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Power System Modelling and Scripting.pdf
1
2
Introduction
3
Power System Modelling
Background
Motivations
Modelling Physical Systems
Hybrid Dynamical Model
4
Power System Architecture
Structure of Software Projects
Classes and Procedures
Modularity
Architecture of a Power System Software Tool
5
Power System Scripting
Open and Closed Programming
Scripting
Scripting Languages for Computational Science
Computer Languages Suitable for Power System Analysis
Python Scripting Language
7
Power System Analysis
8
Power Flow Analysis
Background
Taxonomy of Power Flow Problems
Classical Power Flow Equations
Power Flow Solvers
Jacobi and Gauss-Seidel’s Method
Newton’s Method
Power Flow Jacobian Matrix
Robust Newton’s Method
Iwamoto’s Method
Inexact and Dishonest Newton’s Methods
Fast Decoupled Power Flow
DC Power Flow
Single and Distributed Slack Bus Models
A General Framework for Power Flow Solvers
Stability of the Continuous Newton’s Method
Summary
9
Continuation Power Flow Analysis
Background
System Model
Direct Methods
Saddle-Node Bifurcation
Limit-Induced Bifurcation
Nonlinear Programming
Homotopy Methods
Continuation Power Flow
Predictor Step
Corrector Step
Continuous Newton’s Method and Homotopy
N-1 Contingency Analysis
Summary
10
Optimal Power Flow Analysis
Background
Optimal Power Flow Model
Nonlinear Programming Solvers
Generalized Reduced Gradient Method
Interior Point Method
Summary of IPM Parameters
11
Eigenvalue Analysis
Background
Small Signal Stability Analysis
Bifurcation Points
Participation Factors
Analysis in the Z-Domain
Computing the Eigenvalues
Power Method
Inverse Iteration
Rayleigh’s Iteration
Power Flow Modal Analysis
Singular Value Decomposition
Summary
12
Time Domain Analysis
Background
Power System Model
Current-Injection Model
Power-Injection Model
Numerical Integration Methods
Explicit Methods
Implicit Methods
Numerical Integration Routine
Step Length
Disturbances
Stop Criterion
Electro-magnetic Transients
Quasi-static Analysis
Summary
13
Device Models
14
Device Generalities
General Device Model
Initialization of Device Internal Variables
Devices as Classes
Base Device Class
Methods of the Base Class
15
Power Flow Devices
Topological Elements
Bus
Areas, Zones, Regions and Systems
Static Generators
PV Generator
Constant Voltage Phasor Generator
PQ Generator
Static Loads
PQ Load
Constant Power Factor Load
Shunt Admittance
Switched Shunt Admittances
16
Transmission Devices
Transmission Line
Line Sections
Tie Line
Distributed Transmission Line Models
Effect of Frequency Variation
Coupling Device and Zero-Impedance Line
Transformer
Two-Winding Transformer
Under Load Tap Changer
Phase Shifting Transformer
Three-Winding Transformer
Vectorial Implementation
Incidence Matrix
Jacobian and Hessian Matrices
Network Connectivity
17
OPF Devices
Network Constraints
Bus Voltage Limits
Transmission Line limits
Generator Constraints
Capability Curve
Supply Offer
Reactive Power Payment Function
Generator Power Reserve
Generator Power Ramp
Load Constraints
Demand Bid
Demand Daily Profile
Demand Power Ramp
18
Faults and Protections
Fault
Breaker
Relay
Phasor Measurement Unit
Bus Frequency Estimation
19
Loads
Voltage Dependent Load
ZIP Load
Frequency Dependent Load
Voltage Dependent Load with Dynamic Tap Changer
Exponential Recovery Load
Thermostatically Controlled Load
Jimma’s Load
Mixed Load
20
Alternate-Current Machines
Synchronous Machine
Synchronous Machine Parameters
Initialization
Common Equations
Stator Electrical Equations
Magnetic Equations
Simplified Magnetic Equations
Synchronous Machine Model Taxonomy
Saturation
Center of Inertia
Dynamic Shaft
Sub-synchronous Resonance
Induction Machine
Initialization
Torque Model
Electromechanical Model
Detailed Single-Cage Model
Detailed Double-Cage Model
21
Synchronous Machine Regulators
Turbine Governor
Turbine Governor Type I
Turbine Governor Type II
Automatic Voltage Regulator
Automatic Voltage Regulator Type I
Automatic Voltage Regulator Type II
Automatic Voltage Regulator Type III
Power System Stabilizer
Simplified Power System Stabilizer Model
Power System Stabilizer Type I
Power System Stabilizer Type II
Power System Stabilizer Type III
Over-Excitation Limiter
Under-Excitation Limiter
22
Direct-Current Devices
Direct-Current Nodes
Common Interface Equations for Direct-Current Devices
Ideal Generators
Basic RLC Models
Direct-Current Machines
Other Direct-Current Devices
Solid Oxide Fuel Cell
Solar Photovoltaic Cell
Battery Energy System
23
AC/DC Devices
High-Voltage Direct-Current Transmission System
Per Unit System for DC Quantities
Rectifier Model
Inverter Model
HVDC Control
Voltage Source Converter
Simplified Dynamic VSC Model
Power Flow VSC Model
24
FACTS Devices
Static Var Compensator
SVC Type I
SVC Type II
SVC Initialization
Thyristor Controlled Series Compensator
TCSC Initialization
Static Synchronous Compensator
Detailed Model
Simplified Dynamic Model
Power Flow Model
STATCOM Initialization
Static Synchronous Series Compensator
Detailed Model
Simplified Dynamic Model
Power Flow Model
SSSC Initialization
Unified Power Flow Controller
Detailed Model
Simplified Dynamic Model
Power Flow Model
UPFC Initialization
25
Wind Power Devices
Wind Speed Models
Weibull’s Distribution
Composite Wind Speed Model
Mexican Hat Wavelet Model
Wind Turbines
Single Machine and Aggregate Models
Wind Turbine Initialization
Turbine Model
Dynamic Shaft
Non-Controlled Speed Wind Turbine
Doubly-Fed Asynchronous Generator
Direct-Drive Synchronous Generator
26
Spare Material and Concluding Remarks
27
Data Formats
Data Format Taxonomy
Data Organization and Structures
Kind of Supported Data
Number of Files
Default Values, Prototypes and Data Manipulation
Canonical Model
Common Information Model
Consistent Data Schemes
28
Visualization Matters
Graphical Interface vs. Command Line Approach
Result Visualization
Standard Two-Dimensional Plots
Temperature Maps
Three-Dimensional Plots
Geographic Information System
29
Challenges of Scripting for Power System Education
Concepts and Definitions
Proprietary Software
Open Source Software
Free Software
Free Open Source Software
Education-Oriented FOSS
Pedagogical Issues
Failure of FOSS for Power System Analysis
30
Power Systems
Federico Milano
Power System Modelling and
Scripting
ABC
Dr. Federico Milano
ETSII, University of Castilla - La Mancha
13071, Ciudad Real
Spain
E-mail: Federico.Milano@uclm.es
ISSN 1612-1287
ISBN 978-3-642-13668-9
DOI 10.1007/978-3-642-13669-6
Springer London Dordrecht Heidelberg New York
e-ISSN 1860-4676
e-ISBN 978-3-642-13669-6
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Control Number: 2010928724
c Springer-Verlag London Limited 2010
Apart from any fair dealing for the purposes of research or private study, or criticism or re-
view, as permitted under the Copyright, Designs and Patents Act 1988, this publication may
only be reproduced, stored or transmitted, in any form or by any means, with the prior per-
mission in writing of the publishers, or in the case of reprographic reproduction in accordance
with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning
reproduction outside those terms should be sent to the publishers.
The use of registered names, trademarks, etc. in this publication does not imply, even in
the absence of a specific statement, that such names are exempt from the relevant laws and
regulations and therefore free for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the
information contained in this book and cannot accept any legal responsibility or liability for
any errors or omissions that may be made.
Cover Design: deblik, Berlin, Germany
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
To Yolanda and Alessandro
Plato, Sophist, 365-361 B.C.
2.1 We make ourselves pictures of facts.
2.12 The picture is a model of reality.
2.225 There is no picture which is a priori true.
Ludwig Wittgenstein, Tractatus Logico-Philosophicus, 1922 A.D.
Preface
History the Book
The first draft of these notes was born in the winter of 2002. At that time, I
was a visiting scholar at the University of Waterloo. Originally, those notes
were not intended as a book, but as a quick reference for not forgetting the
models I was implementing for my research. After eight years, I am with
Universidad de Castilla-La Mancha. During these years, the notes have been
growing up little by little, ceaselessly. During the summer of 2009, I have
reorganized the notes in the present book.
Justification of the Title
Power system modelling and scripting is a quite general and ambitious title.
Of course, to embrace all existing aspects of power system modelling would
lead to an encyclopedia. Thus, the book focuses on a subset of power system
models based on the following assumptions: (i) devices are modelled as a set of
nonlinear differential algebraic equations, (ii) all alternate-current devices are
operating in three-phase balanced fundamental frequency, and (iii) the time
frame of the dynamics of interest ranges from tenths to tens of seconds. These
assumptions basically restrict the analysis to transient stability phenomena
and generator controls. The modelling step is not self-sufficient. Mathematical
models have to be translated into computer programming code in order to
be analyzed, understood and “experienced”. It is an object of the book to
provide a general framework for a power system analysis software tool and
hints for filling up this framework with versatile programming code.
Objectives of the Book
This book is for all students and researchers that are looking for a quick
reference on power system models or need some guidelines for starting the
X
Preface
challenging adventure of writing their own code. Thus, the objectives of this
book are twofold.
The primary objective is to provide a selection of the most used device
models ranging from static models for power flow, continuation power flow
and optimal power flow analyses to as complete as possible dynamic electro-
mechanical models for small-signal stability analysis and time domain simula-
tions. This selection includes classical devices (e.g., synchronous machines) as
well as non-conventional distributed energy resources (e.g., wind turbines),
static voltage dependent loads as well as emerging energy storage devices.
While describing each device, no matter if it is a well-known PV bus or a
very specific pitch angle control for wind turbines, the focus is on the model
hypotheses and on the implications of adopted simplifications.
The second objective is to provide a guide for organizing and translating
mathematical models into computer programming code. The purpose is that
the reader understands that there is always a gap between printed equations
and software applications running on computers. Fortunately, this gap is not
so huge and the book attempts to provide the methodological approach to
fill it.
Choice of the Programming Language
When dealing with programming issues, one has to face and answer a tricky
question: which is the most adequate computer language for tackling power
system analysis? Then, after deciding on the language, one already knows
that in a decade that language will be inevitably obsolete and a newer, easier,
classier language will be available. To avoid a quick obsolescence, the goal of
the book is not to provide code, but rather to teach how to design, organize
and eventually write it. Programming issues will be always the same, at least
as far as power systems will be the way they are. Thus, the adopted language
is not so important.
At the end of a careful one-year-long study, I finally opted for the Python
programming language. This language is well documented on the Internet, is
elegant and neat, is fully based on classes and provides efficient libraries for
solving linear algebra, handling sparse matrices and producing publication
quality figures. Last but not least, the Python interpreter is free and open
source. These characteristics do not guarantee that Python will last forever,
but make it very appropriate for educational purposes.
Organization of the Book
The material included in this book is organized in a somewhat unorthodox
way. Since the purpose is to concentrate on modelling, main power system
analysis tools and basic programming concepts are introduced before describ-
ing the devices. The book is organized in five parts, as follows.
Preface
XI
Part I contains introductory concepts. Chapter 1 provides the motivation
of the book, some philosophical foundations of the art of modelling physi-
cal systems and defines the general mathematical model used for describing
the behavior of power systems. Chapter 2 introduces the structure and the
features of a software package for power system analysis while Chapter 3
discusses on the concept of scripting applied to power system analysis. The
latter chapter also attempts to provide general guidelines for thinking power
systems analysis in terms of computer programming. I hope that the results
can be useful for Ph.D. students that, at the very end, will be the only readers
of this book that have time to implement their own software applications.
Part II introduces basic tools for power system analysis. The viewpoint
used for describing these tools is as general as possible. Chapter 4 describes
the power flow analysis, Chapter 5 the continuation power flow, Chapter 6
the optimal power flow, Chapter 7 the small signal stability analysis, and
Chapter 8 the time domain integration. Each topic is huge and, thus, only a
very reduced selection of methods and algorithms is presented. The object is
to provide a starting point for further investigations as well as a basement on
top of which the following part dedicated to device modelling can be built.
Part III is the barycentric and most extended part of the book. It embraces
the most important families of power system devices in an as systematic and
exhaustive way as possible. Chapter 9 provides an introduction to the ba-
sic mathematical aspects of a generic electrical device. Following Chapters
from 10 to 20 describe static power flow devices, transmission lines, static
and regulating transformers, optimal power flow models, faults, protections,
measurement devices, non-conforming static and dynamic loads, synchronous
and induction machines, primary frequency and voltage regulators and power
system stabilizers, dc devices, ac-dc devices, FACTS devices, and wind tur-
bines and other distributed energy resources.
Part IV discusses spare topics that are relevant for power system analysis
but are seldom included in power system books. Chapter 21 introduces the
variegated world of data formats and discusses the challenges for creating
a common model for exchanging power system data. Chapter 22 discusses
the advantages of the Unix-style command line approach versus graphical
user interfaces. Chapter 22 also describes plotting utilities aimed to power
system visualization ranging from conventional plots to advanced 2D and 3D
temperature maps. Chapter 23 describes some relevant educational aspects
of free and open source power system software packages.
Finally Part V contains supporting material in form of appendices. Ap-
pendix A provides a minimal introduction to the Python non-standard scien-
tific libraries used in the book. The aim of Appendix A is to make the book as
self-contained as possible. Appendix B defines Python structures and classes
that are used in the examples of the book. Appendix C discusses control dia-
grams and hard limit models. Finally, Appendix D provides the power system
data used in the example of previous chapters whereas Appendix E describes
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