## 4 Control Operation and Flowchart  
The control diagram of the current equalizer manager is presented in Figure 5, which can be further linked to the same block in Figure 2, to visualize the entire control system of the proposed architecture. As already explained, in this system, the centralized MPPT inverter is responsible for performing MPP tracking of the string by adjusting its input operating point at the DC-link and thereby maximizing the overall power output.  
Figure 5 indicates that the equalizer manager contains two blocks--one is the current equalizer algorithm and the other is a current matching controller. It can be seen that the current and voltage information of each module are given to the current equalizer algorithm block. Then, this block, through its algorithm, which is explained later, generates the corresponding binary On/Off signal for the string switch 'Sn' of each module. The switch signal is then multiplied by \(I_{string}\) after inversion to form the module's target current reference (\(I_{ref}\)) for the controller block. Note that for shaded modules, the binary signal for the string switch will be '0', i.e., OFF; it means that the path of the common \(I_{string}\) will be diverted to the output of the buck converter. Further, the signal of the string switch becomes '1' after inversion, which is multiplied by \(I_{string}\) to set the reference signal. On the other hand, for unshaded modules, the binary signal for the string switches will be '1', and the target \(I_{ref}\) is '0', i.e., no PWM pulses.  
The main task of the current matching controller is to make the output current of the shaded module's buck converter equivalent to \(I_{ref}\) (\(\approx\)\(I_{string}\)). Here, the output current is estimated through \(I_{Mn}/D_{n}\) by using the shaded modules's current \(I_{Mn}\) and duty cycle \(D_{n}\) of its converter. Through this feedback system, the current matching controller generates the PWM pulses of the corresponding buck converter, unless the error becomes equal to zero, as shown in Figure 5. For this purpose, it utilizes the proportional-integral (PI) controller for PWM pulses to ensure the fast response of the system. In this manner, the buck converter of shaded modules supports the common string current.  
Figure 6 shows the working flowchart of the current equalizer algorithm, where it collects each module's current-voltage measurements (\(I_{M1}\), \(V_{M1}\),..., \(I_{Mn}\),\(V_{Mn}\)). The algorithm continuously monitors the power output of each PV module and compares it against a reference power (\(P_{ref}\)), which is derived from the median of all modules' power. Each module's power is then checked to see if it falls below a certain fraction (\(\alpha\)\(\times\)\(P_{ref}\)) of that reference \(P_{ref}\), where the factor \(\alpha\) falls in the range 0.8-0.9. Modules flagged as under-performing are temporarily isolated from the string by making their respective string switch signals as '0', and their respective currents are raised to \(I_{string}\) through a local (MPP) buck converter, as already explained. Meanwhile, modules that are meeting or exceeding  
Figure 5: Control flow diagram of the current equalizer manager, which contains two blocks: (1) current equalizer algorithm and (2) current matching controller.  
the threshold continue normal operation. This process repeats in cycles, ensuring that any mismatched or shaded modules are detected in real time and contribute to maintaining the optimal performance of the overall system.