# Robust Model-Free Control for MMC Inverters in Cold Ironing Systems
## 1 Introduction
### DC Distribution  
As shown in Figure 2c, the main advantage of this topology over other typologies is its flexibility in integrating DC power sources, such as fuel cells, renewable energy sources (e.g., solar panels), and battery storage systems. Power transfer process in this topology occurs in three steps: from the grid to the transformer, then to the rectifier, and finally from the rectifier to the DC bus. To ensure efficient shore power electrification, the energy generated at the dock must be clean, and the shore power supply must be able to provide sufficient, reliable, and stable energy to power all required ship systems. However, integrating these systems poses several technical challenges, particularly due to the variety of voltages and frequencies used by ships. Indeed, power systems vary based on geographical regions and ship types. Some ships operate at low voltage (400 V or 690 V, at 50 Hz or 60 Hz) in accordance with the IEC/ISO/IEEE 80005-3 [12] (low-voltage standard), while others require high voltage (6.6 kV or 11 kV, at 50 Hz or 60 Hz) in accordance with IEC/ISO/IEEE 80005-1 high-voltage standard. This heterogeneity means that port infrastructure must integrate frequency converters and transformers that can adapt power to the specific needs of ships. Additionally, fluctuating loads require solutions that can maintain network stability and power quality. These fluctuations generate a total harmonic distortion (THD) due to electronic equipment and nonlinear loads, which can directly affect the performance and lifespan of onboard equipment. International standards, such as IEC/ISO/IEEE 80005-1, impose a THD below 4% in order to ensure a stable and compliant power supply. To meet these standards, researchers are exploring various control strategies that are designed to minimize THD at the Point of Common Coupling (PCC) and ensure fast disturbance rejection, regardless of the type of load or fluctuations in parameters. THD and disturbance rejection are considered key performance indicators for control methods. As illustrated in Figure 1, several studies on power converter control have been proposed to improve voltage regulation in decentralized generation (DG) systems. Control architectures typically consist of an inner current loop and an outer voltage loop [13; 14; 15]. This structure allows both current and voltage regulation [16]. Various control techniques have been investigated, including classical control methods [17; 18], backstepping [19], and sliding mode control [20; 21]. Figure 2: Topology of shore power systems: (**a**) centralized; (**b**) decentralized; (**c**) DC distribution. The proportional-integral (PI) classical control is widely used due to its simplicity and effectiveness. However, its performance is limited under critical loads due to the need for linearization around the operating point [22], which can reduce the stability margin of the system and lead to stability issues on a large scale, as well as saturation issues. To overcome these limitations, different techniques have been proposed [22; 23]. In [22], a fractional PI controller was developed to enhance disturbance rejection and reduce voltage harmonic distortion (THD). In [23], a fractional Proportional-Resonant (PR) controller was introduced to eliminate steady-state errors and phase shift, thereby improving the accuracy of periodic reference signals. Backstepping control, which is based on a recursive approach, can be used to stabilize complex nonlinear systems by constructing successive control laws from hierarchical subsystems [24; 25]. However, this method becomes increasingly complex with system order and is highly dependent on the model, which can compromise its performance in the presence of uncertainties [26; 27]. The backstepping control method is robust against parameter variations, whereas sliding mode control is susceptible to chattering effects [28; 29].