Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Quantum power flows: from theory to practice

  • Research Article
  • Published:
Quantum Machine Intelligence Aims and scope Submit manuscript

Abstract

The high-level integration of spatial-dispersed renewable energies can greatly enlarge future smart grid size and complicate system operations. Existing numerical methods based on classical computational oracles may be challenged to fulfill efficiency requirements for future smart grid evaluations, where modern advanced computational technologies, specifically quantum computing, have significant potential to help. In this paper, we discuss applications of quantum computing algorithms toward state-of-the-art smart grid problems. We suggest potential, exponential quantum speedup by the use of the Harrow-Hassidim-Lloyd (HHL) algorithms for solving sparse linear systems of equations in Newton’s method of power-flow problems. However, practical implementations of the algorithm are limited by the noise of quantum circuits, the hardness of realizations of quantum random access memories (QRAM), and the depth of the required quantum circuits. We benchmark the hardware and software requirements from the state-of-the-art power-flow algorithms, including QRAM requirements from hybrid phonon-transmon systems, and explicit gate counting used in HHL for explicit realizations. We also develop near-term algorithms of power flow by variational quantum circuits and implement physical experiments for 6 qubits with a truncated version of power flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

No datasets were generated or analyzed during the current study.

Notes

  1. As re-electrification unfolds, transportation and industry sectors will exert extra electric load demand to the existing power grids, creating extremely stressful demand in the near future. For example, by charging household electric vehicles in an unorganized manner, one can easily collapse the distribution system.

  2. We call a node in the power grid a bus.

  3. Usually, we substitute the second equation of Eq. 1.1 to all the other equations to eliminate one variable and one equation.

  4. The inversion error is defined so that the difference between the true solution \(\vec {x}_\textrm{true}\) and the approximate solution \(\vec {x}_\mathrm{approx.}\) satisfies \(|\vec {x}_\textrm{true}-\vec {x}_\mathrm{approx.}|< \epsilon _\textrm{inverse}\).

  5. As used widely for the original HHL framework, we could transform non-Hermitian matrices As to Hermitian matrices by adding one extra qubit. Namely, one could introduce

References

  • Arunachalam S, Gheorghiu V, Jochym-O’Connor T, Mosca M, Srinivasan PV (2015) On the robustness of bucket brigade quantum ram. New J Phys 17(12):123010

    Article  Google Scholar 

  • Augustino B, Nannicini G, Terlaky T, Zuluaga LF (2023) Quantum interior point methods for semidefinite optimization. Quantum 7:1110

    Article  Google Scholar 

  • Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S (2017) Quantum machine learning. Nature 549(7671):195–202

    Article  Google Scholar 

  • Bravo-Prieto C, LaRose R, Cerezo M, Subasi Y, Cincio L, Coles PJ (2019) Variational quantum linear solver. arXiv:1909.05820

  • Cerezo M, Arrasmith A, Babbush R, Benjamin SC, Endo S, Fujii K, McClean JR, Mitarai K, Yuan X, Cincio L et al (2021) Variational quantum algorithms. Nat Rev Phys 3(9):625–644

    Article  Google Scholar 

  • Chiang H-D, Wang T, Sheng H (2017) A novel fast and flexible holomorphic embedding power flow method. IEEE Trans Power Syst 33(3):2551–2562

    Article  Google Scholar 

  • Childs AM, Kothari R, Somma RD (2017) Quantum algorithm for systems of linear equations with exponentially improved dependence on precision. SIAM J Comput 46(6):1920–1950

    Article  MathSciNet  Google Scholar 

  • Corporation NAER (2024) 1200 mw fault induced solar photovoltaic resource interruption disturbance report. Available https://www.nerc.com/pa/rrm/ea/pages/1200-mw-fault-induced-solar-photovoltaic-resource-interruption-disturbance-report.aspx

  • Eskandarpour R, Gokhale P, Khodaei A, Chong FT, Passo A, Bahramirad S (2020) Quantum computing for enhancing grid security. IEEE Trans Power Syst 35(5):4135–4137

    Article  Google Scholar 

  • Eskandarpour R, Ghosh K, Khodaei A, Paaso A (2021) Experimental quantum computing to solve network dc power flow problem. arXiv:2106.12032

  • Eso NG (2024) Information about the 9 august power cut and the eso. Available https://www.nationalgrideso.com/information-about-great-britains-energy-system-and-electricity-system-operator-eso

  • Farhi E, Neven H (2018) Classification with quantum neural networks on near term processors. arXiv:1802.06002

  • Feng F, Zhou Y, Zhang P (2021) Quantum computing for enhancing grid security. IEEE Trans Power Syst 36(4):3810–3812

    Article  Google Scholar 

  • Gao F, Wu G, Guo S, Dai W, Shuang F (2023) Solving dc power flow problems using quantum and hybrid algorithms. Appl Soft Comput 137:110147

    Article  Google Scholar 

  • Giovannetti V, Lloyd S, Maccone L (2008) Quantum random access memory. Phys Rev Lett 100(16):160501

    Article  MathSciNet  Google Scholar 

  • Hann CT (2021) Practicality of quantum random access memory. PhD thesis, Yale University

  • Hann CT, Zou C-L, Zhang Y, Chu Y, Schoelkopf RJ, Girvin SM, Jiang L (2019) Hardware-efficient quantum random access memory with hybrid quantum acoustic systems. Phys Rev Lett 123:250501. https://link.aps.org/doi/10.1103/PhysRevLett.123.250501

  • Hann CT, Lee G, Girvin S, Jiang L (2021) Resilience of quantum random access memory to generic noise. PRX Quantum 2(2):020311

    Article  Google Scholar 

  • Harrow AW, Hassidim A, Lloyd S (2009) Quantum algorithm for linear systems of equations. Phys Rev Lett 103(15):150502

    Article  MathSciNet  Google Scholar 

  • Huang H-Y, Kueng R, Preskill J (2020) Predicting many properties of a quantum system from very few measurements. Nat Phys 16(10):1050–1057

    Article  Google Scholar 

  • Iwamoto S, Tamura Y (1978) A fast load flow method retaining nonlinearity. IEEE Trans Power Appar Syst (5):1586–1599

  • Jiajie L (2023) Power flow calculation of power system based on variable quantum algorithm. Proceedings of the CSEE 43(1):28–36. http://ntps.epri.sgcc.com.cn/djgcxb/EN/10.13334/j.0258-8013.pcsee.212798

  • Jordan R (1957) Rapidly converging digital load flow. Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems 76(3):1433–1438

    Google Scholar 

  • Lapworth L (2022) A hybrid quantum-classical CFD methodology with benchmark hhl solutions. arXiv:2206.00419

  • Liu J, Hann CT, Jiang L (2022) Quantum data center: theories and applications. arXiv:2207.14336

  • McGillis D (1957) Nodal iterative solution of power-flow problem using IBM 604 digital computer. Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems 76(3):803–809

    Google Scholar 

  • Mohammadisiahroudi M, Fakhimi R, Terlaky T (2022) Efficient use of quantum linear system algorithms in interior point methods for linear optimization. arXiv:2205.01220

  • Neufeld D, Hafshejani SF, Gaur D, Benkoczi R (2023) A hybrid quantum algorithm for load flow. arXiv:2310.19953

  • Sævarsson B, Chatzivasileiadis S, Jóhannsson H, Østergaard J (2022) Quantum computing for power flow algorithms: testing on real quantum computers. arXiv:2204.14028

  • Tinney WF, Hart CE (1967) Power flow solution by newton’s method. IEEE Trans Power Appar Syst (11):1449–1460

  • Trias A (2012) The holomorphic embedding load flow method. In: 2012 IEEE Power and energy society general meeting. IEEE, pp 1–8

  • Van Ness JE (1961) Elimination methods for load-flow studies. Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems 80(3):299–302

    Google Scholar 

  • Vazquez AC, Hiptmair R, Woerner S (2022) Enhancing the quantum linear systems algorithm using Richardson extrapolation. ACM Transactions on Quantum Computing 3(1):1–37

  • Wang T, Chiang H-D (2020) Theoretical study of non-iterative holomorphic embedding methods for solving nonlinear power flow equations: algebraic property. IEEE Trans Power Syst 36(4):2934–2945

  • Ward J, Hale H (1956) Digital computer solution of power-flow problems [includes discussion]. Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems 75(3):398–404

    Google Scholar 

  • Woerner S, Egger DJ (2019) Quantum risk analysis. npj Quantum Information 5(1):1–8

    Article  Google Scholar 

  • Wu D, Wang B (2019) Holomorphic embedding based continuation method for identifying multiple power flow solutions. IEEE access 7:86843–86853

    Article  Google Scholar 

  • Wu D, Molzahn DK, Lesieutre BC, Dvijotham K (2017) A deterministic method to identify multiple local extrema for the ac optimal power flow problem. IEEE Trans Power Syst 33(1):654–668

    Article  Google Scholar 

  • Zhou Y, Feng F, Zhang P (2021) Quantum electromagnetic transients program. IEEE Trans Power Syst 36(4):3813–3816

    Article  Google Scholar 

Download references

Acknowledgements

We thank Liang Jiang for the discussions. JL is supported in part by International Business Machines (IBM) Quantum through the Chicago Quantum Exchange, and the Pritzker School of Molecular Engineering at the University of Chicago through AFOSR MURI (FA9550-21-1-0209), MH thanks the STFC Ernest Rutherford Grant ST/R003599/1 and the Royal Society International Exchanges award IEC/R3/213026. DW is supported in part by DOE SETO DE-EE0009031 and NSF CNS-1735463, thanks Dr. Marija Ilic at LIDS, MIT for the helpful discussions and support.

Author information

Author notes

  1. Junyu Liu and Han Zheng contributed equally to this work.

Authors and Affiliations

  1. Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, 60637, USA

    Junyu Liu

  2. qBraid Co., Chicago, IL, 60637, USA

    Junyu Liu, Han Zheng, Masanori Hanada & Kanav Setia

  3. Department of Computer Science, University of Pittsburgh, Pittsburgh, PA 15260, USA

    Junyu Liu

  4. Department of Computer Science, The University of Chicago, Chicago, IL, 60637, USA

    Han Zheng

  5. Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK

    Masanori Hanada

  6. School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China

    Dan Wu

  7. Lab for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Dan Wu

Authors
  1. Junyu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Han Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masanori Hanada
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kanav Setia
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dan Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

JL and DW initialized the idea. JL, HZ, and DW did the most of technical calculations and experiments. JL, HZ, MH, KS, and DW contributed to the discussions and finished the writing of the paper.

Corresponding authors

Correspondence to Junyu Liu or Dan Wu.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Zheng, H., Hanada, M. et al. Quantum power flows: from theory to practice. Quantum Mach. Intell. 6, 55 (2024). https://doi.org/10.1007/s42484-024-00182-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42484-024-00182-z

Keywords

Search

Navigation