Concept:
This question is based on matching important concepts of power systems with their corresponding applications or methods.
Each topic has a standard associated method or characteristic:
• Load flow analysis uses numerical iterative methods,
• Stability studies use equal area criterion,
• Economic dispatch uses B-coefficients,
• Synchronous machines exhibit V-curves.
Step 1: Matching Load Flow Analysis.
Load flow analysis determines:
• bus voltages,
• power flows,
• line losses,
• reactive power distribution.
One commonly used numerical method is:
\[
\text{Gauss-Seidel Method}
\]
Hence:
\[
A \rightarrow III
\]
Step 2: Matching Stability Studies.
Power system stability studies determine whether the system remains synchronized after disturbance.
A famous technique used is:
\[
\text{Equal Area Criterion}
\]
It compares:
• accelerating area,
• decelerating area.
Therefore:
\[
B \rightarrow IV
\]
Step 3: Matching Economic Load Dispatch.
Economic load dispatch allocates generation economically among generators.
Transmission losses are represented using:
\[
\text{B-coefficients}
\]
Hence:
\[
C \rightarrow II
\]
Step 4: Matching Synchronous Machine.
A synchronous machine shows:
\[
\text{V-curves}
\]
These curves represent relation between:
• armature current,
• field current.
Thus:
\[
D \rightarrow I
\]
Step 5: Writing the complete matching.
Therefore:
\[
A-III,\quad B-IV,\quad C-II,\quad D-I
\]
Step 6: Selecting the correct option.
Hence correct option is:
\[
\boxed{(2)}
\]