3.1.1. Protection Coordination Constraints

When a fault occurs in the network, in order to ensure the selectivity of the relay, there should be a reasonable *CTI* between the backup and primary relay operation time and this relationship also exists between the remaining protection and backup protection operation time. The *CTI* can be expressed as Equations (13) and (14):

$$CTI\_{i\cdot 1} = t\_{\text{lc\cdot k}}^{i1} - t\_{pr\cdot k}^{i} \tag{13}$$

$$CTI\_{i\cdot 2} = t\_{bc\cdot k}^{i2} - t\_{bc\cdot k}^{i1} \tag{14}$$

The *CTI* should have a minimum value by considering the operation time of the circuit breaker and a safety margin, where an excessive *CTI* is unfavorable to the stability of the system [31]. Therefore, the *CTIi*·<sup>1</sup> is limited to between 0.2 and 0.5, and the *CTIi*·<sup>2</sup> is greater than 0.2 [32]. It can be represented as follows:

$$
\mathcal{CTI}\_{\text{min}} \le \mathcal{CTI}\_{i \cdot 1} \le \mathcal{CTI}\_{\text{max}} \tag{15}
$$

$$\text{CTI}\_{\text{min}} \le \text{CTI}\_{i:2} \tag{16}$$
