Uso de técnicas de otimização baseadas em derivadas como suporte do planejamento operacional de redes de distribuição de energia elétrica

The usual programs for load flow calculation were in general developped aiming the simulation of electric energy transmission, subtransmission and distribution systems. However, the mathematical methods and algorithms used by the formulations were based, in majority, just on the characteristics of the transmittion systems, which were the main concern focus of engineers and researchers. Though, the physical characteristics of these systems are quite different from the distribution ones. In the transmission systems, the voltage levels are high and the lines are generally very long. These aspects contribute the capacitive and inductive effects that appear in the system to have a considerable influence in the values of the interest quantities, reason why they should be taken into consideration. Still in the transmission systems, the loads have a macro nature, as for example, cities, neiborhoods, or big industries. These loads are, generally, practically balanced, what reduces the necessity of utilization of three-phase methodology for the load flow calculation. Distribution systems, on the other hand, present different characteristics: the voltage levels are small in comparison to the transmission ones. This almost annul the capacitive effects of the lines. The loads are, in this case, transformers, in whose secondaries are connected small consumers, in a sort of times, mono-phase ones, so that the probability of finding an unbalanced circuit is high. This way, the utilization of three-phase methodologies assumes an important dimension. Besides, equipments like voltage regulators, that use simultaneously the concepts of phase and line voltage in their functioning, need a three-phase methodology, in order to allow the simulation of their real behavior. For the exposed reasons, initially was developped, in the scope of this work, a method for three-phase load flow calculation in order to simulate the steady-state behaviour of distribution systems. Aiming to achieve this goal, the Power Summation Algorithm was used, as a base for developing the three phase method. This algorithm was already widely tested and approved by researchers and engineers in the simulation of radial electric energy distribution systems, mainly for single-phase representation. By our formulation, lines are modeled in three-phase circuits, considering the magnetic coupling between the phases; but the earth effect is considered through the Carson reduction. It s important to point out that, in spite of the loads being normally connected to the transformer s secondaries, was considered the hypothesis of existence of star or delta loads connected to the primary circuit. To perform the simulation of voltage regulators, a new model was utilized, allowing the simulation of various types of configurations, according to their real functioning. Finally, was considered the possibility of representation of switches with current measuring in various points of the feeder. The loads are adjusted during the iteractive process, in order to match the current in each switch, converging to the measured value specified by the input data. In a second stage of the work, sensibility parameters were derived taking as base the described load flow, with the objective of suporting further optimization processes. This parameters are found by calculating of the partial derivatives of a variable in respect to another, in general, voltages, losses and reactive powers. After describing the calculation of the sensibility parameters, the Gradient Method was presented, using these parameters to optimize an objective function, that will be defined for each type of study. The first one refers to the reduction of technical losses in a medium voltage feeder, through the installation of capacitor banks; the second one refers to the problem of correction of voltage profile, through the instalation of capacitor banks or voltage regulators. In case of the losses reduction will be considered, as objective function, the sum of the losses in all the parts of the system. To the correction of the voltage profile, the objective function will be the sum of the square voltage deviations in each node, in respect to the rated voltage. In the end of the work, results of application of the described methods in some feeders are presented, aiming to give insight about their performance and acuity

Uso de técnicas de otimização baseadas em derivadas como suporte do planejamento operacional de redes de distribuição de energia elétrica

The usual programs for load flow calculation were in general developped aiming the simulation of electric energy transmission, subtransmission and distribution systems. However, the mathematical methods and algorithms used by the formulations were based, in majority, just on the characteristics of the transmittion systems, which were the main concern focus of engineers and researchers. Though, the physical characteristics of these systems are quite different from the distribution ones. In the transmission systems, the voltage levels are high and the lines are generally very long. These aspects contribute the capacitive and inductive effects that appear in the system to have a considerable influence in the values of the interest quantities, reason why they should be taken into consideration. Still in the transmission systems, the loads have a macro nature, as for example, cities, neiborhoods, or big industries. These loads are, generally, practically balanced, what reduces the necessity of utilization of three-phase methodology for the load flow calculation. Distribution systems, on the other hand, present different characteristics: the voltage levels are small in comparison to the transmission ones. This almost annul the capacitive effects of the lines. The loads are, in this case, transformers, in whose secondaries are connected small consumers, in a sort of times, mono-phase ones, so that the probability of finding an unbalanced circuit is high. This way, the utilization of three-phase methodologies assumes an important dimension. Besides, equipments like voltage regulators, that use simultaneously the concepts of phase and line voltage in their functioning, need a three-phase methodology, in order to allow the simulation of their real behavior. For the exposed reasons, initially was developped, in the scope of this work, a method for three-phase load flow calculation in order to simulate the steady-state behaviour of distribution systems. Aiming to achieve this goal, the Power Summation Algorithm was used, as a base for developping the three phase method. This algorithm was already widely tested and approved by researchers and engineers in the simulation of radial electric energy distribution systems, mainly for single-phase representation. By our formulation, lines are modeled in three-phase circuits, considering the magnetic coupling between the phases; but the earth effect is considered through the Carson reduction. Its important to point out that, in spite of the loads being normally connected to the transformers secondaries, was considered the hypothesis of existence of star or delta loads connected to the primary circuit. To perform the simulation of voltage regulators, a new model was utilized, allowing the simulation of various types of configurations, according to their real functioning. Finally, was considered the possibility of representation of switches with current measuring in various points of the feeder. The loads are adjusted during the iteractive process, in order to match the current in each switch, converging to the measured value specified by the input data. In a second stage of the work, sensibility parameters were derived taking as base the described load flow, with the objective of suporting further optimization processes. This parameters are found by calculating of the partial derivatives of a variable in respect to another, in general, voltages, losses and reactive powers. After describing the calculation of the sensibility parameters, the Gradient Method was presented, using these parameters to optimize an objective function, that will be defined for each type of study. The first one refers to the reduction of technical losses in a medium voltage feeder, through the installation of capacitor banks; the second one refers to the problem of correction of voltage profile, through the instalation of capacitor banks or voltage regulators. In case of the losses reduction will be considered, as objective function, the sum of the losses in all the parts of the system. To the correction of the voltage profile, the objective function will be the sum of the square voltage deviations in each node, in respect to the rated voltage. In the end of the work, results of application of the described methods in some feeders are presented, aiming to give insight about their performance and acuity

Mapeamento da isoterma de Curie na Bacia do Parnaíba estimada através da profundidade da base das fontes magnéticas

Located on the western edge of the Brazilian northeast, the Parnaíba Basin is an intra cratonic basin with oil production. This study aims at understanding its genesis and evolution, using aeromagnetic and gravity data. We used the spectral analysis of aeromagnetic data to map the depth to the bottom of the magnetic sources in order to assimilate this depth with the depth of the Curie isotherm, and infer the geothermal gradient. Using the spectral analysis technique, we succeeded in mapping the surface of the depth to the bottom of magnetic sources (SBFM), which marks the depth that occur magnetization. In the Parnaíba Basin the SBFM presented depths around -20,5 and -28,5 , which was consistent with an inversion of the same dataset using the technique of Magnetization Vector Inversion (MVI). Furthermore, SBFM topography correlates well with Moho depth, which was estimated from satellite gravimetric data from the GOCE mission (Gravity Field and Steady-State Ocean Circulation Explorer). Assuming that SBFM coincides with the Curie isotherm of magnetite (ICM), defined as the surface at which magnetite ( ) looses its ferromagnetic properties, it was possible to estimate the geothermal gradient. The geothermal gradient in the basin showed values between 19.2 and 26.5 , allowing to estimate the heat flow for the Parnaíba basin after assuming a conductivity of 2.69 . The resulting heat flow values ranged between 51.6 and 71.3 , which is consistent with values found in other works throughout the South American continent. Lithospheric thickness using an empirical relationship, finding values between -65.8 and -89.2 . We propose that thermal structure of Parnaíba basin is influenced by a deep thermal anomaly. This anomaly has heated the lithosphere beneath the basin and has resulted in relatively thin values for the lithospheric thickness and relatively high surface heat flow values. The origin of the anomaly is not clear, but the correlation between Curie depth and Moho topography, suggests that tectonic extension processes could have played a role.