A System Reference Frame Approach for Stability Analysis and Control of Power Grids
Authors
Chrysovalantis Spanias, Ioannis Lestas
Abstract
During the last decades, significant advances have been made in the area of power system stability and control. Nevertheless, when this analysis is carried out by means of decentralized conditions in a general network, it has been based on conservative assumptions such as the adoption of lossless networks. In this paper, we present a novel approach for decentralized stability analysis and control of power grids through the transformation of both the network and the bus dynamics into the system reference frame. In particular, the aforementioned transformation allows us to formulate the network model as an input–output system that is shown to be passive even if the network’s lossy nature is taken into account. We then introduce a broad class of bus dynamics that are viewed as multivariable input/output systems compatible with the network formulation, and appropriate passivity conditions are imposed on those that guarantee stability of the power network. We discuss the opportunities and advantages offered by this approach while explaining how this allows the inclusion of advanced models for both generation and power flows. Our analysis is verified through applications to the two area Kundur and the IEEE 68-bus test systems with both primary frequency and voltage regulation mechanisms included.
Citation
- Journal: IEEE Transactions on Power Systems
- Year: 2019
- Volume: 34
- Issue: 2
- Pages: 1105–1115
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/tpwrs.2018.2872549
BibTeX
@article{Spanias_2019,
title={{A System Reference Frame Approach for Stability Analysis and Control of Power Grids}},
volume={34},
ISSN={1558-0679},
DOI={10.1109/tpwrs.2018.2872549},
number={2},
journal={IEEE Transactions on Power Systems},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={Spanias, Chrysovalantis and Lestas, Ioannis},
year={2019},
pages={1105--1115}
}
References
- Horn, R. A. & Johnson, C. R. Matrix Analysis. (2012) doi:10.1017/cbo9781139020411 – 10.1017/cbo9781139020411
- Kottenstette, N. & Antsaklis, P. J. Relationships between positive real, passive dissipative, & positive systems. Proceedings of the 2010 American Control Conference 409–416 (2010) doi:10.1109/acc.2010.5530779 – 10.1109/acc.2010.5530779
- Wang, H. F. & Swift, F. J. A unified model for the analysis of FACTS devices in damping power system oscillations. I. Single-machine infinite-bus power systems. IEEE Transactions on Power Delivery vol. 12 941–946 (1997) – 10.1109/61.584417
- Teodorescu, R., Liserre, M. & Rodríguez, P. Grid Converters for Photovoltaic and Wind Power Systems. (2010) doi:10.1002/9780470667057 – 10.1002/9780470667057
- Hiskens, I. A. & Milanovic, J. V. Load modelling in studies of power system damping. IEEE Transactions on Power Systems vol. 10 1781–1788 (1995) – 10.1109/59.476041
- Venezian, E. & Weiss, G. A warning about the use of reduced models of synchronous generators. 2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE) 1–5 (2016) doi:10.1109/icsee.2016.7806190 – 10.1109/icsee.2016.7806190
- chow, Power system toolbox. (2000)
- rogers, Power System Oscillations (2012)
- HaiFeng Wang. A unified model for the analysis of FACTS devices in damping power system oscillations. III. Unified power flow controller. IEEE Transactions on Power Delivery vol. 15 978–983 (2000) – 10.1109/61.871362
- Wang, H. F., Swift, F. J. & Li, M. A unified model for the analysis of FACTS devices in damping power system oscillations. II. Multi-machine power systems. IEEE Transactions on Power Delivery vol. 13 1355–1362 (1998) – 10.1109/61.714508
- Schiffer, J., Fridman, E., Ortega, R. & Raisch, J. Stability of a class of delayed port-Hamiltonian systems with application to microgrids with distributed rotational and electronic generation. Automatica vol. 74 71–79 (2016) – 10.1016/j.automatica.2016.07.022
- Schiffer, J., Ortega, R., Astolfi, A., Raisch, J. & Sezi, T. Conditions for stability of droop-controlled inverter-based microgrids. Automatica vol. 50 2457–2469 (2014) – 10.1016/j.automatica.2014.08.009
- Caliskan, S. Y. & Tabuada, P. Compositional Transient Stability Analysis of Multimachine Power Networks. IEEE Transactions on Control of Network Systems vol. 1 4–14 (2014) – 10.1109/tcns.2014.2304868
- Stegink, T., De Persis, C. & van der Schaft, A. Optimal power dispatch in networks of high-dimensional models of synchronous machines. 2016 IEEE 55th Conference on Decision and Control (CDC) 4110–4115 (2016) doi:10.1109/cdc.2016.7798892 – 10.1109/cdc.2016.7798892
- Andreasson, M., Wiget, R., Dimarogonas, D. V., Johansson, K. H. & Andersson, G. Distributed primary frequency control through multi-terminal HVDC transmission systems. 2015 American Control Conference (ACC) 5029–5034 (2015) doi:10.1109/acc.2015.7172122 – 10.1109/acc.2015.7172122
- Trip, S., Bürger, M. & De Persis, C. An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages. Automatica vol. 64 240–253 (2016) – 10.1016/j.automatica.2015.11.021
- Kasis, A., Devane, E., Spanias, C. & Lestas, I. Primary Frequency Regulation With Load-Side Participation—Part I: Stability and Optimality. IEEE Transactions on Power Systems vol. 32 3505–3518 (2017) – 10.1109/tpwrs.2016.2636286
- glover, Power System Analysis & Design SI Version (2012)
- kundur, Power System Stability and Control (1994)
- machowski, Power System Dynamics Stability and Control (2011)
- Zhao, C., Topcu, U., Li, N. & Low, S. Design and Stability of Load-Side Primary Frequency Control in Power Systems. IEEE Transactions on Automatic Control vol. 59 1177–1189 (2014) – 10.1109/tac.2014.2298140
- Miyagi, H. & Bergen, A. Stability studies of multimachine power systems with the effects of automatic voltage regulators. IEEE Transactions on Automatic Control vol. 31 210–215 (1986) – 10.1109/tac.1986.1104229
- Kasis, A., Devane, E. & Lestas, I. On the stability and optimality of primary frequency regulation with load-side participation. 2015 54th IEEE Conference on Decision and Control (CDC) 2621–2626 (2015) doi:10.1109/cdc.2015.7402611 – 10.1109/cdc.2015.7402611
- Kirby, B. & Hirst, E. Ancillary Service Details: Voltage Control. http://dx.doi.org/10.2172/607488 (1997) doi:10.2172/607488 – 10.2172/607488
- Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Transactions on Automatic Control vol. 45 1498–1502 (2000) – 10.1109/9.871758
- Machowski, J., Robak, S., Bialek, J. W., Bumby, J. R. & Abi-Samra, N. Decentralized stability-enhancing control of synchronous generator. IEEE Transactions on Power Systems vol. 15 1336–1344 (2000) – 10.1109/59.898110
- van der Schaft, A. J. & Maschke, B. M. Port-Hamiltonian Systems on Graphs. SIAM Journal on Control and Optimization vol. 51 906–937 (2013) – 10.1137/110840091
- Fiaz, S., Zonetti, D., Ortega, R., Scherpen, J. M. A. & van der Schaft, A. J. A port-Hamiltonian approach to power network modeling and analysis. European Journal of Control vol. 19 477–485 (2013) – 10.1016/j.ejcon.2013.09.002
- Yuzhen Wang, Daizhan Cheng, Chunwen Li & You Ge. Dissipative hamiltonian realization and energy-based L/sub 2/-disturbance attenuation control of multimachine power systems. IEEE Transactions on Automatic Control vol. 48 1428–1433 (2003) – 10.1109/tac.2003.815037
- Ma, O. et al. Demand Response for Ancillary Services. IEEE Transactions on Smart Grid vol. 4 1988–1995 (2013) – 10.1109/tsg.2013.2258049
- Stegink, T., De Persis, C. & van der Schaft, A. A Unifying Energy-Based Approach to Stability of Power Grids With Market Dynamics. IEEE Transactions on Automatic Control vol. 62 2612–2622 (2017) – 10.1109/tac.2016.2613901
- Definition and Classification of Power System Stability IEEE/CIGRE Joint Task Force on Stability Terms and Definitions. IEEE Transactions on Power Systems vol. 19 1387–1401 (2004) – 10.1109/tpwrs.2004.825981
- bergen, Power Systems Analysis (2000)
- Schiffer, J. et al. A survey on modeling of microgrids—From fundamental physics to phasors and voltage sources. Automatica vol. 74 135–150 (2016) – 10.1016/j.automatica.2016.07.036
- sauer, Power System Dynamics and Stability (1997)
- Kottenstette, N., McCourt, M. J., Xia, M., Gupta, V. & Antsaklis, P. J. On relationships among passivity, positive realness, and dissipativity in linear systems. Automatica vol. 50 1003–1016 (2014) – 10.1016/j.automatica.2014.02.013
- khalil, Nonlinear Systems (2002)
- Devane, E., Kasis, A., Antoniou, M. & Lestas, I. Primary Frequency Regulation With Load-Side Participation—Part II: Beyond Passivity Approaches. IEEE Transactions on Power Systems vol. 32 3519–3528 (2017) – 10.1109/tpwrs.2016.2636284
- mccourt, Demonstrating passivity and dissipativity using computational methods. (2013)