Derivations of Effective Length Formula of Vertical Grounding Rods and Horizontal Grounding Electrodes Based on Physical Phenomena of Lightning Surge Propagations

Grounding is essential to build effective lightning protection design for electric power equipment. The main role of grounding is to disperse abnormal current such as that from lightning into the soil via a grounding electrode. When the lightning current flows into the grounding electrode, the electrical potential of the electrode rises, and overvoltage arises between the equipment connected to the grounding electrode and nearby equipment. The overvoltage causes equipment to breakdown or malfunction. An effective grounding electrode controls the overvoltage at the equipment in a lightning strike and can ensure the normal operation of electrical equipment. The most common grounding electrodes are the vertical grounding rod and the horizontal buried electrode. A property of these grounding electrodes, known as effective length, has been investigated by many researchers. Many formulas to express effective length have already been proposed, all of which are determined heuristically on the basis of formulas that approximate the property from experimental or analytical test results; they are not formulas derived based on the physical phenomenon of grounding. In this paper, we first report on the results of the derivation of a formula for effective length based on the propagation velocity within the soil and the depth of penetration of the lightning surge into the soil. The aforementioned formula still has unknown constants. To decide those parameters, the finite-difference time-domain method is utilized.