Page 39 - Modern Control of DC-Based Power Systems

4 Modern Control of DC-Based Power Systems

8
R CPL ,2 r
<
L
R CPL ,2 (1.6)
: rC
Replacing R CPL by this inequality the relationship (1.7) is obtained,
which gives the local stability condition for the system.
rC 2 V
2
P , min V ; 0 (1.7)
0
L r
2
The relation P , V =r is less restrictive than the relationship
0
2
P , V =4r which ensures the existence of an operating point for the sys-
0
tem while relation (1.8) gives the stability condition of the system operat-
ing points.
8
R CPL ,2 r
<
L
R CPL ,2 (1.8)
rC
:
It is seen from Eq. (1.8) that a relationship between the stability of sys-
tem, the sizing of the filter (r, L, C, and indirectly E) and the power con-
sumed by the load can be expressed. It is seen that as the capacity of the
inverter increases the system becomes more stable and vice versa for the
inductance of the filter. In addition, these observations show that the neg-
ative resistance is used to excite the system because it “generates” reverse
current changes which are triggered by voltage changes. So, the more
power is consumed the more its conductivity increases until it compen-
sates the overall damping of the system and becomes unstable.
The two possible assumptions regarding how to deal with a CPL—lin-
earized around an operating point or assuming its nonlinear characteris-
tic—will lead to two approaches for assessing the stability.

1.2 COMPENSATING CPLS BY PASSIVE COMPONENTS

In order to increase the stability in a passive way for the system
depicted previously in Fig. 1.1, a filter can be added to the system. This
will increase the damping of the DC bus and thus increase its stability.
This setup was proposed by the authors in [15], where the authors