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arxiv: 1907.03173 · v1 · pith:B5IY4ECDnew · submitted 2019-07-06 · 🧮 math.OC

Plug-n-Play Alternating Projection Algorithm for Large-scale Security Constraint Optimal Power Flow

Tuyen Vu This is my paper

Pith reviewed 2026-05-25 01:24 UTC · model grok-4.3

classification 🧮 math.OC
keywords security constrained optimal power flowalternating projectiondistributed optimizationpower systemsSCOPFper-bus partitioning
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The pith

The SCOPF problem can be solved distributively by partitioning it into per-bus subproblems solved via alternating projections with neighbor exchanges.

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

The paper presents an alternating projection algorithm that first partitions the security-constrained optimal power flow problem into subproblems, each handling the power flow at one electrical bus and sharing only local components with neighbors. Each subproblem is solved locally, after which outputs are exchanged with adjacent buses and the process iterates until a consistent system-wide solution emerges. This structure makes the method a distributed computing approach intended for large-scale power systems. The authors test the algorithm on a modified 14-bus network and report CPU times competitive with commercial solvers.

Core claim

The SCOPF is partitioned into sub-problems which share common power components; the alternating projection method is then applied so that power flow is optimized at each bus, with the local outputs exchanged among neighboring buses to produce the overall solution for the whole power system.

What carries the argument

Alternating projection iterations on partitioned per-bus SCOPF subproblems with neighbor data exchanges.

If this is right

  • The method produces a distributed solution for SCOPF without requiring a central coordinator for the entire system.
  • On the modified 14-bus system the CPU time is competitive with commercial products.
  • The partitioning into bus-level subproblems allows local computation while the exchanges enforce global consistency.
  • The approach is positioned as suitable for large-scale power systems because of its distributed structure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the per-bus partitioning preserves global optimality, the same structure could be applied to other network flow problems with security constraints.
  • Parallel hardware at individual buses could reduce wall-clock time further once the method is implemented on actual control hardware.
  • Convergence rate on systems larger than 14 buses remains untested and would determine whether the iteration count stays practical.
  • The algorithm might serve as a fallback solver when centralized tools become too slow or when communication to a central entity is limited.

Load-bearing premise

Local optimizations at each bus, combined only through neighbor exchanges, will converge to a solution that meets all global security constraints and optimality conditions of the original centralized problem.

What would settle it

Execute the algorithm on the modified 14-bus test case and compare the final objective value and constraint satisfaction against the output of a centralized commercial SCOPF solver; any mismatch in the solution or objective would falsify the claim.

Figures

Figures reproduced from arXiv: 1907.03173 by Tuyen Vu.

Figure 1
Figure 1. Figure 1: Proposed SCOPF Solution Based on the Projection Algorithm within ADMM technique. A 3-Bus power system is an example for illustration. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Euclidean projection of 𝑧௜௝,௞,௛ାଵ,଴ on 𝒞௜,௞ . Projection Algorithm Bus 1 Bus 2 Bus 3 u12,P12 u21,P21 k = 1 x Projection Algorithm Projection Algorithm Contingency [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: IEEE 14-Bus [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Residual profiles in log scale of scenario 1 (Lower value is better). [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
read the original abstract

In this paper, we present an optimization algorithm based on an alternating projection method to solve the large-scale security constraint optimal power flow (SCOPF) problem in power systems. The SCOPF is first partitioned into sub-problems, which share common power components. The proposed algorithm is fundamentally a distributed computing algorithm, which optimizes power flow in each electrical bus. The output of the local optimization problem will be exchanged among neighboring buses for the overall solution for the whole power system. We performed the algorithm against a modified 14-bus power system and demonstrated that the method is competitive with the commercial products regarding the CPU computation time.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes a plug-n-play alternating projection algorithm for large-scale security-constrained optimal power flow (SCOPF). The SCOPF is partitioned into per-bus subproblems whose only coupling occurs via neighbor exchanges of local power variables; the method is presented as a distributed solver, with a single timing comparison on a modified 14-bus system claimed to be competitive with commercial solvers.

Significance. A validated distributed alternating-projection method for SCOPF would be significant for scalability in large power systems. No such validation is present: the manuscript supplies neither a convergence theorem nor a fixed-point characterization ensuring that the per-bus iterations recover global feasibility and optimality under the full set of N-1 security constraints.

major comments (2)
  1. [Abstract] Abstract: the central claim that the distributed iterations produce “the overall solution for the whole power system” is unsupported; no convergence analysis, fixed-point characterization, or proof that the local projections satisfy the global SCOPF optimality conditions and N-1 contingency constraints is provided.
  2. [Numerical results] Numerical experiment (14-bus case): only CPU timing is reported; no comparison of objective value, binding constraints, or feasibility margin against a centralized SCOPF solver is given, so it is impossible to verify that the distributed output solves the original problem.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below regarding the need for convergence analysis and more complete numerical verification.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the distributed iterations produce “the overall solution for the whole power system” is unsupported; no convergence analysis, fixed-point characterization, or proof that the local projections satisfy the global SCOPF optimality conditions and N-1 contingency constraints is provided.

    Authors: We agree that the manuscript does not contain a formal convergence theorem or fixed-point characterization establishing that the per-bus alternating projections recover a globally optimal solution satisfying all N-1 constraints. The algorithm description relies on the standard properties of alternating projections onto convex sets and the local power-balance equations, with neighbor exchanges of active/reactive power variables. In the revised version we will add an explicit fixed-point characterization of the iteration and a discussion of the conditions (including convexity assumptions on the relaxed problem) under which the distributed solution coincides with the centralized SCOPF optimum; the abstract claim will be qualified accordingly. revision: yes

  2. Referee: [Numerical results] Numerical experiment (14-bus case): only CPU timing is reported; no comparison of objective value, binding constraints, or feasibility margin against a centralized SCOPF solver is given, so it is impossible to verify that the distributed output solves the original problem.

    Authors: The reported experiment emphasizes CPU time on the modified 14-bus system to illustrate the distributed, plug-and-play implementation. We acknowledge that objective-value, binding-constraint, and feasibility comparisons with a centralized solver are required to confirm correctness. In the revision we will augment the numerical section with these metrics on the same test case, obtained by running a centralized SCOPF solver in parallel. revision: yes

Circularity Check

0 steps flagged

No circularity detected; algorithmic proposal with empirical timing test

full rationale

The paper proposes partitioning the SCOPF into per-bus subproblems solved via alternating projections with neighbor exchanges of local variables, then reports CPU time competitiveness on a modified 14-bus system. No equations, theorems, fitted parameters, self-citations of uniqueness results, or ansatzes appear in the provided text. The central claim rests on the algorithm description plus an external benchmark comparison rather than any derivation that reduces to its own inputs by construction. This is a standard non-circular presentation of a distributed method.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no equations, parameters, or assumptions; ledger left empty.

pith-pipeline@v0.9.0 · 5623 in / 1042 out tokens · 26589 ms · 2026-05-25T01:24:08.640493+00:00 · methodology

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Reference graph

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