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Reliability Analysis of Smart Grids Using Formal Methods

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Handbook of Smart Energy Systems

Abstract

Smart grids (SG) are complex integrated electric networks, where failures in any zone of the network can cause widespread catastrophic disruption of supply. In recent years, there has been a significant proliferation in the use of renewable energy sources, such as wind/solar systems, for SG power generation due to global warming, pollution, as well as economic and energy security concerns. However, the main obstacle that these energy systems face is their intermittent nature, which greatly affects their ability to deliver constant power to the grid. While this raises several reliability-related concerns, existing sampling-based simulation tools, such as the Monte Carlo approach, cannot guarantee absolute accuracy of the reliability analysis results due to their inherent incompleteness. Therefore, in this chapter, we propose a novel approach that uses formal methods for the accurate and sound reliability analysis of SG systems. This new methodology overcomes the incompleteness of simulation-based analysis and the error-proneness of manual mathematical analysis. In particular, we use higher-order logic (HOL) theorem proving, which is a computer-based mathematical reasoning tool, where we developed a library of fundamental concepts of reliability analysis techniques, such as event trees, functional block diagrams, and cause-consequence diagrams. This library allowed us to conduct formal system-/subsystem-level reliability analysis and determine absolute accuracy of important SG reliability indices, such as system/customer average interruption frequency and duration (SAIFI, SAIDI, and CAIDI), as well as energy indices, such as Energy not Supplied Index (ENS) and loss of energy expectation (LOEE). In order to demonstrate the effectiveness of our proposed methods, we conducted the formal system-/subsystem-level reliability analysis of the standard IEEE 3/39/118-bus electrical power generation/transmission/distribution networks. The results of the proposed formal analysis are extremely useful for the electrical power planners/designers to accurately quantify SG reliability improvements and satisfy the total demand within acceptable risk levels.

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References

  • M. Abdelghany, S. Tahar, Event tree reliability analysis of electrical power generation network using formal techniques, in Electric Power and Energy Conference (IEEE, Edmonton, 2020), pp. 1–7

    Google Scholar 

  • M. Abdelghany, S. Tahar, Cause-consequence diagram reliability analysis using formal techniques with application to electrical power networks. IEEE Access 9, 23929–23943 (2021)

    Article  Google Scholar 

  • M. Abdelghany, W. Ahmad, S. Tahar, S. Nethula, ETMA: an efficient tool for event trees modeling and analysis, in IEEE International Systems Conference (IEEE, Montreal, 2020), pp. 1–8

    Google Scholar 

  • M. Abdelghany, W. Ahmad, S. Tahar, Event tree reliability analysis of safety critical systems using theorem proving. IEEE Syst. J. (2021). [Online]. Available: https://doi.org/10.1109/JSYST.2021.3077558

  • W. Ahmad, Formal dependability analysis using higher-order-logic theorem proving. Ph.D. dissertation, National University of Sciences and Technology, Islamabad, 2017

    Google Scholar 

  • W. Ahmad, O. Hasan, F. Awwad, N. Bastaki, S. Hasan, Formal reliability analysis of an integrated power generation system using theorem proving. IEEE Syst. J. 14(4), 4820–4831 (2020a)

    Article  Google Scholar 

  • W. Ahmad, O. Hasan, S. Tahar, Formal reliability and failure analysis of ethernet based communication networks in a smart grid substation. Form. Asp. Comput. 32(1), 71–111 (2020b)

    Article  Google Scholar 

  • R. Allan, Reliability Evaluation of Power Systems (Springer Science & Business Media, New York, 2013)

    Google Scholar 

  • J. Andrews, Reliability of sequential systems using the cause-consequence diagram method. J. Process Mech. Eng. 215(3), 207–220 (2001)

    Google Scholar 

  • J. Andrews, L. Ridley, Application of the cause-consequence diagram method to static systems. Reliab. Eng. Syst. Saf. 75(1), 47–58 (2002)

    Article  Google Scholar 

  • O. Ansari, N. Safari, C. Chung, Reliability assessment of microgrid with renewable generation and prioritized loads, in Green Energy and Systems Conference (IEEE, 2016), pp. 1–6

    Google Scholar 

  • T. Badings, A. Hartmanns, N. Jansen, M. Suilen, Balancing wind and batteries: towards predictive verification of smart grids, in NASA Formal Methods Symposium (Springer, 2021), pp. 1–18

    Google Scholar 

  • M. Bevilacqua, M. Braglia, R. Gabbrielli, Monte Carlo simulation approach for a modified FMECA in a power plant. Qual. Reliab. Eng. Int. 16(4), 313–324 (2000)

    Article  Google Scholar 

  • Z. Bie, P. Zhang, G. Li, B. Hua, M. Meehan, X. Wang, Reliability evaluation of active distribution systems including microgrids. IEEE Trans. Power Syst. 27(4), 2342–2350 (2012)

    Article  Google Scholar 

  • R. Billinton, A. Sankarakrishnan, Adequacy assessment of composite power systems with HVDC links using Monte Carlo simulation. IEEE Trans. Power Syst. 9(3), 1626–1633 (1994)

    Article  Google Scholar 

  • B. Boussahoua, A. Elmaouhab, Reliability analysis of electrical power system using graph theory and reliability block diagram, in Algerian Large Electrical Network Conference (IEEE, 2019), pp. 1–6

    Google Scholar 

  • M. Bucher, R. Wiget, G. Andersson, C. Franck, Multiterminal HVDC networks – what is the preferred topology? IEEE Trans. Power Delivery 29(1), 406–413 (2013)

    Article  Google Scholar 

  • M. Čepin, Assessment of Power System Reliability: Methods and Applications (Springer Science & Business Media, London, 2011)

    Book  Google Scholar 

  • E. Dialynas, N. Koskolos, Reliability modeling and evaluation of HVDC power transmission systems. IEEE Trans. Power Delivery 9(2), 872–878 (1994)

    Article  Google Scholar 

  • Y. Elderhalli, Dynamic dependability analysis using HOL theorem proving with application in multiprocessor systems. Ph.D. dissertation, Concordia University, 2019

    Google Scholar 

  • X. Fang, S. Misra, G. Xue, D. Yang, Smart grid – the new and improved power grid: a survey. IEEE Commun. Surv. Tutor. 14(4), 944–980 (2011)

    Article  Google Scholar 

  • O. Hasan, S. Tahar, Formal verification methods, in Encyclopedia of Information Science and Technology (IGI Global, 2015), pp. 7162–7170

    Google Scholar 

  • Isograph Software, 2021. [Online]. Available: https://www.isograph.com

  • ITEM Software, 2021 [Online]. Available: https://itemsoft.com/eventtree.html

  • H. Jahanian, Failure mode reasoning, in International Conference on System Reliability and Safety (IEEE, 2019), pp. 295–303

    Google Scholar 

  • M. Javadi, A. Nobakht, A. Meskarbashee, Fault tree analysis approach in reliability assessment of power system. J. Multidiscip. Sci. Eng. 2(6), 46–50 (2011)

    Google Scholar 

  • S. Kabir, K. Aslansefat, I. Sorokos, Y. Papadopoulos, Y. Gheraibia, A conceptual framework to incorporate complex basic events in HiP-HOPS, in Model-Based Safety and Assessment, vol. 11842 (Springer, 2019), pp. 109–124

    Google Scholar 

  • A. Keyhani, M. Albaijat, Smart Power Grids (Springer Science & Business Media, Berlin/Heidelberg, 2012)

    Book  Google Scholar 

  • A. Khurram, H. Ali, A. Tariq, O. Hasan, Formal reliability analysis of protective relays in power distribution systems, in Formal Methods for Industrial Critical Systems (Springer, Berlin/Heidelberg, 2013), pp. 169–183

    Book  Google Scholar 

  • B. Ku, J. Cha, Reliability assessment of catenary of electric railway by using FTA and ETA analysis, in Environment and Electrical Engineering (IEEE, 2011), pp. 1–4

    Google Scholar 

  • K. Larsen, P. Pettersson, W. Yi, UPPAAL in a nutshell. Int. J. Softw. Tools Technol. Transfer 1(1–2), 134–152 (1997)

    Article  Google Scholar 

  • Y. Li, P. Zhang, P. Luh, Formal analysis of networked microgrids dynamics. IEEE Trans. Power Syst. 33(3), 3418–3427 (2017)

    Article  Google Scholar 

  • R. Mackiewicz, Overview of IEC 61850 and benefits, in Power Engineering Society General Meeting (IEEE, Montreal, 2006), pp. 623–630

    Google Scholar 

  • A. Mahmood, O. Hasan, H. Gillani, Y. Saleem, S. Hasan, Formal reliability analysis of protective systems in smart grids, in Region 10 Symposium (IEEE, 2016), pp. 198–202

    Google Scholar 

  • V. Muzik, Z. Vostracky, Possibilities of event tree analysis method for emergency states in power grid, in International Scientific Conference on Electric Power Engineering (IEEE, 2018), pp. 1–5

    Google Scholar 

  • S. Nanou, O. Tzortzopoulos, S. Papathanassiou, Evaluation of an enhanced power dispatch control scheme for multi-terminal HVDC grids using Monte-Carlo simulation. Electric Power Syst. Res. 140, 925–932 (2016)

    Article  Google Scholar 

  • O. Nỳvlt, M. Rausand, Dependencies in event trees analyzed by petri nets. Reliab. Eng. Syst. Saf. 104, 45–57 (2012)

    Google Scholar 

  • F. Ortmeier, W. Reif, G. Schellhorn, Deductive cause-consequence analysis. IFAC Proc. Vol. 38(1), 62–67 (2005)

    Article  Google Scholar 

  • R. Palin, D. Ward, I. Habli, R. Rivett, ISO 26262 safety cases: compliance and assurance, in IET Conference on System Safety, Birmingham (2011), pp. 1–6

    Google Scholar 

  • Y. Papadopoulos, M. Walker et al., Engineering failure analysis and design optimisation with HiP-HOPS. Eng. Failure Anal. 18(2), 590–608 (2011)

    Article  Google Scholar 

  • N. Papakonstantinou, S. Sierla, B. O’Halloran, Y. Tumer, A simulation based approach to automate event tree generation for early complex system designs, in Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 55867 (American Society of Mechanical Engineers, 2013), pp. 1–10

    Google Scholar 

  • I. Papazoglou, Functional block diagrams and automated construction of event trees. Reliab. Eng. Syst. Safety 61(3), 185–214 (1998a)

    Article  Google Scholar 

  • I. Papazoglou, Mathematical foundations of event trees. Reliab. Eng. Syst. Saf. 61(3), 169–183 (1998b)

    Article  Google Scholar 

  • D. Peplow, C. Sulfredge et al., Calculating nuclear power plant vulnerability using integrated geometry and event/fault-tree models. Nucl. Sci. Eng. 146(1), 71–87 (2004)

    Article  Google Scholar 

  • Y. Phulpin, J. Hazra, D. Ernst, Model predictive control of HVDC power flow to improve transient stability in power systems, in International Conference on Smart Grid Communications (IEEE, 2011), pp. 593–598

    Google Scholar 

  • A. Ranjbar, Reliability analysis of modern hybrid micro-grids. Ph.D. dissertation, The University of Texas at Dallas, 2013

    Google Scholar 

  • N. Rasmussen, Reactor Safety Study: An Assessment of Accident Risks in US Commercial Nuclear Power Plants, vol. 7 (NTIS, 1974)

    Google Scholar 

  • S. Shelemy, D. Swatek, Monte Carlo simulation of lightning strikes to the nelson river HVDC transmission lines, in International Conference on Power System Transients (2001), pp. 1–6

    Google Scholar 

  • X. Shi, A. Bazzi, Fault tree reliability analysis of a micro-grid using Monte Carlo simulations, in Power and Energy Conference (IEEE, 2015), pp. 1–5

    Google Scholar 

  • G. Sugumar, R. Selvamuthukumaran et al., Formal validation of supervisory energy management systems for microgrids, in Industrial Electronics Society (IEEE, 2017), pp. 1154–1159

    Google Scholar 

  • G. Sugumar, R. Selvamuthukumaran, M. Novak, T. Dragicevic, Supervisory energy-management systems for microgrids: modeling and formal verification. IEEE Ind. Electron. Mag. 13(1), 26–37 (2019)

    Article  Google Scholar 

  • G. Vyzaite, S. Dunnett, J. Andrews, Cause-consequence analysis of non-repairable phased missions. Reliab. Eng. Syst. Saf. 91(4), 398–406 (2006)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada

    Mohamed Abdelghany & Sofiène Tahar

Authors
  1. Mohamed Abdelghany
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  2. Sofiène Tahar
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Corresponding author

Correspondence to Mohamed Abdelghany .

Editor information

Editors and Affiliations

  1. Information Technology and Decision Sciences, University of North Texas, Denton, TX, USA

    Mahdi Fathi

  2. Department of Energy, Politecnico di Milano, MILANO, Milano, Italy

    Enrico Zio

  3. Industrial & Systems Engineering, University of Florida, GAINESVILLE, FL, USA

    Panos M. Pardalos

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Abdelghany, M., Tahar, S. (2021). Reliability Analysis of Smart Grids Using Formal Methods. In: Fathi, M., Zio, E., Pardalos, P.M. (eds) Handbook of Smart Energy Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-72322-4_81-1

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  • DOI: https://doi.org/10.1007/978-3-030-72322-4_81-1

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  • Print ISBN: 978-3-030-72322-4

  • Online ISBN: 978-3-030-72322-4

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