This paper addresses lightning surges on the transmission systems with a new hybrid method, using a 1D FDTD model for the transmission line and a PEEC model for the tower and lightning channel. Compared with other circuit-based models, mutual coupling between the lightning channel and other parts in the system can be fully considered. This hybrid method has been validated numerically and experimentally, and good agreements are observed. This method then is applied to analyze the lightning surges on a 500 kV double-circuit transmission line system. It is found that the lightning channel has a significant impact on the surge response of the tower struck. Ignoring the coupling from the channel to the tower will weaken the hazard of lightning strikes. However, the influence of its coupling to the transmission line is not critical. The choice of interfacing points between these two models is then suggested. Furthermore, the influence of the tower footing is inves tigated. It is found that the insulator voltage is made of inductive and resistive components. The inductive component becomes dominant in the case of high soil conductivity and low grounding resistance. The voltage generally increases with decreasing soil conductivity and tends to decay slowly with time.

This paper presents an assessment of lightning protection schemes for overhead lines from two aspects: protection performance and economic cost. Considering the random nature of lightning, the Monte-Carlo method with a heuristic technique is applied in the assessment. The one-dimensional finite-difference time-domain method is adopted to evaluate lightning overvoltages on insulators and lightning currents in surge arresters for failure assessment. The failure rate of an overhead line is addressed under both direct lightning and indirect lightning. A reduced set of design parameters are identified. It is found that the line insulation itself with a critical flashover overvoltage of less than 200 kV is not sufficient for lightning protection, especially against direct strokes. With other protection options, however, increasing the insulation level can greatly improve the protection performance. Installing surge arresters on every pole results in the best protection performance, but could be extremely expensive due to the replacement of failed surge arresters. The shielding wire provides moderate protection performance with a relatively low cost. The combination of the shielding wire and surge arresters provides much better performance under a wide range of soil conductivity with a moderate cost. It is worth mentioning that adopting high insulation strength for overhead lines in the new-line design could lead to significant cost savings for lightning protection. Guidelines for selecting design parameter values and protection schemes are provided, as well as a procedure for performance-cost evaluation.

This paper presents a systematic investigation into the performance of a shielding wire on 10 kV overhead lines (OHLs) against indirect lightning, from the design point of view. The design parameters addressed include the grounding interval, grounding resistance, and position of the shielding wire. As a system outage is usually caused by insulator flashover at OHL poles under indirect lightning, the induced voltages there are investigated with the code developed from the Agrawal model. In the evaluation, the location of a lightning return stroke relative to a grounded or ungrounded pole is considered. It is found that the lightning channel positioned in the front of an ungrounded pole could completely wipe out the effect of the shielding wire. This occurs if the wave from the grounding point arrives later than the time to the peak of the voltage directly arising from the lightning return stroke. It is suggested providing the wire grounding at every pole even if the grounding resistance at some poles is much higher than the design value. Grounding spacing does not affect the induced voltages at the pole generally if the pole has been grounded. One critical parameter is identified, i.e., the distance between the shielding and outer phase wires. Minimizing the distance can effectively reduce the lightning-induced voltages.

When concerning the installation and operation costs, it is always desirable to protect an overhead distribution network with a limited quantity of surge arresters (SAs). This paper presents a novel procedure for designing differentiated protection against lightning, by identifying appropriate positions for those SAs on the overhead line. Rather than the traditional flashover rate of a whole line, indices in terms of flashover numbers at individual poles and associated with possible stroke locations are introduced in this paper. Based on these flashover indices, a differentiated configuration of SAs can be identified using a selection strategy. After several rounds of selection, a differentiated SA protection scheme can be obtained, given by a pre-set quantity of SAs. In this procedure, a simplified probability-based approach is proposed to determine the flashover indices. By comparing the traditional Monte Carlo method, this approach can achieve a 10-fold increase in computational efficiency with reasonable accuracy. Two different selection strategies are introduced in this paper. Compared with the selection strategy using the flashover indices at individual poles, the selection strategy based on a group of poles is recommended because it yields a configuration with better lightning performance with the same quantity of SAs. This design procedure is applied to practical distribution networks with a shield wire and nearby structures. The influence of grounding impedance, a shield wire, and nearby structures is addressed. Finally, a generalized step-by-step procedure is provided to assist in a differentiated SA protection design.

This paper presented an assessment of lightning energy absorption by dedicated surge arresters (SA _DT ), which are provided to protect the distribution transformers on 10kV overhead distribution lines (OHLs). A hybrid Partial Element Equivalent Circuit-Multi-conductor Transmission Line (PEEC-MTL) code was applied to evaluate lightning surges on SA _DT . This method has the capability of modeling both short and long wires in OHL systems and is verified numerically and experimentally. A Monte Carlo procedure was adopted to assess the fault rate (FR) of SA _DT . It is found that the direct lightning strokes to the phase wire are the primary threat to the SA _DT , compared with the strokes to the poles as well as indirect strokes to the ground or structure nearby. Several protection schemes are identified, and their performance is evaluated from the aspects of lightning protection and economic cost. The full shielding wire (SW) scheme performs the best, but with the most expensive protection cost. The lightning energy absorption by SA _DT can be suppressed significantly by installing extra SAs on the adjacent poles. The scheme of two or four extra SAs together with a partial SW can achieve a balanced performance of protection effect and economic cost for the OHL. The SW for a section of the OHL alone is not enough to the lightning protection for SA _DT .

This article presents the numerical evaluation of Green's functions for the generalized partial element equivalent circuit (PEEC) formulation in the air and lossy-ground space. Both the source and field points can be located in any layer of the air–ground space. Green's functions are expressed using Sommerfeld integrals (SIs), which have highly oscillating and slowly decaying integrands. As a robust and easy-implemented approach, the direct real-axis integration is presented with the techniques for removing the singularity and accelerating the convergence. Closed-form expressions are derived for the quasi-static and asymptotic approximation of SIs. The results are compared with numerical electromagnetics code NEC2, and good agreements were observed. An image model is developed for quasi-static SIs. Greens’ functions can then be contributed by the source and/or its image. This model is used to derive the frequency-invariant PEEC model for fast transient simulation in the time domain. The proposed numerical procedure can be applied to generate lookup tables of SIs, which are indispensable in the evaluation of PEEC circuit parameters for massive wire segments.