Nonlinear power flow control applications to conventional generator swing equations subject to variable generation

In this paper, the swing equations for 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 generator 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. In particular, this approach extends the work done by by developing a formulation which applies to a larger set of Hamiltonian Systems that has Nearly Hamiltonian Systems as a subset. The results of this research include the determination of the required performance of a proposed Flexible AC Transmission System (FACTS)/storage device to enable the maximum power output of a wind turbine while meeting the power system constraints on frequency and phase. The FACTS/storage device is required to operate as both a generator and load (energy storage) on the power system in this design. The Second Law of Thermodynamics is applied to the power flow equations to determine the stability boundaries (limit cycles) of the renewable generator 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.