Static Voltage Collapse Proximity Indicator. The Line Flow index and bus voltage profiles of the load buses are expressed in fuzzy set notation. Further, they are evaluated using fuzzy rules to compute Criticality Index. Critical buses are ranked based on decreasing order of Criticality Index. The proposed approach is tested on Five Bus Test System. 

## 2 Formulation Of Line Flow Index

Consider a typical transmission line of an interconnected power system shown in Fig.1. Optimal impedance concept used in [9] to develop a simple criterion for voltage stability is as follows; Load impedance ZL∟θ fed by constant voltage source Vs with internal impedance ZS∟ Φ as shown in Fig.2. Application of maximum power transfer theorem to the equivalent circuit shown in Fig.2 results in ZL/ ZS = 1 for maximum power to be flown to the load from the source. ZL/ZS is used as the VCPI Voltage Collapse Proximity Indicator. The system is considered to be voltage stable if this ratio is less than 1, other- wise voltage collapse occurs in the system. 

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![0_image_1.png](0_image_1.png)

The single line model shown in [9] is used, but the system is represented by the admittance model. It is assumed that the load at the bus is total power flow in the represented line. Equivalent admittance model is shown in Fig. 3 where YL∟θ is the line admittance and the YR∟ Φ is the load admittance and 

## Φ = Tan-1[ Qr / Pr]

The indicator is developed with an assumption that only the modulus of the load admittance changes with the change in the system load i.e. it is assumed that always efforts will be made in the system to maintain the constant power factor for the changes in the bus load. Increase in load results in increase in 