*7.1.3 Influence of parameter deviations*

To analyze the impact of parameter variations on the damping efficiency of the proposed control systems, both control systems were tested at different operating points for synchronous generators of different types and nominal powers. In this work, the results are presented for a synchronous generator with nominal power 555 MVA. The data of the considered synchronous generator are shown in **Table 10** [4].

The linearization coefficients for nominal operating point (*P*<sup>N</sup> = 1 [pu], cos *φ*<sup>N</sup> = 0.9) and eigenvalues of the Heffron-Phillips model (λ1, λ2, λ3) are presented in **Table 11**.

The transient response of the noncontrolled synchronous generator with data in **Table 10** and nominal operating point data in **Table 11** are shown in

**Figure 24.** *Excitation voltage* E*FD(*t*) [pu] at nominal operating point* P *= 1.0 [pu] and* Q *= 0.62 [pu], with robust PSS.* **Figure 26.**

**Figure 25.**

*robust PSS.*

*robust PSS.*

**265**

*Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu], with*

*Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu], with*

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

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

*Robust and Adaptive Control for Synchronous Generator's Operation Improvement DOI: http://dx.doi.org/10.5772/intechopen.92558*

**Figure 25.** *Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu], with robust PSS.*

**Figure 26.** *Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu], with robust PSS.*

and robust PSS to the step changes of the mechanical torque and the field excitation voltage, as shown in **Figure 11**. The synchronous generator operates in in the vicinity of the nominal operating point. **Figures 22** and **23** show the generated electrical power, rotor speed, and rotor angle at nominal operating point *P* = 1.0

**Figure 24** shows the excitation voltage produced by a robust PSS at operating point *P* = 1.0 [pu] and *Q* = 0.62 [pu]. The limits of the limiters are seen clearly.

During the operation in the entire operating range, the dynamics of the synchronous generator vary significantly. The sliding mode controller with the calculated parameters was stable and robust and displayed the effective damping in all operating conditions. The theoretical analysis of the invariance of the proposed control system to the disturbances and the variation of the plant parameter are

In this work, the results of the two most extreme operating points are presented

• *P* = 1.0 [pu] and *Q* = 0.1 [pu]: This is a stable operation point with heavily

• *P* = 0.1 [pu] and *Q* = 1.0 [pu]: This is the critical operating point with weakly

**Figure 25** shows the generated electrical power and rotor speed at operating point *P* = 1.0 [pu] and *Q* = 0.1 [pu], and **Figure 26** shows both quantities at

To analyze the impact of parameter variations on the damping efficiency of the proposed control systems, both control systems were tested at different operating points for synchronous generators of different types and nominal powers. In this work, the results are presented for a synchronous generator with nominal power 555 MVA. The data of the considered synchronous generator are shown in **Table 10** [4]. The linearization coefficients for nominal operating point (*P*<sup>N</sup> = 1 [pu], cos *φ*<sup>N</sup> = 0.9) and eigenvalues of the Heffron-Phillips model (λ1, λ2, λ3) are presented in

The transient response of the noncontrolled synchronous generator with data in

*Excitation voltage* E*FD(*t*) [pu] at nominal operating point* P *= 1.0 [pu] and* Q *= 0.62 [pu], with robust PSS.*

**Table 10** and nominal operating point data in **Table 11** are shown in

[pu] and *Q* = 0.62 [pu].

*Automation and Control*

*7.1.2 Influence of load disturbance*

described in detail in [20].

damped oscillations.

damped oscillations.

(the same operating points as described in Section 3.2):

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

*7.1.3 Influence of parameter deviations*

**Table 11**.

**Figure 24.**

**264**

**Figures 27** and **28**. Step changes are simulated in both generators' inputs. **Figure 27** shows the simulated trajectory of the turbine mechanical torque and rotor excitation voltage. Step changes are selected as the worst case in order to maximize the excitation of oscillations.

**Figure 28** shows the response of the generated electrical power and rotor speed on the inputs' trajectories shown in **Figure 27**.


#### **Table 10.**

*Data of the 555 MVA synchronous generator used for the analysis of the impact of parameter variations on the damping efficiency [4].*


**Table 11.**

*Linearization parameters and eigenvalues of the Heffron-Phillips model at the nominal operating point of the 555 MVA synchronous generator.*

The results are presented of the robust control at two operating points:

**Figure 30**.

**Figure 28.**

**Table 12.**

**Table 13.**

**267**

• *P* = 1.0 [pu] and *Q* = 0.1 [pu]: The linearization coefficients and eigenvalues of the Heffron-Phillips model (λ1, λ2, λ3) are presented in **Table 12**, the step changes of the mechanical torque and the field excitation voltage are shown in **Figure 29**, and the generated electrical power and rotor speed are shown in

*Linearization parameters and eigenvalues of the Heffron-Phillips model at operating point* P *= 0.1 [pu] and*

*The 555 MVA synchronous generator outputs' trajectories: Rotor speed* ω*(*t*) [pu] and rotor angle* δ*(*t*) [degrees],*

*P*<sup>N</sup> = 1.0 [pu] *Q*<sup>N</sup> = 0.1 [pu] cos *φ*<sup>N</sup> = 0.995 *K*<sup>1</sup> = 1.1387 *K*<sup>2</sup> = 1.4710 *K*<sup>3</sup> = 0.3168 *K*<sup>4</sup> = 2.1296 *K*<sup>5</sup> = 0.1069 *K*<sup>6</sup> = 0.3281 λ<sup>1</sup> = 0.3140 + 7.8075i λ<sup>2</sup> = 0.3140 - 7.8075i λ<sup>3</sup> = 0.0506

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

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

*Performance in linearization parameters and eigenvalues of the Heffron-Phillips model in operating point*

*P*<sup>N</sup> = 0.1 [pu] *Q*<sup>N</sup> = 1.0 [pu] cos *φ*<sup>N</sup> = 0.099 *K*<sup>1</sup> = 1.2340 *K*<sup>2</sup> = 0.1533 *K*<sup>3</sup> = 0.3168 *K*<sup>4</sup> = 0.1204 *K*<sup>5</sup> = 0.0167 *K*<sup>6</sup> = 0.5720 λ<sup>1</sup> = 0.1430 - 8.1276i λ<sup>2</sup> = 0.1430 + 8.1276i λ<sup>3</sup> = 0.3927

*nominal operating point* P *= 1.0 [pu] and* Q *= 0.48 [pu], without PSS.*

P *= 1.0 [pu] and* Q *= 0.1 [pu] of the 555 MVA synchronous generator.*

Q *= 1.0 [pu] of the 555 MVA synchronous generator.*

• *P* = 0.1 [pu] and *Q* = 1.0 [pu]: The linearization coefficients and eigenvalues of the Heffron-Phillips model (*λ*1, *λ*2, *λ*3) are presented in **Table 13**, the step

#### **Figure 27.**

*The 555 MVA synchronous generator inputs' trajectories: Mechanical torque* T*m(*t*) [pu] and rotor excitation voltage* E*fd(*t*) [pu], nominal operating point* P *= 1.0 [pu] and* Q *= 0.48 [pu].*

*Robust and Adaptive Control for Synchronous Generator's Operation Improvement DOI: http://dx.doi.org/10.5772/intechopen.92558*

#### **Figure 28.**

**Figures 27** and **28**. Step changes are simulated in both generators' inputs. **Figure 27** shows the simulated trajectory of the turbine mechanical torque and rotor excitation voltage. Step changes are selected as the worst case in order to maximize the

**Figure 28** shows the response of the generated electrical power and rotor speed

*S*<sup>N</sup> = 555 [MVA] *V*<sup>N</sup> = 24 [kV] cos *φ*<sup>N</sup> = 0.90

*T'*d0 = 8.0 [pu] *H* = 3.52 [s] *D* = 2.0 [pu] *R*<sup>e</sup> = 0.02 [pu] *L*<sup>e</sup> = 0.4 [pu] *V*IB = 1.0 [pu] *R*<sup>s</sup> = 0.0030 [pu] *R*<sup>F</sup> = 0.0006 [pu] *x'*<sup>d</sup> = 0.300 [pu] *L*<sup>d</sup> = 1.810 [pu] *L*<sup>q</sup> = 1.760 [pu] *L*<sup>F</sup> = 0.165 [pu] *L*<sup>D</sup> = 0.171 [pu] *L*<sup>Q</sup> = 0.084 [pu] *L*AD = 1.660 [pu] *l*<sup>d</sup> = 0.150 [pu] *l*<sup>q</sup> = 0.150 [pu] *L*AQ = 1.610 [pu]

*P*<sup>N</sup> = 1.0 [pu] *Q*<sup>N</sup> = 0.48 [pu] cos *φ*<sup>N</sup> = 0.90 *K*<sup>1</sup> = 1.3306 *K*<sup>2</sup> = 1.2988 *K*<sup>3</sup> = 0.3168 *K*<sup>4</sup> = 1.8578 *K*<sup>5</sup> = 0.0107 *K*<sup>6</sup> = 0.4545 λ<sup>1</sup> = 0.2554 + 8.4389i λ<sup>2</sup> = 0.2554 - 8.4389i λ<sup>3</sup> = -0.1678

*Data of the 555 MVA synchronous generator used for the analysis of the impact of parameter variations on the*

*Linearization parameters and eigenvalues of the Heffron-Phillips model at the nominal operating point of the*

*The 555 MVA synchronous generator inputs' trajectories: Mechanical torque* T*m(*t*) [pu] and rotor excitation*

*voltage* E*fd(*t*) [pu], nominal operating point* P *= 1.0 [pu] and* Q *= 0.48 [pu].*

excitation of oscillations.

*Automation and Control*

*ω*<sup>s</sup> = 377 [rad s<sup>1</sup>

]

**Table 11.**

**Table 10.**

*damping efficiency [4].*

**Figure 27.**

**266**

*555 MVA synchronous generator.*

on the inputs' trajectories shown in **Figure 27**.

*The 555 MVA synchronous generator outputs' trajectories: Rotor speed* ω*(*t*) [pu] and rotor angle* δ*(*t*) [degrees], nominal operating point* P *= 1.0 [pu] and* Q *= 0.48 [pu], without PSS.*


#### **Table 12.**

*Performance in linearization parameters and eigenvalues of the Heffron-Phillips model in operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu] of the 555 MVA synchronous generator.*


#### **Table 13.**

*Linearization parameters and eigenvalues of the Heffron-Phillips model at operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu] of the 555 MVA synchronous generator.*

The results are presented of the robust control at two operating points:


**Figure 29.**

*The 555 MVA synchronous generator inputs' trajectories: Mechanical torque* T*m(*t*) [pu] and rotor excitation voltage* E*fd(*t*) [pu], operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu].*

**7.2 Adaptive PSS**

**Figure 31.**

**Figure 32.**

**269**

The proposed direct adaptive controller guarantees stability of any controlled plant that satisfies ASPR conditions. A synchronous generator with automatic voltage system does not satisfy the necessary ASPR conditions. Augmenting of the plant with a parallel feedforward compensator must be carried out to assure stable operation of the entire adaptive control system. The augmentation is performed such

*The 555 MVA synchronous generator's electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at nominal*

*operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu], with robust PSS.*

*The 555 MVA synchronous generator inputs' trajectories: Mechanical torque* T*m(*t*) [pu] and rotor excitation*

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

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

*voltage* E*fd(*t*) [pu], operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu].*

**Figure 30.**

*The 555 MVA synchronous generator's electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at nominal operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu], with robust PSS.*

changes of the mechanical torque and the field excitation voltage are shown in **Figure 31**, and the generated electrical power and rotor speed are shown in **Figure 32**.

**Figure 25** shows the generated electrical power and rotor speed at heavily damped operating point *P* = 1.0 [pu] and *Q* = 0.1 [pu], and **Figure 26** shows both quantities at weakly damped operating point *P* = 0.1 [pu] and *Q* = 1.0 [pu].

*Robust and Adaptive Control for Synchronous Generator's Operation Improvement DOI: http://dx.doi.org/10.5772/intechopen.92558*

**Figure 31.**

*The 555 MVA synchronous generator inputs' trajectories: Mechanical torque* T*m(*t*) [pu] and rotor excitation voltage* E*fd(*t*) [pu], operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu].*

#### **7.2 Adaptive PSS**

The proposed direct adaptive controller guarantees stability of any controlled plant that satisfies ASPR conditions. A synchronous generator with automatic voltage system does not satisfy the necessary ASPR conditions. Augmenting of the plant with a parallel feedforward compensator must be carried out to assure stable operation of the entire adaptive control system. The augmentation is performed such

#### **Figure 32.**

*The 555 MVA synchronous generator's electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at nominal operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu], with robust PSS.*

changes of the mechanical torque and the field excitation voltage are shown in **Figure 31**, and the generated electrical power and rotor speed are shown in

*The 555 MVA synchronous generator inputs' trajectories: Mechanical torque* T*m(*t*) [pu] and rotor excitation*

*voltage* E*fd(*t*) [pu], operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu].*

*operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu], with robust PSS.*

**Figure 25** shows the generated electrical power and rotor speed at heavily damped operating point *P* = 1.0 [pu] and *Q* = 0.1 [pu], and **Figure 26** shows both quantities at weakly damped operating point *P* = 0.1 [pu] and *Q* = 1.0 [pu].

*The 555 MVA synchronous generator's electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at nominal*

**Figure 32**.

**Figure 30.**

**268**

**Figure 29.**

*Automation and Control*

that the augmented plant fulfills ASPR conditions. The requirement is satisfied in the majority of cases with the introduction of a feedforward compensator *G*ff(s), which is connected in parallel to the basic controlled plant. The suitable feedforward stabilizer represents a first-order low-pass filter with feedforward compensator gain *k*ff and feedforward compensator time constant *T*ff [18].

A block diagram of the direct adaptive PSS is presented in **Figure 33**.

The benefit of the control diagram shown in **Figure 33**, if compared to other adaptive structures, is a very simple realization of the adaptation mechanism. The presented direct adaptive PSS is essentially simplified; namely, a reference model is not required because of the constant (zero) command signal.

The reference terminal voltage *V*t,ref and the mechanical torque *T*<sup>m</sup> variables represent the main disturbances which affect the synchronous generator's dynamics. The variations of the synchronous generator loading can be treated as controlled plant parameters' perturbations. The washout block (input filters) serves as a highpass filter, with the time constant *T*<sup>w</sup> high enough to allow signals associated with oscillations in generator active power *P*<sup>e</sup> to pass unchanged. Without it, steady changes in power would modify the terminal voltage. It allows the PSS to respond only to changes in generator active power. From the viewpoint of the washout function, the value of *T*<sup>w</sup> is not critical and may be in the range of 1–20 s. The main consideration is that it would be long enough to pass stabilizing signals unchanged at the frequencies of interest. Direct adaptive control law is represented with (Eqs. (35)–(42)). The necessary feedforward compensator is described with Eqs. (44) and (45). The same model of the actuator saturation as in Section 7.1.1 was included in the simulations.

The parameters of the adaptation mechanism for the considered linearized controlled plant are determined with the rules described in [2], such as

$$\mathbf{T} = \mathbf{0} \mathbf{1} \cdot \mathbf{1} \mathbf{0}^3 \quad \overline{\mathbf{T}} = 20 \mathbf{0} \cdot \mathbf{1} \mathbf{0}^3 \quad \sigma = 5 \mathbf{0} \cdot \mathbf{1} \mathbf{0}^{-3} \quad k\_{\rm ff} = \mathbf{1} \cdot \mathbf{1} \mathbf{0}^{-3} \quad T\_{\rm ff} = \mathbf{1} \cdot \mathbf{1} \mathbf{0}^{-3} \tag{49}$$

#### *7.2.1 Nominal operating point*

**Figures 34**–**36** show the responses of the seventh-order nonlinear model of the considered 160 MVA synchronous generator equipped with an excitation system and adaptive PSS to the step changes of the mechanical torque and the field excitation voltage, as shown in **Figure 11**. **Figures 34** and **35** show the generated electrical power, rotor speed, and rotor angle at nominal operating point P = 1.0 [pu] and Q = 0.62 [pu].

**Figure 36** shows the excitation voltage produced by an adaptive PSS at nominal operating point *P* = 1.0 [pu] and *Q* = 0.62 [pu].

**Figures 34**–**36** are directly comparable with **Figures 22**–**25**.

*7.2.2 Influence of load disturbance*

are shown in **Figure 37**.

in Sections 3.2 and 7.1.2):

**Figure 34.**

**Figure 35.**

**Figure 36.**

**271**

*adaptive PSS.*

The results of the two most extreme operating points are presented (the same as

*Excitation voltage* E*FD(*t*) [pu] at nominal operating point* P *= 1.0 [pu] and* Q *= 0.62 [pu], with adaptive PSS.*

*Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 1.0 [pu] and* Q *= 0.62 [pu], with*

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

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

*Rotor angle* δ*(*t*) [pu] at nominal operating point* P *= 1.0 [pu] and* Q *= 0.62 [pu], with adaptive PSS.*

• *P* = 1.0 [pu] and *Q* = 0.1 [pu]: The generated electrical power and rotor speed

**Figure 33.** *Block diagram of the direct adaptive PSS.*

*Robust and Adaptive Control for Synchronous Generator's Operation Improvement DOI: http://dx.doi.org/10.5772/intechopen.92558*

**Figure 34.** *Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 1.0 [pu] and* Q *= 0.62 [pu], with adaptive PSS.*

**Figure 36.** *Excitation voltage* E*FD(*t*) [pu] at nominal operating point* P *= 1.0 [pu] and* Q *= 0.62 [pu], with adaptive PSS.*

### *7.2.2 Influence of load disturbance*

The results of the two most extreme operating points are presented (the same as in Sections 3.2 and 7.1.2):

• *P* = 1.0 [pu] and *Q* = 0.1 [pu]: The generated electrical power and rotor speed are shown in **Figure 37**.

that the augmented plant fulfills ASPR conditions. The requirement is satisfied in the majority of cases with the introduction of a feedforward compensator *G*ff(s),

The benefit of the control diagram shown in **Figure 33**, if compared to other adaptive structures, is a very simple realization of the adaptation mechanism. The presented direct adaptive PSS is essentially simplified; namely, a reference model is

The reference terminal voltage *V*t,ref and the mechanical torque *T*<sup>m</sup> variables represent the main disturbances which affect the synchronous generator's dynamics. The variations of the synchronous generator loading can be treated as controlled plant parameters' perturbations. The washout block (input filters) serves as a highpass filter, with the time constant *T*<sup>w</sup> high enough to allow signals associated with oscillations in generator active power *P*<sup>e</sup> to pass unchanged. Without it, steady changes in power would modify the terminal voltage. It allows the PSS to respond only to changes in generator active power. From the viewpoint of the washout function, the value of *T*<sup>w</sup> is not critical and may be in the range of 1–20 s. The main consideration is that it would be long enough to pass stabilizing signals unchanged at the frequencies of interest. Direct adaptive control law is represented with (Eqs. (35)–(42)). The necessary feedforward compensator is described with Eqs. (44) and (45). The same model of the actuator saturation as in Section 7.1.1

The parameters of the adaptation mechanism for the considered linearized con-

**Figures 34**–**36** show the responses of the seventh-order nonlinear model of the considered 160 MVA synchronous generator equipped with an excitation system and adaptive PSS to the step changes of the mechanical torque and the field excitation voltage, as shown in **Figure 11**. **Figures 34** and **35** show the generated electrical power, rotor speed, and rotor angle at nominal operating point P = 1.0 [pu] and

**Figure 36** shows the excitation voltage produced by an adaptive PSS at nominal

(49)

**<sup>T</sup>** <sup>¼</sup> <sup>0</sup>*:*<sup>1</sup> � <sup>10</sup><sup>3</sup> **<sup>T</sup>** <sup>¼</sup> <sup>200</sup> � <sup>10</sup><sup>3</sup> *<sup>σ</sup>* <sup>¼</sup> <sup>50</sup> � <sup>10</sup>�<sup>3</sup> *<sup>k</sup>*ff <sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>3</sup> *<sup>T</sup>*ff <sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>3</sup>

trolled plant are determined with the rules described in [2], such as

**Figures 34**–**36** are directly comparable with **Figures 22**–**25**.

which is connected in parallel to the basic controlled plant. The suitable feedforward stabilizer represents a first-order low-pass filter with feedforward compensator gain *k*ff and feedforward compensator time constant *T*ff [18]. A block diagram of the direct adaptive PSS is presented in **Figure 33**.

not required because of the constant (zero) command signal.

was included in the simulations.

*Automation and Control*

*7.2.1 Nominal operating point*

operating point *P* = 1.0 [pu] and *Q* = 0.62 [pu].

Q = 0.62 [pu].

**Figure 33.**

**270**

*Block diagram of the direct adaptive PSS.*

• *P* = 0.1 [pu] and *Q* = 1.0 [pu]: The generated electrical power and rotor speed

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

The effectiveness of the adaptive PSS for oscillation damping in the presence of parameter deviations is shown with a test on the 555 MVA synchronous generator,

*The 555 MVA synchronous generator's electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point*

*The 555 MVA synchronous generator's electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point*

are shown in **Figure 38**.

**Figure 39.**

**Figure 40.**

**273**

*7.2.3 Influence of parameter deviations*

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

P *= 1.0 [pu] and* Q *= 0.1 [pu], with adaptive PSS.*

P *= 0.1 [pu] and* Q *= 1.0 [pu], with adaptive PSS.*

**Figure 37.** *Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu], with adaptive PSS.*

**Figure 38.** *Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu], with adaptive PSS.*

*Robust and Adaptive Control for Synchronous Generator's Operation Improvement DOI: http://dx.doi.org/10.5772/intechopen.92558*

• *P* = 0.1 [pu] and *Q* = 1.0 [pu]: The generated electrical power and rotor speed are shown in **Figure 38**.

### *7.2.3 Influence of parameter deviations*

The effectiveness of the adaptive PSS for oscillation damping in the presence of parameter deviations is shown with a test on the 555 MVA synchronous generator,

#### **Figure 39.**

**Figure 37.**

**Figure 38.**

**272**

*adaptive PSS.*

*adaptive PSS.*

*Automation and Control*

*Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu], with*

*Electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu], with*

*The 555 MVA synchronous generator's electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 1.0 [pu] and* Q *= 0.1 [pu], with adaptive PSS.*

#### **Figure 40.**

*The 555 MVA synchronous generator's electrical power* P*e(*t*) [pu] and rotor speed* ω*(*t*) [pu] at operating point* P *= 0.1 [pu] and* Q *= 1.0 [pu], with adaptive PSS.*

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