On monitoring methods and load modeling to improve voltage stability assessment efficiency

Universit´ e Libre de Bruxelles (U.L.B.) September 2009 Facult´ e des Sciences appliqu´ ees

Service BEAMS

On monitoring methods and load modeling to improve voltage stability assessment efficiency

Benjamin Genˆet

Th` ese pr´ esent´ ee

en vue de l’obtention du titre de Docteur en Sciences de l’Ing´ enieur

Thesis director: Prof. Jean-Claude Maun President of the committee: Prof. Michel Kinnaert Members of the committee: Prof. Johan Gyselinck

Prof. Nouredine Hadjsa¨ıd Dr. Tevfik Sezi

Prof. Thierry Van Cutsem

Acknowledgements

I would like first to thank my thesis director, Prof. Jean-Claude Maun, who gave me the opportunity to do the research work that led to this thesis. I particularly appreciated the freedom he allowed me to have in the evolution of the work. His approach of the research where industrial collaborations are favored was an important source of motivation for me.

I naturally continue by thanking all the industrial contacts from Siemens, Elia and Tractebel Engineering – GDF Suez with whom I worked. Their contributions to this thesis were highly valuable. My special thanks go to Doctor Tevfik Sezi, for his support and advices, and to Philippe Goossens for his dynamism and his availability.

Two students, Pierre Vergauwe and Bruno Van Tuykom, participated to this research by doing their master thesis with me. I appreciated this joint work and I thank them for their contributions.

I am particularly grateful to all the members of the little team which helped me reviewing this thesis: Julie, Laure, Michael, Sergio and Vanessa. Your comments greatly contributed to the improvement of this document. I am very thankful for your commitment up to the final deposit.

I would like then to thank all my colleagues of the Beams – Energy department. The great working atmosphere certainly contributed to my motivation to work at the university.

Finally, many thanks to Laure who allowed me to work as much as I wanted during the

last few months, and for everything else.

Abstract

Power systems must face new challenges in the current environment. The energy market lib- eralization and the increase in the loading level make the occurrence of instability phenomena leading to large blackouts more likely. Existing tools must be improved and new tools must be developed to avoid them.

The aim of this thesis is the improvement of the voltage stability assessment efficiency.

Two orientations are studied: the monitoring methods and the load modeling.

The purpose of the monitoring methods is to evaluate the voltage stability using only measurements and without running simulations.

The first approach considered is local. The parameters of the Thevenin equivalent seen from a load bus are assessed thanks to a stream of local voltage and current measurements.

Several issues are investigated using measurements coming from complete time-domain sim- ulations. The applicability of this approach is questioned.

The second approach is global and uses measurements acquired by a Wide-Area Measure- ment System (WAMS). An original approach with a certain prediction capability is proposed, along with intuitive visualizations that allow to understand the deterioration process leading to the collapse.

The load modeling quality is certainly the weak point of the voltage security assessment tools which run simulations to predict the stability of the power system depending on different evolutions. Appropriate load models with accurate parameters lead to a direct improvement of the prediction precision.

An innovative procedure starting from data of long measurement campaigns is proposed to

automatically evaluate the parameters of static and dynamic load models. Real measurements

taken in the Belgian power system are used to validate this approach.

Contents

Introduction 1

1 Context . . . . 1

2 Power system operation and control . . . . 2

3 Power system stability . . . . 2

4 Adding a new layer of defense . . . . 3

5 Aims of this work . . . . 3

6 Structure of the document . . . . 4

7 Publications . . . . 5

I Voltage stability monitoring 7 1 Voltage stability phenomenon 9 1.1 Introduction . . . . 9

1.2 Classification of instabilities in power systems . . . . 10

1.3 Voltage collapse mechanisms . . . . 11

1.3.1 Definition . . . . 11

1.3.2 Examples . . . . 14

1.3.3 Countermeasures against voltage collapses . . . . 18

1.4 Online tools to assess voltage stability . . . . 20

1.4.1 Security-oriented tools . . . . 21

1.4.2 Monitoring-oriented tools . . . . 23

1.4.2.1 Local monitoring methods . . . . 23

1.4.2.2 Global monitoring methods . . . . 24

1.4.3 Wide-area measurement system architecture . . . . 25

1.5 Test systems and simulation tool . . . . 26

1.5.1 Power system 1: the simplified Belgian-French test system . . . . 27

1.5.1.1 Description of the power system . . . . 27

1.5.1.2 Voltage instability scenarios . . . . 28

1.5.2 Power system 2: the Nordic 32 . . . . 30

1.5.2.1 Description of the power system . . . . 30

1.5.2.2 Voltage instability scenarios . . . . 32

1.5.3 Simulation tool and methodology . . . . 37

1.6 Conclusion . . . . 37

2 Voltage stability monitoring based on local measurements 39 2.1 Introduction . . . . 40

2.2 Thevenin equivalent assessment based on local measurements . . . . 40

x CONTENTS

2.2.1 The Thevenin equivalent . . . . 40

2.2.2 Equations used by identification algorithms . . . . 41

2.2.3 Simple step computation . . . . 42

2.2.4 Recursive Least Square (RLS) algorithm . . . . 43

2.2.5 Kalman filter algorithm . . . . 43

2.2.6 Comparison . . . . 45

2.3 Local Thevenin equivalent assessment issues . . . . 46

2.3.1 Measurement issues . . . . 46

2.3.1.1 Load variation need . . . . 46

2.3.1.2 Angle reference . . . . 47

2.3.2 Identification issues . . . . 48

2.3.2.1 Identification algorithm parameter choice . . . . 48

2.3.2.2 Wind-up of the RLS scheme . . . . 49

2.3.2.3 Initialization . . . . 49

2.3.3 Improvement . . . . 49

2.3.3.1 Trace limitation . . . . 49

2.3.3.2 Auto-adaptivity of the forgetting factor parameter . . . . 50

2.3.4 Illustration . . . . 51

2.3.4.1 Presentation of the illustrative example . . . . 51

2.3.4.2 Algorithm parameter influence . . . . 53

2.3.4.3 Influence of the angle reference . . . . 56

2.3.4.4 Improvement of the RLS algorithm . . . . 59

2.3.4.5 Conclusions on the illustrative examples . . . . 63

2.4 Results with dynamic simulations of realistic power systems . . . . 65

2.4.1 Algorithm parameter optimization . . . . 65

2.4.1.1 RLS (forgetting factor and trace limitation) . . . . 65

2.4.1.2 Kalman (measurement covariance) . . . . 66

2.4.2 Auto-adaptivity . . . . 68

2.4.3 Angle reference . . . . 70

2.5 Conclusion and perspectives . . . . 74

3 Voltage stability monitoring based on global measurements 77 3.1 Introduction . . . . 78

3.2 Existing global monitoring methods . . . . 79

3.2.1 Regional reactive reserve monitoring . . . . 79

3.2.2 WAMS method to monitor the voltage stability of a corridor . . . . . 80

3.3 Actual Thevenin equivalent computation . . . . 82

3.3.1 Description . . . . 82

3.3.2 Implicit assumptions and limitations . . . . 86

3.3.2.1 Maximum loadability point and limit of stability . . . . 86

3.3.2.2 Static model of a dynamic system . . . . 87

3.3.2.3 Inadequacy to compute power margins . . . . 87

3.3.3 Results . . . . 88

3.4 New method based on PMU Measurements . . . . 88

3.4.1 Concept . . . . 89

3.4.2 Required data . . . . 90

3.4.2.1 Voltage phasors . . . . 91

CONTENTS xi

3.4.2.2 Status of the generators . . . . 92

3.4.2.3 Topology . . . . 93

3.4.3 Algorithm . . . . 93

3.4.4 Improved algorithm with prediction . . . . 97

3.4.5 Interpretation of the V SI value . . . . 99

3.4.6 Results of the basic algorithm . . . 101

3.4.6.1 Bus index . . . 102

3.4.6.2 Power system index . . . 105

3.4.7 Results underlying the advantage of the prediction . . . 106

3.4.8 Example of corrective actions triggered by the PMU method . . . 111

3.5 Visualization of the monitoring information . . . 114

3.5.1 Temporal evolution . . . 114

3.5.2 Geographical representation . . . 114

3.5.2.1 Belgian-French test system – Cigre 2 scenario . . . 115

3.5.2.2 Nordic 32 test system – IL scenario . . . 121

3.5.2.3 Nordic 32 test system – VS1 scenario . . . 125

3.5.3 Geographical representation with display of the nearest generator . . . 128

3.5.3.1 Nordic 32 test system – VS4 scenario . . . 128

3.5.3.2 Nordic 32 test system – VS14 scenario . . . 133

3.5.4 Regional application . . . 137

3.6 Conclusion . . . 139

II Load model assessment 141 4 Load models and identification methods 143 4.1 Introduction . . . 143

4.2 Load models . . . 144

4.2.1 Component-based vs. measurement-based model . . . 145

4.2.2 Static vs. dynamic load model . . . 146

4.2.3 Linear vs. nonlinear . . . 150

4.2.4 Short-term vs. long-term dynamics . . . 150

4.2.5 Small signal vs. large signal models . . . 151

4.2.6 Load model error . . . 152

4.2.7 Other characteristics of load models . . . 152

4.3 Field conditions needed for load model parameter assessment . . . 153

4.3.1 Voluntary small voltage variations . . . 153

4.3.2 Natural voltage variation of small amplitude . . . 154

4.3.3 Natural voltage variation of large amplitude . . . 155

4.4 Parameter identification methods . . . 155

4.5 Conclusion . . . 156

5 Pre-processing of measurements 157 5.1 Introduction . . . 157

5.1.1 Structure . . . 158

5.1.2 Approach . . . 159

5.2 Loading data algorithm . . . 160

xii CONTENTS

5.2.1 Method . . . 160

5.2.2 Presentation of the measurements and results . . . 161

5.2.2.1 Measurement campaign n

1 . . . 161

5.2.2.2 Measurement campaign n

2 . . . 162

5.3 Event detection . . . 163

5.3.1 Method . . . 163

5.3.2 Results . . . 168

5.3.2.1 Influence of the method parameters . . . 168

5.3.2.2 Examples illustrating the windowed Cusum algorithm . . . . 169

5.3.2.3 Examples with active and reactive power . . . 172

5.4 Conclusion . . . 175

6 Static load model parameter assessment 177 6.1 Introduction . . . 177

6.2 Static load model parameter identification . . . 178

6.2.1 Method . . . 178

6.2.2 Results . . . 181

6.2.2.1 Approach to tune the method parameters . . . 181

6.2.2.2 Examples of results . . . 184

6.2.2.3 Statistical results of the two measurement campaigns . . . . 187

6.3 Improvement of reactive load model . . . 192

6.3.1 Reactive load model: theory and existing solutions . . . 192

6.3.1.1 Theoretical explanation . . . 192

6.3.1.2 Existing solutions . . . 194

6.3.2 Method to assess the parameters of the proposed model . . . 196

6.3.3 Results . . . 198

6.4 Conclusion . . . 199

7 Dynamic load model parameter assessment 201 7.1 Introduction . . . 201

7.2 Simplex algorithm . . . 202

7.2.1 Principle and versions . . . 202

7.2.1.1 Principle . . . 202

7.2.1.2 Nelder-Mead simplex . . . 204

7.2.1.3 Original Hanus algorithm . . . 205

7.2.1.4 Hanus algorithm (variant 1) . . . 207

7.2.1.5 Hanus algorithm (variant 2) . . . 207

7.2.1.6 General comments on the different variants . . . 208

7.2.2 Number of vertices in the simplex . . . 209

7.2.3 Initialization . . . 209

7.2.4 Suppression of the bounds of the parameters . . . 211

7.2.5 General comments on the use of the simplex algorithm . . . 212

7.3 Dynamic load model parameter identification on single event . . . 213

7.3.1 Method . . . 213

7.3.1.1 Model and parameters to identify . . . 213

7.3.1.2 Principle . . . 214

7.3.1.3 Cost function . . . 215

CONTENTS xiii

7.3.2 Results . . . 216

7.4 Dynamic load model parameter identification on multiple events . . . 220

7.4.1 Method . . . 220

7.4.2 Results . . . 224

7.4.2.1 Main Results . . . 224

7.4.2.2 Results with events grouped by time classes . . . 228

7.4.2.3 Results with improved reactive load model . . . 230

7.5 Conclusion . . . 231

Conclusion 233 1 Main contributions on voltage stability monitoring . . . 233

2 Main contributions on load model parameter assessment . . . 235

3 Directions for future work . . . 237

Bibliography 239

Introduction

1 Context

Transmission power grids are the largest systems built by men. They extend over distances that can go up to thousands of kilometers and include a huge number of elements: overhead lines, underground power cables, power plants, transformers, loads, and many more. The operation of such systems is a real challenge, totally hidden for the final customer who only wants that the light switches on when he needs it. A reliable power supply has become natural for everyone and maintaining the highest standards of quality is mandatory for power system operators.

However, recent blackouts remind us that this task is not so easy. Their frequency is not high, but the consequences are huge. The following examples are sufficiently relevant:

55,000,000 people affected by the North-East USA blackout on August 14, 2003 ; 56,000,000 suffered from the Italian blackout on September 28, 2003 ; 10,000,000 were the victims of the European incident on November 4, 2006. The economical losses for those country are colossal.

As these examples show, it is well worth developing tools that will help avoiding blackouts.

As if the complexity of the transmission system was not sufficient, the current evolutions make the operations even more complicated. The electrical power consumption is increasing on a regular basis. The current power systems, that were mainly designed more than 50 years ago, are approaching their physical limits. The construction of new transmission lines has become nearly impossible due to political and environmental reasons. The liberalization of the electricity market has also completely changed the way of running the power system.

The different countries were previously interconnected to ensure a mutual support in case of incident. The international tie-lines are now used to buy and sell energy far away. If the main aim – reducing the cost of electricity – is laudable, the consequence is a further weakening of the transmission system.

The operators and the power system engineers have to deal with these challenges. More-

over, they must keep the security of supply to a high level, and even increase it. The only way

consists in improving the knowledge of the power system to operate it in a smarter way. That

can be achieved by improving the current tools which help to operate and protect the power

system and also by developing new tools. The existing layers of defense must be strengthened

and new layers must be created. This multiple-layer architecture will be able to increase the

security of the power system [1].

2 Introduction

2 Power system operation and control

The current practice to avoid large events implying loss of supply is based on a structure with two layers:

• The centralized security-oriented tools are implemented in the control centers of the transmission system operators. They aim at evaluating if the system is able to withstand different evolutions which could be encountered in the next future. A very classical approach is the N − 1 contingency analysis. The system must be able to face the loss of any element without loss of supply.

These tools rely on the measurements taken in the power system to make simulations starting from the current state. As the measurements are asynchronous, they cannot be used together directly. The state estimator must consolidate them to construct a coherent picture of the whole system. Security analysis is then performed and its results inform the operators if their system is able to face any simulated contingency. If this is not the case, preventive actions may be taken to reinforce the system configuration.

The time needed to acquire the measurements, to run the state estimation and the security analysis is of several tens of seconds minimum.

• The local protective devices are placed in the substations. They protect a single element of the power system by taking local measurements. If a fault is detected, the element is temporarily or definitively disconnected. These corrective actions are generally taken in maximum some hundreds of milliseconds.

Remote measurements may also be used, but on a very local basis. The communication is made point-to-point, from one device to another.

The gap between these two layers of defense is enormous. On the one hand, the security tools generally use a static picture of the power system and give a delayed information. On the other hand, the protective devices work very quickly but only locally, with few communi- cations. This approach static/central and dynamic/local was sufficient in the past, when the power systems were not operated so close to their limits.

3 Power system stability

With the increase in the loading level, the occurrence of power system instabilities has become more likely. These complex dynamic phenomena instabilities are sorted in three categories:

angular, frequency and voltage instabilities. They involve at least several elements of the power system and may even extend to a complete large interconnected grid. They are dy- namic, with time constants ranging from less than one second to several tens of minutes.

The operators are currently unable to see these dynamic events because only a static view

of their power system is available to them with the aforementioned measurement method.

4 Adding a new layer of defense 3 However, the power system must be able to face these instabilities, preferably without loss of supply. Often, this is accomplished by adding new tools in the two existing layers of defense. On the superior centralized layer, simulations taking into account the main mecha- nisms of the instabilities are performed to anticipate potential evolutions of the power system.

Preventive actions may be taken when a critical situation is detected. On the bottom local layer, protective relays can also be implemented to take corrective actions if the unstable situations are detectable locally. This is the case for frequency and voltage instabilities.

4 Adding a new layer of defense

A new measurement technique is spreading: the Wide-Area Measurement Systems (WAMSs).

They are constituted of a network of Phasor Measurement Units (PMUs) which are time- synchronized thanks to a Global Positioning System (GPS) signal. Each PMU is thus able to compute phasors from the local measurements in a common angle reference. The measure- ments are then centralized, giving a dynamic view of the power system thanks to the high refreshment rate (up to 50 or 60Hz).

The WAMSs give the opportunity to have a better insight of the phenomena. However, the phasors are only raw data. The relevant information, different for each kind of instability, must be extracted and presented in an intuitive way. This constitutes a monitoring system which takes place between the security and the protective layer. Indeed, it is dynamic and based on the measurements like the protective relays, but it is centralized like the security- oriented tools.

This intermediate layer of defense provides more information to the operators on the condition of the power system regarding dynamic instabilities. Therefore, they can operate the grid accordingly, and possibly take preventive actions. If the instability phenomenon is too fast, automatic corrective actions can also be triggered. Again, the intermediate situation of the layer is visible.

5 Aims of this work

This thesis focuses on the voltage instability phenomenon, also referred to as voltage col- lapse. The emphasis is on the long-term mechanisms leading to this kind of instability. This document offers an attempt at answering the general question:

How can the voltage stability assessment be improved?

4 Introduction

Two angles of attack have been chosen:

• The voltage stability assessment based on monitoring tools is a domain where little research has been done. The first part of this thesis studies the existing monitoring methods, either based on local or global measurements. A new method is proposed based on a WAMS.

• The security-oriented tools assessing voltage stability are already well developed. As stated before, this class of methods run simulations. Therefore, they rely on the models of the different power system elements. Most of them are well known and modeled, the results can thus be considered as quite accurate. There is however one notable exception: the loads. Their diversity, their variability in time and the difficulty to assess their model parameters make the loads the least known element of the power system.

The second part of this thesis proposes several methods to assess in an automated way the parameters of different load models. A special attention is paid to the model dealing with the long-term voltage stability phenomenon.

6 Structure of the document

This document is composed of two parts:

• The first part focuses on the monitoring methods that aim at evaluating the long-term voltage stability of the power system. It is further divided in three chapters:

– Chapter 1 introduces the subject. The mechanisms leading to a voltage collapse are detailed and simple examples are given to illustrate them. A literature review on the existing monitoring methods is then given. Finally, the two power systems that will be used throughout this first part are detailed.

– Chapter 2 deals with the monitoring methods based on local measurements. The theory is derived and analyzed, and some improvements are proposed. The behav- ior of the methods is illustrated on simple examples and on dynamic simulation results.

– Chapter 3 concerns the monitoring methods based on global measurements. The approach used in the existing methods is discussed. The algorithm to compute the actual Thevenin equivalent is given. A new method based on PMUs is then detailed and illustrated with several collapse scenarios. The importance of visualization for the monitoring is finally emphazised.

• The second part addresses the load modeling topic. The goal is to develop methods

that are able to evaluate automatically the parameters of a load model starting from

field measurements. Two long measurement campaigns (up to one month) have been

carried out without provoking any voluntary voltage variations. The methods presented

7 Publications 5 in this part are developed to extract the load parameters thanks to the natural voltage variations observed in the power system. This part is divided in four chapters:

– Chapter 4 is a large literature review of previous works on load modeling. The load models and their characteristics are detailed. The different approaches to identify the parameters are explained with special attention on the field conditions that are required. The identification algorithms are then detailed.

– Chapter 5 describes how the measurements of a long campaign must be treated to be usable in a load model parameter identification algorithm. That includes a robust algorithm to detect the time of the voltage steps in the measurements.

– Chapter 6 details how the parameters of a static load model can be derived ef- ficiently. A particular behavior of the reactive load model is highlighted and an improved model is proposed, along with the technique to identify its parameters.

– Chapter 7 deals with the dynamic load model parameter assessment. The method is presented and a particular importance is granted to the identification technique used. The difficulty of assessing the parameters of a long-term dynamic model is illustrated and an efficient technique is proposed.

Finally, the general conclusions are drawn and some perspectives of the work are given.

7 Publications

The following publications have been made during the research work that has led to this thesis:

• Tevfik Sezi, Jean-Claude Maun, Jacques Warichet and Benjamin Genˆet, Power System Protection and Dynamic Performance Assessment, in Procedings of the Cigr´e Con- ference on Monitoring of Power System Dynamics Performance, Moscow, April 25-27, 2006.

• Benjamin Genˆet and Jean-Claude Maun, On-line Voltage Stability Monitoring Using Synchronized Phasor Measurements, in Proceedings of the 3rd IEEE Young Researchers Symposium in Electrical Power Engineering, Ghent, April 27-28, 2006.

• Benjamin Genˆet and Jean-Claude Maun, Wide-Area System Protection Scheme against Voltage Collapse, in Proceedings of the 15th International Conference on Power System Protection, Bled, Slovenia, September 6-8, 2006.

• Benjamin Genˆet and Jean-Claude Maun, Voltage Stability Monitoring Using Wide Area

Measurement Systems, in Proceedings of the PowerTech Conference, Lausanne, Switzer-

land, July 1-5, 2007.

6 Introduction

• Tevfik Sezi, Jean-Claude Maun and Benjamin Genˆet, Response-based System Integrity Protection Scheme Against Voltage Instability Using Phasor Measurement Units, in Pro- ceedings of the 4th International Conference Power System Protection and Automation, New Delhi, India, 21-22 November, 2007.

• Tevfik Sezi, Jacques Warichet, Benjamin Genˆet and Jean-Claude Maun, Bringing New Visualization Tools for the Detection and Mitigation of Dynamic Phenomena in the Transmission System, in Proceedings of the Cigr´e Session 2008, Paper C2-112.

• Benjamin Genˆet, Tevfik Sezi and Jean-Claude Maun, Comparison of Thevenin’s Equi- valent based Methods to Monitor Voltage Stability, in Proceedings of the Power System Computation Conference (PSCC), Glasgow, Scotland, July 14-18, 2008.

• Benjamin Genˆet and Jean-Claude Maun, Dynamic Load Parameter Assessment Based

on Continuous Recorder Measurements, in Proceedings of the PowerTech Conference,

Bucharest, Romania, June 29 - July 2, 2009.

Part I

Voltage stability monitoring

1

Voltage stability phenomenon

Contents

1.1 Introduction . . . . 9 1.2 Classification of instabilities in power systems . . . . 10 1.3 Voltage collapse mechanisms . . . . 11 1.3.1 Definition . . . . 11 1.3.2 Examples . . . . 14 1.3.3 Countermeasures against voltage collapses . . . . 18 1.4 Online tools to assess voltage stability . . . . 20 1.4.1 Security-oriented tools . . . . 21 1.4.2 Monitoring-oriented tools . . . . 23 1.4.3 Wide-area measurement system architecture . . . . 25 1.5 Test systems and simulation tool . . . . 26 1.5.1 Power system 1: the simplified Belgian-French test system . . . . 27 1.5.2 Power system 2: the Nordic 32 . . . . 30 1.5.3 Simulation tool and methodology . . . . 37 1.6 Conclusion . . . . 37

1.1 Introduction

This chapter introduces the subject studied in the first part of the thesis: the voltage stability

monitoring.

10 Voltage stability phenomenon A general introduction on the classification of the instabilities in the power system is first given. The voltage stability concept is then defined by pointing the different causes of collapse. Easily understandable examples illustrate the concept. The corrective actions that may be taken to stop or slow down the instability process are briefly presented.

A literature review on voltage stability is then given, with a special emphasis on the monitoring methods that can detect the incipient instabilities.

The last section is dedicated to the presentation of the test systems and the scenarios that are used in Chapters 2 and 3. The presentation of some basic results completes the illustration of the voltage collapse mechanism given by the simpler examples.

1.2 Classification of instabilities in power systems

A definition of power system stability is given in [2]:

Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact.

Different kinds of instabilities can be defined and their usual classification is given in Figure 1.1.

Power system stability

Rotor angle stability Frequency stability Voltage stability

Small-disturbance angle stability

Transient stability

Short Term

Short Term Long Term

Short Term Long Term Large-disturbance

voltage stability

Small-disturbance voltage stability

Figure 1.1: Classification of power system stability [2, 3].

The first class of instability is the rotor angular instability. It refers to the ability of

synchronous machines of an interconnected power system to remain in synchronism after a

disturbance [2]. Two groups corresponding to the analysis tools used are further defined. The

1.3 Voltage collapse mechanisms 11 small-disturbance angle stability is studied by linearizing the system around the operating point where a disturbance is applied. The stability is then related to the damping of the oscillations and may expand within a time frame ranging from 10 to 20 seconds. The large- disturbance angle stability or transient stability concerns the ability of generators to maintain the synchronism after a short-circuit or a line trip. It is studied with a dynamic model of the power system. The time frame is generally between 3 and 5 seconds. Both groups are classified as short-term.

The second class relates to frequency instabilities. They happen when a significant im- balance between load and generation power is observed in a power system. This is often due to an islanding of a part of the network which is not at a load/generation equilibrium. Most of the time, this is a short-term phenomenon with a very fast decay of the frequency, but in some complex cases long-term instability may be observed.

The last class is the one on which this thesis focuses. The voltage instability phenomenon, mainly in its long-term form, is detailed in the next section. The following two chapters discuss the monitoring methods that allow to observe this kind of instability. The second part of the thesis addresses the load modeling. The main aim is to improve the load model quality in the voltage stability simulations used in planning studies or in online tools. However, the load modeling is also of crucial importance for other kinds of instabilities such as inter-area oscillations and frequency instabilities. The development described in the second part can certainly improve the quality of their modeling.

It must be stated that the different instability mechanisms are much more strongly linked to each other than it may seem from the above classification. When the point of instability approaches, several problems may appear. For instance, a deterioration of the system mainly driven by the phenomena leading to a voltage collapse may eventually lead to the collapse of the system due to the loss of synchronism of a generator. The classification remains however useful because it defines the modeling requirements needed to study the main cause of instability.

1.3 Voltage collapse mechanisms

The literature on voltage stability is very large and covers a wide domain of applications, ranging from planning studies to protection devices. Reference [4] provides quite an exhaustive bibliography of the published material on the topic up to 1996, covering all aspects of the problem. The books [5, 6] and the Cigr´e report [7] may be consulted to obtain a large overview of this stability problem.

1.3.1 Definition

Voltage stability is a well-known problem which has led to some major blackouts in the last

years. As for the power system stability, a definition is given here [5]:

12 Voltage stability phenomenon

Voltage instability stems from the attempt of load dynamics to restore power consumption beyond the capability of the combined transmission and generation system.

As can be seen in this definition, there are three major causes of voltage instabilities:

• Load dynamics. Loads are the main cause of voltage instabilities. The increase in the power consumption due to the natural evolution along the day or due to some dynamic effects is a source of stress for the power system.

The dynamic effects find their origin in different phenomena:

– The Load Tap Changer (LTC) of the transformers. Their role is to keep the voltage on the low voltage side of the transformer in a defined band near the rated voltage by changing the ratio of the transformer.

As most of the loads are voltage dependent, a disturbance causing a voltage de- crease at a load bus will cause a decrease in the power consumption. This tends to favor stability. However, the LTC will then begin to restore the voltage by chang- ing the ratio step by step with a predefined timing. The increase in voltage will be accompanied by an increase in the power demand which will further weaken the power system stability.

The LTC may also be unstable in themselves. The same post-disturbance situa- tion is supposed. If a voltage decline is observed on the low voltage side of the transformer during the restoration process, the LTC is becoming unstable. The cause is the increase in the voltage drop in the transmission system that has a predominant influence on the change in the ratio. Any further attempt to restore the voltage will lead to a more pronounced reduction of the latter. The process will stop when the system collapses or when the LTC hits its limits. In the second case, the load voltage will be very low. An example is given in Section 1.3.2.

– Thermostatic loads. Electrical heating is generally controlled by a thermostat which has a temperature set point. The thermostat acts by regularly switching the heating resistance on and off. This behavior of each individual load is not seen at a high voltage level thanks to the aggregation of a large number of such loads.

A constant power consumption is observed.

In the case of a voltage decrease, the power consumption, hence the heating power, will be reduced. Therefore, the thermostat will tend to supply the load during a longer time interval. The aggregated response of a huge group of this kind of loads is seen as a restoration of the power, comparable to the one of the LTC.

– Induction motors. They have a dynamic behavior characterized by a shorter time constants. A restoration process is also observable following a voltage reduction because the motor must continue to supply a mechanical load with a torque more or less constant.

A more serious situation arises when the voltage decrease causes a reduction of

the electromagnetic torque sufficient to provoke a motor stalling. In this case, the

reactive power consumption increases drastically and induces an important voltage

drop that may lead to a short-term voltage collapse.

1.3 Voltage collapse mechanisms 13 The load modeling for voltage stability is of the utmost importance. The load mo- dels and their parameters are addressed in the introducing chapter of the second part (Chapter 4).

• Transmission system. Each transmission element, line or transformer, has a limited transfer capability. It is dependent on several factors:

– The impedance of the transmission element ; – The power factor of the load ;

– The presence of voltage controlled sources (generators or Static Var Compensator – SVC) at one or both extremities of the element and the voltage set point of these sources.

– The presence of reactive compensation devices (mechanically switched capacitors or reactors).

The influence of the other two elements highlighted in the definition is clearly apparent.

The theoretical equations are not derived here. The complete theory may be found in [5].

• Generation system. When the power system flows increase, the transmission system consumes more reactive power. The generators must increase their reactive power out- put to supply these losses. Of course, the current that can be delivered is not unlimited for evident thermal reasons. The capability curves that define the accessible operating points of the generator are then derived.

Two kinds of limiters can act to protect the machines from overheating [3]:

– Over-Excitation Limiter (OEL): avoids thermal overheating of the rotor windings due to a field current above a maximum admissible value.

– Stator Current Limiter (SCL): similar to the OEL but for stator windings. The stator current is limited by decreasing the field current.

If these limiters are activated, the reactive power production of the generator is then blocked on the capability curves. The voltage is no longer controlled. This kind of event will cause sudden changes in the stability of the power system, as the second example of Section 1.3.2 shows.

Because these limits are thermal, a current practice consists in taking advantage of the thermal inertia of the machine [8]. A limited overload can thus be allowed for a few tens of seconds (typically 10 to 60 seconds) before decreasing the reactive power output.

During this time, the generator still controls its voltage.

As described above, the three sources are strongly linked one to another. Simple examples

highlighting the separated influence of each element are presented in the next section. In a

real voltage collapse case, the complete instability mechanism generally involves all three

aspects, and often other instability phenomena too.

14 Voltage stability phenomenon Voltage instabilities are also classified according to the time constant of the main phe- nomenon. Figure 1.2 regroups all the power system elements that may be involved in a system collapse. As stated ealier, this thesis mainly deals with the long-term phenomena.

0.8 0.9 1

10

10

10

10

10

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Time [s]

Protective relaying including overload protection

Time [s]

DC converter DC conv. LTC System operator

Generator inertia Boiler dynamics Line overload

SVC Generation change/AGC

UVLS Power plant operators

Mech. react. comp. Excitation limiter Gas Gas turbine start-up Prime mover control Thermostatic load

LTC Generator dynamics

Induction mot. dyn. Load increase

Short-term voltage stability Long-term voltage stability

Figure 1.2: Voltage stability phenomena and time responses [6]

1.3.2 Examples

The simple test system shown in Figure 1.3 illustrates the main mechanisms that may lead to a voltage collapse. This is a simplified version of the example presented in [5]. It is constituted of:

V

V

3

V

V

µ : 1

1 : 1 X_13b = 0.054 X_13a = 0.054

Z_th= j 0.01 E_th= 1.1

P₂= 450MW

Load P₄= P₀ V₄² Q₄= Q₀ V₄² X₂₃= 0.016

X₃₄ = 0.001

Figure 1.3: Small test power system (modified version of an example given in [5]).

1.3 Voltage collapse mechanisms 15

• A load which behaves as an impedance with a constant power factor (tan φ = 0.2) ; P

= P

V

V

Q

= P

5

V

V

(1.1)

• A transformer equipped with LTC which controls the voltage at the load bus with a set point of 1p.u. The reduced ratio is given by µ ;

• A generator connected to bus 3 through a transformer with a fixed ratio. The voltage of bus 2 is controlled by an Automatic Voltage Regulator (AVR) ;

• Two long transmission lines in parallel between busses 1 and 3 ;

• A Thevenin equivalent representing an external network.

The main parameters of the system are indicated on the figure in p.u. or in MW. The base power is 100MVA.

Two examples are described in further detail. The classical PV-curves – or nose curves – of the system are used to explain the different steps of the deterioration that lead to instability.

The results have been obtained with static simulations. Section 1.5 displays the results of dynamic simulations of two larger power systems that complete the examples presented here.

The first example of collapse illustrates the instability of the LTC. The initial event is the trip of local generator G

. Figure 1.4 provides the main tools that allow to understand the succession of events.

Initially, the system is in steady-state at point A. The active load power is equal to 1350MW. The voltage at bus 3 is equal to one. As the controller of the LTC is active, the voltage of bus 4 is in the deadband around the set point. Therefore, V

≈ 1. The blue PV curve gives the potential evolution of voltage V

when power P

is increased in the current configuration of the system.

The turquoise vertical line gives the Long-Term Equilibrium (LTE) of the load. It is reached when the voltage at the load is equal to the voltage set point of the LTC, which is the case in normal conditions when the LTC is active and the system is in steady-state. In the current example, power P

is equal to the nominal power P

represented by the vertical line. The intersection between the upper part of a PV curve and the LTE is a steady-state working point for the power system.

The green curve represents the Short-Term Equilibria (STE) of the load. They give the behavior of the load when a fast voltage change is observed at the load bus, before the action of the LTC. If the reactance of the transformer with LTC is neglected, the STE may be expressed as a function of voltage V

and is plotted in Figure 1.4.

P

= P

V

µV

(1.2)

16 Voltage stability phenomenon

500 1000 1500 2000 2500 3000

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

V3 [pu]

P₄ [MW]

base case loss of G₂

long−term load characteristic short−term load characteristics A

B

C

Figure 1.4: PV curves for the first example.

Then a disturbance occurs: generator G

trips. As the configuration of the system has changed, a new PV curve must be computed (red curve in the figure). The transition between the two PV curves is made along the STE of the load. The new operating point is therefore point B.

The voltage at bus 4 is now smaller than the set point. The LTC controller begins to act and reduces the ratio µ to boost the voltage at the load. The working point moves along the red PV curves towards the new STE. A new STE is represented every time the ratio reaches a reduction of 5%. The voltage at bus 4 increases with the load consumption during all the first tap changes.

A critical point is then reached: point C. From this point, the decrease in the transformer ratio is accompanied with a decrease in the load power, and hence of the voltage at bus 4.

This means that the favorable effect of the tap change on the voltage is more than covered by the increase in voltage drop in the power system. The LTC is thus in an unstable process.

Any further tap change will lead to an aggravation of the situation.

This situation was predictable. Indeed, the red PV curve has no intersection with the

LTE, meaning that the LTC will not be able to bring the voltage at the load bus back to the

set point.

1.3 Voltage collapse mechanisms 17 The instability of the LTC is also illustrated in Figure 1.5. Voltages V

and V

are given as a function of the ratio of the transformer µ when the system is in the situation depicted by the red PV curve. Point B is represented by the intersection of the two curves. When the ratio is reduced, the voltage V

increases. This is the expected behavior of a LTC. Of course, the increase in the load is synonym of a decrease in voltage at bus 3. When µ becomes lower than 0.75, the voltage at bus 4 also begins to decrease. The LTC does not succeed in improving the voltage and causes a deterioration of the state of the power system.

As a concluding remark for this example, it should be noted that the ratio µ has been left free to vary in a very wide range to highlight the instability phenomenon. A real LTC would hit its limit well before instability begins in this example. This practice is common in small examples shown in the literature. However, this is not just a theoretical concept and LTCs in a real power system can become unstable within their range.

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

V [pu]

µ [pu]

V₃ V₄

Figure 1.5: Evolution of the voltages with the reduced ratio of the transformer at both its sides (first example).

The second example illustrates the important effect of generator limiters on the voltage stability of the power system.

The initial situation is again represented by the blue PV curve (Figure 1.6). The LTE and STE of the load are illustrated in the same colors as before. The initial load power is 1800MW.

The first disturbance is caused by the loss of one of the two transmission lines. The red PV curve gives the evolution of the voltage in this new configuration. As in the previous case, the transition from one curve to the other is made by following the STE of the load (from point A to point B).

The LTC then starts its restoration process. Each STE is separated here by a 3% change

of the ratio µ. A significant difference with respect to the previous example is that the new

PV curve has here an intersection with the LTE. The situation is thus not unstable and the

LTC would stop a little before having reduced the ratio by 12%.

18 Voltage stability phenomenon Unfortunately, the system does not have time enough to reach this point. When the system is at point C, it is assumed that generator G

is above its steady-state power limits.

A limited overload has been accepted for some time, but the OEL finally acts to reduce the reactive power output to 400MVAr. The loss of the local voltage control at bus 2 leads to a further shrinking of the PV curve (orange curve). The transition follows the STE and the new operating point is given by point D.

This point is already below the maximum power of the orange PV curve. As in the previous example, subsequent tap changes would further worsen the situation.

500 1000 1500 2000 2500 3000

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

V3 [pu]

P₄ [MW]

base case line opening

line opening + limitation of G₂ long−term load characteristic short−term load characteristics A

B

C

D

Figure 1.6: PV curves for the second example.

1.3.3 Countermeasures against voltage collapses

In addition to the aforementioned books, the report [9] offers a complete classification of all the countermeasures that may be used to mitigate voltage collapses. The classification made in [10] is also useful.

The efficient corrective actions to avoid voltage collapses given in those references are summarized hereafter:

• LTC control modification. It has been seen that the LTCs are an important cause of

voltage instability because their action implies a load restoration. Different strategies

1.3 Voltage collapse mechanisms 19 may be applied using the LTCs if a critical situation regarding voltage stability is detected:

– Tap changers may be blocked on the current tap. This prevents further deterio- ration of the stability but does not improve it. Further control actions will be required to bring the voltage of the weak busses back close to the rated value.

– The set point used by the LTC controller may be decreased [11]. A load where voltage is smaller than the set point will be restored to a lower power. A load where voltage is higher will be decreased, thus provoking an increase in voltage stability.

– The LTC logic may be reversed [12, 13]. Instead of controlling the low voltage side of the transformer, the LTC tries to restore the voltage on the high voltage side. This can be achieved by decreasing the voltage on the load side, which will consequently lead to a decrease in the load power. These actions may be seen as distributed load shedding. No customer is completely disconnected but they are all subjected to a voltage reduction.

• Load shedding. Even though load shedding is a disruptive practice, it is a very effective countermeasure against voltage collapse. In most cases, it results in an immediate voltage improvement. Several successive load sheddings may be performed to get back to an acceptable voltage.

The inconvenience of this action must be evaluated with regard to the situation of the whole power system. If some percents of load shedding are able to save the system from complete failure, the drawback is very minor. This countermeasure is very cost effective. Its implementation is simple and the risk of occurrence of voltage instability is small. However, due to the disturbance caused to the customers that have been shed, this action must be the very last line of defense.

The concept of non-disruptive load control presented in [14, 15] enables to decrease the impact of load shedding on the customers. The idea is to shed non-priority loads on a very local basis. For instance, air-conditioning systems and freezers have long thermal time-constants and their temporary disconnection will not affect the comfort of their users much. The current development of smart grids goes in this direction of demand-side management.

• Action on generation devices. Generation devices has to be understood in this thesis in a broad sense, including generators but also reactive compensation. The following actions may be taken:

– Switch on capacitive compensation, switch off inductive compensation. These mea- sures are obvious and are generally taken in all the power systems when the loading level is high.

– Increase the voltage set point of the generators. This action is effective only if

the load behaves nearly as a constant power load. In this case, an increase in

voltage will yield a decrease in current and thus a decrease in the loading of the

transmission system. It should be noted that a load behind an active LTC may be

considered as a constant power load seen from the transmission system.

20 Voltage stability phenomenon

– Generation rescheduling and/or starting up of gas turbine or hydro-generation. If small generation plants are available in the endangered area, their starting up will greatly increase the stability. Generation rescheduling is a more complex action that must be optimized in simulations before it can be implemented.

1.4 Online tools to assess voltage stability

In this part of the thesis, the focus lies on the online tools which assess the current condition of the power system. Online tools may be separated in two broad categories, depending on the approach used to assess the voltage stability:

• The security-oriented tools are based on simulation of the power system. Starting from the current situation, different evolutions are considered and simulated. Different kinds of indicators may be used. These tools are very similar to those used in planning studies, except that the current state of the power system is used as starting point.

• The monitoring-oriented tools assess voltage stability based on measurements, without running any simulations.

The main advantage of the security oriented tools is the ability to make predictions on the future state of the power system. However, the need to run simulations is also a drawback for three reasons:

• The accuracy of the results will depend on the quality of the modeling of the power system. The load model parameters are generally not well known, even if their im- portance for voltage stability is crucial. The second part of the thesis addresses this issue. More generally, if the models may be considered as very good near to the rated conditions, their precision decreases when the situation of the system deteriorates. For instance, reference [16] presents the results of dynamic simulations made with five dif- ferent industrial-grade power system simulation tools that give conflicting results for some disturbances.

• A large set of scenarios is simulated, including mainly load increases and contingen- cies. However, the set is inevitably limited. If a N-1 contingency analysis may be run completely, going further is often considered as too time consuming. The analysis of recent blackouts demonstrates however that their origin often lies in cascade tripping of transmission elements.

Moreover, the load increase may be achieved through very different approaches: global or local, increase in apparent, active or reactive power... Each choice will give different information and it is difficult to say which one is the most useful.

• Finally, running simulations is time consuming. Therefore, the information given by

the security-oriented tools is delayed.

1.4 Online tools to assess voltage stability 21 As the monitoring methods do not use simulations, they do not have these weaknesses.

Nevertheless, they are currently unable to make predictions on the future evolution of the system.

It is quite clear that these two categories complement each other, the disadvantage of one being the strength of the other, and vice versa. The monitoring methods are able to give a true online information, with a delay mainly dictated by the communication delays while the security oriented tools can offer predictions on the future state of the power system.

The remainder of this section further analyzes these online tools.

1.4.1 Security-oriented tools

Security-oriented methods can further be classified according to the index used.

• Methods based on the Jacobian matrix [17, 7, 18, 5, 19]: These methods study the mathematical characteristics of the Jacobian matrix of the power system. Either the singular value or the eigen value decomposition of the matrix may bring out several informative elements about the voltage stability, mainly:

– The disappearance of the equilibrium of the system ; – The highlighting of the weakest area ;

– The indication of the place where countermeasures will be the most effective.

The singular values and eigen values bring comparable information. The observation of their evolution for several successive states of the power system allows to follow the evolution of its stability and gives a relative indication on how close the system is to the voltage collapse or the singular point. Contingencies and load increase analyses may be performed.

• Methods based on voltage sensitivities [17, 7, 20, 21]: the voltage sensitivities ∂V /∂P and ∂V /∂Q go to infinity at the point of collapse.

As for the method based on the Jacobian matrix, the monitoring of the sensitivity evolution for successive states of the power system – typically with a load increase and/or contingencies – carries information on the distance to collapse.

• Power loss sensitivity method [17, 7]: the voltage collapse phenomenon is accompanied with a fast increase in the line losses. At the point of collapse, the loss increase ratios

∂P

/∂P , ∂P

/∂Q, ∂Q

/∂P and ∂Q

/∂Q go to infinity.

• Methods based on the energy function [17, 7, 22, 23]: These methods gives an information about the distance between the current equilibrium and the closest unstable solution.

As the system approaches collapse, the two solutions merge into one.

22 Voltage stability phenomenon

• Methods based on loading margins [7, 24, 25, 26, 27, 5, 28, 29]: These methods are very popular because of the easy interpretation of the index used. The physical understanding of the loading margin to the point of collapse, that may be given in MW, MVAr or MVA, is quite easy.

These power margins can be computed by continuation power flow methods [7, 24, 25, 27]. Basically, an initial load flow solution is used to compute the state of the power system with a higher loading level. A predictor-corrector approach allows to avoid the computation of a complete power flow at each step, reducing by a factor 3 to 5 the computation time. One of the above mentioned indexes indicates when the stability limit is found. An alternative is to use a modified optimal power flow for which the goal is to maximize power in a given direction (active, reactive, fixed cosφ...) [30].

To improve the modeling of the power system, a complete dynamic model might be used [31, 32]. The load is then progressively increased during a time-domain simulation. All the timing and the dynamics of the controllers are taken into account. That gives a much more accurate simulation of the power system. Indeed, it may happen that a working point is found stable with a static approach but that the dynamic simulation shows that another instability is encountered before reaching this point. Obviously, the computation time is longer than for a static method. An efficient integration technique with variable time step greatly reduces this weakness. This approach is used in Eurostag (more details in Section 1.5.3).

An intermediate solution is offered by the simulations using the Quasi Steady State (QSS) approximation [5, 33, 34, 35, 27, 10]. Time-domain simulations are also used but only the long-term phenomena are completely modeled. The short-term phenomena are replaced by their steady-state equations. The computation burden is then much smaller. This approach is very effective to study the voltage instability phenomenon where the long-term phenomena are predominant.

Contingency analyses may also be considered [36, 37, 10, 35, 33, 34]. The secure opera- tion limit gives the load margins with respect to the maximal pre-contingency load increase for which the system can withstand all contingencies. A margin relative to the acceptable post-contingency load increase may also be derived.

Another approach has been described in [38, 39, 40, 41, 42], but it cannot be classified directly in the previous categories. When a contingency occurs, the system enters in a dynamic phase which might eventually end up in a collapse due to the restoration of the load by the tap changers and by their own dynamics. The idea consists in estimating the dynamic load model parameters online right after the disturbance thanks to a Wide-Area Measurement System (the next section gives more details). The equilibrium of the dynamic load model is determined without time-domain simulation. The future load consumption is then included in the power flow model to determine if the state will be stable.

In this method, no load increase scenario is simulated. Instead, the future load consump-

tion is assessed by taking into account its dynamic recovery. The approach is somewhere

between the security-oriented and the monitoring-oriented tools. It requires the complete

power system model used in the former and the efficient measurement infrastructure needed

in the latter. Moreover, the results of Chapter 7 show that the estimation of the dynamic

1.4 Online tools to assess voltage stability 23 load model parameters is a tough task. The applicability of the method should be established on real measurements.

1.4.2 Monitoring-oriented tools

If the security-oriented approach is already well developed and used in power system, the monitoring approach remains an important field of investigation. The growing availability of new Wide-Area Measurement Systems (WAMSs) increases the demand for efficient monitoring systems. Indeed, measurements themselves do not bring enough information and indexes specifically adapted to each application must be derived.

This section shortly classifies different monitoring methods already proposed. They are grouped into two categories: local and global methods. More details are given on most of these methods in Chapters 2 and 3. Some of them are also tested.

Finally, the architecture of the WAMS is described.

1.4.2.1 Local monitoring methods

The following local methods to monitor the voltage stability of a bus of the power system may be found:

• Method assessing the Thevenin equivalent [43, 44, 45, 46, 47, 48, 49, 50, 51]: This method is largely proposed and cited in the literature. The concept consists in assessing the parameters of a Thevenin equivalent starting from the local measurements of voltage and current. As there are more unknows than equations, the computation must use at least two different working points. Alternatively, a recursive scheme is used. Chapter 2 largely describes and tests this kind of method.

A very similar approach proposed in [52] does not directly assess the Thevenin equivalent but uses instead the V –I characteristic seen from a load bus. Its interpolation from several working points leads to the computation of a power margin.

• Method based on the S-Difference Criterion (SDC) [53, 54, 55, 56]: The method states that, at the point of collapse, all the increase in apparent power at the sending end of a line will supply the increase in the line losses. A line index is derived from local measurements at the receiving end by comparing two successive measurement points.

A variant is proposed in [57] where a bus index is derived instead of the line index.

Even if the use of the Thevenin equivalent is not explicit, the equations are based on this

model and the issues of the local Thevenin equivalent that will be addressed in Chapter

2 apply to this method too. Until now, the method has been tested only on increasing

load scenarios, its effectiveness is yet to be established based on more realistic cases.

24 Voltage stability phenomenon Some other local approaches are widely used and detailed hereafter. They cannot be defined exactly as monitoring methods because they provide no information regarding the distance to collapse in normal operating conditions. They are used to trigger corrective actions when the state of the power system gets very close to instability. These protective schemes have proven to be efficient and must be considered as references. If a local monitoring scheme is used to trigger corrective actions, the effectiveness and added value with respect to these reference methods must be demonstrated.

In this category of local protective schemes, the following approaches may be found:

• Under-Voltage Load Shedding (UVLS) [58, 59, 60, 61, 62, 63, 64]: This is not exactly a monitoring method because the voltage does not give information relative to the distance to the instability in normal operating conditions. Indeed, due to the reactive compensation of the power system, the voltage generally stays around the rated value for a large range of loading conditions. However, when the situation comes close to instability, the capacitive compensation is in general already completely switched on and the voltage will finally decline.

UVLS is an efficient countermeasure against collapse. Nevertheless, its implementation requires an in-depth study to set the shedding thresholds to a correct value: not too high to avoid unnecessary actions and not too low to allow to shed before the system collapses. This tradeoff is particularly difficult in systems where motor loads are highly represented [65].

• Detection of the LTC instability [66, 67, 68, 69]: a local condition based on the evolution of the voltage in the distribution system when a tap change is performed allows to assess the stability of the concerned bus.

1.4.2.2 Global monitoring methods

The two following schemes belong to the category of the voltage stability monitoring methods based on global measurements:

• Monitoring of reactive reserves [70, 71, 72, 73]: this scheme proposes to monitor the reactive reserves available for voltage control in different areas of the power system.

The implementation, detailed for the Italian power system, is very easy because this information is generally already available in the control center if a multi-layer voltage control system is implemented. A similar system has been used in the Bonneville Power Administration system [7].

• Monitoring of the stability of transmission corridor based on a WAMS [74, 75]: starting

from the method locally assessing the Thevenin equivalent, the idea consists in speed-

ing up the estimation of the parameters by taking measurements at both sides of a

transmission corridor.