## 2 Problem Statement  
The main goal of this research was to analyze the impact of a type and location of DG units in present and future distribution network structures on the power supply reliability. The distribution system automation (ASS and APR) has also been considered in the studies. The analysis performed by the authors of this paper has been done for the benchmark structures of the MV distribution networks with the connected DG sources. The benchmark structures (shown in Figures 11, 12 and 13) have also been developed by the authors of this paper. The following reliability indices have been calculated with the use of DlgSILENT PowerFactory software [50; 51]:  
* SAIFI is the System Average Interruption Frequency Index, which provides the average number of interruptions, above 3 min, in the system that a customer experiences during the observation period, mostly in one year. The index is a dimensionless number and can be calculated as follows [52; 53]:\[\text{SAIFI}=\frac{\text{Total number of customer interruptions}}{\text{Total number of customers served}}=\frac{\sum_{i}\text{N}_{i}}{\text{N}_{\text{T}}}[1/\text{yr}]\] (1) where N\({}_{i}\) is the number of customers interrupted by \(i\)-th outage in the observation period and N\({}_{\text{T}}\) is the total number of customers in considered system. * CAIFI (Customer Average Interruption Frequency Index)--total number of all interruptions, above 3 min, divided by the total number of consumers affected by an interruption in the analyzed system. CAIFI can be calculated as follows [53, 54]: \[\text{CAIFI}=\frac{\text{Total number of customer interruptions}}{\text{Total number of customers affected}}=\frac{\sum_{i}\text{N}_{i}}{\text{CN}}[1/\text{yr}]\] (2) where CN is the total number of consumers, which experienced one or more outages. * SAIDI is the System Average Interruption Duration Index, and it measures the total duration of an interruption, above 3 min, for the average customer during a given time period. It is normally calculated for the period of one year and presents customer minutes or hours of interruption. Mathematical representation of SAIDI is given in Equation (3) [52, 53]: \[\text{SAIDI}=\frac{\sum\text{Customer interruption durations}}{\text{Total number of customers served}}=\frac{\sum_{i}\text{r}_{i}\text{N}_{i}}{\text{N}_{\text{T}}}[ \text{hr}/\text{yr}]\] (3) where r\({}_{i}\) is restoration time and failure duration in the case of consumers interrupted by \(i\)-th outage. * CAIDI, the Customer Average Interruption Duration Index represents the average time required to restore service after an outage occurs, which indicates how long an average interruption, above 3 min, lasts. It measures the duration of time that the customer is de-energized per interruption. To calculate the index Equation (4) can be used [52, 53]: \[\text{CAIDI}=\frac{\sum\text{Customer interruption durations}}{\text{Total number of customers interruptions}}=\frac{\sum_{i}\text{r}_{i}\text{N}_{i}}{\sum_{i}\text{N}_{i}}[ \text{hr}]\] (4)
* ASAI (Average Service Availability Index)--the probability of having all loads supplied. The index is often expressed in a percentage, and it can be calculated from Equation (5) [52, 53]: \[\text{ASAI}=\frac{\text{Customer hours service availability}}{\text{Customer hours service demand}}=\frac{\text{N}_{\text{T}}\cdot(T)-\sum_{i}\text{r}_{i}\text{N}_{i}}{\text{N}_{ \text{T}}\cdot(T)}[\text{pu}]\] (5) where \(T\) is the observation time period, usually one year, and in a non-leap year is equal to 8760 h.
* ASUI (Average Service Unavailability Index)--the probability of having one or more loads interrupted, which can be calculated as follows [54]: \[\text{ASUI}=\frac{\text{Customer hours service unavailability}}{\text{Customer hours service demand}}=1-\text{ASAI}\;[\text{pu}]\] (6)
* EENS (Expected Energy Not Supplied)--the total amount of energy which is expected not to be delivered to loads.