# Design of Direct Current Microgrid Converter with Cost-Effective Low-Voltage Battery Storage System
## 8 Simulation Results
For better comparison, we have entered the mean and effective values for all operating modes of the inverter in Table 3. The simulation shows that option (a) is the most inefficient regarding the efficiency ratio and mean or peak current to the same output power. To work in mode (c), it is necessary to use excitation circuits that allow the top (high-side) transistor to be left open for an indefinitely long period. This means that the standard available drivers based on bootstrap technology, i.e., supplying power using a charge pump while switching to the low-side transistor, are not applicable. This solution would imply the need to generate a separate isolated power supply for the driver of both the top (high-side) transistors. Such a solution is cost- and space-inefficient for the chosen power scale. For this reason, we will further discuss the theoretical analysis of the inverter function in mode (b), i.e., always as a function of both inverters being active with a fixed relative switch-on time for the step-down converter. In this mode of operation, the current is ideally trapezoidal when the input voltage equals the desired output voltage, i.e., the slope of the curve in the second interval is zero (see Figure 6). In cases where the input voltage is greater than the output voltage, the slope of the curve in the second interval is positive, i.e., rising. Otherwise, when the input voltage is less than the output voltage, the slope of the current curve is negative, i.e., decreasing. The theoretical assumptions were verified by simulation using the given simulation model. The results of the current waveforms are shown in the graph presented in \[\text{D}_{\text{2 max}}=\frac{(D_{1}\cdot U_{in})-U_{out}}{U_{out}}=\frac{(0.8 \cdot 9)-12}{12}=0.4=40\% \tag{2}\]0  
As a solution for the balancing circuit, we selected a commercially available circuit based on an inverter topology with power flow between cells without galvanic isolation. This method of power transfer is advantageous in terms of space saving. A transmission between two remote cells that are not connected in series to one inverter is problematic. Therefore, we use two identical circuits of two pairs of cells to balance the three cells. Here, then, under the condition of the need for energy transfer between the two outermost cells, the transfer of energy to the common-center cell for both inverters occurs. \begin{table}
\begin{tabular}{c c c c} \hline  & **Variant (a)** & **Variant (b)** & **Variant (c)** \\ \hline
**Current** & D\({}_{1}\) = x; D\({}_{2}\) = x & D\({}_{1}\) = 80\%; D\({}_{2}\) = x & D\({}_{1}\) = 1; D\({}_{2}\) = x \\ \hline I\({}_{\mathrm{avg}}\) [A] & 3.2138 & 1.9716 & 1.6621 \\ I\({}_{\mathrm{rms}}\) [A] & 3.3616 & 2.0406 & 1.6684 \\ \hline \end{tabular} For output power, 18 W (V\({}_{\mathrm{out}}\) = 12 V)  
\end{table} 
Table 3: The effective and average values of the current for each operating mode. Figure 12: Current waveform through inductor for different modes of operation. To build the simulation model, we use the catalog values of the already selected integrated circuit, which contains two internal switches and control logic. The advantage is then the minimum of the external components. The selected type of ETA3000 active balancer operates at a switching frequency of 1 MHz. For the considered mean value of the balancing current \(\mathrm{I_{balAv}}=1\) A, the manufacturer has determined the inductance of the coil L = 1 uH. The recommended values of the filter capacitors are C = 10 uF of MLCC type with a maximum operating voltage of 25 V.  
We transfer all these values to the simulation model (see Figure 14). To verify the simulation model function, we will use off-the-shelf and freely available Li-ion battery models created by the LTspice user community. Balancing the state of charge of large-capacity batteries at a relatively small balancing current is slow; so, for simulation purposes, we reduce the capacity of the batteries to 2 mAh.