Page 287 - Modern Control of DC-Based Power Systems

246 Modern Control of DC-Based Power Systems

case of ideal CPL switched LRCs, such oscillations do not appear for
the switched CPL switched LRCs case.
All decentralized virtual disturbance-based controllers (LQG,
Backstepping, Synergetic) exhibited a certain robustness towards changing
scenario conditions; they exhibited also a robustness towards modeling
error, like the disconnections of a LRC which made the control reaction
of the Synergetic control not usable, as it is a model-based controller.
In the switched LRC simulations, the usage of steady-state Kalman fil-
ter in a closed-loop control did not exhibit any obvious restrictions even
though the system is assumed by definition linear.
The switched LRC simulations also revealed that the Adaptive
Backstepping controller cannot be used in its actual implementation for
switching frequency of 1 kHz, as the duty cycle oscillates rapidly between
0 and 1 and such a behavior would severely limit the lifetime of the
equipment. This explains why in all cited Adaptive Backstepping applica-
tions only low power converters in a cascaded configuration are used
[7,8]. They operate with switching frequencies of 40 kHz 1 MHz.
There the simple discretization procedure seems good enough; however,
detailed plots of the duty cycle are not shown.
To adapt the Adaptive Backstepping controller a time-discrete
Lyapunov design procedure based on sampled data would need to be
undertaken without guaranteeing a 1 kHz switching frequency; moreover,
it seems that with Adaptive Backstepping the duty cycle will always oscil-
late. The observed duty cycle in Fig. 6.20 is a sign that in the nonlinear
process of power estimation in combination with variable structure sys-
tems, hidden dynamics are present which influence the results and do not
let the power estimation process converge to a constant steady-state value.

REFERENCES
[1] N. Doerry, Naval Power Systems: integrated power systems for the continuity of the
electrical power supply, IEEE Electr. Mag. 3 (2) (2015) 12. 21, June.
[2] IEEE Recommended Practice for 1 kV to 35 kV Medium-Voltage DC Power
Systems on Ships, IEEE Std. 1709 2010, pp. 1, 54, Nov. 2 2010.
[3] R.W. Erickson, D. Maksimovi´ c, Fundamentals of Power Electronics, second ed.,
Kluwer Academic, Norwell, Mass, 2001.
[4] I. Kondratiev, A Synergetic Control for Parallel-connected DC-DC Buck Converters,
PhD Dissertation, University of South Carolina, College of Engineering and
Information Technology, 2005.
[5] I. Kondratiev, R. Dougal, General synergetic control strategies for arbitrary number
of paralleled buck converters feeding constant power load: implementation of dynamic
current sharing, 2006 IEEE Int. Symp. Ind. Electr. vol. 1 (2006). no., pp. 257, 261,
9-13 July.