# A Heuristic Algorithm for Locating Line-to-Line Faults in Photovoltaic Systems
## 3 Proposed Method
### Heuristic Algorithm for Line-to-Line Fault Location
#### 3.2.4 Threshold Determination  
In the heuristic algorithm for line-to-line fault location, a critical component is appropriately setting the \(\Delta V_{threshold}\) in the fault marking process. If \(\Delta V_{threshold}\) is set too high, it may prevent milder faults from being accurately marked. Conversely, if \(\Delta V_{threshold}\) is set too low, it could lead to unnecessary misjudgments. Therefore, determining the optimal \(\Delta V_{threshold}\) is essential. This section primarily explores how to set \(\Delta V_{threshold}\) based on the array structure and the module group voltage measurement range. Typically, an intuitive approach is to set \(\Delta V_{threshold}\) to be able to detect the mildest fault condition as a primary requirement. Therefore, using a \(21\times 2\) array configuration with three modules per module group as an example, this paper discusses the settings for both intra-string and cross-string line-to-line short-circuit faults. In the intra-string fault type, the mildest fault condition occurs when a single PV module experiences a short circuit, as shown in Figure 17. If a short-circuit fault occurs in module group \(V_{i,j}\), the voltage change rates related to \(V_{i,j}\) are \(\Delta V_{i,j+1}\) and \(\Delta V_{i,j}\). Based on the voltage distribution, \(\mid\Delta V_{i,j+1}\mid\) can be calculated as 33.33%, and \(\mid\Delta V_{i,j}\mid\) as 50%. Therefore, in the intra-string fault type, the minimum \(\Delta V_{threshold}\) should be set below 33.33%. Figure 16: Fault location troubleshooting scope (**a**) module group voltage measurement range; (**b**) fault endpoint located between two module groups. In the intra-string fault type, the mildest fault condition is also analyzed. As shown in Figure 18, a line-to-line short-circuit fault occurs between two strings with only one PV module difference. However, due to different positions, there are 19 possible fault scenarios from the top to the bottom of the array. The following section will simulate these 19 scenarios and calculate the minimum \(\mid\Delta V_{i,j}\mid\) for each case. In addition to the NOCT, the simulation environment parameters also explore four more extreme combinations of irradiance and module temperature: G = 100 W/m\({}^{2}\), T = 10 \({}^{\circ}\)C; G = 100 W/m\({}^{2}\), T = 85 \({}^{\circ}\)C; G = 1000 W/m\({}^{2}\), T = 10 \({}^{\circ}\)C; and G = 1000 W/m\({}^{2}\), T = 85 \({}^{\circ}\)C.  
The simulation results are shown in Table 8, which indicate that \(\mid\Delta V_{i,j}\mid\) is lower at lower temperatures. The minimum \(\mid\Delta V_{i,j}\mid\) across all conditions occurs under the environment parameters G = 100 W/m\({}^{2}\), T = 10 \({}^{\circ}\)C, with a value of 2.1304%. Therefore, in the cross-string fault type, the minimum \(\Delta V_{threshold}\) should be set below 2.1304% to ensure accurate fault location. Figure 17: Illustration of the mildest intra-string short-circuit fault. Figure 18: Illustration of the mildest cross-string short-circuit fault. Finally, combining the minimum \(\Delta V_{threshold}\) settings for both intra-string and cross-string fault types, this paper ultimately selects 2% as the \(\Delta V_{threshold}\) for the 21 \(\times\) 2 array configuration. This ensures that the heuristic line-to-line fault location algorithm can identify all possible fault locations. The \(\Delta V_{threshold}\) is primarily determined based on the array configuration and environmental conditions, as demonstrated for the 21 \(\times\) 2 array in this study. For different array sizes or module groupings, the threshold should be recalibrated accordingly. Similarly, environmental factors such as irradiance and temperature affect the voltage differences and thus the threshold value. Developing adaptive thresholding techniques that automatically adjust to varying array configurations and operational conditions is an important direction for future research to improve the robustness and applicability of the proposed algorithm.