*4.2. Case 1. Three-Phase Failure Cleared after Eight Cycles*

This study considers a StatCom integrated to the power system at bus 8, as presented in Figure 4. Initially, the StatCom operation was forced to keep the system behavior very similar to one without StatCom and PSS. Therefore, the power flow solution is used to feed the calculation of initial conditions by the prefault situation of angles and voltage magnitude. At bus 8, the voltage magnitude is *V*<sup>8</sup> = 0.9556 pu, close to the lower limit.

A three phase fault at 0.1 s is presented near to node 7 in one of the transmission lines 7–8. Several fault duration times were tested. Figures 6 and 7 exhibit the power system performance when the StatCom and PSS have a positive interaction. The fault is cleared after eight cycles, which was the fault duration for the power system to become unstable on the base case. There is a comparison using StatCom with and without PSS for making the system stable. The StatCom inclusion is not enough to improve the global power system damping, however, it diminishes the magnitude of the oscillations and improves the damping ratio respect to the system without controllers in the same period.

**Figure 6.** Angular difference of each machine with respect to number one, case 1: 8 cycles until the fault is cleared.

Figure 6 depicts the angular difference of each generator. The proposed control design methodology shows a positive interaction between controllers and the overshoot has an important reduction with and without the PSS, but the oscillations are eliminated in a fast way when PSS is included. Figure 7a presents the active power on the generator two and Figure 7b the voltage magnitude in PCC node where the StatCom is included.

Table 5 presents the main characteristics of transient response for case 1. Where the quantitative comparison is obtained in the case: (i) with StatCom and without PSS (wS/woPSS); and (ii) with StatCom and with PSS (wS/wPSS). The transient responses of the angular differences are improved with the correct coordination of controllers. In the case of *δ*<sup>21</sup> the settling time is diminished in about 80.5%, for the overshot a marginal improves percent is obtained. However, the overall performance of the proposed technique permits to attain a similar behavior in terms of overshot, in some case better, but in all responses the settling time is drastically enhanced.

**Figure 7.** Case 1: (**a**) real power at generator 2; (**b**) voltage magnitude in bus of StatCom connection.


**Table 5.** Analysis in time domain of the responses for case 1.

The settling time is improved with the following percentages; for *δ*31, 86.3%; for *δ*41, 81.9%, and *Pe*2, 85.5%, which is concentrated in Table 6. The rise time and peak time are similar for both controller's tuning. Like the previous dynamic performance of the power system, for the case 2, also the transient response features are determined, Table 6. Now, the proposed adaptive strategy has impacted in two main features in time domain transient response. Both settling time and overshoot are clearly enhanced by the proposed control coordination scheme. The following improvement values are attained: *δ*21, 83%; *δ*31, 87.5%; *δ*41, 86%, and *Pe*<sup>2</sup> in 85%. In Table 6, the results are presented. It is evident the correct performance of the proposed algorithm to diminish the exhibited low frequency oscillations in a faster way. Additionally, the percent that diminishes the overshoot in this case is:*δ*21, 65%; *δ*31, 70%; *δ*41, 79%, and *Pe*<sup>2</sup> in 43.3%.


**Table 6.** Analysis in time domain of the responses for case 2.
