Transient losses in synchronizing renewable energy integrated power networks

This paper quantifies the transient power losses incurred in re-synchronizing a network of generators and loads. The power system is represented using a network preserving model with loads and asynchronous generators modeled as frequency dependent power injections, which we refer to as `first-order oscillators'. Coupling these models with the swing equations of traditional generators leads to a mixed-oscillator system. The power flows used to maintain network synchronization induce resistive (real power) losses in the system, which we quantify through an H2 norm that is shown to scale with network size. Our results also show that given a fixed network size, this H2 norm is the same for first-order, second-order and mixed-oscillator systems, provided that the damping coefficients are all equal. Therefore, if the renewable power generators being added to a power network can be controlled so that their effective dampings match those of the existing generators, they will not increase transient power losses in the system.

[1]  Bassam Bamieh,et al.  The Price of Synchrony: Evaluating the Resistive Losses in Synchronizing Power Networks , 2015, IEEE Transactions on Control of Network Systems.

[2]  Milad Siami,et al.  Fundamental limits on robustness measures in networks of interconnected systems , 2013, 52nd IEEE Conference on Decision and Control.

[3]  Peter W. Sauer,et al.  Development and comparative study of induction machine based dynamic P, Q load models , 1995 .

[4]  J. G. Slootweg,et al.  Impacts of Wind Power on Power System Dynamics , 2005 .

[5]  Florian Dörfler,et al.  Droop-Controlled Inverters are Kuramoto Oscillators , 2012, ArXiv.

[6]  Enrique Mallada,et al.  Improving damping of power networks: Power scheduling and impedance adaptation , 2011, IEEE Conference on Decision and Control and European Control Conference.

[7]  Ulla Miekkala,et al.  Graph properties for splitting with grounded Laplacian matrices , 1993 .

[8]  Seth A. Myers,et al.  Spontaneous synchrony in power-grid networks , 2013, Nature Physics.

[9]  Pravin Varaiya,et al.  Smart Operation of Smart Grid: Risk-Limiting Dispatch , 2011, Proceedings of the IEEE.

[10]  F.F. Wu,et al.  Direct methods for transient stability analysis of power systems: Recent results , 1985, Proceedings of the IEEE.

[11]  Emma Sj,et al.  The Price of Synchrony: Evaluating Transient Power Losses in Renewable Energy Integrated Power Networks , 2013 .

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

[13]  Michael Chertkov,et al.  Synchronization in complex oscillator networks and smart grids , 2012, Proceedings of the National Academy of Sciences.

[14]  Leon Freris,et al.  Renewable energy in power systems , 2008 .

[15]  Stephen P. Boyd,et al.  Minimizing Effective Resistance of a Graph , 2008, SIAM Rev..

[16]  End Use.  Annual energy outlook : with projections to ... , 1983 .

[17]  H. Chiang.  Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundation, BCU Methodologies, and Applications , 2010 .

[18]  P. Kundur,et al.  Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions , 2004, IEEE Transactions on Power Systems.

[19]  Janaka Ekanayake,et al.  Dynamic modeling of doubly fed induction generator wind turbines , 2003 .

[20]  G. Boyle.  Renewable Energy: Power for a Sustainable Future , 2012 .

[21]  Marco Liserre,et al.  Grid Converters for Photovoltaic and Wind Power Systems , 2011 .

[22]  David G. Wilson,et al.  Transient stability and control of renewable generators based on Hamiltonian Surface Shaping and Power Flow Control: Part I-theory , 2010, 2010 IEEE International Conference on Control Applications.

[23]  Godfrey Boyle,et al.  Renewable Energy: Power for a Sustainable Future (3rd ed.) , 2012 .

[24]  A. V. Meier.  Electric power systems : a conceptual introduction , 2006 .

[25]  Bassam Bamieh,et al.  The price of synchrony: Resistive losses due to phase synchronization in power networks , 2012, 2013 American Control Conference.

[26]  J. G. Slootweg,et al.  Reduced‐Order Modelling of Wind Turbines , 2012 .