Part II: Analysis Methods of Electrical Power Systems CONTENTS ...

Part II:
Analysis Methods of
Electrical Power Systems









CONTENTS

Chapter 1: Functions of Electrical Energy Systems

1.1. Introduction
1.2. Hierarchy and representation of electrical power systems
1.2.1. Transmission lines and apparatus
1.2.2. Transformers
1.2.3. Electric loads
1.2.4. Generators

Chapter 2: Network Representation
2.1. Graphical and topological description of a network
2.1.1. Review of graph theory
2.2. Network global modeling: CIM model
2.3. Matrix representation of networks
2.3.1. Network matrices
2.3.1.1. Incidence matrix
2.3.1.2. Matrix of elementary network
2.3.1.3. Transfer matrix

Chapter 3: Formation of Network Matrices
3.1. Formation of the Ybus matrix
3.2. Formation of the Zbus matrix
3.2.1. Adding branches
3.2.1.1. Calculation of Zqi terms
3.2.1.2. Calculation of Zqq terms
3.2.2. Adding cords
3.2.2.1. Calculation of augmented matrix elements
3.2.2.2. Elimination of fictitious node
3.3 Exercises
3.3.1 Exercise No. 12: Construction of Zbus matrix
3.3.2 Exercise No. 13: Construction of network matrices

Chapter 4: Load Flow Calculations
4.1. Objectives
4.1.1. Definition of network state
4.1.2. Device current rating
4.1.3. Line losses
4.1.4. Strategy for adjustment and control
4.1.5. Optimizing power transfer capacity
4.2. Model of network elements
4.2.1. Lines and transformers
4.2.2. Generators and loads
4.2.3. Representations of voltage
4.3. Problem formulation
4.3.1. General equations
4.3.2. Simplified models
4.4. Solution methods
4.4.1. Gauss-Seidel method
4.4.2. Newton-Raphson method
4.4.3. Calculation of power flows
4.5. Software tools for network analysis
4.6. Appendix: principle of numerical iterative methods
4.6.1. Gauss-Seidel method
4.6.2. Newton-Raphson method
4.7 Exercises
4.7.1 Exercise No. 14: Load flow calculation
4.7.2 Exercise No. 15: Power flow
4.7.3 Exercise No. 16: Matrices and load flow

Chapter 5: Transient Analysis Methods
5.1. Interest in transient analysis
5.2. Transient network analyzer
5.2.1. Principle of operation
5.2.2. Advantages and disadvantages
5.3. Method of traveling waves
5.3.1. Principle
5.3.2. Representation of a line (or cable)
5.3.3. Representation of a resistor
5.3.4. Representation of an inductor
5.3.5. Representation of a capacitor
5.3.6. Representation of a voltage source
5.3.7. Operating principle
5.3.8. Illustration example
5.4. Conclusions
5.5. Exercises
5.5.1. Exercise No. 17: Transient analysis on a line
5.5.2 Exercise No. 18. Matrices and transient analysis
5.5.3 Exercise No. 19. Transient analysis under lightning
strike

Chapter 6: Fault Current Calculations
6.1. Definition
6.2. Effects of short-circuit conditions
6.3. Common causes of faults
6.4. Importance of short-circuit current calculations
6.5. Types of short-circuits
6.6. Notion of short-circuit power
6.7. Polyphase balanced and unbalanced systems
6.7.1. Balanced three-phase systems
6.7.2. Complex representation
6.7.3. Symmetrical components
6.7.4. Powers in terms of symmetrical components
6.7.5. Symmetrical components and impedance/admittance matrices
6.7.6. Concept of circulating matrices
6.7.7. Case of the synchronous machines
6.7.8. Short-circuit current calculations
6.7.8.1. Single-phase-to-ground fault
6.7.8.2. Two-phase-to-ground fault
6.7.9. Other types of faults
6.8. Generalization of fault calculation in complex networks
6.9. Symmetrical (three-phase) faults
6.10. Symmetrical fault currents: systematic approach
6.11. Short-circuit power
6.12. Unsymmetrical fault current calculations
6.12.1. Generalization of symmetrical components
6.12.1.1. Positive sequence (direct) network
6.12.1.2. Negative sequence (inverse) network
6.12.1.3. Zero sequence (homopolar) network
6.12.2. Neutral and homopolar currents
6.12.3. Impedances of network components
6.12.3.1. Impedance of rotating machines
6.12.3.2. Impedance of lines and transformers
6.12.3.3. Homopolar impedance of lines
6.12.3.4. Homopolar impedance of transformers
6.12.4. Illustration example
6.12.5. Systematic calculation of unsymmetrical fault currents
6.13 Exercises
6.13.1 Exercise No. 20: Fault current in a simple network
6.13.2 Exercise No. 21: Symmetrical faults in a network



Chapter 7: Stability Analysis of Power Systems
7.1. Objective
7.2. Introduction
7.3. Categories and classes of stability problems
7.4. The equation of motion
7.5. Simplified model of synchronous machine
7.6. Power-angle considerations at steady-state
7.7. Case of small perturbations
7.8. Transient stability
7.9. Application of equal-area criteria
7.9.1. Case of a short-circuit at generator terminals
7.9.2. Critical fault clearing time
7.9.3. Case of a short-circuit on a line
7.10. Case of a multi-machine system
7.11 Exercises
7.11.1 Exercise No. 22: Stability and critical fault clearing
time

Bibliography






CHAPTER 1

Functions of Electrical Energy Systems

1.1. Introduction

Electrical energy is produced in particular sites related to the nature of
the primary energy source:
- mountain for hydroelectric plants;
- rivers for hydroelectric or nuclear installations;
- seaside for nuclear installations and the tidal power plants;
- Countryside and coal mines for the thermal plants.
This energy is used in centers of consumption which are often located in
places away from the generating plants. These include
- urban centers;
- industrial centers;
- steel and metallurgical processing plants;
- electrical railway systems;
- etc ...

Since electric energy cannot be stored in large quantities, it is necessary
to produce it, transmit it, and distribute it in real time to various
customers for consumption. The role of the transmission network is to
essentially carry the energy produced from various power plants to the load
centers where it is consumed.

From the operational point of view, we recall that the crucial role of the
network is to allow the supply of power at every moment power required by
the consumer under guaranteed frequency and voltage magnitudes. However,
this constraint requires an adjustment of the generating machines and
equipment so that:

- all apparatus operate in good conditions;
- the energy losses are minimized;
- the use of the spinning reserves is optimized;
- The limits of the network variables are respected under normal
circumstances.

While the network is operated such that the above constrained are met under
normal circumstances through monitoring and adjustments, there exist
however unexpected incidents such as,

- short-circuits;
- bad weather (e.g., lightning strikes);
- Unintentional tripping.

The role of preventive maintenance and the security of the network are to
assure that the above incidents should not lead to widespread power outage.

The old electrical networks were oversized and thus redundant by their
design, which took into account the requirements of security. Today's
networks, however, are very often exploited under conditions close to their
limits of operation because of high capital costs, stricter environmental
and societal constraints (i.e., the acceptability building new transmission
lines becoming increasingly problematic). The liberalization of the energy
markets facilitated power transactions between many players, energy
producers as well as consumers, who can be located in different
territories. This led to an increase in the number and volume of energy
transfers on the network that was originally designed to operate in a
monopolistic mode. These power exchanges, which significantly increased
after the introduction of market competition, are straining many parts of
the transmission network.

This situation of fragility, with respect to incidents being able to occur
in the course of exploitation, has led the network operators to set up
means of reacting in an adequate way at the time of critical situations for
several decades (well before the advent of competition). The diagram of
Figure 1.1 below illustrates the installation of these measures. These
issues which are matters of analysis concern all the elements of the life
of the network, from its long-term planning to the study of fast transient
phenomena.


















Translation:
Necessity de decisions rapides: Necessity of rapid decisions
Automatization des actions: Automated actions
Control en temps reel: Real time control
Resolution prealable de nombreux problems: Priority resolution of the
numerous problems

Figure 1.1. Strategic elements of network control.

The list below shows the majority of the above subjects. The analytical
methods developed in the chapters that follow will allow a precise and
thorough study:

- network planning;
- reliability studies;
- simulation of operation;
- load forecasting and distribution;
- sho