Athanasios Troupakis. Robust Security Constrained OPF for systems with high wind penetration - Effects on multi-area systems. Semester Thesis PSL1212

Transcription

1 eeh power systems laboratory Athanasios Troupakis Robust Security Constrained OPF for systems with high wind penetration - Effects on multi-area systems Semester Thesis PSL1212 Department: EEH Power Systems Laboratory, ETH Zürich Examiner: Prof. Dr. Göran Andersson, ETH Zürich Dipl. El. Eng. MSc. Supervisors: Maria Vrakopoulou, ETH Zürich Olli Mäkelä, ETH Zürich Zürich, October 212

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3 Abstract In the face of modern challenges due to market liberalization and fluctuating renewable energy sources, the operational security of power systems is put under question. Substantial scientific work is being conducted, in various levels, in order to tackle these issues. The overall goal of this semester project is to evaluate the operational security of the whole interconnected European system and to investigate ways of improving the security level. As a first step towards this goal, a robust security constrained Optimal Power Flow (OPF) Algorithm was designed. This algorithm was built based on the N-1 security concept with simultaneous consideration of uncertainties induced by the fluctuating wind power. The second part of the project was dedicated to examining whether the uncertainties of wind power can cause security violations in the multi-area system, based on two different approaches for coordination among Transmission System Operators (TSOs). iii

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5 Kurzfassung Angesichts der heutigen Herausforderungen steht die Betriebssicherheit von Energiesystemen immer mehr in Frage. Das allgemeine Ziel dieser Semesterarbeit ist es, die Betriebssicherheit des europäischen Energiesystems insgesamt zu bewerten und Möglichkeiten zur Verbesserung des Sicherheitsniveaus zu untersuchen. Als ersten Schritt in diese Richtung wurde ein robuster Optimaler Lastfluss Algorithmus mit sicherheitsbasierten Nebenbedingungen entwickelt. Dieser Algorithmus wurde auf der Grundlage des N-1 Konzepts gebaut, mit gleichzeitiger Berücksichtigung von Unsicherheiten aufgrung schwankenden Windenergie. Der zweite Teil dieser Arbeit zielte darauf ab, ob die Unsicherheiten der Windenergie Sicherheitsverletzungen im System verursachen können zu prüfen. Zu diesem Zweck wurden zwei unterschiedliche Ansätze für die Koordination zwischen Netzbetreibern (TSOs) angenommen. v

6 vi KURZFASSUNG

7 Acknowledgements I would like to express my thanks to the head of the Power Systems Lab, Prof. Dr. Göran Andersson, for providing me with the opportunity to work on such an interesting topic. Moreover, I would like to thank my supervisors, Maria Vrakopoulou and Olli Mäkelä, for their valuable inputs, their continuous support and the time they invested on this Project. Last but not least, I would like to express my gratitude to all members of the Power Systems lab for their friendliness and their help during the months that I worked there. Also, I would like to thank my family and friends for supporting me during the years of my studies. Athanasios Troupakis, Zürich, October 212 vii

8 viii Acknowledgements

9 Contents 1 Introduction 1 2 Operation tools for power systems Security management Security assessment Remedial actions Optimal Power Flow Security of multi-area systems Framework presentation Typical Structures of multi-area systems Interconnecting the European power system Operational security principles of the UCTE Cooperation initiatives Formulation and model specification Interconnected system model Wind farm location and modeling DC Power Flow Formulating the optimization problem Applying the optimization algorithm Snapshot dispatch analysis Benchmark approach analysis Proposed approach analysis Simulation results Optimal Power Flow results Security assessment of the multi-area system Conclusions 39 References 41 Appendix 43 ix

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11 List of Figures 1.1 Cumulative Installed Wind Power Capacity based on 3 different scenarios. Source: GWEC UCTE Reconnection. Source:[1] Member countries of Coreso. Source:[13] Member countries of TSC. Source:[14] UCTE System Model Installed wind capacity in Germany. Source: GWEC Representation of the UCTE system in PowerWorld Viewer Security assessment for Germany-snapshot dispatch Security assessment for Germany-optimal dispatch Security assessment for France-snapshot dispatch Security assessment for France-optimal dispatch Security assessment for Switzerland-snapshot dispatch Security assessment for Switzerland-optimal dispatch UCTE security assessment-snapshot dispatch UCTE Security assessment-benchmark approach UCTE Security assessment-proposed approach Critical lines per country Security assessment of Austria Security assessment of Belgium Security assessment of Croatia Security assessment of Czech Republic Security assessment of Denmark Security assessment of Hungary Security assessment of Italy Security assessment of Luxembourg Security assessment of Netherlands Security assessment of Poland Security assessment of Portugal Security assessment of Slovakia xi

12 xii LIST OF FIGURES 13 Security assessment of Slovenia Security assessment of Spain

13 Chapter 1 Introduction Electricity supply is one of the most important infrastructures for the functioning of modern society. Other important infrastructures (such as communication, traffic and transportation systems, gas and water supply, financial operations etc.) depend directly on the reliable supply of electricity. The interdependencies among different infrastructures can be either physical, geographical, cyber or logical. In order to assess the performance of power systems, one could use various criteria: reliability, economy, quality, environmental impact etc. Reliability is the overall objective of the power system design and operation and it is directly linked to security. In order to be reliable, a power system must be secure most of the time [1]. Security of a power system refers to the degree of risk in the ability of the system to survive imminent disturbances without interruption of customer service. Security relates to robustness of the system to imminent disturbances and, hence, depends on the system operating conditions and on the contingent probability of these disturbances. Another aspect of security is system integrity, which is the ability to maintain interconnected operation. Integrity relates to the preservation of interconnected system operation, or avoidance of uncontrolled separation, in the presence of specified disturbances [2]. In case security is not preserved, a disturbance in the power system may lead to catastrophic effects with serious impacts on society. The restoration procedure in order to bring the system back to a secure state is a complex and very laborious task. Apart from being related to other critical infrastructures, power systems are interconnected with each other, thus forming big systems covering large geographical areas. These connections are mainly established on transmission system level. The main reason for this is that transmission systems have a meshed structure which can provide higher redundancy and preserve system integrity in case of a line outage. Overall, the basic incentives for interconnection are of both technical and economical nature: 1

14 2 CHAPTER 1. INTRODUCTION 1. Increased level of system security 2. Coordinated use of power plants in redispatch 3. Sharing and optimal use of power reserves 4. Opportunities for energy trading However, in large interconnected systems there exists always the potential of having disturbances from one area spreading over other areas [1]. In addition, one of the major challenges for modern power systems is the integration of renewable energy sources. Due to the fact that electricity production from these sources can not be predicted without forecast errors, it imposes in addition to loads an extra degree of uncertainty in the operational security of power systems. Based on the data provided by the Global Wind Energy Council (GWEC) which are presented in Figure 1.1, the cumulative installed capacity of wind power is expected to grow substantially worldwide in the years to come. Figure 1.1: Cumulative Installed Wind Power Capacity based on 3 different scenarios. Source: GWEC Especially the European electricity system integrates more and more electricity from renewable energy sources. This fact is in accordance with the general European Energy Policy that focuses on the reduction of Greenhouse Gas Emissions (e.g. through the targets of EU 2-2-2) [3]. Particularly wind power is increasing quickly in Germany and has a great impact not only on the daily operation in the main control centers in Germany but also on the load flows and on the system operation in neighboring countries. Furthermore, it is to expect higher integration of renewable energy sources in the years to come, as some European countries have decided to enter a nuclear phase-out stage in their electricity production.

15 3 Transmission System Operators (TSOs) are supposed to play a key role in the effort of preserving the security of the interconnected system. Not only should TSOs focus on securing their own system but they should also cooperate in order to face the rising common challenges. This project is aimed at investigating ways of increasing the level of security of the multiarea system of the UCTE by combining an individual process followed by each individual TSO with a level of cooperation through an information exchange scheme.

16 4 CHAPTER 1. INTRODUCTION

17 Chapter 2 Operation tools for power systems In order to preserve the operational security of a Power System, a number of tools and control schemes are available. Depending on the state of the system, one can decide on the most appropriate control action so as to restore the normal operation. A detailed analysis of these schemes is beyond the scope of this project. In this section, two of the basic operation tools will be briefly discussed, namely the Security Assessment and the Optimal Power Flow (OPF). 2.1 Security management Bearing in mind that Security is one of the most important attributes for the normal operation of a power system, it follows that operators should be able to assess the level of security at any point in time. A specific procedure, called security assessment is followed for this purpose. The results of the security assessment procedure can help the operator decide on whether remedial actions should be implemented to increase the security margin of the system. The main objective of the operator would be to maintain the security of the system by complying with the N-1 criterion. Based on this criterion, a possible outage of any single component of the system should not cause unacceptable stresses or lead to instability problems [1] Security assessment Security assessment can be implemented both in the real-time operation and in the planning stage (both short- and long-term) of a power system. In the operation stage, security assessment is used as a method of normal and preventive control. This control scheme is implemented mainly when the system is in alert state with the overall goal of avoiding further disturbances 5

18 6 CHAPTER 2. OPERATION TOOLS FOR POWER SYSTEMS on the system and restore back the normal operation. Security assessment is usually part of the Energy Management System (EMS) and can be executed either in a continuous basis (every 5 or 15 minutes) or upon request of the system operator. As long as the most likely state of the system is available through the results of State Estimation (SE), the consequences of possible outages are examined. Typical examined consequences can be the operation of components outside their limits (overloadings, overvoltages etc.), voltage instability and transient instability. Security assessment is usually executed in two steps: 1. In the first stage, the complete set of possible contingencies is evaluated using static analysis, neglecting system dynamics. This fast procedure is called contingency screening. 2. The most severe contingencies identified in the first stage are analyzed in more detail with consideration of all relevant system dynamics. In order to check for unacceptable component stresses, a purely static analysis is sufficient. After each outage, a power flow computation is done and the results of the post-contingency state are compared with the operational limits of the components. If this procedure is followed, the whole security assessment is referred to as Static Security Assessment (SSA). When a time-domain simulation is performed, the term Dynamic Security Assessment (DSA) is used. Security Assessment can also be part of the computation and analysis stage in the long-term planning for power systems. In this case, the term security assessment refers to the simulation of dangerous scenarios with possible impacts on the system stability and security. These simulations take place after having forecasted the load and generation patterns through the load forecast and adequacy assessment techniques. The simulated scenarios often include peak load conditions with single and multiple contingencies. In the presence of unacceptable system performance, remedial actions should be taken. In the short-term (one to several days ahead) these actions include the modification of operation decisions, whereas in the long-term (weeks to months ahead) possible system extensions must be considered Remedial actions Remedial actions refer to measures applied by a TSO in order to restore the normal operation of the power system. Remedial actions can be both preventive (normal control) or curative (emergency control)[12]. Both preventive and curative remedial actions are supposed to be prepared in the operational planning stage of the system and the corresponding time horizons can vary from year ahead to weak and even day ahead. After evaluating the effectiveness of these actions against possible constraints, the TSO should inform

19 2.2. OPTIMAL POWER FLOW 7 neighboring TSOs in case the activation of these measures can affect other areas. In real time operation, given that the system state may be different than the one evaluated in the operational planning, TSOs must check again if the formerly prepared remedial actions are still appropriate. If not, remedial actions should be adapted to the current situation with respect to system state and in coordination with neighboring TSOs. In case a TSO is no more compliant to the N-1 criterion based on the state of the system and the anticipation of a possible contingency, it implements remedial actions as soon as possible. The efficiency of these actions should be checked in advance by a security analysis and necessary power flow calculations. The main preventive remedial actions are summarized below[12]. Topology changes Use of phase shifting transformers Changes in the patterns of reactive power flow Re-dispatch within the TSO s own network Cross-border coordinated re-dispatch Reduction of interconnection capacities Reduction of requested active power in favor of additional reactive power Tap changing of transformers Adjustments in power flows Switching of shunt elements (reactors, capacitors) 2.2 Optimal Power Flow Optimal Power Flow (OPF) refers to a set of computations aiming at determining how some control measures could be modified in order to achieve a desired performance for the system. OPF computations are also an integral part of the EMS and can be executed both in day-ahead operation planning and in real-time operation. As done in the security assessment, the initial state of the system is derived from the state estimation. The general optimization framework can be formulated as follows: min x,u f(x, u) subject to g(x, u) = h(x, u) (2.1)

20 8 CHAPTER 2. OPERATION TOOLS FOR POWER SYSTEMS where x is the system state and u the control variables. The desired system performance is given by the objective function and the overall system is subjected to the equality and inequality constraints. The objective function typically expresses the total cost of generation and the goal of the OPF is to minimize it. Other objectives could be the minimization of losses, of component stresses in normal operation, of total cost of control actions, or the maximization of reactive power reserves through minimizing the reactive power output of generators. Equality constraints usually refer to the power flow equations or the power balance of the system and they should always hold. Inequality constraints usually express system limitations and may also bound the system state x and the control variables u. Voltage magnitudes or loadings of lines, as system states, should be within the defined component limits. The generator s active power production (as a control variable) is restricted by upper bounds by the capacity of the generator. If we take into account the N-1 criterion, OPF is referred to as security constrained OPF.

21 Chapter 3 Security of interconnected power systems A big part of this project is devoted to the security assessment of large interconnected power systems. In this section the reasons for studying these issues are presented. In addition, the present practices and procedures of large interconnected systems (mainly the ones of the UCTE) are examined. 3.1 Framework presentation All over the world the electric sector is undergoing important changes that influence the system s security. These changes are mainly linked to the liberalization of the electricity market that moves to a more market oriented scheme. On the one hand, generating companies try to maximize their profits without considering the technical limits of the transmission system. On the other hand, system operators tend to provide cross-border capacity to the market in order to allow for more competition. In an unbundled environment, network operators are not allowed to interfere with market forces unless the system is at stake [6]. In multi-area system operation it has been advocated that new interconnections and new overhead lines should be developed not only for economic reasons but also for operating the systems at higher security margins by sharing power reserves among different areas. However, the process of building new infrastructure in lines is now more difficult than ever and can be related to effects such as the fear of negative impacts on the landscape or the fear of hypothetical electromagnetic effects. All other solutions apart from building new lines are usually more complex and involve phase-shifting transformers (PSTs), new conductors on existing lines, long underground HVAC cables or HVDC cables. It is then expected that complexity will increase in the future causing more implications on the way power systems are operated [7]. Security could also be increased through a better collaboration and ac- 9

22 1 CHAPTER 3. SECURITY OF MULTI-AREA SYSTEMS tion coordination of TSOs. In fact, it has been suggested that insufficiently coordinated operation may increase the risk of blackouts for multi-area interconnected systems [8]. 3.2 Typical Structures of multi-area systems Large interconnected power systems are usually decomposed into areas based on various criteria and operation and control of the whole system is shared by TSOs responsible for their respective areas. The common consensus that the control of one TSO may influence the variables of its neighboring areas has led to two major trends in the organization and control of large interconnected power systems [9]. On the one hand, the emergence of Mega TSOs is observed which resulted from the aggregation of several smaller ones. Typical example of this case is the regional transmission organization (RTO) called PJM which has expanded its operation in the USA over the years and it actually serves the reliability of the electric power supply system in 13 states and the district of Columbia. On the other hand, serious efforts have been made for coordination of several TSOs in cases where the regrouping into large scale entities did not occur. Especially from a European perspective, it is not possible (at least for the time being) to set up a transnational security coordinator that would have the authority to handle the security assessment for the whole or for a big part of the European interconnected system. A very important specificity for Europe relies on the way the interconnection is organized and regulated. The European Union has no structure nor any legal power to essentially enforce a common way of organizing the present situation. On the top level, European Directives provide common objectives, general guidelines and principles. On the bottom level, the implementation of these guidelines is organized by each member state. In each country the rules and laws are created in order to comply with the European Directives and to fit the local political organization and economic structure. In addition, there was no transnational body to play a role such as the Federal Energy Regulatory Commission (FERC) in the USA, and the coordination of different TSOs is based on multi-lateral negotiation and cooperation through gentlemen s agreements [6]. A new body has been established recently, namely the Agency for the Cooperation of Energy Regulators (ACER) which aims at assisting national authorities of EU-member states and at facilitating the necessary transnational cooperation. In general, European power industries have traditionally been very cautious in terms of confidentiality and security of information about their systems. Reasons for this tendency can be both technical (insufficient communication infrastructure, different softwares and data formats etc.) and

23 3.3. INTERCONNECTING THE EUROPEAN POWER SYSTEM 11 non-technical (conflicts in social and commercial interests). The efforts towards standardization of operation policies are summarized in the UCTE operation handbook. 3.3 Interconnecting the European power system The interconnection of the independent European systems into one system has been the task of various bodies and associations over the years. Through the course of time, 6 different associations were formed, each one with different tasks and areas of focus. The various committees, working groups and task forces have been integrated into a new body, called European Network for Transmission System Operators for Electricity (ENTSO-E). Two of the main predecessors of ENTSO-E are presented in the following part. UCTE The Union for the Co-ordination of Transmission of Electricity (UCTE) has since 1951 coordinated the operation and development of the electricity transmission grid for the Continental Europe. Initially, the Union was formed from a small number of interconnected companies that followed various stages of growing. In its final year of existence, UCTE was the biggest interconnected system, represented 29 TSOs, 24 countries and it was serving 5 million customers. Apart from ensuring the synchronous operation of its member areas, UCTE was involved also in other activities such as the adequacy assessment and the coordination of operating policies. The main goals of the UCTE have been: Optimal use of power plants (from both economical and environmental point of view) Sharing and optimal use of reserves (both short- and long-term) Increase of security Providing a platform for electricity trading In autumn 1991, the synchronous system which was then called Union for Coordination, Production and Transport of Electricity (UCPTE) was split into two zones due to the war in former Yugoslavia and the destruction of some key substations and the associated lines in Croatia and Bosnia & Herzegovina. The size of the two UCTE synchronous zones, the character of their interface and the amount of work needed, made the reconnection process one of the largest, most complex and most challenging projects in the history of UCTE. The reconnection process was a three-step project that invovled:

24 12 CHAPTER 3. SECURITY OF MULTI-AREA SYSTEMS Figure 3.1: UCTE Reconnection. Source:[1] 1. Replacement of the missing infrastructure 2. Creation of a UCTE team for North-South resynchronization 3. Physical interconnection, followed by a trial operation period A close cooperation for almost two years led to the preparation of a detailed resynchronization program. This program was a multilateral agreement, since TSOs from both sides of the interface between the two UCTE zones and the involved TSOs in the region had to agree with it. Apart from this program, serious infrastructure work had to be done in order to provide a solid basis for the interconnection. On October 1th 24, the power system of South Eastern Europe was reconnected to the rest of the Continental Europe after 13 years. The reconnection followed a test phase of some weeks until also market transactions were made possible on November 1st 24. In 1999, UCTE redefined itself as an association of TSOs in the context of internal energy market. UCTE managed to turn its recommended technical standards more binding through the operation handbook. These standards became essential for the reliable operation of the interconnected system, based on one common basis: the 5 Hz frequency and the related balance between generation and demand. ETSO The development of the internal electricity market in the European Union led to the emergence of several issues, mainly related to the

25 3.3. INTERCONNECTING THE EUROPEAN POWER SYSTEM 13 network usage. Thus the main European associations (including the UCTE) recognized the need for an EU-wide harmonization of network access and usage conditions, especially for cross-border electricity trade. The founding members of European Transmission System Operators (ETSO) were: UCTE, Nordel (Association of TSOs in Denmark, Finland, Iceland, Norway and Sweden), UKTSOA (UK Transmission System Operators Association) and ATSOI (Association of the Transmission Operators of Ireland). ETSO soon became an international association with membership of 32 TSOs from 15 countries in the European Union plus from Norway and Switzerland. Right before ETSO was merged into ENTSO-E, it represented 4 TSOs as members. The main objectives of ETSO were the following: The development of common principles regarding the harmonization and establishment of rules for enhancing the network operation and maintaining the system security To facilitate the establishment of an Internal European Market for electricity The communication and cooperation with organizations with similar objectives The investigation and solution of scientific and regulatory issues related to the TSO industry All previously mentioned associations (UCTE, ETSO, UKTSOA, AT- SOI and Nordel) and their respective operational tasks were merged into ENTSO-E ENTSO-E Since July 1st 29, ENTSO-E is the sole association of Transmission System Operators in Europe for Electricity. ENTSO-E is an initiative that responds to the 3rd EU Energy Package [11], focusing on both technical as well as market issues and having relevant committees. In addition, ENTSO-E provides an essential interface to power system users, EU institutions, regulators and national governments. The main mission of ENSTO-E is to promote important aspects of energy policy in the face of the following significant challenges: Security-by pursuing coordinated, reliable and secure operation of the transmission network Adequacy-by promoting the maintenance and expansion of the interconnected European grid Market issues-by offering a platform for the market and by proposing and implementing standardized market integration and transparency frameworks

26 14 CHAPTER 3. SECURITY OF MULTI-AREA SYSTEMS Sustainability-by integrating in a secure way new generation sources, mainly renewable energy following the EU targets. 3.4 Operational security principles of the UCTE UCTE had a long experience in setting standards, rules and suggestions to TSOs in order to ease the operation of the system. The transition from the recommendation stage to a more binding level was made possible when all technical standards and procedures were included in the operation handbook [12]. In the handbook, there exists a specific chapter regarding the operational security. One of the purposes of the operation handbook is to define methods of cooperation also in operational stages in which factors outside of the control area can limit the ability of the respective TSO to operate its system within the operating limits. In an interconnected system, there exist numerous interdependencies of the system components and the usage of these elements from market players can lead to impacts in other areas. According to the operation handbook, the basic principle of the interconnected operation is that each TSO is responsible for the security of its own area and aims at eliminating cascading effects with impacts outside its borders. A certain level of coordination (in bi- or multi-lateral level) is requested in order to assess the consequences of domestic decisions. The most relevant rules regarding the secure interconnected operation are related to the functioning of interconnections (tie-lines) between areas. When moving from a local to a regional approach some modifications to the operating framework are made. Each TSO has its own responsibility area, meaning its own system and the interconnections to adjacent TSOs. The outage of either an internal or an external element is compared against a specific number that quantifies the highest effect of the outage, this number is called influence factor. Any outage with an influence factor higher than a specific threshold is considered having a significant impact on the responsibility area of the TSO. External elements with a high influence factor form the external observability list. The branches forming that list and their terminal buses may not form a consistent external network. It is necessary that some additional elements are included in order to form a consistent observability area. Therefore, starting from the initial responsibility area and by adding the external observability list and the necessary supplement, we end up in forming the complete observability area for each TSO. In this way, TSOs are aware of the risks in their own system due to both inside and outside contingencies. In real time operation, on-line exchange of topology data and measurements may be proved crucial in order to preserve a quality of the state estimation and to get reliable results from the N-1 calculations.

27 3.5. COOPERATION INITIATIVES Cooperation initiatives The associations presented before are mainly focused on rule-setting and on establishing procedures that must be followed in order to ease the operation of the interconnected European System. Over the years, there have been some cooperation initiatives among different TSOs in order to have a central body that would act as a central TSO with the responsibility of the multiarea system. It needs to be stressed out that these initiatives do not have any binding force to impose specific control actions on individual TSOs. The procedures adopted from these initiatives are based on the following steps: 1. Collecting data from different TSOs 2. Building a common data set 3. Perform N-1 security analysis in a centralized manner 4. Distribute results 5. Analyze & suggest remedial actions to TSOs 6. TSOs decide on control measures The most important initiatives will be presented in the following part. Coreso Coreso is a cooperation initiative of TSOs in France, Belgium, Italy, Great Britain and North-eastern Germany, representing almost 4% of EU s population. Coreso is a Regional Coordination Service Center with services regarding the forecast and operation of electricity flows [13]. The activities of Coreso can vary from real-time to 2 days ahead. Coreso delivers advice, proposes solutions to participating TSOs and coordinates the agreement on the remedial actions needed to master the emerging constraints. The decision to implement these remedial actions remains the responsibility of the TSOs. Real Time Operation: Coreso has developed an intra-day process to evaluate its forecasts during the day. This process is based on a continuous check of the differences between the reality and the forecasts on the observability area of Coreso by a tool called DADS (Data Acquisition and Display System). Various indicators may trigger alerts and alarms that together with other data collected from many different sources may lead to the need for updated studies to check whether the recommendations made previously are still valid. Furthermore, Coreso is able to perform security analysis every 15 minutes, simulating faults on each 38

28 16 CHAPTER 3. SECURITY OF MULTI-AREA SYSTEMS Figure 3.2: Member countries of Coreso. Source:[13] kv line, main generation unit or busbar in strategic substations, following the principles of UCTE regarding normal contingencies. Some TSOs provide every 15 minutes real-time snapshot files which represent their own grid: including topology, power flows, voltage, generation, load, and technical characteristics of the network. These files are then merged in order to have a fully described grid of the West of Europe. In case of missing data, they are replaced by the most recent data forecast. A security analysis is done for each snapshot (96 per day) and based on the results national control center may be notified with proposed solutions, with the final decision of which remedial action to take remaining with the national control centers. Day-Ahead: The aim is to guarantee to have a full 24 hour vision of the next day of the security risks on the grid. To achieve this, the D-1 activity includes several steps: Every day, each TSO member of the Regional Group of ENTSO-E creates the Day-Ahead Congestion Forecast (DACF) file. This forecast is a vision of the specific grid for the following day. It contains all relevant information regarding generation and load, grid elements (planned outages, technical data etc.) and global power balance including flows from tie lines, with additional respect to market data. The DACF files made available by each TSO are merged to create a merged file for the whole Continental Europe. From this merged file, the security analysis performed centrally in Coreso simulating the tripping of elements regarded as normal

29 3.5. COOPERATION INITIATIVES 17 contingencies. Also, tripping of 38kV busbars are simulated in Belgium and in France, as stated by the policies of the respective TSOs. This complete analysis is processed for a minimum of 6 timestamps defined by original DACF files. In addition, in case of a particular situation induced by any special context, additional timestamps are added to the security analysis. The last step for D-1 activities consists of analyzing the constraints detected for the following day and finding remedial actions to solve them. Some variations could also be studied, such as the the fluctuation in exchange programs on particular borders or an alternative hypothesis for wind power generation. These solutions are then discussed by phone with the concerned TSOs, agreed and tracked within a common tool and published in a Day-Ahead Report. 2 Days-Ahead: A memorandum of understanding signed by the governments of member states of Coreso includes provision for the development of market mechanisms, notably extending market coupling arrangements to the entire zone, using a new method based on physical electricity flows (flow based market coupling). In this framework, the TSOs have decided to launch a common project, to design and set up a technical coordinated process related to market coupling. Available Transfer Capacity (ATC) based and flow-based projects are the parts of the project, that should lead to the regional market coupling in the years to come. The technical data needed are based on files called D2CF (Day 2 Ahead Congestion Forecast), which are the results of single (corresponding to one TSO) D2CF files merged together. Each day, Coreso shall receive files representing the best two-days forecast of each TSO and merge them before making results available for the different actors. The overall D-2 process is at an experimentation stage and Coreso is responsible for the above mentioned merging activities and for acting as a common feedback interface. TSC TSO Security Cooperation (TSC) is a group of fourteen TSOs with the goal to ensure the electricity supply for almost 185 million European citizens while seeking to improve the security of electricity supply across Europe. This initiative encompasses a permanent TSO security panel (formed by a group of security experts) and implements a shared IT platform for exchanging data and assessing mutual security needs [14]. The main tasks of TSC include: 1. Exchange of experiences on inter-tso remedial actions using state-of-the-art data flows

30 18 CHAPTER 3. SECURITY OF MULTI-AREA SYSTEMS Figure 3.3: Member countries of TSC. Source:[14] 2. Sharing of knowledge and expertise gleaned through system monitoring 3. Developing and implementing new multilateral procedures and remedial actions, and thus maintaining high system security levels In effect, TSC helps TSOs to better manage their expanding operations, especially with respect to integrating wind energy and handling increases in cross-border trading and electricity transmission. Common Cooperation Platform (CTDS): The CTDS-system includes a common IT Platform for data exchange and N-1security assessment. Member TSOs provide TSC with operation forecast data. These data are transferred to the IT Platform where they are merged into a database as the basis for all subsequent grid security calculations and the analysis of other aspects of interest. Once the grid security calculations are complete, member TSOs can access the results. The TSC IT tool allows member TSOs to access key data and provides them with access to advanced methods for choosing appropriate remedial actions. These IT services can be used by TSOs for many operations in their regions, starting first with day-ahead planning processes. These services may be expanded to grant TSOs with nearly real-time control over their operations. Real-Time Awareness & Alarm system (RAAS): RAAS provides a global view of the status of the electricity system in eleven control centers allowing them to better take care of their

31 3.5. COOPERATION INITIATIVES 19 responsibility. RAAS aims at easing the daily cooperation of European TSOs and at enhancing the overall electrical system security in Central Europe. It also provides awareness and alarms on the grid status of the whole region to all participating TSOs in real-time operation. Wind data exchange: The German TSOs participating in the TSC provide their wind forecast and near-to-real time data of wind generation to their partners of the TSC. This allows TSOs in other countries (Austria, Czech Republic, Netherlands, Poland and Switzerland) to have instantly a better and broader view of the interconnected electricity system in order to better take care of their respective responsibilities. This wind data sharing is a further important step to better manage the growing operational needs with special regard to the integration of wind energy, increasing cross-border trading and increasing electricity transport.

32 2 CHAPTER 3. SECURITY OF MULTI-AREA SYSTEMS

33 Chapter 4 Mathematical formulation and model specification This section is aimed at presenting the mathematical background of the computations performed, and at providing some further information about the way the overall model was built. The final part of this section provides a detailed description of the simulation procedure followed. 4.1 Interconnected system model As mentioned above, this project used as a case study the model of the interconnected European power system. This model is based on the data of the Union of the Co-ordination of the Transmission of Electricity (UCTE) and refers to the 22 Winter peak of the system [15]. Therefore, the data provided refer to the period prior to the reconnection of the UCTE system after the splitting of Countries included are mainly those of Continental Europe whereas countries of South Eastern Europe are excluded. A graphic representation of the system is provided in Figure 4.1. The lines marked in red represent the tie-lines between countries or connections with countries outside the UCTE network. The basic characteristics of the system and of individual countries are summarized in Tables 4.1 and 4.2. Table 4.1: UCTE model characteristics Countries 17 Buses 1254 Lines 1944 Generators

34 22 CHAPTER 4. FORMULATION AND MODEL SPECIFICATION Figure 4.1: UCTE System Model Table 4.2: Country characteristics Country Buses Lines France Germany Switzerland Italy Portugal Spain Austria Czech Republic Denmark 8 8 Poland Hungary Slovakia Croatia Slovenia 8 8 Belgium Netherlands Luxembourg 3 2

35 4.2. WIND FARM LOCATION AND MODELING 23 The most important element missing for the analysis was the rating of the lines. It has been assumed in the model that the rating of each line would be 7% of the maximum power transfer of the line. The power exchange over a line connecting two nodes (1 and 2) is given by the following equation where P 12 = U 1U 2 X sin(φ 1 φ 2 ) (4.1) U 1, U 1 : voltage magnitudes at terminal nodes 1, 2 φ 1, φ 2 : voltage angles at the nodes X : the reactance of the line. The maximum power exchange is then given for sin(φ 1 φ 2 ) = 1 P 12,max = U 1U 2 (4.2) X Assuming relatively small voltage deviations and setting the limit at 7% of the maximum power transfer, the line ratings were set at LineRating =.7X 1 (4.3) Another assumption made in order to derive the limits of the generators, was that in the data provided generators were operating at 6% of their nominal capacity. 4.2 Wind farm location and modeling The uncertainties introduced in the model were related to the wind power production, as mentioned above. Considering the high wind penetration in Germany, wind farms were modeled in this area. The modeling procedure was based on the map of the installed capacity of wind power plants, provided by the Global Wind Energy Council (GWEC). Instead of modeling many units distributed over the whole of Germany, only 8 big wind farms were modeled in order to capture the concentration of installed capacity in the Northern and Central part of the country. The location of these 8 wind farms is depicted in Figure 4.2 with the use of black boxes. The modeled capacity of these farms varies from 5 to 15 MW, depending on the data provided by the map. After having selected the nominal capacity of the plants, the issue of modeling the location had to be resolved. For this reason, the PowerWorld viewer [16] was used which allowed to map the geographical location of the plants with the respective buses in the system. In case of multiple buses near the

36 24 CHAPTER 4. FORMULATION AND MODEL SPECIFICATION Figure 4.2: Installed wind capacity in Germany. Source: GWEC selected location, the bus with the highest power infeed in the snapshot was selected as the one to host the wind farm. Figure 4.3: Representation of the UCTE system in PowerWorld Viewer Wind deviations were assumed to be a given percentage (e.g. 5%) of the total capacity of the wind farm. That means for a farm of 1 MW, deviations of +/- 5 MW. For the 8 wind farms, all possible binary combinations

37 4.3. DC POWER FLOW 25 were considered, which resulted in having 256 wind scenarios. This approach may be conservative since combinations that may not exist in reality were considered, but it is robust since it accounts for all possible combinations, including of course the worst case scenarios in which all wind farms reach their maximum or minimum. Given that in all cases the power balance should be guaranteed, all wind deviations were compensated by the generators in Germany, following thus the principles of automatic load frequency control. 4.3 DC Power Flow The basic tool for the analysis of the power system in this project was the DC power flow method. This approximative solution of the power flow problem has been proved to be of great value, given that power flow equations are solved consequently during the operation of power systems. In general approximative methods can be used in order to identify critical conditions of the system, or to provide good initial guesses for solving the problem with exact methods [17]. In our analysis, the basic concepts of the DC power flow method were used in order to derive a relation between the power injections in different nodes of the system and the resulting flows on the lines. The starting point in this analysis would be the linearization of the power flow equation along a transmission line, between buses k and m. where: P km = U 2 k g km U k U m g km cosθ km U k U m b km sinθ km (4.4) U k, U m : voltage magnitudes at terminal buses k, m θ km : difference of the voltage angles at the terminal buses k, m of the line: θ km = θ k θ m g km, b km : the conductance and the susceptance of the line. The terms corresponding to the active power losses are ignored since for transmission lines it generally stands that the line reactance is bigger than the line resistance (X R). One then gets the simplified version of the power flow equation: P km = U k U m b km sinθ km (4.5) Some further approximations can be valid, especially under low load conditions (small values of θ km ) : U k U m 1p.u. (4.6)

38 26 CHAPTER 4. FORMULATION AND MODEL SPECIFICATION It also stands that sinθ km θ km (4.7) b km = 1/x km (4.8) Based on the above, we can simplify the equation for the active power flow P km between nodes k and m as follows: P km = θ km /x km (4.9) Having this approximative equation as starting point, we could derive a formula for calculating the power flows in all lines of a system to be analyzed. This equation can be written as follows in matrix format: where: P f = B f θ (4.1) P f is a vector with l elements, as many as the lines of the system θ is a vector with the phase angles of different buses (k number of elements) θ = [θ 1 θ 2...θ k ] B f is a matrix with dimension (l k) with the following specifications B f,ij = -1/x i, if bus j is the terminal node of line i B f,ij = 1/x i, if bus j is the departing node of line i B f,ij =, elsewhere The matrix B f can also be derived by the multiplication of the admittance matrix Y of the system with an adjacency matrix T that describes the way buses are connected to form the lines of the system. The active power injection at bus k is given by the following equation: P k = x 1 km θkm = ( x 1 km )θ k + ( x 1 km θ m) (4.11) m Ω k m Ω k m Ω k where Ω k denotes the set of buses adjacent to bus k. This equation can also be written in matrix form as follows: where P inj = B bus θ (4.12) P inj is a vector with the net power injections in buses P k

39 4.4. FORMULATING THE OPTIMIZATION PROBLEM 27 B bus is a nodal admittance matrix (k k) with the following characteristics: B bus,km = 1/x km B bus,kk = m Ω k x 1 km By combining equations 4.1 and 4.12, one can obtain a formula for the power flows without calculating the angle vector: P f = B f B (4.13) where B is a matrix (k 1) is derived from B bus and P inj. Since B has replaced the angle vector, one should account for the presence of the slack bus and modify the matrix accordingly. Assuming that bus k=1 is the slack bus, matrix B will have the following formulation: [ ] B = ˆB 1 ˆ (4.14) where: P inj ˆB : is a matrix (k 1 k 1) that is derived from B bus after removing the row and column related to the slack bus ˆ P inj : is a vector similar to P inj but without the element for the slack bus [(k 1) elements]. Through equation 4.13, a direct coupling between the power injections in all buses of the system with the power flows in the lines is derived. By knowing or changing the power injections P inj in all buses of the system, we could evaluate the flows on the lines. 4.4 Formulating the optimization problem A basic part of this project is the formulation of an optimization algorithm for each specific area of the interconnected system. This algorithm has a double target: to minimize the total cost of generation in each area, while respecting the security constraints of this area (based on the N-1 security criterion) and considering various degrees of uncertainty. The Optimal Power Flow (OPF) procedure is, as presented in Section 2.2, one of the most important elements in the planning and operation stages of power systems. In this project the basic assumptions related to the optimization had to do with the supply and demand part. For the supply side, generators with quadratic cost curves were assumed, whereas the demand side consisted of totally inelastic loads. The optimization algorithm can be then easily formulated, following the standard procedure for such problems, by the use

40 28 CHAPTER 4. FORMULATION AND MODEL SPECIFICATION of an objective function and a number of constraints (either equality or inequality). These equations for each area follow the structure introduced in [18] and are described below: subject to min P Gi N Gen i=1 C i (P Gi ) (4.15) N Gen (P Gi d i P mis,t ) i=1 P min Gi N Load j=1 P Lj + P mis,t + P f W = (4.16) P Gi d i P mis,t P max Gi (4.17) P kl,t P max kl (4.18) for all t=,1,2,...n cont where P Gi is the power produced by generator i C i is the cost function of generator i P Lj is the power consumption of load j t is the possible contingency in the network or the possible tie-line deviation (zero value corresponds to the base case) P mis,t is the generation-load mismatch caused by a contingency t: outage of a generator, outage of load/generator due to line tripping d i is the distribution vector for generator i P f W is the wind power deviations in the specific area (if applicable) Equality constraint 4.16 refers to the power balance of the system. Inequality constraints 4.17 and 4.18 refer to the generator and line limits respectively for all possible contingencies. The power flow over a line (connecting points k and l will be a function of the injected power from the generators and of the wind power production. P kl = f(p G, P W ) (4.19)

41 4.5. APPLYING THE OPTIMIZATION ALGORITHM 29 Since this is a security constrained OPF, all possible outages of the system and their potential impacts are considered. In case of an outage, generators in the affected area must react and compensate for the power mismatch, following the principles of secondary (or load) frequency control. In our model, this power mismatch is distributed proportionally to the generators of the area according to their installed capacity. As expected the compensation factor has a negative sign since the reaction of generators is normally at the opposite direction of the induced disturbance (e.g. in case of negative power injection [loss of generator], the reaction will cause a positive injection [increase in the produced power of the remaining generators]). 4.5 Applying the optimization algorithm After having the full model of the interconnected system, the model for the wind power uncertainties and the optimization algorithm, one could proceed with the simulations in order to extract the necessary results. In our analysis, we followed 3 discrete steps which will be described in this section Snapshot dispatch analysis In this part the data from the snapshot of the UCTE model were used. Initially, all wind deviations in Germany were considered and the respective power flows were computed. A detailed contingency analysis was then performed for each individual area and for the whole interconnected system. All possible outages of single lines and loss of single generating units were considered. We have also evaluated the number of critical lines and generators for the whole UCTE system. In this project, we denote as critical lines or generators of an area that if tripped cause overloadings in lines of another area. In this part the optimization algorithm was not used Benchmark approach analysis In the second part of the analysis, the optimization algorithm was used. However, it has been assumed that no coordination exists among different TSOs. This means that each TSO seeks to optimize its own network, considering the uncertainties of its own area alone. Each TSO follows the algorithm described above and thus performs a security constrained optimization. It is expected that all individual areas will be secure. Nevertheless, the whole interconnected system may not be secure and that is due to the fact that each TSO considers its own uncertainties. Specifically, only the responsible for the German area considers the wind power deviations.

42 3 CHAPTER 4. FORMULATION AND MODEL SPECIFICATION Proposed approach analysis The third approach of the analysis was based on the assumption that there is some level of coordination among the responsible agents of each area. This approach follows the framework of TSC (as described in Section 3.5), especially the part of the wind data exchange. All areas are optimized based on the N-1 criterion, but with also some knowledge about the uncertainties in other areas. Based on the characteristics of the project, the additional knowledge to be considered is the possible deviations on the tie-lines due to the variable wind power production in Germany. For each area, tie-lines were modeled as power injections (or outtakes) based on the calculations performed in the Snapshot dispatch analysis for varying wind outputs. The different simulations were performed in MATLAB R and the optimization procedure was facilitated by the use of Cplex[19].

43 Chapter 5 Simulation results In this section the results of the simulations are presented. Firstly, the results of the security constrained optimal power flow are being presented and evaluated. The contingency analysis for the whole multi-area system comes next with the presentation of the results and some comments. 5.1 Optimal Power Flow results As a first step, the security assessment described in Section was done for the snapshot dispatch for each country of the UCTE system. In this procedure uncertainties about the wind power production in Germany and the resulting deviations in power flows on tie-lines were included. The procedure was based on the static security assessment (SSA), which means that after an outage (of line or generator) power flow calculations were performed and the results were compared to the loading limits of lines. These limits were based on the assumptions described in Section 4.1. For most of the countries, namely 12 out of 17, the security assessment revealed that the Snapshot Dispatch was not secure based on the N-1 principle. In the second step, the security constrained OPF algorithm was implemented in order to derive a secure dispatch for all countries. The optimization was initially based on the benchmark approach, which assumes no coordination among TSOs. In this way, each area is optimized based on its own sources of uncertainty. The optimization was then performed again following the proposed approach, in which individual operators receive some information regarding the uncertainties of other countries, namely the deviations on tie-line flows due to wind output in Germany. The results of some typical countries are presented in the following part. Optimal dispatch refers to the resulting dispatch after running the optimization algorithm with the proposed approach. 31

44 32 CHAPTER 5. SIMULATION RESULTS Figure 5.1: Security assessment for Germany-snapshot dispatch Figure 5.2: Security assessment for Germany-optimal dispatch

45 5.1. OPTIMAL POWER FLOW RESULTS Figure 5.3: Security assessment for France-snapshot dispatch Figure 5.4: Security assessment for France-optimal dispatch

46 34 CHAPTER 5. SIMULATION RESULTS Figure 5.5: Security assessment for Switzerland-snapshot dispatch Figure 5.6: Security assessment for Switzerland-optimal dispatch

47 5.2. SECURITY ASSESSMENT OF THE MULTI-AREA SYSTEM 35 As shown in Figures 5.1 and 5.3, the snapshot dispatch is not secure for Germany and France respectively. Especially for France the maximum loading of some lines exceeds by far the assumed line limits. A typical example is that there exist lines in France that have an average loading of above 1%. Given that the optimization algorithm implemented is security constrained, it results in a secure dispatch for both countries (Figures 5.2 and 5.4). Based on Figure 5.5, it is observed that Switzerland is secure with the snapshot dispatch based on the security assessment performed. Apart from Switzerland, the countries that could maintain an adequate security level with the snapshot dispatch were: Denmark, Luxembourg, Slovakia and Hungary. 5.2 Security assessment of the multi-area system After having obtained the optimal dispatch for each country, it is necessary to examine whether the whole interconnected system is in a secure state. Therefore, a similar procedure is followed for the multi-area system. In this section, the main focus would be to determine if an outage in one area (mainly country) can cause overloadings in other areas. The security assessment for the multi-area system is performed for all cases: snapshot dispatch and optimal dispatch based on both approaches (benchmark and proposed). All wind deviations are considered and special attention is paid so as to follow the Automatic Generation Control (AGC) concept. Based on this control scheme, which is followed by most European countries, generators participating in the AGC of a specific area will react after a disturbance so as to restore the frequency back to normal levels. The results are presented in Figures On the X-axis, the identifying number of the line tripped is shown whereas on the Y-axis we observe the resulting overloadings. Vertical dashed lines distinguish the lines per country.

48 36 CHAPTER 5. SIMULATION RESULTS In the analysis for the Snapshot Dispatch (Figure 5.7), 127 critical lines are observed. These lines are located in 7 different countries, most of them in France and Spain. An interesting finding is that one line outage in France can cause up to 2 overloadings. Figure 5.7: UCTE security assessment-snapshot dispatch The optimal dispatch from the benchmark approach (Figure 5.8) results in a better overall profile. The critical lines are eliminated from Austria and Czech Republic and the total number of critical lines is reduced to 88. Finally with the Proposed Approach the problem is limited to two countries (France and Germany) with a total number of 2 critical lines. Another reduction is also observed in the maximum number of resulting overloadings which are reduced to 5 (Figure 5.9). The gradual reduction of critical lines for each step of the security assessment can be more easily evaluated based on the Figure 5.1, where it is also shown how these lines are distributed among different countries. If the same analysis is done for critical generators, we end up with 12 critical generators in France.

49 5.2. SECURITY ASSESSMENT OF THE MULTI-AREA SYSTEM 37 Figure 5.8: UCTE Security assessment-benchmark approach Figure 5.9: UCTE Security assessment-proposed approach

50 38 CHAPTER 5. SIMULATION RESULTS Figure 5.1: Critical lines per country

51 Chapter 6 Conclusions Based on the analysis conducted in our project the following conclusions can be drawn. Firstly, it is obvious that the snapshot dispatch was not secure for integrating wind power in Germany for most of the countries. In addition, the overall security of the interconnected system could not be guaranteed as the outage of many lines could cause security violations in other areas of the system. By implementing a security constrained OPF, the network of each specific area (mainly country) is considered secure but the question about the overall security remains. If no coordination among different TSOs is assumed, thus following the benchmark approach, it is to expect that the tripping of some lines will still cause overloadings in other areas of the system. The implementation of some level of coordination among TSOs leads to an improved profile with significantly less critical lines and generators that could endanger the secure operation of the system. The fact that TSOs do not consider, when optimizing their network, the state of neighboring systems is the main reason for critical lines an generators remaining in the system. Therefore, the basic information exchange among TSOs that includes only information about the deviations on tie-line flows is proved to be insufficient. To cope with this situation, an extended information exchange framework should be introduced. This framework should aim at allowing TSOs to have a better understanding of the state of neighboring systems when optimizing their own network. Specific attention should be paid in the designing process of this framework as it should meet several prerequisites. The basic features of the proposed framework should be the costeffectiveness in terms of computational burden and the compliance with the principles of confidentiality and security related to the communication among different TSOs. One proposed way to achieve this goal would be to design a comprehensive framework and then, through a detailed analysis, reduce the amount of information exchanged by keeping only the most crucial for the decision making process. 39

52 4 CHAPTER 6. CONCLUSIONS

53 Bibliography [1] M. Zima, M. Bočkarjova, Operation, Monitoring and Control Technology of Power Systems, ETH Zürich, March 27. [2] P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. Van Cutsen, and V. Vittal Definition and Classification of Power System Stability, IEEE/CIGRE Joint Task Force on Stability Terms and Definitions IEEE Transactions on Power Systems, Vol.19, no.2, May 24. [3] Directive of the European Parliament and the of the Council on the promotion of the use of energy from renewable sources, EU website: [4] G. Andersson, Dynamics and Control of Electric Power Systems, ETH Zürich, February 212. [5] A.J. Wood and B.F. Wollenberg, Power Generation, Operation and Control, Wiley and Sons, [6] L. Wehenkel, M. Glavic, D. Ernst, On multi-area security assessment of large interconnected power systems, Proc. of Second Carnegie Mellon Conference in Electric Power Systems, pp.6, 26. [7] P. Panciatici, The need of more Optimization in the Decision Making Process, Presentation of Pan-European Grid Advanced Simulation and State Estimation (PEGASE)-National Technical University of Athens, 212. [8] J. Bialek, Are blackouts contagious?, IEEE Power Eng., Vol. 17, pp , 23. [9] L. Day, Control area trends: principles and responses, IEEE Comput. Appl. Power, Vol. 8, pp , [1] Reconnection of the electricity power system of continental Europe, European Network of Transmission System Operators for Electricity-ENTSO-E, ENTSO-E website: entsoe.eu. 41

54 42 BIBLIOGRAPHY [11] Proposal for a Directive of the European Parliament and of the Council amending Directive 23/54/EC concerning common rules for the internal market in electricity, EU website: [12] Union for the Coordination of Transmission of Electricity, UCTE Operation Handbook [13] CORESO official website: [14] TSO Security Cooperation (TSC) official website: [15] Q. Zhou, J. W. Bialek Approximate Model of European Inteconnected System as a Benchmark System to study Effects on Cross-border Trades, IEEE Transactions on Power Systems, Vol. 2, No. 2, May 25 [16] Power World Viewer website: viewer [17] G. Andersson, Power System Analysis, ETH Zürich, September 211. [18] M. Vrakopoulou, K. Margellos, J. Lygeros, G. Andersson, Probabilistic guarantees for the N-1 security of systems with wind power generation, Proceedings of PMAPS 212, Instanbul, Turkey, June 1-14, 212. [19] IBM website:

55 Appendix Results for individual countries The resulting plots from the security assessment of each individual country are presented in this section. Contingency analysis with Snapshot Dispatch A Contingency analysis with Optimal Dispatch A Figure 1: Security assessment of Austria 43

56 44 APPENDIX Contingency analysis with Snapshot Dispatch B Contingency analysis with Optimal Dispatch B Figure 2: Security assessment of Belgium Contingency analysis with Snapshot Dispatch CRT 1 Contingency analysis with Optimal Dispatch CRT Figure 3: Security assessment of Croatia

57 45 Contingency analysis with Snapshot Dispatch CZ Contingency analysis with Optimal Dispatch CZ Figure 4: Security assessment of Czech Republic Contingency analysis with Snapshot Dispatch DK Contingency analysis with Optimal Dispatch DK Figure 5: Security assessment of Denmark

58 46 APPENDIX Contingency analysis with Snapshot Dispatch HU Contingency analysis with Optimal Dispatch HU Figure 6: Security assessment of Hungary Contingency analysis with Snapshot Dispatch IT Contingency analysis with Optimal Dispatch IT Figure 7: Security assessment of Italy

59 47 Contingency analysis with Snapshot Dispatch LX Contingency analysis with Optimal Dispatch LX Figure 8: Security assessment of Luxembourg Contingency analysis with Snapshot Dispatch NL Contingency analysis with Optimal Dispatch NL Figure 9: Security assessment of Netherlands

60 48 APPENDIX Contingency analysis with Snapshot Dispatch PL Contingency analysis with Optimal Dispatch PL Figure 1: Security assessment of Poland Contingency analysis with Snapshot Dispatch P Contingency analysis with Optimal Dispatch P Figure 11: Security assessment of Portugal

61 49 Contingency analysis with Snapshot Dispatch SK Contingency analysis with Optimal Dispatch SK Figure 12: Security assessment of Slovakia Contingency analysis with Snapshot Dispatch SV Contingency analysis with Optimal Dispatch SV Figure 13: Security assessment of Slovenia

62 5 APPENDIX Contingency analysis with Snapshot Dispatch E Contingency analysis with Optimal Dispatch E Figure 14: Security assessment of Spain