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arxiv: 2605.04746 · v2 · submitted 2026-05-06 · 🧮 math.OC

Recognition: no theorem link

Distributed Energy System Design including Unbalanced AC Power Flow for Large LV Networks with ADMM

Robert Steven (1) , Oleksiy V. Klymenko (1 , 2) , Michael Short (1 , 2) ((1) School of Chemistry , Chemical Engineering , University of Surrey , UK
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(2) Institute for Sustainability UK)
Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:22 UTC · model grok-4.3

classification 🧮 math.OC
keywords distributed energy system designADMMunbalanced AC power flowMINLP decompositionlow voltage networksDER siting and sizingcomplementarity reformulation
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The pith

Decomposing the DES design MINLP into MILP then ADMM-solved NLP and complementarity steps solves unbalanced AC power flow problems for 55-load LV networks up to 13 times faster with gaps below 0.61 percent.

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

The paper presents a decomposition strategy for the combined siting, sizing and dispatch of distributed energy resources while enforcing unbalanced three-phase AC power flow constraints in low-voltage networks. The full model is a non-convex mixed-integer nonlinear program that becomes intractable as network size and time horizon grow. The method first solves a mixed-integer linear program that ignores network constraints, fixes the resulting binary decisions, then applies a hybrid spatial and temporal decomposition together with the alternating direction method of multipliers to the remaining nonlinear program and a complementarity reformulation. On European low-voltage test feeders with up to 55 loads and 120 time points the approach delivers speed-ups of up to 13 times under parallel subproblem computation while keeping the optimality gap at or below 0.61 percent. A reader would care because the technique makes it feasible to optimise renewable and storage placement in real distribution grids without dropping voltage and current limits.

Core claim

The authors claim that an initial mixed-integer linear program without power-flow constraints, followed by binary fixing and alternating direction method of multipliers solution of the nonlinear program and complementarity reformulation steps, produces solutions whose quality remains acceptable for the original non-convex mixed-integer nonlinear program even as network size and time horizon increase.

What carries the argument

The hybrid spatial/temporal decomposition with the alternating direction method of multipliers applied to the nonlinear program and complementarity reformulation after binary fixing from the initial mixed-integer linear program.

If this is right

  • The method scales to networks with 55 loads and 120 time points while respecting unbalanced AC power flow constraints.
  • Parallel computation of the decomposed subproblems produces speed-ups reaching 13 times.
  • Optimality gaps stay at or below 0.61 percent across the tested instances.
  • The complementarity reformulation allows removal of operational binary variables without destroying solvability under the alternating direction method of multipliers.

Where Pith is reading between the lines

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

  • The same decomposition pattern could be applied to other mixed-integer nonlinear programs in energy systems that combine discrete decisions with continuous network constraints.
  • Further parallelisation across more processors might push the method to networks several times larger than 55 loads.
  • Testing the fixed-binary solutions against a full mixed-integer nonlinear program solver on a handful of medium-sized instances would quantify how often the early fixing misses better configurations.
  • If the approach is embedded in a rolling-horizon planner, the small observed gaps suggest it could support real-time operational adjustments in distribution networks.

Load-bearing premise

Fixing binary variables from the initial network-unconstrained mixed-integer linear program and then solving the power-flow-inclusive nonlinear program via alternating direction method of multipliers still yields acceptable quality solutions to the full non-convex mixed-integer nonlinear program as network size and time horizon grow.

What would settle it

A larger network test in which the final solution violates safety constraints or exceeds a one percent optimality gap relative to a global solver on the original mixed-integer nonlinear program would show the decomposition fails to preserve quality.

Figures

Figures reproduced from arXiv: 2605.04746 by 2), 2) ((1) School of Chemistry, (2) Institute for Sustainability, Chemical Engineering, Michael Short (1, Oleksiy V. Klymenko (1, Robert Steven (1), UK, UK), University of Surrey.

Figure 1
Figure 1. Figure 1: Solution Algorithm Overview 2.2.3 Robust Season In addition to the representative 24h periods for each season that are considered, a “robust” 24h period is also included, giving a total of 120 timepoints. To include this in the main model, linking constraints for the siting/sizing decision variables are added, such that these decisions must meet the robust loads and environmental conditions. The OPEX cost … view at source ↗
Figure 2
Figure 2. Figure 2: Problem Decomposition Structure inefficiency of some subproblems having to wait for others to finish before the algorithm can progress. Preliminary tests were carried out to measure the solve times of both load and no-load subproblems with varying numbers of loads and buses. Here, it was observed that the solve time for a given subproblem depends strongly on the total number of buses present in the subprob… view at source ↗
Figure 3
Figure 3. Figure 3: Partitioning of Example 25-Load Network (partitions marked in colour) view at source ↗
Figure 4
Figure 4. Figure 4: ELV-TF 55-Load Test Case 2.5.1 Building Load & Environmental Data For the electrical and heat load input data, using a representative seasonal approach, hourly electrical and heat demand values for each building over a single 24h period in each season are used. Electrical load data for the ELV-TF test case is provided as minute-resolution data for a single winter day [10]. Using the same methodology as De … view at source ↗
Figure 5
Figure 5. Figure 5: Central Objective Value and Solve Time             view at source ↗
Figure 6
Figure 6. Figure 6: Central No. of Variables and Constraints view at source ↗
Figure 7
Figure 7. Figure 7: Central 55 Load Cost Components As is noted in Section 2.6.1, relaxed solver parameters were used when solving using ADMM vs centrally. To determine the effect on solver performance that these would have had if run centrally, the problem was solved centrally using both strict and relaxed parameters. The comparison in terms of objective value is shown in Figure 8a and solve time in Figure 8b for the NLP for… view at source ↗
Figure 8
Figure 8. Figure 8: Central NLP Solve Strict vs Relaxed Solver Parameters view at source ↗
Figure 9
Figure 9. Figure 9: Central Complementarity Solve Strict vs Relaxed Solver Parameters view at source ↗
Figure 10
Figure 10. Figure 10: ELV-TF NLP 5-Load Parameter Sweep 23 view at source ↗
Figure 11
Figure 11. Figure 11: ELV-TF NLP 15-Load Parameter Sweep               view at source ↗
Figure 12
Figure 12. Figure 12: ELV-TF NLP 25-Load Parameter Sweep 24 view at source ↗
Figure 13
Figure 13. Figure 13: ELV-TF Complementarity 5-Load Parameter Sweep view at source ↗
Figure 14
Figure 14. Figure 14: ELV-TF Complementarity 15-Load Parameter Sweep view at source ↗
Figure 15
Figure 15. Figure 15: ELV-TF Complementarity 25-Load Parameter Sweep view at source ↗
Figure 16
Figure 16. Figure 16: ADMM NLP Objective Gap and Solve Time Ratio view at source ↗
Figure 17
Figure 17. Figure 17: ADMM Complementarity Objective Gap Percentage and Solve Time Ratio view at source ↗
Figure 18
Figure 18. Figure 18: ELV-TF 55-Load NLP and Complementarity Centralised vs Distributed Cost Component view at source ↗
read the original abstract

With the addition of large numbers of distributed energy resources (DERs) to distribution networks comes the increasing risk that their operation may violate the safety constraints of these networks. The problem considered in this paper is that of combined siting, sizing and dispatch of these DERs, also known as distributed energy system (DES) design, to help meet electrical and heat loads within the network. Here, the operation of these DERs is modelled, along with the unbalanced three-phase alternating current (AC) power flow in the network. When this network power flow is considered, this admits a non-convex mixed-integer nonlinear program (MINLP) model formulation which scales poorly with network size in terms of solve time. To address this, the problem is decomposed into a series of algorithmic steps, starting with a mixed-integer linear program (MILP) formulation that does not consider network constraints, then fixing binary variables, adding power flow constraints and solving as a nonlinear program (NLP) and finally removing operational binary variables and replacing them with a complementarity reformulation. As the main contributors to the overall solve time, the NLP and Complementarity steps are solved using a hybrid spatial/temporal decomposition strategy and the alternating direction method of multipliers (ADMM) distributed optimisation method. Results are presented for networks based on the European low voltage test feeder with up to 55 loads and 120 timepoints, with the ADMM approach showing speed-ups of up to 13x when considering parallel computation of the subproblems, for a maximum observed optimality gap of 0.61%.

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 / 2 minor

Summary. The manuscript presents a multi-step decomposition algorithm for solving a non-convex mixed-integer nonlinear program (MINLP) for distributed energy system (DES) design in large low-voltage (LV) networks, incorporating unbalanced three-phase AC power flow. The approach begins with a mixed-integer linear program (MILP) that ignores network constraints to determine binary decisions, fixes those binaries, solves a nonlinear program (NLP) with power flow constraints, and uses a complementarity reformulation solved via the alternating direction method of multipliers (ADMM) for the operational aspects. Empirical results on European LV test feeders with up to 55 loads and 120 time points demonstrate speed-ups of up to 13x with parallel ADMM and a maximum optimality gap of 0.61%.

Significance. If the reported performance holds and generalizes, this work provides a practical method to optimize DER siting, sizing, and dispatch while respecting network safety constraints in unbalanced networks, which is significant for renewable integration in distribution systems. The hybrid decomposition and ADMM application to this MINLP is a notable contribution, with concrete speed-up numbers on standard test cases.

major comments (2)
  1. [Abstract] Abstract: The claim of a 'maximum observed optimality gap of 0.61%' is load-bearing for the central performance claim but provides no details on the gap measurement method (e.g., comparison to a global MINLP solver, relaxation bound, or specific metric), limiting verification of solution quality for the original non-convex problem.
  2. [Methods (decomposition strategy)] The decomposition fixes binary variables (siting/sizing/dispatch) from the network-ignorant MILP before restoring unbalanced AC power flow constraints in the NLP and complementarity steps; this assumption is load-bearing for claiming near-optimality of the final solution, yet no sensitivity analysis, bound, or results for networks larger than 55 loads are provided to confirm the gap remains small as coupling effects grow.
minor comments (2)
  1. [Methods] The description of the complementarity reformulation replacing operational binary variables could be expanded with explicit equations for clarity.
  2. [Results] Convergence plots or tables for the ADMM subproblems would strengthen the presentation of the 13x speedup claim under parallel computation.

Simulated Author's Rebuttal

2 responses · 1 unresolved

Thank you for the constructive referee report. We address each major comment point-by-point below, proposing revisions to improve clarity and acknowledge limitations where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim of a 'maximum observed optimality gap of 0.61%' is load-bearing for the central performance claim but provides no details on the gap measurement method (e.g., comparison to a global MINLP solver, relaxation bound, or specific metric), limiting verification of solution quality for the original non-convex problem.

    Authors: We thank the referee for this observation. The 0.61% figure represents the maximum relative difference between the objective value of the final decomposed solution and the objective value obtained from the initial network-ignorant MILP (used as a reference point, since solving the full non-convex MINLP to global optimality is intractable for these instances). To improve verifiability, we will revise the abstract to briefly state the measurement method and add a short paragraph in Section 3 (Methods) detailing the exact metric, including that it is an observed gap relative to the MILP reference rather than a proven bound. revision: yes

  2. Referee: [Methods (decomposition strategy)] The decomposition fixes binary variables (siting/sizing/dispatch) from the network-ignorant MILP before restoring unbalanced AC power flow constraints in the NLP and complementarity steps; this assumption is load-bearing for claiming near-optimality of the final solution, yet no sensitivity analysis, bound, or results for networks larger than 55 loads are provided to confirm the gap remains small as coupling effects grow.

    Authors: We agree that the binary-fixing step is a key modeling choice whose impact on solution quality merits explicit discussion. The manuscript reports empirical gaps no larger than 0.61% across the tested European LV feeders (up to 55 loads), but does not include sensitivity studies on larger networks or theoretical bounds. We will expand the discussion in Section 5 to note that stronger network coupling in larger systems could increase the gap and to recommend this as future work. However, generating new results for networks substantially larger than 55 loads is not feasible within the scope of this revision. revision: partial

standing simulated objections not resolved
  • Providing sensitivity analysis, bounds, or computational results for networks larger than 55 loads

Circularity Check

0 steps flagged

No significant circularity; decomposition relies on standard primitives with empirical validation

full rationale

The paper describes a sequential decomposition heuristic (MILP without network constraints, binary fixing, NLP with unbalanced AC power flow, complementarity reformulation solved via ADMM) for a non-convex MINLP. All performance claims (up to 13x speedup, 0.61% observed gap) are presented as empirical results on test networks up to 55 loads and 120 timepoints. No equations or steps reduce a claimed result to its own inputs by construction, no self-citations justify load-bearing uniqueness or ansatzes, and no fitted parameters are relabeled as predictions. The approach is a procedural algorithm using established optimization methods, with the central contribution being computational scaling rather than a closed-form derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the approach rests on standard power-system modeling assumptions and the empirical effectiveness of the decomposition for near-optimality.

axioms (1)
  • domain assumption Unbalanced three-phase AC power flow can be represented by a set of nonlinear equality constraints that remain tractable once binary variables are fixed.
    Invoked when moving from the MILP to the NLP step.

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Works this paper leans on

74 extracted references · 74 canonical work pages

  1. [1]

    UN DESA.The Sustainable Development Goals Report 2023: Special Edition - July 2023. Tech. rep. UN DESA, 2023.url:https://unstats.un.org/sdgs/report/2023/

    work page 2023

  2. [2]

    Technical Summary

    M. Pathak et al. “Technical Summary”. In:Climate Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovern- mental Panel on Climate Change. Ed. by P.R. Shukla et al. Cambridge University Press, 2022, pp. 51–148.doi:10.1017/9781009157926.002

    work page doi:10.1017/9781009157926.002 2022

  3. [3]

    Distribution Systems

    William H. Kersting. “Distribution Systems”. In:Electric Power Generation, Transmission, and Distribution. Ed. by L. L. Grigsby. 3rd ed. CRC Press, 2012, pp. 420–581.isbn: 9781439856376. url:https://ebookcentral.proquest.com/lib/surrey/detail.action?docID=911986

    work page 2012

  4. [4]

    Distribution system optimization to manage DERs for grid services

    Anamika Dubey and Sumit Paudyal. “Distribution System Optimization to Manage Distributed Energy Resources (DERs) for Grid Services”. In:Foundations and Trends®in Electric Energy Systems6 (3-4 June 2023), pp. 120–264.issn: 2332-6557.doi:10.1561/3100000030

    work page doi:10.1561/3100000030 2023

  5. [5]

    Newton Power Flow Methods for Un- balanced Three-Phase Distribution Networks

    Baljinnyam Sereeter, Kees Vuik, and Cees Witteveen. “Newton Power Flow Methods for Un- balanced Three-Phase Distribution Networks”. In:Energies10 (10 Oct. 2017), p. 1658.issn: 1996-1073.doi:10.3390/en10101658

    work page doi:10.3390/en10101658 2017

  6. [6]

    An introduction to optimal power flow: Theory, formu- lation, and examples

    Stephen Frank and Steffen Rebennack. “An introduction to optimal power flow: Theory, formu- lation, and examples”. In:IIE Transactions48 (12 Dec. 2016), pp. 1172–1197.issn: 0740-817X. doi:10.1080/0740817X.2016.1189626

    work page doi:10.1080/0740817x.2016.1189626 2016

  7. [7]

    (accessed: 18/11/2024)

    Ofgem.Smart Export Guarantee (SEG).url:https://www.ofgem.gov.uk/environmental- and-social-schemes/smart-export-guarantee-seg. (accessed: 18/11/2024)

    work page 2024

  8. [8]

    Advancing sustainable distribution networks: Technologies and strategies

    Robert Steven, Oleksiy V. Klymenko, and Michael Short. “Advancing sustainable distribution networks: Technologies and strategies”. In:Reference Module in Materials Science and Materials Engineering. Elsevier, 2025.doi:10.1016/B978-0-443-29210-1.00030-3

    work page doi:10.1016/b978-0-443-29210-1.00030-3 2025

  9. [9]

    Balancing accuracy and complexity in optimisation models of distributed energy systems and microgrids with optimal power flow: A review

    Ishanki De Mel, Oleksiy V Klymenko, and Michael Short. “Balancing accuracy and complexity in optimisation models of distributed energy systems and microgrids with optimal power flow: A review”. In:Sustainable Energy Technologies and Assessments52 (2022), p. 102066.issn: 2213- 1388.doi:10.1016/j.seta.2022.102066

    work page doi:10.1016/j.seta.2022.102066 2022

  10. [10]

    Complementarity reformulations for the optimal design of distributed energy systems with multiphase optimal power flow

    Ishanki De Mel, Oleksiy V. Klymenko, and Michael Short. “Complementarity reformulations for the optimal design of distributed energy systems with multiphase optimal power flow”. In:Interna- tional Journal of Electrical Power & Energy Systems155 (Jan. 2024), p. 109610.issn: 0142-0615. doi:10.1016/j.ijepes.2023.109610

    work page doi:10.1016/j.ijepes.2023.109610 2024

  11. [11]

    Metaheuristic search in smart grid: A review with emphasis on plan- ning, scheduling and power flow optimization applications

    M. Papadimitrakis et al. “Metaheuristic search in smart grid: A review with emphasis on plan- ning, scheduling and power flow optimization applications”. In:Renewable and Sustainable Energy Reviews145 (July 2021), p. 111072.issn: 1364-0321.doi:10.1016/j.rser.2021.111072

    work page doi:10.1016/j.rser.2021.111072 2021

  12. [12]

    Zero Duality Gap in Optimal Power Flow Problem

    J Lavaei and S H Low. “Zero Duality Gap in Optimal Power Flow Problem”. In:IEEE Transactions on Power Systems27 (1 2012), pp. 92–107.issn: 1558-0679.doi:10.1109/TPWRS.2011.2160974

    work page doi:10.1109/tpwrs.2011.2160974 2012

  13. [13]

    Convex relaxations and linear approximation for optimal power flow in multiphase radial networks

    Lingwen Gan and Steven H. Low. “Convex relaxations and linear approximation for optimal power flow in multiphase radial networks”. In:2014 Power Systems Computation Conference. IEEE, Aug. 2014, pp. 1–9.isbn: 978-83-935801-3-2.doi:10.1109/PSCC.2014.7038399. 30

    work page doi:10.1109/pscc.2014.7038399 2014

  14. [14]

    Second-order cone relaxations of the optimal power flow for active distribution grids: Comparison of methods

    Lucien Bobo, Andreas Venzke, and Spyros Chatzivasileiadis. “Second-order cone relaxations of the optimal power flow for active distribution grids: Comparison of methods”. In:International Journal of Electrical Power & Energy Systems127 (2021), p. 106625.issn: 0142-0615.doi:10. 1016/j.ijepes.2020.106625

    work page arXiv 2021

  15. [15]

    A distributed approach to the OPF problem

    Tomaso Erseghe. “A distributed approach to the OPF problem”. In:EURASIP Journal on Ad- vances in Signal Processing2015 (1 May 2015), pp. 45–58.issn: 1687-6180.doi:10.1186/s13634- 015-0226-x

    work page doi:10.1186/s13634- 2015

  16. [16]

    A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems

    Daniel K. Molzahn et al. “A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems”. In:IEEE Transactions on Smart Grid8 (6 Nov. 2017), pp. 2941–2962. issn: 1949-3061.doi:10.1109/TSG.2017.2720471

    work page doi:10.1109/tsg.2017.2720471 2017

  17. [17]

    Foundations and Trends® in Machine Learning , author =

    Stephen Boyd et al. “Distributed Optimization and Statistical Learning via the Alternating Direc- tion Method of Multipliers”. In:Foundations and Trends®in Machine Learning3 (1 Jan. 2011), pp. 1–122.issn: 1935-8237.doi:10.1561/2200000016

    work page doi:10.1561/2200000016 2011

  18. [18]

    Toward Distributed/Decentralized DC Optimal Power Flow Implementa- tion in Future Electric Power Systems

    Amin Kargarian et al. “Toward Distributed/Decentralized DC Optimal Power Flow Implementa- tion in Future Electric Power Systems”. In:IEEE Transactions on Smart Grid9 (4 July 2018), pp. 2574–2594.issn: 1949-3061.doi:10.1109/TSG.2016.2614904

    work page doi:10.1109/tsg.2016.2614904 2018

  19. [19]

    PowerModelsADA: A Framework for Solving Optimal Power Flow Using Distributed Algorithms

    Mohannad Alkhraijah et al. “PowerModelsADA: A Framework for Solving Optimal Power Flow Using Distributed Algorithms”. In:IEEE Transactions on Power Systems39 (1 2024), pp. 2357– 2360.doi:10.1109/TPWRS.2023.3318858

    work page doi:10.1109/tpwrs.2023.3318858 2024

  20. [20]

    Machine learning-accelerated dis- tributed optimisation methods for optimal power flow: A review

    Robert Steven, Oleksiy V. Klymenko, and Michael Short. “Machine learning-accelerated dis- tributed optimisation methods for optimal power flow: A review”. In:Renewable and Sustainable Energy Reviews226 (Jan. 2026), p. 116190.issn: 13640321.doi:10.1016/j.rser.2025.116190

    work page doi:10.1016/j.rser.2025.116190 2026

  21. [21]

    Toward Distributed OPF Using ALADIN

    Alexander Engelmann et al. “Toward Distributed OPF Using ALADIN”. In:IEEE Transactions on Power Systems34 (1 Jan. 2019), pp. 584–594.issn: 1558-0679.doi:10.1109/TPWRS.2018. 2867682

    work page doi:10.1109/tpwrs.2018 2019

  22. [22]

    doi: 10.1109/TIE.2016.2636810

    Junyao Guo, Gabriela Hug, and Ozan K. Tonguz. “A Case for Nonconvex Distributed Optimization in Large-Scale Power Systems”. In:IEEE Transactions on Power Systems32 (5 Sept. 2017), pp. 3842–3851.issn: 1558-0679.doi:10.1109/TPWRS.2016.2636811

    work page doi:10.1109/tpwrs.2016.2636811 2017

  23. [23]

    Nicolás, The bar derived category of a curved dg algebra, Journal of Pure and Applied Algebra 212 (2008) 2633–2659

    Mostafa Nick, Rachid Cherkaoui, and Mario Paolone. “Optimal siting and sizing of distributed energy storage systems via alternating direction method of multipliers”. In:International Journal of Electrical Power & Energy Systems72 (2015), pp. 33–39.issn: 0142-0615.doi:10.1016/j. ijepes.2015.02.008

    work page doi:10.1016/j 2015

  24. [24]

    Joint planning for PV-SESS-MESS in distribution network towards 100% self-consumption of PV via consensus-based ADMM

    Tianqi Liu et al. “Joint planning for PV-SESS-MESS in distribution network towards 100% self-consumption of PV via consensus-based ADMM”. In:Journal of Energy Storage90 (2024), p. 111747.issn: 2352-152X.doi:10.1016/j.est.2024.111747

    work page doi:10.1016/j.est.2024.111747 2024

  25. [25]

    Alternating direction method of multipliers for the optimal siting, sizing, and technology selection of Li-ion battery storage

    Timur Sayfutdinov, Mazhar Ali, and Oleg Khamisov. “Alternating direction method of multipliers for the optimal siting, sizing, and technology selection of Li-ion battery storage”. In:Electric Power Systems Research185 (2020), p. 106388.issn: 0378-7796.doi:10.1016/j.epsr.2020.106388

    work page doi:10.1016/j.epsr.2020.106388 2020

  26. [26]

    Solving Combined Sizing and Dispatch of PV and Battery Storage for a Microgrid using ADMM

    Robert Steven, Oleksiy Klymenko, and Michael Short. “Solving Combined Sizing and Dispatch of PV and Battery Storage for a Microgrid using ADMM”. In:34th European Symposium on Computer Aided Process Engineering / 15th International Symposium on Process Systems Engi- neering. Ed. by Flavio Manenti and Gintaras V Reklaitis. Vol. 53. Elsevier, 2024, pp. 2299–...

    work page doi:10.1016/b978-0-443-28824-1.50384-7 2024

  27. [27]

    An Improved ADMM-based Approach for Decentralized Planning of Distribution Network

    Y Liu et al. “An Improved ADMM-based Approach for Decentralized Planning of Distribution Network”. In:2023 Panda Forum on Power and Energy (PandaFPE). 2023, pp. 231–236.doi: 10.1109/PandaFPE57779.2023.10140909

    work page doi:10.1109/pandafpe57779.2023.10140909 2023

  28. [28]

    Fully distributed planning method for coordinated distribution and urban trans- portation networks considering three-phase unbalance mitigation

    Haojie Shi et al. “Fully distributed planning method for coordinated distribution and urban trans- portation networks considering three-phase unbalance mitigation”. In:Applied Energy377 (2025), p. 124449.issn: 0306-2619.doi:10.1016/j.apenergy.2024.124449

    work page doi:10.1016/j.apenergy.2024.124449 2025

  29. [29]

    Coordinated Planning of Unbalanced Flexible Interconnected Distribution Networks Based on Distributed Optimization

    Jinghua Zhu et al. “Coordinated Planning of Unbalanced Flexible Interconnected Distribution Networks Based on Distributed Optimization”. In:Energies19 (7 Apr. 2026), p. 1769.doi:10. 3390/en19071769

    work page 2026

  30. [30]

    Distributed Energy Resource and Energy Storage Investment for Enhancing Flexibility Under a TSO-DSO Coordination Framework

    C Gu, J Wang, and L Wu. “Distributed Energy Resource and Energy Storage Investment for Enhancing Flexibility Under a TSO-DSO Coordination Framework”. In:IEEE Transactions on Automation Science and Engineering21 (3 2024), pp. 2961–2973.issn: 1558-3783.doi:10.1109/ TASE.2023.3272532

    work page arXiv 2024

  31. [31]

    Optimizing residential heating and energy storage flexibility for frequency re- serves

    Olli Kilkki et al. “Optimizing residential heating and energy storage flexibility for frequency re- serves”. In:International Journal of Electrical Power & Energy Systems100 (2018), pp. 540–549. issn: 0142-0615.doi:10.1016/j.ijepes.2018.02.047

    work page doi:10.1016/j.ijepes.2018.02.047 2018

  32. [32]

    A decision-support framework for residential heating decarbonisation pol- icymaking

    Ishanki De Mel et al. “A decision-support framework for residential heating decarbonisation pol- icymaking”. In:Energy268 (Apr. 2023), p. 126651.issn: 0360-5442.doi:10.1016/j.energy. 2023.126651

    work page doi:10.1016/j.energy 2023

  33. [33]

    Mitsubishi Electric.Ecodan Data Book Vol 6.0. Tech. rep. Nov. 2023.url:https://library. mitsubishielectric . co . uk / pdf / book / Ecodan _ ATW _ Databook _ Vol . 6 _ .0 _ .pdf. (accessed: 11/02/2026)

    work page 2023

  34. [34]

    SciPy 1.0: fundamental algorithms for scientific computing in Python

    Pauli Virtanen et al. “SciPy 1.0: fundamental algorithms for scientific computing in Python”. In: Nature Methods17 (3 Mar. 2020), pp. 261–272.issn: 1548-7091.doi:10 .1038/ s41592- 019- 0686-2

    work page 2020

  35. [35]

    Confidence region estimation techniques for nonlinear regression in ground- water flow: Three case studies

    K. W. Vugrin et al. “Confidence region estimation techniques for nonlinear regression in ground- water flow: Three case studies”. In:Water Resources Research43 (3 Mar. 2007).issn: 0043-1397. doi:10.1029/2005WR004804

    work page doi:10.1029/2005wr004804 2007

  36. [36]

    2024.url:https : / / www

    Gurobi Optimization LLC.Gurobi Optimizer Reference Manual. 2024.url:https : / / www . gurobi.com

    work page 2024

  37. [37]

    Three-phase cogenerator and transformer models for distribution system anal- ysis

    T.-H. Chen et al. “Three-phase cogenerator and transformer models for distribution system anal- ysis”. In:IEEE Transactions on Power Delivery6 (4 1991), pp. 1671–1681.issn: 08858977.doi: 10.1109/61.97706

    work page doi:10.1109/61.97706 1991

  38. [38]

    2026.url:https://www.epri.com/pages/sa/ opendss

    Electric Power Research Institute.OpenDSS. 2026.url:https://www.epri.com/pages/sa/ opendss. (accessed: 26/03/2026)

    work page 2026

  39. [39]

    2021.url: https://www.ovoenergy.com/guides/energy- guides/smart- export- guarantee

    Aimee Tweedale.Smart Export Guarantee explained: how much could you save?Apr. 2021.url: https://www.ovoenergy.com/guides/energy- guides/smart- export- guarantee. (accessed: 18/11/2024)

    work page 2021

  40. [40]

    Analytic Considerations and Design Basis for the IEEE Distribution Test Feeders

    K. P. Schneider et al. “Analytic Considerations and Design Basis for the IEEE Distribution Test Feeders”. In:IEEE Transactions on Power Systems33 (3 2018), pp. 3181–3188.doi:10.1109/ TPWRS.2017.2760011. 32

    work page arXiv 2018

  41. [41]

    Long-term patterns of European PV output using 30 years of validated hourly reanalysis and satellite data

    Stefan Pfenninger and Iain Staffell. “Long-term patterns of European PV output using 30 years of validated hourly reanalysis and satellite data”. In:Energy114 (2016), pp. 1251–1265.issn: 0360-5442.doi:10.1016/j.energy.2016.08.060.url:https://www.renewables.ninja/

    work page doi:10.1016/j.energy.2016.08.060.url:https://www.renewables.ninja/ 2016

  42. [42]

    Using bias-corrected reanalysis to simulate current and future wind power output

    Iain Staffell and Stefan Pfenninger. “Using bias-corrected reanalysis to simulate current and future wind power output”. In:Energy114 (2016), pp. 1224–1239.issn: 0360-5442.doi:j.energy.2016. 08.068.url:https://www.renewables.ninja/

    work page 2016

  43. [43]

    2016.url:https : / / www

    Stefan Pfenninger and Iain Staffell.Renewables.ninja. 2016.url:https : / / www . renewables . ninja/. (accessed: 07/05/2026)

    work page 2016

  44. [44]

    Seasonal variation in household electricity de- mand: A comparison of monitored and synthetic daily load profiles

    Matthew Li, David Allinson, and Miaomiao He. “Seasonal variation in household electricity de- mand: A comparison of monitored and synthetic daily load profiles”. In:Energy and Buildings179 (2018), pp. 292–300.issn: 0378-7788.doi:https://doi.org/10.1016/j.enbuild.2018.09.018

    work page doi:10.1016/j.enbuild.2018.09.018 2018

  45. [45]

    Bezanson, A

    Jeff Bezanson et al. “Julia: A Fresh Approach to Numerical Computing”. In:SIAM Review59 (1 Jan. 2017), pp. 65–98.issn: 0036-1445.doi:10.1137/141000671

    work page doi:10.1137/141000671 2017

  46. [46]

    JuMP 1.0: recent improvements to a modeling language for mathematical optimization

    Miles Lubin et al. “JuMP 1.0: recent improvements to a modeling language for mathematical optimization”. In:Mathematical Programming Computation15 (3 Sept. 2023), pp. 581–589.issn: 1867-2949.doi:10.1007/s12532-023-00239-3

    work page doi:10.1007/s12532-023-00239-3 2023

  47. [47]

    CONOPT: A GRG code for large sparse dynamic nonlinear optimization prob- lems

    Arne Drud. “CONOPT: A GRG code for large sparse dynamic nonlinear optimization prob- lems”. In:Mathematical Programming31 (2 1985), pp. 153–191.issn: 1436-4646.doi:10.1007/ BF02591747

    work page 1985

  48. [48]

    Bussieck and Arne S

    Michael R. Bussieck and Arne S. Drud.SBB: A New Solver for Mixed Integer Nonlinear Program- ming. Tech. rep. 2001

    work page 2001

  49. [49]

    June 2023

    GAMS Development Corporation.General Algebraic Modeling System (GAMS) Release 43.3.1. June 2023

    work page 2023

  50. [50]

    Mathematical Programming 106, 25-57 (2006)

    Andreas W¨ achter and Lorenz T. Biegler. “On the implementation of an interior-point filter line- search algorithm for large-scale nonlinear programming”. In:Mathematical Programming106 (1 Mar. 2006), pp. 25–57.issn: 1436-4646.doi:10.1007/s10107-004-0559-y

    work page doi:10.1007/s10107-004-0559-y 2006

  51. [51]

    UKRI Science and Technology Facilities Council.HSL, a collection of Fortran codes for large-scale scientific computation. Apr. 2018.url:https://www.hsl.rl.ac.uk/

    work page 2018

  52. [52]

    CreateSpace, 2009.isbn: 1441412697

    Guido Van Rossum and Fred L Drake.Python 3 Reference Manual. CreateSpace, 2009.isbn: 1441412697

    work page 2009

  53. [53]

    2024.url:https://www.mathworks

    The MathWorks Inc.MATLAB version: 24.2.0 (R2024b). 2024.url:https://www.mathworks. com

    work page 2024

  54. [54]

    2021.url:https : / / github

    James Fairbanks et al.JuliaGraphs/Graphs.jl: an optimized graphs package for the Julia pro- gramming language. 2021.url:https : / / github . com / JuliaGraphs / Graphs . jl/. (accessed: 24/03/2026)

    work page 2021

  55. [55]

    2016.url:https://juliapackages.com/p/graphrecipes

    Thomas Breloff.GraphRecipes.jl. 2016.url:https://juliapackages.com/p/graphrecipes

    work page 2016

  56. [56]

    The Pandas Development Team.pandas-dev/pandas: Pandas. Sept. 2024.doi:10.5281/zenodo. 13819579

    work page doi:10.5281/zenodo 2024

  57. [57]

    2010 , keywords =

    Wes McKinney. “Data Structures for Statistical Computing in Python”. In:Proceedings of the 9th Python in Science Conference. Ed. by St´ efan van der Walt and Jarrod Millman. 2010, pp. 56–61. doi:10.25080/Majora-92bf1922-00a. 33

    work page doi:10.25080/majora-92bf1922-00a 2010

  58. [58]

    Computing in Science and Engineering , keywords =

    J. D. Hunter. “Matplotlib: A 2D Graphics Environment”. In:Computing in Science & Engineering 9 (3 2007), pp. 90–95.doi:10.1109/MCSE.2007.55

    work page doi:10.1109/mcse.2007.55 2007

  59. [59]

    Waskom , title =

    Michael L Waskom. “Seaborn: Statistical Data Visualization”. In:Journal of Open Source Software 6 (60 2021), p. 3021.doi:10.21105/joss.03021

    work page doi:10.21105/joss.03021 2021

  60. [60]

    2026.url:https://copilot.cloud.microsoft

    Microsoft.Copilot. 2026.url:https://copilot.cloud.microsoft

    work page 2026

  61. [61]

    Optimally Managing the Impacts of Convergence Tolerance for Distributed Optimal Power Flow

    R Harris, M Alkhraijah, and D K Molzahn. “Optimally Managing the Impacts of Convergence Tolerance for Distributed Optimal Power Flow”. In:IEEE Transactions on Power Systems(2025), pp. 1–12.issn: 1558-0679.doi:10.1109/TPWRS.2025.3538500

    work page doi:10.1109/tpwrs.2025.3538500 2025

  62. [62]

    Pandapower—An Open-Source Python Tool for Convenient Modeling, Anal- ysis, and Optimization of Electric Power Systems

    Leon Thurner et al. “Pandapower—An Open-Source Python Tool for Convenient Modeling, Anal- ysis, and Optimization of Electric Power Systems”. In:IEEE Transactions on Power Systems33 (6 Nov. 2018), pp. 6510–6521.issn: 1558-0679.doi:10.1109/TPWRS.2018.2829021

    work page doi:10.1109/tpwrs.2018.2829021 2018

  63. [63]

    Johnson.PyCall.jl

    Steven G. Johnson.PyCall.jl. 2023.url:https://github.com/JuliaPy/PyCall.jl. (accessed: 24/03/2026)

    work page 2023

  64. [64]

    Robert Steven, Oleksiy Klymenko, and Michael Short.Dataset for ”Distributed Energy System Design including Unbalanced AC Power Flow for Large LV Networks with ADMM”. Mar. 2026. doi:10.15126/surreydata.902032

    work page doi:10.15126/surreydata.902032 2026

  65. [65]

    Optimal Design of Distributed Energy Systems Considering the Impacts on Electrical Power Networks

    Ishanki De Mel, Oleksiy V. Klymenko, and Michael Short. “Optimal Design of Distributed Energy Systems Considering the Impacts on Electrical Power Networks”. In:arXiv(2022).doi:10.48550/ arXiv.2109.11228.url:https://arxiv.org/abs/2109.11228v2

    work page arXiv 2022

  66. [66]

    fox - ess

    Fox ESS.Fox ESS EP5 Battery.url:https : / / www . fox - ess . com / products / battery / 25. (accessed: 22/03/2026)

    work page 2026

  67. [67]

    2025.url:https://heatable.co.uk/

    Heatable.Heatable. 2025.url:https://heatable.co.uk/. (accessed: 18/03/2025)

    work page 2025

  68. [68]

    (accessed: 11/02/2026)

    City Plumbing.Mitsubishi Ecodan PUZ-WM50VHA 5kW Heat Pump Unit Only 497740.url: https://www.cityplumbing.co.uk/p/mitsubishi- ecodan- puz- wm50vha- 5kw- heat- pump- unit-only-497740/p/202264. (accessed: 11/02/2026)

    work page 2026

  69. [69]

    (accessed: 11/02/2026)

    City Plumbing.Mitsubishi Ecodan PUZ-WM60VAA 6KW Heat Pump Unit Only 499782.url: https://www.cityplumbing.co.uk/p/mitsubishi- ecodan- puz- wm60vaa- 6kw- heat- pump- unit-only-499782/p/101792. (accessed: 11/02/2026)

    work page 2026

  70. [70]

    (accessed: 11/02/2026)

    City Plumbing.Mitsubishi Ecodan R290 Heat Pump PUZ-WZ80VAA 8Kw Heat Pump Unit Only 676734.url:https://www.cityplumbing.co.uk/p/mitsubishi- ecodan- r290- heat- pump- puz-wz80vaa-8kw-heat-pump-unit-only-676734/p/794581. (accessed: 11/02/2026)

    work page 2026

  71. [71]

    (accessed: 11/02/2026)

    City Plumbing.Mitsubishi Ecodan R290 Heat Pump PUZ-WZ60VAA 6Kw Heat Pump Unit Only 676733.url:https://www.cityplumbing.co.uk/p/mitsubishi- ecodan- r290- heat- pump- puz-wz60vaa-6kw-heat-pump-unit-only-676733/p/794769. (accessed: 11/02/2026)

    work page 2026

  72. [72]

    (accessed: 11/02/2026)

    City Plumbing.Mitsubishi Ecodan R290 Heat Pump PUZ-WZ50VAA 5Kw Heat Pump Unit Only 676732.url:https://www.cityplumbing.co.uk/p/mitsubishi- ecodan- r290- heat- pump- puz-wz50vaa-5kw-heat-pump-unit-only-676732/p/794821. (accessed: 11/02/2026)

    work page 2026

  73. [73]

    co.uk/Mitsubishi-Ecodan-Heat-Pump-PUZ-HWM140VHA.html

    Saturn Sales.Mitsubishi Ecodan Heat Pump PUZ-HWM140VHA.url:https://www.saturnsales. co.uk/Mitsubishi-Ecodan-Heat-Pump-PUZ-HWM140VHA.html. (accessed: 11/02/2026). 34

    work page 2026

  74. [74]

    A new approach to retrofitting FHE campus buildings using a whole life carbon assessment

    Robert Steven et al. “A new approach to retrofitting FHE campus buildings using a whole life carbon assessment”. In:Energy335 (Oct. 2025), p. 138101.issn: 03605442.doi:10 . 1016 / j . energy.2025.138101. Appendix A DES Model Parameters & Variables 35 A.1 Parameters A.1.1 General Table 8: General Model Parameters Name V alue Unit Description Source nyears ...

    work page arXiv 2025