Publications
Transient stability and control of renewable generators based on Hamiltonian surface shaping and power flow control. Part II, analysis
The swing equations for renewable generators connected to the grid are developed and 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 non-conservative forces. A two-step process referred to as Hamiltonian Surface Shaping and Power Flow Control (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 non-conservative 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 non-conservative 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 natural Hamiltonian system with externally applied non-conservative forces. The time derivative of the Hamiltonian produces the work/rate (power flow) equation which is 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. This paper will present the analysis and numerical simulation results for two nonlinear control design examples that include: (1) the One-Machine Infinite Bus (OMIB) system with a Unified Power Flow Controller (UPFC) and (2) the swing equation for a wind turbine connected to an infinite bus through a UPFC to determine the required performance of the UPFC to enable the maximum power output of a wind turbine subject to stochastic inputs while meeting the power system constraints on frequency and phase. The energy storage requirements will also be identified from the UPFC and/or FACTS devices while working in combination with the wind turbine.