# Reduction of Dust on Solar Panels through Unipolar Electrostatic Traveling Wave
## 3 Electrode Design  
The design of the electrodes is considered to create a uniform electric field between them, and therefore the distribution of the electric field may be assumed as V = Ed, where V is the potential between the electrodes and d is the electrode separation. For an electrode separation of 26 mm and potential of 11 kV, the electric field will be 4.23 \(\times\) 10\({}^{5}\) V/m, which is less than the air breakdown value E0 = 3 \(\times\) 10\({}^{6}\) V/m. In one simulation study, the width of the electrodes as copper tracks (electrodes) on Fr4 material with 2 mm thickness was considered to be 0.1 mm and a potential was applied between the electrodes as a single channel using 11 kV and 0 V [28]. It was observed that as electrode width increases, then the particles were attracted more strongly to the negative electrode, resulting in the particles travelling a greater distance in the same time period. It was also noted that the optimal width of the electrodes to produce greatest transport distance was 0.3-0.5 mm. This study therefore uses an electrode width of 0.4 mm. However, as separation between electrodes increases, the electric field decreases [28,44], and this study has selected a separation  
Figure 1: Electrostatic cleaner card: (**a**) Controller card and I/O signals, (**b**) Display, (**c**) Waveforms. between the electrodes of 26 mm. This study investigates four designs for the copper electrodes. In order to examine the electric field changes of the models, three separate lines passing along the main axis of the panel from top to bottom were drawn (Figure 2). Models of the electrode array were developed using the Ansys Maxwell 3D Electrostatic Solver software simulation package. This uses finite element method (FEM) to solve two/three-dimensional (2D/3D) eddy current, electrostatic, magnetostatic, dc conduction, and transient problems. Table 1 summarizes the simulation process of the 3D models with the calculation time of the finite element analysis (FEA), the total number of elements, and the energy error. Routing the copper tracks away from being parallel lines affects the distribution of the electrical field. An electric field becomes concentrated in areas where there are sharp lines [8], distorting the electric field. This will affect the drift rate that can be produced to transport particles away from the surface. The distribution of the electric field in each of the 4 models, with detail around the lines, is shown in Figures 3 and 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Analysis Data** & **M1 Model** & **M2 Model** & **M3 Model** & **M4 Model** \\ \hline Total number of model elements & 848,914 & 2,514,898 & 1,257,488 & 876,010 \\ \hline Energy error (\%) & 0.653 & 0.407 & 0.401 & 0.694 \\ \hline Analysis time (min) & 14:09 & 56:57 & 25:54 & 13:07 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of 3D Finite Element Analysis simulation. Figure 2: Electrode array models: (**a**) two-dimensional view of models; (**b**) view of models. Figure 4 shows the detail of the distribution of the electric field around the regional transitions of the wires. It is expected that the electric field distribution in M3 and M4 will result in greater dust movement than in M2 and M1 [38]. However it is difficult to calculate analytically the net thrust produced at the panel surface to cause the particles to take off that is given by gravitational force, the electrodynamic force, and viscous force [30; 38]. Figure 3: 3D FEA electric field distribution: (**a**) M1 model, (**b**) M2 model. M1 has a uniform electric field distribution, while M2 is little different from a uniform electric field. Note also that the distribution of the electric field between the top and bottom of the plate is not uniform. Figures 5 and 6 show the magnitude of the distribution in detail along three lines passing along the main axis of the panel from top to bottom.