PSO-based Sliding Mode Current Control of Grid-Forming Inverter in Rotating Frame

Akhtar Hussain; Guilherme Vieira Hollweg; Quang-Manh Hoang; Sina Zarrabian; Van-Hai Bui; Wencong Su

REVIEW 4 major objections 5 minor 15 references

PSO-based Sliding Mode Current Control of Grid-Forming Inverter in Rotating Frame

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Offline particle-swarm tuning of sliding-mode current control cuts tracking error by 11.61% and converges in three iterations.

desk verdict A plausible but in-sample PSO-tuning study whose headline claim is measured on the same scenarios used to fit the parameters. read the letter →

arxiv 2501.11633 v1 pith:R45RW3RM submitted 2025-01-20 eess.SY cs.SY

Quang-Manh Hoang , Guilherme Vieira Hollweg , Akhtar Hussain , Sina Zarrabian , Wencong Su , Van-Hai Bui This is my paper · ORCID

classification eess.SYcs.SY

keywords grid-forminginverterslidingmodecurrentcontrolparticleswarmoptimizationdecoupledaveragemodelintegralabsoluteerrorchatteringreductioninverter-basedresourcesrotatingdqframe

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Grid-forming inverters need current controllers that respond quickly, hold a fixed switching frequency, and avoid overshoot; the decoupled average-model sliding mode current controller (DAM-SMC) meets these needs, but its three tuning parameters are usually chosen by expert judgment. This paper claims those parameters can instead be tuned offline with particle swarm optimization (PSO), using the integral absolute tracking error as the cost. In simulations, the PSO-tuned controller reduces the mean tracking error by 11.61% compared with the expert-tuned DAM-SMC and reaches the target fitness in 3 iterations, versus 22 for genetic algorithm tuning and 27 for simulated annealing. The tuned controller also keeps the current close to its reference when the plant inductance and resistance are varied by 40%, which the paper reads as robustness to model uncertainty.

What carries the argument

The key machinery is the combination of the DAM-SMC law in the rotating dq frame, whose three tunable parameters $k_{\mathrm{sat}}$, $k_{\mathrm{cd}}$, and $k_{\mathrm{cq}}$ shape the saturation boundary and switching gains, with particle swarm optimization as an offline search over those parameters. PSO treats each candidate parameter set as a particle, updates particle velocity from inertia and from attraction to the best personal and global solutions, and evaluates every candidate by running the Simulink model and computing the integral absolute error. The result is a tuned parameter set that the existing controller law can use without structural change.

What would settle it

Run the PSO-optimized controller on a scenario not used in tuning, such as a different load step size, a new nonlinear load impedance, or a d-q reference step, and compare its IAE with the conventional DAM-SMC under identical conditions. If the improvement disappears or reverses, the reported 11.61% gain is an artifact of the tuning scenarios rather than a general property of the controller.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the DAM-SMC's control parameters $k_{\mathrm{sat}}$, $k_{\mathrm{cd}}$, and $k_{\mathrm{cq}}$ form a low-dimensional search space that PSO can optimize more efficiently than genetic algorithms or simulated annealing, and the resulting controller beats the expert-chosen baseline. The paper reports a mean IAE of 0.08108 with PSO, an 11.61% improvement over the conventional DAM-SMC's 0.09173, and convergence to IAE = 0.037 in 3 iterations compared with 22 for GA and 27 for SA. These numbers come from ten runs of each optimizer on a MATLAB/Simulink model covering linear load change, nonlinear load connection, and a 40% increase in inductance and resistance.

Load-bearing premise

The paper assumes that the average absolute tracking error computed over its three fixed simulation scenarios is a valid measure of control quality, and that parameters optimized against those scenarios will also perform better in normal operation.

Editorial extensions

If this is right

The optimized parameter set can be embedded into existing DAM-SMC current controllers with no hardware change, turning a manual tuning step into a one-time offline computation.
Because chattering is reduced while fixed switching frequency is retained, the approach may extend the usable life of switching devices and simplify filter design.
PSO's 3-iteration convergence makes offline re-tuning practical whenever the plant parameters drift or the operating envelope changes.
The 40% parameter-mismatch test suggests the optimized controller tolerates aging or estimation errors in the LC filter and load, rather than relying on exact model knowledge.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A direct extension the paper does not test is out-of-sample performance: evaluating the PSO-tuned parameters on load profiles or operating points outside the three training scenarios would show whether the 11.61% gain generalizes or reflects overfitting to the chosen events.
The optimization could be reformulated to include chattering amplitude or switching effort in the cost function alongside IAE, which would make the chattering reduction an explicit objective rather than an indirect outcome.
The same PSO wrapper could be applied to the outer PI voltage loop, since the cascade structure means the inner-loop optimization's benefit depends partly on the fixed outer-loop gains.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Routine tuning paper, and the abstract nearly says so. The new bit is taking the Decoupled Average Model-based Sliding Mode Current Controller (DAM-SMC) from [7], keeping its control law, and optimizing its three parameters (ksat, kcd, kcq) offline with PSO. That specific application — PSO-tuned DAM-SMC for a grid-forming inverter in rotating frame, benchmarked against GA and SA — is not in the cited literature, so the novelty is narrow but real. There is no new control law, no new model, and no new stability result.

What it does well: the system setup is clearly described, the three test scenarios (load change at 0.1 s, nonlinear load at 0.2 s, 40% parameter mismatch at 0.5 s) are reasonable stress tests, and benchmarking against two other metaheuristics is a sensible thing to do. The 3-iteration convergence of PSO versus 22-27 for GA/SA is a concrete practical observation, though the convergence comparison uses an arbitrarily chosen IAE threshold of 0.037.

The soft spot is the one the stress-test note flags, and it lands. The PSO minimizes IAE over the exact 0.7 s simulation that Table II uses to compute the 11.61% improvement. That makes the improvement a measure of how well PSO fits those scenarios, not evidence of a general gain. The robustness scenario (the 40% parameter variation) is also inside the same simulation the optimizer sees, so it is not an out-of-sample test. The authors report no variance or confidence intervals for the 10 runs, and they never give the optimized parameter values — a strange omission for a tuning study. The improvement numbers are also inconsistent across the paper (11.61% in the abstract, 11.67% in the introduction, 31.27% and 14.375% in scenario-specific discussions). These issues are fixable, not disqualifying.

The central argument — that PSO can tune this controller at least as well as GA or SA — holds up for the scenarios tested. What does not hold up is the stronger claim that the improvement will carry over to other operating conditions. There is no experiment beyond the in-sample simulation.

This paper is for practitioners in inverter control who want a quick way to tune an SMC. It is not for someone seeking a new control concept. I would not cite it in my own work, but it is coherent and honest in its method. I would send it to review rather than desk-reject: the topic is relevant and the issues are addressable, but a reviewer should demand the missing parameter values, a validation on a scenario not used for fitting, and run-to-run statistics.

Referee Report

4 major / 5 minor

Summary. The paper proposes a Particle Swarm Optimization (PSO)-based tuning method for the three control parameters (ksat, kcd, kcq) of a Decoupled Average Model-based Sliding Mode Current Controller (DAM-SMC) for a grid-forming inverter with an LC filter. The control laws are taken from prior work [7], and the parameters are optimized offline by minimizing the integral absolute error (IAE) of the dq-axis inductor currents over a 0.7 s simulation that includes a linear load change, connection of a nonlinear load, and a 40% parameter variation. The optimized controller is compared with the heuristic DAM-SMC of [7], a GA-based DAM-SMC, and an SA-based DAM-SMC. The paper reports an 11.61% IAE reduction compared to the heuristic controller and a much faster convergence of the PSO (3 iterations) versus GA (22) and SA (27).

Significance. If the reported improvements are generalizable, the paper offers a simple, practical way to replace expert-knowledge tuning of an existing sliding-mode current controller with a standard metaheuristic, while preserving fixed switching frequency and low computational cost. The manuscript is clearly organized, provides a complete plant and controller model, and makes a fair algorithmic comparison in the sense that all three optimizers minimize the same IAE over the same simulation scenarios with the same population size and number of iterations. The inclusion of a 40% parameter-uncertainty scenario is a useful stress test. However, the central claim is validated only on the same scenarios used for optimization, and the reported statistics are too thin to establish that the PSO result is reliably better than GA or SA.

major comments (4)

[Section III (Algorithm 1, Eq. (9)) and Section IV-B (Table II)] The IAE defined in Eq. (9) over the 0.7 s simulation with the three fixed scenarios is both the objective minimized by PSO and the performance metric reported in Table II. Therefore the reported 11.61% improvement over the heuristic DAM-SMC of [7] measures in-sample fit to those specific scenarios, not a validated advantage under new operating conditions. I recommend an out-of-sample evaluation, for example by re-tuning on a subset of scenarios and testing on the remaining scenario, or by applying the optimized parameters to a different load profile and parameter variation.
[Section IV-A and Table II] The text states that each algorithm is run 10 times and the mean IAE is obtained, but Table II reports only means. No standard deviation, confidence interval, or significance test is provided. The differences among PSO (0.08108), GA (0.08324), and SA (0.08320) are small relative to typical run-to-run variability of stochastic optimizers; without dispersion measures or a statistical test, the ranking of the algorithms is not supported.
[Section IV-B and Figure 5] The convergence-speed comparison uses an arbitrary threshold IAE = 0.037, with no justification for this value. The number of iterations needed to reach a threshold depends on the threshold choice and on the scale of the IAE; a more principled comparison would report full convergence curves or define a stopping rule based on stagnation of the best fitness.
[Section III (Algorithm 1) and Table I] The optimized parameter values kopt_sat, kopt_cd, and kopt_cq are never reported. Without these values the experiment is not reproducible, and it is impossible to verify that the optimizer actually moved the parameters away from the expert-knowledge values used in [7] in a meaningful way. The manuscript should list the optimized parameters for all three algorithms.

minor comments (5)

[Abstract and Section I] The abstract reports an 11.61% improvement, while the introduction states approximately 11.67%; these numbers should be reconciled.
[Section IV-B] Scenario-specific improvements (31.27% at the linear load change, 14.375% at the nonlinear load connection) are presented alongside the overall IAE improvement of 11.61%; the paper should clarify that the scenario-specific numbers are local IAE reductions, not the overall metric in Table II, and should define how each is computed.
[Table I] The labels for the optimization bounds appear reversed: the row labeled "Upper limit" lists [1, 1, 0.001] and the row labeled "Lower limit" lists [2000, 2000, 15], which contradicts the text in Section III that the boundaries are [1,2000] for kcd and kcq and [0.001,15] for ksat. Please correct the labels or the values.
[Figure 3] The figure includes a text label "IAE = 0.0016" that is not defined or referenced in the body of the paper; please add an explanation or remove the label.
[Section III and Table I] The PSO hyperparameters (inertia range, c1, c2) and the GA/SA settings are listed without justification or sensitivity analysis; a brief explanation or a reference for these choices would strengthen the comparison.

Circularity Check

1 steps flagged · score 6.0 of 10

The headline 11.61% IAE improvement is the optimized objective evaluated on the training scenarios, not an out-of-sample prediction.

fitted input called prediction [Section III, Algorithm 1 and Eq. (9); Section IV-B, Table II]
"Calculate IAE values (9) of all particles IAE(t)i by running Simulink model... At the end of optimization process, the optimized control parameters k_opt_sat, k_opt_cd, k_opt_cq are obtained and used to run the Simulink model to achieve the optimized results. ... Table. II shows a significant improvement in the PSO-based DAM-SMC controller in terms of IAE, with an 11.61% improvement compared to the previous control scheme in [7]."

The IAE of Eq. (9) is both the objective minimized by Algorithm 1 and the performance metric reported in Table II. The same 0.7 s simulation, including the load change, nonlinear load connection, and +40% parameter variation, is used both to fit k_sat, k_cd, k_cq and to measure the 11.61% improvement. The baseline [7] parameters are a single heuristic point in the search space, so an optimizer minimizing IAE over that space will generally produce a lower or equal IAE by construction. The reported improvement is therefore a measure of how well PSO fits the chosen scenarios, not an independent validation of control quality under new operating conditions.

full rationale

The central numerical claim reduces to the optimization objective: PSO minimizes IAE over the same simulation scenarios on which the IAE improvement is later reported, so the 11.61% gain over the expert-tuned baseline is an expected consequence of fitting rather than an out-of-sample result. The comparison among PSO, GA, and SA is fair because all three minimize the same cost, but the paper provides no separate test scenario or load profile to establish generalization. The self-citation to [7] is used only as the baseline control law and is not load-bearing for the claimed optimization contribution. No uniqueness theorem or ansatz is smuggled in via citation. The convergence-time comparison uses an arbitrary threshold (IAE = 0.037), which is a methodological weakness but not circular. Overall, the paper contains one significant fitted-input-called-prediction step, so the circularity score is 6.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim depends on three controller parameters being fitted to the IAE objective, plus hand-chosen optimization bounds and comparison thresholds. No new physical entities are introduced.

free parameters (4)

ksat = not reported
Saturation boundary in the DAM-SMC control law, optimized by PSO to minimize IAE (Eq. 9, Algorithm 1).
kcd = not reported
d-axis control gain in Eq. 8, optimized by PSO to minimize IAE.
kcq = not reported
q-axis control gain in Eq. 8, optimized by PSO to minimize IAE.
IAE threshold for convergence comparison = 0.037
Chosen by hand without justification to compare convergence iterations of PSO, GA, and SA in Figure 5.

assumptions (4)

domain assumption Park transformation and the decoupled average model accurately represent the three-phase LC-filtered inverter under studied conditions.
The controller design in Section II depends on the validity of Eqs. 2-5 and the average model from [7].
domain assumption The three simulation scenarios (linear load change, nonlinear load, 40% parameter variation) are representative of real operating conditions.
The IAE is computed over these scenarios and used as the optimization objective; no out-of-sample validation is provided.
ad hoc to paper The control parameter boundaries [kcd,kcq,ksat] in [1,2000] and [0.001,15] are chosen based on expert knowledge.
These bounds constrain the search space and are not derived from any formal method (Table I).
ad hoc to paper Maximum iteration count 45 is chosen so that fitness values can be fairly compared across algorithms.
Stated in Section III without a convergence criterion; the choice is arbitrary and may affect the comparison.

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Cite this review

Pith. "Pith review of PSO-based Sliding Mode Current Control of Grid-Forming Inverter in Rotating Frame." pith.science (2026). https://pith.science/paper/R45RW3RM

@misc{pith2026250111633,
  author       = {Pith},
  title        = {Pith review of: PSO-based Sliding Mode Current Control of Grid-Forming Inverter in Rotating Frame},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R45RW3RM}},
  note         = {Machine review of arXiv:2501.11633}
}

read the original abstract

The Grid-Forming Inverter (GFMI) is an emerging topic that is attracting significant attention from both academic and industrial communities, particularly in the area of control design. The Decoupled Average Model-based Sliding Mode Current Controller (DAM-SMC) has been used to address the need such as fast response, fixed switching frequency, and no overshoot to avoid exceeding current limits. Typically, the control parameters for DAM-SMC are chosen based on expert knowledge and certain assumptions. However, these parameters may not achieve optimized performance due to system dynamics and uncertainties. To address this, this paper proposes a Particle Swarm Optimization (PSO)-based DAM-SMC controller, which inherits the control laws from DAM-SMC but optimizes the control parameters offline using PSO. The main goal is to reduce chattering and achieve smaller tracking errors. The proposed method is compared with other metaheuristic optimization algorithms, such as Genetic Algorithm (GA) and Simulated Annealing (SA). Simulations are performed in MATLAB/Simulink across various scenarios to evaluate the effectiveness of the proposed controller. The proposed approach achieves a substantial reduction in convergence time, decreasing it by 86.36% compared to the GA and by 88.89% compared to SA. Furthermore, the tracking error is reduced by 11.61% compared to the conventional DAM-SMC algorithm. The robustness of the proposed method is validated under critical conditions, where plant and control model parameters varied by up to 40%.

Figures

Figures reproduced from arXiv: 2501.11633 by the authors.

**Figure 1.** also shows the control structure featuring the cascade control scheme. In this section, we briefly outline the procedure for modeling the studied system and designing the DAM-SMC control, based on [7]. A. Modeling studied system As mentioned previously, the studied system consists of a three-phase LC-filter inverter operating as a GFMI, an RL linear load, and a three-phase full-bridge diode rectifier connected to an… view at source ↗

**Figure 2.** In this situation, the superior control performance [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 5.** Fitness function for the optimization methods. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

Figures from the paper (2 more)

**Figure 3.** Figure 3: dq inductor currents under non-linear load. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]

**Figure 4.** Figure 4: dq inductor currents under uncertainty. ACKNOWLEDGMENT The authors work was supported by the University of Michigan-Dearborn’s Office of Research “Research Initiation and Development". 3 22 27 0.037 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [7]

Decoupled average model-based sliding mode current control of lc-filtered inverters in rotating frame,

Q.-M. Hoang, B.-H. Nguyễn, T. Vo-Duy, J. P . F. Trovão, and M. C. Ta, “Decoupled average model-based sliding mode current control of lc-filtered inverters in rotating frame,” Mathematics and Computers in Simulation, 2024

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[2] [1]

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work page 2022

[3] [2]

Control and simulation of a grid-forming inverter for hybrid pv-battery plants in power system black start,

Q. Nguyen, M. R. Vallem, B. Vyakaranam, A. Tbaileh, X. Ke, and N. Samaan, “Control and simulation of a grid-forming inverter for hybrid pv-battery plants in power system black start,” in 2021 IEEE Power & Energy Society General Meeting (PESGM) , pp. 1–5, 2021

work page 2021

[4] [3]

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D. Pattabiraman, R. H. Lasseter., and T. M. Jahns, “Comparison of grid following and grid forming control for a high inverter penetration power system,” in 2018 IEEE Power & Energy Society General Meeting (PESGM), pp. 1–5, 2018

work page 2018

[5] [4]

Stability studies of grid-forming and grid-following in- verter penetrated systems with different external power system models,

F. Li and J. Ma, “Stability studies of grid-forming and grid-following in- verter penetrated systems with different external power system models,” IEEE Transactions on Power Delivery , 2024

work page 2024

[6] [5]

Multifunctional cascade control of voltage-source converters equipped with an lc filter,

V . Pirsto, J. Kukkola, and M. Hinkkanen, “Multifunctional cascade control of voltage-source converters equipped with an lc filter,” IEEE Transactions on Industrial Electronics , vol. 69, no. 3, pp. 2610–2620, 2022

work page 2022

[7] [6]

Predictive current control of a new three-phase voltage source inverter with phase shift compensation,

Y . Luo, C. Liu, and F. Yu, “Predictive current control of a new three-phase voltage source inverter with phase shift compensation,” IET Electric Power Applications , vol. 11, no. 5, pp. 740–748, 2017

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[8] [8]

Feasibility assessment of adaptive sliding mode controllers for grid-tied inverters with lcl filter,

G. V . Hollweg, P . J. D. de Oliveira Evald, E. Mattos, R. V . Tambara, and H. A. Gr ¨undling, “Feasibility assessment of adaptive sliding mode controllers for grid-tied inverters with lcl filter,” Journal of Control, Automation and Electrical Systems , pp. 1–14, 2022

work page 2022