An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages

The power grid can be regarded as a large interconnected network of different subsystems, called control area’s. In order to guarantee reliable operation the frequency is tightly regulated around its nominal value, e.g. 50 Hz. Automatic regulation of the frequency in power grid is traditionally achieved by primary proportional control (droop-control) and a secondary PI-control on the generators, where economic considerations are largely neglected. Recently we proposed a novel distributed controller in [1] that controls power production such that the frequency is regulated in an economic efficient way. Main advantage of our approach, based on passivity properties of the system, is that it has the potential to deal with more complex models of dynamical networks and fairly rich classes of external perturbations.

[1]  Claudio De Persis,et al.  Internal Models for Nonlinear Output Agreement and Optimal Flow Control , 2013, NOLCOS.

[2]  Aranya Chakrabortty,et al.  Topology identification for dynamic equivalent models of large power system networks , 2013, 2013 American Control Conference.

[3]  John T. Wen,et al.  Cooperative Control Design - A Systematic, Passivity-Based Approach , 2011, Communications and control engineering.

[4]  I. V. D. Hoven POWER SPECTRUM OF HORIZONTAL WIND SPEED IN THE FREQUENCY RANGE FROM 0.0007 TO 900 CYCLES PER HOUR , 1957 .

[5]  Joe H. Chow,et al.  A Measurement-Based Framework for Dynamic Equivalencing of Large Power Systems Using Wide-Area Phasor Measurements , 2011, IEEE Transactions on Smart Grid.

[6]  Na Li,et al.  Connecting Automatic Generation Control and Economic Dispatch From an Optimization View , 2014, IEEE Transactions on Control of Network Systems.

[7]  Chia-Chi Chu,et al.  Direct stability analysis of electric power systems using energy functions: theory, applications, and perspective , 1995, Proc. IEEE.

[8]  Claudio De Persis,et al.  Balancing time-varying demand-supply in distribution networks: An internal model approach , 2013, 2013 European Control Conference (ECC).

[9]  Francesco Bullo,et al.  Breaking the Hierarchy: Distributed Control and Economic Optimality in Microgrids , 2014, IEEE Transactions on Control of Network Systems.

[10]  Ibraheem,et al.  Recent philosophies of automatic generation control strategies in power systems , 2005, IEEE Transactions on Power Systems.

[11]  F. Bullo,et al.  Novel insights into lossless AC and DC power flow , 2013, 2013 IEEE Power & Energy Society General Meeting.

[12]  L.-A. Dessaint,et al.  Dynamic equivalent modeling of large power systems using structure preservation technique , 2006, IEEE Transactions on Power Systems.

[13]  Peter W. Sauer,et al.  Automatic Generation Control and Its Implementation in Real Time , 2014, 2014 47th Hawaii International Conference on System Sciences.

[14]  Lorenzo Marconi,et al.  Semi-global nonlinear output regulation with adaptive internal model , 2001, IEEE Trans. Autom. Control..

[15]  Jacquelien M. A. Scherpen,et al.  A port-Hamiltonian approach to power network modeling and analysis , 2013, Eur. J. Control.

[16]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems on Graphs , 2011, SIAM J. Control. Optim..

[17]  Rodolphe Sepulchre,et al.  Analysis of Interconnected Oscillators by Dissipativity Theory , 2007, IEEE Transactions on Automatic Control.

[18]  Xuan Zhang,et al.  A real-time control framework for smart power networks with star topology , 2013, 2013 American Control Conference.

[19]  BürgerMathias,et al.  An internal model approach to (optimal) frequency regulation in power grids with time-varying voltages , 2016 .

[20]  Ufuk Topcu,et al.  Power System Dynamics as Primal-Dual Algorithm for Optimal Load Control , 2013, ArXiv.

[21]  R. Plemmons M-matrix characterizations.I—nonsingular M-matrices , 1977 .

[22]  Arthur R. Bergen,et al.  Power Systems Analysis , 1986 .

[23]  Frank Allgöwer,et al.  Dynamic Pricing Control for Constrained Distribution Networks With Storage , 2015, IEEE Transactions on Control of Network Systems.

[24]  Lorenzo Marconi,et al.  Incremental passivity and output regulation , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[25]  Karl Henrik Johansson,et al.  Distributed vs. centralized power systems frequency control , 2013, 2013 European Control Conference (ECC).

[26]  A.R. Bergen,et al.  A Structure Preserving Model for Power System Stability Analysis , 1981, IEEE Transactions on Power Apparatus and Systems.

[27]  Frank Allgöwer,et al.  An internal model principle is necessary and sufficient for linear output synchronization , 2011, Autom..

[28]  Luis A. Aguirre,et al.  Dynamical prediction and pattern mapping in short-term load forecasting , 2008 .

[29]  J. Peinke,et al.  Turbulent character of wind energy. , 2013, Physical review letters.

[30]  Hsiao-Dong Chiang,et al.  Constructing analytical energy functions for lossless network-reduction power system models: Framework and new developments , 1999 .

[31]  Juan C. Vasquez,et al.  Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization , 2009, IEEE Transactions on Industrial Electronics.

[32]  Frank Allgöwer,et al.  Optimal pricing control in distribution networks with time-varying supply and demand , 2014, ArXiv.

[33]  Claudio De Persis,et al.  On the Internal Model Principle in the Coordination of Nonlinear Systems , 2014, IEEE Transactions on Control of Network Systems.

[34]  Francesco Bullo,et al.  Synchronization and power sharing for droop-controlled inverters in islanded microgrids , 2012, Autom..

[35]  H. Miyagi,et al.  Stability studies of multimachine power systems with the effects of automatic voltage regulators , 1986 .

[36]  Lorenzo Marconi,et al.  Hybrid internal models for robust spline tracking , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[37]  Janusz Bialek,et al.  Power System Dynamics: Stability and Control , 2008 .

[38]  Steven H. Low,et al.  Decentralized Primary Frequency Control in Power Networks , 2014, ArXiv.

[39]  Paulo Tabuada,et al.  Compositional Transient Stability Analysis of Multimachine Power Networks , 2013, IEEE Transactions on Control of Network Systems.

[40]  Johannes Schiffer,et al.  Synchronization of droop-controlled microgrids with distributed rotational and electronic generation , 2013, 52nd IEEE Conference on Decision and Control.

[41]  Romeo Ortega,et al.  Passivity of Nonlinear Incremental Systems: Application to PI Stabilization of Nonlinear RLC Circuits , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[42]  Claudio De Persis,et al.  Dynamic coupling design for nonlinear output agreement and time-varying flow control , 2013, Autom..

[43]  Frank Allgöwer,et al.  Duality and network theory in passivity-based cooperative control , 2013, Autom..

[44]  Lorenzo Marconi,et al.  Robust output synchronization of a network of heterogeneous nonlinear agents via nonlinear regulation theory , 2013, 52nd IEEE Conference on Decision and Control.

[45]  Johannes Falnes,et al.  A REVIEW OF WAVE-ENERGY EXTRACTION , 2007 .

[46]  Florian Dörfler,et al.  Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators , 2009, Proceedings of the 2010 American Control Conference.

[47]  Ufuk Topcu,et al.  Design and Stability of Load-Side Primary Frequency Control in Power Systems , 2013, IEEE Transactions on Automatic Control.