# Predicting the Life of Varistors via a Nonlinear Coefficient Based on a Small-Scale Data Model
## 2 Materials and Methods  
### Electrical Parameters of the Varistor  
In research, breakdown voltage, leakage current and nonlinear coefficient are common electrical parameters used to measure the performance of a varistor. They can be measured directly by professional equipment. Breakdown voltage refers to the voltage across the varistor when 1 mA of direct current flows through it. Leakage current refers to the current flowing through the varistor at a specified temperature and maximum direct current voltage. Figure 1 shows the changes in these three electrical parameters with various times of impacts in a measured experiment. As there is a large difference in the range, in order to compare the trends of changes in the three electrical parameters more intuitively, the data have been normalized. It can be seen that there is no correlation between the leakage flow curve and the impact times. The level remains low until the varistor is completely damaged and then increases sharply. Therefore, it can only reflect the working state of the varistor and not its deterioration. The breakdown voltage and nonlinear coefficient are both negatively correlated with the number of impacts. But it is clear that the change in the breakdown voltage lags behind the change in the nonlinear coefficient. Even after the 35 th impact, when the varistor is close to damage, the breakdown voltage is still more than 70% of its peak value, which cannot reflect the deterioration of the varistor over time. Therefore, the nonlinear coefficient is chosen as the electrical parameter used to construct the life prediction model. Nonlinearity is an inherent characteristic of MOV. When the terminal voltage is lower than a certain threshold, the flux of the varistor is about zero. When the terminal voltage exceeds this threshold, the through current in the varistor increases sharply with the increase in the terminal voltage, and its volt-ampere characteristic curve is shown in Figure 2.  
Within a certain range greater than the terminal voltage threshold, the volt-ampere characteristic curve is approximately a straight line, and its curve can be approximately expressed as  
\[\text{lgI}=\text{AlgU}-\text{b}, \tag{1}\]  
where \(\text{lgI}\) is the vertical coordinate in Figure 2, \(\text{lgU}\) is the horizontal coordinate in Figure 2, and A is the slope of the straight line, i.e.,  
\[\text{A}=\text{lg}\theta, \tag{2}\]  
\(\theta\) is the angle at which the approximate line intersects the coordinate axis, and b is the intercept of the straight line. Let b = AlgC, where C is the material parameter of the varistor, i.e.,  
\[\text{I}=(\text{U}/\text{C})^{\text{A}}, \tag{3}\]  
It can be seen that the volt-ampere characteristic of the varistor in this range is determined by the parameters A and C. A is the nonlinear coefficient, which is an electrical  
Figure 1: The changes in electrical parameters with the time of impact (the values were normalized). parameter describing the nonlinear degree of MOV. The larger the A value, the steeper the volt-ampere characteristic curve in this voltage range, and the stronger the absorption ability of the varistor for large currents. After experiencing multiple surge impacts, the varistor deteriorates; ions on both sides of the forward and reverse bias barriers migrate, resulting in a drop in the varistor voltage and a deterioration in the volt-ampere characteristics of the varistor, as shown in Figure 3. At the same time, the nonlinear coefficient A also decreases, and the current absorption ability of the varistor decreases. When nonlinear coefficient A decreases to a certain extent, the varistor fails and cannot play the role in overcurrent protection. This paper focuses on the trend of change in the nonlinear coefficient in the process of deterioration, and establishes a life prediction model based on experimental data. Figure 3: Change in volt-ampere characteristic curve before and after surge impact. Figure 2: Volt-ampere characteristic curve for the varistor.