question Input Output
Forward (otex-regional) What's the LCOE if I install P_gross MW at each site? p_gross LCOE, AEP per site
Inverse (otex-regional-optimal) What plant design minimises LCOE at each site? bounds on x optimal x = (p_gross, dT_WW, dT_CW, depth_CW) per site

Both modes coexist — the forward pipeline is untouched and keeps serving the case where plant size comes from an external constraint (demand, capital budget, regulatory cap). Use the inverse mode when you want OTEX itself to recommend the design.

The optimisation problem

Per site, OTEX solves a 4-D continuous non-linear program:

minimise   LCOE(x)
                                    ← continuous decision vector
   x = (p_gross,         kW, negative
        dT_WW,           °C, warm-side temperature drop
        dT_CW,           °C, cold-side temperature rise
        depth_CW)        m,  cold-water intake depth

subject to:
   physical constraints g_i(x) ≤ 0:
      • dT_WW + dT_CW + pinch margins ≤ available T_WW − T_CW
      • evaporator and condenser pinch points respected
      • pipe inner diameter ≤ max physical limit (~8 m)
      • parasitic ratio (P_pump / |P_gross|) ≤ 40 %
      • cold-water intake fits the site bathymetry
      • net power positive
   user-defined exogenous caps (any subset, all optional):
      • max AEP per plant (MWh/yr)
      • max net delivered power (MW)
      • max gross plant size (MW)
      • max total CAPEX (M USD)
      • max parasitic ratio
   box bounds on x.

Categorical design choices (cycle type, working fluid, installation type) are exogenous — they change the entire model structure entirely. Compare alternatives by running the optimiser several times with each combination.

The constrained problem is collapsed to an unconstrained one via a quadratic penalty method on every constraint. The solver is scipy.optimize.minimize(method='L-BFGS-B') operating on a normalised [0,1] cube: each variable is rescaled so SLSQP-style finite-difference gradients work cleanly across the wildly different physical magnitudes (p_gross ~10⁵ kW vs dT ~5 K vs depth ~10³ m).

Why is the user constraint mandatory in practice? Without an exogenous cap, the LCOE function is monotonically decreasing in p_gross over OTEX's modelled range — the cost correlations C ∝ p^α are concave (economies of scale) and the internal physics doesn't impose a hard upper limit on plant size. The "optimum" degenerates to the upper box bound and the solver is reduced to a box-bound oracle. Setting at least one --max-… flag — whatever cap your decision context imposes — produces a genuine interior optimum.

A typical site converges in 200-600 L-BFGS-B evaluations (0.3-1 s with polynomial fluid properties, 5-10 s with CoolProp).

Quick start

Decide what limits your plant size, then pass it on the CLI:

# "I can build no more than 100 MW gross per plant"
otex-regional-optimal Jamaica --year-start 2020 --year-end 2023 \
    --max-p-gross-MW 100

# "Each plant must stay below USD 800 M CAPEX"
otex-regional-optimal Jamaica --year-start 2020 --year-end 2023 \
    --max-capex-MUSD 800

# "I want at most 50 MW of net delivered power per site"
otex-regional-optimal Jamaica --year-start 2020 --year-end 2023 \
    --max-p-net-MW 50

The Python API mirrors the CLI:

from otex.optimization import (
    run_regional_optimization, Bounds, UserConstraints,
)

df = run_regional_optimization(
    studied_region='Jamaica',
    year_start=2020, year_end=2023,
    bounds=Bounds(
        p_gross=(-500_000, -1_000),
        dT_WW=(1.0, 6.0),
        dT_CW=(1.0, 6.0),
        depth_CW=(600.0, 3000.0),
    ),
    user_constraints=UserConstraints(
        max_p_gross_MW=120,        # cap any one of these
        # max_capex_MUSD=800,
        # max_p_net_MW=50,
        # max_aep_MWh=400_000,
        # max_parasitic_ratio=0.30,
    ),
)
print(df.head())

Output columns

The optimiser writes OTEC_sites_optimal_<region>_<year_label>_<cost_level>.csv to the region directory with:

Column Meaning
id, longitude, latitude Site identifier
T_WW_design, T_CW_design Design-point temperatures used (median across the year range)
p_gross_opt_MW Optimal gross plant size
dT_WW_opt, dT_CW_opt Optimal heat-exchanger ΔT
depth_CW_opt Optimal cold-water intake depth
lcoe_min LCOE at the optimum (¢/kWh)
p_net_kW, capex_total_MUSD, opex_MUSDyr Headline numbers at the optimum
max_violation Maximum constraint violation magnitude
feasible True if max_violation ≤ 0.01 (1 % of pinch margin)
success, n_evaluations, message SLSQP diagnostics
g_dT_total, g_pinch_evap, … Per-constraint values at the optimum

How to read the results

  • feasible = True plus a small max_violation (~0.003 K) is normal. The evaporator pinch constraint is active at every LCOE-minimum, so the optimum sits exactly on it modulo numerical noise. The 1 % threshold is well below the engineering uncertainty of the pinch margin itself.
  • feasible = False at every site usually means the bounds are inconsistent with the site's available ΔT (T_WW − T_CW is too low for the requested dT_WW + dT_CW + pinch margin). Loosen the dT bounds or skip the marginal sites.
  • dT_CW_opt at the upper bound is common — bigger cold-side ΔT extracts more energy per unit mass. If you can engineer a larger cold-water HX, raising --dT-max lets the optimum keep going.
  • depth_CW_opt at the lower bound (600 m) indicates the optimum wants the shallowest cold-water intake the depth bracket allows. Real OTEC pilots have stayed at 1000 m for thermal-margin reasons; tighten --depth-min-m if you want to enforce a colder intake.

Comparing forward and inverse outputs

import pandas as pd
fwd = pd.read_csv("…/OTEC_sites_<region>_…_100.0_MW_low_cost.csv", sep=';')
opt = pd.read_csv("…/OTEC_sites_optimal_<region>_…_low_cost.csv", sep=';')

merged = fwd.merge(
    opt[['longitude','latitude','lcoe_min','p_gross_opt_MW']],
    on=['longitude','latitude'],
)
merged['ΔLCOE_pct'] = 100*(merged.LCOE - merged.lcoe_min) / merged.LCOE
print(merged[['p_gross_opt_MW', 'LCOE', 'lcoe_min', 'ΔLCOE_pct']].describe())

For Jamaica 2020-2023, the inverse mode delivers a median 12.7 % LCOE reduction vs a fixed 100 MW design.

Limitations of the MVP

  • Local optimiser, single start. L-BFGS-B is a local solver. Per-site multi-start or a global optimiser (CMA-ES, differential evolution) is a planned follow-up; for now the warm-start that respects active user constraints gives reproducible and good — but possibly not globally optimal — results.
  • Cost correlations were calibrated around 100 MW. Designs outside [10, 200] MW are mild extrapolations of OTEX's economic scheme; the optimisation itself is mathematically valid but the numerical LCOE for very small or very large optima carries extra uncertainty. Pin --max-p-gross-MW to a realistic upper bound to stay in the calibrated range.
  • No portfolio-level constraints. Each site is optimised independently. Joint constraints (regional capacity target, shared transmission infrastructure, complementarity bonuses) are a follow-on feature.