A New Efficient Methodology for AC Transmission Network Expansion Planning in The Presence of Uncertainties

Ashu Verma; P. R. Bijwe; Soumya Das

REVIEW 3 major objections 5 minor 29 references

A New Efficient Methodology for AC Transmission Network Expansion Planning in The Presence of Uncertainties

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A two-stage point-estimate and bee-colony search solves probabilistic AC transmission planning with near-identical plans and over 99 percent less computation.

desk verdict Heuristic speedup for probabilistic AC TNEP with a sensible two-stage structure, but the Bernoulli-to-PEM mapping is undefined and the 'almost identical' claim rests on a single small system. read the letter →

arxiv 1908.00710 v1 pith:JOPUS3TS submitted 2019-08-02 math.OC

Soumya Das , Ashu Verma , P. R. Bijwe This is my paper · ORCID

classification math.OC

keywords ACtransmissionnetworkexpansionplanningprobabilisticpointestimatemethodmodifiedartificialbeecolonywindpoweruncertaintyN-1contingencyflow

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

The paper targets transmission network expansion planning—deciding which new power lines to build—under wind, load, and line-outage uncertainty, using the full alternating-current (AC) power-flow model. It tries to establish that a two-stage solution method can solve this probabilistic planning problem with near-identical results to a rigorous single-stage search while cutting computation by more than 99 percent. Stage one solves the deterministic version of the problem to get a starting plan and a cost lower bound; stage two uses a $2m+1$ point estimate method inside a modified artificial bee colony (MABC) algorithm to estimate expected constraint penalties, and prunes away candidate plans that are too costly, too large, or already infeasible in early checks. On a standard 6-bus test system the method finds the same expansion plan as the rigorous method in 104.93 seconds instead of 3.57 hours, a 99.18 percent time reduction. If the claim holds, medium-sized AC transmission planning under realistic uncertainties becomes tractable on a desktop computer rather than effectively unsolvable.

What carries the argument

The central mechanism is the pairing of a modified artificial bee colony (MABC) metaheuristic with the $2m+1$ point estimate method (PEM) for power-flow uncertainty, guarded by pruning rules. PEM approximates the expected value of a function of random inputs by solving deterministic AC power flow at $2m+1$ selected sample points—two per uncertain variable plus one joint-mean point—instead of running thousands of random scenarios. MABC proposes candidate line-addition plans, and each candidate is scored by line investment cost plus the estimated expected penalty; the pruning rules restrict which candidates receive a full probabilistic power-flow evaluation. Because each inner evaluation is a full AC power flow, the decisive factor for the reported speedup is the reduction in how many of these evaluations the search performs.

What would settle it

On the 6-bus test case, replace the shortcut samples for line outages with exhaustive enumeration of all line in/out combinations (keeping the paper's wind and load sampling), and compare the expected penalty and final plan. If the plan or the ranking of candidate plans changes, the shortcut is computing a different expectation than the stated probabilistic problem.

Watch

Extended reading notes

Core claim

The central claim is that the computational bottleneck of probabilistic AC transmission network expansion planning—the repeated power-flow solves needed to evaluate each candidate expansion plan—can be bypassed without losing plan quality. The proposed recipe solves the crisp/deterministic expansion problem first, then solves the probabilistic problem with a modified artificial bee colony search whose fitness is investment cost plus expected constraint penalty, where the expectation is estimated by the $2m+1$ point estimate method. Four pruning rules decide when a full probabilistic power flow is actually run: the number of new corridors and total new lines must sit in bands set from the deterministic solution, the cost must lie between the deterministic cost and twice that value, and evaluation stops at the first infeasible sample or the first failed single-line outage contingency. In the 6-bus test case the method returns the same plan and same total cost as the rigorous single-stage method while reducing solution time from 3.57 hours to 104.93 seconds; in the 24-bus case it reports plans and timings without a rigorous comparison, and the paper explicitly frames the results as good-quality sub-optimal solutions.

Load-bearing premise

The argument assumes that a line's random in/out state can be fed through the shortcut statistical method even when the sampled states fall between 'line present' and 'line absent'—an assumption the paper does not justify.

Editorial extensions

If this is right

Single-line-outage (N-1) security checks can be included in probabilistic AC expansion planning for medium test systems in minutes rather than hours.
Planners can retain full AC power-flow fidelity while modeling wind, load, and line-availability uncertainties, reducing the need to fall back on simplified linearized models.
The reported time savings make repeated metaheuristic trials affordable, which matters because the reported plans are best-of-50 results and tuning depends on running many trials.
The deterministic solution serves as both a warm start and a cost floor, so the method guarantees that probabilistic planning cost never falls below the crisp-plan cost.

Reading between the lines

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

I would not carry the 99 percent time-reduction claim beyond the 6-bus case: the paper reports no rigorous comparison for the 24-bus system, so its accuracy there is untested.
The pruning bounds (e.g., final cost at most twice the crisp cost, corridor counts in a 90–130 percent band) are tuned by experiment on these systems; on other networks they could exclude the true optimum or fail to prune, so the speedup is not guaranteed to transfer without retuning.
The same two-stage pattern—solve an inexpensive deterministic surrogate, then run a probabilistic refinement with early termination—could be applied to other expensive stochastic mixed-integer nonlinear planning problems, not only transmission expansion.

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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

This one is worth a look if you care about probabilistic AC transmission expansion planning. The core idea is simple and sensible: solve a deterministic ACTNEP first, then use that solution to seed a metaheuristic and to define search bounds (corridors, total lines, cost cap) so that the expensive probabilistic power flow is only run for 'worthy' candidate plans. That package is new as a combination, and the reported speedups are dramatic—99% on the 6-bus case, 90% on the DC 24-bus case. The authors are up front that they are after good sub-optimal solutions, not exact ones.

What the paper does well: it attacks a real computational wall, the two-stage structure is a legitimate way to cut the search space, and they test on two standard systems with N-1 contingencies plus wind and load uncertainty. The deterministic-first-stage is a reasonable warm start, and the dynamic cost cap does adapt during the search.

The soft spots are real. The most serious is in the probabilistic modelling. Section II.C.3 models each line outage as a Bernoulli random variable. Then Section III says the 2m+1 point estimate method is applied to all uncertain variables. For a Bernoulli, the PEM locations are mu +/- xi*sigma and mu, which are not 0 or 1 in general. The paper never says how to run the AC power flow for a line with fractional availability—whether to scale admittance, rating, or both. The constraints in (2)-(8) are defined for integer numbers of lines. So E(F_pen) in eq. (15) is not actually well-defined on the face of the paper. If the rigorous comparison method in Table II uses the same PEM, then the 'almost identical' result is comparing two versions of the same undefined scheme, not validating against the true Bernoulli model. That's a load-bearing gap, not a rounding error.

Second, the central AC claim rests on one small system. The Garver 6-bus comparison against a rigorous method is the only evidence for 'almost identical solutions.' On IEEE 24-bus, only the proposed method is run; there is no rigorous baseline. The DCTNEP comparison to [5] is good, but that is the DC problem. The bounds (90-130% corridors, 70-200% lines, 2*v_cr cost cap) are fitted parameters, and the cost cap directly truncates the search, so the observation that final costs stay within it is partly enforced. The claim that bounds are from 'numerous trials' is plausible but not a substitute for a sensitivity study.

Who is this for? A reader working on heuristic TNEP or on probabilistic power flow will find the two-stage idea and the bound strategies worth discussing. It is not a paper whose numerical claims you can rely on as-is. For peer review: I would send it to referees. The topic matters, the speedup is real if the objective can be defined, and the Bernoulli/PEM issue is fixable (e.g., treat line outages as separate discrete states or use a mixed-integer formulation for those states). It needs major revision, not desk rejection.

Bottom line: the engineering instinct is right, the technical execution has a hole in the middle. Worth engaging with, but do not cite the numerical results until the mapping is clarified.

Referee Report

3 major / 5 minor

Summary. The paper proposes a two-stage heuristic methodology for probabilistic AC transmission network expansion planning (PrACTNEP) under wind, load, and line-outage uncertainties. Stage 1 solves a deterministic AC TNEP to provide a warm start and to derive heuristic bounds; Stage 2 reduces the number of probabilistic AC power-flow evaluations by filtering candidate line plans through corridor-count bounds (90-130% of the crisp value), line-count bounds (70-200%), an upper cost limit v_ulim = 2*v_cr, and early truncation when a contingency or point-estimate evaluation is infeasible. The optimizer is a modified artificial bee colony (MABC) algorithm, and the expected penalty is computed with the 2m+1 point-estimate method (PEM). Results are reported for Garver 6-bus and IEEE 24-bus test systems, including a comparison with a single-stage rigorous MABC on the 6-bus AC case (same plan, 99.18% time reduction) and with a published DC TNEP method on both systems (over 90% time reduction).

Significance. If the methodology is valid, it offers a practically useful, low-computational-cost way to obtain first-cut probabilistic AC expansion plans, a problem that is otherwise computationally prohibitive. The paper is transparent about its heuristic nature, reports reproducible test-system data, and addresses a practically relevant combination of probabilistic wind, load, and N-1 line-outage modeling. The computational gains reported are substantial. However, the central claims rest on a single rigorous validation on a 6-bus system, and the treatment of discrete line outages through the continuous PEM raises a correctness question that needs resolution before the results can be considered trustworthy.

major comments (3)

[Section II.C.3, Section III, Section IV.B.3] The Bernoulli line-outage model is passed through the continuous 2m+1 point-estimate method without specifying how a fractional line state is mapped to the AC power-flow model. For a Bernoulli variable with FOR=0.99, the PEM locations are approximately 0.00015 and 1.0, with the central point at the mean 0.01; none of these values is a physically meaningful line state for the constraints (2)-(8), which are defined for integer numbers of in-service lines. No rule is given for scaling line admittance, line rating, or both for a fractional state, so E(F_pen) in Eq. (15) is not well-defined. Because this expected-penalty objective drives the MABC search, the reported plans and the 'almost identical' claim rest on an underspecified optimization problem. The authors must either treat Bernoulli outages exactly (e.g., by a two-point evaluation with probabilities rho_FOR and 1-rho_FOR) or specify and justify a consistent fractional-state power-flow model.
[Section IV.B.1, Section IV.B.2] The corridor bound (90-130%), the line-count bound (70-200%), and the upper cost limit v_ulim = 2*v_cr are empirical filters 'obtained through numerous trials' on the test systems. These filters directly restrict which candidate plans are evaluated by the probabilistic power flow. The paper's observation that the final solution cost is within the v_ulim bound is therefore partly a consequence of the filter, not an independent finding. No sensitivity analysis is provided, and no argument is given that the bounds are wide enough to contain the true optimum for the 24-bus system. As the method is explicitly sub-optimal, the authors should provide a sensitivity study or a formal justification (e.g., comparison with a relaxed or exhaustive reference solution) to show that the tuned bounds do not materially exclude high-quality plans.
[Section V.A.2, Section V.B.2] The central claim that the proposed method 'is able to obtain almost identical solutions' is validated on only one small system: Table II shows that for the Garver 6-bus AC case the proposed and rigorous methods yield the same plan and cost, with a 99.18% time reduction. For the IEEE 24-bus AC case, no rigorous comparison is provided (Table IV), and the reported >90% reductions for the DC case are against a published method on possibly different hardware and implementation. The paper also reports only the best result of 50 trials, with no information about the distribution (median, min/max, standard deviation) or any optimality gap. To support the generalization claim, the authors should report trial statistics and provide at least a lower bound or a limited rigorous reference solution for the 24-bus AC case.

minor comments (5)

[Section II.A, Eqs. (3)-(6)] The use of the index k both for the contingency state and for a corridor (in 'l ≠ k' and 'for l = k, k ≠ 0') creates a notation clash that makes the contingency constraints hard to parse; please distinguish the contingency index from the corridor index.
[Section III, Eq. (22)] The coefficient of variation is usually defined as sigma_x/mu_x, but Eq. (22) defines nu_x = mu_x/sigma_x; this appears to be a typo.
[Section IV.B.2] The statement that 'the final PrACTNEP cost remains within twice of the crisp ACTNEP cost' is presented as a fact; please explicitly label it as an empirical observation from the authors' trials and describe the systems over which it was tested.
[Table I] The 15.38% cost reduction over [5] should be qualified with the scenario assumptions (wind level, load variation, no-load-shedding condition) to ensure the comparison is commensurable.
[Section V, MABC settings] The MABC parameters (csN=20, psi=2, lim=6, iter=30, wg=1.5) are taken from previous papers by the same authors; a brief statement on their sensitivity for the present problem would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Garver 6-bus claim is backed by a head-to-head rigorous-method comparison, and the heuristic filters do not encode the reported plan.

full rationale

The proposed methodology's derivation chain is: solve deterministic ACTNEP (Section IV.A) to initialize MABC; evaluate probabilistic ACPF via 2m+1 PEM (Section III); prune candidate combinations with the corridor count bound (90-130%), line-count bound (70-200%), and dynamic upper cost limit v_ulim=2*v_cr (Section IV.B); compare the resulting plan against a single-stage rigorous method (Table II) and against externally reported DC results [5] (Tables I and III). None of these steps reduces to its own input by construction. The bounds in Section IV.B are explicitly described as heuristics tuned by prior trials ('the bound used in this study has been obtained through numerous trials'), not as consequences of the target output; they exclude candidates but do not force the specific final plan, since many accepted candidates are later rejected on ACPF-penalty grounds. The MABC settings are inherited from the authors' prior work [25]-[27], but this is parameter reuse for the optimizer, not a load-bearing derivation of the planning result; the central efficiency claim is independently evidenced by Table II's same-plan/same-cost comparison with the rigorous method and by the DC comparisons against [5]. The Bernoulli-outage-through-PEM issue raised in Section II.C.3/III is a technical correctness concern about how fractional line states are mapped into ACPF, not a circularity: it affects both the proposed and rigorous implementations equally and does not make the reported solution equal to the model's inputs. Overall, the paper's central claim is an empirical computational-efficiency result, not a prediction that is an input by definition.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on several fitted heuristic bounds (corridor, line, cost) and on the unexamined use of Bernoulli line states inside a continuous point-estimate scheme. No new physical entities are introduced.

free parameters (5)

Corridor bound range = 90% to 130% of the number of corridors in the crisp ACTNEP solution
Used in Stage 2 to filter MABC combinations; authors say it was obtained through numerous trials (Section IV.B.1).
New-line bound range = 70% to 200% of the number of new lines in the crisp solution
Filters combinations; tuned through trials (Section IV.B.1).
Upper cost limit factor = 2 x v_cr (twice crisp investment cost)
Combinations with estimated cost above this bound are penalized; bound is set from trials and updated dynamically (Section IV.B.2).
MABC algorithm settings = c_sN=20, psi=2, lim=6, iter=30, wg=1.5
Taken from the authors' prior papers [25]-[27], not re-derived or justified in this work.
FOR (forced outage rate) = 0.99
The paper states 'A FOR of 0.99 is considered'; this value is either a typo or an extreme reliability assumption, and it is not justified.

assumptions (4)

ad hoc to paper The final probabilistic ACTNEP cost remains within twice the crisp ACTNEP cost.
Stated as observed from trials and used to set the upper cost bound v_ulim (Section IV.B.2). If false, optimal plans may be discarded.
domain assumption Line outage states can be represented as Bernoulli random variables and processed via the 2m+1 point estimate method.
Section II.C.3 and III assume PEM applies to discrete Bernoulli line states; no justification for physically meaningful point estimates is given.
domain assumption Reactive power planning is fixed to the deterministic ACTNEP plan and is adequate for probabilistic cases.
Section IV.B.5 states RPP is fixed to crisp planning, based on the observation that accurate RPP has little effect on line cost under generous voltage limits.
domain assumption Wind speed follows Weibull and load follows normal distribution with the specified parameters.
Standard probabilistic models; parameters are taken from test system data and [5].

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Pith. "Pith review of A New Efficient Methodology for AC Transmission Network Expansion Planning in The Presence of Uncertainties." pith.science (2026). https://pith.science/paper/JOPUS3TS

@misc{pith2026190800710,
  author       = {Pith},
  title        = {Pith review of: A New Efficient Methodology for AC Transmission Network Expansion Planning in The Presence of Uncertainties},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JOPUS3TS}},
  note         = {Machine review of arXiv:1908.00710}
}

read the original abstract

Consideration of generation, load and network uncertainties in modern transmission network expansion planning (TNEP) is gaining interest due to large-scale integration of renewable energy sources with the existing grid. However, it is a formidable task when iterative AC formulation is used. Computational burden for solving the usual ACTNEP with these uncertainties is such that, it is almost impossible to obtain a solution even for a medium-sized system within a viable time frame. In this work, a two-stage solution methodology is proposed to obtain quick, good-quality, sub-optimal solutions with reasonable computational burden. Probabilistic formulation is used to account for the different uncertainties. Probabilistic TNEP is solved by 2m+1-point estimate method along with a modified artificial bee colony (MABC) algorithm, for Garver 6 bus and IEEE 24 bus systems. In both the systems, rated wind generation is considered to be more than one-tenth of the total generation capacity. When compared with the conventional single stage and existing solution methods, the proposed methodology is able to obtain almost identical solutions with extremely low computational burdens. Therefore, the proposed method provides a tool for efficient solution of future probabilistic ACTNEP problems with greater level of complexity.

Figures

Figures reproduced from arXiv: 1908.00710 by the authors.

**Figure 1.** Flow Chart of the Proposed Solution Methodology V. RESULTS AND DISCUSSION To demonstrate the potential of the proposed methodology, it is used to solve probabilistic TNEP for Garver 6 bus [5], [28] and IEEE 24 bus [5], [28], [29] systems. Planning problems for both the systems are solved considering dispatchable thermal generations for nonrenewable resources. Wind generations present are considered to be operating … view at source ↗

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Transmission Expansion Planning of Systems With Increasing Wind Power Integration,

G. A. Orfanos, P. S. Georgilakis, and N. D. Hatziargyriou, “Transmission Expansion Planning of Systems With Increasing Wind Power Integration,” IEEE Trans. Power Syst. , vol. 28, no. 2, pp. 1355 –1362, May. 2013

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H. Yu, C. Y. Chung, K. P. Wong, and J. H. Zhang, “A Chance Constrained Transmission Network E xpansion Planning Method With Consideration of Load and Wind Farm Uncertainties,” IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1568–1576, Aug. 2009

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M. C. Rocha, and J. T. Saraiva, “A discrete evolutionary PSO based approach to the multiyear transmission expansion planning problem considering demand uncertainties,” Int. J. Electr. Power Energy Syst., vol. 45, no. 1, pp. 427–442, Feb. 2013

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A Multi -Objective Transmission Expansion Planning Framework in Deregulated Power Systems With Wind Generation,

A. Arabali, M. Ghofrani, M. Etezadi-Amoli, M. S. Fadali, and M. Moeini- Aghtaie, “A Multi -Objective Transmission Expansion Planning Framework in Deregulated Power Systems With Wind Generation,” IEEE Trans. Power Syst., vol. 29, no. 6, pp. 3003–3011, Nov. 2014

work page 2014