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IBR references

This bibliography is organised by the layer of physics it supports. A reference appearing here does not imply that every mechanism in it is implemented.

Verification status of individual entries

Entries marked † were added during a design review to close attribution gaps identified below. Their authors, titles, venues, and years are stated from the reviewer's knowledge; volumes, pages, and DOIs have not been checked against live sources and no DOI is given for them. Verify each one before it appears in a submitted manuscript, exactly as the unmarked entries already were. Where an entry is a standard whose designation itself is uncertain, that is stated in the entry.

Algebraic and optimisation models

  1. R. Heidari and F. Geth, “Improved algebraic inverter modeling for four-wire power flow optimization,” Electric Power Systems Research, vol. 234, 110825, 2024. doi:10.1016/j.epsr.2024.110825. Primary basis for internal/external nodes, four-conductor KVL/KCL, topology, sequence limits, losses, and steady-state GFL/GFM constraints.
  2. M. Deakin, R. Heidari, and X. Deng, “Power converter DC link ripple and network unbalance as active constraints in distribution system optimal power flow,” arXiv:2512.18293, 2025. doi:10.48550/arXiv.2512.18293. Primary basis for $\widetilde S$, the small-ripple DC-link relation, and the six equation/PLECS benchmark cases.
  3. M. Deakin, R. Heidari, and X. Deng, “DC link capacitor ripple constraints limit benefits of utility-owned four-wire power converters,” arXiv:2606.21934,
    1. arXiv:2606.21934.
    Primary basis for simultaneous capacitor ripple allocation and the distinction among 3-leg, 4-leg, and reconfigurable split-link return paths.
  4. E. O. Badmus and A. Pandey, “Two-stage bidirectional inverter equivalent circuit model for distribution grid steady-state analysis and optimization,” IEEE Transactions on Power Systems, in press, 2026. Follow this work for two-stage DC/DC-plus-DC/AC coupling when the public final article is available.

Items 2, 3, and 21 are cited from preprints. Replace each with its published version, and update the table/figure numbers used by the regression tests, before any of them supports a manuscript claim.

Split link, ripple, and switching physics

  1. I. Ziyat, J. Wang, and P. R. Palmer, “Voltage ripple model and capacitor sizing for the three-phase four-wire converter used for power redistribution,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 12, no. 2, pp. 1437-1445, 2024. doi:10.1109/JESTPE.2023.3289485. Basis for treating the split midpoint as a charge-balance problem and for retaining the two half-banks as distinct physical components. PowerOptLab's unequal-capacitance and bounded-charge equations are quasi-static reductions, not a reproduction of the paper's switching/control dynamics.
  2. J. Liang, T. C. Green, C. Feng, and G. Weiss, “Increasing voltage utilization in split-link, four-wire inverters,” IEEE Transactions on Power Electronics, vol. 24, no. 6, pp. 1562-1569, 2009. doi:10.1109/TPEL.2009.2013351.
  3. A. Viatkin et al., “Analysis of the output current ripple of the three-phase four-leg inverter with a neutral inductor,” Energies, vol. 14, 1430, 2021. doi:10.3390/en14051430. Basis for phase/neutral ripple with an arbitrary neutral-to-phase inductance ratio and for the corresponding topology-ordering tests.
  4. R. Mandrioli et al., “Prediction of DC-link voltage switching ripple in three-phase four-leg PWM inverters,” Energies, vol. 14, 1434, 2021. doi:10.3390/en14051434. Basis for the ideal shared-carrier DC-link audit and the balanced SPWM and centered-PWM closed-form regression tests.
  5. M. Vujacic, M. Hammami, M. Srndovic, and G. Grandi, “Analysis of dc-link voltage switching ripple in three-phase PWM inverters,” Energies, vol. 11, 471, 2018. doi:10.3390/en11020471. Basis for the finite series R–L source branch, DC-node harmonic current sharing, and high-source-impedance limit. The implementation extends that circuit beyond the paper's balanced centered-PWM operating cases.
  6. A. Hammami et al., “Analysis of input voltage switching ripple in three-phase four-wire split capacitor PWM inverters,” Energies, vol. 13, 5076, 2020. doi:10.3390/en13195076. Split-capacitor switching-ripple basis and an independent source for future modulation/load-angle map regressions.
  7. R. Mandrioli, M. Hammami, A. Viatkin, R. Barbone, D. Pontara, and M. Ricco, “Phase and neutral current ripple analysis in three-phase four-wire split-capacitor grid converter for EV chargers,” Electronics, vol. 10, 1016, 2021. doi:10.3390/electronics10091016. Source of the implemented split-link SPWM phase and neutral RMS regression formulas, scaling laws, and experimental parameter set.
  8. R. Mandrioli, F. Lo Franco, M. Ricco, and G. Grandi, “A generalized approach for determining the current ripple RMS in four-leg inverters with the neutral inductor,” Energies, vol. 16, 1710, 2023. doi:10.3390/en16041710. General arbitrary-common-mode/neutral-inductance formulation, validated for SPWM, SVPWM, DPWM, and THIPWM in simulation and experiment.
  9. † R. Zhang, V. H. Prasad, D. Boroyevich, and F. C. Lee, “Three-dimensional space vector modulation for four-leg voltage-source converters,” IEEE Transactions on Power Electronics, 2002. The canonical four-leg modulation reference. PowerOptLab's four-leg switching hull is a sampled two-level rail feasibility region, not a modulation strategy; this is the reference against which any future four-leg modulation claim should be positioned.

Items 7-13 support the implemented DC-link and AC-side carrier audits; i_sw remains a separate allowance for residual unmodelled content. The package's harmonic-network solve generalizes the papers' independent-inductor circuits to the supplied primitive L/LCL model, but not their full experimental validation matrix. Items 5-6 remain validation anchors for unequal half-bank dynamics, active balancing, and improved voltage utilisation beyond the present steady-state charge abstraction.

Filters, impedance, and frequency coupling

  1. M. Liserre, F. Blaabjerg, and S. Hansen, “Design and control of an LCL- filter-based three-phase active rectifier,” IEEE Transactions on Industry Applications, vol. 41, no. 5, pp. 1281-1291, 2005. doi:10.1109/TIA.2005.853373. Basis for separating converter- and grid-side inductive arms, the midpoint capacitor/damping branch, and the scalar undamped resonance screening formula. PowerOptLab optimises the passive circuit at the fundamental and optionally audits its constant R/L/C primitives at carrier harmonics; it does not implement the paper's control-design or stability layer.
  2. J. Sun, “Impedance-based stability criterion for grid-connected inverters,” IEEE Transactions on Power Electronics, vol. 26, no. 11, pp. 3075-3078, 2011. doi:10.1109/TPEL.2011.2136439.
  3. A. Rygg, M. Molinas, C. Zhang, and X. Cai, “A modified sequence-domain impedance definition and its equivalence to the dq-domain impedance definition for the stability analysis of AC power electronic systems,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 4, no. 4, pp. 1383-1396, 2016. doi:10.1109/JESTPE.2016.2588733.

Items 15-16 define a separate future model layer: frequency-dependent controller, PLL, grid, and sequence-coupling impedances. They should not be collapsed into the present fundamental-frequency passive LCL algebraic model.

Numerical methods and smoothing

These support the package's own claims about smoothing bias, conditioning, and locality of solutions. They were previously recorded only in source comments.

  1. Yu. Nesterov, “Smooth minimization of non-smooth functions,” Mathematical Programming, vol. 103, pp. 127-152, 2005. doi:10.1007/s10107-004-0552-5. The classical accuracy-versus-smoothness trade-off: $O(\mu)$ approximation error against an $O(1/\mu)$ gradient Lipschitz constant. Its worst-case bound is over a function class and is not what the package's own measurements show, because here the smoothed norm is one term in a problem whose conditioning is set by the network equations.
  2. C. Chen and O. L. Mangasarian, “A class of smoothing functions for nonlinear and mixed complementarity problems,” Computational Optimization and Applications, vol. 5, pp. 97-138, 1996. doi:10.1007/BF00249052. The smoothing class that $\sqrt{x^2+\epsilon^2}$ belongs to, and therefore the reference for every smooth min/max selector in the control laws.
  3. P. Charbonnier, L. Blanc-Féraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Transactions on Image Processing, vol. 6, no. 2, pp. 298-311, 1997. doi:10.1109/83.551699. The same function under its pseudo-Huber/Charbonnier name.
  4. A. Wächter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Mathematical Programming, vol. 106, pp. 25-57, 2006. doi:10.1007/s10107-004-0559-y. Ipopt. Its tolerance design sets the accuracy floor of every implicit magnitude equality here, and its Eqn 35 bound relaxation is the mechanism behind the per-unit rating-violation note in the AdvancedInverter docstring and the publication gate in Verification and benchmark cases.

Converter-level sequence control

  1. C. L. Fortescue, “Method of symmetrical co-ordinates applied to the solution of polyphase networks,” Transactions of the AIEE, vol. 37, pp. 1027-1140, 1918. doi:10.1109/T-AIEE.1918.4765570.
  2. C. J. O'Rourke, M. M. Qasim, M. R. Overlin, and J. L. Kirtley, “A geometric interpretation of reference frames and transformations: dq0, Clarke, and Park,” IEEE Transactions on Energy Conversion, vol. 34, no. 4, pp. 2070-2083, 2019. doi:10.1109/TEC.2019.2941175.
  3. † H.-S. Song and K. Nam, “Dual current control scheme for PWM converter under unbalanced input voltage conditions,” IEEE Transactions on Industrial Electronics, 1999. The classical dual-sequence current-control scheme, and the origin of treating positive- and negative-sequence current references as two independently commanded channels.
  4. † H.-S. Suh and T. A. Lipo, work on instantaneous active and reactive power of a PWM AC/DC converter under generalized unbalanced network conditions, IEEE Transactions, 2006. The derivation of the mean plus twice-fundamental power algebra under unbalance, and of the four real degrees of freedom available to a three-wire converter. This is the provenance of the $S$ and $\widetilde S$ decomposition used in Phase-aware local control laws, which currently attributes it only to item 30. Confirm which of the two Suh–Lipo 2006 papers to cite.
  5. † P. Rodríguez, A. V. Timbus, R. Teodorescu, M. Liserre, and F. Blaabjerg, “Flexible active power control of distributed power generation systems during grid faults,” IEEE Transactions on Industrial Electronics,
    1. Flexible positive/negative-sequence current-reference generation with
    a single scalar weighting between the two sequences. This is the direct antecedent of the implemented ripple_blend $\lambda$ and should be cited wherever that blend is introduced.
  6. † R. Teodorescu, M. Liserre, and P. Rodríguez, Grid Converters for Photovoltaic and Wind Power Systems, Wiley, 2011. Textbook treatment of sequence extraction, dual-sequence reference generation, and the associated power-oscillation algebra.
  7. F. Nejabatkhah, Y. W. Li, and B. Wu, “Control strategies of three-phase distributed generation inverters for grid unbalanced voltage compensation,” IEEE Transactions on Power Electronics, vol. 31, no. 7, pp. 5228-5241,
    1. doi:10.1109/TPEL.2015.2479601.
    Basis for treating positive- and negative-sequence current references as separate control degrees of freedom under unbalanced voltage.
  8. Y. Guo, B. C. Pal, and R. A. Jabr, “On the optimality of voltage unbalance attenuation by inverters,” arXiv:2109.10974, 2021. doi:10.48550/arXiv.2109.10974. Demonstrates why current, active-power, feasibility, and synchronization constraints belong in negative-sequence voltage-attenuation design.
  9. N. Helaly, “A predictive negative sequence current control algorithm for voltage imbalance compensation and power oscillation minimization under unbalanced conditions,” Applied Science and Engineering Progress, vol. 16, no. 4, 6562, 2023. doi:10.14416/j.asep.2023.01.003. Provides a control-oriented example of explicitly trading voltage-unbalance compensation against oscillating power.
  10. † M. Savaghebi, A. Jalilian, J. C. Vasquez, and J. M. Guerrero, “Secondary control scheme for voltage unbalance compensation in an islanded droop-controlled microgrid,” IEEE Transactions on Smart Grid, 2012. Representative of the negative-sequence virtual-admittance/virtual-impedance family that the implemented $I_2^v=-\kappa e^{-j\phi_2}U_2$ law belongs to. Cite it so the admittance form is not read as novel.

Items 23-30 motivate the candidate local laws in Phase-aware local control laws and are the converter-control prior art for the dual-sequence reference generation used here. They do not by themselves validate the PowerOptLab allocator or its interaction with the implemented switching and capacitor constraints. The contribution under study is the fixed-structure algebraic surrogate and its network embedding, not the sequence reference itself, and the bibliography should make that ordering obvious.

Grid-forming and validation guardrails

  1. Y. Lin et al., Research Roadmap on Grid-Forming Inverters, NREL/TP-5D00-73476, 2020. NREL report.
  2. S. Shah and D. Ramasubramanian, Testing the Performance of Grid-Forming Resources: Test Methods and Performance Metrics for Evaluating the Voltage Source Behavior of Grid-Forming Resources, NREL/TP-5D00-94378, 2025. report record.
  3. † J. Rocabert, A. Luna, F. Blaabjerg, and P. Rodríguez, “Control of power converters in AC microgrids,” IEEE Transactions on Power Electronics,
    1. The standard grid-following/grid-forming taxonomy; useful for keeping
    the steady-state grid_forming=true constraint clearly separated from the control class it is named after.

Items 31-33 are guardrails on terminology and validation: a steady-state balanced internal EMF is only one property of a GFM resource. Dynamic voltage-source behaviour, current limiting, fault recovery, interaction stability, and hardware testing need their own models and performance tests.

Local voltage control and unbalance in distribution networks

This layer motivates the distribution-side question the control study asks. It was absent from earlier revisions of this bibliography, which cited only converter-side control.

  1. † K. Turitsyn, P. Šulc, S. Backhaus, and M. Chertkov, “Options for control of reactive power by distributed photovoltaic generators,” Proceedings of the IEEE, 2011. Foundational treatment of local reactive control by distributed PV.
  2. † M. Jahangiri and D. C. Aliprantis, “Distributed Volt/VAr control by PV inverters,” IEEE Transactions on Power Systems, 2013.
  3. † M. Farivar, X. Chen, and S. H. Low, “Equilibrium and dynamics of local voltage control in distribution systems,” IEEE Conference on Decision and Control, 2013. Existence, uniqueness, and convergence of the equilibrium of a local Volt-var droop. This is the theory behind the repeated caveat that a solved equilibrium is not a stability result, and behind the argument that a discontinuous conflict rule may admit no equilibrium near the tie surface.
  4. † H. Zhu and H. J. Liu, “Fast local voltage control under limited reactive power: optimality and stability analysis,” IEEE Transactions on Power Systems, 2016. Local droop as a surrogate-gradient method, with convergence conditions on the droop slope. Directly relevant to bounding the curve slopes stamped here.
  5. † K. Baker, A. Bernstein, E. Dall'Anese, and C. Zhao, “Network-cognizant voltage droop control for distribution grids,” IEEE Transactions on Power Systems, 2018. Droop gains designed from network sensitivities; the closest published relative of the $\widehat H_2^{-1}$ sensitivity idea in the negative-sequence section.
  6. † E. Dall'Anese and A. Simonetto, “Optimal power flow pursuit,” IEEE Transactions on Smart Grid, 2018. Local controllers that track the solution of an optimization problem online. The candidate closest-feasible per-phase projection law is a member of this family and should be positioned against it rather than presented as a bespoke oracle.
  7. † N. Weckx and J. Driesen, “Load balancing with EV chargers and PV inverters in unbalanced distribution grids,” IEEE Transactions on Sustainable Energy, 2015. Unbalance mitigation by distributed inverters at feeder scale — the distribution-side counterpart of the converter-side references above. (Confirm the first author's initials.)
  8. † F. Shahnia, R. Majumder, A. Ghosh, G. Ledwich, and F. Zare, “Voltage imbalance analysis in residential low voltage distribution networks with rooftop PV,” Electric Power Systems Research, 2011. Establishes the magnitude and mechanism of the LV unbalance this work is trying to control.
  9. † P. Pillay and M. Manyage, “Definitions of voltage unbalance,” IEEE Power Engineering Review, 2001. The distinction between the true $|U_2|/|U_1|$ factor and the NEMA/IEEE approximations. Cite it wherever voltage_unbalance_factor is defined, so the reported metric is unambiguous.
  10. † V. Girigoudar and L. A. Roald, work on voltage-unbalance metrics and unbalance constraints in distribution-system optimization, Electric Power Systems Research and related venues, from 2020. The closest prior work on putting unbalance metrics inside an optimization model, and therefore the natural comparison for the VUF reported by the study layer.

Standards and reference implementations

  1. IEEE Std 1547-2018, IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces. IEEE record.
  2. IEEE Std 1547.1-2020, IEEE Standard Conformance Test Procedures for Equipment Interconnecting Distributed Energy Resources with Electric Power Systems and Associated Interfaces. IEEE record.
  3. † IEEE Std 2800-2022, IEEE Standard for Interconnection and Interoperability of Inverter-Based Resources (IBRs) Interconnecting with Associated Transmission Electric Power Systems. IEEE record. The only standard cited here that addresses negative-sequence current behaviour normatively. It is a bulk-system document and is not an LV controller specification, but a discussion of unbalance control that omits it is incomplete.
  4. AS/NZS 4777.2, Grid connection of energy systems via inverters, Part 2: Inverter requirements. AEMO standards overview. The licensed clause specifying which voltage a multi-phase inverter observes for Volt-var and Volt-watt has not been read; see the open novelty check in Phase-aware local control laws.
  5. † EN 50549-1 and EN 50549-2, Requirements for generating plants to be connected in parallel with distribution networks. European connection-code comparator. Designation and edition unverified here.
  6. † VDE-AR-N 4105, Generators connected to the low-voltage distribution network. German LV connection rule. Designation and edition unverified here.
  7. IEC 61000-4-30:2025, Electromagnetic compatibility — Testing and measurement techniques — Power quality measurement methods. IEC record.
  8. IEC TR 61000-3-13:2008, Assessment of emission limits for the connection of unbalanced installations to MV, HV and EHV power systems. IEC record.
  9. † EN 50160, Voltage characteristics of electricity supplied by public distribution networks. Cited in the standards-mapping table of Phase-aware local control laws but previously absent from this bibliography. The designation, title, and edition are unverified; pin them, or remove the mapping-table row, before the supply-voltage-characteristics comparison is used in a manuscript.
  10. EPRI OpenDSS documentation, InvControl monitored-voltage, Volt-watt-axis, and inverter-priority properties. monitored voltage, Volt-watt bases, capability priority.

Items 44-53 define terminology, test scope, and independent reference-tool behaviour. PowerOptLab does not reproduce their complete profiles or claim conformance; any such study must use the current licensed standard and its prescribed measurement and response-time procedures.

Literature watch list

The highest-value additions are:

  • the licensed AS/NZS 4777.2 and IEEE 1547-2018 clauses that specify the monitored voltage for a multi-phase DER, which decide whether the worst-phase envelope is a contribution or prior art;
  • parameter-identical EMT validation datasets for all three implemented topologies;
  • dynamic midpoint balancing with leakage, actuator power/loss, and per-half overvoltage protection;
  • frequency- and temperature-dependent capacitor ESR/ESL electrical and thermal models, including lifetime/ageing feedback;
  • zero-sequence/common-mode grounding and parasitic-capacitance paths, which also determine what a three-wire inverter's voltage sensor actually measures;
  • frequency-dependent phase/neutral magnetic models, plus dead time, discontinuous PWM, interleaved carriers, and overmodulation;
  • measured broadband battery/DC-stage impedance, source-control interaction, and validation beyond the implemented constant series R–L approximation;
  • control-aware harmonic linearisation with positive/negative-sequence coupling;
  • current-limited GFM equilibria linked to dynamic fault-ride-through models;
  • multilevel and two-stage DC/DC-plus-DC/AC converters; and
  • an explicit reconfigurable four-leg-plus-split-link topology before any soft open point work is attempted.