Integration of Dynamic Line Rating within a Risk-Based Security Assessment Framework

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MSc ET 17004

Examensarbete 30 hp

July 2017

Integration of Dynamic Line

Rating within a Risk-Based Security

Assessment Framework

Marcelo Francisco Amaral

Martijn de Jong

Dr. George Papaefthymiou

Prof. Peter Palensky

Prof. Cajsa Bartusch

Masterprogrammet i energiteknik

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Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Integration of Dynamic Line Rating within a

Risk-Based Security Assessment Framework

Marcelo Francisco Amaral

The following work applies Dynamic Line Rating (DLR) to a Risk-Based Security Assessment (RBSA) methodology with the ultimate goal to perform day-ahead forecast

analysis. DLR quantifies transmission capacities of overhead lines whilst being dependent on ambient conditions. It takes into account variations in its surroundings, therefore making DLR less conservative compared to the traditional worst-case scenario oriented Static Line Rating (SLR). Applying DLR to overhead transmission lines (OHLs) entails different spans of potential benefits for solving grid exhaustion problems due to crescent electrical consumptions.

The RBSA methodology allows for the assessment of security of power system operations in a future state under uncertainties that arise from contingencies and forecast errors, e.g., loads or renewable infeeds. The methodology models input uncertainty with a copula integration with Monte-Carlo (MC) sampling framework. Several case-studies are executed for the assessment of DLR impacts, especially comparing them to SLR through the evaluation of system risk. Two case-studies are performed for a specific time of the day, one analyzing risk and ratings and the other concerning system impacts upon evolution of system forecast uncertainty (SFU) to values above day-ahead analysis usual intervals. The following two cases are the extensions to 24 point analyses, with the same goal, although more generalized. The final case study analyzes the economical impact of DLR applications and assesses an alternative system configuration behavior. This alternative setup is in constant comparison with the original configuration used throughout the project, advantages and drawbacks of both configurations are discussed. Finally, success of this

integration and assessment of impact and methodology is addressed in the end.

MSc ET 17004

Examinator: Joakim Widén Ämnesgranskare: Cajsa Bartusch Handledare: Martijn de Jong

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Declaration of Authorship

I, Marcelo AMARAL, declare that this thesis titled, “Integration of Dynamic Line Rating within Risk-Based Security Assessment Framework” and the work presented in it are my own. I confirm that:

• This work was done wholly or mainly while in candidature for a research de-gree at this University.

• Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.

• Where I have consulted the published work of others, this is always clearly attributed.

• Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.

• I have acknowledged all main sources of help.

• Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed my-self.

Signed: Date:

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“Às vezes, as árvores centenárias também caem...”

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Scientific Summary

Introduction and background. In nowadays energy markets, controlling risk can be a powerful tool for its successful operation, however, it can be highly challenging to objectively quantify. In the numerical analysis department of TU Delft, in a joint project with several other entities called UMBRELLA, a specific framework was de-veloped in this sense. The goal was to provide a working toolbox for Transmission System Operators (TSOs). By providing tools for risk-based assessment, TSOs could have the possibility of anticipating system states and this anticipation could or could not include some corrective measures. The second big concept present in this mas-ter thesis work is related to transmission line ratings, i.e., the limit of power that can be transmitted via the considered conductor. The difference between static and dy-namic is that DLR quantifies transmission capacities of overhead lines whilst being dependent on ambient conditions. It takes into account variations in its surround-ings, therefore making DLR less conservative compared to the traditional worst-case scenario oriented SLR. Applying DLR to overhead transmission lines (OHLs) entails different spans of potential benefits for solving grid exhaustion problems due to cres-cent electrical consumptions. The present work integrates this two concepts: DLR in a RBSA methodology with the ultimate goal to perform day-ahead forecast analysis. Like addressed in the abstract, the RBSA methodology allows for the assessment of security of power system operations in a future state under uncertainties that arise from contingencies and forecast errors, e.g., loads or renewable infeeds. This is done considering input uncertainty with a copula integration with Monte-Carlo (MC) sampling framework and all its building blocks.

Main results. Several case-studies are executed for the assessment of DLR impacts, especially comparing them to SLR through the evaluation of system risk. Two case-studies are performed for a specific time of the day, one analyzing risk and ratings and the other concerning system impacts upon evolution of system forecast uncer-tainty (SFU) to values above day-ahead analysis usual intervals. The following two cases are the extensions to 24 point analyses, with the same goal, although more generalized. With case-study number 1 and 3 it is shown the extent of the impact of this integration on line ratings, system severity and expected risk. With case-study number 2 and 4 it is verified the impact of the evolution of SFU, with high impli-cations on system severity. With the integration of DLR the system is verified to be more resilient to this crescent evolution. The final case study analyzes the econom-ical impact of DLR applications and assesses an alternative system configuration behavior. This alternative setup is in constant comparison with the original config-uration used throughout the project, with the advantage of being cost-optimal in all situations, but sacrificing a security optimal state for higher degrees of SFU.

Addressing results in a more general note, it is demonstrated that DLR integration in the power grid can avoid building new transmission lines, solving some of the first grid problems due to RES generation development rapid growth. Bearing in mind the ultimate goal the present work as an improvement and achievement of higher extents of efficiency in system operating while reducing risk, the results provided demonstrate that this was done successfully, taking into account the obvious limita-tions of the simulation.

Wider implications. The theoretical model presented provides a firm but limited basis for comparison with experiments and for prediction of new experimental features.

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For a successful integration in a real global case, a real and complex power grid, establishment of the framework and the upgrade of the equipment still needs time and innovation. Several simplifications have considerable impacts on the integra-tion and these are not contemplated in this work for practical reasons.

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Acknowledgements

For the purpose of this document I would like to thank Uppsala University for allow-ing me, without any complications whatsoever, to have an opportunity in another university, experiencing a new country and new learning challenges. A special thank you to the program coordinator Joakim Widén and to my UU supervisor, Prof. Cajsa Bartusch.

Secondly I would like to thank TU Delft for receiving me so well, to my department colleagues, to Prof. Peter Palensky, to Dr. George Papaefthymiou for the meetings and suggestions, to Chanpreet Talwar, my colleague in this project and partner in scientific discussions and a very special acknowledgement to Martijn de Jong, my daily supervisor, my mentor and the whole reason I came this far with this work. Thank you Martijn for all the guidance, motivation and long hours of work and meetings because of this project. I know how lucky I was to get you as my supervi-sor and I’m really glad that I did. You made this experience really worthwhile. Once again, thank you, it was an absolute pleasure learning and working with you. A special thank you to my program colleagues Marco, Albert, Tiago, Lukas, Hasan and Christoph, for helping me reaching successful results in Sweden and in the mas-ters and most importantly, have fun and enjoy my first experience abroad.

Additionally, a special warm thank you to several mysterious entities that only I (and them) need to know. To Vara, to Yolt, to the Wolfpack and to Pingas, without you people this would, for sure be impossible. Thank you for always making me feel at home even far away and for guiding me with your successful examples. I cannot thank enough all my new friends made in the Netherlands, to the Kanaal-family, to the Portuguese Mafia, to Luisinha for her patience, to all my visitors and to several others, thank you for so much fun here.

Finally, to my nucleus: my Mother, my Father and my little Brother and Sister. For every personal value since I was born and for the fights only us know how hard we fought, a very very big thank you. My dedication to this for the past 6 months is highly because of you.

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List of Figures

2.1 Comparison Study on the impact of MC samples. RAG stands for

Redispatched Active Generation . . . 8

2.2 RBSA applied methodology for 1 MC sample. . . 14

4.1 IEEE 24-bus test system . . . 30

4.2 Sensitivity Analysis on Wind Speed . . . 33

4.3 Sensitivity Analysis on Wind Attack Angle . . . 33

4.4 Sensitivity Analysis on Ambient Temperature . . . 34

4.5 Sensitivity Analysis on Solar Radiation . . . 35

4.6 5.000 samples test on 24-bus system . . . 36

4.7 Comparison System SLR vs. DLR for a single snapshot. . . 38

4.8 SLR Box Plot and Histogram for Load Factor - Line 23 . . . 39

4.9 DLR Box Plot and Histogram for Load Factor - Line 23 . . . 39

4.10 Generation Profiles for Generator #23 with SLR and applied DLR . . . 40

4.11 Overlap of Sensitivity Analysis on SFU to SLR and to applied DLR on snapshot #21. Note: In the X-axis it should be read "SFU". . . 41

4.12 Comparison of the RAG in a full day analysis between SLR and ap-plied DLR . . . 42

4.13 Comparison of line ratings in a full day analysis between SLR and applied DLR . . . 42

4.14 Two dimensional sensitivity analysis for SFU considering SLR. Note: In the Y-axis it should be read "SFU". . . 43

4.15 Two dimensional sensitivity analysis for SFU considering DLR. Note: In the Y-axis it should be read "SFU". . . 44

4.16 SCI risk assessment with cost computation for 5% in SFU . . . 45

4.17 SCII risk assessment with cost computation for 5% in SFU . . . 45

4.18 SCI risk assessment with cost computation for 15% in SFU . . . 45

4.19 SCII risk assessment with cost computation for 15% in SFU . . . 46

A.1 24 bus system case format for bus bars parameters . . . 49

A.2 24 bus system case format for generators parameters . . . 50

A.3 24 bus system case format for branches (transmission lines) parame-ters, rate A (the sixth column in the matrix) was the modified column to have mathematical accordance (Check section 4.1 Test Case for more) 51 A.4 24 bus system case format for generator costs parameters . . . 52

B.1 WindGuru Data Archive for 2014 . . . 54

B.4 Histogram Wind Speeds for 2014 to 2016. The y-axis represents a 3 hour step, the y-axis is the wind speed in m/s . . . 57

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C.2 Load flows for the selection of lines . . . 60 D.1 SLR Box plot and Histogram for line 10 . . . 62 D.2 DLR Box plot detailing for line 23 and line 28 . . . 63

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List of Tables

2.1 PLF considered specifications . . . 7

4.1 Considered 24 hour Load Profile . . . 31

4.2 Values Assumed for the sensitivity analysis performed . . . 31

4.3 Considered case format considered for line 1 . . . 32

4.4 Considered 24 hour Wind Speed Profile . . . 32

4.5 Description of considered lines and ratings in single snapshot #19 . . . 37

4.6 Risk Assessment for snapshot #19 . . . 38

4.7 Impacts on line ratings for a 24-snapshot analysis . . . 42

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List of Abbreviations

AC Alternating Current

CDF Cumulative Distribution Function

DC Direct Current

DG Distributed Generation

DSA Deterministic Security Assessment

DLR Dynamic Line Rating

DSO Distribution System Operator

ED Economic Dispatch

EV Electric Vehicle

HBE Heat Balance Equation

LP Linear Programming

MC Monte Carlo

OPF Optimal Power Flow

OHL Over Head Line

PDF Probabilistic Density Function

PLF Probabilistic Load Flow

RAG Redispatched Active Generation

RES Renewable Energy Sources

RBSA Risk-Based Security Assessment

SC System Configuration

SCOPF Security Constrained Optimal Power Flow

SFU System Forecast Uncertainty

SLR Static Line Rating

TSO Transmission System Operator

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Dedicated to my brother, Rodrigo and my sister, Leonor. Let

this work be an inspiration for them as they were for me when I

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1

Chapter 1

Introduction

1.1 Purpose & Motivation

The energy market is facing major changes in its original shape. The growth of re-newable energy sources (RES) and scarcity of fossil fuels are good indicators of the very likely occurrence of such scenarios and the main limitation to higher power transferring are usually transmission lines themselves.

An extensive evolution from a regulated monopoly to a deregulated competitive market in the electricity industry is turning monitoring, controlling, and safeguard-ing the reliability of power systems and grid increassafeguard-ingly more complex. Havsafeguard-ing that said, an increase in the variety of participants, while on the other hand the con-ditions under which power systems are operated become more diverse.

The integration of higher shares of electricity generated from fluctuating RES as well as increasing market-based cross-border flows and related physical flows are leading to rising uncertainties in transmission network operation. All additional system uncertainties and risks are derived from different developments being re-searched everywhere around the world. With particular relevance in Europe, the interconnected electricity system has emerged from the interconnection of national grids that were designed for power transport from generation units to loads com-paratively close to each other. Moreover, the power to be transported by the grid used to be rather predictable. Mainly due to the constant changes in RES in-feeds in the network, stakeholders involved in the energy system management in the Euro-pean interconnected system are increasingly faced with situations where real-time power flows are significantly different from the previously accounted ones, i.e., the estimated power flows.

Ultimately, with significant increases in the amount of wind generation, challenges related to the uncertainty of such weather conditions are expected to become more significant for system operation. Even nowadays, transmission system operators (TSOs) are increasingly facing an exhaustion of alternative operational measures, to keep the system in normal operational conditions. Including such operational uncer-tainty in system operation is of utmost importance for managing the interconnected system of the future. The reason lies on the fact that central Europe, despite being an electric synchronous area, has considerable differences between actual physical flows and dynamic market exchanges. Large investments in the implementation of renewable energy generation, impacts of market couplings and introduced cross-border intraday mechanisms are all contributing to the occurrence of this phenom-ena.

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2 Chapter 1. Introduction Here lies the motivation of all the projects being developed within the field of elec-trical power grids. In order to address these challenges, innovation needs to be taking place and strategic measures have to be taken into account. First and fore-most, forecasting errors need to be more controlled and significantly diminished. The usage of flexible generation units represents very important mitigations at the national level that are currently accounted to address these challenges. It is impor-tant to state though, that parties responsible for ensuring the real-time matching of production and consumption in their control areas, the TSOs, are already actively developing and innovating this aspect of electricity system operation. The second point is directly related to currently used criterion for the assessment of system se-curity. This covers all aspects from its limitations in presence of the above-described uncertainties. The N-1 criterion is still being put into practice as we speak, by the responsible entities, posing a highly conservative measure. Especially considering todays framework and supply/demand conditions. This rather rigid criterion treats every element of the system the same way and does not allow for distinguishing the relevance of different parts of the network.

1.2 Key Contributions

Generally, the quantification of system security levels has been and still is being done using deterministic approaches. The Deterministic Security Assessment (DSA) has its focus on securing the system operation against a set of plausible contingen-cies and worst case scenarios that the system should endure without compromising any of the stakeholders involved. The usage of the DSA methodology is very con-venient because of its simplicity, especially for system operators. However, it lacks some resilience with the increasing stress in the electrical grids. Hence raising the awareness for the development of alternative assessment methods such as the RSBA. The goal of the present work is an integration of the concept of dynamic line rat-ing DLR within the existrat-ing RBSA methodology, by integratrat-ing DLR the system can benefit in several ways. Namely in system security and in capacity of the grid. The DLR technique has simple implementation processes and does not involve any ma-jor infrastructures or line rebuilding, making this approach extremely interesting in grids that nowadays suffer from a crescent state of overloads.

Implementation within the RBSA was made following stages of complexity, with the final development being an implementation that’s fairly realistic for time steps of one hour. Daily data profiles in wind, temperature, load, etc. pose as inputs for this framework that then calculates and applies a dynamic rating to previously overloaded lines and assesses the new state of security of the system. Forecast un-certainty is also taken into account, which seeks to deal with the required inputs with the most realism possible.

1.3 Project Background

The development of this research work has precedent investigation and research. This was included in a project denominated, at its time, UMBRELLA Project. The project consisted of a toolbox for common forecasting, risk assessment and opera-tional optimization in grid security cooperations of TSOs [1]. It was supported by the European Commission under the 7th Framework Programme and it consisted

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1.4. Outline of the Thesis 3 of a partnership between several European universities, companies and research centers. With a competitive market forcing system operators to operate close to their traditional deterministic limits, leading to highly stressed and vulnerable net-works, new numerous responsibilities raise upon R&D departments and academic researchers. This increased complexity and higher required performance come to-gether with high uncertainty and high risk. To be able to cope with the uncertainty and risk, the ability to obtain, manage, and use large amounts of information has be-come of primary concern. Leading to the main reason in investing and developing projects of this sort.

1.4 Outline of the Thesis

After this short introduction done in Chapter 1, follows Chapter 2 where a theoret-ical context is made towards the fundamental concept of RBSA and all its building blocks. In Chapter 3 the concept of DLR is introduced, a literature review featuring some recent research work and practical applications is made and, finally, all the implementation details, applied mathematics and assumptions are presented and discussed. In Chapter 4 all the practical and computing parts are addressed, de-scribing the test case, decisions taken around the used available case files and data, assumptions and relations used in the weather parameters and a description of the different stages of the project embodied in the shape of case-studies involving differ-ent analysis. Finally, for Chapter 5 results are assessed, followed by the conclusions and some future possibilities.

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5

Chapter 2

Risk-Based Security Assessment

Framework

2.1 The RBSA Methodologies

Being a complex concept, several theoretical approaches and methods are available in the literature. When considering probabilistic risk-based approaches, while it has been commonly used for many decades applied to power system planning as done in [2], the employment of this technique in security assessment is considered a rather recent application. Another interesting analysis made in this subject according to [3] is that the N-1 criterion is still accounted as one of the best trade-offs between fairly accurate, safe results and computational time.

However, literature offers a wide scope of different approaches going all the way back to work developed in the 1970’s. In the more accessible literature, as the case of [4], the available on-line records start around 2002. For the purpose of this work and literature review, we shall focus on the most recent work from the latest years of 2014 onwards.

The present work, as stated before, is embedded within UMBRELLAs project frame-work, a perfect example of RBSA methodology being put into practice. In total, the project managed to generate from its execution over 35 publications, giving an im-portant contribute to the development of several concepts revolving the developed toolbox. This toolbox consisted of the following key-functions [1]: 1) Simulation of uncertainty caused by market activities and RES; 2) Deterministic and probabilistic optimization framework for corrective actions to cope with simulated risks on dif-ferent timescales and increasing system complexity1; 3) Risk-based assessment tools for anticipated system states with and without corrective actions.

One of the major demonstrations within the project is the ability of the UMBRELLA Toolbox Optimization Framework to speed up current processes significantly, usu-ally made by experience, by avoiding unnecessary iteration steps. This is due to the fact that conflicting activation of remedial actions by different TSOs is avoided. Ul-timately, operators and operational planners are given the necessary time to prepare the actual implementation of the proposed remedies.

The project also had a scope for the future, projecting its goals and ambitions. Fur-ther development of the Toolbox and work is currently being prepared by the TSO

1_{Where the aim is to reduce the total cost of uncertainty while also increasing system security and}

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6 Chapter 2. Risk-Based Security Assessment Framework Security Cooperation initiative. Such actions will enable TSOs to identify optimal settings for the Toolbox in order to implement it in daily operational planning pro-cesses as well as in real-time operations.

The iTesla project (2012 to 2016), [5] is one good example of alternative applications in terms of RBSA. This project worked hand in hand with UMBRELLA, sharing sev-eral common interests and workshops as in [6] to [8]. The goal was to compose a toolbox in order to support the decision-making process ranging from two-day ahead (D-2) to intra-day planning. Project stakeholders faced several challenges described in their literature. These can be briefly stated as 1) performing security assessments in the most accurate way whilst taking into consideration all the sys-tem dynamics, using time domain simulations; 2) keeping the entire syssys-tem in a state of security with relevant proposals of preventive and/or remedial actions; 3) accounting for all sources of forecast uncertainties, especially regarding RES inter-mittent power generation, all probabilities for the contingencies and the lack of ef-fectiveness (or even failure) of remedial actions (generation re-dispatching, change in transformer tap position, topology of substations, set-point values of high voltage DC lines (HVDC) or phase-shifting transformers).

Furthermore, the project [9], consisting of in-depth security analyses of power sys-tems was also part of the analysis for these methodologies sections. The analysis performed has a requirement to take into account vulnerabilities from either natu-ral causes or man-made threats. From this, multiple dependent contingencies may arise. In spite of this, high system impacts are often caused due to such events, making all the decisions involved, with an aim to enhance security, extremely chal-lenging. With the introduction of uncertainty in each contingency, risks can be as-sessed and then subsequently ranked. The cited work bases its outline in a descrip-tion of an in-depth security assessment methodology, established on an definidescrip-tion of risk somehow more complete than the normal concept. This is due to the fact of having within its domain all the threats, vulnerabilities, contingencies, and impacts involved in its essence. Being the projects main scope the operation of a risk as-sessment of the integrated power and information and communication technology systems and after addressing their results, the work concluded with the application to test cases and realistic power systems. These measures ended up providing added value to the proposed methodology with respect to conventional security analyses in regard to dealing with uncertainty of threats, vulnerabilities, and system response. Another interesting development in the same thematics is done in [10]. Despite the face that the scope of the project is not so related to this framework, the established procedure to solve the problem makes it "cite-worthy". The work consists of a two-step approach, starting by the modeling of stochastic uncertainties present within the power system to produced probability density functions for stability indicators. These are then decomposed into regions based on user-specified threshold values. The outputs from this decomposition are analyzed using fuzzy techniques to com-plete the second phase and, of course, the risk assessment of instability.

Concepts commonly involved in the essence of a RBSA methodologies are described below as follows.

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2.2. Probabilistic Load Flow 7

2.2 Probabilistic Load Flow

The approach of probabilistic load flow (PLF) was firstly taught back in the year of 1974 according to [11] and was developed ever since with several applications. From power systems operations, to short and long term planning and some other areas developed by several publications as the ones in [12],[13]. With the advance-ment in studies some key simplifying assumptions were outlined by [14]:

1) The steady-state model is linearized around an operating point; 2) The system inputs are assumed to be normally distributed; 3) The system inputs are assumed to be statistically independent.

In order to obtain the system state and the required power flows, the PLF framework requires probabilistic density functions (PDF) and cumulative distribution functions (CDF) as inputs, this way all system uncertainties can be taken into account when obtaining the final outcome. The two most common ways of solving the PLF prob-lem are: i) numerically, i.e. using a MC method or ii) analytically using a convolution method or a combination of them [14].

When modeling PLF considering the numerical way, several specifications have to be taken into account, as in the case of MC samples, SFU, any possible adjustments per zone, rank correlation, a correlation matrix and a random generation seed. In the following implementation the values considered were as organized in Table 2.1. SFU is simply a consideration revolving each point of the system. This meaning, for

MC Samples SFU Adj. per Zone Rank Corr. Corr. Matrix Seed

5.000 0.05 1 0.8 2 1

TABLE2.1: PLF considered specifications

each bus a normal distribution is considered that has a mean value, the average load value for a specific bus, and a standard deviation, that we address as SFU and that is uniform for all buses in the system. Zonal adjustments can be also considered, although in the present work there no adjustment is considered. For The correlation matrix value 2 stands for a zone-wise uniform correlation matrix.

2.2.1 Monte-Carlo sampling

Within the framework of the project being presented, the MC method is the one selected to integrate the RBSA developing tool. The reasoning behind it lies in the fact that an MC framework allows for capturing the complex stochasticity of the sys-tem inputs, for example non-normal infeed distributions resulting from wind power forecast uncertainty. That way, mapping of specific, representing rare/high impact events with possible catastrophic outcomes for the system is enabled [15].

With a larger number of samples, the computation time increases significantly. How-ever, results can be considered more general once there’s a higher number of differ-ent situations contemplated in the method, thus generating more accurate results. To better demonstrate the impact of the number of samples in the results of a sim-ulation, the tests presented in Figure 2.1 were conducted. Calculating the same dis-patch, with the exact same conditions. The only difference between the two studies

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8 Chapter 2. Risk-Based Security Assessment Framework

FIGURE2.1: Comparison Study on the impact of MC samples. RAG stands for Redispatched Active Generation

is the number of considered MC samples. There is a considerable lack of under-standing of the systems response when computing simulations for the usage of an undervalued number of samples. Which can lead to severe underestimations of sys-tem parameters, therefore to negative impacts on the syssys-tem such as overloading, cascading or even system collapses.

Making use of the mathematical formulation stated in [16], affirming that the 95% confidence interval for any quantity, let’s say for instance, lost load, redispatched generation, etc., is given by:

ˆ µ − 1.96√s N, ˆµ + 1.96 s √ N , (2.1)

where ˆµ is the sample mean, s represents the sample standard deviation and N the number of MC samples in use for the analysis. As observed, by increasing the num-ber of MC samples, N , the confidence interval is diminished, creating, therefore, a higher accuracy of the analysis. Several variance reduction techniques are available in the literature as in [17] or [18], but given their complexity in solving and imple-mentation, the trade off is solely made between number of samples and computation time.

2.2.2 Copula Theory

Copulas can be defined as functions that "join together one-dimensional distribution functions to form multivariate distribution functions" as firstly approached by [19]. This functions take a specific form, such that one-dimensional marginal distribution func-tions, the so-called marginals, are uniform between 0 (zero) and 1 (one) [20].

An integration between MC and the Copula Theory, that generates the samples used in MC, taking into account marginals and at the same time the correlations between the buses, increments significantly the reality in the whole simulation.

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2.3. Economic Dispatch 9

2.3 Economic Dispatch

Following its terminology, the word economy goes hand in hand with prices and cost structures. Determining the generation schedule that minimizes the system op-erating cost constitutes the objective of the economic dispatch (ED) of an electric energy system. This can be measured in terms of fuel costs for the thermal plants and of "shadow" costs for the energy limited hydro plants. Naturally, it cannot vi-olate any of the system operating constraints such as maximum line flows or bus voltage levels [21].

According to [22], ED can be classified in 4 distinct categories, being: 1) optimal power flow; 2) ED in relation to automatic generation control; 3) dynamic dispatch and 4) ED with non-conventional generation sources. Research is being developed and applied in these four diverse classes.

It is important, though, to bear in mind the constraints of such tool: from equal-ity constraints, as load generation balance, to inequalequal-ity constraints, i.e., between an interval, such as upper and lower limits on generating units output. This being pointed out, ED has its own limitations such as the fact that generating units and loads are not all connected to the same bus or the economic dispatch may result in unacceptable flows or voltages in the network.

2.4 Power Flow

In the Power Flow method, the problem is stated by specifying the loads in mega watts and mega vars to be supplied at certain nodes, or the so-called busbars, of a transmission system and by the generated powers and the voltage magnitudes at the remaining nodes of this system. This is done together with a complete topo-logical description of the system, also including its impedances. The objective is to determine the complex nodal voltages from which all other quantities like line flows, currents and losses can be derived. The model of the transmission system is given in complex quantities since an alternating current (AC) system is assumed to generate and supply the powers and loads [23].

2.5 Optimal Power Flow

Nowadays the construction of an efficient electric grid involves major challenges due to a diverse contribution of different factors. From the increasing demand for electricity to the overwhelming growth of the renewable energies penetration on the grid, a huge variety of constraints are introduced into the massive equation. Creat-ing an efficient and resilient grid then constitutes a complex process for all parties involved.

After a review of [24], it can be stated that with an increase in the distributed gen-eration (DG) presence in power grids, optimal power flow (OPF) formulations are necessary to maximize the amounts of DG capable of being connected to the net-work without incurring in any voltage, thermal or fault level violations.

The main difference between power flow (PF) and OPF is the following - OPF is an extension of the PF framework, accounting not only for flows, but also for the

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10 Chapter 2. Risk-Based Security Assessment Framework economic dispatches involved in the process. This tool faces several challenges that research is trying to tackle. A first challenge is the size and complexity of the prob-lem, with thousands of lines, buses and different variables. Being a linear, non-convex problem are also a big issues. Additionally, the difficulty in determining which of the inequality constraints, present in the problem, are binding is another question mark. In order for the reader to have a better understanding of the concept, the OPF can be compactly formulated as:

min f (x0, u0),

which is subject to

g(x0, u0) = 0,

h(x0, u0) ≤ 0.

The equality constraints, g, represent mainly the power flow equations. Whereas the set of inequalities, h, represents the operating limits of the different system devices, these can be generators or transmission lines, that naturally have their own physical limits.

As for the formula, x0 the vector of state variables, say, voltage magnitude or

an-gle at each bus, and u0 the vector of control variables. There are several examples

for this, for instance: generator active and reactive powers; transformer ratios; phase shifter angles; reactive power of the capacitor or reactor banks; flexible AC transmis-sion systems and variables related to network switching, among others [25].

2.5.1 Objective Function

According to [23] the minimum generating cost consists in the most intuitive ob-jective function. The application of such a criterion immediately assumes variable input powers and bus voltages which have to be determined in such a way that a minimum of the cost of generating these powers is achieved.

Another objective function to be considered, is load shedding minimization, re-quired in extreme network contingency scenarios, in order to prevent system col-lapse and/or return the system to secure operation [24]. The load shedding min-imization function is extensively used in publications throughout the researching panorama. In this project this is also case, particularly active load shedding.

Adding to the previous ones, also amongst the most common objective functions we have the minimization of active power losses, the minimization of reactive power losses and the minimization of cost to remove a congestion. Maximization can also be contemplated in the objective function. Among other choices, we have the maxi-mization of loadability limit or the maximaxi-mization of social benefit [26].

2.5.2 Security-Constrained Optimal Power Flow

As presented above, the economic dispatch may have its limitations, meaning it may not keep the system in an equilibrium state after major perturbations, for example considering a line and/or generator outage. This led to the concept of system secu-rity, where the main goal in system operation is to keep the power network in an equilibrium state during periods between disturbances. Additionally, it has to en-sure that, on the occurrence of a major disturbance, the system does not depart from

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2.5. Optimal Power Flow 11 its normal state [27].

In [28] sequential Linear Programming (LP) algorithm in Security-Constrained Op-timal Power Flow (SCOPF) was developed. This development does not address the problem of non-convergence. The approaches are focused on the solution of the SCOPF assuming that a solution exists. In a considerable amount of SCOPF prob-lems, there is no way to predict whether a solution exists or not. The way of formu-lating the SCOPF problem has to be done in such a way that in case of nonexistence of the solution the solving methodology should provide a partial solution and also identifying any of the violations or limitations of the system in operation when at its optimal point.

The N-1 security criterion is used commonly in SCOPF. As defined in [29], a sys-tem that meets the N-1 criterion would not reveal any violations during any of the primary contingencies, or during any of the secondary contingencies, posing the primary contingencies as reference case. This essentially means that system is com-pletely secure against any single outage of a component, for example branches or generators. With that said, and if all effective system adjustments are well-understood, contingency analysis may be one of the most valuable tools used.

In the same thinking process as the OPF presented above, the SCOPF can also be simply stated mathematically. This visualization can be considered quite relevant once all practical differences from a comparison with OPF can be easily identified. The SCOPF is represented as follows [25]:

min f0(x0, u0),

which is subject to

gk(xk, uk) = 0, k = 0, ..., N,

hk(xk, uk) ≤ 0, k = 0, ..., N,

uk= mk(u0), k = 0, ..., N,

where N is the number of postulated contingencies, and for the k-th system con-figuration, xkdenotes the vector of state variables, uk denotes the vector of control

variables, k = 0 corresponds to the pre-contingency configuration, k = 1, ..., N cor-responds to the N post-contingency configurations.

2.5.3 Review of OPF Different Methodologies

When addressing solving the OPF problem using gradient methods [30][31], the main identified problems consisted in slow convergence, the condition for the ob-jective function and constraints to be differentiable, the difficulties in the handling of the inequality constraints, the binding of inequality constraints changes being part of the solutions progresses and the difficulty in the enforcing of complementary slackness conditions.

Solving the OPF problem with interior methods [26][32] instead, performs much better when a full AC solution is desired. Its way to handle inequality constraints consists in the usage of barrier functions. It initiates the analysis from a point in the “interior” of the solution space, the so-called feasible domain, and its main ad-vantage in comparison to gradient methods is the availability of efficient solution

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12 Chapter 2. Risk-Based Security Assessment Framework engines for its execution.

Linearizing the OPF problem [33] creates a linear system of equations without de-composition, unnecessary constraints or omissions. A major advantage from this is that the problem becomes convex, but the constraints need careful consideration for its successful formulation. Being a linearized problem, a lot of simplifications come with this condition. In the objective function a linear or piecewise linear cost function is used. In the linear OPF problem, the equality constraints are imposed by the DC power flow instead of by the AC power flow. Finally, when it comes to the inequality constraints, DC power flow provides linear relations between injections (control variables) and line flows.

Another similar method is the sequential linear programming OPF [34]. As a con-sequence of the linear approximations, all the solutions presented may be not ideal, additionally constraints may not be respected exactly. There is also the need to iter-ate the solution of the linearized problem, which for the active power may not be so complex, but the same does not occur in the reactive power aspects, i.e., in the case of VAr flows. In an overview of the strong suits of this methodology, the algorithm is considered fast, also due to the fact that there are optimization engines available. Moreover, another major advantage of this method is that it is commonly used to calculate nodal prices in electricity markets.

The analysis to all methods and information regarding ED, OPF and SCOPF was done based upon the cited papers and articles but also with information extracted from the Daniel Kirschens "Optimal Power Flow" lecture [35].

2.6 Severity Functions

Work developed in [36] refers to the term severity as the "extent to which operating limits are violated". Which essentially means that the impact of the contingency is most severe in the case of the absence of alternative credible combinations of system configurations, contingencies, and operating conditions that have even a more se-vere impact.

Despite the fact that severity functions can be linear, piecewise linear or quadratic, etc., a predefined list of contingencies can also be used. This predefined list ac-counts for an amount of most credible outages to check for with an RBSA method. These functions are used to quantify risk against numerous system problems, such as, severity against voltage that’s under its inferior limits, circuit overload, voltage instability and cascading. Cascading events are usually modeled with a looping mechanism based on hard limits on the maximum allowable power through the cir-cuit. Finally, the severity functions must be simple in nature and should be tied to deterministic criteria to make them easily accessible for operators [25].

In the project considered, an implementation of linear severity functions is followed, as proposed in related literature. Other type of severity functions, such as exponen-tial or quadratic functions, can be implemented for all or a set of the system circuits and buses to increase the sensitivity of the algorithm to specific system areas.

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2.7. Proposed RBSA method 13

2.7 Proposed RBSA method

As already briefly introduced in the section "Key Contributions", the project has a RBSA method of its own. The building blocks used in order to perform this analysis are the ones described above. All of this converges into a unique alternative method not available anywhere else. Ideal for an efficient, but at the same time realistic in-tegration of DLR. This can pose a rather valuable advantage for TSOs in order to perform day-ahead risk assessments, especially with the inclusion of DLR usage in the analysis.

On a complementary note previous sections and based in [15], it is also relevant to say that due to the combination between the Copula Theory, MC, full AC computa-tions and the usage of OPF, high levels of accuracy can be provided by the developed tool. Additionally, the previous developed work shows that neglecting forecast un-certainty and/or correlation can lead to a severe underestimation of the system risk, this can constitute a serious issue to TSOs. Finally, one final key conclusion of the previous work is related to voltage aspects. It is stated that a system where voltage problems often occur, when using tools that rely on DC approximations, may also result in a severe underestimate of system risks.

The expected benefits of using a RBSA methodology are extensive and can be briefly indicated as in [36]:

a) Risk explicitly assigns an expected cost due to possible insecurity problems mea-suring the economic consequence. This property provides a direct bridge between power system economics and security;

b) Risk index, when using available information, can decide in the present in prepa-ration for a future condition. Risk index can, therefore, be leading indicator;

c) There is a functional dependence of risk on pre-contingency operating conditions that operators are able to monitor, understand, and control, this is clearly illustrated by RBSA results;

d) As risk is computed for each security problem, each contingency and each com-ponent, it is easy to identify the reason causing or incurring in the security problem. Risk can be assigned to the appropriate entities;

e) Risk computation reflects, for a local operating region or an entire system. A measure of the overall security level of the region can be provided;

f) In the presence of sequential trajectory of operating conditions through time, then risk can be calculated for each operating condition and summed over all time. Cu-mulative risk assessment is extremely useful for assessing the influence on security level of a particular facility plan;

g) RBSA provides the capability to manage security based on the decision maker(s) preference regarding risk exposure. Identification of preference is done in the con-text of decision analysis.

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14 Chapter 2. Risk-Based Security Assessment Framework in Figure 2.2, can clearly indicate the computation and coding processes involved in the generation of this RBSA method. The figure applies for each single MC sam-ple considered and was developed and provided by the previous framework in this project [37]. Scenario (MC sample) > 1 island? AGC Run AC PF Converged? Heavily overloaded circuits? Remove circuits > 1 island? 2 or more islands! AGC Result Yes No No Yes Yes Yes No No

Risk computation

using I and/or II

cascading loop (A) Overall Methodology. Overloaded circuits or voltage violations? Remedial actions Feasible solution? Compute load lost Compute severity Add high penalty System collapse (all load lost)

System stabilized Yes No No Yes No I: Fast screening

II: Detailed analysis

(B) Detail on Risk Computation (I or II).

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2.8. Risk Quantification 15

2.8 Risk Quantification

Risk can be quantified in several different ways, however, this can only be done due to the fact of using the so-called risk metrics. These are 1) fast screening and 2) detailed analysis. Fast screening is solely based on severity functions, as described above, giving a brief overview of the system risk and constituting almost no com-putational time when compared with risk metric 2). As for the second, a detailed analysis includes optimal remedial actions determined using an AC OPF tool. As for the quantification, sparse number of criteria is available for this. From severity, to re-dispatching active power, reactive power, or both. Moreover, lost load can also be a good quantifier of risk, as well as the probability of cascading.

With this said, risk can be quite challenging to quantify in a practical and intuitive way for the least experienced researcher, especially when applied to power systems where its underestimation can lead to serious problems.

In most of the applications of this work, risk will be represented by the Redispatched Active Generation (RAG), which sometimes can be conjugated with the lost active load or the lost load due to system collapses. What determines this conjugation is the extent to which the system is stressed. In the case-studies sections both light stress (e.g. the single snapshot without uncertainty factors) and heavy stress to the system (e.g. the single snapshot forecast uncertainty sensitivity analysis) will be contem-plated. In the least severe cases RAG can represent the system risk in an acceptable way, in the most severe cases lost load and lost load due to system collapse need to be also included in the analysis to avoid risk underestimation.

2.8.1 Redispatched Active Generation

To make sure it is clear how this quantification is done, a brief definition of RAG, also referred to as Active Generation Redispatch, is included in this chapter. Trans-mission lines are limited by their ratings, which often is attained in power system operations and day to day energy flowing. One of the strategies to decrease the load factor in order to respect the OHL ratings is by generation redispatch. The utiliza-tion of phase shifters or simply load reducutiliza-tion are also viable oputiliza-tions.

The term redispatch means to adjust the real power a power plant or generator is providing, in order to avoid or eliminate line congestions or further problems. By lowering the real power output of one or more power plants and at the same time increasing the real power output of one or more other power plants, it is possible to relieve congestion while keeping the total real power in the grid close to constant. With this said, in power flow problems a lot more is going on simultaneously and even though RAG can be considered a fair estimate idea of risk, constant cascading events, islanding and possible outages may affect the results obtained.

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17

Chapter 3

Dynamic Line Rating

3.1 Background

In the current situation, one fundamental topic of discussion is on how to act to-wards power grids crescent usage. With an upcoming electrical revolution, as is with the growth of electric vehicles (EVs) or the constant development of renewable ways of producing electricity for example, power networks need to be prepared to cover the required demand. Involved parties, in particular the TSOs, started to in-vestigate what could be the possible solutions to cover this new foreseeable demand. One of them relies on a more intensive utilization of the already built grids. This in-volves an important concept denominated line rating.

As found in the literature, there are several methods and standards to calculate power rating in OHL. The SLR is based on the line ampacity, which is calculated considering static weather conditions. For its computation worst case weather pa-rameters are assumed so that the maximum flow current is obtained without vio-lating temperature limits [38]. This way of operating the ratings does not consider a real-time analysis approach [39] and often is excessively conservative. By under-utilizing the already built assets, with worst-case scenario conservative approaches, power networks are not being put into optimal usage and, therefore, are posing un-necessary compromises to both TSO’s supply and electricity consumers demands. Naturally, it will be easy to assume that dynamic rates take into account real-time analysis: changing weather conditions, with a high significance on wind behav-ior/variability. Dynamic line rating (DLR) brings the possibility of providing the operator with the OHLs’ actual ability to carry power at any moment in time de-pending on the respective zonal weather conditions. At the same time all design limits are being respected, such as conductor temperature [40].

This solution is of utmost interest of TSOs since by utilizing the existing assets in terms of transmission lines, the invested capital into this section is fairly diminished when comparing to rebuilding more resilient systems from scratch. Not to mention the complexity in alternative demand covering and extensive legal procedures in-volved in this process.

Grid operators also have the advantage of a better management in load traffic since ratings are applied to lines in real-time. This way congestion is highly mitigated, decreasing the risk of contingencies in the system. According to [41] a DLR system has relatively low cost and its abilities to be rapidly deployed and relocated make it ideal for projects facing the uncertainty of changing generation and load topologies.

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18 Chapter 3. Dynamic Line Rating Furthermore, to better attain the impact of DLR utilization, with the real-time rat-ing analysis there is an average decrease in operators intervention need of around 80% as shown in [40].

For this we can assume different methods for the implementation of DLR, all in-volving different input parameters, advantages and problems. Briefly mentioning them we have I) DLR forecast from system loading and weather forecasting [42], [43], II) DLR estimation from indirect measuring [44] and III) real-time DLR evalua-tion integrating actual meteorological data [45].

There are two main publishers of industry standards for the calculation of overhead line ampacity, the IEEE Standard for Calculating the Current Temperature Relationship of Bare Overhead Conductors [46] and CIGRÉ Thermal Behavior of Overhead Conductors [47]. They both use the Heat Balance Equation (HBE) methodology but different ap-proaches are considered in order to do it. In a comparison study done in [48] the overall difference was inferior to 1% in most typical applications. The conclusion of the comparison study is quite curious, as the author says: "There should be an effort to combine these two standards into one (...)".

The IEEE standard and the HBE method will be discussed in depth in the imple-mentation section of this report.

3.2 Literature Review

3.2.1 DLR Recent Research

A lot of research is being put nowadays into DLR as found by this literature review. As stated previously, the effectiveness of DLR is highly dependent on weather con-ditions and has several methods to its implementation. One fundamental point has to be that, DLR can provide an efficient solution of power networks overloads or congestions [49].

Evaluation of Available Transfer Capacity

DLR has many different benefits in several contexts within electrical power grids. One of which was developed by [50] consisting on the application of DLR to evaluate the ATC. ATC can be defined as the superior limit of power that can be transferred stably between a generation and a demand point. This parameter can be determined by either thermal constraints, voltage constraints or stability constraints. In Europe the constraints most taken into consideration are thermal constraints once intercon-nections are securely built, the other two constraints pose no significant threat to the system. For thermal constraints what determines upper limits is overloading of the lines. This overload is caused when the power flow exceeds this limit previously determined by the thermal constraints imposed to the specific line.

In this work, like stated before, ATC is considering thermal constraints limited by weather conditions, where dynamic ratings pose the function of estimating it. With the occurrence of high wind speeds, increments in ATC were much higher, once ATC and dynamic ratings go hand to hand in parameter dependence. Which means, ver-ifying high wind speeds on the system with a lower temperature only creates more

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3.2. Literature Review 19 potential for the incrementing of ATC. This is shown with 24 one hour snapshots organized in a table with a changing weather scenario.

Schedule of Reserves Impact Assessment

Considering the scheduling of reserve services, DLR can also represent a positive im-pact [51]. By proposing a two-stage stochastic optimization model integrated with DLR in the grid and also including RES penetration, namely wind generation. The model is formulated with mixed integer linear programing (MILP) methodology and the two stages of the process consist of 1) co-optimization of energy and reserve holding levels for the previously expected conditions followed by 2) re-dispatch ac-tions (for instance, wind curtailment) under real-time forecast error scenarios. One key aspect mentioned in this article is the lack of correlations between wind gener-ation and DLR forecast errors, absolutely crucial to a better control of uncertainty. Therefore, after the analysis of the preliminary results the study suggests that the system benefits significantly when associated with a reduction of forecast horizons, thus predicting line ratings closer to the actual time frame.

Integration with a Security Constrained Unit Commitment

The application of DLR in security constrained unit commitment (SCUC) systems has also been investigated by some research groups such as in [52]. Firstly, address-ing the concept of SCUC, and startaddress-ing by just unit commitment (UC). A UC poses the function to determine commitment states and generation levels of all generators over the scheduling horizon to minimize the total generation cost. This is done while agreeing with all constraints, such as system load balance, spinning reserve require-ments, and individual unit operating constraints [53][54]. Due to the fact that power grids are being driven to operate closer and closer to their security margins, a need to consider security transmission constraints in the equation emerges. This means essentially that SCUC becomes indispensable in the newly deregulated power mar-ket [55]. In the current operation practice, a generation schedule is obtained from SCUC in day-ahead market and taken as an energy delivery schedule on an hourly basis in real-time [56].

The aim of this integration in [52] is to enhance the overall system security as well as its technological and economical performances. This is done by coupling SCUC with AC-Optimal Power Flow (AC-OPF) constraints. The HBE is also included in the process via linearization of the radiation and convection heat losses expressions which might, at first glance, be considered as an excessive simplification but actually better account for the impacts of reactive power flow and voltage constraints. Var-ious sensitivity analysis such as the HBE discretization time step and linear versus piecewise linear HBE as well as several data plotting come to show the effectiveness of the proposed method, not only in optimality but in computation time and security of the overall system.

Affine Arithmetic Based Modeling

In [57] the published scientific article addresses indirect methods for dynamic load-ability. Stating limitations of these indirect methods, such as high uncertainty fore-casting and trying to overcome them with a solution deployment based on complex modeling and affine arithmetic, which is in contrast with the most popular method,

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20 Chapter 3. Dynamic Line Rating namely interval mathematics (IM). A completely novel solution methodology is pro-posed, consisting in the marriage between pervasive sensor networks and reliable computing. The methodology is recognized as computationally light, cheap to be implemented, not invasive, accurate, and robust.

The way to proceed would be by deploying a network of environmental sensors (suggested 10 per line dispersed throughout its route) measuring the environmental temperature, the wind speed and the wind direction at the ground level providing all the possible observable variables along the line. Solar irradiance is estimated us-ing the previous data and the bounds of the conductor temperatures for each mon-itored span are estimated by solving the dynamical model presented in the article. This allows the identification of the hottest conductor temperature (i.e. ’hot spot’). The article concluded comparing the proposed solution to the standard IM, stating that there exists a propagation of uncertainties in order to keep track of their correla-tions. This results in a mitigated impact by long interval computations that usually are cause for precision losses.

DLR integration in Variable Renewable Energy Sources

The increasing use of RES as a part of the electrical grid can benefit heavily from the integration with DLR. The focus of the article was clear [58]:

1) Derive algorithm for DLR model, including line rating and conductor surface temperature calculation;

2) Assess relevant ambient conditions effect on DLR; 3) Reconstruction of these ambient conditions;

4) Establish a benchmark power system model with high renewable energy shares and test its improvement on power transmission performance once DLR is applied;

5) Full-year DC OPF dispatch simulations.

The method used for modeling DLR in this article was based on the stead-state HBE and uses the same principles as the ones assumed in our methodology. One interest-ing approach by the authors is the direct calculation of DLR computation parameters such as wind velocity and solar radiation data via reconstruction from wind and PV in-feeds. Ambient temperature data is generated from daily maximum and mini-mum temperature with a sinusoidal approximation method, all based in previous records from the intended test-case, in Germany. Load demands are also assumed as previous records obtained by the authors.

3.2.2 Practical Applications

The application of DLR in real world can be used in three different ways. These include clearance warning method, on-demand rating method and continuous real-time rating method [59].

Tension Monitoring in New Zealand

Back in the year of 1996, a New Zealand company named Transpower New Zealand Limited joined forces with The Valley Group, Inc. in order to set up an application test case of DLR in strategic lines of their system1. This was one of the first initiatives

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3.2. Literature Review 21 to put in practice the brand new concept, at the time, of using dynamic ratings in OHLs. The method used for its implementation was line-tension monitoring using a CAT-1 tension monitoring system [60]. Following, in the results presentation three different situations were analyzed:

1) Typical summer day in December with a high availability of DLR; 2) Typical summer day in February with an average availability of DLR; 3) Typical winter day in September with a mixed availability of DLR.

By the graphic results presented in the article [59] it was verified the rating drops with approaching dusk. The reason laid in the fact that wind speed for summer days is much higher than average, this due to natural convection. First pieces of evi-dence on the fundamental influence of the presence of wind in DLR scenarios. Hours of daylight as the period of highest availability for dynamic ratings are also coinci-dent with load peaks in the system, thus DLR can contribute to relieving constraints, avoid unnecessary load shedding and outages, and defer capital expenditure. The article concludes with a crucial cumulative frequency plot for the overall system (in-cluding both summer and winter) with DLR rating providing 43% more capacity over the static rating for 60% of the time, 70% more capacity for 40% of the time and 100% more capacity for 20% of the time. Even though the results are quite satisfac-tory, there will be times during a contingency when these ratings are not available. In such situations, other measures like rearranging generation schedules, load shed-ding, etc. are suggested by the paper.

Another important conclusion of this study, besides important quantitative results, was that DLR by weather monitoring is more economical and also reliable to some extent but is susceptible to error resulting from variation of the terrain and fore-casting of weather patterns. Therefore it cannot forecast ampacity rating for micro-climates.

Assessment of Weather Conditions Impact

Advancing a few years in history, on-site testing has also been performed with deeply refined methodology and technological resources by the same company The Valley Group, Inc. and presented in [40], showing empirical impacts of the different weather parameters in a case study2:

1) Assessing the impact of ambient temperature, the study uses two main mea-surement criteria: small variations such as a couple degrees Celsius fluctuations and night temperature drops3. For the first case the capacity suffered a residual impact of around ± 2% (temperature raising affects negatively the capacity of a transmis-sion line). A night temperature drop, i.e, the second considered case, had a positive impact on the capacity of 11%.

2) As for the effects of solar radiation on the impact of DLR implementation two distinct situations are considered in the analysis of the problem. These are the pres-ence of clouds, blocking the solar radiation to irradiate the transmission lines and a night scenario, with solar radiation is close to inexistent. For the first set up the

2_{Test case done in Australia, on a 20 mile transmission line (795 ACSR) under static thermal rating}

of 787 amps at 40 degrees Celsius ambient, zero wind, and mid-day summer.

Integration of Dynamic Line Rating within a Risk-Based Security Assessment Framework

Examensarbete 30 hp

July 2017

Integration of Dynamic Line

Rating within a Risk-Based Security

Assessment Framework

Marcelo Francisco Amaral

Martijn de Jong

Dr. George Papaefthymiou

Prof. Peter Palensky

Prof. Cajsa Bartusch

Masterprogrammet i energiteknik

Abstract

Integration of Dynamic Line Rating within a

Risk-Based Security Assessment Framework

Marcelo Francisco Amaral

Declaration of Authorship

Scientific Summary

Acknowledgements

Contents

List of Figures

List of Tables

List of Abbreviations

Dedicated to my brother, Rodrigo and my sister, Leonor. Let

this work be an inspiration for them as they were for me when I

Chapter 1

Introduction

1.1

Purpose & Motivation

1.2

Key Contributions

1.3

Project Background

1.4

Outline of the Thesis

Chapter 2

Risk-Based Security Assessment

Framework

2.1

The RBSA Methodologies

2.2

Probabilistic Load Flow

2.3

Economic Dispatch

2.4

Power Flow

2.5

Optimal Power Flow

2.6

Severity Functions

2.7

Proposed RBSA method

Risk computation

using I and/or II

2.8

Risk Quantification

Chapter 3

Dynamic Line Rating

3.1

Background

3.2

Literature Review