MATHEMATICAL MODELING Virtual Inertial Response of Doubly Fed Induction Generator Wind Turbines Elena van Hove1, Jonathan Devadason2 1Purdue University 2The University of Tennessee, Knoxville Load decreases DFIG power decreases and speed increases which is good At about 65 s P looks bad W looks good until 65 s MOTIVATION Conventional energy sources Provide constant source of energy but are harmful to the environment Can quickly adjust to fluctuations in load power demand Use inertial response of synchronous generators Inertial response is taking kinetic energy from generator’s rotor Wind turbines Predominately use induction generators Do not have inertial response Want to make controls that mimic inertial response Common case of sudden frequency fluctuation is generator fall out Deviation from 60 Hz is bad, machines heat up Customer satisfaction is important Simulation I. Approximate variable initial values Change in load MATHEMATICAL MODELING Equations derived from block diagram: II. Find steady state values using derived equations III. Apply load change at 50 seconds Doubly-Fed Induction Generator (DFIG) equation derivation to model inertial response in MATLAB 34 state and algebraic variables RESULTS Inertial response very sensitive to KPF and KDF controllers Important for frequency to stay near constant All initial load values are Po= 0.5 p.u. and Qo= 0.1 p.u. Example of load decrease DFIG power appropriately decreases as synchronous generator speed increases Figure 1: Block diagram of DFIG wind turbine model   Figure 2: Circuit realization of DFIG wind turbine model (1) (2) (3) (4) (5) (6) (7) (8)   FUTURE WORK Make robust conclusions on DFIG model Investigate KPF and KDF controllers Compare another virtual inertial response model This work was supported primarily by the ERC Program of the National Science Foundation and DOE under NSF Award Number EEC-1041877. Other US government and industrial sponsors of CURENT research are also gratefully acknowledged.