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Time To Intibility Index : Time-To-Instability Index Of A Series Component

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Figure 4.1 sinφ_ij vs. φ_ij,shows the angles ├ φ_ij ┤|_(max+), ├ φ_ij ┤|_(max-)and ├ φ_ij ┤|_UEP. Time-to-Instability Index (TII) Time-to-Instability Index of a series component provides a measure of time-vicinity to the instability region of this component by measuring the time based on the rate of change of the phase angle, (dφ_ij)/dt. The index does not provide real-time to instability as the speeds, (dφ_ij)/dt, vary during the system dynamics but it can be used as an assessment measure to rank the critical series components. A smaller TII value of a series component means that it is more critical than others with larger TII. It must be noticed that a negative TII value indicates that the corresponding phase angle has already passed the …show more content…

Moreover, when speed decreases during a disturbance, TII of the critical series components increases and does not provide accurate stability assessment. To overcome this issue, the local minimums of the TII are considered. When the present value of TII is lower than the previous local minimum value, it would replace the local minimum value. It means that the critical series component keeps its critical status until its next local minimum. When its local minimum increases, it means more stable case. To clarify this matter, TII and modified TII of transformer 11-32, the most critical series component, for previous fault are shown in Figure 4.4. Figure 4.4 shows that the system is first-swing stable as the modified TII increases with time. First-swing Stability Assessment After a large disturbance, direct methods assess the system stability by comparing the total system energy to the maximum potential energy or the system critical energy. Similar to direct methods, the proposed method considers the system is first-swing unstable if the energy of at least one of the series components passes its maximum allowable value during the first-swing, i.e., phase angles constantly increase and passes UEP, ├ φ_ij ┤|_UEP in Figure 4.1, otherwise, the system is first-swing stable. However, the proposed method exhibits the following advantages over direct methods: The proposed

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