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Beyond Higher-Pulse Rectification: Operational Harmonic Coordination in Renewable P2H Systems

Yangjun Zeng, Yiwei Qiu, Jie Zhu, Yi Zhou, Tao Wu, Xin Meng, Shi Chen, Buxiang Zhou, Kaigui Xie

arXiv:2609.03531v1math.OCeess.SY

TL;DR

The paper targets grid-code harmonic violations from low-cost TR supplies in renewable power-to-hydrogen plants. It combines harmonic modeling with two-layer electrolyzer scheduling, renewable tracking, and RCT tap-based mitigation. The resulting coordination raises profit over current-only regulation and enables coordinated 12-pulse TRs to reduce rectification-stage cost relative to 24-pulse hardware.

  • Problem

    RCT tap and electrolytic-current coordination for making 12-pulse TRs harmonic-compliant while maintaining production and voltage security remained insufficiently modeled and practically unclear.

  • Method

    The paper models harmonic phasors from operating conditions and coordinates ELZ scheduling within a harmonic feasible region with minute-level current allocation and RCT OLTC adjustment.

  • Results

    31% higher operating profit than current-only regulation and 37.5% lower rectification-stage cost than the 24-pulse alternative are reported.

  • Takeaways & Limitations

    Coordinated operation can make 12-pulse TRs a cost-effective harmonic-compliant alternative to higher-pulse rectifiers within the evaluated ReP2H settings.

Abstract

from arXiv · show

Thyristor rectifiers (TRs) are cost-effective electrolysis power supplies for renewable power-to-hydrogen (ReP2H) systems, but their harmonics may violate grid-code limits. In contrast to conventional solutions that rely on higher-pulse (such as 24-pulse) rectifiers, this paper proposes an operational harmonic coordination scheme that enables low-cost 12-pulse TRs to meet harmonic requirements through coordinated operation. First, a harmonic model quantifies the effects of rectifier transformer (RCT) tap positions and electrolytic currents, enabling harmonic cancellation among multiple electrolyzers (ELZs). A two-layer framework then coordinates hydrogen production and harmonic mitigation. Hourly scheduling determines ELZ commitment within the harmonic feasible region under renewable uncertainty using stochastic programming and a modified progressive hedging algorithm, while minute-level dispatch tracks renewable power and mitigates harmonics. A decomposition algorithm separates production dispatch from harmonic mitigation to improve computational efficiency. Case studies based on real-life projects show that the proposed method increases profit by 31% over current-only regulation. Annual simulations further show that coordinated 12-pulse TRs can replace 24-pulse rectifiers for harmonic compliance by exchanging additional RCT tap actions for lower transformer investment, reducing rectification-stage cost by 37.5%.

A. Abbreviations

The paper defines abbreviations for system components, operating variables, ELZ states, network quantities, and optimization parameters.

  • ELZ denotes electrolyzer, while ReP2H denotes renewable power-to-hydrogen and TR denotes thyristor rectifier.
  • RCT and NWT refer to rectifier transformer and network transformer, while OLTC denotes on-load tap changer.
  • P_Stack and U_Stack denote electrolytic power and voltage, while I and Y_H2 denote electrolytic current and hydrogen output rate.
  • b_On, b_By, and b_Idle represent ELZ production, standby, and idle states, with b_SU and b_SD representing startup and shutdown actions.
  • p_j,t and q_j,t denote active and reactive bus injections, while P_WT, P_PV, and P_G denote wind, photovoltaic, and grid power.
  • N_t, Δt, and Δτ specify scheduling and dispatch horizons or step lengths, while c_H2, c_SU, c_SD, and c_G denote hydrogen, startup, shutdown, and electricity prices.

I. INTRODUCTION

The paper addresses harmonic compliance in low-cost 12-pulse TR-based ReP2H plants by coordinating electrolyzer currents and transformer taps across scheduling and real-time dispatch. It develops a harmonic model and evaluates operational coordination as an alternative to higher-pulse hardware.

  • Motivation: TRs provide high-power, efficient, low-cost electrolysis supplies, but phase-controlled rectification produces PCC harmonics subject to IEEE 519 and GB/T 14549-1993 limits.
  • Motivation: 12-pulse TRs reduce harmonics at relatively low cost, whereas 24-pulse configurations require additional phase-shifting hardware that can represent approximately 40% of rectification-stage investment.
  • Related Work: Existing harmonic-mitigation methods use multi-pulse rectifiers, filters, auxiliary converters, or specialized current-shaping designs, increasing hardware cost or plant complexity.
  • Research Gap: RCT tap positions affect firing angles, commutation overlaps, and harmonic phasors, but their coordination with electrolytic currents had not been fully modeled or exploited.
  • Contributions: The proposed scheme coordinates ELZ commitment, load allocation, and RCT tap control across hourly scheduling and minute-level dispatch under variable renewable generation, while maintaining harmonic and voltage constraints.
  • Contributions: 48% harmonic reduction and 31% higher profit over current-only regulation are reported, while coordinated 12-pulse TRs reduce rectification-stage cost by 37.5% versus the higher-pulse alternative.

B. Harmonic Characteristics of ELZs

The harmonic model connects TR waveform behavior and electrical operating conditions to harmonic phasors. RCT tap regulation is then used with electrolyzer current control to coordinate harmonic cancellation among ELZs.

  • A. Harmonic Model of Multi-Pulse TR: Equations (3)–(7) link harmonic current to electrolytic current, stack temperature, RCT turns ratio, and AC-side voltage through stack, commutation, and power-conservation relationships.
  • B. Harmonic Characteristics of ELZs: The RCT vacuum OLTC makes the turns ratio a discrete tap-dependent variable, enabling tap regulation to adjust firing angles and support harmonic cancellation while current controllers preserve electrolytic-current references.

C. Harmonic Cancellation via OLTC Adjustment and Harmonic Feasible Region

OLTC tap positions and electrolytic currents jointly shape harmonic magnitude and phase, enabling coordinated cancellation within harmonic-feasible operating regions. The framework uses these controls while accounting for grid limits and firing-angle feasibility.

  • Harmonic cancellation: RCT tap ratios change harmonic-current magnitude and phase, enabling phasor cancellation among electrolyzers.At I = 3.5 kA, taps krec = 14 and krec = 5 reduce the 11th harmonic by more than 80% versus centered krec = 9.
  • Harmonic feasible region: Electrolytic currents and OLTC taps are coordinated by dividing N ELZs into two-ELZ groups with assigned harmonic limits of 2Ih/N.The equal allocation is a conservative sufficient condition for plant-level compliance and supports independent parallel dispatch.
  • Harmonic feasible region: The harmonic feasible region contains operating points satisfying assigned limits, while OLTC-infeasible points result from invalid firing angles below αmin = 5°.Tap changes modify α and γ, allowing the aggregated harmonic phasor to decrease even when identical ELZ currents produce the largest injection.
  • Operational coupling: OLTC adjustment can prevent harmonic violations for arbitrary current allocations within a two-ELZ group while maintaining electrolytic current.Tap changes also affect the TR reactive load through firing and overlap angles, and this coupling is included in the network models.
  • Single-ELZ feasibility: For a single online ELZ, harmonic injection remains within the prescribed limit, but high-load operation narrows the feasible region for the (12 ± 1)th harmonics.A safety margin is imposed to improve robustness against weaker-grid conditions and real-time SCC variations.

III. TWO-LAYER COORDINATION OF PRODUCTION SCHEDULING AND HARMONIC MITIGATION

The proposed operation embeds harmonic mitigation into ReP2H production planning by coordinating ELZ states, renewable utilization, network conditions, and reactive-power controls. Its models represent the plant and grid constraints needed for this coordination.

  • Framework: A two-layer framework coordinates hydrogen production, renewable-power tracking, and harmonic mitigation while accounting for reactive load, voltage, and network losses.Hourly scheduling determines ELZ states within the harmonic feasible region under renewable uncertainty, while real-time dispatch coordinates currents and taps.
  • Network model: The radial ReP2H network is modeled with DistFlow equations for branch flows, losses, and voltage profiles.Nodal injections include wind/PV generation, grid exchange, var compensation, and the electrolyzer plant load.
  • Network constraints: The formulation enforces PCC power-factor limits and models reactive-power compensation from static var generators and the step-down substation OLTC.These controls are incorporated alongside renewable-generation and network constraints.
  • ELZ operation: Each ELZ has mutually exclusive production, standby, and idle states, with startup, shutdown, and transition delays represented in the scheduling model.ELZ active power includes electrolytic power, balance-of-plant consumption, and rectifier losses.

P ELZ

The ELZ model links Faradaic efficiency, reactive demand, thermal dynamics, and computational reformulation to represent production and grid interactions. A rolling upper layer and real-time lower layer then implement coordinated operation.

  • ELZ production model: Faradaic efficiency is modeled through coefficients f1 and f2 and determines the relationship between electrolytic current and hydrogen output.The model identifies ηn,t as Faradaic efficiency and f1 and f2 as its coefficients.
  • Reactive power demand: ELZ reactive power includes fundamental phase-shift and harmonic-distortion components, with ν denoting the harmonic factor and φ the power-factor angle.Harmonic mitigation changes firing and overlap angles, thereby affecting reactive power, voltage, and network losses.
  • Thermal dynamics: ELZ temperature dynamics are modeled from heat generation, dissipation, cooling, and the thermal neutral voltage Utn.Temperature is carried through the operational model as a state affecting ELZ behavior.
  • Optimization formulation: Polynomial fitting, piecewise linearization, and Big-M reformulations transform nonlinear operational terms into a mixed-integer second-order cone programming problem.This reformulation provides the computational model used for coordinated optimization.
  • Rolling coordination: Hourly rolling scheduling passes only the first hour’s ELZ commitment to the real-time layer, while later decisions are reoptimized at the next update.The lower layer uses 2-min dispatch intervals to allocate currents, adjust RCT taps, update temperatures, and return terminal states hourly.

1) Two-Stage Stochastic Programming:

The upper-layer model schedules electrolyzer commitments and operations under renewable uncertainty while minimizing net operating cost. A modified progressive hedging procedure resolves scenario inconsistency in the mixed-integer stochastic problem.

  • The scheduling objective minimizes startup/shutdown and electricity-purchase costs minus hydrogen sales revenue.
  • RCT taps remain centered during hourly scheduling, while actual tap settings and reactive-power demand are updated during real-time dispatch.
  • Renewable uncertainty is represented by sampled and reduced scenarios, with non-anticipative ELZ commitments and scenario-dependent operating decisions.
  • Modified progressive hedging decomposes the stochastic problem into scenario subproblems while enforcing non-anticipativity of ELZ commitment.
  • Residual inconsistency is resolved by enumerating at most 2^z ≤ 4 combinations after fewer than three binary variables remain inconsistent.

D. Real-Time Dispatch at a 2-min Resolution

The real-time layer decomposes production tracking and harmonic mitigation into coordinated subproblems. Hydrogen production allocates currents, while harmonic mitigation adjusts currents and transformer taps with limited deviation from production objectives.

  • The real-time problem separates one hydrogen-production subproblem from N/2 harmonic-mitigation subproblems for RCT tap coordination.
  • The production subproblem allocates electrolytic currents to maximize hydrogen yield under network constraints.
  • Production outputs, including currents, AC voltage, and stack temperatures, are passed to the harmonic-mitigation subproblems.
  • Harmonic mitigation adjusts electrolytic currents and RCT tap positions to satisfy limits while minimizing production deviation and unnecessary tap changes.
  • A large production-priority weight and an OLTC action cost balance hydrogen output against tap changes, while each two-ELZ subproblem remains efficiently solvable.

3) Iterative Solution Approach:

The iterative solution approach alternates harmonic mitigation and network-aware hydrogen dispatch because RCT taps affect reactive power and network voltages. Case studies evaluate coordinated operation across small- and large-scale ReP2H systems under renewable scenarios.

  • 3) Iterative Solution Approach:: RCT tap changes modify rectifier firing variables, reactive power, and network voltages, which feed back into current, temperature, and AC-voltage dispatch.
  • 3) Iterative Solution Approach:: The algorithm alternates harmonic mitigation and network-aware hydrogen-production dispatch until convergence, with voltage-update limiting to suppress oscillations.
  • Case studies: The case studies use two Inner Mongolia ReP2H systems with wind and PV generation scenarios and associated probabilities.
  • Case studies: The small-scale system contains four alkaline ELZs, while the large-scale system contains twenty alkaline ELZs for scalability assessment.
  • Day-Ahead Scheduling: During low renewable generation, some ELZs reduce current or enter idle or standby states, whereas high generation commits all ELZs and nearly evenly shares load.
  • Real-Time Dispatch: Real-time electrolytic loads follow renewable variation, while harmonic adjustment is provided mainly by coordinated RCT tap changes rather than current reallocation.
  • Real-Time Dispatch: The 11th and 23rd harmonic currents remain below limits, network losses increase by about 0.03%, and bus voltages remain within 0.954–1.050 p.u.

B. Comparisons With Other Operational Schemes

The proposed method coordinates electrolytic currents and RCT taps to preserve production while maintaining harmonic compliance. Compared with current-only or harmonic-unconstrained operation, it improves economic and production outcomes and scales to larger ELZ systems.

  • Comparison with M1: 31.0% higher operating profit and 13.9% higher hydrogen production are achieved by PM relative to current-only regulation, with comparable compliant harmonic levels.M1 uses fixed RCT taps and a narrower harmonic feasible region, limiting renewable accommodation and hydrogen output.
  • Comparison with M2: M2 produces nearly the same hydrogen output as PM but violates harmonic limits, with the high-load 11th harmonic exceeding its limit by 106.3%.The comparison shows the production benefit of unconstrained operation comes at the expense of harmonic compliance.
  • Comparison with M2: PM reduces average 11th and 23rd harmonic currents by 48.0% and 43.2%, respectively, relative to harmonic-unconstrained operation.PM incurs only a negligible profit reduction from RCT tap actions while restoring compliance.
  • Scalability: In the 20-ELZ system, upper-layer commitments remain feasible while group-wise current and tap coordination keeps 11th and 23rd harmonics below their limits.The system is divided into ten two-ELZ groups, supporting application of the framework at larger scale.
  • Computational performance: The modified progressive hedging algorithm converges within limited iterations, while independent group-level harmonic subproblems enable rapid real-time convergence.Day-ahead scheduling requires 1.6 minutes for the 4-ELZ system and 12 minutes for the 20-ELZ system.

V. DISCUSSION AND ENGINEERING IMPLICATIONS

The engineering comparison favors coordinated 12-pulse rectifiers when harmonic compliance is achieved through additional OLTC actions rather than higher rectifier investment. Annual and sensitivity analyses indicate comparable hydrogen production while exposing the tradeoff among harmonic duty, investment, and operating conditions.

  • Engineering tradeoff: 24-pulse rectifiers offer stronger inherent harmonic cancellation, but require additional phase-shifting transformers and bridges, increasing capital cost and transformer losses.Their smaller DC-side ripple provides approximately 0.1% higher rectification efficiency, while the larger 12-pulse ripple has negligible reported impact on electrolyzer degradation.
  • Annual comparison: The 12-pulse and 24-pulse schemes produce nearly identical hydrogen amounts, with differences concentrated in harmonic levels, rectifier investment, and OLTC actions.The 24-pulse efficiency advantage is largely offset by losses in its additional phase-shifting transformer.
  • Annual comparison: 28,105 annual tap-changing actions for coordinated 12-pulse rectifiers versus 8030 for 24-pulse rectifiers reflect the 12-pulse scheme’s larger inherent harmonics.The additional annual OLTC action cost is 0.101 × 10^5 CNY, compared with a 1.630 × 10^5 CNY reduction in annualized rectifier investment.
  • Annual comparison: 37.5% reduction in rectification-stage cost results for coordinated 12-pulse rectifiers relative to the 24-pulse scheme.The net saving is 1.529 × 10^5 CNY, based on the reported investment and OLTC cost differences.
  • Economic boundary: The 12-pulse scheme remains preferable when its per-unit investment is more than 2.5 × 10^4 CNY below that of the 24-pulse scheme.This threshold is reported as much smaller than the market cost difference, supporting coordinated 12-pulse rectifiers as a practical alternative.
  • Sensitivity analysis: Across SCC values from −20% to +10% of the base value, both schemes remain harmonic compliant through OLTC adjustment without reducing hydrogen production.Lower SCC requires more tap changes, particularly for 12-pulse rectifiers, while a stronger grid reduces the required OLTC actions.
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