Direct Model Predictive Control (MPC) or Finite-Control-Set variant (FCS-MPC), offers a conceptually simple yet powerful framework for controlling power converters, electric drives, and large-scale systems such as electrical grids. MPC provides key advantages over traditional control methods, including the ability to directly incorporate system constraints, consider multiple modes of operation, and handle complex requirements in a unified optimization-based structure.

Despite its benefits, standard FCS-MPC suffers from several steady-state performance limitations, such as distributed voltage/current spectra, uneven power loss distribution, and high common-mode voltages, among others. The goal of this tutorial is to present recent advancements in MPC that address these challenges — achieving harmonic-improved steady-state behaviour without compromising fast dynamic response.

The tutorial begins with a control-theoretic foundation, including the mathematical formulation of MPC, sufficient conditions for closed-loop stability, and the link between stability guarantees and power converter performance. From a power electronics perspective, we then explore how modulation stages (e.g., SVM and PS-PWM) can be directly embedded into the MPC cost function. This allows the controller to exploit the frequency-domain properties of these modulators.
The first approach discussed is Optimal Switching Sequence MPC, which incorporates space vector modulation to determine commutation instants directly. The second is Phase-Shifted MPC, which integrates PS-PWM into the control loop, making it suitable for modular converters. This strategy also enables optimization of phase-shift angles under unbalanced conditions, improving THD compared to standard PS-PWM.

We further examine Multistep MPC, which leverages long prediction horizons to improve harmonic performance in low-switching-frequency, high-power converters. Finally, we introduce the use of real-time optimized pulse patterns within the MPC framework to achieve spectrum shaping that meets grid code requirements, even under distorted grid conditions.

Applications will be discussed throughout the tutorial, including high-power PV systems, second-life battery inverters, high-power drives, and active filters. Overall, the tutorial aims to bridge theory and practice, equipping attendees with advanced tools for harmonic-aware predictive control of high-power converters.