import math import ezdxf import numpy as np gCAD = None gMSP = None 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), (200, 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, hgav, hcav, dgc): # 用牛顿法求解 x = 300 y = 300 for bar in range(0, 10): A = [[-2 * x, -2 * (y - hgav)], [-2 * (x - dgc), -2 * (y - hcav)]] b = [ x ** 2 + (y - hgav) ** 2 - rs ** 2, (x - dgc) ** 2 + (y - hcav) ** 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(rc, rg, h_cav, dgc): # TODO: 需要考虑地面捕雷线与暴露弧完全没交点的情况 r = (rc ** 2 - (rg - h_cav) ** 2) ** 0.5 + dgc 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 * (math.cos(angle) ** 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) return r def rg_fun(i, h_cav): if h_cav < 40: rg = (3.6 + 1.7 ** math.log(43 - h_cav)) ** 0.65 else: rg = 5.5 * (i ** 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, h_cav, dgc ) # 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]) # 考虑雷电入射角度，所以theta1可以小于0，即计算从侧面击中的雷 # if theta1 < 0: # # print(f"θ_1角度为负数{theta1:.4f},人为设置为0") # theta1 = 0 return np.array([theta1, theta2]) def distance_point_line(point_x, point_y, line_x, line_y, k): d = abs(k * point_x - point_y - k * line_x + line_y) / ((k ** 2 + 1) ** 0.5) return d 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) rc = rc_fun(i_curt, u_ph) rs = rs_fun(i_curt) rg = rg_fun(i_curt, h_cav) # 求暴露弧上一点的切线 line_x = math.cos(theta1) * rc + dgc line_y = math.sin(theta1) * rc + h_cav max_w = 0 # 入射角 if theta1 < 0: max_w = theta1 + math.pi / 2 k = math.tan(max_w) # 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) max_w = math.atan(new_k) # 用于保护弧相切的角度 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) ) gMSP.add_line((0, rg), (1000, rg)) gCAD.save() pass # k=tangent_line_k(point_x, point_y, dgc, h_cav,rc) # 暂时不考虑雷电入射角的影响 r = (math.cos(theta1) - math.cos(theta2)) * rc return r # r1=rc*(-math.cos(thyta2)+math.cos(thyta1)) # 入射角密度函数积分 # arrival_angle_fineness=0.0001 # for calculus_arv_angle in np.linspace() 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 # TODO:应该找到两个角度值后再比较 k = init_k 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 ) d_k = -fk / d_fk k += d_k if abs(d_k) < 1e-5: dd = distance_point_line(center_x, center_y, line_x, line_y, k) if abs(dd - radius) < 1e-5: return k return None def egm(): u_ph = 750 / 1.732 # 运行相电压 h_cav = 160 # 导线对地平均高 h_gav = h_cav + 9.5 + 2.7 dgc = -2 # 导地线水平距离 # 迭代法计算最大电流 i_max = 0 _min_i = 20 # 尝试的最小电流 _max_i = 80 # 尝试的最大电流 for i_bar in np.linspace(_min_i, _max_i, int((_max_i - _min_i) / 0.01)): # 雷电流 print(f"尝试计算电流为{i_bar:.2f}") rs = rs_fun(i_bar) if not np.isreal(rs): continue rc = rc_fun(i_bar, u_ph) if not np.isreal(rc): continue rg = rg_fun(i_bar, h_cav) if not np.isreal(rg): continue circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc) if not circle_intersection: # if circle_intersection is [] continue circle_line_intersection = solve_circle_line_intersection(rc, rg, h_cav, dgc) min_distance_intersection = ( np.sum( (np.array(circle_intersection) - np.array(circle_line_intersection)) ** 2 ) ** 0.5 ) # 计算两圆交点和地面直线交点的最小距离 i_max = i_bar if min_distance_intersection < 0.1: break i_min = min_i(6.78, 750 / 1.732) cad = Draw() cad.draw(i_min, u_ph, h_gav, h_cav, dgc, 2) cad.draw(i_max, u_ph, h_gav, h_cav, dgc, 6) cad.save() if abs(i_max - _max_i) < 1e-5: print("无法找到最大电流，可能是杆塔较高。") i_max = 300 print(f"最大电流设置为自然界最大电流{i_max}kA") print(f"最大电流为{i_max:.2f}") print(f"最小电流为{i_min:.2f}") if i_min > i_max: print("最大电流小于最小电流，没有暴露弧，程序结束。") return # 开始积分 curt_fineness = 0.1 # 电流积分细度 curt_segment_n = int((i_max - i_min) / curt_fineness) # 分成多少份 calculus = 0 i_curt_samples, d_curt = np.linspace(i_min, i_max, curt_segment_n + 1, retstep=True) for i_curt in i_curt_samples: cal_bd_first = bd_area(i_curt, u_ph, dgc, h_gav, h_cav) cal_bd_second = bd_area(i_curt + d_curt, u_ph, dgc, h_gav, h_cav) cal_thunder_density_first = thunder_density(i_curt) cal_thunder_density_second = thunder_density(i_curt + d_curt) calculus += ( ( cal_bd_first * cal_thunder_density_first + cal_bd_second * cal_thunder_density_second ) / 2 * d_curt ) n_sf = 2 * 2.7 / 10 * calculus # 调整率 print(f"跳闸率是{n_sf:.6}") # draw(rs, rc, rg, h_gav, h_cav, dgc) if __name__ == "__main__": thunder_density(2) egm() print("Finished.")