GATE EE 2015 Set 1 — Question 52

Examining the assertionIn the fast decoupled load flow (FDLF) method the approximations are made only while building the Jacobian: the $P$-$\delta$ and $Q$-$V$ sub-problems are decoupled and the constant matrices $B'$ and $B''$ are formed by assuming $\cos\delta_{ij} \approx 1$, $G_{ij}\sin\delta_{ij} \ll B_{ij}$ and $Q_i \ll B_{ii}V_i^2$.The mismatch equations that are actually driven to zero,$$\Delta P_i = P_i^{sch} - P_i^{calc}, \qquad \Delta Q_i = Q_i^{sch} - Q_i^{calc},$$are the exact power-flow equations. An approximate Jacobian only changes the search direction, i.e. the number of iterations needed, not the point the iteration converges to. Hence the converged FDLF solution is not an approximate solution, and the assertion is false.Examining the reasonThe iteration is stopped when every element of the power mismatch vector falls below a prescribed tolerance $\varepsilon$. How close the final bus voltages and angles are to the true solution is therefore decided by that tolerance - a tighter $\varepsilon$ gives a more accurate answer. The reason is a true statement (and it is in fact the statement that explains why the FDLF result is as accurate as one wants it to be).Conclusion[a] is false and [r] is true, so option (D) is the correct choice. Options (A) and (B) are ruled out because they require [a] to be true, and (C) is ruled out because [r] is true.Answer: (D) [a] is false and [r] is true.