Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Structure-Preserving Model Order Reduction for Nonlinear DAE Models of Power Networks (2405.07587v2)

Published 13 May 2024 in eess.SY and cs.SY

Abstract: This paper deals with the joint reduction of the number of dynamic and algebraic states of a nonlinear differential-algebraic equation (NDAE) model of a power network. The dynamic states depict the internal states of generators, loads, renewables, whereas the algebraic ones define network states such as voltages and phase angles. In the current literature of power system model order reduction (MOR), the algebraic constraints are usually neglected and the power network is commonly modeled via a set of ordinary differential equations (ODEs) instead of NDAEs. Thus, reduction is usually carried out for the dynamic states only and the algebraic variables are kept intact. This leaves a significant part of the system's size and complexity unreduced. This paper addresses this aforementioned limitation by jointly reducing both dynamic and algebraic variables. As compared to the literature the proposed MOR techniques are endowed with the following features: (i) no system linearization is required, (ii) require no transformation to an equivalent or approximate ODE representation, (iii) guarantee that the reduced order model to be NDAE-structured and thus preserves the differential-algebraic structure of original power system model, and (iv) can seamlessly reduce both dynamic and algebraic variables while maintaining high accuracy. Case studies performed on a 2000-bus power system reveal that the proposed MOR techniques are able to reduce system order while maintaining accuracy.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (27)
  1. A. Yogarathinam, J. Kaur, and N. R. Chaudhuri, “A new h-irka approach for model reduction with explicit modal preservation: Application on grids with renewable penetration,” IEEE Transactions on Control Systems Technology, vol. 27, no. 2, pp. 880–888, 2017.
  2. M. Nadeem, M. Bahavarnia, and A. F. Taha, “Robust feedback control of power systems with solar plants and composite loads,” IEEE Transactions on Power Systems, (Early Access), 2023.
  3. F. Ma and V. Vittal, “Right-sized power system dynamic equivalents for power system operation,” IEEE Transactions on Power Systems, vol. 26, no. 4, pp. 1998–2005, 2011.
  4. J. Qi, J. Wang, H. Liu, and A. D. Dimitrovski, “Nonlinear model reduction in power systems by balancing of empirical controllability and observability covariances,” IEEE Transactions on Power Systems, vol. 32, no. 1, pp. 114–126, 2016.
  5. B. Safaee and S. Gugercin, “Structure-preserving model reduction for nonlinear power grid network,” arXiv preprint arXiv:2203.09021, 2022.
  6. J. Kaur and N. R. Chaudhuri, “Challenges of model reduction in modern power grid with wind generation,” in 2016 North American Power Symposium (NAPS).   IEEE, 2016, pp. 1–6.
  7. F. D. Freitas, J. Rommes, and N. Martins, “Gramian-based reduction method applied to large sparse power system descriptor models,” IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1258–1270, 2008.
  8. J. Rommes and N. Martins, “Efficient computation of multivariable transfer function dominant poles using subspace acceleration,” IEEE transactions on power systems, vol. 21, no. 4, pp. 1471–1483, 2006.
  9. N. Martins, P. C. Pellanda, and J. Rommes, “Computation of transfer function dominant zeros with applications to oscillation damping control of large power systems,” IEEE transactions on power systems, vol. 22, no. 4, pp. 1657–1664, 2007.
  10. R. Singh, M. Elizondo, and S. Lu, “A review of dynamic generator reduction methods for transient stability studies,” in 2011 IEEE Power and Energy Society General Meeting.   IEEE, 2011, pp. 1–8.
  11. S. D. Đukić and A. T. Sarić, “Dynamic model reduction: An overview of available techniques with application to power systems,” Serbian journal of electrical engineering, vol. 9, no. 2, pp. 131–169, 2012.
  12. T. Groß, S. Trenn, and A. Wirsen, “Solvability and stability of a power system dae model,” Systems and Control Letters, vol. 97, pp. 12–17, 2016. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0167691116301098
  13. D. Wu and B. Wang, “Influence of load models on equilibria, stability and algebraic manifolds of power system differential-algebraic system,” 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 787–795, 2019.
  14. S. Muntwiler, O. Stanojev, A. Zanelli, G. Hug, and M. N. Zeilinger, “A stiffness-oriented model order reduction method for low-inertia power systems,” arXiv preprint arXiv:2310.10137, 2023.
  15. M. Rewienski and J. White, “A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices,” IEEE Transactions on computer-aided design of integrated circuits and systems, vol. 22, no. 2, pp. 155–170, 2003.
  16. T. Sadamoto, A. Chakrabortty, T. Ishizaki, and J.-i. Imura, “Dynamic modeling, stability, and control of power systems with distributed energy resources: Handling faults using two control methods in tandem,” IEEE Control Systems Magazine, vol. 39, no. 2, pp. 34–65, 2019.
  17. R. Reinout, “Empirical model reduction of differential-algebraic equation systems,” https://www.avt.rwth-aachen.de/go/id/iavo/lidx/1/file/565860, 2015.
  18. S. Lall, J. E. Marsden, and S. Glavaški, “A subspace approach to balanced truncation for model reduction of nonlinear control systems,” International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal, vol. 12, no. 6, pp. 519–535, 2002.
  19. J. Hahn and T. F. Edgar, “Balancing approach to minimal realization and model reduction of stable nonlinear systems,” Industrial & engineering chemistry research, vol. 41, no. 9, pp. 2204–2212, 2002.
  20. J. Hahn, T. F. Edgar, and W. Marquardt, “Controllability and observability covariance matrices for the analysis and order reduction of stable nonlinear systems,” Journal of process control, vol. 13, no. 2, pp. 115–127, 2003.
  21. C. Sun and J. Hahn, “Reduction of stable differential–algebraic equation systems via projections and system identification,” Journal of process control, vol. 15, no. 6, pp. 639–650, 2005.
  22. I. C. for a Smarter Electric Grid (ICSEG), “Inf. trust inst., univ. illinois urbana-champaign, urbana, il, usa,,” https://icseg.iti.illinois.edu/power-cases/, Jun. 2016.
  23. S. Lall, J. E. Marsden, and S. Glavaški, “Empirical model reduction of controlled nonlinear systems,” IFAC Proceedings Volumes, vol. 32, no. 2, pp. 2598–2603, 1999.
  24. S. Liu, “Dynamic-data driven real-time identification for electric power systems, ph.d. diss., university of illinois at urbana-champaign.”
  25. C. W. Rowley, “Model reduction for fluids, using balanced proper orthogonal decomposition,” International Journal of Bifurcation and Chaos, vol. 15, no. 03, pp. 997–1013, 2005.
  26. S. Roy and H. N. Villegas Pico, “Transient stability and active protection of power systems with grid-forming pv power plants,” IEEE Transactions on Power Systems, pp. 1–1, 2022.
  27. O. Wasynczuk, S. Sudhoff, T. Tran, D. Clayton, and H. Hegner, “A voltage control strategy for current-regulated pwm inverters,” IEEE Transactions on Power Electronics, vol. 11, no. 1, pp. 7–15, 1996.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now