## 5 Conclusions  
We proposed a non-contact diagnostic method for the local reverse voltage caused by partial shading and mismatch loss using surface potential meters. We expect this method to help prevent fires from PV modules and detect degraded or underperforming solar cells inside the PV module using non-contact and non-destructive methods.  
For the assessment of the fire risk, the following contributions were made by this work.  
* We developed a non-contact measurement method by detecting the carrier movement by the electrical field generated by the surface potential of the solar cell inside the module (in between the cover glass and the back sheet). The heat dissipation of the solar cell leading to a fire hazard is quantitatively calculated by the product of the circuit current and the detected reverse-bias voltage.
* The above method was validated by measuring each cell's reverse-bias voltage without cutting the circuit in the module. The error range was sufficiently small for the fire risk assessment.
* Demonstration of the fire-risk assessment by the non-contact measurement by the following steps: 1. Non-contact measurement of the reverse-bias voltage under the controlled operating condition. 2. Calculate each solar cell's heat dissipation per area (W/cm\({}^{2}\)) by multiplying the reverse-bias voltage and output current by the load resistance. 3. Estimation of the maximum temperature of each cell under a given condition. The worst-case solar irradiance may be 1400 W/m\({}^{2}\), and the maximum temperature is proportional to the solar irradiance level. The typical calculation of the worst-case temperature with typical values follows: (261 \({}^{\circ}\)C: Worst-case temperature) = (13 V: Reverse-bias voltage tested at 1000 W/m\({}^{2}\)) \(\times\) (38 mA/cm\({}^{2}\): Short-circuit current density of the cells per area, under standard testing condition, 1000 W/m\({}^{2}\)) \(\times\) (280 Kcm\({}^{2}\)/W: Temperature rise per unit heat dissipation) \(\times\) (1.38: Current correction on solar irradiance correction for the worst-case) + (70 \({}^{\circ}\)C: Operating temperature of the solar cell under worst-case solar irradiance) \(>\) (250 \({}^{\circ}\)C: Firing point of woods) In this case, the photovoltaic module under inspection is categorized as \"Risk of fire\".  
In other words, a typical criterion of the maximum reverse-current voltage in the photovoltaic module to avoid fire risk is \"\(-\)13 V,\" which is almost the same level as the maximum acceptable reverse-bias voltage of silicon solar cells, which are typically known as \"\(-\)13 V\" [37; 38; 39] given the international standards of IEC61215 [45] and IEC6173 [46]. In the current technology, the screening of the solar cells in the maximum reverse-bias voltage was inspected at the cell level before assembling the photovoltaic module. The reverse-bias voltage of each cell is not monitored or inspected after the module assembly due to the lack of non-contacting technology of the reverse-bias voltages, even when some cells are degraded. The innovative approach to this work is the inspection applicable after the assembly of the module and after installation and operation.  
Note that we have not intensively examined the reproducibility as the fire assessment but only show the possibility of an innovative non-contact and non-destructive assessment of the fire risk. We believe this method will be a standard method after intensive examination of the reproducibility, like blind tests by testing laboratories.  
Conceptualization, K.N.; validation, R.S., Y.O. and A.N.; writing--original draft preparation, R.S.; writing--review and editing, K.A.; supervision, K.N. All authors have read and agreed to the published version of the manuscript.  
This study received no external funding.  
Not applicable.  
Data Availability Statement: Data will be made available on request.  
We thank [PERSON] at Ritsumeikan University for fruitful discussions on surface potential measurement technology.  
The authors declare no conflict of interest.