Optimal Microgrid Operation with Open-cycle Ocean Thermal Energy Conversion for Islands

Abstract: Ocean thermal energy conversion (OTEC) is a zero-carbon technology that harnesses the ocean's thermal gradient to generate electricity. Among OTEC variants, open-cycle OTEC is particularly attractive to island communities, as it can co-generate electricity and freshwater. This paper develops an integrated model that captures both the thermodynamic process of open-cycle OTEC and its operational role in an island microgrid. A two-stage robust scheduling model is formulated for the island microgrid, with a budget uncertainty set to capture the renewable output deviations. The resulting model is solved via an inexact column-and-constraint generation algorithm, which accelerates convergence by permitting inexact solutions of the first-stage problem in early iterations. Numerical experiments demonstrate that open-cycle OTEC can fully substitute for conventional generators on island microgrids and provide more reliable and dispatchable output than volatile renewable sources.

• The paper develops a thermodynamic open-cycle OTEC model within a two-stage robust microgrid scheduler, coupling electricity, freshwater production, storage, demand response, and renewable uncertainty through an iCCG algorithm.
• The simulations show OTEC can replace fuel-based generation under favorable autumn conditions, while winter temperatures can nearly quadruple costs and summer pump minimum-flow constraints create unexpected inefficiencies.
• The paper demonstrates that freshwater sink capacity directly limits OTEC’s ability to displace conventional generators, while iCCG cuts runtime by up to 90% for uncertainty budgets up to Γ=7 but struggles at larger budgets.

Overview

This paper develops an integrated operational model for island microgrids that incorporate open-cycle ocean thermal energy conversion (OTEC), a technology in which warm surface seawater is flash-evaporated under vacuum, expanded through a steam turbine, and condensed by cold deep seawater—yielding both electricity and freshwater. The authors embed a component-level thermodynamic model of the OTEC plant within a two-stage robust microgrid scheduling problem, solved via an inexact column-and-constraint generation (iCCG) algorithm (2607.23546). The work addresses two gaps: most OTEC research targets closed-cycle systems and device-level design rather than open-cycle operation, and prior microgrid studies rarely treat OTEC as a dispatchable, water-coupled resource.

Thermodynamic modeling of open-cycle OTEC

The plant model comprises five components: flash evaporator, steam turbine, condenser, seawater pumps, and exhaust system. Key modeling choices include:

• Flash evaporator: heat release is scaled by an effectiveness factor $\lambda^{\mathrm{evap}}$ with empirical value 0.95 under normal conditions; steam production follows from the latent heat of vaporization.
• Turbine: isentropic expansion is handled via steam-table lookups at fixed evaporation ($21\,^\circ$C) and condensation ($12\,^\circ$C) temperatures, with turbine and generator efficiencies applied to the theoretical work.
• Condenser: cold-seawater flow is controlled so that outlet temperature equals $T^{\mathrm{cond}} - \Delta T^{\mathrm{term}}$, balancing condensation capability against pumping cost; $\Delta T^{\mathrm{term}}$ ranges from 2.8 to 5.6 $^\circ$C.
• Pumps: pump heads are computed from empirical friction, minor-loss, and density-head expressions that are nonlinear in flow velocity; piecewise linearization is used for tractability.
• Exhaust system: modeled as a fixed 7.6% fraction of gross thermal power.

A notable contribution is the four-status operational framework defined by a low-temperature signal $x^{\mathrm{OTEC}}$ (triggered when the degree of superheat falls below 1.7 $^\circ$C) and a unit commitment signal $y^{\mathrm{OTEC}}$. In "low-temperature operation," evaporator effectiveness drops to zero and pumps are shut off, capturing realistic standby behavior absent from prior models. Products of binary variables are linearized via standard techniques.

Two-stage robust scheduling formulation

The first stage fixes day-ahead generator commitment, scheduled output, and spinning reserves; standard minimum up/down time and ramping constraints apply. OTEC units carry no start-up/shut-down constraints because their components respond within one hour. The second stage dispatches generators, energy storage, OTEC units, demand response, and a shared freshwater sink under worst-case renewable deviations. Uncertainty is captured by a budget set limiting the number of periods in which PV or wind output deviates by up to 20%, with budget parameter $\Gamma$. Power flows use a PTDF-based linear network model on a modified IEEE 123-node feeder configured as an isolated island; water balance couples OTEC freshwater output, a buffer sink, and water demand response. The objective minimizes first-stage commitment cost plus worst-case second-stage operating cost.

The max–min structure is converted to a single-level problem via strong duality, with the bilinear dual–uncertainty term linearized using Big-$21\,^\circ$0 auxiliary variables, yielding a mixed-integer subproblem.

Solution methodology: iCCG

Because the master problem accumulates many binaries and cuts, the authors adopt iCCG [tsang2023inexact], which alternates between exploration (solving the master inexactly with an aggressive dynamic lower bound) and exploitation (resetting the lower bound to the last valid value and tightening the master tolerance by contraction factor $21\,^\circ$1). This trades guaranteed per-iteration optimality for faster bound improvement.

Numerical findings

Experiments use South China Sea temperature data, a 24-hour horizon, Gurobi 12.0.1, and a 20,000-second limit. Three results stand out:

1. Full substitution of conventional generation. Under default autumn conditions, OTEC serves as the primary power source throughout most of the day, and the paper claims OTEC can fully replace fuel-based generators while providing more dependable output than volatile PV and wind. A corollary of the power–water coupling is that high electricity output produces surplus freshwater, which must be absorbed by the sink.
2. Strong seasonal sensitivity—with a counterintuitive summer effect. Costs rank winter > summer > spring > autumn. Winter's low inlet temperatures trigger frequent low-temperature operation, forcing aggressive seawater flows and reliance on generators and demand response, nearly quadrupling total cost relative to other seasons. Unexpectedly, summer costs exceed spring and autumn despite higher temperatures: the warm-pump minimum flow constraint (at least 500 kg/s) forces excessive steam generation, which in turn requires elevated cold-seawater flow and pumping power. This identifies pump minimum-flow constraints—not thermodynamic potential—as a binding design consideration.
3. Water–electricity coordination matters. Demand-scaling sensitivity shows a steeper cost gradient along the electricity axis, since OTEC's freshwater capacity exceeds its power capacity. With a reduced sink height ($21\,^\circ$2 m instead of 20 m), sink saturation forces generator commitment even at high electricity demand, demonstrating that sink sizing directly constrains OTEC's ability to displace conventional units.

On computation, iCCG reduces runtime by up to 90% versus standard CCG for $21\,^\circ$3 (e.g., 22.37 s vs. 243.28 s at $21\,^\circ$4). At $21\,^\circ$5, however, CCG outperforms iCCG (1,011 s vs. 13,452 s), because additional exploitation iterations compound with harder subproblems. At $21\,^\circ$6—roughly 1.3 trillion scenarios—neither algorithm converges within the limit. Sensitivity over $21\,^\circ$7 shows moderate values ($21\,^\circ$8) minimize average runtime.

Limitations and open questions

Several caveats bear directly on the headline claims. The full-substitution result holds only under autumn temperatures and the tested feeder configuration; winter results show generators remain necessary when superheat is insufficient, so the claim is season-dependent. The uncertainty model assumes a maximum relative deviation of 20% and a small budget $21\,^\circ$9, and scalability collapses beyond $12\,^\circ$0, leaving open how the framework handles larger uncertainty budgets or longer horizons. The exhaust system is modeled with a fixed consumption rate, nonlinearity is handled by piecewise approximation whose tightness is not independently validated, and the water network is simplified to a single shared sink—the multi-sink extension is acknowledged but not analyzed. Whether the iCCG advantage persists across other network topologies and cost structures also remains untested.

Conclusion

The paper provides a thermodynamically grounded, dispatch-level model of open-cycle OTEC embedded in a robust island microgrid scheduling problem, together with an efficient iCCG-based solution method. Its principal findings—that open-cycle OTEC can serve as the backbone zero-carbon resource for islands, that seasonal temperature variation can quadruple operating costs, and that water-sink sizing constrains power displacement—are supported by concrete numerical evidence, while the computational limits at high uncertainty budgets mark the current boundary of the approach.