Case Study #5: Renewable Energy Microgrid Design

  • Rush D. RobinettIII
  • David G. Wilson
Part of the Understanding Complex Systems book series (UCS)


The swing equations for renewable generators connected to the grid and islanded configuration are developed. A wind turbine is used as an example. The swing equations for the renewable generators are formulated as a natural Hamiltonian system with externally applied nonconservative forces. HSSPFC is used to analyze and design feedback controllers for the renewable generators system. This formulation extends previous results on the analytical verification of the Potential Energy Boundary Surface (PEBS) method to nonlinear control analysis and design and justifies the decomposition of the system into conservative and nonconservative systems to enable a two-step, serial analysis and design procedure. The first step is to analyze the system as a conservative natural Hamiltonian system with no externally applied nonconservative forces. The Hamiltonian surface of the swing equations is related to the Equal-Area Criterion and the PEBS method to formulate the nonlinear transient stability problem. This formulation demonstrates the effectiveness of proportional feedback control to expand the stability region. The second step is to analyze the system as a natural Hamiltonian system with externally applied nonconservative forces. The time derivative of the Hamiltonian produces the work/rate (power flow) equations that are used to ensure balanced power flows from the renewable generators to the loads. The Second Law of Thermodynamics is applied to the power flow equations to determine the stability boundaries (limit cycles) of the renewable generators system and enable design of feedback controllers that meet stability requirements while maximizing the power generation and flow to the load. Necessary and sufficient conditions for stability of renewable generators systems are determined based on the concepts of Hamiltonian systems, power flow, exergy (the maximum work that can be extracted from an energy flow) rate, and entropy rate.


Wind Turbine Power Flow Unify Power Flow Controller Renewable Generator Nonconservative Force 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Sandia National LaboratoriesAlbuquerqueUSA

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