Utiliza-se o método de decomposições do índice Theil-L para encontrar determinantes da desigualdade de desempenho escolar das crianças da 4ª série do ensino fundamental do estado de São Paulo. Os dados de proficiência dos alunos em português e matemática são extraídos da Prova Brasil 2005 e combinados com os dados do Censo Escolar 2005. A análise das contribuições brutas e marginais geradas por meio do índice Theil L mostra que variáveis comumente utilizadas como medidas de background sócioeconômico dos alunos explicam pouco da desigualdade das notas, menos de 2%. Ao mesmo tempo, as contribuições brutas e marginais apontam para a importância significativa das escolas, que explicam 14,58% da desigualdade de desempenho dos alunos em matemática e 13,27% do desempenho dos alunos em português. A única variável que explica significativamente a desigualdade entre as escolas é o município, 14,56% da desigualdade em matemática e 13,98% em português. As demais variáveis quando consideradas isoladamente, respondem por menos de 2,5% da desigualdade. Quando tomadas em grupos, seu poder explicativo aumenta. As variáveis de infraestrutura escolar explicam 18,68% da desigualdade entre as escolas em português e 20% da desigualdade em matemática. As variáveis referentes ao background dos colegas respondem respectivamente por 8,79 e 9,40%. Conclui-se que o impacto das diferentes variáveis no desempenho dos alunos se dá por meio de sua interação mais do que pelo efeito de variáveis específicas. Reitera-se também a importância de se entender o impacto dos insumos escolares para compreender a proficiência dos alunos. O trabalho aponta ainda o efeito que os municípios têm sobre as escolas e oferece base para uma melhor compreensão posterior desse fenômeno. / This research uses the method of Theil-L decomposition to find determinants of the inequality among students scores of the 4th grade of the fundamental school in the state of São Paulo. The data is provided by a combination of Prova Brasil 2005 standardized tests and the Censo Escolar 2005. The analysis of the gross and marginal contributions measured by the Theil-L indez indicates that the variables normally used for students social and economic background give few explanation about the total inequality measured. The analysis of the decompositions also shows that schools play a main role in the inequalities among students, explaining 14,58% of the students inequality in math and 13,27% in Portuguese. The only single variable that shows an important impact in the score inequalities among schools is the municipality, 14,56% for math and 13,98% for Portuguese. The other variables have no impact over 2,5% when considered solely. By the other side, when these variables are considered in groups, there is a gain in explanation. The school infra-structure explain 18,68% of the inequality among schools in Portuguese and 20% of the inequality in math. The variables about the peers background are responsible for 8,79 and 9,40% respectively. It is concluded that the impact of differents variables in students learning are more due to their interaction, than by their direct effects. It is reinforced the importance of a better understanding of school variables to understand children apprenticeship as shown by part of the literature. This research points to the importance of municipalities for schools and gives a basis for further discussion on this matter.

Utiliza-se o método de decomposições do índice Theil-L para encontrar determinantes da desigualdade de desempenho escolar das crianças da 4ª série do ensino fundamental do estado de São Paulo. Os dados de proficiência dos alunos em português e matemática são extraídos da Prova Brasil 2005 e combinados com os dados do Censo Escolar 2005. A análise das contribuições brutas e marginais geradas por meio do índice Theil L mostra que variáveis comumente utilizadas como medidas de background sócioeconômico dos alunos explicam pouco da desigualdade das notas, menos de 2%. Ao mesmo tempo, as contribuições brutas e marginais apontam para a importância significativa das escolas, que explicam 14,58% da desigualdade de desempenho dos alunos em matemática e 13,27% do desempenho dos alunos em português. A única variável que explica significativamente a desigualdade entre as escolas é o município, 14,56% da desigualdade em matemática e 13,98% em português. As demais variáveis quando consideradas isoladamente, respondem por menos de 2,5% da desigualdade. Quando tomadas em grupos, seu poder explicativo aumenta. As variáveis de infraestrutura escolar explicam 18,68% da desigualdade entre as escolas em português e 20% da desigualdade em matemática. As variáveis referentes ao background dos colegas respondem respectivamente por 8,79 e 9,40%. Conclui-se que o impacto das diferentes variáveis no desempenho dos alunos se dá por meio de sua interação mais do que pelo efeito de variáveis específicas. Reitera-se também a importância de se entender o impacto dos insumos escolares para compreender a proficiência dos alunos. O trabalho aponta ainda o efeito que os municípios têm sobre as escolas e oferece base para uma melhor compreensão posterior desse fenômeno. / This research uses the method of Theil-L decomposition to find determinants of the inequality among students scores of the 4th grade of the fundamental school in the state of São Paulo. The data is provided by a combination of Prova Brasil 2005 standardized tests and the Censo Escolar 2005. The analysis of the gross and marginal contributions measured by the Theil-L indez indicates that the variables normally used for students social and economic background give few explanation about the total inequality measured. The analysis of the decompositions also shows that schools play a main role in the inequalities among students, explaining 14,58% of the students inequality in math and 13,27% in Portuguese. The only single variable that shows an important impact in the score inequalities among schools is the municipality, 14,56% for math and 13,98% for Portuguese. The other variables have no impact over 2,5% when considered solely. By the other side, when these variables are considered in groups, there is a gain in explanation. The school infra-structure explain 18,68% of the inequality among schools in Portuguese and 20% of the inequality in math. The variables about the peers background are responsible for 8,79 and 9,40% respectively. It is concluded that the impact of differents variables in students learning are more due to their interaction, than by their direct effects. It is reinforced the importance of a better understanding of school variables to understand children apprenticeship as shown by part of the literature. This research points to the importance of municipalities for schools and gives a basis for further discussion on this matter.

The modern day power system is witnessing a tremendous change. There has been a rapid rise in the distributed generation, along with this the deregulation has resulted in a more complex system. The power demand is on a rise, the generation and trans-mission infrastructure hasn't yet adapted to this growing demand. The economic and operational constraints have forced the system to be operated close to its design limits, making the system vulnerable to disturbances and possible grid failure. This makes the study of voltage stability of the system important more than ever. Generally, voltage stability studies are carried on a single phase equivalent system assuming that the system is perfectly balanced. However, the three phase power system is not always in balanced state. There are a number of untransposed lines, single phase and double phase lines. This thesis deals with three phase voltage stability analysis, in particular the voltage stability index known as L-Index. The equivalent single phase analysis for voltage stability fails to work in case of any unbalance in the system or in presence of asymmetrical contingency. Moreover, as the system operators are giving importance to synchrophasor measurements, PMUs are being installed throughout the system. Hence, the three phase voltages can be obtained, making three phase analysis easier. To study the effect of unbalanced system on voltage stability a three phase L-Index based on traditional L-Index has been proposed. The proposed index takes into consideration the unbalance resulting due to untransposed transmission lines and unbalanced loads in the system. This index can handle any unbalance in the system and is much more realistic. To obtain bus voltages during unbalanced operation of the system a three phase decoupled Newton Raphson load ow was used. Reactive power distribution in a system can be altered using generators voltage set-ting, transformers OLTC settings and SVC settings. All these settings are usually in balanced mode i.e. all the phases have the same setting. Based on this reactive power optimization using LP technique on an equivalent single phase system is proposed. This method takes into account generator voltage settings, OLTC settings of transformers and SVC settings. The optimal settings so obtained are applied to corresponding three phase system. The effectiveness of the optimal settings during unbalanced scenario is studied. This method ensures better voltage pro les and decrease in power loss. Case studies of the proposed methods are carried on 12 bus and 24 bus EHV systems of southern Indian grid and a modified IEEE 30 bus system. Both balanced and unbalanced systems are studied and the results are compared.