Skip to main content

MathEnergy – Mathematical Key Technologies for Evolving Energy Grids

  • Chapter
  • First Online:
Mathematical Modeling, Simulation and Optimization for Power Engineering and Management

Abstract

For a sustainable and CO\(_2\) neutral power supply, the entire energy cycles for power, gas and heating grids have to be taken into account simultaneously. Despite rapid progress, the energy industry is insufficiently equipped for the superordinate planning, monitoring and control tasks, based on increasingly large and coupled network simulation models. The German MathEnergy project aims to overcome these shortcomings by developing selected mathematical key technologies for energy networks and respective software. This chapter gives an overview of MathEnergy by discussing selected new developments related to model order reduction for gas networks, state estimation for gas and power networks, as well as cross-sectoral modeling, simulation and ensemble analysis. Several new theoretical results as well as related software prototypes are introduced. Results for selected gas and power networks are presented, including a first version of the partDE-Hy demonstrator for analysis of power-to-gas scenarios.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Anderson, P.M., Fouad, A.A.A.: Power System Control and Stability, 1st edn. Iowa State Univ. Press, Ames, Iowa (1977)

    Google Scholar 

  2. Arnold, M., Günther, M.: Preconditioned dynamic iteration for coupled differential-algebraic systems. BIT 41, 1–25 (2001). https://doi.org/10.1023/A:1021909032551

  3. Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50(2), 174–188 (2002). https://doi.org/10.1109/78.978374

    Article  Google Scholar 

  4. Baldin, A., Cassirer, K., Clees, T., Klaassen, B., Nikitin, I., Nikitina, L., Torgovitskaia, I.: Universal translation algorithm for formulation of transport network problems. In: 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications, SIMULTECH 2018. Proceedings, pp. 315–322 (2018). https://doi.org/10.5220/0006831903150322

  5. Baldin, A., Clees, T., Fuchs, B., Klaassen, B., Nikitin, I., Nikitina, L., Torgovitskaia, I.: Topological reduction of gas transport networks. In: INFOCOMP 2019, the Ninth International Conference on Advanced Communications and Computation, pp. 15–20 (2019). http://www.thinkmind.org/download.php?articleid=infocomp_2019_2_10_68001

  6. Banagaaya, N., Benner, P., Grundel, S.: Index-preserving model order reduction for differential-algebraic systems arising in gas transport networks. In: Progress in Industrial Mathematics at ECMI 2018, Mathematics in Industry, vol. 30, pp. 291–297 (2019). https://doi.org/10.1007/978-3-030-27550-1_36

  7. Banagaaya, N., Grundel, S., Benner, P.: Index-aware MOR for gas transport networks with many supply inputs. IUTAM Symposium on Model Order Reduction of Coupled Systems, IUTAM Bookseries 36, 191–207 (2019). https://doi.org/10.1007/978-3-030-21013-7_14

  8. Bartel, A., Brunk, M., Günther, M., Schöps, S.: Dynamic iteration for coupled problems of electric circuits and distributed devices. SIAM J. Sci. Comput. 35(2), B315–B335 (2013). https://doi.org/10.1137/120867111

    Article  MathSciNet  MATH  Google Scholar 

  9. Benner, P., Braukmüller, M., Grundel, S.: A direct index 1 DAE model of gas networks. In: Keiper, W., Milde, A., Volkwein, S. (eds.) Reduced-Order Modeling (ROM) for Simulation and Optimization, pp. 99–119. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75319-5_5

  10. Benner, P., Grundel, S., Himpe, C., Huck, C., Streubel, T., Tischendorf, C.: Gas network benchmark models. In: Applications of Differential Algebraic Equations: Examples and Benchmarks, Differential-Algebraic Equation Forum, pp. 171–197. Springer, Cham (2018). https://doi.org/10.1007/11221_2018_5

  11. Benner, P., Himpe, C.: Cross-Gramian-based dominant subspaces. Adv. Comput. Math. 45(5), 2533–2553 (2019). https://doi.org/10.1007/s10444-019-09724-7

    Article  MathSciNet  MATH  Google Scholar 

  12. Benner, P., Himpe, C., Mitchell, T.: On reduced input-output dynamic mode decomposition. Adv. Comput. Math. 44(6), 1821–1844 (2018). https://doi.org/10.1007/s10444-018-9592-x

    Article  MathSciNet  MATH  Google Scholar 

  13. Caliskan, S.Y., Tabuada, P.: Uses and abuses of the swing equation model. In: 2015 54th IEEE Conference on Decision and Control (CDC), pp. 6662–6667. IEEE (15.12.2015 - 18.12.2015). https://doi.org/10.1109/CDC.2015.7403268

  14. Chaczykowski, M.: Sensitivity of pipeline gas flow model to the selection of the equation of state. Chem. Eng. Res. Des. 87, 1596–1603 (2009). https://doi.org/10.1016/j.cherd.2009.06.008

    Article  Google Scholar 

  15. Clees, T., Baldin, A., Klaassen, B., Nikitina, L., Nikitin, I., Spelten, P.: Efficient modeling and simulation of long-distance gas transport networks with large amounts of hydrogen injection. In: SWEDES 2020, Procs. 15th Conf. Sustainable Development of Energy, Water and Environment Systems, Cologne, Sep 1-5, 2020. Accepted as archival paper

    Google Scholar 

  16. Clees, T., Cassirer, K., Hornung, N., Klaassen, B., Nikitin, I., Nikitina, L., Suter, R., Torgovitskaia, I.: MYNTS: Multi-phYsics NeTwork Simulator. In: SIMULTECH 2016, 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. Proceedings, pp. 179–186 (2016). https://doi.org/10.5220/0005961001790186

  17. Clees, T., Hornung, N., Nikitin, I., Nikitina, L.: A globally convergent method for generalized resistive systems and its application to stationary problems in gas transport networks. In: SIMULTECH 2016, 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. Proceedings, pp. 64–70 (2016)

    Google Scholar 

  18. Clees, T., Nikitin, I., Nikitina, L.: Advanced modeling of gas compressors for globally convergent stationary network solvers. In: Seventh International Conference on Advanced Communications and Computation, INFOCOMP 2017, pp. 52–57 (2017)

    Google Scholar 

  19. Clees, T., Nikitin, I., Nikitina, L.: Making network solvers globally convergent. In: Simulation and Modeling Methodologies, Technologies and Applications. International Conference, SIMULTECH 2016, pp. 140–153 (2018). https://doi.org/10.1007/978-3-319-69832-8_9

  20. Clees, T., Nikitin, I., Nikitina, L., Segiet, L.: Modeling of gas compressors and hierarchical reduction for globally convergent stationary network solvers. Int. J. Adv. Syst. Meas. 11(1-2), 61–71 (2018). https://www.thinkmind.org/download.php?articleid=sysmea_v11_n12_2018_6

  21. Dihlmann, M., Haasdonk, B.: A reduced basis Kalman filter for parametrized partial differential equations. ESAIM: COCV 22(3), 625–669 (2016). https://doi.org/10.1051/cocv/2015019

  22. Doetsch, C., Clees, T.: SystemansÃdtze und -komponenten für cross-sektorale Netze, pp. 311–340 (2017). https://doi.org/10.1007/978-3-658-15737-1_17

  23. Dörfler, F.A.: Dynamics and control in power grids and complex oscillator networks. University of California, Santa Barbara, [Santa Barbara, Calif.] (2013)

    Google Scholar 

  24. Egger, H., Kugler, T., Liljegren-Sailer, B., Marheineke, N., Mehrmann, V.: On structure-preserving model reduction for damped wave propagation in transport networks. SIAM J. Sci. Comput. 40, A331–A365 (2017). https://doi.org/10.1137/17M1125303

    Article  MathSciNet  MATH  Google Scholar 

  25. Finnemore, E., Franzini, J.: Fluid Mechanics with Engineering Applications, 10th edn. Asia Higher Education Engineering/Computer Science Civil Engineering, McGraw-Hill Higher Education (2001)

    Google Scholar 

  26. Gerner, A.L., Veroy, K.: Certified reduced basis methods for parametrized saddle point problems. SIAM J. Sci. Comput. 34(5), A2812–A2836 (2012). https://doi.org/10.1137/110854084

    Article  MathSciNet  MATH  Google Scholar 

  27. Grainger, J., Stevenson, W.: Power System Analysis. McGraw-Hill (1994)

    Google Scholar 

  28. Groß, T., Trenn, S., Wirsen, A.: Solvability and stability of a power system DAE model. Syst. Control Lett. 97, 12–17 (2016). https://doi.org/10.1016/j.sysconle.2016.08.003

    Article  MathSciNet  MATH  Google Scholar 

  29. Groß, T.B.: DAE-Modellierung und mathematische Stabilitätsanalyse von Energieversorgungsnetzen. Fraunhofer IRB Verlag, Stuttgart (2016)

    Google Scholar 

  30. Gross, T.B., Trenn, S., Wirsen, A.: Topological solvability and index characterizations for a common DAE power system model. In: 2014 IEEE Conference on Control Applications (CCA), pp. 9–14. IEEE (08.10.2014 - 10.10.2014). https://doi.org/10.1109/CCA.2014.6981321

  31. Grundel, S., Herty, M.: Hyperbolic discretization of the isothermal Euler equation via Riemann invariants. Cornell University (2019). 2005.12158. Math.NA

  32. Grundel, S., Himpe, C., Saak, J.: On empirical system Gramians. Proc. Appl. Math. Mech. 19(1), e201900006 (2019). https://doi.org/10.1002/PAMM.201900006

  33. Grundel, S., Jansen, L.: Efficient simulation of transient gas networks using IMEX integration schemes and MOR methods. In: 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, pp. 4579–4584 (2015). https://doi.org/10.1109/CDC.2015.7402934

  34. Grundel, S., Jansen, L., Hornung, N., Clees, T., Tischendorf, C., Benner, P.: Model order reduction of differential algebraic equations arising from the simulation of gas transport networks. In: Progress in Differential-Algebraic Equations, Differential-Algebraic Equations Forum, pp. 183–205. Springer Berlin Heidelberg (2014). https://doi.org/10.1007/978-3-662-44926-4_9

  35. Himpe, C.: emgr - the Empirical Gramian Framework. Algorithms 11(7), 91 (2018). https://doi.org/10.3390/a11070091

  36. Himpe, C.: emgr – EMpirical GRamian framework (version 5.7) (2019). https://gramian.de. https://doi.org/10.5281/zenodo.2577980

  37. Himpe, C., Leibner, T., Rave, S.: Hierarchical approximate proper orthogonal decomposition. SIAM J. Sci. Comput. 40(5), A3267–A3292 (2018). https://doi.org/10.1137/16M1085413

    Article  MathSciNet  MATH  Google Scholar 

  38. Himpe, C., Leibner, T., Rave, S., Saak, J.: Fast low-rank empirical cross Gramians. Proc. Appl. Math. Mech. 17(1), 841–842 (2017). https://doi.org/10.1002/pamm.201710388

    Article  Google Scholar 

  39. Huck, C.: Perturbation analysis and numerical discretisation of hyperbolic partial differential algebraic equations describing flow networks. Ph.D. thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät (2018). https://doi.org/10.18452/19596

  40. International Standard: Iso 12213-2: Natural gas - calculation of compression factor - part 2: Calculation using molar-composition analysis (2nd ed. 2006-11-15)

    Google Scholar 

  41. Kalman, R.E.: A new approach to linear filtering and prediction problems. J. Basic Eng. 82(1), 35–45 (1960). https://doi.org/10.1115/1.3662552

    Article  MathSciNet  Google Scholar 

  42. Koch, T., Hiller, B., Pfetsch, M., Schewe, L.: Evaluating Gas Network Capacities. Society for Industrial and Applied Mathematics, Philadelphia, PA (2015). https://doi.org/10.1137/1.9781611973693

  43. Kunz, O., Wagner, W.: The GERG-2008 wide-range equation of state for natural gases and other mixtures: an expansion of GERG-2004. J. Chem. Eng. Data 57, 3032–3091 (2012). https://doi.org/10.1021/je300655b

    Article  Google Scholar 

  44. Küsters, F.: Switch Observability for Differential-Algebraic Systems: Analysis. Observer Design and Application to Power Networks. Fraunhofer Verlag, Stuttgart (2018)

    Google Scholar 

  45. Küsters, F., Trenn, S., Wirsen, A.: Switch-observer for switched linear systems. In: Proceedings of the IEEE Conference on Decision and Control. IEEE (2017). https://doi.org/10.1109/CDC.2017.8263903

  46. Lamour, R., März, R., Tischendorf, C.: Differential-Algebraic Equations. A Projector Based Analysis. Springer, Berlin (2013)

    Google Scholar 

  47. Lelarasmee, E.: The waveform relaxation method for time domain analysis of large scale integrated circuits: theory and applications. College of Engineering, University of Berkeley, Electronics Research Laboratory (1982)

    Google Scholar 

  48. Li, J.Y., Kokkinaki, A., Ghorbanidehno, H., Darve, E.F., Kitanidis, P.K.: The compressed state Kalman filter for nonlinear state estimation: application to large-scale reservoir monitoring. Water Resour. Res. 51(12), 9942–9963 (2015). https://doi.org/10.1002/2015WR017203

    Article  Google Scholar 

  49. Lurie, M.: Modeling of Oil Product and Gas Pipeline Transportation. Wiley-VCH Verlag GmbH Co. KGaA (2008). https://doi.org/10.1002/9783527626199

  50. Pade, J., Tischendorf, C.: Waveform relaxation: a convergence criterion for differential-algebraic equations. Numer. Algorithms 81, 1327–1342 (2019). https://doi.org/10.1007/s11075-018-0645-5

    Article  MathSciNet  MATH  Google Scholar 

  51. Pasqualetti, F., Dorfler, F., Bullo, F.: Attack detection and identification in cyber-physical systems. IEEE Trans. Autom. Control 58(11), 2715–2729 (2013). https://doi.org/10.1109/TAC.2013.2266831

    Article  MathSciNet  MATH  Google Scholar 

  52. Sastry, S., Varaiya, P.: Hierarchical stability and alert state steering control of interconnected power systems. IEEE Trans. Circuits Syst. 27(11), 1102–1112 (1980). https://doi.org/10.1109/TCS.1980.1084747

    Article  MathSciNet  MATH  Google Scholar 

  53. Scholz, E.: Observer-based monitors and distributed wave controllers for electromechanical disturbances in power systems. Ph.d. thesis, Massachusetts Institute of Technology (2004). https://dspace.mit.edu/bitstream/handle/1721.1/26723/59669742-MIT.pdf?sequence=2

  54. Schöps, S.: Multiscale modeling and multirate time-integration of field/circuit coupled problems. Ph.D. thesis, Universität Wuppertal, Fakultät für Mathematik und Naturwissenschaften (2018)

    Google Scholar 

  55. Stahl, N., Marheineke, N.: Filtering and model reduction of PDAEs with stochastic boundary data. Proc. Appl. Math. Mech. 19(1), e201900130 (2019). https://doi.org/10.1002/pamm.201900130

  56. Trenn, S.: Distributional differential algebraic equations. \(<Ilmenau>|\)Universitätsverlag Ilmenau (2009)

    Google Scholar 

  57. TUB-ER: partDE data set, Technical University of Berlin (2019). https://www.er.tu-berlin.de/menue/home/parameter/en/

  58. Walther, T., Hiller, B., Saitenmacher, R.: Polyhedral 3d models for compressors in gas networks. In: Kliewer, N., Ehmke, J.F., Borndörfer, R. (eds.) Operations Research Proceedings 2017, pp. 517–523. Springer International Publishing, Cham (2018). https://doi.org/10.1007/978-3-319-89920-6_69

  59. Zimmerman, R.D., Murillo-Sánchez, C.E.: Matpower: Users manual (2016)

    Google Scholar 

Download references

Acknowledgements

This work is supported by the German Federal Ministry for Economic Affairs and Energy, in the joint project: “MathEnergy – Mathematical Key Technologies for Evolving Energy Grids” with its subprojects 0324019A, 0324019B, 0324019E, and 0324019F. The authors thank Philipp Spelten (Fraunhofer SCAI) for providing locations and dimensions of the PtG plants.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tanja Clees .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Clees, T. et al. (2021). MathEnergy – Mathematical Key Technologies for Evolving Energy Grids. In: Göttlich, S., Herty, M., Milde, A. (eds) Mathematical Modeling, Simulation and Optimization for Power Engineering and Management. Mathematics in Industry, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-62732-4_11

Download citation

Publish with us

Policies and ethics