282 lines
9.3 KiB
Python
282 lines
9.3 KiB
Python
import math
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import ezdxf
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import numpy as np
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gCAD = None
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gMSP = None
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gCount = 1
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class Draw:
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def __init__(self):
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self._doc = ezdxf.new(dxfversion="R2010")
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self._doc.layers.add("EGM", color=2)
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global gCAD
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gCAD = self
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def draw(self, i_curt, u_ph, h_gav, h_cav, dgc, color):
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doc = self._doc
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msp = doc.modelspace()
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global gMSP
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gMSP = msp
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rs = rs_fun(i_curt)
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rc = rc_fun(i_curt, u_ph)
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rg = rg_fun(i_curt, h_cav)
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msp.add_circle((0, h_gav), rs, dxfattribs={"color": color})
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msp.add_line((0, 0), (0, h_gav)) # 地线
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msp.add_circle((dgc, h_cav), rc, dxfattribs={"color": color})
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msp.add_line((dgc, 0), (dgc, h_cav)) # 导线
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msp.add_line((0, h_gav), (dgc, h_cav))
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msp.add_line((0, rg), (2000, rg), dxfattribs={"color": color})
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# 计算圆交点
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# circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc)
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# msp.add_line((0, h_gav), circle_intersection) # 地线
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# msp.add_line((dgc, h_cav), circle_intersection) # 导线
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# circle_line_section = solve_circle_line_intersection(rc, rg, h_cav, dgc)
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# msp.add_line((0, 0), circle_line_section) # 导线和圆的交点
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def save(self):
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doc = self._doc
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doc.saveas("egm.dxf")
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# 圆交点
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def solve_circle_intersection(rs, rc, hgav, hcav, dgc):
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# 用牛顿法求解
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x = rc # 初始值
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y = rc # 初始值
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for bar in range(0, 10):
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A = [[-2 * x, -2 * (y - hgav)], [-2 * (x - dgc), -2 * (y - hcav)]]
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b = [
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x ** 2 + (y - hgav) ** 2 - rs ** 2,
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(x - dgc) ** 2 + (y - hcav) ** 2 - rc ** 2,
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]
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X_set = np.linalg.solve(A, b)
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x += X_set[0]
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y += X_set[1]
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if np.all(np.abs(X_set) < 1e-5):
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return [x, y]
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return []
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# 圆与地面线交点
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def solve_circle_line_intersection(radius, rg, center_x, center_y):
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distance = distance_point_line(center_x, center_y, 0, rg, 0) # 捕雷线到暴露圆中点的距离
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if distance > radius:
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return []
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else:
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r = (radius ** 2 - (rg - center_y) ** 2) ** 0.5 + center_x
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return [r, rg]
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def min_i(string_len, u_ph):
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u_50 = 530 * string_len + 35
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z_0 = 300 # 雷电波阻抗
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z_c = 251 # 导线波阻抗
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r = (u_50 + 2 * z_0 / (2 * z_0 + z_c) * u_ph) * (2 * z_0 + z_c) / (z_0 * z_c)
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return r
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def thunder_density(i): # l雷电流幅值密度函数
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r = -(10 ** (-i / 44)) * math.log(10) * (-1 / 44)
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return r
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def angel_density(angle): # 入射角密度函数 angle单位是弧度
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r = 0.75 * (math.cos(angle - math.pi / 2) ** 3)
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return r
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def rs_fun(i):
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r = 10 * (i ** 0.65)
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return r
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def rc_fun(i, u_ph):
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r = 1.63 * ((5.015 * (i ** 0.578) - 0.001 * u_ph) ** 1.125)
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# r=14.7*(i**0.42)
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return r
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def rg_fun(i_curt, h_cav):
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if h_cav < 40:
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rg = (3.6 + 1.7 ** math.log(43 - h_cav)) * (i_curt ** 0.65)
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else:
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rg = 5.5 * (i_curt ** 0.65)
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return rg
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def intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph): # 暴露弧的角度
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rs = rs_fun(i_curt)
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rc = rc_fun(i_curt, u_ph)
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rg = rg_fun(i_curt, h_cav)
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circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc) # 两圆的交点
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circle_line_intersection = solve_circle_line_intersection(
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rc, rg, dgc, h_cav
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) # 暴露圆和补雷线的交点
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np_circle_intersection = np.array(circle_intersection)
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# TODO to be removed
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if not circle_intersection:
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abc = 123
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theta2_line = np_circle_intersection - np.array([dgc, h_cav])
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theta2 = math.atan(theta2_line[1] / theta2_line[0])
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np_circle_line_intersection = np.array(circle_line_intersection)
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theta1_line = np_circle_line_intersection - np.array([dgc, h_cav])
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theta1 = math.atan(theta1_line[1] / theta1_line[0])
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return np.array([theta1, theta2])
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def distance_point_line(point_x, point_y, line_x, line_y, k):
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d = abs(k * point_x - point_y - k * line_x + line_y) / ((k ** 2 + 1) ** 0.5)
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return d
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def func_calculus_pw(theta, max_w):
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w_fineness = 0.01
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r_pw = 0
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# TODO to be removed
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if int(max_w / w_fineness) < 0:
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abc = 123
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pass
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w_samples, d_w = np.linspace(0, max_w, int(max_w / w_fineness), retstep=True)
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for cal_w in w_samples[:-1]:
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r_pw += (
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(
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abs(angel_density(cal_w)) * math.sin(theta - (cal_w - math.pi / 2))
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+ abs(angel_density(cal_w + d_w))
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* math.sin(theta - (cal_w + d_w - math.pi / 2))
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)
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/ 2
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) * d_w
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return r_pw
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def calculus_bd(theta, rc, rs, rg, dgc, h_cav, h_gav): # 对θ进行积分
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max_w = 0
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# 求暴露弧上一点的切线
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line_x = math.cos(theta) * rc + dgc
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line_y = math.sin(theta) * rc + h_cav
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k = math.tan(theta + math.pi / 2) # 入射角
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# 求保护弧到直线的距离，判断是否相交
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d_to_rs = distance_point_line(0, h_gav, line_x, line_y, k)
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if d_to_rs < rs: # 相交
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# 要用过直线上一点到暴露弧的切线
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new_k = tangent_line_k(line_x, line_y, 0, h_gav, rs, init_k=k)
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# TODO to be removed
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if not new_k:
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a = 12
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tangent_line_k(line_x, line_y, 0, h_gav, rs, init_k=k)
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if new_k >= 0:
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max_w = math.atan(new_k) # 用于保护弧相切的角度
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elif new_k < 0:
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max_w = math.atan(new_k) + math.pi
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# TODO to be removed
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if max_w < 0:
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abc = 123
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tangent_line_k(line_x, line_y, 0, h_gav, rs, init_k=k)
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# TODO to be removed
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global gCount
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gCount += 1
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if gCount % 100 == 0:
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# gMSP.add_circle((0, h_gav), rs)
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# gMSP.add_circle((dgc, h_cav), rc)
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# gMSP.add_line((dgc, h_cav), (line_x, line_y))
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# gMSP.add_line(
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# (-500, new_k * (-500 - line_x) + line_y),
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# (500, new_k * (500 - line_x) + line_y),
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# )
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# gCAD.save()
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pass
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else:
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max_w = theta + math.pi / 2 # 入射角
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# TODO to be removed
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if gCount % 200 == 0:
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# # intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph)
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# gMSP.add_circle((0, h_gav), rs)
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# gMSP.add_circle((dgc, h_cav), rc)
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# gMSP.add_line((dgc, h_cav), (line_x, line_y))
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# gMSP.add_line(
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# (-500, k * (-500 - line_x) + line_y),
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# (500, k * (500 - line_x) + line_y),
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# )
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# gCAD.save()
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pass
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r = rc / math.cos(theta) * func_calculus_pw(theta, max_w)
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return r
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def bd_area(i_curt, u_ph, dgc, h_gav, h_cav): # 暴露弧的投影面积
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theta1, theta2 = intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph) # θ角度
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theta_fineness = 0.01
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rc = rc_fun(i_curt, u_ph)
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rs = rs_fun(i_curt)
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rg = rg_fun(i_curt, h_cav)
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r_bd = 0
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theta_sample, d_theta = np.linspace(
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theta1, theta2, int((theta2 - theta1) / theta_fineness), retstep=True
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)
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for calculus_theta in theta_sample[:-1]:
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r_bd += (
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(
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calculus_bd(calculus_theta, rc, rs, rg, dgc, h_cav, h_gav)
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+ calculus_bd(calculus_theta + d_theta, rc, rs, rg, dgc, h_cav, h_gav)
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)
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/ 2
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* d_theta
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)
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return r_bd
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def tangent_line_k(line_x, line_y, center_x, center_y, radius, init_k=10.0):
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# 直线方程为 y-y0=k(x-x0)，x0和y0为经过直线的任意一点
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# 牛顿法求解k
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# f(k)=(k*x1-y1-k*x0+y0)**2-R**2*(k**2+1) x1,y1是圆心
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k_candidate = [-100, 100]
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if abs(center_y - line_y) < 1 and abs(line_x - center_x - radius) < 1:
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# k不存在
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k_candidate = [99999999, 99999999]
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else:
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for ind, k_cdi in enumerate(list(k_candidate)):
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k = k_candidate[ind]
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k_candidate[ind] = None
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for bar in range(0, 30):
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fk = (k * center_x - center_y - k * line_x + line_y) ** 2 - (
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radius ** 2
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) * (k ** 2 + 1)
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d_fk = (
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2
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* (k * center_x - center_y - k * line_x + line_y)
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* (center_x - line_x)
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- 2 * (radius ** 2) * k
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)
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if abs(d_fk) < 1e-5 and abs(line_x - center_x - radius) < 1e-5:
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# k不存在，角度为90°，k取一个很大的正数
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k_candidate[ind] = 99999999999999
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break
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d_k = -fk / d_fk
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k += d_k
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if abs(d_k) < 1e-3:
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dd = distance_point_line(center_x, center_y, line_x, line_y, k)
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if abs(dd - radius) < 1:
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k_candidate[ind] = k
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break
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# 把k转化成相应的角度，从x开始，逆时针为正
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k_angle = []
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for kk in k_candidate:
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if kk is None:
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abc = 123
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# tangent_line_k(line_x, line_y, center_x, center_y, radius)
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pass
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if kk >= 0:
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k_angle.append(math.atan(kk))
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if kk < 0:
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k_angle.append(math.pi + math.atan(kk))
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# 返回相对x轴最大的角度k
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return np.array(k_candidate)[np.max(k_angle) == k_angle].tolist()[-1]
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def func_ng(td): # 地闪密度
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return 0.023 * (td ** 1.3)
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