Page 212 - Modern Control of DC-Based Power Systems

176 Modern Control of DC-Based Power Systems

Figure 5.46 ISPS I L15L25L3 virtual distribution BS for ideal CPL and 30.9 - 53.4 MW.

no longer linear as it was when using the steady-state Kalman filter but it
is nonlinear through the CPL characteristic. In a nutshell the procedure is
the application of the normal Backstepping algorithm and introducing an
estimate with its corresponding estimation error, to formulate it, in an
adaptive algorithm that is able to track the unknown time-varying load
power changes. The theoretic foundation for a decentralized adaptive
control algorithm with unmodeled dynamics was presented in [63].
In Section 5.6.1 the procedure of Adaptive Backstepping is explained.
The reader who is familiar with those theoretical concepts will find in
Section 5.6.2 the application of the Adaptive Backstepping theory on the
ISPS circuit.

5.6.1 Procedure Adaptive Backstepping

At this point, a new dynamic controller design is introduced. The advan-
tage of this approach is that the steady-state error resulting from uncer-
tainties is avoided. This can be achieved by adaptively changing the
uncertain parameters in the controller as described in [51]. The same
example as in Section 5.5.2 is used which is based on [6,61,64].
In (5.147), it is assumed that the model was completely known. This
is of course not always the case. This time, a model of the form (5.172) is
examined, which is given in strict feedback form. For strict feedback
form it is important that nonlinearities f i and h i of the derivative of state
x i are only dependent on the previous states which are fed back.