Nonlinear power flow control design for combined conventional and variable generation systems: Part I-theory

The swing equations for conventional and renewable generators connected to the electric power grid and microgrids are developed. Simple diesel and wind turbine generators with Unified Power Flow Control (UPFC) are used as an example. The swing equations for a renewable generator and conventional generators in an islanded microgrid 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 and islanded microgrid systems. This paper presents the analysis and design of nonlinear controller examples that include a two-machine infinite bus system with UPFC´s in an islanded microgrid and applied to simplified diesel and wind turbine generators connected to the grid. The needed power and energy storage/charging responses are also determined. 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.