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加入了计算最大入射角度的公式

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facat 2021-09-12 16:55:11 +08:00
parent 5cbf463ab0
commit db2788f116
1 changed files with 90 additions and 40 deletions
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130
main.py
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@ -2,30 +2,37 @@ import math
import ezdxf import ezdxf
import numpy as np import numpy as np
gCAD = None
gMSP = None
class Draw: class Draw:
def __init__(self): def __init__(self):
self._doc = ezdxf.new(dxfversion="R2010") self._doc = ezdxf.new(dxfversion="R2010")
self._doc.layers.add("EGM", color=2) self._doc.layers.add("EGM", color=2)
global gCAD
gCAD = self
def draw(self, i_curt, u_ph, h_gav, h_cav, dgc): def draw(self, i_curt, u_ph, h_gav, h_cav, dgc, color):
doc = self._doc doc = self._doc
msp = doc.modelspace() msp = doc.modelspace()
global gMSP
gMSP = msp
rs = rs_fun(i_curt) rs = rs_fun(i_curt)
rc = rc_fun(i_curt, u_ph) rc = rc_fun(i_curt, u_ph)
rg = rg_fun(i_curt, h_cav) rg = rg_fun(i_curt, h_cav)
msp.add_circle((0, h_gav), rs) msp.add_circle((0, h_gav), rs, dxfattribs={"color": color})
msp.add_line((0, 0), (0, h_gav)) # 地线 msp.add_line((0, 0), (0, h_gav)) # 地线
msp.add_circle((dgc, h_cav), rc) msp.add_circle((dgc, h_cav), rc, dxfattribs={"color": color})
msp.add_line((dgc, 0), (dgc, h_cav)) # 导线 msp.add_line((dgc, 0), (dgc, h_cav)) # 导线
msp.add_line((0, h_gav), (dgc, h_cav)) msp.add_line((0, h_gav), (dgc, h_cav))
msp.add_line((0, rg), (200, rg)) msp.add_line((0, rg), (200, rg), dxfattribs={"color": color})
# 计算圆交点 # 计算圆交点
circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc) # 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((0, h_gav), circle_intersection) # 地线
msp.add_line((dgc, h_cav), circle_intersection) # 导线 # msp.add_line((dgc, h_cav), circle_intersection) # 导线
circle_line_section = solve_circle_line_intersection(rc, rg, h_cav, dgc) # 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 # msp.add_line((0, 0), circle_line_section) # 导线和圆的交点
def save(self): def save(self):
doc = self._doc doc = self._doc
@ -34,12 +41,6 @@ class Draw:
# 圆交点 # 圆交点
def solve_circle_intersection(rs, rc, hgav, hcav, dgc): def solve_circle_intersection(rs, rc, hgav, hcav, dgc):
# x = Symbol('x', real=True)
# y = Symbol('y', real=True)
# equ = [
# x ** 2 + (y - hgav) ** 2 - rs ** 2,
# (x - dgc) ** 2 + (y - hcav) ** 2 - rc ** 2,
# ]
# 用牛顿法求解 # 用牛顿法求解
x = 300 x = 300
y = 300 y = 300
@ -55,22 +56,12 @@ def solve_circle_intersection(rs, rc, hgav, hcav, dgc):
if np.all(np.abs(X_set) < 1e-5): if np.all(np.abs(X_set) < 1e-5):
return [x, y] return [x, y]
return [] return []
# list_set = list(X_set)
# solve_set = nonlinsolve(equ, [x, y])
# print(ask(Q.real(solve_set)))
# list_set = list(solve_set)
# pprint(list_set)
# if not np.all(np.isreal(list_set)):
# return []
# for value in list_set:
# if value[0] > 0 and value[1] > 1:
# return value
# return []
# 圆与地面线交点 # 圆与地面线交点
def solve_circle_line_intersection(rc, rg, hcav, dgc): def solve_circle_line_intersection(rc, rg, h_cav, dgc):
r = (rc ** 2 - (rg - hcav) ** 2) ** 0.5 + 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] return [r, rg]
@ -110,27 +101,62 @@ def rg_fun(i, h_cav):
return rg return rg
def intersection_angel(dgc, h_gav, h_cav, i_curt, u_ph): # 暴露弧的角度 def intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph): # 暴露弧的角度
rs = rs_fun(i_curt) rs = rs_fun(i_curt)
rc = rc_fun(i_curt, u_ph) rc = rc_fun(i_curt, u_ph)
rg = rg_fun(i_curt, h_cav) rg = rg_fun(i_curt, h_cav)
circle_intersection = solve_circle_intersection(rs, rc, h_gav, h_cav, dgc) 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) 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) np_circle_intersection = np.array(circle_intersection)
theta2_line = np_circle_intersection - np.array([dgc, h_cav]) theta2_line = np_circle_intersection - np.array([dgc, h_cav])
theta2 = math.atan(theta2_line[1] / theta2_line[0]) theta2 = math.atan(theta2_line[1] / theta2_line[0])
np_circle_line_intersection = np.array(circle_line_intersection) np_circle_line_intersection = np.array(circle_line_intersection)
theta1_line = np_circle_line_intersection - np.array([dgc, h_cav]) theta1_line = np_circle_line_intersection - np.array([dgc, h_cav])
theta1 = math.atan(theta1_line[1] / theta1_line[0]) theta1 = math.atan(theta1_line[1] / theta1_line[0])
if theta1 < 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
# print(f"θ_1角度为负数{theta1:.4f},人为设置为0") # if theta1 < 0:
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]) 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 def bd_area(i_curt, u_ph, dgc, h_gav, h_cav): # 暴露弧的投影面积
theta1, theta2 = intersection_angel(dgc, h_gav, h_cav, i_curt, u_ph) theta1, theta2 = intersection_angle(dgc, h_gav, h_cav, i_curt, u_ph)
rc = rc_fun(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 # 暂时不考虑雷电入射角的影响
r = (math.cos(theta1) - math.cos(theta2)) * rc r = (math.cos(theta1) - math.cos(theta2)) * rc
return r return r
@ -140,11 +166,35 @@ def bd_area(i_curt, u_ph, dgc, h_gav, h_cav): # 暴露弧的投影面积
# for calculus_arv_angle in np.linspace() # 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(): def egm():
u_ph = 750 / 1.732 # 运行相电压 u_ph = 750 / 1.732 # 运行相电压
h_cav = 160 # 导线对地平均高 h_cav = 160 # 导线对地平均高
h_gav = h_cav + 9.5 + 2.2 h_gav = h_cav + 9.5 + 2.7
dgc = 2 # 导地线水平距离 dgc = -2 # 导地线水平距离
# 迭代法计算最大电流 # 迭代法计算最大电流
i_max = 0 i_max = 0
_min_i = 20 # 尝试的最小电流 _min_i = 20 # 尝试的最小电流
@ -176,8 +226,8 @@ def egm():
break break
i_min = min_i(6.78, 750 / 1.732) i_min = min_i(6.78, 750 / 1.732)
cad = Draw() cad = Draw()
cad.draw(i_min, u_ph, h_gav, h_cav, dgc) cad.draw(i_min, u_ph, h_gav, h_cav, dgc, 2)
cad.draw(i_max, u_ph, h_gav, h_cav, dgc) cad.draw(i_max, u_ph, h_gav, h_cav, dgc, 6)
cad.save() cad.save()
if abs(i_max - _max_i) < 1e-5: if abs(i_max - _max_i) < 1e-5:
print("无法找到最大电流，可能是杆塔较高。") print("无法找到最大电流，可能是杆塔较高。")
@ -189,7 +239,7 @@ def egm():
print("最大电流小于最小电流，没有暴露弧，程序结束。") print("最大电流小于最小电流，没有暴露弧，程序结束。")
return return
# 开始积分 # 开始积分
curt_fineness = 0.001 # 电流积分细度 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 curt_segment_n = int((i_max - i_min) / curt_fineness) # 分成多少份
calculus = 0 calculus = 0
i_curt_samples, d_curt = np.linspace(i_min, i_max, curt_segment_n + 1, retstep=True) i_curt_samples, d_curt = np.linspace(i_min, i_max, curt_segment_n + 1, retstep=True)