## 3 Results
### Case Study: Faults in the Lithuanian Distribution Grid  
#### 3.2.1 Correlation with Grid Reliability Indexes  
In 2015-2018, most faults (80% by quantity, 87% by repair duration) occurred in the 0.4 kV grid; however, their influence on total unplanned SAIFI and SAIDI was 15-17%. This can be explained by the low connected customer density, i.e., the fact that the number of customers connected to 0.4 kV nodes is relatively low. Despite a high customer density, the impact of the 35 kV grid on SAIFI and SAIDI was the lowest (up to 5%) due to the following aspects: (1) very low share of the total failure rate (up to 1% by both quantity and repair duration); (2) 35 kV lines have the smallest share of the total length; (3) the 10 kV grid level of automation is sufficient to recover power supply from healthy reserve lines. The share of 10 kV faults was 20% by quantity and 13% by repair duration, but they had the heaviest weight on the reliability indexes--approximately 80%. The regression analysis of the Lithuanian distribution grid is given in Figures 62-68. In all cases, the coefficient of determination (and, respectively, linear correlation) is (very) high, which means a strong interconnection between the annual fault rate and the reliability indexes (correlation with SAIFI is stronger than with SAIDI): almost all correlation coefficients are higher than 0.70 (except the 0.58 of Figure 68b). Please note that events in the 35 kV grid without ACR (Figure 63) are an exception--the relationship does not exist. On the other hand, as has been mentioned before, since the share of the 35 kV grid in total SAIFI and SAIDI was the lowest (up to 5% including ACR events; an average of  
Figure 61: Simulation scenarios in the industrial grid. 32 failures per year excluding ACR events), the appearance of a tendency can be expected with an increase in the number of observations (according to the law of large numbers). Moreover, all values of the tangent of \(\theta\), calculated according to Equation (7), are very small, and a small regression slope means a low sensitivity of change of the function's output with respect to the input, which is a highly desirable (positive) feature of any electrical grid. Please note that each figure has its own independent (different) scale (adjusted for visualization purposes). It is noteworthy that SAIFI and SAIDI, investigated in this paper, are the most popular reliability indexes. A summary of reliability indexes used by European grid operators can be found in [50] (pp. 34-36). Figure 64: Regression analysis of the Lithuanian 10 kV grid, 2015–2018. (**a**) Interdependence between SAIFI and the fault rate; (**b**) Interdependence between SAIDI and the fault rate. Figure 62: Regression analysis of the Lithuanian 0.4 kV grid, 2015–2018. (**a**) Interdependence between SAIFI and the fault rate; (**b**) Interdependence between SAIDI and the fault rate. Figure 66: Regression analysis of the Lithuanian 10 kV cable lines, 2015–2018. (**a**) Interdependence between SAIFI and the fault rate; (**b**) Interdependence between SAIDI and the fault rate. Figure 67: Regression analysis of the Lithuanian 10/0.4 kV substations, 2015–2018. (**a**) Interdependence between SAIFI and the fault rate; (**b**) Interdependence between SAIDI and the fault rate. Figure 68: Regression analysis of the Lithuanian 10/0.4 kV transformers, 2014–2018. (**a**) Interdependence between SAIFI and the fault rate; (**b**) Interdependence between SAIDI and the fault rate. Unfortunately, currently, detailed classification by PQ event type is not possible (or is barely possible), thus the term 'fault' should be understood in the broader context, i.e., when voltage sag, transient interruption, short interruption, and long interruption are covered. What is more, the type of PQ event observed in different nodes depends on automation and mitigation devices (e.g., distributed generation). Also, it is probable that some part of non-dangerous voltage sags was skipped.