**7.3 Assessment of the presented power system stabilizers**

From the results presented in Sections 7.1 and 7.2 presented in **Figures 22**–**32** and **34**–**40**, it is seen clearly that robust and adaptive PSS improve the damping of oscillations of the synchronous generators significantly (shorter time of oscillations, smaller overshoot, and better damping). The numerical assessment was done for better insight into the effectiveness of both control algorithms. The integral square root performance index of rotor speed oscillation (Ð *ω*2*dt*) was introduced for more objective numerical evaluation of the proposed control approaches. The time responses shown in **Figures 13, 16, 19, 22, 25, 26, 34, 37**, and **38** were considered

for a synchronous generator with nominal power 160 MVA. The calculated performance indexes are shown in **Table 14**. The improvements of the performance index by means of proposed control systems regarding the noncontrolled synchronous

*The improvements of the integral square root performance index of rotor speed oscillation of the 555 MVA*

**Synchronous generator with nominal power SN = 555 [MVA]** *P* **[pu]** *Q* **[pu] cos** *φ* **Improvement of performance index regarding the case without**

1.0 0.1 0.995 56 [%] 47 [%] 1.0 0.62 0.85 43 [%] 47 [%] 0.1 1.0 0.099 15 [%] 15 [%]

*Robust and Adaptive Control for Synchronous Generator's Operation Improvement*

*synchronous generator at different operating points following the use of robust or adaptive PSS.*

**PSS [%] Robust PSS Adaptive PSS**

The time responses shown in **Figures 28, 30, 32, 39**, and **40** were considered for

From the obtained numerical results, it is obvious that the proposed robust and adaptive PSS assure significant damping improvement in the entire operating range. The effectiveness of both proposed stabilizers are similar. They depend on the type of generator, largeness of the generator, operating point (loading), etc. In general, we can conclude that, according to the introduced performance index, their

Changes in construction of synchronous generators and the introduction of additional control systems into power systems have led to significant increase of oscillations in power systems and related stability problems. Conventional linear power system stabilizers are not able to solve these problems. Advanced control theories seem appropriate to design more powerful power system stabilizers. Two power system stabilizers were developed based on robust control theory and adaptive control theory. The effectiveness of both stabilizers was evaluated as objectively as possible. The proposed control approaches were evaluated on a basis of a theoretical analysis and numerical simulations. The sliding mode stabilizer and direct adaptive stabilizer have the following advantages in comparison to conven-

• The proofs of the stability of the entire closed-loop system exist for both

• Both controllers require minimal preknowledge of the controlled plant

• Both controllers have an uncomplicated tuning procedure.

a synchronous generator with nominal power 555 MVA. The calculated performance indexes of the synchronous generator without PSS, with robust PSS, or with adaptive PSS are shown in **Table 16**. The improvements of the performance index by means of proposed control systems regarding the noncontrolled synchronous

generator are presented in **Table 15**.

*DOI: http://dx.doi.org/10.5772/intechopen.92558*

generator are presented in **Table 17**.

improvement is in the range of 10–60 [%].

**8. Conclusion**

**Table 17.**

tional linear stabilizers:

**275**

controllers presented.

structure and parameters.


#### **Table 14.**

*Integral square root performance index of rotor speed oscillation of the 160 MVA synchronous generator without PSS, with robust PSS, or with adaptive PSS at different operating points.*


#### **Table 15.**

*The improvements of the integral square root performance index of rotor speed oscillation of the 160 MVA synchronous generator at different operating points following the use of robust or adaptive PSS.*


#### **Table 16.**

*Integral square root performance index of rotor speed oscillation of the 555 MVA synchronous generator without PSS, with robust PSS, or with adaptive PSS at different operating points.*


**Table 17.**

as in Section 7.1.3. **Figure 39** shows the generated electrical power and rotor speed at operating point *P* = 1.0 [pu] and *Q* = 0.1 [pu], and **Figure 40** shows both

From the results presented in Sections 7.1 and 7.2 presented in **Figures 22**–**32** and **34**–**40**, it is seen clearly that robust and adaptive PSS improve the damping of oscillations of the synchronous generators significantly (shorter time of oscillations, smaller overshoot, and better damping). The numerical assessment was done for better insight into the effectiveness of both control algorithms. The integral square

objective numerical evaluation of the proposed control approaches. The time responses shown in **Figures 13, 16, 19, 22, 25, 26, 34, 37**, and **38** were considered

*P* **[pu]** *Q* **[pu] cos** *φ* **Performance index**

*without PSS, with robust PSS, or with adaptive PSS at different operating points.*

**Synchronous generator with nominal power** *S***<sup>N</sup> = 160 [MVA]**

1.0 0.1 0.995 1.98 10<sup>6</sup> 0.96 10<sup>6</sup> 0.91 10<sup>6</sup> 1.0 0.62 0.85 0.99 10<sup>6</sup> 0.56 10<sup>6</sup> 0.44 10<sup>6</sup> 0.1 1.0 0.099 0.56 10<sup>6</sup> 0.41 10<sup>6</sup> 0.42 10<sup>6</sup>

*Integral square root performance index of rotor speed oscillation of the 160 MVA synchronous generator*

**Synchronous generator with nominal power** *S***<sup>N</sup> = 160 [MVA]** *P* **[pu]** *Q* **[pu] cos** *φ* **Improvement of performance index regarding the case without**

*The improvements of the integral square root performance index of rotor speed oscillation of the 160 MVA*

**Synchronous generator with nominal power** *S***<sup>N</sup> = 555 [MVA]**

1.0 0.1 0.995 1.73 10<sup>6</sup> 0.76 10<sup>6</sup> 0.92 10<sup>6</sup> 1.0 0.62 0.85 0.89 10<sup>6</sup> 0.51 10<sup>6</sup> 0.47 10<sup>6</sup> 0.1 1.0 0.099 0.33 10<sup>6</sup> 0.28 10<sup>6</sup> 0.28 10<sup>6</sup>

*Integral square root performance index of rotor speed oscillation of the 555 MVA synchronous generator*

1.0 0.1 0.995 51 [%] 54 [%] 1.0 0.62 0.85 43 [%] 55 [%] 0.1 1.0 0.099 26 [%] 25 [%]

*synchronous generator at different operating points following the use of robust or adaptive PSS.*

*P* **[pu]** *Q* **[pu] cos** *φ* **Performance index**

*without PSS, with robust PSS, or with adaptive PSS at different operating points.*

*ω*2*dt*) was introduced for more

**Without PSS Robust PSS Adaptive PSS**

**PSS [%] Robust PSS Adaptive PSS**

**Without PSS Robust PSS Adaptive PSS**

quantities at operating point *P* = 0.1 [pu] and *Q* = 1.0 [pu].

*Automation and Control*

**7.3 Assessment of the presented power system stabilizers**

root performance index of rotor speed oscillation (Ð

**Table 14.**

**Table 15.**

**Table 16.**

**274**

*The improvements of the integral square root performance index of rotor speed oscillation of the 555 MVA synchronous generator at different operating points following the use of robust or adaptive PSS.*

for a synchronous generator with nominal power 160 MVA. The calculated performance indexes are shown in **Table 14**. The improvements of the performance index by means of proposed control systems regarding the noncontrolled synchronous generator are presented in **Table 15**.

The time responses shown in **Figures 28, 30, 32, 39**, and **40** were considered for a synchronous generator with nominal power 555 MVA. The calculated performance indexes of the synchronous generator without PSS, with robust PSS, or with adaptive PSS are shown in **Table 16**. The improvements of the performance index by means of proposed control systems regarding the noncontrolled synchronous generator are presented in **Table 17**.

From the obtained numerical results, it is obvious that the proposed robust and adaptive PSS assure significant damping improvement in the entire operating range. The effectiveness of both proposed stabilizers are similar. They depend on the type of generator, largeness of the generator, operating point (loading), etc. In general, we can conclude that, according to the introduced performance index, their improvement is in the range of 10–60 [%].
