Topics in matrix theory: Elementary canonical forms: digitalisation, triangulation, primary and secondary decompositions, Jordan canonical forms and applications. Introduction to optimization theory: The optimization problem and illustrative examples; necessary and sufficient conditions for optima; convex sets, convex functions, optima of convex functions; constrained minimization- linear and non-linear constraints, equality and inequality constraints, optimality conditions, Karush Kuhn Tucker optimality conditions; unconstrained optimization- steepest descent, Newton and quasi Newton methods, conjugate direction methods. Calculus of variation- The method of variations in problems with fixed boundaries, Variation of a functional, Euler’s equation, functionals involving derivatives of higher order, optimal control as a problem of variational calculus.

**Texts/References**
1. K. Hoffman and R. Kunz, Linear Algebra, Prentice Hall India, 2001.

2. J.Luenberger D.G. Introduction to Linear and Nonlinear Programming, 2/e, Addison Wesley, 1984.

3. J. L. Troutman, Variational Calculus and Optimal Control: Optimization with Elementary Convexity, 2/e, Springer Verlag, 1996.

** Advanced Control Systems ** |
** EC - 351** |
** 3-0-0-6** |

Frequency response design: Design of lag, lead, lag-lead and PID controllers, the Nyquist criterion, analysis and design, relative stability and the Bode diagram, closed-loop response, sensitivity, time delays; Root locus design: construction of root loci, phase-lead and phase-lag design, PID controller design; Modern design: controllability and observability, state feedback with integral control, reduced order observer; Optimal control design: Solution-time criterion, Control-area criterion, Performance indices, Zero steady state step error systems; Modern control performance index: Quadratic performance index, Ricatti equation; Digital controllers: Use of z-transform for closed loop transient response, stability analysis using bilinear transform and Jury method, deadbeat control, Digital control design using state feedback; On-line identification and control: On-line estimation of model and controller parameters.

**Texts/References**
1. G. F. Franklin, J. D. Powel and A. E. Emami-Naeini: Feedback Control of Dynamic Systems, Prentice Hall Inc. 2002.

2. M. Gopal: Control Systems, 3/e, Tata McGraw Hill, 2008.

3. M. Gopal: Digital Control and State Variable Methods, Tata McGraw Hill, 2003.

4. K. J. Astrom and T. Hagglund: Advanced PID Control, ISA, Research Triangle Park, NC 27709, 2005.

**Electrical Power Systems** |
**EC - 380** |
** 3-0-0-6** |

Generation of electrical energy: Basic structure of power system; demand of electrical system – base load, peak load; controlling power balance between generator and load, advantages of interconnected system; Thermal power plant – general layout, turbines, alternators, excitation system, governing system, efficiency; Hydel power plant – typical layout, turbines, alternators; Nuclear power plant – principle of energy conversion, types of nuclear reactors; brief overview of renewable energy sources. Transmission of electrical energy: Evaluation of Transmission line parameters- types of conductors, representation of transmission line, inductance calculation of single/three phase lines, concept of GMD and GMR, transposition of lines, bundled conductors, skin effect, proximity effect, capacitance calculation of single/three phase lines, effect of earth on calculation of capacitance, line resistance, line conductance; Analysis of transmission lines – representation, short/medium/long transmission lines, nominal T/π network, ABCD parameters, surge impedance, Ferranti effect, power flow through a transmission line, reactive power compensation of transmission line; corona loss; Insulators for overhead transmission lines – types of insulators, string efficiency, methods to improve string efficiency; Insulated cables – insulating material, grading of cables, capacitance of single/three core cable, dielectric loss; methods of grounding; Transient analysis – travelling waves, reflection and refraction, lattice diagram; mechanical design of transmission line. Distribution of Electrical Energy: D.C and A.C. distribution, radial and ring main distribution, medium voltage distribution network, low voltage distribution network, single line diagram, substation layout, substation equipments.

**Texts**
1. L. M. Faulkenberry and Walter Coffer, Electrical Power Distribution and Transmission, 2/e, Pearson Education Inc., 2007.

2. S. N. Singh: Electric Power Generation, Transmission and Distribution, Prentice-Hall, 2007.

**References**
1. J. D. Glover, M. S. Sarma and T. J. Overbye, Power System Analysis and Design, 4/e, Thomson Learning Inc., 2007.

2. James Green and R. Wolson, Control and Automation of Electric Power Distribution System, Taylor and Francis, 2006.

3. B. Sorensen, Renewable Energy, Academic Press, 2/e, 2000.

4. Tarun Gonen, Electric Power Distribution System, McGraw-Hill, 1986.

5. W. D. Stevenson, Elements of Power System Analysis, McGraw-Hill, 4/e, 1982.

6. D. P. Kothari and I. J. Nagrath, Modern Power System Analysis, McGraw-Hill, 2006.

** Electrical Power System Operation and Controls ** |
** EC - 480** |
** 3-0-0-6** |

Power system analysis: modeling of power system components - integrated operation of power systems, load flow studies, economic load dispatch, load frequency control, automatic generation control (AGC), power system stability; Power system protection: Symmetrical components, fault analysis, switchgear, fuses, circuit breakers and relays. Economics of power supply systems: Economic choice of conductor size and voltage level, maximum demand and diversity factor, tariffs, power factor correction; Introduction to high voltage DC transmission (HVDC), flexible AC transmission system (FACTS), supervisory control and data acquisition (SCADA).

**Texts**
1. D. P. Kothari and I. J. Nagrath, Modern Power System Analysis, McGraw-Hill, 2006.

2. P. Kundur, Power System Stability and Control, McGraw-Hill, 1995.

**References**
1. Narain G. Hingorani and Laszlo Gyugyi, Understanding FACTS, Wiley-IEEE Press, 1999.

2. Jos Arrillaga, High voltage direct current transmission, IEE Power Engineering Series, 2/e, 1998.

3. A. J. Wood and B. F. Wollenberg, Power Generation Operation and Control, John Wiley and Sons, 2/e, 1996.

4. A. Wright and C. Christopoulos, Electrical Power system protection, Chapman & Hall, 1993.

**Power Electronics and Drives** |
**EC - 481** |
** 3-0-0-6** |

Power Semiconductor Devices: Diode, BJT, MOSFET, SCR, Triac, GTO, IGBT, MCT and their V-I characteristics, ratings, driver circuits, protection and cooling; AC-DC Converters (Rectifiers): Diode rectifier, thyristor based rectifier, effect of source inductance, single/three phase rectifiers, semi/full rectifiers, power factor, harmonics; DC-AC Converters (Inverters): Concept of switched mode inverters, PWM switching, voltage and frequency control of single/ three phase inverters, harmonics reduction, other switching schemes - square wave pulse switching, programmed harmonic elimination switching, current regulated modulation switching - tolerance band control, fixed frequency control; voltage source inverter (VSI), current source inverter (CSI); DC-DC Converters (Chopper): Principle; buck, boost and buck-boost converters; AC Voltage Controllers: Principle of ON-OFF control and phase control, single/three phase controllers, PWM AC voltage controller, cycloconverters; Electric drives: introduction and classification. DC motor drives: speed-torque characteristics of shunt, series, PMDC motors; dynamic models; speed and position control methods; AC motor drives: d-q model of induction motor; constant flux speed control structure; vector control model; vector control structure.

**Texts**
1. N. Mohan: Power Electronics- Converters, Applications and Design, 3/e, John Wiley & Sons, 2003.

2. G. K. Dubey, Fundamentals of Electrical Drives, Narosa Publishing House, 2003.

**References**
1. Muhammad Rashid, Power Electronics- Circuits, Devices and Applications, 3/e, Prentice Hall, 2004.

2. B. K. Bose, Modern Power Electronics and AC Drives, Pearson Education, 2003.

3. Andrzej M. Trzynadlowski, Introduction to Modern Power Electronics, John Wiley & Sons, 1998.

4. Muhammad Rashid, Power Electronics Handbook, Academic Press-Elsevier, 2001.

** Advanced Electrical Engineering Laboratory ** |
** EC - 482** |
** 0-0-3-3** |

Reactive power compensation, synchronization of alternators, load angle characteristics of transmission line, ABCD parameters of transmission lines, fault analysis based on over-current and differential relays, design of simple inverters and voltage controllers, speed control of electric drives.

**Texts/References**
1. C. S. Indulkar, Laboratory Experiments in Electrical Power Engineering, Khanna Publishers, 2003.

2. G. K. Dubey, Fundamentals of Electrical Drives, Narosa Publishing House, 2003.

3. S. N. Singh: Electric Power Generation, Transmission and Distribution, Prentice-Hall, 2007.

4. R. K. Rajput, Electrical Machines, Laxmi Publications (P) Ltd, 3/e, 2003.

5. P. Kundur, Power System Stability and Control, McGraw-Hill, 1995.