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Optimal Dispatch of a Hydrogen-Colocated Renewable-Powered Desalination Plant

Guochen Zhao, Ahmed S. Alahmed

arXiv:2609.09868v1eess.SYcs.SY

TL;DR

Colocated desalination and hydrogen production create a coupled dispatch problem because water is both a product and an electrolysis input, while existing analytical policies do not capture all the relevant technologies and grid exchange. This paper develops a profit-maximizing dispatch framework and characterizes its operating modes. In the studied configurations, the hybrid RO+TDP+PV+H2 plant earns the highest daily profit, 75.945 k$.

  • Problem

    Analytical dispatch policies for the coupled thermal desalination, RO, hydrogen, and bidirectional grid setting are absent, while existing frameworks can omit the internal water dynamics of colocated hydrogen production.

    Source: §I · p. 1

  • Method

    The paper formulates a profit-maximizing model of coupled water, electricity, and hydrogen flows and characterizes threshold-based dispatch, including marginal-value priorities in net-zero operation.

    Source: §I · p. 1

  • Results

    75.945 k$ daily profit was achieved by the full RO+TDP+PV+H2 configuration, the highest among the cases studied.

    Source: B. Daily Profit Across Different… · p. 4, §V · p. 5

  • Takeaways & Limitations

    Hydrogen production can improve profit, and its value is higher when combined with hybrid desalination than with a single desalination technology.

    Source: §V · pp. 4–5

    The theorem’s generic cases assume distinct marginal values strictly inside grid prices; at boundary values an optimizer may be nonunique, without a new qualitative dispatch pattern.

    Source: Appendix B · p. 7

Abstract

from arXiv · show

This paper develops an analytical framework for profit-maximizing dispatch of water, electricity, and green hydrogen in a renewable-powered water desalination plant (WDP) combining thermal and reverse osmosis (RO) desalination. The optimal dispatch reveals that the schedules of the desalination units, electrolyzer, and grid interaction can all be characterized in closed form as functions of renewable generation. At low renewable output, the plant relies on thermal desalination and grid power while maintaining RO desalination and hydrogen production at their minimum setpoints. At high output, it reduces thermal desalination, increases RO desalination, and allocates surplus power and water to hydrogen production. For renewable output within a precomputed intermediate range, the WDP balances energy internally, allocating resources based on the relative marginal values of hydrogen and RO water. Simulations using real solar and plant data show that integrating RO and thermal desalination with renewable generation and hydrogen production achieves the highest daily profit of 75.945 k$, exceeding the best configuration without hydrogen by 15.1%.

I. INTRODUCTION

The paper addresses the lack of analytical dispatch policies for colocated desalination and hydrogen production by modeling their coupled water, electricity, and hydrogen flows. It introduces a profit-maximizing hybrid plant whose thermal unit cogenerates water and electricity.

I. INTRODUCTION

  • Analytical dispatch policies for thermal desalination, RO, hydrogen production, and bidirectional grid participation remain absent, while existing frameworks often treat water as terminal and omit colocated hydrogen dynamics.Prior studies mainly consider RO-dominant frameworks,; the paper complements the WDP framework in [7].Source: §I · p. 1
  • The profit-maximizing model captures coupling among water, electricity, and hydrogen, including electrolyzer water demand and thermal-plant cogeneration.The study also validates the analytical results with local solar data and compares daily profits across plant configurations.Source: §I · p. 1

II. HYDROGEN-COLOCATED RENEWABLE-POWERED DESALINATION PLANT

  • The plant combines thermal and membrane-based desalination with renewable generation, an electrolyzer, and grid exchange.Desalinated water is both a delivered product and an internal feedstock for electrolysis.Source: §II · pp. 1–2, §I · p. 1

1) TDP:

  • The TDP consumes fuel and jointly produces desalinated water and electricity under linear conversion relationships.Its fuel cost is assumed strictly convex, continuously differentiable, and nondecreasing.Source: 1) TDP · p. 2

2) RODP:

The plant model specifies how its desalination and electrolysis units convert inputs, then couples their water and electricity balances to market payments and a profit-maximizing dispatch problem.

2) RODP:

  • The RODP uses membrane separation to consume electricity and produce water, modeled with a constant-specific-energy approximation.Its water output is bounded between minimum and maximum flowrates.Source: 2) RODP · p. 2

3) Electrolyzer:

  • The electrolyzer consumes electricity and desalinated water to produce hydrogen under linear production and water-use relationships.Its power consumption is bounded by minimum and maximum setpoints.Source: 3) Electrolyzer · p. 2

4) Renewable Generation:

B. WDP Water, Electricity, and Hydrogen Payments

  • Delivered water equals thermal and RO output minus electrolyzer water use, while net grid exchange balances RO and electrolyzer loads against thermal output and renewable generation.Water delivery must meet a minimum requirement, and the sign of net exchange distinguishes import, export, and net-zero modes.Source: B. WDP Water, Electricity, and… · p. 2

C. WDP Profit and Dispatch Problem

  • The WDP profit function is optimized over dispatch decisions, with global optimality supported when the delivered-water constraint is nonbinding and import price is at least export price.Source: C. WDP Profit and Dispatch Problem · p. 2

III. OPTIMAL DISPATCH POLICY

Optimal WDP dispatch is organized by renewable-output thresholds into import, net-zero, and export modes, with six thresholds defining seven dispatch regions. In net-zero operation, the relative marginal values of RO desalination and hydrogen determine allocation priority.

A. Threshold-Based Dispatch

  • Renewable output determines whether the plant imports power, operates at net zero, or exports power.The three modes correspond to z > 0, z = 0, and z < 0, respectively.Source: §III · p. 2, A. Threshold-Based Dispatch · p. 3
  • The dispatch policy uses renewable-generation thresholds to set internal allocations and maximize profit within each operating mode.The threshold definitions include boundaries for grid interaction and internal allocation.Source: §III · p. 2, A. Threshold-Based Dispatch · p. 3
  • In import and export modes, the grid sets the marginal price, and the thermal desalination plant optimizes output using stationarity conditions.The resulting thermal-plant water flows are specified for those two modes.Source: A. Threshold-Based Dispatch · p. 3
  • Six thresholds define seven optimal-dispatch regions when the RO and hydrogen marginal values are distinct and strictly between grid prices.Cases outside this condition are treated in Appendix B.Source: A. Threshold-Based Dispatch · p. 3
  • In net-zero operation, π−<ρr<ρe<π+ gives hydrogen priority, while π−<ρe<ρr<π+ gives RO priority; only this mode depends on their ordering.The dispatch figure illustrates the two priority cases.Source: A. Threshold-Based Dispatch · pp. 3–4, Figure 2 · p. 3

A. Parameter Setting and Dispatch Validation

The validation uses a 2019 Dhahran solar profile and compares two price cases that prioritize hydrogen or RO. The dispatch illustrates how the units respond as solar generation increases.

A. Parameter Setting and Dispatch Validation

  • The validation uses a 2019 Dhahran solar profile derived from MERRA-2 and scaled to a 115 MW array, with representative conversion parameters and operating limits.The electrolyzer upper limit is 30 MW; RO and TDP upper limits are 8,333 m3/h and 3,000 m3/h, respectively.Source: A. Parameter Setting and Dispatch… · p. 4
  • Scenario A prices water at 0.50 and hydrogen at 5.50, giving hydrogen priority; Scenario B prices them at 0.65 and 4.50, giving RO priority.The comparison uses πw and πH2 prices, respectively.Source: A. Parameter Setting and Dispatch… · p. 4
  • As solar generation rises, the hydrogen-priority case increases electrolyzer use before RO, while the RO-priority case increases RO first; both export near peak solar output.At low and moderate solar output, both cases operate in net-zero mode; import is absent because ΓIM < 0.Source: A. Parameter Setting and Dispatch… · p. 4, Figure 3 · p. 4

B. Daily Profit Across Different Resource Compositions

Across the configurations studied, the full RO+TDP+PV+H2 system earns the highest daily profit, while the value of hydrogen production depends on the desalination technologies paired with it. The short-run analysis omits nonlinear conversion behavior and large-scale storage and distribution costs.

B. Daily Profit Across Different Resource Compositions

  • 75.945 k$ is the highest daily profit, achieved by RO+TDP+PV+H2, versus 65.998 k$ for RO+TDP+PV.The comparison covers an average daily cycle at πw = 0.575$/m3 and πH2 = 5.0$/kg.Source: B. Daily Profit Across Different… · p. 4, §V · p. 5
  • Adding hydrogen to RO+PV raises daily profit from 51.226 k$ to 59.659 k$, but remains below the 65.998 k$ earned by RO+TDP+PV.The paper reports that hydrogen's value is higher when coordinated with hybrid desalination.Source: B. Daily Profit Across Different… · p. 4

V. CONCLUSION

  • The conclusion identifies hybrid desalination, rather than a single desalination technology, as the more profitable pairing for hydrogen among the cases studied.The full RO+TDP+PV+H2 configuration achieved the highest profit.Source: §V · pp. 4–5
  • The short-run model omits nonlinear conversion behavior under different operating conditions and large-scale water and hydrogen storage and distribution costs.The paper identifies incorporating these factors into long-term planning models as future work.Source: §V · p. 5

APPENDIX A PROOF OF THEOREM 1

The proof reduces the dispatch to a convex minimization and analyzes import, net-zero, and export modes. In the import and export modes, the marginal electricity prices determine the direction of the RO and electrolyzer choices, while TDP dispatch accounts for its bounds.

APPENDIX A PROOF OF THEOREM 1

  • The proof rewrites the dispatch objective up to decision-independent constants and omits the delivered-water constraint under the nonbinding-water-constraint assumption wd ≥ Wd.It then considers an equivalent convex minimization problem.Source: Appendix A · p. 5
  • The analysis separates import, net-zero, and export modes, with IM defined by z > 0, NZ by z = 0, and EX by z < 0.Within each mode, convexity and affine or box constraints make the KKT conditions necessary and sufficient for optimality.Source: Appendix A · p. 5

1) Import and export modes:

  • In import mode, when ρr and ρe are below π+, increasing qr or qe raises the minimization objective; in export mode, when both exceed π−, increasing them lowers it.The proof derives the import and export solutions using the box constraints.Source: 1) Import and export modes · pp. 5–6
  • For the TDP, the proof applies stationarity with respect to qh and incorporates its operating bounds through complementary slackness in both import and export modes.The resulting dispatch is valid subject to the mode-specific conditions.Source: 1) Import and export modes · pp. 5–6

2) Net-zero mode:

In net-zero mode, a balance constraint couples RO, electrolyzer, TDP, and renewable generation, and its multiplier represents the internal marginal value of electricity. The proof uses this value to characterize unit dispatch.

2) Net-zero mode:

  • The net-zero dispatch is constrained by qr + qe − qh − g = 0, whose Lagrange multiplier μ represents the internal marginal value of electricity.The proof derives stationarity conditions and combines them with complementary slackness.Source: 2) Net-zero mode · p. 6
  • The RO unit can be marginal only when μ = ρr; the proof derives its dispatch from complementary slackness and applies the same argument to the electrolyzer.It also states that the TDP dispatch qh(μ) is nondecreasing in μ.Source: 2) Net-zero mode · p. 6
  • At z = 0, a small increase in net consumption is priced at π+, while a small decrease is valued at π−, bounding the net-zero shadow price.The passage states that the shadow price must satisfy a condition based on these two prices.Source: 2) Net-zero mode · p. 6

3) Hydrogen-priority case:

In the hydrogen-priority case, the shadow price reaches the electrolyzer’s marginal value before the RO unit’s. Internal thresholds mark when each unit becomes marginal, while the dispatch changes with renewable output.

3) Hydrogen-priority case:

  • As μ falls from π+ toward π−, it reaches ρe before ρr, so the electrolyzer becomes marginal before the RO unit.Source: 3) Hydrogen-priority case · p. 6
  • Γ1 and Γ2 occur at μ = ρe while RO remains at qr; Γ3 and Γ4 occur at μ = ρr while the electrolyzer remains at qe.Source: 3) Hydrogen-priority case · p. 6
  • Across renewable-output regions, qh takes endpoint or marginal-value levels, alternating with the balancing level qr + qe − g.The thresholds divide these operating regions.Source: 3) Hydrogen-priority case · p. 6
  • The internal power schedules map to water and hydrogen quantities through wh = ηhqh, wr = αrqr, and y = γeqe.Source: 3) Hydrogen-priority case · p. 6

4) RO-priority case:

In the RO-priority case, the RO unit becomes marginal before the electrolyzer. The dispatch combines the import, net-zero, and export modes in a closed-form policy.

4) RO-priority case:

  • The shadow price reaches ρr before ρe, so the RO unit becomes marginal before the electrolyzer.Source: 4) RO-priority case · p. 7
  • The internal power schedules map to water and hydrogen quantities through wh = ηhqh, wr = αrqr, and y = γeqe.Source: 4) RO-priority case · p. 7
  • The dispatch combines import, net-zero, and export modes, with z positive, zero, and negative in those respective regions.Source: 4) RO-priority case · p. 7
  • The closed-form dispatch expressions and outer mode structure are established for the RO-priority case.Source: 4) RO-priority case · p. 7

APPENDIX B REMARKS ON OTHER ORDERINGS AND BOUNDARY CASES

The appendix extends the threshold policy beyond distinct interior marginal values and describes how ties, boundary values, and infeasible thresholds affect its regions.

APPENDIX B REMARKS ON OTHER ORDERINGS AND BOUNDARY CASES

  • When ρr = ρe inside (π−, π+), the plant is indifferent between assigning marginal net-zero power to RO or electrolysis; the optimizer may be nonunique while the optimal value is unchanged.Source: Appendix B · p. 7
  • If a resource’s marginal value lies outside (π−, π+), it may remain at a bound, reducing the internal net-zero thresholds to at most two or eliminating internal segments.Source: Appendix B · p. 7
  • Negative algebraic thresholds can place transitions outside feasible renewable output, causing dispatch modes or segments to disappear without changing the threshold form.Source: Appendix B · p. 7
  • At ρi = π− or π+, resource i is indifferent at a market margin, and the optimizer may be nonunique or require tie-breaking.No new qualitative dispatch pattern arises at these singular boundaries.Source: Appendix B · p. 7
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