Emerging techniques in power system analysis Kỹ thuật mới nổi trong phân tích hệ thống điện

Zhaoyang Dong Pei Zhang et al Emerging Techniques in Power System Analysis Zhaoyang Dong Pei Zhang et al Emerging Techniques in Power System Analysis With 67 Figures Authors Zhaoyang Dong Pei Zhang Department of Electrical Engineering Electric Power Research Institute The Hong Kong Polytechnic University 3412 Hillview Ave, Palo Alto, Hong Kong, China CA 94304-1395, USA E-mail: eezydong@polyu.edu.hk E-mail: pzhang@epri.com ISBN 978-7-04-027977-1 Higher Education Press, Beijing ISBN 978-3-642-04281-2 e-ISBN 978-3-642-04282-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2009933777 c Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Violations are liable to prosecution under the German Copyright Law The use of general descriptive names, 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 protective laws and regulations and therefore free for general use Cover design: Frido Steinen-Broo, EStudio Calamar, Spain Printed on acid-free paper Springer is part of Springer Science + Business Media (www.springer.com) Preface Electrical power systems are one of the most complex large scale systems Over the past decades, with deregulation and increasing demand in many countries, power systems have been operated in a stressed condition and subject to higher risks of instability and more uncertainties System operators are responsible for secure system operations in order to supply electricity to consumers efficiently and reliably Consequently, power system analysis tasks have become increasingly challenging and require more advanced techniques This book provides an overview of some the key emerging techniques for power system analysis It also sheds lights on the next generation technology innovations given the rapid changes occurring in the power industry, especially with the recent initiatives toward a smart grid Chapter introduces the recent changes of the power industry and the challenging issues including, load modeling, distributed generations, situational awareness, and control and protection Chapter provides an overview of the key emerging technologies following the evolvement of the power industry Since it is impossible to cover all of emerging technologies in this book, only selected key emerging technologies are described in details in the subsequent chapters Other techniques are recommended for further reading Chapter describes s the first key emerging technique: data mining Data mining has been proved an effective technology to analyze very complex problems, e.g cascading failure and electricity market signal analysis Data mining theories and application examples are presented in this chapter Chapter covers another important technique: grid computing Grid computing techniques provide an effective approach to improve computational efficiency The methodology has been used in practice for real time power system stability assessment Grid computing platforms and application examples are described in this chapter Chapter emphasizes the importance of probabilistic power system analysis, including load flow, stability, reliability, and planning tasks Probabilistic approaches can effectively quantify the increasing uncertainties in power systems and assist operators and planning in making objective decisions Various probabilistic analysis techniques are introduced in this chapter vi Preface Chapter describes the application of an increasingly important device, phasor measurement units (PMUs) in power system analysis PMUs are able to provide real time synchronized system measurement information which can be used for various operational and planning analyses such as load modeling and dynamic security assessment The PMU technology is the last key emerging technique covered in this book Chapter provides information leading to further reading on emerging techniques for power system analysis With the new initiatives and continuously evolving power industry, technology advances will continue and more emerging techniques will appear., The emerging technologies such as smart grid, renewable energy, plug-in electric vehicles, emission trading, distributed generation, UVAC/DC transmission, FACTS, and demand side response will create significant impact on power system Hopefully, this book will increase the awareness of this trend and provide a useful reference for the selected key emerging techniques covered Zhaoyang Dong, Pei Zhang Hong Kong and Palo Alto August 2009 Contents Introduction· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 1.1 Principles of Deregulation· · · · · · · · · · · · · · · · · · · · · · · · · · · 1.2 Overview of Deregulation Worldwide· · · · · · · · · · · · · · · · · · · 1.2.1 Regulated vs Deregulated · · · · · · · · · · · · · · · · · · · · · · 1.2.2 Typical Electricity Markets· · · · · · · · · · · · · · · · · · · · · 1.3 Uncertainties in a Power System · · · · · · · · · · · · · · · · · · · · · · 1.3.1 Load Modeling Issues · · · · · · · · · · · · · · · · · · · · · · · · · 1.3.2 Distributed Generation· · · · · · · · · · · · · · · · · · · · · · · · 10 1.4 Situational Awareness · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10 1.5 Control Performance · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 11 1.5.1 Local Protection and Control · · · · · · · · · · · · · · · · · · · 12 1.5.2 Centralized Protection and Control · · · · · · · · · · · · · · · 14 1.5.3 Possible Coordination Problem in the Existing Protection and Control System · · · · · · · · · · · · · · · · · · 15 1.5.4 Two Scenarios to Illustrate the Coordination Issues Among Protection and Control Systems · · · · · · · · · · · 16 1.6 Summary· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 19 References · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 19 Fundamentals of Emerging Techniques · · · · · · · · · · · · · · · · · 23 2.1 Power System Cascading Failure and Analysis Techniques · · · 23 2.2 Data Mining and Its Application in Power System Analysis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 27 2.3 Grid Computing· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 29 viii Contents 2.4 Probabilistic vs Deterministic Approaches · · · · · · · · · · · · · · · 31 2.5 Phasor Measurement Units · · · · · · · · · · · · · · · · · · · · · · · · · · 34 2.6 Topological Methods · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 35 2.7 Power System Vulnerability Assessment· · · · · · · · · · · · · · · · · 36 2.8 Summary· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 39 References · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 39 Data Mining Techniques and Its Application in Power Industry · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 45 3.1 Introduction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 45 3.2 Fundamentals of Data Mining· · · · · · · · · · · · · · · · · · · · · · · · 46 3.3 Correlation, Classification and Regression · · · · · · · · · · · · · · · 47 3.4 Available Data Mining Tools· · · · · · · · · · · · · · · · · · · · · · · · · 49 3.5 Data Mining based Market Data Analysis · · · · · · · · · · · · · · · 51 3.5.1 Introduction to Electricity Price Forecasting · · · · · · · · 51 3.5.2 The Price Spikes in an Electricity Market · · · · · · · · · · 52 3.5.3 Framework for Price Spike Forecasting · · · · · · · · · · · · 54 3.5.4 Problem Formulation of Interval Price Forecasting · · · · 63 3.5.5 The Interval Forecasting Approach · · · · · · · · · · · · · · · 65 3.6 Data Mining based Power System Security Assessment· · · · · · 70 3.6.1 Background · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 72 3.6.2 Network Pattern Mining and Instability Prediction · · · 74 3.7 Case Studies · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 79 3.7.1 Case Study on Price Spike Forecasting · · · · · · · · · · · · 80 3.7.2 Case Study on Interval Price Forecasting · · · · · · · · · · · 83 3.7.3 Case Study on Security Assessment· · · · · · · · · · · · · · · 89 3.8 Summary· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 92 References · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 92 Grid Computing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 95 4.1 Introduction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 95 4.2 Fundamentals of Grid Computing · · · · · · · · · · · · · · · · · · · · · 96 4.2.1 Architecture· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 97 4.2.2 Features and Functionalities · · · · · · · · · · · · · · · · · · · · 98 Contents ix 4.2.3 Grid Computing vs Parallel and Distributed Computing · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 100 4.3 Commonly used Grid Computing Packages · · · · · · · · · · · · · · 101 4.3.1 Available Packages · · · · · · · · · · · · · · · · · · · · · · · · · · · 101 4.3.2 Projects· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 102 4.3.3 Applications in Power Systems · · · · · · · · · · · · · · · · · · 104 4.4 Grid Computing based Security Assessment· · · · · · · · · · · · · · 105 4.5 Grid Computing based Reliability Assessment · · · · · · · · · · · · 107 4.6 Grid Computing based Power Market Analysis · · · · · · · · · · · 108 4.7 Case Studies · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 109 4.7.1 Probabilistic Load Flow · · · · · · · · · · · · · · · · · · · · · · · 109 4.7.2 Power System Contingency Analysis · · · · · · · · · · · · · · 111 4.7.3 Performance Comparison · · · · · · · · · · · · · · · · · · · · · · 111 4.8 Summary· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 113 References · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 113 Probabilistic vs Deterministic Power System Stability and Reliability Assessment · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 117 5.1 Introduction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 117 5.2 Identify the Needs for The Probabilistic Approach · · · · · · · · · 118 5.2.1 Power System Stability Analysis · · · · · · · · · · · · · · · · · 118 5.2.2 Power System Reliability Analysis· · · · · · · · · · · · · · · · 119 5.2.3 Power System Planning · · · · · · · · · · · · · · · · · · · · · · · 120 5.3 Available Tools for Probabilistic Analysis · · · · · · · · · · · · · · · 121 5.3.1 Power System Stability Analysis · · · · · · · · · · · · · · · · · 121 5.3.2 Power System Reliability Analysis· · · · · · · · · · · · · · · · 123 5.3.3 Power System Planning · · · · · · · · · · · · · · · · · · · · · · · 123 5.4 Probabilistic Stability Assessment · · · · · · · · · · · · · · · · · · · · · 125 5.4.1 Probabilistic Transient Stability Assessment Methodology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 125 5.4.2 Probabilistic Small Signal Stability Assessment Methodology · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 127 x Contents 5.5 Probabilistic Reliability Assessment · · · · · · · · · · · · · · · · · · · 128 5.5.1 Power System Reliability Assessment · · · · · · · · · · · · · 128 5.5.2 Probabilistic Reliability Assessment Methodology · · · · 131 5.6 Probabilistic System Planning· · · · · · · · · · · · · · · · · · · · · · · · 135 5.6.1 Candidates Pool Construction· · · · · · · · · · · · · · · · · · · 136 5.6.2 Feasible Options Selection · · · · · · · · · · · · · · · · · · · · · 136 5.6.3 Reliability and Cost Evaluation· · · · · · · · · · · · · · · · · · 136 5.6.4 Final Adjustment · · · · · · · · · · · · · · · · · · · · · · · · · · · · 136 5.7 Case Studies · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 137 5.7.1 A Probabilistic Small Signal Stability Assessment Example · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 137 5.7.2 Probabilistic Load Flow · · · · · · · · · · · · · · · · · · · · · · · 140 5.8 Summary· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 142 References · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 143 Phasor Measurement Unit and Its Application in Modern Power Systems · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 147 6.1 Introduction · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 147 6.2 State Estimation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 151 6.2.1 An Overview · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 151 6.2.2 Weighted Least Squares Method · · · · · · · · · · · · · · · · 152 6.2.3 Enhanced State Estimation· · · · · · · · · · · · · · · · · · · · · 154 6.3 Stability Analysis · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 157 6.3.1 Voltage and Transient Stability · · · · · · · · · · · · · · · · · · 158 6.3.2 Small Signal Stability — Oscillations · · · · · · · · · · · · · · 160 6.4 Event Identification and Fault Location· · · · · · · · · · · · · · · · · 162 6.5 Enhance Situation Awareness · · · · · · · · · · · · · · · · · · · · · · · · 164 6.6 Model Validation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 167 6.7 Case Study · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 169 6.7.1 Overview · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 170 6.7.2 Formulation of Characteristic Ellipsoids· · · · · · · · · · · · 170 6.7.3 Geometry Properties of Characteristic Ellipsoids · · · · · 172 6.7.4 Interpretation Rules for Characteristic Ellipsoids · · · · · 173 7.3 Further Reading 187 7.3 Further Reading Following the major trends in power engineering development, further reading in the areas of emissions trading impacts on power system operations and planning, renewable technology developments and their impacts on power systems, and the smart grid are recommended 7.3.1 Economic Impact of Emission Trading Schemes and Carbon Production Reduction Schemes As global warming and climate change are threatening the ecosystems and economies of the world, many countries have realized the urgent need to reduce greenhouse gas (GHG) emissions and achieve sustainable development Many efforts towards emission reduction have already been made in the form of government policies and international agreements In the scientific and engineering literature, traditional command and control regulations have been criticized and the call for establishing more effective environmental policies for sustainable development never stops Jordan et al (2003) argued that even the most sophisticated forms of environmental regulation cannot alone achieve sustainable development Schubert and Zerlauth (1999) argued that the cost of complying with command-and-control regulations excessively limits business profitability and competitiveness It throttles back technological and environmental innovation and consequently economic growth According to the articles by Janicke, 1997 and Mol, 2000, new and more novel approaches such as voluntary agreements and market-based instruments are needed by governments and non-legislative organizations for emission reduction purpose Partially, in view of these arguments, a Europe-wide Emission Trading Scheme (ETS) was introduced by the European Union (EU) from the 1st of January 2005, which obligated major stationary sources of GHGs to participate in a cap and trade scheme Emission trading is designed to achieve a cost-efficient emission reduction through the equalization of marginal abatement cost The EU-ETS is the current major policy instrument across Europe to manage emissions of carbon dioxide (CO2 ) and other greenhouse gases Since the introduction of EU-ETS, it remains a hot topic for discussion and the debate is mainly focused on emission right allocations Whether emission allowances should be provided free of charge or through purchase (auction) is the centre of the debate Economists argue, based on the assumption of profit maximization, that the existence of a carbon price implies an extra cost for every fossil generator; and in a competitive market, the generator will pass this extra cost through to consumers by means of the electricity price Because of this, free allocation of emissions allowances represents a large windfall to generation 188 Conclusions and Future Trends in Emerging Techniques companies Burtraw et al (1998) compared three different allocation options for the electricity sector in the US and found that the costs to society through auctioning are about half compared to the other two free-of-charge options, i.e emission-based allocation and production-based allocation options Zhou et al (2009) presented an overview of emission trading schemes and the carbon reduction scheme impacts on the Australian National Electricity Market (NEM) Quirion (2003) suggested that to achieve profit neutrality only 10 – 15% of allowances need to be freely allocated Bovenberg and Goulder (2000) also proposed that no more than 15% of allowances need to be freely allocated to secure profits and equity values after they did research on the coal, oil and gas industries in the US Sijm et al (2006) suggested that overall auctioning seems to be a better option than free allocation, because auctioning can avoid windfall profits among producers, internalizes the costs of carbon emission into the power price, raises public revenue to mitigate rising power prices and avoids potential distortions of new investment decisions Emission allocation is also a political issue and needs to be compared against allowances auction when considering the additional financial costs of emitters, therefore, power producers and other carbon-intensive industries covered by EU-ETS The generation sector is among those contributing the most to green house emissions (Sijm et al., 2006; Zhou et al., 2009) Consequently, the ETS has been introduced mainly targeting at the generation sector following the Kyoto protocol The exact impacts of ETS on the generation composition, profitability, dispatching order, and generation new entry into the market are to be clearly depicted However, it can be quite confidently anticipated that the generators in an electricity market will definitely be affected Should ETS be implemented, there will be more renewable and combine cycle generators and less, if not completely no, coal fired power stations entering the market Take the Australian National Electricity Market (NEM) for instance Australian government signed the Kyoto protocol in 2008 and encourages renewable resources into the NEM (Garnut, 2008) Zhou et al (2009) studied the emissions tradition scheme impacts on the Australian National Electricity Market (NEM) and compared the profits and costs of generators under different emission allocation schemes vs business as usual, i.e., no ETS scenarios The study indicates that the impact on the profitability of generators and the reduction of GHG in the Australian NEM is small if the carbon price is low The pricing of carbon is still yet to be determined in Australia Currently, the generation connection inquiries to the transmission network service providers by wind generators have been increasing rapidly in SA, VIC, and TAS where wind resources are abundant Another important fact to be considered in this aspect is the Carbon Pollution Reduction Scheme (CPRS) promoted by the Australian government (Yin 2009) CPRS is expected to commence on July 2011 The Australian government expects that CPRS can guarantee that the emissions in Australia are to be reduced by 25% of 2000 levels by 2020 The ETS and CPRS impacts will have to be considered after 2010 in operations and planning in the whole power sector For generation companies, 7.3 Further Reading 189 this means that the impacts must be considered in forming optimal bidding strategies and selecting optimal portfolios For transmission network service providers (TNSPs), this means that transmission network expansion planning will deal with increasing number of connection requests from generators using renewable sources For distribution network service providers, distributed generation using renewable resources will become more widespread, and the consequent distribution network operation, control and planning will have to accommodate such changes as well 7.3.2 Power Generation based on Renewable Resources such as Wind Increasing power generation from renewable sources such as wind would help in reducing carbon emissions and hence minimize the effect on global warming Wind energy is one of the fastest growing industries worldwide Various actions have been taken by the utilities and government authorities across the world to achieve this objective Most of the states in USA have Renewable Portfolios Standard (a state policy aiming at obtaining certain percentage of their power form renewable energy sources by certain date) ranging from 10% – 20% of total capacity by 2020 (US Department of Energy, 2007) This increasing penetration of renewable sources of energy, in particular wind energy conversion systems (WECS), in the conventional power system has put tremendous challenges to the power system operators/planners, who have to ensure the reliable and secure grid operation As power generation from WECS is significantly increasing, it is of paramount importance to study the effect of wind integrated power systems on overall system stability One of the key technologies for wind power is the modeling and control of wind generator systems The Doubly Fed Induction Generator (DFIG) is the main type of generators in variable-speed wind energy generation systems, especially for high-power applications This is because of its higher energy transfer capability, reduced mechanical stress on the wind turbine, relatively low power rating of the connected power electronics converter, low investment and flexible controls (Eriksen et al., 2005; Wu et al., 2007; Yang et al., 2009a) DFIG is different from the conventional induction generator in a way that it employs a series voltage-source converter to feed the wound rotor The feedback converters consist of a Rotor Side Converter (RSC) and a Grid Side Converter (GSC) The control capability of these converters gives DFIG an additional advantage of flexible control and stability over other induction generators (Mishra et al., 2009a) With an increasing penetration level of DFIG type wind turbines into the grid, there is a genuine concern that the stability issue of the DFIG connected system needs proper investigation A DFIG wind turbine system, including an induction generator, two-mass drive train, power converters and feedback controllers, is a multivariable, nonlin- 190 Conclusions and Future Trends in Emerging Techniques ear, and strongly coupled system (Kumar et al., 2009) In order to assess the stability of the system, dynamics of the DFIG system including generators and controls as well as the power system where the DFIG system is connected need to be analyzed as an overall complex system (Yang et al., 2009a; Mishra et al., 2009b) The interaction between system dynamics and DFIG dynamics needs to be considered carefully The characteristics of DFIG systems and the increased complexity of DFIG connected power systems also require new control methodologies (Yang et al., 2009b) DFIG control is normally a decoupled control of active and reactive power of DFIG Vector control strategy based on proportional-integral (PI) controllers has been used to realize this decoupled control objective by the industry (Yamamoto and Motoyoshi, 1991; Pena et al., 1996; Muller et al., 2002; Miao et al., 2009; Xu and Wang, 2007; Brekken and Mohan, 2007) 7.3.3 Smart Grid Following the initiative of greenhouse gas emission reduction and also aiming at reducing energy costs, the smart grid has been promoted as the most important development for the power industry in a number of major economic powerhouses from 2009 For example, in the USA, the Smart Grid project is expected to attract US$150 billion investments Clearly, in addition to the original objective of sustainable and reliable energy supply, it also serves as a major investment to stimulate the economic development Similarly, huge amount of investments are also expected in the development of the Smart Grid in China and Europe nations as well In USA, the 2007 Energy Independence and Security Act (EISA) gives the US Department of commerce, National Institute of Standards and Technology (NIST) the responsibility for issues related to smart grid developments in the USA In June 2009, Electric Power Research Institute (EPRI, 2009) submitted a report detailing the interoperability standards of the Smart Grid, gaps in current standards and priorities for new standards In this document, EPRI summarized the high level architecture development in the smart grid including conceptual models, architectural principles and methods, and cyber security strategies for the smart grid It also summarized the implementation of the conceptual model of the smart grid, and principles of enabling the smart grid to support new technologies and business models According to the EISA of 2007 and EPRI’s IntelliGrid initiative (2001 – 2009), the Smart Grid refers to the development of the power grid which links itself with communications and computer control so that it can monitor, protect and automatically optimize the operation of the components including generation, transmission, distribution and consumers of electricity It also coordinates in an optimal way the operation of energy storage systems and other appliances such as electric vehicles and air-conditions According 7.4 Summary 191 to EPRI (2009), the Smart Grid is characterized by “a two-way flow of electricity and information to an automated, widely distributed energy delivery network” The benefits of the Smart Grid (EPRI, 2009) are summarized as to be able to achieve: (1) reliability and power quality improvement; (2) enhanced grid safety and cyber security; (3) higher energy efficiency; (4) more sustainability in energy supply; (5) a wider range of economic benefits to participants of the smart grid including both the supplier and consumer sides Along the line of the smart grid development, a group of techniques need to be further explored, these include automated metering infrastructure (AMI), demand side participation, plug in electric vehicles, wide area measurement based measurement and control techniques, communications, distributed generation and energy storage techniques Moreover, Transportation of renewable and alternative electricity generation to the end user may require more interconnections in a power system Given the increasing interconnection of power systems in many countries, electric transportation, especially ultra-high voltage AC and DC transmission techniques, are other important issues for the development of a very large scale smart grid 7.4 Summary The power industry in many countries today has been experiencing various developments which lead to continuously emerging challenges Power system analysis techniques need to be advanced as well in order to follow these challenges This book presents an overview of some key emerging techniques being developed and implemented over the past decades It also summarized the trends in power industry and the emerging technology development The authors of this book hope to provide readers a picture of the technological advances that have happened in the past decade However, as we stated in the book, technological development will not stop, there are new challenges emerging and the research and development of power system analysis techniques will continue References Bovenberg AL, Goulder LH (2000) Neutralizing the adverse industry impacts of CO2 abatement policies: what does it cost NBER Working Paper No W7654 192 Conclusions and Future Trends in Emerging Techniques Available at SSRN: http: //ssrn com/abstract=228128 Accessed June 2009 Brekken TKA, Mohan N (2007) Control of a doubly fed induction wind generator under unbalanced grid voltage conditions IEEE Trans Energy Conversion 22(1): 129 – 135 Burtraw D, Harrision KW, Turner P (1998) Improving efficiency in bilateral emission trading Environ Resour Econ 11(1): 19 – 33 EPRI IntelliGridSM Initiative (2001 – 2009) http://intelligrid.epri.com Accessed July 2009 EPRI (2009) Report to NIST on the Smart Grid Interoperability Standards Roadmap, 17 June 2009 Eriksen PB, Ackermann T, Abildgaard H, et al (2005) System operation with high wind penetration IEEE Power Energy Manag 3(6): 65 – 74 Kumar V, Kong S, Mishra Y, et al (2009) Doubly fed induction generators: overview and intelligent control strategies for wind energy conversion systems Chapter 5, Metaxiotis edt Intelligent Information Systems and Knowledge Management for Energy: Applications for Decision Support, Usage, and Environmental Protection, IGI Global publication Janicke M (1997) The political system’s capacity for environmental policy In National Environmental Policies: a Comparative Study of Capacity-Building Janicke M, Weidner H Springer, Heidelberg, pp – 24 Garnaut R (2008) Garnaut climate change review, emissions trading scheme discussion paper Melbourne http://www.garnautreview.org.au Accessed July 2009 Miao Z, Fan L, Osborn D, et al (2009) Control of DFIG-based wind generation to improve interarea oscillation damping IEEE Trans Energy Conversion 24(2): 415 – 422 Mishra Y, Mishra S, Li F, et al (2009) Small signal stability analysis of a DFIG based wind power system with tuned damping controller under super/subsynchronous mode of operation IEEE Trans Energy Conversion Mishra Y, Mishra S, Tripathy M, et al (2009) Improving stability of a DFIG-based wind power system with tuned damping controller IEEE Trans on Energy Conversion Mol APJ (2000) The environmental movement in an era of ecological modernization Geoforum 31(1): 45 – 56 Muller S, Deicke M, De Doncker RW (2002) Doubly fed induction generator system for wind turbines IEEE Industry Appl Mag 8(3):26 – 33 Pena R, Clare JC, Asher GM (1996) Doubly fed induction generator using backto-back PWM converters and its application to variable speed wind-energy generation IEE Proceedings on Electric Power Applications, 143(3):231 – 241 Quirion P (2003) Allocation of CO2 allowances and competitiveness: A case study on the european iron and steel industry European Council on Energy Efficient Economy (ECEEE) 2003 Summer Study proceedings http://www.eceee.org/ conference proceedings/eceee/2003c/Panel 5/5060quirion/ Accessed 28 April 2008 Schubert U, Zerlauth A (1999) Innovative regional environmental policy: the RECLAIM-emission trading policy Environ Manag and Health 10(3): 130 – 143 Sijm JPM, Bakker SJA, Chen Y, et al (2006) CO2 price dynamics: the implications of EU emissions trading for electricity prices & operations IEEE PES General Meeting, Montreal, 18 – 22 June 2006 US Deptment of Energy (2007) EERE state activities and partnerships http:// apps1.eere.energy.gov/states/maps/renewable portfolio states.cfm Accessed July 2009 Wu F, Zhang XP, Godfrey K, et al (2007) Small signal stability analysis and optimal References 193 control of a wind turbine with doubly fed induction generator IET Gener Transm Distrib 1(5): 751 – 760 Xu L, Wang Y (2007) Dynamic modeling and control of DFIG-based wind turbines under unbalanced network conditions IEEE Trans Power Syst 22(1): 314 – 323 Yamamoto M, Motoyoshi O (1991) Active and reactive power control for doubly-fed wound rotor induction generator IEEE Trans Power Electron 6(4): 624 – 629 Yang LH, Xu Z, Østergaard J, Dong ZY, et al (2009) Oscillatory stability and eigenvalue sensitivity analysis of a doubly fed induction generator wind turbine system IEEE Trans Power Syst (submitted) Yang LH, Yang GY, Xu Z, et al (2009) Optimal controller design of a wind turbine with doubly fed induction generator for small signal stability enhancement In Wang et al ed Wind Power Systems: Applications of Computational Intelligence Springer, New York Yin X (2009) Building and investigating generators’ bidding strategies in an electricity market PhD thesis, Australian National University, Canberra Zhou X, James G, Liebman A, et al (2009) Partial carbon permits allocation of potential emission trading scheme in australian electricity market IEEE Trans Power Syst Appendix ZhaoYang Dong and Pei Zhang A.1 Weibull Distribution Other than the often used normal distribution, Weibull distribution has been used in many applications to model different distributions of power system parameters in probabilistic analysis Some important properties of this distribution are reviewed here Weibull Probability density function is defined as follows, f (t) = β η T −γ η β−1 e −( T −γ η )β , where η is the scale parameter (η > 0), γ is the location parameter (−∞ < γ < ∞) and β is the shape parameter (β > 0) f (t) and T or γ The Mean T of the Weibull pfd is given by Abernethy, 1996; Dodson, 1994: +1 T = γ + ηΓ β The kth raw moment μk of a distribution f (x) is defined by ⎧ ⎪ discrete distribution xk f (x), ⎪ ⎨ μk = ⎪ ⎪ ⎩ xk f (x)dx, continuous distribution 196 Appendix A1.1 An Illustrative Example Since the variable T > 0, according to the moment definition, +∞ μk = f (x)xk dx The kth raw moment of the two-parameter Weibull probability density function is +∞ μk = β η +∞ = +∞ = βη k ηk +∞ = ηk 0 Let T η β = x, then T η k T η β T e −( η ) T k d T β e −( η ) T k d β−1 T η T η β T e−( η ) T k · dT β−1 T η Tk ηk +∞ = ηk β−1 T η β β−1 T η β T T β e−( η ) βd e −( η ) d T η T η (A.1) T η β = x β Therefore, k T η k = xβ (A.2) Substitute Eq (A.2) into Eq (A.1), +∞ μk = η k Set k x β e−x dx (A.3) xn e−x dx (A.4) k = n, β +∞ μk = η k Since the gamma function is defined as +∞ Γ(n) = xn−1 e−x dx (A.5) Then, the kth raw moment of two-parameter Weibull probability density function is ⎧ ⎪ ⎨ μk = η k Γ(n + 1), (A.6) k ⎪ +1 ⎩ μk = η k Γ β A.2 Eigenvalues and Eigenvectors 197 The central moment definition is +∞ μk = f (x) x − T k dx, where T is the mean of Weibull distribution, and T = γ + ηΓ +1 β The central moments μk can be expressed as terms of the raw moments μk using the binomial transform k μk = j=0 k j (−1)k−j μj μ1k−j , (A.7) with μ0 = (Ni et al., 2003) k k μk = j=0 j (−1)k−j η j Γ j + μ1k−j , β where μ1 = T k k μk = (−1)k−j η j Γ j j=0 k = ηk j=0 k j (−1)k−j Γ j +1 β ηΓ +1 β j +1 β Γ +1 β k−j k−j A.2 Eigenvalues and Eigenvectors Power system small signal stability analysis is based on linearised system analysis which requires eigenvalue analysis This section gives an overview of eigenvalue and eigenvectors Consider a square matrix A = [ai,j ]n×n which can be the state matrix of a linearised dynamic power system model The eigenvalue calculation is to find a nonzero vector x = [xi ]1×n and scalar λ such that Ax = λx, (A.8) where λ is the eigenvalue, also known as characteristic value or proper value, of matrix A, and x is the corresponding right eigenvector (also known as the characteristic vector or proper vector) of matrix A 198 Appendix The necessary and sufficient condition for the above equation to have a non-trivial solution for vector x is that the matrix (λI − A) is singular This can be represented as a characteristic equation of A shown below, det(λI − A) = 0, (A.9) where I is the identity matrix The eigenvalues [λ1 , λ2 , , λn ] are the roots of this characteristic equation The characteristic polynomial of A is S(λ) = an λn + an−1 λn−1 + + a1 λ + a0 , (A.10) where λk , k = 1, , n, are the corresponding k− th powers of λ, and ak , k = 1, , n, are the coefficients determined via the elements aij of A Eq (A.11) can be obtained by expansion of det(λI − A as a scalar function of λ Each eigenvalue also corresponds to a left eigenvector y which is the right eigenvector of transpose of A, and (λI − AT )y = (A.11) For power system analysis, singular values are used in some stability studies They can be obtained through singular value decomposition Consider an m × n matrix B, if B can be transformed as in Eq (A.13), U ∗ BV = S 0 , where S = diag[σ1 , σ2 , , σr ], (A.12) where Um×m and Vn×n are orthogonal matrices, and all σk 0, then Eq (A.13) is called singular value decomposition and the singular values of B are σ1 , σ2 , , σr ; and r is the rank of B If B is a symmetric matrix, then matrices U and V coincide, and σk are the absolute values of eigenvalues of B Eq (A.13) is often used in the least square method, especially when B is ill-conditioned (Deif, 1991) A.3 Eigenvalues and Stability Power system small signal stability is based on modal analysis of linearised system around an operating point The time domain characteristics of a mode corresponding to an eigenvalue λi is eλi t , correspondingly the stability of the system is determined by the eigenvalues of the (linearised) system state matrix (Makarov and Dong, 2000; Kundur 1994; Dong, 1998) • Nonoscillatory modes: Real eigenvalues of a system correspond to nonoscillaotry modes A positive real eigenvalue leads to aperiodic instability and A negative real eigenvalue represents a decaying mode A.3 Eigenvalues and Stability 199 • Oscillatory modes: Conjugate pairs of complex eigenvalues correspond to oscillatory modes The real part and imaginary part of the eigenvalues define the damping and frequency of corresponding oscillations Let σ and ω represent the real and imaginary part of a complex of eigenvalues, λ = −σ ± jω, the frequency of oscillation in hertz is f= ω , 2π (A.13) and the damping ratio is −σ ξ= √ σ2 + ω2 (A.14) A dynamic system such as a power system can be modeled by Differentialand Algebraic Equations (DAEs): x˙ = f (x, y, p), f : Rn+m+q → Rn = g(x, y, p), g : Rm+n+q → Rm (A.15) where x ∈ Rn , y ∈ Rm , p ∈ Rq ; x is the vector of dynamic state variables, y is the vector of static or instantaneous state variables, and p is a system parameter which may change and therefore affects the system small disturbance stability properties The system is in an equilibrium condition if it satisfies = f (x, y, p), = g(x, y, p) (A.16) Solutions to Eq (A.17) are the system equilibrium points of Eq (A.16) which can be linearised at an equilibrium point when it is subject to small disturbances, ⎧ f f ⎪ ⎪ ⎨ Δx˙ = x Δx + y Δy, (A.17) ⎪ g g ⎪ ⎩0 = Δx + Δy, x y or in a simpler form as Δx˙ = AΔx + BΔy, = CΔx + DΔy, (A.18) If det D = 0, the state matrix As can be obtained by As = A − BD −1 C (A.19) It can then be analyzed for system small disturbance stability studies using eigenvalues and eigenvectors 200 Appendix References Abernethy RB (1996) The New Weibull Handbook Gulf Publishing, Houston Deif AS (1991) Advanced Matrix Theory for Scientists and Engineers, 2nd edn Abacus, New York Dodson B (1994) Weibull Analysis Amer Society for Quality, Milwaukee Dong ZY (1998) Advanced Technique for Power System Small Signal Stability and Control, PhD thesis, Sydney University, Sydney Kundur P (1994) Power System Stability and Control McGraw-Hill, New York Makarov YV, Dong ZY (2000) Eigenvalues and eigenfunctions Computational Science & Engineering, Encyclopedia of Electrical and Electronics Engineering, Wiley, pp 208 – 320 Ni M, McCalley JD, Vittal V et al (2003) Online risk-based security assessment IEEE Trans Power Syst 18(1): 258 – 265 Index A a heteroscedastic time series 63 area control error (ACE) 13, 65 automatic generation control (AGC) 12, 151 available transfer capacity (ATC) 160 B bilateral contract blackout 18, 71 5, C cascading failure 23 classification 29, 47–49, 59, 81, 118 correlation 47–49, 71, 72, 75 critical clearing time (CCT) 122, 158 cumulant 129 D deregulation 1, 2, 19, 108 distributed computing 100 E eigenvalue 197, 198 Electric Power Research Institute (EPRI) 27 electricity market 2, 52, 57, 188 Energy Management System (EMS) 30, 95, 151 equal area criteria (EAC) 160 extended equal area criteria (EEAC) 160 F facts 24 feature extraction 71 G Game theory 43 genetic algorithm (GA) 155 grid computing 29, 31, 95–97, 100, 101, 105, 107, 108 grid middleware 97 H heteroscedastic time series 52, 63, 84 high performance computing (HPC) 29 I independent system operator (ISO) K knowledge discovery in (KDD) 46 L lagrange multiplier 63 linear programming 155 database 202 Index load flow 109, 129, 140 load forecasting, 49, 112, 151 load modeling local correlation network pattern (LCNP) 71 local correlation network pattern (LNCP) 76 M Monte Carlo 32, 33, 108, 109, 122, 127, 128, 138, 139, 141–143 N neural network 93, 115, 179 O On-Load Tap Changer (OLTC) 13 optimal power flow (OPF) 107, 151 oscillatory modes 199 out-of-step relay 14 P parallel computing 114 phasor measurement unit (PMU) 34 power system stabilizer (PSS) 13 probabilistic load flow (PLF) 109, 129, 140 probabilistic reliability assessment (PRA) 41, 117, 123, 128, 129, 131, 135 probabilistic reliability index (PRI) 131 PSS E 111, 114 resource layer 97 S scale-free networks 35 service layer 98 simulated annealing (SA) 155 small signal stability 119, 122, 127, 137, 160 small world 26 state estimation 157 STATic COMpensator (STATCOM) 13 static var compensator (SVC) 13 supervisory control and data acquisition (SCADA) 151 support vector machine (SVM) 28, 48, 49 system restoration 35 T time series 37, 62, 72-29, 93 transient stability 118, 121, 125, 158 U under-frequency load shedding (UFLS) 14 under-voltage load shedding (UVLS) 14 V voltage stability 158 vulnerability 36 W R regression relay 12 29, 47–49 Weibull distribution 195 wide-area measurement/monitoring system (WAMS) 148 [...]... Planning Proceedings of the of the14th ISAP, November, 2007 2 Fundamentals of Emerging Techniques Xia Yin, Zhaoyang Dong, and Pei Zhang Following the new challenges of the power industry outlined in Chapter 1, new techniques for power system analysis are needed These emerging techniques cover various aspects of power system analysis including stability assessment, reliability, planning, cascading failure... cascading failure analysis, and market analysis In order to better understand the functionalities and needs for these emerging techniques, it is necessary to give an overview of these emerging techniques and compare these emerging ones with traditional approaches In this chapter, the following emerging techniques will be outlined Some of the key techniques and their applications in power engineering will be... pricing options to best meet individual customer needs (Shahidehpour et al., 2002) 1.3 Uncertainties in a Power System Uncertainties have existed in power systems from the beginning of the power industry Uncertainties from demand and generator availability have been studied in reliability assessment for decades However, with the deregula- 1.3 Uncertainties in a Power System 7 tion and other new initiatives... detailed in the subsequent chapters The main objective is to provide a holistic picture of the technological trends in power system analysis over the recent years 2.1 Power System Cascading Failure and Analysis Techniques In 2003, there were several major blackouts, which were regarded as results of cascading failures of power systems The increasing number of system instability events is mainly because... to investigate the impacts of DG on power system analysis, especially in the planning process The uncertainties DG brings to the system also need to be considered in power system analysis 1.4 Situational Awareness The huge impact in economic terms as well as interruptions of daily life from the 2003 blackouts in North America and the following blackouts in UL and Italy clearly showed the need for techniques. .. been obtained, cross validation is still needed because it is still possible that the derived load model may fail to present the system dynamics in some system operating conditions involving system transients It is worth noting that both research and engineering practice in load modeling are still facing many challenges There are many complex load modeling problems causing difficulties to the power industry;... significantly in many countries, which resulted in increasingly stressed power systems The insufficient investment in the infrastructure for reliable electricity supply had been regarded as a key factor leading to several major blackouts in North America and Europe in 2003 More recently, the initiative toward development of the smart grid again introduced many additional new challenges and uncertainties to the power. .. difficulties in power system analysis Recent major power system blackouts also remind the power industry of the need for situational awareness and more effective tools in order to ensure more secure operation of the system This chapter has reviewed these important aspects of the power system worldwide This chapter serves as an introduction and forms the basis for further discussion on the emerging techniques in. .. happening in the power industry, the level of uncertainty has been increasing dramatically For example, in a deregulated environment, although generation planning is considered in the overall planning process, it is difficult for the transmission planner to access accurate information concerning generation expansion Transmission planning is no longer coordinated with generation planning by a single planner... address the joint interactions among system components during cascading scenarios In the article by Chen et al., 2005, cascading dynamics is investigated under different system operating conditions via a hidden failure model This model employs linear programming (LP) generation redispatch jointed with dc load flow for power distribution and emphasizes the possible failures existing in the relay system Chen ...Zhaoyang Dong Pei Zhang et al Emerging Techniques in Power System Analysis Zhaoyang Dong Pei Zhang et al Emerging Techniques in Power System Analysis With 67 Figures Authors Zhaoyang... last key emerging technique covered in this book Chapter provides information leading to further reading on emerging techniques for power system analysis With the new initiatives and continuously... Fundamentals of Emerging Techniques · · · · · · · · · · · · · · · · · 23 2.1 Power System Cascading Failure and Analysis Techniques · · · 23 2.2 Data Mining and Its Application in Power System Analysis