Line outage distribution factor is determined by [Where ‘l’ corresponds to the line under study, i.e

Question

Line outage distribution factor is determined by [Where ‘l’ corresponds to the line under study, i.e. between the buses ‘n’ and ‘m’ and ‘k’ corresponds to the outage of the line which is connected between buses ‘i’ and ‘j’]

A

dl,k=xkxlxin-xjn+xim+xjmxk-xii+xjj-2 xij

B

dl,k=xkxlxin-xjn-xim+xjmxk-xii+xjj+2 xij

C

dl,k=xkxlxin-xjn-xim+xjmxk-xii+xjj-2 xij

D

Any of above

Examoogle · Accepted Answer

d_{l, k} = \frac{\frac{x_{k}}{x_{l}} [x_{i n} - x_{j n} - x_{i m} + x_{j m}]}{x_{k} - [x_{i i} + x_{j j} - 2 x_{i j}]}

Explanation: The Line Outage Distribution Factor (LODF) is a sensitivity factor used in power system contingency analysis to estimate the change in power flow on a monitored line 'l' due to the outage of another line 'k'. It represents the portion of the power previously flowing through line 'k' that redistributes to line 'l' after the outage, under the DC power flow model assumptions. Working Principle: In DC power flow analysis, the distribution of power depends on the line reactances ($x$). When line 'k' (between buses i and j) is removed, its original flow must follow alternate paths. The LODF ($d_{l,k}$) is calculated using the system reactance matrix (or Z-bus properties), specifically the change in bus voltage angles derived from the reactance values between nodes. The numerator $[x_{in} - x_{jn} - x_{im} + x_{jm}]$ represents the change in relative phase angle across line 'l', and the denominator $[x_k - (x_{ii} + x_{jj} - 2x_{ij})]$ represents the net change in reactance of the network seen by the outage. Key Formulas: $d_{l,k} = \frac{\Delta P_l}{\Delta P_k^0}$ — where $d_{l,k}$ is the shift factor of line $l$ for an outage on $k$; $x_{ij} = X_{ii} + X_{jj} - 2X_{ij}$ — total branch reactance between buses $i$ and $j$ Key Points: LODFs are critical for N-1 contingency analysis in power system operation.; The calculation assumes a linearized DC power flow model where losses are ignored.; The sum of LODFs over all paths is constant, ensuring the conservation of power flow.; It helps identify lines that are likely to become overloaded following a contingency. Advantages: Computationally very efficient for large-scale contingency screening.; Provides immediate insight into power flow redistribution without full AC power flow re-solution. Disadvantages: Inaccurate for systems with high R/X ratios where voltage magnitude changes are significant.; Assumes constant bus voltage magnitudes (1.0 p.u.), which may lead to errors in heavily loaded systems. Applications: Real-time security assessment by Transmission System Operators (TSOs).; Determining Total Transfer Capability (TTC) for electricity markets. Additional Info: The numerator reflects the relative sensitivity of the phase angle difference across line 'l' to a power injection change at buses 'i' and 'j'.. Option C is the standard mathematical expression found in power system literature (e.g., Saadat, 'Power System Analysis'). Answer: C is correct — It represents the accurate mathematical derivation of the LODF based on the DC network reactance matrix components. Exam Tip: Always verify the signs of the reactances in the numerator ($x_{in} - x_{jn} - x_{im} + x_{jm}$) as they correspond to the change in phase angle difference between the terminals of the monitored line.

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