Admittance space stability analysis of power electronic systems

Power electronics based power distribution systems (PEDSs) can offer excellent load regulation, transient performance, and, with proper architecture, a high degree of fault tolerance. They are excellent candidates in power distribution systems that need to be fullyor semi-autonomous. Typical applications include ships [1], submarines [1], aircraft [2, 3], and spacecraft [4]. Unfortunately, PEDSs also have disadvantages, one of which is the potential for negative impedance instability [5]. This type of instability is brought about by the nearly ideal regulation capability of modern power converters. As an example, consider a dc/dc converter whose input is connected to a power distribution bus and whose output supplies a load. It is relatively easy to design a power converter in which the output is controlled so well that the load is essentially unaffected by perturbations at the input of the power converter. As a result, the power going into this converter is constant with respect to the input voltage (at least for perturbations within a certain range). In a small signal sense, it can be readily shown that this constant power load appears as a negative resistance–an intuitively destabilizing effect. As a result, the stability analysis of PEDSs is a more critical task than in conventional power distribution systems. Most stability analysis of PEDSs is based on impedance/admittance methods. These are based on the fact that small signal stability at a given operating point can be determined by examining the Nyquist contour of the product of the source impedance (Zs) and the load admittance (Yl) in a single bus dc system. The most straightforward of the impedance/admittance methods is the Middlebrook criterion [5] which states that such a system will be stable provided that the Nyquist contour of ZsYl remains within the unit circle. The key feature of this method is that it is very design oriented. For example, given the source impedance it is easy to set forth a bound on the load admittance that will ensure that the system is stable in a small signal sense. This is very important in view of the fact that most PEDSs are developed not by one company or corporation, but instead by several corporations (typically a system integrator with multiple subcontractors or vendors). The primary disadvantage of the Middlebrook criterion is that it leads to artificially conservative designs. In particular, much of the region in the Nyquist plane which is forbidden when using this criterion actually has little influence on stability. This leads to control loops which are slower than they need to be, bus capacitance which is higher than it needs to be, or the use of dampers (active or passive) for the sake of fitting the mathematical formulation rather