Page 52 - Modern Control of DC-Based Power Systems

Small-Signal Analysis of Cascaded Systems 17

presented in Section 2.4. In particular, a comprehensive small-signal sta-
bility analysis of based on the well-known Nyquist Stability Criterion is
presented. After reviewing the criterion itself and its further extensions,
the focus of Section 2.6 moves to the practical aspects of stability analysis
by using a cascade system example. It is shown through a simulation
example how the interface impedances play a key role on the assessment
of the stability of such a system. Given the fundamental importance of
interface impedances in the stability analysis, the section also presents an
emerging online technique to measure such impedances by using the
existing converters of the cascade system. The technique is called
Wideband System Identification (WSI) and allows measuring impedances
in real time while the system is operating in steady state by using a short-
time small-signal wideband perturbation. The WSI technique is finally
contrasted in a simulation example to the well-known digital analyzer
technique and practical advantages of the WSI are derived.

2.2 CONVERTER MODEL
2.2.1 Single Converter—Open Loop
In order to analyze the stability of MVDC systems, an ideal constant
power assumption is often applied [3]. However, this assumption has lim-
itations when the input characteristic of a load deviates from the CPL
behavior. Furthermore, the assumption of an ideal CPL does not take
into account the influence of the controller design and operating condi-
tions on the system stability. Therefore, it is necessary to establish detailed
models of the power system to fully account for the dynamic behavior
and its influence on stability [4 10].
Nonetheless, until now the interdependency of the control bandwidth
of the load side converter on the control goal of the generation side con-
verter with respect to the control variable (e.g., the voltage of the DC
bus) has not been sufficiently addressed; in effect the ideal CPL assump-
tion in the form of a nonlinear controlled source inherits the time con-
stant of the passive components of the DC link.
In the following sections it will be shown how the practical results of
different converter power levels and loads, switching frequencies, and
control bandwidths yield at a load behavior different from the ideal CPL