# Comparative Technical-Economical Analysis of Transient Stability Improvements in a Power System
## 5 Frequency Stability  
In this section, the solutions presented are tested to analyze their impact on frequency stability, analyzing the same network and contingency as before.  
The simulations are performed for each solution already presented (SVC, STATCOM, EXST4B, and a new parallel line) and the frequency trends obtained are shown in Figure 8.  
The three-phase short circuit causes a frequency transient characterized by oscillations. It can be seen from Figure 8 that the oscillations occurring in the base case are suppressed with the solution considered in this paper.  
The structural and preemptive solution, i.e., the addition of a parallel line, has a small effect on the frequency stability. On the other hand, the emergency solutions implemented with FACTS, especially SVC and STATCOM, and the fast-acting exciter, i.e., EXST4B, have a better impact on the frequency stability, especially during the underfrequency period.  
Figure 8: Frequency transient curves following a three-phase short circuit.  
Figure 7: Rotor angle of generator 2, FCT equal to 0.35 s, SVC, and STATCOM comparison.  
This is because these devices also operate under dynamic conditions, which allows the control of electrical quantities such as voltage during the transient. SVC, STATCOM, and the fast exciter act mainly on the voltage of the bus to which they are connected, which is a crucial variable during a transient caused by a short circuit.  
Among the different solutions, the fast exciter is the most effective for frequency stability, and its fluctuations are the most damped, resulting in the lowest oscillation, which reaches a low point of 49.85 Hz.  
In order to measure the effect of the SVC and STATCOM solutions on frequency stability, they are compared with an existing solution used in underfrequency problems, namely, load shedding.  
The criterion used for this comparison is expressed by (1).  
\[\text{f}_{\text{nadir}}^{\text{tested device}}=\text{f}_{\text{nadir}}^{ \text{LS}} \tag{1}\]  
The comparison based on the frequency nadir is performed by varying the percentage of the load to be disconnected from bus 8 to achieve the same minimum frequency achieved with the tested devices. The simulations are performed by switching off an increasing percentage of the load from bus 8, the same bus to which the devices are connected.  
The disconnection is performed using the frequency relay of the load, which is set to 49.0 Hz [18].  
The results of this comparison are shown in Figure 9.  
From Figure 9, it can be seen that even with a 100% load shedding at bus 8, the frequency nadir never reaches the value obtained with FACTS devices. Looking at this, the use of these devices makes it possible to avoid load shedding and thus save money for the system.  
Using these values for the load to be shed, the obtained frequency trends are compared with the frequency trends obtained with both SVC and STATCOM. The comparisons of the frequency trends are shown in Figures 10 and 11. From these figures, it can be seen that SVC and STATCOM provide faster settling time, higher damping of frequency oscillations at underfrequency, and slight attenuation of overfrequency response. Another important feature of the two diagrams is that the disconnection of loads introduces a power imbalance between the generation and the load, which leads to different steady-state values for the frequency after the transient periods so that secondary frequency control is required.  
Figure 9: Frequency nadir comparison, SVC, STATCOM, and load shedding.