## 3 Results
### Settings of Protective Devices  
The most common protection devices used in distribution systems are OC relays. The OC relays are used as the main protection devices for radial distribution systems [30]. An OC relay measures the current flowing through it and determines whether to send a signal to open a circuit breaker [26; 36]. An OC relay trip settings are determined by \"pickup current (Ip)\" and \"time delay\" parameters. Pickup current is the threshold current value and is sensed by current level detection principle, which has to be exceeded for relay trip [27]. The pickup current of an OC relay is set in such a manner that it is larger than the rated current of the feeder but less than the minimum short-circuit current of the protected zone. When the DG unit and the substation are feeding the fault in parallel, the fault current detected by the OC relay is reduced (due to the contribution of DG to the fault current). This causes the relay to under reach its required protective zone. In other words, the relay is \"blind\" to the fault [37; 38]. In distribution feeder protection, the most important variable in optimal coordination of OC relays is the time multiplier setting (TMS). The operating time of a relay is a function of TMS, Ip and short-circuit current seen by the relay. The operating time of relay is given by Equation (4):  
\[t_{op}=\frac{\alpha\times TMS}{\left(\frac{I_{f}}{I_{p}}\right)^{\beta}-\gamma} \tag{4}\]  
where \(\alpha\), \(\beta\) and \(\gamma\) are constants that are used to represent a mathematical form of an inverse-definite minimum time (IDMT) type of OC relay characteristic. The values of 0.14, 0.02 and 1.0 are, respectively, set for \(\alpha\), \(\beta\) and \(\gamma\) to define an IDMT OC relay. Similarly, the recloser relay also has an inverse-time OC characteristic [39]. In this section, the OC relay settings of the DG and substation feeder are presented, and the recloser relay settings is then adjusted. The calculation of DG protective relay at Point of Common Coupling (PCC) is based on the generator transient stability. The overcurrent relay time constraint settings of generators for three-phase faults should be under 0.35 s [40]. The OC pickup of the relay is:  
\[P.S=1.2\times I_{n}=141\times 1.2=170A \tag{5}\]  
Figure 2: Single diagram of real distribution network with DG. The formulation of relay operating time with normally inverse characteristic is given by Equation (4) (\(\alpha\) = 0.14, \(\beta\) = 0.02):  
\[t=\frac{0.14}{\left(\left(\frac{I_{f}}{T_{p}}\right)^{0.02}-1\right)}\times TMS \tag{6}\]  
The TMS of an overcurrent relay of DG is calculated as follows:  
\[TMS=\frac{0.35\times\left(\left(\frac{1686}{170}\right)^{0.02}-1\right)}{0.14}= 0.117\approx 0.12 \tag{7}\]  
Table 2 provides the protective relay settings of DG at the PCC point. In addition, the settings of the 20 kV feeder does not change and is fixed. The relay settings of the substation 20 kV feeder are presented in Table 3.  
Connecting DG to the distribution network boosts the severity of short-circuit. In the case study, the short-circuit current increases to 14.31 kA after connecting DG to the main feeder. The recloser relay settings should be set to avoid blind areas. Therefore, the recloser should operate faster than the OC relay. The pickup current of the recloser relay is around twice the maximum feeder current. Figure 3 shows the substation OC and recloser relays characteristic curves in DIgSILENT. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**OC Settings** & \begin{tabular}{c} **Current** \\ **Transformer (CT)** \\ **ratio** \\ \end{tabular} & \begin{tabular}{c} **Pickup Current** \\ **(I\({}_{\text{Pickup}}\)) (A)** \\ \end{tabular} & **Curve** & \
\begin{tabular}{c} **Fault** \\ **Current (I\({}_{\text{P}}\))** \\ **(kA)** \\ \end{tabular} & **TMS** &
\begin{tabular}{c} **Instantaneous** \\ **Current** \\ \end{tabular} \\ \cline{2-7}  & 200/1 & 0.85\({}^{\circ}\)In & N.I & 8.89 & 0.12 & 10\({}^{\circ}\)In \\ \hline \hline \end{tabular}
\end{table}