Existing studies of the spatial allocation of wind farms are typically based on turbine power generation efficiency and rarely consider the damage caused by lightning strikes. However, lightning damage seriously affects the economic performance of wind farms because of the high cost of repairing or replacing damaged blades. This paper proposes a method for the spatial optimization of multiple turbines based on lightning protection dependability. Firstly, the lightning protection efficiency of turbine blade protection systems is analyzed by combining the physical mechanisms of lightning leader progression with a conventional electro-geometric model to develop an electro-geometric model of turbine blades (EGMTB). Then, the optimized spatial allocation of multiple turbines in a wind farm is investigated using the EGMTB. The results are illustrated from an example wind farm with 1.5 MW turbines, which shows that the optimal spacing between two turbines perpendicular to the prevailing wind direction L ⊥ is 4R-6R, where R is the length of a turbine blade. This spacing is shown to effectively shield turbine blades from lightning damage over a wide range of lightning currents (>26-60 kA). Note that, the suggested L ⊥ will be smaller considering the influence of lightning polarity as it takes more difficulty developing upward leader (UL) in the condition of positive lightning striking. Experiments verify the effectiveness and correctness of this method. KEYWORDS dynamic striking distance, lightning leader progression model, lightning protection, optimized spatial allocation, wind farm NOMENCLATURE: EGMTB, Electro-geometric model of turbine blades; R, Length of a turbine blade; Dw, Prevailing wind direction; L⊥, Spacing between two turbines in the perpendicular direction relative to the prevailing wind direction D w ; L // , Spacing between two turbines in the parallel direction relative to the prevailing wind direction D (assumed to be 0.55 × 10 8 ); R0, Electrode curvature radius; R1, Impact ionization area boundaries; Q, Free electrons; KQ, Environmental factor with a value of 3.5 × 10-11 C/(V m); qL, A constant that represents the charge necessary for per-unit length to achieve the thermal transition from a streamer to the leader channel; Rr, Striking distances of the receptor; Rb, Striking distances of the blade body; I max , Maximum lightning current at which the LPS may fail; I risk , Minimum lightning current that begins to damage the blade material when subjected to lightning; l MN , Exposed distance representing the horizontal distance between two endpoints of the exposed arc; l MO , Total distance of the vertical projection of the entire investigated blade on the ground; D, Spacing between two turbines in the perpendicular direction relative to the prevailing wind direction Dw; Dmax, The maximum shielding distance between two turbines considering EGMTB; Lf, Maximum horizontal distance of the striking distance envelope arc; keraunic level, Average annual thunderstorm days or thunderstorm hours per year
