# Machine Learning-Based Monitoring of DC-DC Converters in Photovoltaic Applications
## 2 Materials and Methods
### Zeta Converter  
The DC-DC converter considered in this paper is a Zeta converter, which is a fourth-order non-inverted step-up/step-down circuit that guarantees high voltage gain and low ripples in the output voltage and current [18; 29]. A Simulink model is used to verify the operation of the converter connected to the photovoltaic source and that of the monitoring method. Figure 2 shows the whole system reproduced in Simulink and used during the simulation procedure: a Pulse Width Modulation (PWM) technique is implemented to drive the converter switches \(S_{1}\) and \(S_{2}\) (N-channel Power MOSFET) with opposite phases. When the switch \(S_{1}\) is in conduction mode, the inductor \(L_{1}\) absorbs energy from the DC source, and, at the same time, \(L_{2}\) absorbs energy from the source and capacitor \(C_{1}\). This means that the input current \(i_{S}(t)\) is equal to the sum \(i_{L1}(t)+i_{L2}(t)\), and these two currents increase linearly, as shown in Figure 3a,b, which are extracted from the Simulink model considering a solar irradiance of 1000 W/m\({}^{2}\) and an operating temperature of 25 \({}^{\circ}\)C. In the opposite condition (\(S_{1}\) Off and \(S_{2}\) On), the input current is zero, and the current \(i_{L1}(t)\) flows through \(S_{2}\) to charge capacitor \(C_{1}\). Simultaneously, \(i_{L2}(t)\) crosses the circuit (\(C_{2}\)-R) and returns through the closed switch \(S_{2}\). Figure 2: General diagram of the photovoltaic system and Zeta converter circuit. The currents \(i_{L1}(t)\), \(i_{L2}(t)\), and \(i_{S2}(t)\) present three different ripples, \(\Delta i_{L1}(t)\), \(\Delta i_{L2}(t)\), and \(\Delta i_{S2}(t)\), respectively. The latter is the most important to define the conduction mode of the circuit: if current \(i_{S2}(t)\) becomes zero during the Switch-Off period, the converter works in the Discontinuous Conduction Mode (DCM). Otherwise, the Continuous Conduction Mode (CCM) requires a non-zero current in \(S_{2}\) when the switching from off to on mode occurs. By operating in CCM, it is possible to reduce the electrical stress on the converter components and obtain a lower ripple on the output quantities. For this reason, only the CCM is considered in this work, and the dimensioning of the analog components has been performed to ensure this condition. As shown in [18], the voltage gain \(G\) of the Zeta converter can be calculated through Formula (1), where \(V_{S}\) is the input voltage imposed by the photovoltaic source and \(V_{O}\) is the output voltage of the converter. Consequently, Formula (2) is used to describe the relationship between the mean value of the input current \(I_{S}\) and the output current \(I_{O}\). \[G=\frac{V_{O}}{V_{S}}=\frac{D}{1-D} \tag{1}\]  
\[I_{O}=\frac{1-D}{D}I_{S} \tag{2}\]  
As for the dimensioning of the passive components, one of the main aspects is to ensure a sufficient margin between CCM and DCM. In addition, ripples of voltages and currents are also considered, as shown in [18]. The variation ratios of the currents \(i_{L1}\) and \(i_{L2}\) are expressed by the terms \(\eta\) and \(\zeta\), respectively, and are calculated as follows,  
\[\eta=\frac{\Delta_{i_{L1}}/2}{I_{L1}}=\frac{1-D}{2\;G}\;\frac{R}{f\;L_{1}} \tag{3}\]  
\[\zeta=\frac{\Delta_{i_{L2}}/2}{I_{L2}}=\frac{D}{2\;G}\;\frac{R}{f\;L_{2}} \tag{4}\]  
where capital letters are used to indicate the average values of the quantities, and \(R\) represents the load resistance. Similarly, the variation ratios of the voltages are calculated as,  
\[\rho=\frac{\Delta_{v_{C}}/2}{V_{C1}}=\frac{D}{2}\;\frac{1}{f\;C_{1}\;R} \tag{5}\]  
\[\varepsilon=\frac{\Delta_{v_{0}}/2}{V_{o}}=\frac{D}{8\;G}\;\frac{1}{f^{2}\;C_ {2}\;L_{2}} \tag{6}\]  
where \(\rho\) is the variation ratio of the voltage across C\({}_{1}\), and \(\varepsilon\) is that of the output voltage. Table 2 summarizes the nominal values of the converter components that ensure CCM operation and limit the output ripple to 5%.