Interest in Distributed Generation (DG) in power system networks has been growing rapidly. This increase can be explained by factors such as environmental concerns, the restructuring of electricity businesses, and the development of technologies for small-scale power generation. DG units are typically connected so as to work in parallel with the utility grid; however, with the increased penetration level of these units and the advancements in unit’s control techniques, there is a great possibility for these units to be operated in an autonomous mode known as a microgrid. Integrating DG units into distribution systems can have an impact on different practices such as voltage profile, power flow, power quality, stability, reliability, and protection. The impact of the DG units on stability problem can be further classified into three issues: voltage stability, angle stability, and frequency stability. As both angle and frequency stability are not often seen in distribution systems, voltage stability is considered to be the most significant in such systems. In fact, the distribution system in its typical design doesn’t suffer from any stability problems, given that all its active and reactive supplies are guaranteed through the substation. However, the following facts alter this situation: • With the development of economy, load demands in distribution networks are sharply increasing. Hence, the distribution networks are operating more close to the voltage instability boundaries. • The integration of distributed generation in distribution system introduces possibility of encountering some active/reactive power mismatches resulting in some stability concerns at the distribution level. Motivated by these facts, the target of this thesis is to investigate, analyze and enhance the voltage stability of distribution systems with high penetration of distributed generation. This study is important for the utilities because it can be applied with Connection Impact Assessment (CIA ). The study can be added as a complement assessment to study the impacts of the installation of DG units on voltage stability. In order to accomplish this target, this study is divided into three perspectives: 1) utilize the DG units to improve the voltage stability margin and propose a method to allocate DG units for this purpose, 2) investigate the impact of the DG units on proximity to voltage stability 3) conduct harmonic resonance analysis to visualize the impacts of both parallel and series resonance on the system’s stability. These perspectives will be tackled in Chapter 3, Chapter 4, and Chapter 5, respectively. Chapter 3 tackles placing and sizing of the DG units to improve the voltage stability margin and consider the probabilistic nature of both the renewable energy resources and the load. In fact, placement and sizing of DG units with an objective of improving the voltage stability margin while considering renewable DG generation and load probability might be a complicated problem, due to the complexity of running continuous load flow and at the same time considering the probabilistic nature of the load and the DG unit’s resources. Therefore, this thesis proposes a modified voltage index method to place and size the DG units to improve the voltage stability margin, with conditions of both not exceeding the buses’ voltage, and staying within the feeder current limits. The probability of the load and DG units are modeled and included in the formulation of the sizing and placing of the DG units. Chapter 4 presents a model and analysis to study the impact of the DG units on proximity to voltage instability. Most of the modern DG units are equipped with power electronic converters at their terminals. The power electronic converter plays a vital role to match the characteristics of the DG units with the requirements of the grid connections, such as frequency, voltage, control of active and reactive power, and harmonic minimization. Due to the power electronics interfacing, these DG units have negligible inertia. Thus, they make the system potentially prone to oscillations resulting from the network disturbances. The main goal of this chapter is to model and analyze the impact of distributed generation DG units on the proximity of voltage instability, with high penetration level of DG units. Chapter 5 studies the harmonic resonance due to the integration of DG units in distribution systems. Normally, the harmonic resonance phenomenon is classified as a power quality problem, however, this phenomenon can affect the stability of the system due to the parallel and series resonance. Thus, the main goal of this chapter is to study and analyze the impact of the integration of distributed generation on harmonic resonance by modeling different types of DG units and applying impedance frequency scan method.

Η αστάθεια τάσης αποτελεί ένα σημαντικό πρόβλημα για τα συστήματα ηλεκτρικής ενέργειας. Ένα σύστημα εισέρχεται σε κατάσταση αστάθειας τάσης λόγω αύξησης της ζήτησης, μιας ξαφνικής, ευρείας κλίμακας διαταραχής ή αλλαγής στην κατάσταση του, που μπορεί να προκαλέσει μια σταδιακή και ανεξέλεγκτη πτώση τάσης. Παρουσιάζει, λοιπόν, ιδιαίτερο ενδιαφέρον η μεταβατική συμπεριφορά του συστήματος σε σχέση με την ευστάθεια της τάσης. Επίσης, κατά τη λειτουργία ενός Σ.Η.Ε., είναι σημαντικό για το χειριστή να γνωρίζει το μέγιστο επιτρεπτό φορτίο του συστήματος χωρίς να κινδυνεύει από αστάθεια τάσης. Η δυναμική ευστάθεια τάσης μπορεί να διαιρεθεί σε βραχυπρόθεσμη και μακροπρόθεσμη. Στην παρούσα διπλωματική εργασία θα δώσουμε έμφαση στη βραχυπρόθεσμη ευστάθεια τάσης. Για το σκοπό αυτό, αναπτύσσονται δυναμικά μοντέλα που περιγράφουν τη λειτουργία απλών συστημάτων ηλεκτρικής ενέργειας στο περιβάλλον του MATLAB/SIMULINK. Διερευνάται η επίδραση του φορτίου επαγωγικού κινητήρα ενός απλού Σ.Η.Ε., όσον αφορά στη βραχυπρόθεσμη ευστάθεια τάσης, χρησιμοποιώντας τις P-V καμπύλες τόσο του κινητήρα όσο και του δικτύου. Τα αποτελέσματα που προκύπτουν, κατόπιν επαληθεύονται παρατηρώντας τις καταστάσεις του συστήματος στο πεδίο του χρόνου. Με την ανάλυση φαίνεται ότι με την ανάλυση φαίνεται ότι μετά από βραχυκύκλωμα η τάση του συστήματος μειώνεται δραστικά και αυτό μπορεί να προκαλέσει την κατάρρευση του συστήματος όταν αυτό έχει ως φορτίο επαγωγικό κινητήρα. Η κατάρρευση αυτή μπορεί να αποφευχθεί με την όσο το δυνατόν ταχύτερη εκκαθάριση του σφάλματος. Σημαντικός παράγων γι’ αυτό είναι ο καθορισμός του κρίσιμου χρόνου εκκαθάρισης του σφάλματος με σκοπό την αποφυγή της εμφάνισης αστάθειας. Το πρόβλημα αυτό αναλύεται διεξοδικά και ορίζονται με αναλυτικό τρόπο τόσο ο κρίσιμος χρόνος εκκαθάρισης όσο και η κρίσιμη τιμή της ολίσθησης του επαγωγικού κινητήρα. Χρησιμοποιώντας επιπλέον χωρητική αντιστάθμιση αέργου ισχύος αναλύεται ο τρόπος που αυτή βελτιώνει τα περιθώρια ευσταθούς λειτουργίας κατά τη διάρκεια σφαλμάτων. Στη συνέχεια, για τον καθορισμό ενός δείκτη ευστάθειας τάσης σε σχέση με το μέγιστο επιτρεπτό φορτίο σε ένα δίκτυο, περιγράφεται μία διαδικασία καθορισμού ενός τέτοιου δείκτη, η οποία βασίζεται στη σύνθετη τιμή της τάσης όλων των ζυγών ενός συστήματος. Ο προτεινόμενος δείκτης χρησιμοποιείται για την εκτίμηση της μέγιστης φόρτισης του συστήματος. Επιπροσθέτως, καθορίζονται τα πιο «αδύναμα» τμήματα του συστήματος (κρίσιμος ζυγός και κρίσιμη γραμμή) για κατάλληλη άεργο αντιστάθμιση προς αποφυγή κατάρρευσης της τάσης. / Voltage instability has been a great concern for quite a long time in electric power industry. A system enters a state of voltage instability due to increase in demand, a sudden large disturbance or a change in system condition that causes a progressive and uncontrollable decline in voltage. It is therefore interesting to study both the dynamic and static aspects of voltage stability. Dynamic voltage stability can be divided into short-term and long-term based on the dynamics of the components that affect the voltage stability. In this project, we will emphasize on short-term stability. In this study, dynamic models of various power system components are successfully developed in MATLAB/SIMULINK platform. The effect of induction motor load on short-term voltage stability of a simple power system is investigated using the network and motor P-V curves and the results are found and then verified by observing the system states in time domain. Once the reason of voltage instability is identified, a remedial action using fixed capacitive reactive support is suggested to prevent the voltage instability. During a fault, the system voltage reduces drastically and that may cause to stall the induction motors. Stalling of induction motor can be prevented by clearing the fault as quickly as possible. A technique of determining the critical fault clearing time to prevent stalling of induction motor is also presented. In power system operation, it is important for the dispatcher to have knowledge on the maximum permissible loading of the system without reaching voltage instability. In this study, a method of determining the voltage stability index of a system based on the complex voltage of all buses in the system is described. The proposed index is then used in estimating the maximum loading of the system and is based on the information of present and past operating points. In addition, the weakest segments (critical bus and critical line) of the system are also identified for appropriate reactive compensations to avoid voltage collapse. The correctness of the identified critical bus and critical line is then verified by placing shunt/series capacitors at various locations and comparing the corresponding critical load multiplier factors

Η αστάθεια τάσης αποτελεί ένα σημαντικό πρόβλημα για τα συστήματα ηλεκτρικής ενέργειας. Ένα σύστημα εισέρχεται σε κατάσταση αστάθειας τάσης λόγω αύξησης της ζήτησης, μιας ξαφνικής, ευρείας κλίμακας διαταραχής ή αλλαγής στην κατάσταση του, που μπορεί να προκαλέσει μια σταδιακή και ανεξέλεγκτη πτώση τάσης. Παρουσιάζει, λοιπόν, ιδιαίτερο ενδιαφέρον η μεταβατική συμπεριφορά του συστήματος σε σχέση με την ευστάθεια της τάσης. Επίσης, κατά τη λειτουργία ενός Σ.Η.Ε., είναι σημαντικό για το χειριστή να γνωρίζει το μέγιστο επιτρεπτό φορτίο του συστήματος χωρίς να κινδυνεύει από αστάθεια τάσης. Η δυναμική ευστάθεια τάσης μπορεί να διαιρεθεί σε βραχυπρόθεσμη και μακροπρόθεσμη. Στην παρούσα διπλωματική εργασία θα δώσουμε έμφαση στη βραχυπρόθεσμη ευστάθεια τάσης. Για το σκοπό αυτό, αναπτύσσονται δυναμικά μοντέλα που περιγράφουν τη λειτουργία απλών συστημάτων ηλεκτρικής ενέργειας στο περιβάλλον του MATLAB/SIMULINK. Διερευνάται η επίδραση του φορτίου επαγωγικού κινητήρα ενός απλού Σ.Η.Ε., όσον αφορά στη βραχυπρόθεσμη ευστάθεια τάσης, χρησιμοποιώντας τις P-V καμπύλες τόσο του κινητήρα όσο και του δικτύου. Τα αποτελέσματα που προκύπτουν, κατόπιν επαληθεύονται παρατηρώντας τις καταστάσεις του συστήματος στο πεδίο του χρόνου. Με την ανάλυση φαίνεται ότι με την ανάλυση φαίνεται ότι μετά από βραχυκύκλωμα η τάση του συστήματος μειώνεται δραστικά και αυτό μπορεί να προκαλέσει την κατάρρευση του συστήματος όταν αυτό έχει ως φορτίο επαγωγικό κινητήρα. Η κατάρρευση αυτή μπορεί να αποφευχθεί με την όσο το δυνατόν ταχύτερη εκκαθάριση του σφάλματος. Σημαντικός παράγων γι’ αυτό είναι ο καθορισμός του κρίσιμου χρόνου εκκαθάρισης του σφάλματος με σκοπό την αποφυγή της εμφάνισης αστάθειας. Το πρόβλημα αυτό αναλύεται διεξοδικά και ορίζονται με αναλυτικό τρόπο τόσο ο κρίσιμος χρόνος εκκαθάρισης όσο και η κρίσιμη τιμή της ολίσθησης του επαγωγικού κινητήρα. Χρησιμοποιώντας επιπλέον χωρητική αντιστάθμιση αέργου ισχύος αναλύεται ο τρόπος που αυτή βελτιώνει τα περιθώρια ευσταθούς λειτουργίας κατά τη διάρκεια σφαλμάτων. Στη συνέχεια, για τον καθορισμό ενός δείκτη ευστάθειας τάσης σε σχέση με το μέγιστο επιτρεπτό φορτίο σε ένα δίκτυο, περιγράφεται μία διαδικασία καθορισμού ενός τέτοιου δείκτη, η οποία βασίζεται στη σύνθετη τιμή της τάσης όλων των ζυγών ενός συστήματος. Ο προτεινόμενος δείκτης χρησιμοποιείται για την εκτίμηση της μέγιστης φόρτισης του συστήματος. Επιπροσθέτως, καθορίζονται τα πιο «αδύναμα» τμήματα του συστήματος (κρίσιμος ζυγός και κρίσιμη γραμμή) για κατάλληλη άεργο αντιστάθμιση προς αποφυγή κατάρρευσης της τάσης. / Voltage instability has been a great concern for quite a long time in electric power industry. A system enters a state of voltage instability due to increase in demand, a sudden large disturbance or a change in system condition that causes a progressive and uncontrollable decline in voltage. It is therefore interesting to study both the dynamic and static aspects of voltage stability. Dynamic voltage stability can be divided into short-term and long-term based on the dynamics of the components that affect the voltage stability. In this project, we will emphasize on short-term stability. In this study, dynamic models of various power system components are successfully developed in MATLAB/SIMULINK platform. The effect of induction motor load on short-term voltage stability of a simple power system is investigated using the network and motor P-V curves and the results are found and then verified by observing the system states in time domain. Once the reason of voltage instability is identified, a remedial action using fixed capacitive reactive support is suggested to prevent the voltage instability. During a fault, the system voltage reduces drastically and that may cause to stall the induction motors. Stalling of induction motor can be prevented by clearing the fault as quickly as possible. A technique of determining the critical fault clearing time to prevent stalling of induction motor is also presented. In power system operation, it is important for the dispatcher to have knowledge on the maximum permissible loading of the system without reaching voltage instability. In this study, a method of determining the voltage stability index of a system based on the complex voltage of all buses in the system is described. The proposed index is then used in estimating the maximum loading of the system and is based on the information of present and past operating points. In addition, the weakest segments (critical bus and critical line) of the system are also identified for appropriate reactive compensations to avoid voltage collapse. The correctness of the identified critical bus and critical line is then verified by placing shunt/series capacitors at various locations and comparing the corresponding critical load multiplier factors

abstract: Voltage stability is always a major concern in power system operation. Recently Fault Induced Delayed Voltage Recovery (FIDVR) has gained increased attention. It is widely believed that the motor-driven loads of high efficiency, low inertia air conditioners are one of the main causes of FIDVR events. Simulation tools that assist power system operation and planning have been found insufficient to reproduce FIDVR events. This is because of their inaccurate load modeling of single-phase motor loads. Conventionally three-phase motor models have been used to represent the aggregation effect of single-phase motor load. However researchers have found that this modeling method is far from an accurate representation of single-phase induction motors. In this work a simulation method is proposed to study the precise influence of single-phase motor load in context of FIDVR. The load, as seen the transmission bus, is replaced with a detailed distribution system. Each single-phase motor in the distribution system is represented by an equipment-level model for best accuracy. This is to enable the simulation to capture stalling effects of air conditioner compressor motors as they are related to FIDVR events. The single phase motor models are compared against the traditional three phase aggregate approximation. Also different percentages of single-phase motor load are compared and analyzed. Simulation result shows that proposed method is able to reproduce FIDVR events. This method also provides a reasonable estimation of the power system voltage stability under the contingencies. / Dissertation/Thesis / M.S. Electrical Engineering 2012

[pt] Após a incidência de alguns colapsos de tensão em sistemas de transmissão de energia a nível mundial, a segurança de tensão tornou-se um assunto de muito interesse nos últimos anos devido à importância do seu impacto. O fenômeno de estabilidade de tensão deve-se a fluxos de potência ativa e reativa excessivos na rede de transmissão e está associado às restrições ambientais e econômicas que impedem a expansão da rede. Atualmente, sabese da existência de uma máxima carga que pode ser alimentada pela rede e é a manifestação mais conhecida do fenômeno mas, também, é possível que o problema manifeste-se pela existência de uma máxima injeção de potência ativa e reativa na rede por geradores e compensadores síncronos. E mais, em situações de carregamento elevado da rede, é possível que ações de controle de tensão tenham efeito oposto ao usual. É apresentado um método seqüencial iterativo de avaliação e reforço para as condições de carregamento da rede em barras de tensão controlada, embora na literatura somente as barras de carga são analisadas. A verificação do comportamento do gerador e compensador síncrono como dispositivo de controle torna-se necessária já que, se funcionar de forma inversa, poderá levar o sistema ao colapso por problemas de tensão. Uma vez que a avaliação do carregamento da rede de transmissão detectou uma barra de geração crítica em um determinado ponto de operação, o reforço consiste do cálculo de ações de controle para aumentar a distância ou margem de potência entre a geração daquela barra e o novo máximo permitido. Muitas vezes isso pode ser conseguido através da alteração do perfil de tensão com a conseqüente redução nas perdas. Muitas outras vezes, o redespacho de potência ativa torna-se necessário. As etapas do método são: identificar a barra crítica, identificar a sub-rede utilizada para transmitir potência ativa dessa barra para as cargas, nessa sub-rede determinar o caminho e ramo mais carregados e, desviar o fluxo de potência do ramo mais carregado para outros. A seqüência é repetida até que as novas margens de potência sejam consideradas aceitáveis. Exemplos numéricos ilustrativos reais com o sistema brasileiro são apresentados. É verificado que o método proposto realmente produz os resultados desejados. / [en] After the incidence of some voltage collapses in the energy transmission systems in the world, the voltage security became an issue of great interest in the last years due to the importance of its impact. The phenomenon of voltage stability is due to the excessive active and reactive power flow in the electrical transmission network and has been associated with environment questions and lack of financial resources for transmission system expansion. Nowadays, it is well-known that there is a maximum power that the network can transmit to a load bus and is the best known manifestation of the phenomenon, but, is not familiar to many that there is a maximum power that can be injected by generators and synchronous compensators into the network. Moreover, in heavy loading conditions is possible that voltage control actions would have the inverse effect. It is shown a sequential iterative method for assessment and voltage security reinforcement in voltage-controlled buses, although the literature only the load buses are analyzed. The verification of the behaviour of the generator and synchronous compensator as control device becomes necessary since, if it works in an inverse way, it can take the system to the voltage collapse. Once the assessment is performed and is detected one generation critical bus in some operating point, the objective of the reinforcement function is to calculate adequate control actions in order to increase the distance or power margin between the actual generation and the new maximum power flow. Several times this may be achieved by voltage profile changes and consequent loss reduction. Sometimes that procedure is not enough and active generation rescheduling is recommended. The stages of the method are: identify the critical bus, identify the sub-network used to transmit active power flow from this bus to load buses, in this sub-network the critical transmission path and critical branch are determined and redirect the power flow from the branch more loaded to others. The sequence is repeated until resultant power margins are judged suitable. Illustrative real life numerical examples with the Brazilian system are provided. It is verified that the proposed method really produces the desired results.

[pt] Este trabalho analisa o fenômeno da estabilidade de tensão no domínio do tempo incluindo fenômenos rápidos (transitórios) e lentos (longo-termo). As diferentes formas de estabilidade existentes nos sistemas elétricos de potência são definidas e classificadas de acordo com a variável de interesse e com a amplitude do distúrbio. Utilizando-se um simples sistema elétrico de potência, verifica-se através de formulações dinâmicas fatores relevantes ao fenômeno da estabilidade de tensão. Investiga-se a influência de cargas do tipo potência constante e impedância constante sobre a estabilidade de tensão. Compensadores estáticos são incluídos nas análises e verifica-se a existência de regiões de operação onde as ações de controle não apresentam o efeito esperado. Investiga-se através de cenários o efeito adverso de dispositivos de controle com o limitador de sobre- excitação e o transformador de tape variável sobre a estabilidade de tensão. A partir de uma versão do programa de estabilidade transitória TRANSTAB, foram desenvolvidas duas versões do programa computacional VOLTDYN para simular no domínio do tempo o fenômeno da estabilidade de tensão. A primeira versão do programa Utiliza um algoritmo de integração de passo variável usando o método trapezoidal implícito enquanto que a segunda versão utiliza o método de Adams-Bashforth- Moulton. Diversos testes computacionais com as duas versões são realizados comprovando-se a importância desta forma de análise. / [en] This work is concerned with voltage stability analysis in time domain including transient and long-term time frames. Different power system stability forms are defined and classified according to the variable of interest and with the disturbance magnitude. Using a simple power system model, it is shown through dynamics formulations important aspects of the voltage stability phenomenon. Important aspects of load characteristics of constant power type and mixed (constant power/constant impedance) type on voltage stability are investigated. A static compensator model is included in the analysis and it is verified that under specific operation conditions the control actions are not efficient. Scenarios show the adverse effects of long-term control devices such as overexcitation limiters and under load tap changers on voltage stability. One version of the transient stability program TRANSTAB is modified in order to simulate transient and long-term voltage phenomena. The resulting modified computer program is called VOLTDYN. Two versions of the VOLTDYN progran are available. The first version uses a variable step-size algorithm based on the trapezoidal method. The other includes a variable step-size algorithm based on the Adams- Bashforth-Moulton method.

abstract: In the recent past, due to regulatory hurdles and the inability to expand transmission systems, the bulk power system is increasingly being operated close to its limits. Among the various phenomenon encountered, static voltage stability has received increased attention among electric utilities. One approach to investigate static voltage stability is to run a set of power flow simulations and derive the voltage stability limit based on the analysis of power flow results. Power flow problems are formulated as a set of nonlinear algebraic equations usually solved by iterative methods. The most commonly used method is the Newton-Raphson method. However, at the static voltage stability limit, the Jacobian becomes singular. Hence, the power flow solution may fail to converge close to the true limit. To carefully examine the limitations of conventional power flow software packages in determining voltage stability limits, two lines of research are pursued in this study. The first line of the research is to investigate the capability of different power flow solution techniques, such as conventional power flow and non-iterative power flow techniques to obtain the voltage collapse point. The software packages used in this study include Newton-based methods contained in PSSE, PSLF, PSAT, PowerWorld, VSAT and a non-iterative technique known as the holomorphic embedding method (HEM). The second line is to investigate the impact of the available control options and solution parameter settings that can be utilized to obtain solutions closer to the voltage collapse point. Such as the starting point, generator reactive power limits, shunt device control modes, area interchange control, and other such parameters. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2017

Made available in DSpace on 2014-06-11T19:22:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-23Bitstream added on 2014-06-13T20:09:48Z : No. of bitstreams: 1 martins_lfb_me_bauru.pdf: 963421 bytes, checksum: 7c1f9175f040c64a63fdf8db9f7a10a1 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho foi feita uma análise comparativa entre diferentes escolhas dos pontos utilizados pelo método look ahead na estimação do ponto de máximo carregamento de um sistema elétrico de potência. O Fluxo de Cargo Continuado é utilizado na geração dos pontos de operação utilizados pelo método look ahead e para servir como referência na comparação entre os resultados previstos e o ponto de máximo carregamento real. Uma vez que a exatidão dessa estimativa é fortemente afetada pela escolha desses pontos, o FCC é modificado para fornecer pontos mais adequados para o bom funcionamento do método look ahead. A metodologia proposta é aplicada ao sistema IEEE de 300 barras, os resultados obtidos mostram o seu bom funcionamento / Here we did a comparative analysis between different choices of the points used by the look ahead method for estimating maximum loading point of a power system. The Continued Power Flow (CPF) is used in the generation of operating points used by the look ahead method and to serve as a reference in comparison between the predicted results and the real maximum loading point. Since the accurancy of this estimative is strongly affected by choicen of these points, the CPF is modified to provide the most appropriate for the proper functioning of the method look ahead. The proposed methodology system is applied to IEEE 300 buses, the results have shown its good functioning

abstract: Recently, a novel non-iterative power flow (PF) method known as the Holomorphic Embedding Method (HEM) was applied to the power-flow problem. Its superiority over other traditional iterative methods such as Gauss-Seidel (GS), Newton-Raphson (NR), Fast Decoupled Load Flow (FDLF) and their variants is that it is theoretically guaranteed to find the operable solution, if one exists, and will unequivocally signal if no solution exists. However, while theoretical convergence is guaranteed by Stahl’s theorem, numerical convergence is not. Numerically, the HEM may require extended precision to converge, especially for heavily-loaded and ill-conditioned power system models. In light of the advantages and disadvantages of the HEM, this report focuses on three topics: 1. Exploring the effect of double and extended precision on the performance of HEM, 2. Investigating the performance of different embedding formulations of HEM, and 3. Estimating the saddle-node bifurcation point (SNBP) from HEM-based Thévenin-like networks using pseudo-measurements. The HEM algorithm consists of three distinct procedures that might accumulate roundoff error and cause precision loss during the calculations: the matrix equation solution calculation, the power series inversion calculation and the Padé approximant calculation. Numerical experiments have been performed to investigate which aspect of the HEM algorithm causes the most precision loss and needs extended precision. It is shown that extended precision must be used for the entire algorithm to improve numerical performance. A comparison of two common embedding formulations, a scalable formulation and a non-scalable formulation, is conducted and it is shown that these two formulations could have extremely different numerical properties on some power systems. The application of HEM to the SNBP estimation using local-measurements is explored. The maximum power transfer theorem (MPTT) obtained for nonlinear Thévenin-like networks is validated with high precision. Different numerical methods based on MPTT are investigated. Numerical results show that the MPTT method works reasonably well for weak buses in the system. The roots method, as an alternative, is also studied. It is shown to be less effective than the MPTT method but the roots of the Padé approximant can be used as a research tool for determining the effects of noisy measurements on the accuracy of SNBP prediction. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2018

[pt] A falta de recursos e a questão ecológica tem limitado a expansão do sistema de transmissão. Esta realidade, em conjunto com o crescimento da carga, faz com que os sistemas elétricos trabalhem bastante carregados. Esta nova condição pode levar a situações de colapso de tensão. O desenvolvimento de métodos para a avaliação do carregamento da rede de transmissão tornou-se necessário e imprescindível para que se possa entender o funcionamento do sistema nestas condições e possibilitar a sua operação de modo correto. O carregamento da rede de transmissão pode ser avaliado por condições nodais associadas ao máximo fluxo de potência ativa e reativa que pode ser transmitida dos geradores para as cargas. Estas condições nodais são avaliadas por uma ferramenta analítica com base em modelo matemático, simples mas poderoso, de uma direta interpretação física do fenômeno. Índices abrangentes e significativos são obtidos a partir da matriz Jacobiano do sistema. Eles indicam a região de operação na curva V x P, Q a margem em MVA para o máximo carregamento, a importância relativa entre as barras, e uma medida de dificuldade de transmissão. O controle de tensão influi diretamente nas condições de operação e portanto, deve ser incluído na modelagem do problema. Usualmente são: controle de tensão por ajuste de tap de LTCs e controle de tensão (local e remota) por injeção de potência reativa. O controle é restrito pelos limites dos taps de transformadores, limites de injeção de potência reativa e limites de tensão. Neste trabalho é mostrada a forma como se deve incluir os controles e limites relacionados com a tensão, na ferramenta analítica de avaliação do carregamento da rede de transmissão. O índice calculado apropriadamente é nulo no ponto de máxima transferência de potência. É mostrado que os controles e limites de tensão do sistema podem e devem ser representados na matriz Jacobiano do sistema linearizado de equações que modelam o sistema, exceto os da barra em análise, mesmo se esta tiver sua tensão controlada. / [en] The lack of investiments and the ecological matter have limited the expansion of the transmission system. This reality, together with the growth of the load, makes the electric systems to work heavy loaded. This new condition can lead to situations of voltage collapse. The development of methods for evaluation the loading of the transmission network became necessary and indispensable in understanding the performance of the system under these conditions and in making possible the operating in a correct way. The transmission system loading can be evaluated by nodal conditions associated to the maximum active and reactive power flow that can be transmitted from generators to loads. These nodal conditions are assessed by an analytic tool based on a a mathematical model. Simple but powerful, derived directly from a physical interpretation of the phenomenon. Meaningful and comprehensive indexes are obtained from a partition of the jacobian matrix of the system. They indicate the operation area in the V x P, Q curve, the margin in MVA for the maximu loading, the relative importance among the busbars, and a measure of transmission difficulty. The voltage control is of paramount importance on operating consitions and therefore should be included in the problem modeling. Usually they are voltage control by tap adjstment of LTCs and voltage control (local and remote) by injection of reactive power. The control is constrained by limits on the taps of transformers, on reactive power injection and on voltage magnitudes. In this work it is shown how the controls and limits related with the voltage should be include in the analytical tool for the evaluation of the transmission system loading. The index calculated adequately is null in the point of maximum power transfer, positive in the upper half and negative in the lower half of the V x P, Q curve. It is shown that the voltage controls and limits of the system can and should be represented in the Jacobian matrix of the linearised system of equations, except on bus under analysis, even if it is a voltage controlled bus.