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Computer Methods in Power Systems
10EE71
SYLLABUS
PART - A
UNIT - 1
NETWORK TOPOLOGY: Introduction, Elementary graph theory – oriented graph, tree,
co-tree, basic cut-sets, basic loops; Incidence matrices – Element-node, Bus incidence,
Tree-branch path, Basic cut-set, Augmented cut-set, Basic loop and Augmented loop;
Primitive network – impedance form and admittance form.
6 Hours
UNIT - 2
NETWORK MATRICES: Introduction, Formation of YBUS – by method of inspection
(including transformer off-nominal tap setting), by method of singular transformation
(YBUS = ATyA); Formation of Bus Impedance Matrix by step by step building algorithm
(without mutual coupling elements).
6 Hours
UNIT - 3 & 4
LOAD FLOW STUDIES: Introduction, Power flow equations, Classification of buses,
Operating constraints, Data for load flow; Gauss-Seidal Method – Algorithm and flow
chart for PQ and PV buses (numerical problem for one iteration only), Acceleration of
convergence; Newton Raphson Method – Algorithm and flow chart for NR method in
polar coordinates (numerical problem for one iteration only); Algorithm for Fast
Decoupled load flow method; Comparison of Load Flow Methods.
14 Hours
PART - B
UNIT - 5 & 6
ECONOMIC OPERATION OF POWER SYSTEM: Introduction, Performance curves,
Economic generation scheduling neglecting losses and generator limits, Economic
generation scheduling including generator limits and neglecting losses; Iterative
techniques; Economic Dispatch including transmission losses – approximate penalty
factor, iterative technique for solution of economic dispatch with losses; Derivation of
transmission loss formula; Optimal scheduling for Hydrothermal plants – problem
formulation, solution procedure and algorithm.
12 Hours
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Computer Methods in Power Systems
10EE71
UNIT - 7 & 8
TRANSIENT STABILITY STUDIES: Numerical solution of Swing Equation – Pointby-point method, Modified Euler‟s method, Runge-Kutta method, Milne‟s predictor
corrector method. Representation of power system for transient stability studies – load
representation, network performance equations. Solution techniques with flow charts.
14 Hours
TEXT BOOKS:
1. Computer Methods in Power System Analysis- Stag, G. W., and EI-Abiad, A.
H.- McGraw Hill International Student Edition. 1968
2. Computer Techniques in Power System Analysis- Pai, M. A- TMH, 2nd
edition, 2006.
REFERENCE BOOKS:
1. Modern Power System Analysis- Nagrath, I. J., and Kothari, D. P., -TMH,
2003.
2. Advanced Power System Analysis and Dynamics- Singh, L. P.,
New Age International (P) Ltd, New Delhi, 2001.
3. Computer
Aided
Power
System
Operations
and
Analysis”- Dhar, R. N- TMH, New Delhi, 1984.
4. Power System Analysis- Haadi Sadat, -TMH, 2nd , 12th reprint, 2007
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Computer Methods in Power Systems
10EE71
CONTENTS
Sl.
No
TOPICS
PAGE NO.
1.
UNIT - 1
NETWORK TOPOLOGY
04-18
2.
UNIT - 2
NETWORK MATRICES
19-50
UNIT - 3 & 4
LOAD FLOW STUDIES
51-84
UNIT - 5 & 6
ECONOMIC OPERATION OF POWER SYSTEM
85-109
UNIT - 7 & 8
TRANSIENT STABILITY STUDIES
110-144
3.
4.
5.
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Computer Methods in Power Systems
10EE71
UNIT-1
NETWORK TOPOLOGY
1. INTRODUCTION
The solution of a given linear network problem requires the formation of a set of equations
describing the response of the network. The mathematical model so derived, must describe
the characteristics of the individual network components, as well as the relationship which
governs the interconnection of the individual components. In the bus frame of reference
the variables are the node voltages and node currents. The independent variables in any
reference frame can be either currents or voltages. Correspondingly, the coefficient matrix
relating the dependent variables and the independent variables will be either an impedance
or admittance matrix. The formulation of the appropriate relationships between the
independent and dependent variables is an integral part of a digital computer program for
the solution of power system problems. The formulation of the network equations in
different frames of reference requires the knowledge of graph theory. Elementary graph
theory concepts are presented here, followed by development of network equations in the
bus frame of reference.
1.1 ELEMENTARY LINEAR GRAPH THEORY: IMPORTANT TERMS
The geometrical interconnection of the various branches of a network is called the
topology of the network. The connection of the network topology, shown by replacing all
its elements by lines is called a graph. A linear graph consists of a set of objects called
nodes and another set called elements such that each element is identified with an ordered
pair of nodes. An element is defined as any line segment of the graph irrespective of the
characteristics of the components involved. A graph in which a direction is assigned to
each element is called an oriented graph or a directed graph. It is to be noted that the
directions of currents in various elements are arbitrarily assigned and the network
equations are derived, consistent with the assigned directions. Elements are indicated by
numbers and the nodes by encircled numbers. The ground node is taken as the reference
node. In electric networks the convention is to use associated directions for the voltage
drops. This means the voltage drop in a branch is taken to be in the direction of the current
through the branch. Hence, we need not mark the voltage polarities in the oriented graph.
Connected Graph : This is a graph where at least one path (disregarding orientation)
exists between any two nodes of the graph. A representative power system and its oriented
graph are as shown in Fig 1, with:
e = number of elements = 6
n = number of nodes = 4
b = number of branches = n-1 = 3
l = number of links = e-b = 3
Tree = T(1,2,3) and
Co-tree = T(4,5,6)
Sub-graph : sG is a sub-graph of G if the following conditions are satisfied:
· sG is itself a graph
· Every node of sG is also a node of G
· Every branch of sG is a branch of G
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