269 lines
9.1 KiB
Python
269 lines
9.1 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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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), (200, 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 = 300
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y = 300
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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(rc, rg, h_cav, dgc):
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# TODO: 需要考虑地面捕雷线与暴露弧完全没交点的情况
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r = (rc ** 2 - (rg - h_cav) ** 2) ** 0.5 + dgc
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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) ** 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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return r
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def rg_fun(i, h_cav):
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if h_cav < 40:
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rg = (3.6 + 1.7 ** math.log(43 - h_cav)) ** 0.65
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else:
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rg = 5.5 * (i ** 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, h_cav, dgc
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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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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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# 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
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# if theta1 < 0:
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# # print(f"θ_1角度为负数{theta1:.4f},人为设置为0")
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# theta1 = 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 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)
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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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# 求暴露弧上一点的切线
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line_x = math.cos(theta1) * rc + dgc
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line_y = math.sin(theta1) * rc + h_cav
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max_w = 0 # 入射角
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if theta1 < 0:
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max_w = theta1 + math.pi / 2
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k = math.tan(max_w)
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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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max_w = math.atan(new_k) # 用于保护弧相切的角度
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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), (500, k * (500 - line_x) + line_y)
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)
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gMSP.add_line((0, rg), (1000, rg))
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gCAD.save()
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pass
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# k=tangent_line_k(point_x, point_y, dgc, h_cav,rc)
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# 暂时不考虑雷电入射角的影响
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r = (math.cos(theta1) - math.cos(theta2)) * rc
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return r
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# r1=rc*(-math.cos(thyta2)+math.cos(thyta1))
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# 入射角密度函数积分
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# arrival_angle_fineness=0.0001
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# for calculus_arv_angle in np.linspace()
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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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# TODO:应该找到两个角度值后再比较
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k = init_k
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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 - (radius ** 2) * (
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k ** 2 + 1
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)
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d_fk = (
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2 * (k * center_x - center_y - k * line_x + line_y) * (center_x - line_x)
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- 2 * (radius ** 2) * k
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)
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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-5:
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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) < 1e-5:
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return k
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return None
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def egm():
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u_ph = 750 / 1.732 # 运行相电压
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h_cav = 160 # 导线对地平均高
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h_gav = h_cav + 9.5 + 2.7
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dgc = -2 # 导地线水平距离
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# 迭代法计算最大电流
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i_max = 0
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_min_i = 20 # 尝试的最小电流
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_max_i = 80 # 尝试的最大电流
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for i_bar in np.linspace(_min_i, _max_i, int((_max_i - _min_i) / 0.01)): # 雷电流
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print(f"尝试计算电流为{i_bar:.2f}")
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rs = rs_fun(i_bar)
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if not np.isreal(rs):
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continue
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rc = rc_fun(i_bar, u_ph)
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if not np.isreal(rc):
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continue
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rg = rg_fun(i_bar, h_cav)
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if not np.isreal(rg):
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continue
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circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc)
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if not circle_intersection: # if circle_intersection is []
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continue
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circle_line_intersection = solve_circle_line_intersection(rc, rg, h_cav, dgc)
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min_distance_intersection = (
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np.sum(
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(np.array(circle_intersection) - np.array(circle_line_intersection))
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** 2
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)
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** 0.5
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) # 计算两圆交点和地面直线交点的最小距离
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i_max = i_bar
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if min_distance_intersection < 0.1:
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break
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i_min = min_i(6.78, 750 / 1.732)
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cad = Draw()
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cad.draw(i_min, u_ph, h_gav, h_cav, dgc, 2)
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cad.draw(i_max, u_ph, h_gav, h_cav, dgc, 6)
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cad.save()
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if abs(i_max - _max_i) < 1e-5:
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print("无法找到最大电流，可能是杆塔较高。")
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i_max = 300
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print(f"最大电流设置为自然界最大电流{i_max}kA")
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print(f"最大电流为{i_max:.2f}")
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print(f"最小电流为{i_min:.2f}")
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if i_min > i_max:
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print("最大电流小于最小电流，没有暴露弧，程序结束。")
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return
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# 开始积分
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curt_fineness = 0.1 # 电流积分细度
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curt_segment_n = int((i_max - i_min) / curt_fineness) # 分成多少份
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calculus = 0
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i_curt_samples, d_curt = np.linspace(i_min, i_max, curt_segment_n + 1, retstep=True)
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for i_curt in i_curt_samples:
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cal_bd_first = bd_area(i_curt, u_ph, dgc, h_gav, h_cav)
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cal_bd_second = bd_area(i_curt + d_curt, u_ph, dgc, h_gav, h_cav)
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cal_thunder_density_first = thunder_density(i_curt)
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cal_thunder_density_second = thunder_density(i_curt + d_curt)
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calculus += (
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(
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cal_bd_first * cal_thunder_density_first
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+ cal_bd_second * cal_thunder_density_second
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)
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/ 2
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* d_curt
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)
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n_sf = 2 * 2.7 / 10 * calculus # 调整率
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print(f"跳闸率是{n_sf:.6}")
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# draw(rs, rc, rg, h_gav, h_cav, dgc)
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if __name__ == "__main__":
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thunder_density(2)
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egm()
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print("Finished.")
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