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Electric field analysis is an important basis for the insulation design of high-voltage direct-current equipment. The resistivity is a strong function of temperature and electric field, which may lead to the divergence of a numerical solution, and the initial approximations are the key to convergence. Therefore, a novel approach for nonlinear electric field indirect coupling analysis is developed. This algorithm converts the original nonlinear electric field into homotopy equations under a specific parameter, and uses the numerical continuation method to gradually approximate the true solution. Taking a fictive ±200 kV direct-current cable extrusion molded joint as an example, two homotopy equations are constructed to successfully calculate the nonlinear electric field based on the numerical continuation method combined with Steffensen iterative formula. On the contrary, divergence occurs in the conventional indirect coupling calculation method, indicating the superiority of this approach. Subsequently, some factors affecting the convergence of the homotopy continuation method are discussed. Finally, the calculated results and the solution times using the presented approach are compared with the direct coupling method by COMSOL. The proposed algorithm can enlarge the region of convergence in nonlinear electric field analysis based on the indirect coupling method and effectively overcome the divergent issue due to the inappropriate choice of initial approximations. [ABSTRACT FROM AUTHOR]

Complex gap discharge voltage is an important parameter to determine the approach path and the minimum air insulation distance for helicopter live-line work (HLLW) by platform method. This paper proposes a novel approach for discharge voltage prediction of complex gaps with a floating object, combining electric field calculation, feature extraction, machine learning and intelligent prediction based on support vector machine (SVM). The methodology is performed by twice electric field calculations and SVM predictions to obtain the withstand voltages of the primary gap and the secondary gap, thus to compute the dielectric strength of the complex gap. A simulation model of the HLLW platform near the 1000 kV UHV AC transmission line is presented for electric field calculations, and some electric field features (EFF) are extracted from the calculation results to parameterize the complex gap configuration. Taking the EFF as input variables, a SVM model is applied to predict the switching impulse discharge voltages of different gap configurations relevant to HLLW. The validity of the proposed methodology is demonstrated through comparison with the experimental results. This study offers a possible way to determine the minimum safe gap distance for HLLW by numerical calculation rather than costly and time-consuming experiments. [ABSTRACT FROM AUTHOR]

Electrostatic field distribution has a decisive influence on the strength of air insulation. To predict air‐gap breakdown voltages according to electric field calculation results, a set of electrostatic field features is defined on the shortest interelectrode path of the rod–plane gap. These features are taken as the input parameters of a machine learning model established by support vector regression (SVR), thus to describe their relationships with the output breakdown voltage. Trained by small‐sample data randomly selected according to the distribution ranges of the electric field non‐uniform coefficient, the SVR model is applied to predict the breakdown voltages of rod–plane gaps with the rod diameter of 20, 25 and 30 mm, and the gap distance ranging from 1 to 9 cm. The predicted results agree well with the experimental data, while the mean absolute percentage errors of the six predictions are within 2.5%. Furthermore, the Φ27 mm rod–plane gap breakdown voltages are also predicted, and the results fall in the range between those of Φ25 and Φ30 mm rod–plane gaps, which conform to the actual law. The results validate the validity of the electrostatic field features and the generalisation performance of the SVR model. [ABSTRACT FROM AUTHOR]

The electric field calculations cannot effectively guide the insulation design of high voltage equipment since the insulation strengths of dielectrics cannot be predicted according to the electromagnetic analysis. In this paper, some features related to the electric field distribution such as the electric field strength, electric field gradient, path length, and the electric field integral are defined and extracted from finite element calculations of air gaps. The electric field features are taken as the input parameters of a grey correlative model established by support vector machine (SVM), so as to establish the multi-dimensional nonlinear relationships between these features and the discharge voltage of an air gap. The grid search (GS) method was used to search the optimal parameters of the SVM. This model was applied to predict the 50% discharge voltages of large sphere-plane air gaps in UHVDC valve halls. The predicted results were obtained after multiple iterative calculations, using the golden section search method. Compared to experimental data, the relative errors of the predicted results are within an acceptable range in view of engineering applications, which indicates the validity of the proposed method. This paper achieves the discharge voltage of air gaps by numerical computations instead of costly experiments. [ABSTRACT FROM AUTHOR]

It has been a long sought goal to determine the critical flashover voltages of long air gaps by mathematical calculations instead of experiments. In this paper, a predictive model is proposed for 50% discharge voltage (U50) prediction of long air gaps subjected to switching impulses. This model is developed on the basis of the physical thought that air breakdown can be viewed as out-of-limit of the capacitive energy stored in the electric field. Two groups of features are defined to characterize the energy storage status of an air gap, from the perspective of electric field distribution and impulse voltage waveform, respectively representing the space distribution and time accumulation of the energy. The predictive model is established by support vector machine (SVM), and the input data are the energy storage features. Giving an estimated applied voltage range, the predicted result of the critical flashover voltage is searched by the golden section method. Trained by 6 known experimental data, this model is used to predict the U50 of rod-plane, rod-rod and rod-conductor long air gaps subjected to negative switching impulse voltages. The mean absolute percentage errors of 5 groups of test samples are respectively 6.0%, 5.8%, 6.3%, 3.2% and 1.7%, which are in an acceptable range in the view of engineering applications. The proposed method might be useful to predict the U50 of long air gaps with various geometries and under different voltage waveshapes, therefore reducing the required test work for insulation design of high voltage equipments. [ABSTRACT FROM PUBLISHER]

The most determinant factor for the dielectric strength of an air gap is the inhomogeneity of the electric field. This paper attempts to establish the internal relation between the electric field distributions of air gaps with different electrode geometries, and so as to predict the breakdown voltage of the air gap with atypical electrodes. A classification model is established based on support vector machine (SVM), which considers that the breakdown or withstand of an air gap under an applied voltage can be viewed as 1 or -1. 28 features are defined and applied to characterize the electric field distribution of an inter-electrode air gap. Taking these features as input parameters of the SVM model, the grey correlation between the air gap breakdown voltage and its electric field distribution can be trained by some training samples, which are selected from typical air gaps like sphere-sphere and rodplane gaps according to the electric field distribution similarity along the shortest discharge path. The SVM model is applied to predict the breakdown voltages of atypical air gaps including the serial gaps, the ring gaps and the stranded conductor gaps. The predicted results are in good agreement with the experimental data, and the mean absolute percentage errors of these gap arrangements are within 5.4%. This method provides an alternative for the breakdown voltage prediction of air gaps with complex geometries, and therefore helps minimizing the required test work. [ABSTRACT FROM PUBLISHER]

The frequent forest fires become a serious threat to the performance of transmission lines' external insulation. Gap breakdown in forest fire relates to many factors, such as flame temperature, conductivity and particles. Large quantities of smoke (carbon black) and flying ash are produced during the combustion of vegetation, causing the dielectric strength of gap to decrease drastically. In order to analyze the influence of forest fire particles on the breakdown characteristics of air gap, the experimental setup consisting of a conductor-plane was built to simulate the effect of forest fire particles. At the same time, a theoretical model was developed to analyze the influence mechanism of multiple particles on the discharge characteristics of gap. Experimental results show that, a chain of carbon particles has been formed between flame and conductor by the action of electric field. The gap's insulation strength decreases significantly, which is about 40% of that in the pure air under AC voltage. The particles movement and the breakdown characteristics of air gap have an evident effect of polarity characteristic under DC voltage and the breakdown voltage is reduced to about 29% of that in the air gap under negative DC voltage. The simulation results show that, the electric field distribution between conductor and plane become uneven, and the distortion degree of the elongated particle to the background electric field is not related to the distance between particles with high-voltage electrode. According to the electric field diagram, it is obvious that the particles make the background electric field distortion, and the maximum field strength increased by about 100%. More close to the conductor, the greater electric field strength is at the both ends of particles. [ABSTRACT FROM AUTHOR]

Live-line work methods using helicopters in the vicinity of 1000-kV transmission lines were simulated with finite-element modeling of the electric-field distributions. The effect of the approach path of the helicopter live-line work platform toward the energized conductor was computed. Predicted electric fields on the line worker head, body, arms, and legs were compared with measured results from a single-phase ultra-high-voltage (UHV) mock-up, and with calculation results from the simulation of an extra-high-voltage (EHV) 500-kV transmission-line geometry. The UHV conductor-to-work platform discharge occurred at a distance of about 2 m, in line with standard flashover models. Additional shielding efficiency of about 4 dB is recommended for the electrically conductive clothing when working on the UHV lines in China, compared to EHV lines. [ABSTRACT FROM PUBLISHER]

This paper attempts to establish the grey correlation between the breakdown voltage of air gap and its energy storage status before discharge inception. A new method is presented for the breakdown voltage prediction of short air gaps. This method is based on an orthogonal design array and support vector machine (SVM). A hybrid model is established to predict the power frequency breakdown voltage of three typical air gaps including sphere-sphere, rod-plane, and rod-rod gaps. The input data are fifty parameters extracted from the static electric field distribution of the air gap, and the output of the model is whether the gap will breakdown under a given voltage. This model is trained by 9 samples selected by L9(33) orthogonal array and applied to predict the breakdown voltage of 90 test samples. With effective feature dimension reduction and parameter optimization of the SVM model, the predicted results coincide well with the experimental data, and the mean absolute percentage error (MAPE) is only 3.9%. The SVM model is also applied to predict the breakdown voltage of some atypical short air gaps including sphere-plane gaps, rod-sphere gaps, sphere-sphere gaps with different diameters, and rod-plane-sphere gaps. The MAPEs are respectively 4.3, 3.2, 4.2, and 6.4%, which verifies the validity and generalization performance of the proposed method. This model provides a new way to gain the critical breakdown voltage of air gaps, and therefore contributes to reducing the required test work. [ABSTRACT FROM AUTHOR]

Breakdown voltage of the air gap is of vital importance for the design of the external insulation in high-voltage transmission and transformation projects. In this paper, a new prediction method for the breakdown voltages of typical air gaps based on the electric field features and support vector machine (SVM) was proposed. According to the finite element calculation results of static electric field distribution, the electric field values in the whole region, discharge channel, surface of the electrode and the shortest path were extracted and post-processed, which constituted the electric field features characterizing the gap structure. Then, the breakdown voltage prediction model of the air gap was established by using electric field features as the input parameters to SVM, and whether the gap breakdown would happen as the output parameters of SVM, which changing the regression problem to a binary classification problem. This model was applied to predict the power frequency breakdown voltages of different short air gaps including sphere-sphere gaps, rod-plane gaps, sphere-plane gaps and sphereplane- sphere gaps. The power frequency breakdown voltages of longer air gaps which are affected by corona, and the 50% positive switching impulse breakdown voltages of long sphere-plane gaps and rod-plane gaps were predicted as well. The predicted results agree well with experimental values and simulated results of the published models, which validate the effectiveness of the proposed model. This method supplies a new possible way to obtain the breakdown voltage of air gaps. [ABSTRACT FROM PUBLISHER]

This paper focuses on the security condition of line worker during the implementation of helicopter live-line work by platform method on 1000 kV ultrahigh voltage (UHV) transmission lines. First, a model of helicopter live-line work is presented, and the electric field distribution of line worker when performing live-line work on 1000 kV UHV transmission lines is analyzed. Then, the capacitances between helicopter live-line work platform, transmission lines, and ground are obtained by energy method, and an equivalent circuit model is presented to analyze the current characteristic of bonding procedure. At the end of this paper, an experiment of helicopter live-line work is performed, the electric field distributions of line worker and the discharge current are measured and compared with simulation results, which will be used to judge the security condition of line worker and the feasibility of helicopter live-line work by platform method on 1000 kV UHV transmission lines. [ABSTRACT FROM PUBLISHER]

The space charges produced by the corona discharge of the DC voltage divider's high-voltage electrode can move under the effect of the electric field force, and parts of them can attach to the surface of the insulation sheds. Because of the influence of the space charges and the charges on the insulator sheds' surface, the electric field around has a big difference with the situation in the electrostatic field. In the paper, a 2-D axisymmetric upwind finite element method (upwind FEM) is used to calculate the electric field distribution on the surface of the DC voltage divider's insulation sheds. The space charge density inside the insulation sheds is set to be 0, and the charge density on the surface of the sheds is calculated by the iterative process. The ionized field of a 3-D sphere electrode model is calculated, and the 2-D axisymmetric upwind FEM is verified by comparing the numerical results with the analytical results. In the end the ionized field of the 500 kV voltage divider is calculated. The simulation results show that the existence of space charges affect evidently on the electric field distribution characteristic, and hence improve the uniformity of the electric field intensity along the sheds surface. [ABSTRACT FROM AUTHOR]

The ionized field produced by corona discharge from a high-voltage direct current (HVDC) transmission line has a great influence on the electromagnetic environment. In this paper, a highly stable iterative algorithm based on an upwind finite-element method is introduced to analyze the ionized field of HVDC transmission line in the presence of the wind. The Kaptzov's assumption is introduced on the conductor surface as a boundary condition. In the iterative procedure presented by Takuma, the controlling method is added to guarantee the convergence of the iteration, which has been tested to be effective. The impact of the wind on the ground-level electric-field intensity and ion current density of a bipolar HVDC transmission line is analyzed, and we find the wind has a significant influence on the ionized field which has to be considered in the engineering design. [ABSTRACT FROM PUBLISHER]