(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 deals with the study of generation, transmission, distribution, and utilization of electrical power, along with mathematical tools used to analyze system performance under normal and fault conditions. This subject is extremely important for electrical engineers because it helps in planning, operation, stability assessment, and protection of power systems.

The subject mainly covers:

Single line diagrams and per-unit system                      Load flow (power flow) analysis

Fault analysis using symmetrical components               Power system stability

Transmission line performance and surge phenomena

The question paper is divided into three sections: A, B, and C, and students must attempt all sections as per instructions.

SECTION A – Basic Concepts & Definitions

(2 × 10 = 20 marks)

Section A tests your fundamental understanding. Answers must be short, clear, and conceptually correct.

A single line diagram represents a three-phase power system using a single line, showing generators, transformers, transmission lines, circuit breakers, and loads from generation to utilization level.

An impedance diagram shows resistance, reactance, and impedance of system elements, while a reactance diagram neglects resistance and focuses only on reactance for fault and stability studies.

Sub-transient reactance is the reactance of a synchronous machine during the first few cycles after a fault, when current is very high due to damper windings.

Feeder reactors are inductive devices installed in feeders to limit short-circuit currents and protect equipment.

Matrix partitioning in load flow separates bus variables to simplify numerical solutions, especially in Newton-Raphson and fast decoupled methods.

A load bus (PQ bus) has specified active and reactive power, a generator bus (PV bus) has specified power and voltage magnitude, and a slack bus balances system power and sets reference angle.

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

A swing curve shows variation of rotor angle with time during transient conditions and is used in stability analysis.

Characteristic impedance loading (CIL) or surge impedance loading (SIL) is the power transmitted when line reactance equals line capacitance effect, resulting in no reactive power flow.

The CIL of a 200 kV transmission line is calculated using standard SIL formula, assuming typical surge impedance.

 SECTION B – Analytical & Numerical Problems

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

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

Per Unit Reactance Diagram

You are required to convert all given machine, transformer, and line reactances to a common MVA base, then draw the per-unit reactance diagram. This simplifies system analysis and fault calculations.

Switching Operation in Series R-L Circuit

This question explains transient current behavior when a switch is opened or closed. Due to inductance, current does not change instantly, leading to exponential rise or decay governed by time constant L/R.

Formation of Y-Bus Matrix

Using given line impedances and shunt admittances, the bus admittance matrix (Y-Bus) is formed. Diagonal elements represent self-admittances, while off-diagonal elements represent mutual admittances between buses.

Swing Equation Derivation

The swing equation relates rotor angle acceleration to the difference between mechanical input power and electrical output power. It forms the basis of transient stability analysis.

Wave Equations for Lossless Transmission Line

By applying KVL and KCL to a differential line section, voltage and current wave equations are derived, showing that waves propagate along the line with constant velocity.

SECTION C – Advanced Power System Analysis

(5 questions × 10 marks = 50 marks)

This section has the highest weightage and tests deep conceptual understanding.

Question 3 – Symmetrical Components

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

Alternatively, sequence impedances of generators, loads, and transmission lines are explained, along with balanced star-connected loads and their sequence networks.

Question 4 – Z-Bus & Fault Analysis

Z-Bus Formation

The bus impedance matrix (Z-Bus) is developed step-by-step using building algorithms. It is used extensively in fault studies.

Single Line-to-Ground (LG) Fault

The relationship for LG fault current is derived using interconnection of positive, negative, and zero 
sequence networks in series. An equivalent network diagram is drawn.

Question 5 – Load Flow Analysis

Newton-Raphson Method

This explains iterative solution of nonlinear load flow equations using Jacobian matrix when all buses are PQ buses. It is accurate and widely used for large systems.

Fast Decoupled Load Flow

This method simplifies NR equations by decoupling real and reactive power, resulting in faster computation with acceptable accuracy.

Question 6 – Stability Analysis

Maximum Power Transfer

It is shown mathematically that maximum power is transmitted when transmission line reactance dominates resistance, and power angle is 90°.

Equal Area Criterion

This graphical method determines transient stability by comparing accelerating and decelerating areas on power-angle curve for an alternator connected to infinite bus.

Question 7 – Transmission Line Transients

Reflection & Transmission Coefficients

When a transmission line is terminated by a resistance, part of the incident wave is reflected. Coefficients are derived using impedance matching principles.

Bewley’s Lattice Diagram

This diagram graphically represents multiple reflections of surge waves on transmission lines. Surge phenomena and protection methods like surge arresters and shielding are explained.