*Automation and Control*

losses by active power generation. The results are presented in two different operating points. In the first one, the electric angle between generator internal voltage and infinite bus voltage was 10°, and, in the second one, the angle amounts to 40°. The results of the rotor speed oscillations' variations are presented in the amplitude range from 0 to 20% of the synchronous speed by frequencies 1 and 2 [Hz]. From the obtained results, it is evident that there is no influence of the oscillations on power losses in the transmission line.

that the influence of the oscillations on power losses in the transmission line

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

The Heffron-Phillips model described in Section 2 is used for the analysis of the dynamic characteristics of the synchronous generator. The impact of the inputs' variations on the oscillations is studied on the synchronous generator with the

New parameters in **Table 6** are as follows: *S*<sup>N</sup> is nominal power [MVA], *V*<sup>N</sup> is nominal voltage [kV], cos *φ*<sup>N</sup> is a nominal power factor, and *x*'<sup>d</sup> is unsaturated

From the data in **Table 6**, the equilibrium state for the Heffron-Phillips model is calculated by means of a phasor diagram. Phasor equations permit the solution of the initial conditions that exist prior to the application of the inputs' variations. The linearization coefficients of the Heffron-Phillips model are calculated for the synchronous generator with data in **Table 6** and for the calculated equilibrium state's data. The linearization coefficients for nominal operating point (*P*<sup>N</sup> = 1 [pu], cos *φ*<sup>N</sup> = 0.85), and eigenvalues of the Heffron-Phillips model (λ1, λ2, and λ3) are

The linearized Heffron-Phillips model of a synchronous generator has three eigenvalues. The damping ratio and frequency of rotor angle oscillation are seen directly from the dominant conjugate complex eigenvalues. Therefore, it is very transparent to investigate the dependence of the synchronous generator's oscillation dynamics from the operating point by means of eigenvalue analysis. By changing the operating point, the Heffron-Phillips model's eigenvalues also change.

Transient response of the synchronous generator with data in **Table 6** and nominal operating point with data in **Table 7** are shown in **Figures 11**–**13**. Step changes are simulated in both generator's inputs. **Figure 11** shows the simulated

*S*<sup>N</sup> = 160 [MVA] *V*<sup>N</sup> = 15 [kV] cos *φ*<sup>N</sup> = 0.85

*T'*d0 = 5.9 [pu] *H* = 2.37 [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> = 0.0011 [pu] *R*<sup>F</sup> = 0.0007 [pu] *x'*<sup>d</sup> = 0.245 [pu] *L*<sup>d</sup> = 1.700 [pu] *L*<sup>q</sup> = 1.640 [pu] *L*<sup>F</sup> = 0.101 [pu] *L*<sup>D</sup> = 0.055 [pu] *L*<sup>Q</sup> = 0.036 [pu] *L*AD = 1.550 [pu] *l*<sup>d</sup> = 0.150 [pu] *l*<sup>q</sup> = 0.150 [pu] *L*AQ = 1.490 [pu]

*P*<sup>N</sup> = 1.0 [pu] *Q*<sup>N</sup> = 0.62 [pu] cos *φ*<sup>N</sup> = 0.85 *K*<sup>1</sup> = 1.4478 *K*<sup>2</sup> = 1.3174 *K*<sup>3</sup> = 0.3072 *K*<sup>4</sup> = 1.8052 *K*<sup>5</sup> = 0.0294 *K*<sup>6</sup> = 0.5257 λ<sup>1</sup> = 0.3502 + 10.7270i λ<sup>2</sup> = 0.3502 10.7270i λ<sup>3</sup> = 0.2732

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

is negligible.

**3.2 Dynamic analysis**

following data [4]:

presented in **Table 7**.

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

**Table 6.**

**Table 7.**

**251**

]

*Data of the synchronous generator used for dynamic analysis [4].*

d-axis transient reactance [pu].

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

**Table 5** shows the impact of the rotor speed oscillations on the losses by reactive power generation. The results are presented at two different operating points. In the first one, the generator's internal voltage was 10% bigger than the infinite bus voltage, and, in the second one, the difference amounts to 50%. The results of rotor speed oscillations' variations are presented in the amplitude range from 0 to 20% of the synchronous speed by frequencies 1 and 2 [Hz]. From the results, it is obvious


**Table 4.**

*Mean values of three-phase transmitted power to the infinite bus (*P*IB) and three-phase power losses in the transmission line* P*<sup>L</sup> as a function of the angle between the generator's internal voltage and infinite bus voltage (*φ*1-*φ*2) by different amplitudes (*A*ao,* A*fo) and frequencies (*F*ao,* F*fo) of amplitude and frequency oscillations in the generator's internal voltage by active power transmission.*


#### **Table 5.**

*Mean values of three-phase transmitted power to the infinite bus (*P*IB) and three-phase power losses in the transmission line* P*<sup>L</sup> as a function of the generator's internal voltage (*V*1e) by different amplitudes (*A*ao,* A*fo) and frequencies (*F*ao,* F*fo) of amplitude and frequency oscillations in the generator's internal voltage by reactive power transmission.*

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

that the influence of the oscillations on power losses in the transmission line is negligible.
