import math import ezdxf import numba import numpy as np gCAD = None gMSP = None gCount = 1 class Draw: def __init__(self): self._doc = ezdxf.new(dxfversion="R2010") self._doc.layers.add("EGM", color=2) global gCAD gCAD = self def draw(self, i_curt, u_ph, h_gav, h_cav, dgc, color): doc = self._doc msp = doc.modelspace() global gMSP gMSP = msp rs = rs_fun(i_curt) rc = rc_fun(i_curt, u_ph) rg = rg_fun(i_curt, h_cav) msp.add_circle((0, h_gav), rs, dxfattribs={"color": color}) msp.add_line((0, 0), (0, h_gav)) # 地线 msp.add_circle((dgc, h_cav), rc, dxfattribs={"color": color}) msp.add_line((dgc, 0), (dgc, h_cav)) # 导线 msp.add_line((0, h_gav), (dgc, h_cav)) msp.add_line((0, rg), (2000, rg), dxfattribs={"color": color}) # 计算圆交点 # circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc) # msp.add_line((0, h_gav), circle_intersection) # 地线 # msp.add_line((dgc, h_cav), circle_intersection) # 导线 # circle_line_section = solve_circle_line_intersection(rc, rg, h_cav, dgc) # msp.add_line((0, 0), circle_line_section) # 导线和圆的交点 def save(self): doc = self._doc doc.saveas("egm.dxf") # 圆交点 def solve_circle_intersection(rs, rc, h_gav, h_cav, dgc): # 用牛顿法求解 x = rc # 初始值 y = rc # 初始值 for bar in range(0, 10): A = [[-2 * x, -2 * (y - h_gav)], [-2 * (x - dgc), -2 * (y - h_cav)]] b = [ x ** 2 + (y - h_gav) ** 2 - rs ** 2, (x - dgc) ** 2 + (y - h_cav) ** 2 - rc ** 2, ] X_set = np.linalg.solve(A, b) x += X_set[0] y += X_set[1] if np.all(np.abs(X_set) < 1e-5): return [x, y] return [] # 圆与地面线交点 def solve_circle_line_intersection(radius, rg, center_x, center_y): distance = distance_point_line(center_x, center_y, 0, rg, 0) # 捕雷线到暴露圆中点的距离 if distance > radius: return [] else: r = (radius ** 2 - (rg - center_y) ** 2) ** 0.5 + center_x return [r, rg] def min_i(string_len, u_ph): u_50 = 530 * string_len + 35 z_0 = 300 # 雷电波阻抗 z_c = 251 # 导线波阻抗 r = (u_50 + 2 * z_0 / (2 * z_0 + z_c) * u_ph) * (2 * z_0 + z_c) / (z_0 * z_c) return r def thunder_density(i): # l雷电流幅值密度函数 r = -(10 ** (-i / 44)) * math.log(10) * (-1 / 44) return r def angel_density(angle): # 入射角密度函数 angle单位是弧度 r = 0.75 * (np.cos(angle - math.pi / 2) ** 3) return r def rs_fun(i): r = 10 * (i ** 0.65) return r def rc_fun(i, u_ph): r = 1.63 * ((5.015 * (i ** 0.578) - 0.001 * u_ph) ** 1.125) # r=14.7*(i**0.42) return r def rg_fun(i_curt, h_cav): if h_cav < 40: rg = (3.6 + 1.7 ** math.log(43 - h_cav)) * (i_curt ** 0.65) else: rg = 5.5 * (i_curt ** 0.65) return rg def intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph): # 暴露弧的角度 rs = rs_fun(i_curt) rc = rc_fun(i_curt, u_ph) rg = rg_fun(i_curt, h_cav) circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc) # 两圆的交点 circle_line_intersection = solve_circle_line_intersection( rc, rg, dgc, h_cav ) # 暴露圆和补雷线的交点 np_circle_intersection = np.array(circle_intersection) theta2_line = np_circle_intersection - np.array([dgc, h_cav]) theta2 = math.atan(theta2_line[1] / theta2_line[0]) np_circle_line_intersection = np.array(circle_line_intersection) theta1_line = np_circle_line_intersection - np.array([dgc, h_cav]) theta1 = math.atan(theta1_line[1] / theta1_line[0]) return np.array([theta1, theta2]) def distance_point_line(point_x, point_y, line_x, line_y, k) -> float: d = abs(k * point_x - point_y - k * line_x + line_y) / ((k ** 2 + 1) ** 0.5) return d def func_calculus_pw(theta, max_w): w_fineness = 0.01 w_samples, d_w = np.linspace(0, max_w, int(max_w / w_fineness), retstep=True) cal_w_np = abs(angel_density(w_samples)) * np.sin(theta - (w_samples - math.pi / 2)) r_pw = np.sum((cal_w_np[:-1] + cal_w_np[1:])) / 2 * d_w return r_pw def calculus_bd(theta, rc, rs, rg, dgc, h_cav, h_gav): # 对θ进行积分 max_w = 0 # 求暴露弧上一点的切线 line_x = math.cos(theta) * rc + dgc line_y = math.sin(theta) * rc + h_cav k = math.tan(theta + math.pi / 2) # 入射角 # 求保护弧到直线的距离，判断是否相交 d_to_rs = distance_point_line(0, h_gav, line_x, line_y, k) if d_to_rs < rs: # 相交 # 要用过直线上一点到暴露弧的切线 new_k = tangent_line_k(line_x, line_y, 0, h_gav, rs, init_k=k) if new_k >= 0: max_w = math.atan(new_k) # 用于保护弧相切的角度 elif new_k < 0: max_w = math.atan(new_k) + math.pi # TODO to be removed # global gCount # gCount = gCount+1 # if gCount % 100 == 0: # gMSP.add_circle((0, h_gav), rs) # gMSP.add_circle((dgc, h_cav), rc) # gMSP.add_line((dgc, h_cav), (line_x, line_y)) # gMSP.add_line( # (-500, new_k * (-500 - line_x) + line_y), # (500, new_k * (500 - line_x) + line_y), # ) # gCAD.save() # pass else: max_w = theta + math.pi / 2 # 入射角 # TODO to be removed if gCount % 200 == 0: # # intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph) # gMSP.add_circle((0, h_gav), rs) # gMSP.add_circle((dgc, h_cav), rc) # gMSP.add_line((dgc, h_cav), (line_x, line_y)) # gMSP.add_line( # (-500, k * (-500 - line_x) + line_y), # (500, k * (500 - line_x) + line_y), # ) # gCAD.save() pass r = rc / math.cos(theta) * func_calculus_pw(theta, max_w) return r def bd_area(i_curt, u_ph, dgc, h_gav, h_cav): # 暴露弧的投影面积 theta1, theta2 = intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph) # θ角度 theta_fineness = 0.01 rc = rc_fun(i_curt, u_ph) rs = rs_fun(i_curt) rg = rg_fun(i_curt, h_cav) r_bd = 0 theta_sample, d_theta = np.linspace( theta1, theta2, int((theta2 - theta1) / theta_fineness), retstep=True ) if len(theta_sample) < 2: return 0 vec_calculus_bd = np.vectorize(calculus_bd) calculus_bd_np = vec_calculus_bd(theta_sample, rc, rs, rg, dgc, h_cav, h_gav) r_bd = np.sum(calculus_bd_np[:-1] + calculus_bd_np[1:]) / 2 * d_theta # for calculus_theta in theta_sample[:-1]: # r_bd += ( # ( # calculus_bd(calculus_theta, rc, rs, rg, dgc, h_cav, h_gav) # + calculus_bd(calculus_theta + d_theta, rc, rs, rg, dgc, h_cav, h_gav) # ) # / 2 # * d_theta # ) return r_bd def tangent_line_k(line_x, line_y, center_x, center_y, radius, init_k=10.0): # 直线方程为 y-y0=k(x-x0)，x0和y0为经过直线的任意一点 # 牛顿法求解k # f(k)=(k*x1-y1-k*x0+y0)**2-R**2*(k**2+1) x1,y1是圆心 k_candidate = [-100, 100] if abs(center_y - line_y) < 1 and abs(line_x - center_x - radius) < 1: # k不存在 k_candidate = [99999999, 99999999] else: for ind, k_cdi in enumerate(list(k_candidate)): k = k_candidate[ind] k_candidate[ind] = None for bar in range(0, 30): fk = (k * center_x - center_y - k * line_x + line_y) ** 2 - ( radius ** 2 ) * (k ** 2 + 1) d_fk = ( 2 * (k * center_x - center_y - k * line_x + line_y) * (center_x - line_x) - 2 * (radius ** 2) * k ) if abs(d_fk) < 1e-5 and abs(line_x - center_x - radius) < 1e-5: # k不存在，角度为90°，k取一个很大的正数 k_candidate[ind] = 99999999999999 break d_k = -fk / d_fk k += d_k if abs(d_k) < 1e-3: dd = distance_point_line(center_x, center_y, line_x, line_y, k) if abs(dd - radius) < 1: k_candidate[ind] = k break # 把k转化成相应的角度，从x开始，逆时针为正 k_angle = [] for kk in k_candidate: if kk is None: abc = 123 # tangent_line_k(line_x, line_y, center_x, center_y, radius) pass if kk >= 0: k_angle.append(math.atan(kk)) if kk < 0: k_angle.append(math.pi + math.atan(kk)) # 返回相对x轴最大的角度k return np.array(k_candidate)[np.max(k_angle) == k_angle].tolist()[-1] def func_ng(td): # 地闪密度 return 0.023 * (td ** 1.3)