Solution of polynomial and transcendental
equations – Bisection method, Newton-Raphson method and Regula-Falsi method. Finite
differences, Relation between operators, Interpolation using Newton’s forward and backward
difference formulae. Interpolation with unequal intervals: Newton’s divided difference and
Numerical Differentiation, Numerical
integration: Trapezoidal rule and Simpson’s 1/3rd and 3/8 rules. Solution of Simultaneous
Linear Algebraic Equations by Gauss’s Elimination, Gauss’s Jordan, Crout’s methods,
Jacobi’s, Gauss-Seidal, and Relaxation method.
Ordinary differential equations: Taylor’s
series, Euler and modified Euler’s methods. RungeKutta method of fourth order for solving
first and second order equations. Milne’s and Adam’s predicator-corrector methods. Partial
differential equations: Finite difference solution two dimensional Laplace equation and
Poission equation, Implicit and explicit methods for one dimensional heat equation
(BenderSchmidt and Crank-Nicholson
methods), Finite difference explicit method for wave equation.
Laplace Transform, Properties of Laplace
Transform, Laplace transform of periodic functions. Finding inverse Laplace transform by
different methods, convolution theorem. Evaluation of integrals by Laplace transform,
solving ODEs by Laplace Transform method, Fourier transforms.
Probability Mass function, Probability
Density Function, Discrete Distribution: Binomial, Poisson’s, Continuous Distribution:
Normal Distribution, Exponential Distribution.
Working principle, e.mf. equation, construction, phasor diagrams, equivalent
circuit, voltage regulation, losses, separation of hysteresis and eddy current losses, efficiency, tests:
open circuit and short circuit, load, Sumpner’s test, Condition for maximum efficiency and
regulation, Power and distribution transformer, allday efficiency, Excitation phenomenon.
Autotransformer: working, advantages, its equivalent circuit and phasor diagram.
Three phase transformer: its construction, groups and connections,
their working and applications; Scottconnection; Parallel operation of Transformers:
application, advantages, requirement and load sharing; Tap changers, cooling, conservator
and breather. Pulse and high frequency transformers.
Working principle, construction, comparison of slip ring
and squirrel cage motors, steady state analysis, phasor diagram and equivalent circuit, power
flow diagram, torque-speed and power-speed characteristics, Losses and efficiency, No load
and block rotor test, circle diagram.
Starting of squirrel cage and slip ring motors, power
factor control, Cogging & Crawling, Double cage &Deep bar Indication Motor,
impact of unbalanced supply and harmonics on performance, speed control, braking,
Induction Generator, Applications.
Single Phase Induction motor; double revolving field
theory, equivalent circuit and its determination, performance calculation, starting methods
and types of single phase Induction motors: their working principle and applications,
comparison with three phases Induction Motor. Single phase A.C. series motor,
Servo motors, Linear Induction Motor.
Digital number systems, base conversion, Binary, Decimal,
octal, Hexadecimal, number system with radix r, Gray codes.Alphanumeric codes – ASCII
code and BCD codes, concept of parity, complementr’s& (r-1)’s, subtraction with
complements, signed Binary numbers, Error Detecting & Correcting codes. Basic Theorems &
Properties of Boolean algebra: AND, OR, NOT operators, laws of Boolean algebra,
Demorgon’s theorem, Boolean expression & logic diagram. Negative logic, Alternate logic
gate representation (concept of bubbled gates) canonical and standard Forms
(Minterms&Maxterms), sum of minterms& product of maxterms, conversion between
canonical forms. Truth table & maps, 2,3,4,5 and 6 variable maps, solving digital problems
using Maps, Don’t care conditions, Tabular minimization. Sum of product & product of sum
reduction, Exclusive OR & Exclusive NOR circuits, Parity generator &checkers.
Design procedure, Adders (half and Full), subtractor (half and full)
code convertors, Analysis of design, Universal building blocks, Implementation of any logic
circuit with only NAND gates or with only NOR gates, Binary serial adder, parallel adder,
serial/parallel adder, look ahead carry generator, BCD adder, Binary multiplier, Magnitude
comparator, Decoder, Demultiplexer, Encoders, priority encoder, Multiplexers &
implementation of combinational logic diagram.
Latches, SR latch with NAND & NOR gates, D latch, edge
triggered flip flop, J-K flip flop, T flip flop, Master slave flip flop, Analysis of clocked
sequential circuit, state table, state diagram, state reduction state equations, state assignments,
flip flop excitation table & characteristic equations, Design procedure for sequential circuits,
Design with state reduction, Applications of flipflop.
Asynchronous and Synchronous counter, counters with MOD
numbers, Down counter, UP/DOWN counter, propagation delay in ripple counter,
programmable counter, Pre- settable counter, BCD counter, cascading, counter applications,
Decoding in counter, Decoding glitches, Ring Counter, Johnson counter, Rotate left & Rotate
right counter, Registers – Buffer, Shift left, shift right, shift left/Right registers, parallel in
parallel out, serial in serial out, parallel in serial out, serial in parallel out registers.
Random Access Memory, Timing waveform, Memory Decoding, Internal Construction,
Coincident decoding, Addressmultiplexing, Read only memory – Combinational circuit
implementation, Type of ROMs, combinational PLDs, Programmable Logic Array (PLA),
Programmable Array Logic (PAL), sequential programmable device. Analog todigital
conversion – Ramp type, dual slope, integration, successive approximation, parallel conversion,
parallel/ serial conversion, convertor specifications, Digital to Analog convertors – Binary
weighted & R/2R D to A convertors.
An overview of Electrical Energy Generation General background, structure and components of
power network. Power generation – Introduction to conventional, non-conventional & distributed
generation, Effect of transmission voltage on power system economy. Selection of size of feeder.
Comparison of isolated versus interconnected power system. Problems associated with modern
large interconnected power system. Power Plant Economics - Load curves, base load, peak load,
load factor, demand factor, diversity factor, capacity factor, utilization factor, cost of electricity,
capital cost, fuel and operation cost.
Inductance resistance and capacitance of transmission line, Calculation of inductance for 1-Φ
and 3- Φ, Single and double circuit line, Concept of GMR and GMD, Symmetrical &
asymmetrical conduction configuration, Calculation of capacitance for 2 wire and 3 wire
systems, Effect of ground or capacitance, Capacitance calculation for symmetrical and
asymmetrical 1-phase and three phase, Single and double circuit line, Charging current,
Transposition of line, Composite conductor, Skin and proximity effect, bundle conductor.
Underground Cable Comparison of cables and overhead transmission lines, Classification of
cables, requirement of cable construction, capacitance of single and multi-core cable, economic
core diameter, dielectric stress in cable, Grading of cables, ionization of Heating of cables,
Phenomena of dielectric losses and sheath loss in cables, Thermal resistance of cables
Various systems of transmission, effect of system voltage, comparison of conductor materials
required for various overhead systems. Short, Medium & long transmission line and their
representation, Nominal T, Nominal Л, Equivalent T and equivalent Л, network models, ABCD
constants for symmetrical &asymmetrical network, Mathematical solution to estimate regulation
& efficiency of all types of lines. Surge Impedance, loading, Interpretation of long line equation
and its equivalent equation. Tuned power lines. Power flow through transmission line, Circle
diagram, Method of voltage control, Static & rotating VAR generator, transformer control.
Insulator & Mechanical design, types of conductors used in overhead transmission line, Types of
line supports and towers, Distribution of conductors over transmission towers, Spacing between
conductors, Length of span and sag tension calculation for transmission line, Wind & ice
loading, support of line at two different levels, string chart, Sag template, Stringing of conductor,
Vibration and Vibration dampers. Insulator Materials used for transmission line insulations,
Types of insulator for overhead transmission line failure of insulator, Voltage distribution of
suspension insulator, String efficiency, Shielding and grading.
AC single phase, 3 phase, 3wire & 4 wire distribution, Kelvin’s law for most economical size of
conductor Substation layout showing substation equipment, bus bar single bus bar and
sectionalized bus bar, main and transfer for bus bar system, sectionalized double bus bar system,
Modeling of dynamic systems: Electrical, Mechanical and hydraulic systems, Concept of transfer
function, Laplace Transform, State space description of dynamic systems: Open and closed loop
systems, Signal flow graph, Mason’s formula, Components of control systems: Error detectors
(Synchros& Potentiometer), Servomotors (AC & DC), tacho-generators, power amplifier,
Time – domain analysis of closed loop systems: Test signals, time response of first and second
order systems, Time domain performance specifications, Steady state error & error constants
Feedback control actions: Proportional, derivative and integral control.
Stability: Routh-Hurwitz stability analysis Characteristics equation of closed loop system root
loci, construction of loci, Effect of adding, poles and Zeros on the loci, Stability by root loci.
Frequency, Domain analysis, Bode plots, Effect of adding, poles and Zeros, Polar plot, Nyquist
stability analysis, Relative stability: Gain and phase margins.
Design of control systems with PD/PI/PID Control in time domain and Frequency domain, leadlag, Lag-lead compensation,
Design of compensating networks. Solution of state equation:
Eigen values & eigenvectors digitalization state transitive matrix.