Page 216 - Modern Control of DC-Based Power Systems

180 Modern Control of DC-Based Power Systems

5.6.2 Application to MVDC System Adaptive Backstepping
With Power Estimation
In contrast to the Backstepping controller which was designed so far, the
following control approach tries to incorporate the nonlinearity of the
CPL and take advantage of it. Therefore, the constant power is estimated
twice using one update law for each estimate. The update laws are
retrieved from the Lyapunov condition for stability and are derived in the
following. The overall structure of the controller which is designed in the
end is depicted in Fig. 5.47.
The circuit model of the decentralized buck converter modeled in
averaged mode with this corresponding DC link is depicted in Fig. 5.48.
The model includes the constant power P which is estimated in the com-
plete controller.
State-space representation (5.191) is derived according to the model
in Fig. 5.48, where the current going through the CPL is I CPL 5 P=V.
P
x 2 x 1
_ x 1 5 2 2
C f R L C f x 1 C f
(5.191)
dE x 2 R f x 1
_ x 2 5 2 2
L f L f L f

Parameter estimation Calculation of duty cycle
^
ʃ P
1
Vbus ,IL ^ ^
d(V bus , I , P , P )
L
2
1
^
ʃ P
2
Measurements Plant: Control signal
generators and loads
Figure 5.47 Overview of the Adaptive Backstepping with Power Estimation scheme.

R f L f I L

d·E C f V R L I CPL = P/V

Figure 5.48 Averaged converter model with disturbance power.