Frequency-adaptive periodic control
Connecting power converters to the electrical networks has become a crucial issue due to the fast-growing penetration of renewable energy sources and distributed generation systems. In these practical applications, the frequency of the periodic signals of interest is not constant always but slowly time-varying due to the imbalance between the power generation and the load demand. Both fundamental and advanced PC schemes can achieve zero steady-state error tracking of any periodic signal with a known period due to the introduction of high gains at the interested harmonic frequencies by embedding the corresponding internal models. However, frequency variations will lead to mismatch between their embedded nominal internal models and the actual periodic references/ disturbances, and will shift high gains away from the actual frequency of interest. Thus these PC schemes will fail to accurately track the varying-frequency periodic signals. It means that their internal models are sensitive to frequency variations. Moreover, delay-based PC schemes in their digital forms, such as the digital classic repetitive control (RC), discrete Fourier transform (DFT)-based RC, digital selective harmonic control (SHC), and so on, even require that the period of the references/disturbances can be represented as integer multiple of the sample time of the digital control system. This means that the period of the interested periodic signal should be an integer, but the period will not be an exact integer except by chance. A varying frequency often induces fractional-period harmonics. Such mismatches between the given integer period and actual fractional period will lead these PC strategies to yield low gains at the interested harmonic frequencies and thus produce poor tracking accuracy. For example, the grid frequency is usually varying within a certain range (e.g., 49 Hz ~ 51 Hz) due to the generation-load imbalance and/or continuously connecting and disconnecting of large generation units. The PC schemes may fail to force grid-tied converters to feed good quality power into the grid in the presence of a time-varying grid frequency. Therefore, it calls for frequency-adaptive PC solutions that are able to self-tune the corresponding internal model to match the external signal closely and then accurately compensate the varying-frequency voltages and/or currents for good power quality and also stable operation of the grid-connected systems. The performance of the PC systems depends on how precise the match is between the PC signal generator period and the actual signal period. Addressing the above issues, this chapter explores the frequency-adaptive internal model principle (IMP)-based PC strategies to compensate frequency-varying harmonics. A direct frequency-adaptive resonant controller is investigated. A fractional-delay filter-based internal model is introduced to provide a general frequency-adaptive PC solution to the compensation of frequency-varying periodic signals. The frequency sensitivity, design, and implementation methodology of frequency-adaptive PC systems are discussed. Compatible synthesis methods for plug-in frequency-adaptive PC schemes are also presented.