## 1 Introduction  
Maximum power point tracking (MPPT) is an essential part of photovoltaic (PV) systems [1, 2, 3, 4, 5, 6]. With the increasing demand of solar PV energy, improving the performance and efficiency of the MPPT process is a necessity and a challenge at the same time [7, 8, 9, 10, 11]. Classically, the MPPT is performed using either the inverter directly or by a DC-DC converter as a previous stage [12, 13]. In either case, the whole amount of power passes through the converter and gets processed to achieve maximum power. The higher the size of the PV system, the higher the size of the converter, making it more challenging to maintain efficiency and compactness while processing this amount of power. However, in most PV applications, variations in solar irradiance, module degradation, or shading can cause individual modules in a string to operate at different power levels, leading to energy losses and reduced overall efficiency [14; 15; 16]. Recently, designers have introduced a new power processing method, which is known as partial power processing (PPP) [17; 18; 19]. In this approach, modules are connected in series and the bulk of available energy is transferred directly to the inverter. Any other mismatch is processed through a power optimizer converter. PPP-based architectures are comprised of DC-DC converters that are specially designed to only process part of the power to achieve MPPT across the entire string [20; 21]. This gives many advantages in the design of such converters, making them smaller and more compact. The power loss of such converters is much lower, even if the efficiency of the converter is lower because only a fraction of the power is processed and the majority is transferred directly. PPP-based architectures can be categorized into Differential Power Converters (DPCs), Partial Power Converters (PPCs), and Mixed PPP Strategies [22; 23]. DPCs are designed to balance current mismatches between series-connected elements, such as battery cells or photovoltaic (PV) modules. Instead of processing the full power flowing from the source to the load, DPCs only handle the power imbalance between elements, significantly improving system efficiency while reducing conversion losses and thermal stress. They can be further classified into Element-to-Element (E2E) converters, which transfer power between adjacent elements, and Bus-to-Element (B2E) converters, which transfer power between an element and a common bus [24]. E2E architectures, often implemented using Boost type [25], buck-boost [26], or Flyback topologies [21], offer lower component stress and reduced switching losses but require complex control mechanisms to ensure stable operation. B2E architectures, though, offer greater modularity and higher efficiency; however, these architectures require higher voltage-rated components and suffer from increasing cost and greater complexity. DPC control strategies are different depending on the topologies used and the systems architecture. In E2E, the control scheme focuses on redistributing power among neighboring modules (or cells), so each converter must sense and regulate the current flow only between adjacent elements. Consequently, the control is typically more decentralized, with each E2E unit operating in a cooperative manner to balance local mismatches across the chain. In [27], each differential power processing (DPP) converter asynchronously performs local MPPT on its submodule by regulating the submodule current to match its maximum power point. Concurrently, a central (string-level) controller or inverter regulates the bus voltage by adjusting the overall string current. In [28], each module uses a dual-loop control, with an inner voltage loop regulating its local PV module voltage and an outer power loop that runs a local MPPT algorithm to set the voltage reference.