Efficient Frequency Control in Microgrids Using Padula and Visioli-Tuned PID Strategy Based on FOPDT Model

Frequency instability of an isolated microgrid (IMG) often arises due to load variations and uncertain power outputs of renewable sources. This contribution addresses the frequency instability issue by designing a Padula and Visioli (PV) tuned proportional-integral-derivative (PID) controller for IMG. The considered IMG model is novel due to the integration of eco-friendly generation sources, including a biogas turbine generator (BTG) and a biodiesel engine generator (BEG), along with other distributed generation units (DGUs) and energy storage devices (ESDs). In this contribution, mathematical modeling of considered units is derived as first-order model. Further, an overall transfer function of the IMG system is obtained using first-order transfer functions of IMG components and system dynamics. Thus, the obtained transfer function is then approximated into a first-order plus time delay (FOPTD) model to facilitate a simpler PID control design. PID controller parameters are computed using PV method for set point (SP) and load disturbance (LD) modes, keeping maximum sensitivity as a constraint. Various PID controller i.e. PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SP</i>1.4</sub>, PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>SP</i>2.0</sub>, PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LD</i>1.4</sub>, and PID-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PV</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>LD</i>2.0</sub> is designed for SP and LD modes. The efficacy of PID control design is tested by analyzing its impact on frequency deviation and mitigation of error with acceptable transient response for SP and LD mode. A comparative study is also performed based on tabulated data featuring error indices, time domain indicators, control efforts, and frequency plots to validate PV method-based PID control designs for IMG. Moreover, the real-time simulator, i.e., OPAL-RT, is utilized to further validate the efficacy of the PID controller in frequency error mitigation of the considered IMG model.