Page 162 - Modern Control of DC-Based Power Systems

126 Modern Control of DC-Based Power Systems

Three conditions have to be fulfilled by the manifold [15]:
• Reachability of the manifold;
• A control that keeps the system on the manifold;
• Stability of the system has to be guaranteed while being on the
manifold.
To guarantee stability a locus of steady-state operating points has to be
identified. In the case of power converters this characterizes a curve
gxðÞ 5 0 in the state plane which is characterized by the duty cycle d.
Afterwards a function F has to be identified whose directional derivative
along its trajectories corresponds to (5.43), where b 5 const.

dF @F
5 (5.43)
dt @x _ x 5 bg xðÞ
After the synergetic control design is completed an analytical control law
is the result which ensures stable motion to the equilibrium point of the
closed-loop system. The trajectory depends on the structure of the manifold.
Subsequently the stability conditions on the manifold have to be analyzed.
The fact that synergetic control uses a model of the system for control
synthesis can be considered both an advantage and a disadvantage. It
appears desirable that the control uses all available information on the sys-
tem for control purposes, but on the other hand it makes the control
more sensitive to model and parameter errors [17].

5.2.2 Application to MVDC System
The Synergetic control is a centralized nonlinear control architecture
which includes a model of the controlled system. In contrast to linear
control, synergetic control is capable of handling system nonlinear
dynamics and ensuring global system stability [15], while systems consist-
ing of parallel-connected power converters under linear control may not
show proper behavior and may lead to system collapse [24].
In this chapter the synergetic control is applied to the MVDC System.
The overall procedure can be summarized as following (Fig. 5.7):
1. Derivation of state-space model and state variable definition;
2. Definition of macrovariable as function of state variables;
3. Calculation of control law.
Fig. 5.8 shows a system with parallel-connected converters. This sys-
tem is under several assumptions: The system operates in continuous con-
duction mode (CCM). The switching occurs at a high-frequency (1 kHz)
relative to the filter dynamics. The parasitic effects are ignored. The state
variables are the voltage over the capacitor v and the inductor currents i Li