Kerr electro-optic theory and measurements of electric fields withmagnitude and direction varying along the light path

Differential equations that govern light propagation in Kerr media are derived when the applied electric field direction and magnitude vary along the light path. Case studies predict Kerr electro-optic fringe patterns for the specific case of point/plane electrodes. We apply the characteristic directions theory of photoelasticity to understand these fringes. We also study birefringent media with small Kerr constant, in particular transformer oil. For this case we show that simplifications in the characteristic parameter theory is possible, resulting in simple integral relationships between the characteristic parameters and the applied electric field. We use these simple relationships to extend the ac modulation method to measure the characteristic parameters for small Kerr constant media. Measurements of the characteristic parameters using the ac modulation method are presented for point/plane electrodes in transformer oil. The measurements agree reasonably well with space charge free theory for infinite extent electrodes for which analytical expressions are available. We finally employ the `onion peeling' method to reconstruct the axisymmetric electric field magnitude and direction from the measured characteristic parameters and compare the results to the analytically obtained electric field     

Finite element based Kerr electro-optic reconstruction of spacecharge

Recently we used the onion peeling method to reconstruct the axisymmetric electric field distribution of point/plane electrodes from Kerr electro-optic measurements. The method accurately reconstructed the electric field from numerically generated data. However in the presence of experimental noise the performance was less satisfactory. The measurements were especially noisy and unstable near the needle tip which is also the interesting region since most charge injection initiates here. We develop a new algorithm for Kerr electro-optic reconstruction of space charge in axisymmetric point/plane electrode geometries. The algorithm is built on the finite element method (FEM) for Poisson's equation and will be called finite element based Kerr electro-optic reconstruction (FEBKER) hereafter. FEBKER calculates the space charge density directly to avoid the numerical problems associated with taking the divergence of the electric field, uses single parameter light intensity measurements to enable transient analysis, which otherwise is difficult since multiple parameter intensity measurements are slow due to the rotation of polarizers, and is capable of reconstruction even when the number and/or position of measurements are limited by the electrodes and/or the experimental setup. The performance of the algorithm is tested on synthetic Kerr electro-optic data obtained for an axisymmetric point/plane electrode geometry in transformer oil with specified space charge density distributions. The impact of experimental error is analyzed by incorporating random error to the synthetic data. Regularization techniques that decrease the impact of experimental error are applied. In principle FEBKER is applicable to arbitrary three-dimensional geometries as well     

Transform relationship between Kerr-effect optical phase shift andnonuniform electric field distributions

Electric field distributions measured using the Kerr effect cause a phase shift between light components polarized parallel and perpendicular to the electric field, proportional to the magnitude squared of the electric field components in the plane perpendicular to light propagation integrated over the light path length. One wishes to recover the electric field distribution from measurements of light phase shifts. For axisymmetric geometries where the electric field depends only on the radial coordinate and whose direction is constant along the light path, as is the case along a planar electrode, the total phase shift for light propagating at a constant distance from the center of symmetry and the electric field distribution are related by an Abel transform pair, a special case of Radon transforms typically used in image reconstructions with medical tomography and holography. The more general Radon transform relates the optical phase shift to non-axisymmetric electric field distributions but is restricted to cases where the applied electric field is perpendicular to the plane of light propagation. If the applied electric field direction changes along the light path, it becomes necessary to account for the change in direction of the light components parallel and perpendicular to the applied electric field and the light polarization equations are generalized     

基于克尔电光效应的新型CCD光电测试系统

根据克尔电光效应原理 ,用稳定性好、动态范围大、灵敏度更高的CCD 30 0 0光电接收装置建立的新测量系统动态测量了克尔常数较小的液体介质如变压器油中的电场分布 ,并得出在一定电压范围内 ,克尔试验盒中两电极间的光强分布和电场分布之间的对应关系 ,还通过分析光强的空间分布和变化规律得出电场的空间分布和变化规律 ,为液体介质中的电场及空间电荷分布测量提供了一条新途径     

Optical, electrical and electromechanical measurement methodologiesof field, charge and polarization in dielectrics

A selective review is presented of the use of optical, electrical, and electromechanical measurement methodologies of the electric field, charge, conductivity, and permittivity in dielectrics. Kerr electro-optic measurements are presented to demonstrate how volume charge distributions can distort the electric field distribution significantly and how the field and charge distributions depend on dielectric and electrode materials and geometry, and on voltage magnitude, polarity, and time duration. A new class of interdigital dielectrometry sensors is reviewed which from one side can measure profiles in dielectric permittivity and conductivity and related physical properties such as moisture content. Electromechanical devices such as the absolute charge sensor, a flow loop, and the couette charger (cc) with a rotating cylindrical electrode are reviewed for their applications in liquid flow electrification measurements     

基于Kerr电光效应的冲击电压下液体电介质空间电荷高速CCD测量

空间电荷的存在直接影响液体电介质的绝缘击穿性能,为了更好地研究空间电荷的动态变化过程,建立了基于Kerr电光效应的冲击电压下液体电介质空间电荷的高速电荷耦合器件(CCD)测量系统。运用高精度光电传感器的测量方法,得到了室温下液体碳酸丙烯酯的Kerr常数。进而通过高速CCD的动态光电测量,并结合图像处理技术,求取了冲击电压下平行板铜电极间电场和空间电荷的动态分布曲线。实验研究表明:在平行板铜电极间,当液体介质中电场达到一定程度时会出现空间电荷的注入与输运,使得极间电场呈现出中间高两边低的分布情况。另外还分析了空间电荷的分布和输运对液体绝缘特性的影响,该研究为分析冲击电压作用下液体介质中空间电荷的产生机制及空间电荷对流注放电的影响奠定了基础。     

Influence of insulating barrier on the creepage discharge intransformer oil

The propagation aspects of a creepage discharge in transformer oil are observed simultaneously and in detail under a positive impulse voltage condition, by means of a high-speed Schlieren optical system, an LED current measurement system and a charge measurement system using a capacitor. In the present paper, the influence of the material type and the thickness of insulating barriers on the propagation of the impulse creepage discharge are discussed for a point to plane electrode geometry. In addition, the influence of a barrier surface to the electric field direction on the propagation of the impulse creepage discharge is discussed for a parallel plane electrode gap with a protruding point     

Computation methods for one-dimensional bipolar charge injection

Kerr electrooptic field-mapping measurements have shown strong space charge effects in high-voltage stressed dielectrics, where the magnitude and sign of injected charge depends on electrode material. With appropriate choice of electrode material combinations and voltage polarity is possible to have uncharged, unipolar positively or negatively charged, or bipolar charged dielectrics. The bipolar homocharge case lowers the electric field at both electrodes due to space-charge shielding, and thus allows a higher voltage without breakdown. Using charge-transport analysis the authors consider the general case of charge injection from both electrodes and solve time and space dependences of the electric field and charge distributions and the time dependences of the terminal voltage and current. This analysis extends earlier work by including nonequilibrium charge dissociation and recombination so that the effective ohmic conductivity is not constant but varies with time and position due to local net charge density. Specific cases discussed are the open-circuit voltage decay of an initially charged capacitor, the charging and discharging by a Marx generator, and alternating voltage excitations     

Charge behavior in flowing oil in oil/ pressboard insulation system by electro-optic field measurement

The electrical insulation structure of most power transformers is a combination of insulating oil and solid materials. One of the crucial problems we face in transformer operation is flow electrification, which occurs at a flowing oil/solid material interface. Thus, for the transformer insulation design, we need to clarify the now electrification phenomena. In this paper, we measured the electric field strength in an oil/pressboard composite insulation system using an electro-optic method of the Kerr effect. We obtained the time variation of electric field distribution in both flowing uncharged and charged oil. It is notable that we could quantitatively clarify the electric field distortion in flowing charged oil by flow electrification. Furthermore, we measured the leakage current from divided electrodes and derived a charge density distribution along the flow direction. Finally, we quantitatively discussed the electric field distribution and the charge behavior from the measurement results.     

Development of Kerr electro-optic 3-d electric field measuringtechnique and its experimental verification

We have developed a method to measure 3-dimensional electric field distributions in liquid dielectrics using the Kerr electro-optic effect combined with ac field modulation and circularly polarized light. We derived theoretical relations between an arbitrary electric field vector and a transmitted light intensity. The derived equations were verified by comparing the theoretical electric field profile with the experimental one in transformer oil with an axisymmetric electrode configuration, i.e. measured electric field vectors proved to agree well with theoretical ones. The light intensities experimentally obtained were transformed into axisymmetric electrode configuration by Abel transformation to calculate the electric field distribution     

Kerr electro-optic field measurement and charge dynamics intransformer-oil/solid composite insulation systems

We measured the electric field in transformer oil/solid composite insulation system under dc voltage application using a Kerr electro-optic measurement system. When a pressboard was inserted at the center between two parallel-plane electrodes, the electric field at the mid-point between the pressboard and the cathode decreased with time. On the other hand, the electric field at the mid-point between the pressboard and the anode increased initially with time, reached a maximum value and then fell down. We measured also the electric field before and after polarity reversal of the dc voltage. The results revealed that the electric field after polarity reversal reached a magnitude 2.7× as much as the average dc applied field. We interpreted the above results on the time transition of the electric field in terms of a charge dynamic model, considering the difference in charge accumulation speed on the pressboard between positive and negative charges. This model was verified to be applicable to the time transition of the electric field in oil/solid composite system and BTA added oil/solid composite system as well     

Electrohydrodynamically induced dielectric liquid flow through pure conduction in point/plane geometry

Mildly polar liquids generally exhibit an ohmic behavior when subjected to electric fields of limited values. The resulting conduction is then associated with heterocharge layers of finite thickness in the vicinity of the electrodes. In the absence of charge injection or induction, a simple conduction model based on the processes of dissociation of a neutral electrolytic species and recombination of the generated ions is presented. This model is first applied to parallel plane electrode geometry to describe the build-up of the heterocharge. Then, the case of point/plane configuration is considered where the effect of Coulomb force is different in the two layers next to the electrodes. A net motion toward the point electrode is predicted to occur. With a rough approximation for the harmonic field, an analysis is presented which leads to an expression for the axial component of the net force exerted on the liquid. A simple static pump is designed and built to experimentally investigate the pressure head generated through pure conduction. Two working fluids (refrigerant R-123 and n-hexane) and two different electrode designs are considered in this study. The experimental results are qualitatively compared to the theoretical predictions.     

Measurement of the space charge field in transformer oil using itsKerr effect

Nonuniform electric fields >80 kV/cm, have been measured via a relative optical intensity measurement by exploiting the Kerr effect in transformer oil. Transformer oil was used as a Kerr medium in these measurements. Neither a knowledge of the Kerr coefficient nor the actual value of maximum transmitted intensity are required to obtain the absolute value of the electric fields. Electric fields were measured with ac and dc excitations. Space charges resulting from charge injection have been found in transformer oil at room temperature under electric stresses >150 kV/cm with ac excitation and 90 kV/cm under dc excitation. The magnitudes of space charges in transformer oil with ac applied voltages varied from 2 to 50 nC/cm³. The magnitudes of space charges with dc excitation varied from 60 pC/cm³ to 10 nC/cm³. The results illustrate the limitations of the electro-optic technique for investigations of the interfacial electric fields (gas-solid) with transformer oil as the Kerr medium     

Particle Charging in Combined Corona-Electrostatic Fields

The association of several ionizing and nonionizing electrodes generates combined corona-electrostatic fields, characterized by space charge zones of well-defined extensions. In a previous paper, the authors presented an effective numerical method for the computation of such fields. The aim of this present work is to show how these results can be employed for estimating the charge acquired by insulating and conducting particles when passing through the space charge zones generated by various corona-electrostatic electrode geometries. The study is done under several assumptions that authorize the use of Pauthenier's formula. Diffusion charging can be neglected, the applied electric field is quasi-uniform in the vicinity of particles, and particle speed is low compared with that of air ions. The charging model takes into account the computed spatial distribution of the electric field and charge density. The computations were performed for various values of the geometrical parameters of the electrode system and of the particle transit time through the corona discharge zone. The results can be used for the design of the electrode system of any electrostatic process employing corona discharge fields.      

Optical measurement of electric field vector distribution in a liquid insulator using simultaneous three‐direction optical measurement system

We have already reported on reconstructions of the symmetrical and nonsymmetrical electric field vector distribution using the Kerr electrooptic effect and our unique reconstruction method, a modified computed tomography technique. This reconstruction technique gives an electric field map, that is, the strength and the direction of the electric field vector, on any plane. For the reconstruction of one field vector distribution, it was necessary to measure the light intensity twice while changing the optical axis of optical wedges. Moreover, the intensity measurement must be carried out at many points around the electrode system. Therefore, considerable time was required to measure the electric field distribution. We therefore developed a simultaneous three‐direction optical measurement system with three optical systems combined with the two‐beam method. Using the new measurement system, we measured the electric field distribution on planes in a sphere‐to‐sphere electrode system. It took about 0.1 second to measure the light intensity data for the reconstruction. © 2002 Scripta Technica, Electr Eng Jpn, 139(1): 9–15, 2002; DOI 10.1002/eej.1141     

Modeling of Corona Characteristics in a Wire-Duct Precipitator Using the Charge Simulation Technique

The charge simulation technique has been adapted to model the electrostatic and the corona characteristics in clean air of a duct-type electrostatic precipitator. The study involves the evaluation of the electric potential, electric field, and charge density in the interelectrode space as a function of corona current. The results show good agreement with published experimental data. The method developed can be applied to other geometries in the presence of space charge. The commonly used assumption that the space charge affects the magnitude but not the direction of the electric field is shown to be inadequate for large values of corona current. Also, the effect of using different values for the mobility of negative ions is presented.     

Three-dimensional (3-D) model of electric field and space charge inthe barbed plate-to-plate precipitator

A finite-element/method-of-characteristics model of three-dimensional (3-D) electrode geometries with corona discharge is used to predict space charge density, current density, electric potential and electric field in point-to-plane, single-barb plate-to-plane, and hexagonal multiple-barbed plate-to-plate electrostatic precipitator (ESP) geometries. Although a modification of Peek's formula for the hyperboid-to-plane was initially used to establish a boundary condition at the edge of the corona, predicted total current did not agree with measured values. As a result, it was necessary to use measured current-voltage characteristics to establish the space charge density at the outer surface of the corona sheath. An additional problem in modeling point discharges is specification of shape and size of the corona sheath. Both the authors' results and much earlier work by Trichel suggest that the thickness of the corona sheath cannot be automatically neglected     

Fundamental property of electric field in rapeseed ester oil based on Kerr electro-optic measurement

In the future, environmentally friendly insulating oil such as rapeseed ester oil is expected to be utilized as a substitute for mineral oil for power transformers. In addition, electrical insulation design for transformers becomes more important regarding size reduction and enhancement of electric field stress. The fundamental property of the electric field distribution in the rapeseed ester oil and in the oil/solid dielectrics composite insulation system should be clarified. In this paper, we have directly measured the electric field in the rapeseed ester oil with parallel-plane electrode and the rapeseed ester oil/pressboard (PB) composite insulation systems under DC voltage application using the Kerr electro-optic technique. From the results, we compared measurements of electric field and charge behavior for the rapeseed ester oil and the mineral oil and confirmed the applicability of the rapeseed ester oil for use in transformers.     

同轴电极下非线性绝缘介质阶跃响应仿真分析

为了验证非线性绝缘材料在非均匀电极结构下均化电场分布的内在机理,以典型非均匀电极结构(同轴电极)下填充电导率为非线性的绝缘介质所构成的绝缘结构为研究对象,采用有限元软件ElecNet仿真分析了不同幅值阶跃电压作用下非线性绝缘介质中瞬态响应的空间分布,得到的非线性绝缘介质内部空间电荷的分布揭露了非线性绝缘介质能自行均化电场的根本原因是空间电荷效应。稳态电场的计算结果表明:阶跃电压幅值越高,绝缘介质非线性程度越高,电场改善的程度越好。     

Measurement of space charge distributions in PLZT using Kerr effect

Kerr effect technique is an optical measurement technique used to determine space charge distributions of a dielectric liquid under applied electric stress. In other words, such measurement can be used to study the conduction mechanisms of a dielectric liquid, such as charge injection threshold, bulk electric field stress, and aging. In this study, an instrument was set up to measure the absolute value of the electric field distributions in lead–lanthanum–zirconium–titanium (PLZT). PLZT was selected for the study of the instrumentation because the material has a high Kerr constant. In the experiment, charge injection threshold and bulk field strength of PLZT were measured under low applied voltages. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.