## 6 Analysis of Power Loss and Efficiency  
Power loss and efficiency analysis is carried out in order to study the impact of the online tuning mechanism in reducing power loss, improving efficiency and contributing to a uniform distribution of power loss among switches. In order to properly evaluate the effectiveness of the tuning scheme, a comparison is made between the proposed PI controller and the conventional PI controller. Power loss is highlighted in the calculation of conduction loss and switching loss. In this analysis, the power switches chosen are IGBT model IRG4 PC40 UDPbF from International Rectifier. From the IGBT datasheet, relevant points are extracted to obtain several curves for the calculation of the losses. A MATLAB curve-fitting tool is used to derive the mathematical models for the IGBT as given below:  
\[\mathrm{V_{CE}}=3.141e^{0.003496i(t)}-2.296e^{-0.01392i(t)} \tag{11}\]  
\[\mathrm{V_{FW}}=1.396e^{0.009157i(t)}-0.5844e^{-0.1733i(t)} \tag{12}\]  
\[\mathrm{E_{SL,ICBT}}=15.62(e^{0.009769i(t)}-e^{0.009764i(t)}) \tag{13}\]  
Here, \(\mathrm{V_{FW}}\) is the forward voltage drop, \(\mathrm{V_{CE}}\) is the collector-to-emitter voltage, \(\mathrm{E_{SL,IGBT}}\) is the sum of the IGBT switching energy loss and i(t) is the current flowing via the IGBT. In order to determine the conduction loss of the IGBT, the following equations are used:  
\[\mathrm{P_{CL,Diode}}=\frac{1}{T_{PO}}\;\int\;\mathrm{V_{FW}}\;\mathrm{i(t)}\; \mathrm{dt} \tag{14}\]  
\[\mathrm{P_{CL,IGBT}}=\frac{1}{T_{PO}}\;\int\;\mathrm{V_{CE}}\;\mathrm{i(t)}\; \mathrm{dt} \tag{15}\]  
Here, \(\mathrm{P_{CL,Diode}}\) and \(\mathrm{P_{CL,IGBT}}\) are the conduction losses of diodes and IGBTs, respectively, and \(T_{PO}\) is the period for one cycle. The overall switching power loss of IGBTs, \(\mathrm{P_{SL,IGBT}}\) is given as follows:  
\[\mathrm{P_{SL,IGBT}}=\frac{1}{T_{PO}}\;\sum\;\mathrm{E_{SL,IGBT}} \tag{16}\]  
The switching loss of diode, \(\mathrm{E_{SL,DIODE}}\) is estimated by multiplying the reverse recovery time with the reverse recovery current as well as the reverse voltage drop resulting in:  
\[\mathrm{E_{SL,DIODE}}=(16.2e^{0.003252i(t)}-10.4e^{-0.076497i(t)}-1.815e^{-0.0 76441i(t)}+1.166e^{-0.1562i(t)}\;)\times 10^{-6} \tag{17}\]  
Consequently, the total switching power loss of diodes, \(\mathrm{P_{SL,DIODE}}\) is determined as below:  
\[\mathrm{P_{SL,DIODE}}=\frac{1}{T_{PO}}\;\sum\;\mathrm{E_{SL,DIODE}} \tag{18}\]  
The total power loss, \(\mathrm{P_{L}}\) is the sum of conduction and switching losses, which is represented in the following:  
\[\mathrm{P_{L}}=\mathrm{P_{CL,DIODE}}+\mathrm{P_{CL,IGBT}}+\mathrm{P_{SL,DIODE} }+\mathrm{P_{SL,IGBT}} \tag{19}\]  
The equation below is used to calculate the efficiency, \(\eta\) of the converter, in which \(\mathrm{P_{O}}\) stands for the output power of the converter:  
\[\eta=\frac{\mathrm{P_{O}}}{\mathrm{P_{O}}+\mathrm{P_{L}}}\;\times\;100\% \tag{20}\]  
MATLAB/SIMULINK is utilized to conduct the power loss simulation with the same condition as presented in Section 5. Figure 10 displays the simulation results, which indicate that the higher the modulation index, then the higher the total power loss and efficiency become. The improvement in efficiency is contributed to the rise in the outputpower, which is more than the increase in power loss. The highest power loss recorded for the proposed controller is 6.14 W at a modulation index of 1.0. This is lower than the power loss when the conventional controller is applied, namely 6.65 W that occurs at 0.9 modulation index. The highest efficiency achieved for the proposed controller is 96.9% at 1.0 modulation index, which is slightly higher than that when the conventional controller is employed. The distribution of the power loss among the power switches that are observed at 0.9 modulation index is shown in Figure 10c. The power loss for every power switch accounts for both conduction and switching losses of the IGBTs.