Power System Voltage Stability

Voltage collapse has been recognized as a series threat in power system stability and operation. Fast and accurate indications and allocations of voltage stability in power systems are a challenging task to accomplish. Voltage violations and undesirable line outages might be inevitable when power systems operated close to its transmission capacity limits. Unexpected load increases or insufficient reactive power supply may contribute to partial or total voltage collapse threatening system security. The ability to draw a clear and complete picture of system voltage stability with accurate indications and precise voltage collapse allocations allow operators to take the necessary action to prevent such incidents. A successful avoidance of such system collapse is based on method’s accuracy, speed of indication, and very low computation time.

This paper presents a new approach of studying voltage stability in power systems at which voltage stability in transmission lines and system buses are carefully analysed based on their V-Q and V-P relationships. Four indices are proposed; two for voltage stability analysis at system buses designated as VPIbus and VQIbus studying the dynamics of loads and generators while VPILine and VQILine are for line voltage stability analysis studying transmission lines stress and outages. Voltage collapse is precisely predicted by the proposed indices for the system as a whole and for every bus and line. These developed indices are simple, fast, and accurate proving a clear and complete picture of power flow dynamics indicating maximum active and reactive power transfers through transmission systems. The proposed approach was demonstrated on the IEEE 14-bus and 118-bus systems and compared with existing methods to show its effectiveness and efficiency. 


Voltage stability is well-defined and classified in [10] while addressing an appropriate analysis for voltage stability phenomena among engineering and researches are still debatable. Voltage stability has been studied using two main approaches: static and dynamic analysis, where voltage instability as fact is considered as dynamic phenomenon. Although the dynamic analysis is preferable by most utilities, the static voltage stability approach is commonly used in research and on-line applications providing an insight into stability problems with high speed analysis.    

Several methods have been used for static voltage stability analysis to measure voltage stability proximity estimating the point of voltage collapse. A number of methods proposed in the literature use the singularity of power flow Jacobian matrix as base, sing or indicator of voltage collapse. Several methods are developed using eigenvalue or Jacobian matrix singularity monitoring the smallest eigenvalue[11-14], are based on a reducing Jacobian determinants[15, 16], identifying the critical buses using a tangent vector [17], or computing eigenvalues and eigenvectors of a reduced Jacobian matrix as introduced in[11, 18] and named as modal analysis. Other methods took another approach determining maximum loadability at line [19-23] while others are specifying system stability margins at bus attempting to determine the weaken bus [24-27].

Recently, voltage collapse prediction index (VCPI) has been introduced in [28] to evaluate voltage stability and predict voltage collapse while an improved voltage stability index designated as Lij has been described in [29] taken into account the influence of the load model.   

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  • Rajdeep Janorkar

    Power System Voltage Stability 5 months ago