Abstract
We examine two wave equation models for strings of generators connected to a wind farm. The first one, with point source boundary condition leads to a purely discrete system, i.e. a delay system without (continuous) dynamics; the second one, with power flow boundary condition is equivalent to a neutral delay system. We then investigate the differential flatness of the systems.
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References
Anna, F., Quadrat, A.: Applications of the quillen-suslin theorem to multidimensional systems theory. In: Park, H., Regensburger, G. (eds.) Gröbner Bases in Control Theory and Signal Processing, Radon Series on Computation and Applied Mathematics, pp. 23–106. de Gruyter publisher (2007)
Brethé, D., Loiseau, J.: A result that could bear fruit for the control of delay differential systems. In: Proceedings of the 4th IEEE Mediterranean Symposium on Control and Automation, pp. 168–172. Chania, Greece (1996)
Chandra, S., Gayme, D., Chakrabortty, A.: Coordinating wind farms and battery management systems for inter-area oscillation damping: a frequency-domain approach. IEEE Trans. Power Syst. 29, 1454–1462 (2014)
Fliess, M.: Some basic structural properties of generalized linear systems. Syst. Control Lett. 15, 391–396 (1990)
Fliess, M., Mounier, H.: Controllability and observability of linear delay systems : an algebraic approach. ESAIM Control Optim. Calc. Var. 3, 301–314 (1998)
Fliess, M., Mounier, H.: An Algebraic Framework for Infinite Dimensional Linear Systems. e-STA (Sciences et Technologies de l’Automatique) (2004)
Fliess, M., Mounier, H., Rouchon, P., Rudolph, J.: Controllability and motion planning for linear delay systems with an application to a flexible rod. In: Proceedings of the 34th Conference on Decision and Control, pp. 2046–2051. New Orleans, USA (1995)
Gayme, D.F., Chakrabortty, A.: A spatio-temporal framework for spectral analysis and control of interarea oscillations in wind-integrated power systems. IEEE Trans. Control Syst. Technol. 22, 1658–1665 (2014)
Glüsing-Lüerßen, H.: A behavioral approach to delay-differential systems. SIAM J. Control Optim., 480–499 (1997)
Magar, K., Balas, M., Gayme, D.: Adaptive suppression of inter-area oscillation using multiple wind power systems in a distributed parameter control methodology. In: Proceedings of the 19th IFAC World Congress, Cape Town, South Africa (2014)
Mounier, H., Greco, L.: Modelling and structural properties of distributed parameter wind power systems (i). In Proceedings of the MTNS: Minneapolis, p. 2016. MN, USA (2016)
Mounier, H., Rudolph, J., Woittennek, F.: Boundary value problems and convolutional systems over rings of ultradistributions. In: Advances in the Theory of Control, Signals and Systems with Physical Modeling. Lecture Notes in Control and Information Science, vol. 407, pp. 179–188. Springer, Berlin (2010)
Parashar, M., Thorp, J.S.: Continuum modeling of electromechanical dynamics in large-scale power systems. IEEE Trans. Circuits Syst. 51, 1848–1858 (2004)
Rotman, J.J.: An introduction to Homological Algebra. Springer, New York (1979)
Rudolph, J., Woittennek, F.: Motion planning and open loop control design for linear distributed parameter systems with lumped controls. Int. J. Control 81, 457–474 (2008)
Thorp, J.S., Seyler, C.E., Phadke, A.G.: Electromechanical wave propagation in large electric power systems. IEEE Trans. Circuit Syst. I 45 (1998)
Woittennek, F., Mounier, H.: Controllability of networks of spatially one-dimensional second order pde - an algebraic approach. SIAM J. Control Optim. 48, 3882–3902 (2010)
Xu, Y., Wen, F., Ledwich, G., Xue, Y.: Electromechanical wave in power systems: theory and applications. J. Mod. Power Syst. Clean Energy 2, 163–172 (2014)
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Mounier, H., Greco, L. (2019). Wave Equation Modelling and Freeness Properties for Wind Power Systems. In: Valmorbida, G., Seuret, A., Boussaada, I., Sipahi, R. (eds) Delays and Interconnections: Methodology, Algorithms and Applications. Advances in Delays and Dynamics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-11554-8_13
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