Static Voltage Stability Analysis of Distribution Systems Based on Network-Load Admittance Ratio

It is well known that a single (constant power) load infinite-bus system reaches a static voltage stability limit point, or equivalently, a singularity point of the power flow Jacobian, at the unity line-load admittance ratio, i.e., the equivalent admittance of the load has the same modulus as the transmission line admittance. In this paper, we rigorously extend this result to generic distribution systems with distributed generators (DGs). We introduce a new concept called the network-load admittance ratio that is in terms of the parameters of power network, loads, and DGs. This concept is a generalization of the line-load admittance ratio that characterizes the loading status of a distribution system with the effects of DGs included. We prove that the power flow Jacobian is singular if and only if the network-load admittance ratio is unity, which provides new insights into the mechanism of voltage stability. In addition, we establish a new voltage stability index by using the network-load admittance ratio. Numerical simulations on several IEEE test systems show that the index has good linearity with load increase and estimates voltage stability margin with high precision. The index also reflects the impact of DG penetration level and control mode on voltage stability. The obtained results can be extended to ZIP load models, unbalanced three-phase networks, and mesh networks with slight modifications.