1、 64 A. Griffo, J. Wang / Electric Power Systems Research 82 (2012 5967 Fig. 6. DQ axis generator voltages (a; DQ axis generator currents (b; DC bus voltage and current (c, obtained with behavioral model (top and functional model (bottom. Modes #1 to #5 are found to be well damped in all operating co

2、nditions. They are mainly related to synchronous generator damper windings dynamics and AC capacitor. Modes #8 to #11 are also relatively well damped and are mostly associated with the current and speed control loops of the motor drive. Modes #14 and #15 are essentially related to the AC voltage reg

3、ulator, while modes #16 and #17 are related to the time constant of the motor stator windings. It has been veried that the system stability mostly depends on the two pairs #6,7 and #12,13 of complex eigenvalues, which are closely associated with DC bus dynamics and AC bus voltage regulator, respecti

4、vely. By way of example, Fig. 7a shows the eigenvalue loci when the motor drive output power is varied from 90 kW to 150 kW with other parameters and operating condition being the same as stated in Section 3. The remaining eigenvalues whose real part is less than 250 are not shown. As will be seen,

5、the mode #6,7 with a natural frequency of 800 Hz becomes unstable when the load power is greater than 120 kW. In order to illustrate the destabilizing effects of negative impedance characteristic of the tightly regulated motor drive load, Fig. 7b shows the eigenvalues loci when the current control l

6、oop bandwidth fc of the motor drive load is varied from 500 Hz to 2000 Hz while the speed control loop bandwidth is set to (1/3fc . Again it is evident that the 800 Hz mode #6,7 become unstable when fc is above 1.8 kHz. However, the lower frequency pair #12,13 associated with the AC bus regulator is

7、 virtually left unaffected by the variations in fc . It can also be seen A. Griffo, J. Wang / Electric Power Systems Research 82 (2012 5967 65 Fig. 7. Inuence of load power (a; current control bandwidth fc of the motor drive (b; generator control parameters (c and generator operating frequency s (d

8、on eigenvalues. that the eigenvalues of modes, #8 to #11, which are closely related to the current and speed control loops, moves to the left as the control bandwidth increases. These modes are nevertheless well damped although a complex pair is present. It should be noted that the instability due t

9、o high bandwidth drive controllers predicted by the eigenvalue analysis is in agreement with the results obtained from time domain simulations shown in Fig. 6 when fc = 2 kHz. Conversely, the dependency of the low frequency pair eigenvalues, i.e., modes #12 and 13 of on the AVR control parameters is

10、 illustrated in Fig. 7c for different combinations of the closed loop damping ratio and bandwidth n . However, these variations have little effect on the other eigenvalues. The inuence of synchronous operating frequency on the system stability is shown in Fig. 7d. As the frequency increases, the sta

11、bility margins associated with modes #6,7, i.e. the DC bus dynamic behavior improves. This is due to the fact that the damping effect introduced by the commutation overlap of the ATRU increases with frequency. However, an opposite trend is observed for the eigenvalues of mode #11,12 which is related

12、 to the AVR control gains. This is because the control gains according to Eq. (7 should be inversely proportional to the generator operating frequency. However, for a classic AVR, xed gains designed against a nominal operating frequency of 400 Hz with a damping ratio of 0.8 and natural frequency of

13、50 Hz are assumed in the eigenvalue analysis. Consequently, as the operating frequency increases, the effective loop gain of the AVR increases which leads to a more oscillatory response but the system remains stable over the frequency range s /2 = 250800 Hz. Fig. 8a shows the stabilizing effect of i

14、ncreasing the DC bus capacitance Cdc on modes #6,7. It is also evident that the variation of Cdc has little effect on modes #12,13. The opposite trend is observed in Fig. 8b when the DC lter inductance Ldc , is increased from 5 to 40 H, which implies that modes #6,7 is less stable with increase in t

15、he inductance. On contrary, an improvement in stability margins for modes #6,7 is visible in Fig. 8c when the equivalent AC commutation inductance Lac is increased. This is again due to the fact that the damping associated with the commutation overlap increases with the increase in Lac which represe

16、nts the combined effect of the AC bus cable inductance and leakage inductance of the ATRU. An increase in the AC capacitance CAC have been found, as shown in Fig. 8d, to reduce the natural frequencies of modes #1,2 and #3,4 with their damping ratios being increased. However, the AC capacitance also

17、affects the eigenvalues of modes #6,7 and #12,13 as shown in the inset in Fig. 8d. While modes #6,7 are more stable by an increase in CAC , the stability margin of modes #12,13 are adversely affected. The underlining cause of this problem lies in the fact that the design of the AVR controller assume

18、s open-circuit, and the effect of the capacitive load is not taken into account. From the foregoing analyses it can be concluded that the dynamic stability of the analysed system is mostly determined by the quasi- constant power load behavior of the motor drive load. Simulation results conrmed by sm

19、all-signal analyses have demonstrated that instability is determined by an increase in load power demand above 120 kW. It is also demonstrated that an increase in the motor drive controller bandwidth makes the load closer to a constant-power load and therefore decreases stability margins. The stabil

20、ity of the DC bus voltage related modes can be increased by increasing the DC lter capacitance while an increase in DC lter inductance reduces stability margins. Synchronous generator regulation by means of the AVR can affect the dynamics of the low 66 A. Griffo, J. Wang / Electric Power Systems Res

21、earch 82 (2012 5967 Fig. 8. Inuence of DC bus capacitance Cdc (a; DC lter inductance Ldc (b; AC commutation inductance Lac (c and AC capacitance CAC (d on eigenvalues. frequency modes but does not affect signicantly the response of the high-frequency dynamics related to the DC bus. Stability could i

22、n principle be improved also by including additional stabilizing control loops in the motor drive loads which can be used to modulate the power drawn from the DC bus in response to the occurrence of DC link oscillations 30. Similar stabilization loops could also be included in the controller of DCDC

23、 converters connected to suitable batteries or supercapacitors that can be used to store energy and release it at the occurence of unstable conditions. The advantages of this latter solution must however be considered against the additional complexity and weight associated with the storage devices.

24、6. Conclusion As vehicular power systems grow in complexity and power ratings a clear understanding of systems dynamic behavior is of paramount importance for their design and safe operation. An accurate and computationally efcient model of a typical power system for more electric aircraft has been

25、established in the paper. Through detailed simulations the developed model has been shown to accurately capture the dynamic behavior of power system transients. The utilities of the linearized model for small-signal stability analysis has been demonstrated and validated. Comprehensive and quantitati

26、ve analyses of the inuence of design parameters and operating conditions on stability margins have been undertaken. It has been shown that the system stability is essentially dominated by two complex modes associated with the DC and AC bus voltage transients. The modeling and stability assessment te

27、chnique provide an effective tool for design optimization of the passive lter and for evaluation of the stability robustness against parametric uncertainties. They can be readily extended to more complex, multiple loads architectures or adapted to other vehicular or terrestrial power systems that include power electronics controlled components. Appendix A. List of symbols: Synchrono