(SEM VI) THEORY EXAMINATION 2017-18 POWER SYSTEM ANALYSIS

Power System Analysis (NEE-601)

Complete Section-Wise Explanation – B.Tech Semester VI

Introduction to the Subject

Power System Analysis is a core electrical engineering subject that deals with the modeling, analysis, and performance evaluation of electrical power systems. It helps engineers understand how power flows from generating stations to consumers, how systems behave under normal and abnormal conditions, and how stability and protection are ensured.

This subject mainly focuses on:                        Single-line and per-unit representation

Load flow (power flow) analysis                        Fault analysis using symmetrical components

Power system stability                                       Transmission line behavior and surge phenomena

The question paper is divided into three sections: A, B, and C, all of which must be attempted as instructed.

SECTION A – Short Answer Questions

(2 × 10 = 20 marks)
 

Section A tests your basic conceptual clarity. Answers should be short, precise, and technically correct.

Explanation of Section A Questions

A single line diagram represents a complete three-phase power system using a single line. It shows generators, transformers, transmission lines, circuit breakers, feeders, and loads from generation to utilization level, making system analysis simple and clear.

An impedance diagram represents the resistance and reactance of all system components, whereas a reactance diagram neglects resistance and shows only reactances, mainly used for fault and stability studies.

Sub-transient reactance is the effective reactance of a synchronous machine immediately after a fault occurs. During this period, fault current is very high due to damper winding effects.

Feeder reactors are inductive devices connected in series with feeders to limit short-circuit currents and protect equipment like circuit breakers.

Matrix partitioning in load flow separates known and unknown variables to simplify numerical calculations in methods such as Newton-Raphson and fast decoupled load flow.

A load bus (PQ bus) has specified real and reactive power, a generator bus (PV bus) has specified real power and voltage magnitude, and a slack bus maintains power balance and provides reference angle.

Steady-state stability can be improved by increasing excitation, reducing line reactance, using series compensation, and installing FACTS devices.

A swing curve shows the variation of rotor angle with time after a disturbance and is used to assess transient stability.

Characteristic impedance loading (CIL) or surge impedance loading (SIL) is the power transmitted when reactive power generated equals reactive power absorbed by the line.

The CIL of a 200 kV transmission line is calculated using standard SIL relations based on surge impedance.

SECTION B – Analytical & Numerical Questions

(Attempt any three, 10 × 3 = 30 marks)

Section B focuses on numerical problems, derivations, and analytical understanding.

Per-Unit Reactance Diagram

Using the data given in the figure (page 1), all generator, transformer, and line reactances are converted to a common MVA base. A per-unit reactance diagram is then drawn, simplifying system modeling and fault analysis.

Switching Operation in Series R-L Circuit

When a switch is opened or closed in an R-L circuit, current does not change instantaneously due to inductance. The current follows an exponential rise or decay governed by the time constant L/R.

Formation of Y-Bus Matrix

Using the given line series and shunt impedances (page 2), the bus admittance matrix [YBus] is formed. Diagonal elements represent self-admittances, while off-diagonal elements represent mutual admittances between buses.

Swing Equation Derivation

The swing equation is derived by equating accelerating power to the rate of change of angular momentum. It relates rotor angle dynamics to mechanical and electrical power and is fundamental in stability studies.

Wave Equation for Lossless Transmission Line

By applying KVL and KCL to an elemental length of a lossless line, voltage and current wave equations are derived, showing that electromagnetic waves propagate along the line with constant velocity.

SECTION C – Long Answer & Advanced Topics

(5 × 10 = 50 marks)

Section C carries the highest weightage and requires structured, in-depth answers.

Question 3 – Symmetrical Components

When one conductor of a three-phase line is open (page 3), the system becomes unbalanced. Using Fortescue’s theorem, line currents are resolved into positive, negative, and zero sequence components.

Alternatively, sequence impedances of generators, loads, and transmission lines are explained. Balanced star-connected loads and their sequence networks are also discussed.

Question 4 – Z-Bus & Fault Analysis

The Z-Bus matrix is developed step by step for the given network (page 2).
For a single line-to-ground (LG) fault, the fault current equation is derived by connecting positive, negative, and zero sequence networks in series, and an equivalent network diagram is drawn.

Question 5 – Load Flow Analysis

The Newton-Raphson method for load flow is explained when all buses are PQ buses, covering mismatch equations and Jacobian matrix formulation.

The fast decoupled load flow method simplifies calculations by decoupling real and reactive power equations, making it faster for large systems.

Question 6 – Stability Analysis

It is shown mathematically that maximum power transfer occurs when transmission line resistance is negligible compared to reactance.

The equal-area criterion is explained for an alternator connected to an infinite bus, using power-angle curves to assess transient stability.

Question 7 – Transmission Line Transients

Reflection and transmission coefficients are derived for a transmission line terminated by a resistance.

Bewley’s lattice diagram (page 3) is explained as a graphical tool to analyze multiple reflections of surge waves. Surge phenomena and protection methods such as surge arresters and shielding are discussed