Probabilistic load flow calculation for AC traction supplies with AT feeding

Power load flow analysis is essential for system planning, operation, development and maintenance. Its application on railway supply system is no exception. Railway power supplies system distinguishes itself in terms of load pattern and mobility, as well as feeding system structure. An attempt has been made to apply probability load flow (PLF) techniques on electrified railways in order to examine the loading on the feeding substations and the voltage profiles of the trains. This study is to formulate a simple and reliable model to support the necessary calculations for probability load flow analysis in railway systems with autotransformer (AT) feeding system, and describe the development of a software suite to realise the computation.

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

Load flow in electrified railway

Probabilistic load flow techniques have been adopted in AC electrified railways to study the load demand under various train service conditions. This paper highlights the differences in probabilistic load flow analysis between the usual power systems and power supply systems in AC railways; discusses the possible difficulties in problem formulation and presents the link between train movement and the corresponding power demand for load flow calculation.

Dedução de Funções de Alívio para Priorização de Variantes de Chaveamento Adequadas à Eliminação de Sobrecargas

Eventually, violations of voltage limits at buses or admissible loadings of transmission lines and/or power transformers may occur by the power system operation. If violations are detected in the supervision process, corrective measures may be carried out in order to eliminate them or to reduce their intensity. Loading restriction is an extreme solution and should only be adopted as the last control action. Previous researches have shown that it is possible to control constraints in electrical systems by changing the network topology, using the technique named Corrective Switching, which requires no additional costs. In previous works, the proposed calculations for verifying the ability of a switching variant in eliminating an overload in a specific branch were based on network reduction or heuristic analysis. The purpose of this work is to develop analytical derivation of linear equations to estimate current changes in a specific branch (due to switching measures) by means of few calculations. For bus-bar coupling, derivations will be based on short-circuit theory and Relief Function methodology. For bus-bar splitting, a Relief Function will be derived based on a technique of equivalent circuit. Although systems of linear equations are used to substantiate deductions, its formal solution for each variant, in real time does not become necessary. A priority list of promising variants is then assigned for final check by an exact load flow calculation and a transient analysis using ATP Alternative Transient Program. At last, results obtained by simulation in networks with different features will be presented

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

Implementação de um algoritmo para a análise de curtos-circuitos de alta impedância baseado no fluxo de carga soma de potências

This work has as main objective to show all the particularities regarding the Three-phase Power Summation Method, used for load flow calculation, in what it says respect to the influence of the magnetic coupling among the phases, as well as to the losses presented in all the existent transformers in the feeder to be analyzed. Besides, its application is detailed in the study of the short-circuits, that happen in the presence of high impedance values, which possess a problem, that is its difficult detection and consequent elimination on the part of common devices of protection. That happens due to the characteristic presented by the current of short¬ circuit, in being generally of the same order of greatness that the load currents. Results of simulations accomplished in several situations will be shown, objectifying a complete analysis of the behavior of the proposed method in several types of short-circuits. Confront of the results obtained by the method with results of another works will be presented to verify its effectiveness

Stress and load calculation for unknown building

Not available.

Verification of the time-response method for heat load calculation.

"Office of the Assistant Secretary for Policy Development and Research, Dept. of Housing and Urban Development."

Bearing damage analysis by calculation of capacitive coupling between inner and outer races of a ball bearing

Bearing damage in modern inverter-fed AC drive systems is more common than in motors working with 50 or 60 Hz power supply. Fast switching transients and common mode voltage generated by a PWM inverter cause unwanted shaft voltage and resultant bearing currents. Parasitic capacitive coupling creates a path to discharge current in rotors and bearings. In order to analyze bearing current discharges and their effect on bearing damage under different conditions, calculation of the capacitive coupling between the outer and inner races is needed. During motor operation, the distances between the balls and races may change the capacitance values. Due to changing of the thickness and spatial distribution of the lubricating grease, this capacitance does not have a constant value and is known to change with speed and load. Thus, the resultant electric field between the races and balls varies with motor speed. The lubricating grease in the ball bearing cannot withstand high voltages and a short circuit through the lubricated grease can occur. At low speeds, because of gravity, balls and shaft voltage may shift down and the system (ball positions and shaft) will be asymmetric. In this study, two different asymmetric cases (asymmetric ball position, asymmetric shaft position) are analyzed and the results are compared with the symmetric case. The objective of this paper is to calculate the capacitive coupling and electric fields between the outer and inner races and the balls at different motor speeds in symmetrical and asymmetrical shaft and balls positions. The analysis is carried out using finite element simulations to determine the conditions which will increase the probability of high rates of bearing failure due to current discharges through the balls and races.

Probabilistic load flow in AC electrified railways

System analysis within the traction power system is vital to the design and operation of an electrified railway. Loads in traction power systems are often characterised by their mobility, wide range of power variations, regeneration and service dependence. In addition, the feeding systems may take different forms in AC electrified railways. Comprehensive system studies are usually carried out by computer simulation. A number of traction power simulators have been available and they allow calculation of electrical interaction among trains and deterministic solutions of the power network. In the paper, a different approach is presented to enable load-flow analysis on various feeding systems and service demands in AC railways by adopting probabilistic techniques. It is intended to provide a different viewpoint to the load condition. Simulation results are given to verify the probabilistic-load-flow models.

A three-dimensional tunnel model for calculation of train-induced ground vibration

The frequency range of interest for ground vibration from underground urban railways is approximately 20 to 100 Hz. For typical soils, the wavelengths of ground vibration in this frequency range are of the order of the spacing of train axles, the tunnel diameter and the distance from the tunnel to nearby building foundations. For accurate modelling, the interactions between these entities therefore have to be taken into account. This paper describes an analytical three-dimensional model for the dynamics of a deep underground railway tunnel of circular cross-section. The tunnel is conceptualised as an infinitely long, thin cylindrical shell surrounded by soil of infinite radial extent. The soil is modelled by means of the wave equations for an elastic continuum. The coupled problem is solved in the frequency domain by Fourier decomposition into ring modes circumferentially and a Fourier transform into the wavenumber domain longitudinally. Numerical results for the tunnel and soil responses due to a normal point load applied to the tunnel invert are presented. The tunnel model is suitable for use in combination with track models to calculate the ground vibration due to excitation by running trains and to evaluate different track configurations. © 2006 Elsevier Ltd. All rights reserved.

Failure of fiber bundles with local load sharing

We develop a recursion-relation approach for calculating the failure probabilities of a fiber bundle with local load sharing. This recursion relation is exact, so it provides a way to test the validity of the various approximate methods. Applying the exact calculation to uniform and Weibull threshold distributions, we find that the most probable failure load coincides with the average strength as the size of the system N --> infinity.

Determination of Power System Response during Small Load Fluctuations

This paper proposes a calculation method to determine power system response during small load perturbations or minor disturbances. The method establishes the initial value of active power transient using traditional reduction technique on admittance matrix, which incorporates voltage variations in the determination. The method examines active power distribution among generators when several loads simultaneously change, and verifies that the superposition principle is applicable for this scenario. The theoretical derivation provided in the paper is validated by numerical simulations using a 3-generator 9-bus benchmark model. The results indicate that the inclusion of voltage variation renders an independent and precise measure of active power response during transient conditions.