# Non-Uniform Distribution of Contamination on Composite Insulators in HVDC Transmission Lines
## 5 Discussion
### Numerical Calculation and Analysis of Electric Field Force
In order to further illustrate the influence of electric field force on the movement of particles around insulators, we estimate the acceleration of particles in vertical direction. The formula for calculating the quality of particles is as follows. \[m_{g}=\frac{4}{3}\rho_{p}\pi(\frac{d_{p}}{2})^{3} \tag{7}\]  
where \(\rho_{p}\) is the density of particles, its value of SiO\({}_{2}\) is 2320 kg/m\({}^{3}\). The particles are subjected to gravity and aerodynamic drag on the \(Y\) axis. It is observed from experiments that the movement of particles near insulator is basically horizontal under non-energized condition, so there is balance force on particles in the direction of \(Y\) axis, which means that \(f_{w}=-f_{g}\), where \(f_{w}\) is aerodynamic drag on particles and \(f_{g}\) is gravity of particles. The formula for calculating the acceleration of particles is as follows. \[a=f/mg \tag{8}\]  
where \(f\) is the resultant force, which is approximately equal to the force of the electric field in the direction of \(Y\) axis. The calculated acceleration of different meshes particles at the high voltage group and middle group are shown in Figure 10. The calculated results show that the acceleration in vertical direction of the particles at the high voltage group is about 1.62 times that at the middle group. This calculated value is very close to the actual K\({}_{\text{H/M}}\) value. Then, we can get the trajectory trend of charged particles, as shown in the Figure 8.0 \"+\" represents a particle with positive charge and \"-\" represents a particle with negative charge. Figure 8.1 The calculated \(Y\)-axis acceleration. It can be seen from Figure 11 that the charged particle moves toward the shed's surface due to the effect of the electric field force, increasing the probability of particles hitting the sheds surface of the insulator. Thus, the amplitude of particle deflection at the high voltage group is greater than that at the middle group due to a larger acceleration of particles, causing the increasing probability of sorption of contamination particle, which explained the cause of non-uniform contamination distribution along the string. Besides, after calculating the electric field around the field insulators, we have to transfer the situation from the field insulators to our model. According to the steps of Section 5.1 above, the acceleration in vertical direction of the particles can be obtained. The calculated results show that the acceleration in vertical direction of the particles at the high voltage group is about 2.51 times that at the middle group. Which means that \(\mathrm{K_{H/M}}\) in theory is about 1/0.40, we can see clearly that there is about 35% error in the result of the field test. This shows that the model is more accurate in the application of wind tunnel contamination, however there are still some errors in the application of field contamination. The main reason for the error is that the scouring of the rainwater reduced contamination inhomogeneity of field insulators between the high voltage group and middle group.