493 lines
17 KiB
Python
493 lines
17 KiB
Python
import math
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import ezdxf
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import numpy as np
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from typing import List
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gCAD = None
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gMSP = None
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gCount = 1
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class Parameter:
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h_g_sag: float # 地线弧垂
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h_c_sag: float # 导线弧垂
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voltage_n: int # 工作电压分成多少份来计算
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td: int # 雷暴日
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insulator_c_len: float # 串子绝缘长度
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string_c_len: float
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string_g_len: float
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gc_x: List[float] # 导、地线水平坐标
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ground_angels: List[float] # 地面倾角，向下为正
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h_arm: float # 导、地线垂直坐标
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altitude: int # 海拔，单位米
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max_i: float # 最大尝试电流，单位kA
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rated_voltage: float # 额定电压
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ng: float # 地闪密度 次/(每平方公里·每年)
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Ip_a: float # 概率密度曲线系数a
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Ip_b: float # 概率密度曲线系数b
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para = Parameter()
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def rg_line_function_factory(_rg, ground_angel): # 返回一个地面捕雷线的直线方程
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y_d = _rg / math.cos(ground_angel) # y轴上的截距
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# 利用公式y-y0=k(x-x0) 得到直线公式
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y0 = y_d
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x0 = 0
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k = math.tan(math.pi - ground_angel)
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def f(x):
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return y0 + k * (x - x0)
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return f
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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(
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self,
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i_curt,
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u_ph,
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rs_x,
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rs_y,
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rc_x,
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rc_y,
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rg_x,
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rg_y,
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rg_type,
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ground_angel,
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color,
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):
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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, rc_y, u_ph, typ=rg_type)
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msp.add_circle((rs_x, rs_y), rs, dxfattribs={"color": color})
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msp.add_line((0, 0), (rs_x, rs_y)) # 地线
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msp.add_circle((rc_x, rc_y), rc, dxfattribs={"color": color + 2})
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msp.add_line((rc_x, 0), (rc_x, rc_y)) # 导线
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msp.add_line((rs_x, rs_y), (rc_x, rc_y))
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# 角度线
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circle_intersection = solve_circle_intersection(rs, rc, rs_x, rs_y, rc_x, rc_y)
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msp.add_line(
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(rc_x, rc_y), circle_intersection, dxfattribs={"color": color}
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) # 地线
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if rg_type == "g":
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ground_angel_func = rg_line_function_factory(rg, ground_angel)
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msp.add_line(
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(0, ground_angel_func(0)),
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(2000, ground_angel_func(2000)),
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dxfattribs={"color": color},
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)
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circle_line_section = solve_circle_line_intersection(
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rc, rc_x, rc_y, ground_angel_func
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)
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if not circle_line_section:
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pass
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else:
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msp.add_line(
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(rc_x, rc_y), circle_line_section, dxfattribs={"color": color}
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) # 导线和圆的交点
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if rg_type == "c":
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msp.add_circle((rg_x, rg_y), rg, dxfattribs={"color": color})
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rg_rc_intersection = solve_circle_intersection(
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rg, rc, rg_x, rg_y, rc_x, rc_y
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)
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if rg_rc_intersection:
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msp.add_line(
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(rc_x, rc_y), rg_rc_intersection, dxfattribs={"color": color}
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) # 圆和圆的交点
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# 计算圆交点
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# msp.add_line((dgc, h_cav), circle_intersection) # 导线
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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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def save_as(self, file_name):
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doc = self._doc
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doc.saveas(file_name)
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# 圆交点
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def solve_circle_intersection(
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radius1,
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radius2,
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center_x1,
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center_y1,
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center_x2,
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center_y2,
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):
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# 用牛顿法求解
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x = radius2 + center_x2 # 初始值
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y = radius2 + center_y2 # 初始值
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# TODO 考虑出现2个解的情况
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for _ in range(0, 10):
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A = [
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[-2 * (x - center_x1), -2 * (y - center_y1)],
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[-2 * (x - center_x2), -2 * (y - center_y2)],
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]
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b = [
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(x - center_x1) ** 2 + (y - center_y1) ** 2 - radius1**2,
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(x - center_x2) ** 2 + (y - center_y2) ** 2 - radius2**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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# 圆与捕雷线交点
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def solve_circle_line_intersection(
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radius, center_x, center_y, ground_surface_func
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): # 返回交点的x和y坐标
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x0 = 0
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y0 = ground_surface_func(x0)
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x1 = 1
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y1 = ground_surface_func(x1)
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k = (y1 - y0) / (x1 - x0)
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distance = distance_point_line(center_x, center_y, x0, y0, k) # 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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a = center_x
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b = center_y
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c = y0
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d = x0
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bb = -2 * a + 2 * c * k - 2 * d * (k**2) - 2 * b * k
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aa = 1 + k**2
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rr = radius
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cc = (
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a**2
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+ c**2
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- 2 * c * k * d
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+ (k**2) * (d**2)
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- 2 * b * (c - k * d)
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+ b**2
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- rr**2
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)
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_x = (-bb + (bb**2 - 4 * aa * cc) ** 0.5) / 2 / aa
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_y = ground_surface_func(_x)
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# 验算结果
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equ = (center_x - _x) ** 2 + (center_y - _y) ** 2 - radius**2
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assert abs(equ) < 1e-5
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return [_x, _y]
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def min_i(string_len, u_ph):
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# 海拔修正
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altitude = para.altitude
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if altitude > 1000:
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k_a = math.exp((altitude - 1000) / 8150) # 气隙海拔修正
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else:
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k_a = 1
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u_50 = 1 / k_a * (530 * string_len + 35) # 50045 上附录的公式，实际应该用负极性电压的公式
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# u_50 = 1 / k_a * (533 * string_len + 132) # 串放电路径 1000m海拔
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# u_50 = 1 / k_a * (477 * string_len + 99) # 串放电路径 2000m海拔
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# u_50 = 615 * string_len # 导线对塔身放电 1000m海拔
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# u_50= 263.32647401+533.90081562*string_len
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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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# 新版大手册公式 3-277
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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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# r = 2 * (u_50 - u_ph) / z_c
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return r
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def thunder_density(i, td, ip_a, ip_b): # 雷电流幅值密度函数
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# td = para.td
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r = None
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# ip_a = para.Ip_a
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# ip_b = para.Ip_b
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if ip_a > 0 and ip_b > 0:
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r = -(
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-ip_b / ip_a / ((1 + (i / ip_a) ** ip_b) ** 2) * ((i / ip_a) ** (ip_b - 1))
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)
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return r
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else:
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if td == 20:
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r = -(10 ** (-i / 44)) * math.log(10) * (-1 / 44) # 雷暴日20d
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return r
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if td == 40:
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r = -(10 ** (-i / 88)) * math.log(10) * (-1 / 88) # 雷暴日40d
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return r
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raise Exception("检查雷电参数!")
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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 * abs((np.cos(angle - math.pi / 2) ** 3)) # 新版大手册公式3-275
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return r
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def rs_fun(i):
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r = 10 * (i**0.65) # 新版大手册公式3-271
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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) ** 1.125) # 新版大手册公式3-272
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return r
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# typ 如果是g，代表捕雷线公式，c代表暴露弧公式
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def rg_fun(i_curt, h_cav, u_ph, typ="g"):
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rg = None
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if typ == "g":
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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) # 新版大手册公式3-273
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else:
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rg = 5.5 * (i_curt**0.65) # 新版大手册公式3-273
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elif typ == "c": # 此时返回的是圆半径
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rg = rc_fun(i_curt, u_ph)
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return rg
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def intersection_angle(
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rc_x, rc_y, rs_x, rs_y, rg_x, rg_y, i_curt, u_ph, ground_angel, rg_type
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): # 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, rc_y, u_ph, typ=rg_type)
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circle_intersection = solve_circle_intersection(
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rs, rc, rs_x, rs_y, rc_x, rc_y
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) # 两圆的交点
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circle_line_or_rg_intersection = None
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rg_line_func = rg_line_function_factory(rg, ground_angel)
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if rg_type == "g":
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circle_line_or_rg_intersection = solve_circle_line_intersection(
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rc, rc_x, rc_y, rg_line_func
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) # 暴露圆和补雷线的交点
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if rg_type == "c":
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circle_line_or_rg_intersection = solve_circle_intersection(
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rg, rc, rg_x, rg_y, rc_x, rc_y
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) # 两圆的交点
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# TODO 应该是不存在落到地面线以下的情况，先把以下注释掉
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# if circle_line_or_rg_intersection:
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# (
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# circle_line_or_rg_intersection_x,
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# circle_line_or_rg_intersection_y,
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# ) = circle_line_or_rg_intersection
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# if (
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# ground_surface(rg, circle_line_or_rg_intersection_x)
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# > circle_line_or_rg_intersection_y
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# ): # 交点在地面线以下，就可以不积分
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# # 找到暴露弧和地面线的交点
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# circle_line_or_rg_intersection = circle_ground_surface_intersection(
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# rc, rc_x, rc_y, ground_surface
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# )
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theta1 = None
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np_circle_intersection = np.array(circle_intersection)
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theta2_line = np_circle_intersection - np.array([rc_x, rc_y])
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theta2 = math.atan(theta2_line[1] / theta2_line[0])
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np_circle_line_or_rg_intersection = np.array(circle_line_or_rg_intersection)
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if not circle_line_or_rg_intersection:
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if rc_y - rc > rg_line_func(rc_x): # rg在rc下面
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# 捕捉线太低了，对高塔无保护，θ_1从-90°开始计算，即从与地面垂直的角度开始就已经暴露了。
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theta1 = -math.pi / 2
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else:
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theta1_line = np_circle_line_or_rg_intersection - np.array([rc_x, rc_y])
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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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# 点到直线的距离
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def distance_point_line(point_x, point_y, line_x, line_y, k) -> float:
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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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segments = int(max_w / w_fineness)
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if segments < 2: # 最大最小太小，没有可以积分的
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return 0
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w_samples, d_w = np.linspace(0, max_w, segments, retstep=True)
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# 童中宇 750KV信洛Ⅰ线雷电防护性能研究 公式 3-10
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cal_w_np = abs(angel_density(w_samples)) * np.sin(theta - (w_samples - math.pi / 2))
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r_pw = np.sum((cal_w_np[:-1] + cal_w_np[1:])) / 2 * d_w
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return r_pw
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def calculus_bd(theta, rc, rs, rg, rc_x, rc_y, rs_x, rs_y): # 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 + rc_x
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line_y = math.sin(theta) * rc + rc_y
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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(rs_x, rs_y, line_x, line_y, k)
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if d_to_rs < rs: # 相交
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# 要用过这一点到保护弧的切线
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new_k = tangent_line_k(line_x, line_y, rs_x, rs_y, 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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# global gCount
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# gCount = 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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# 童中宇 750KV信洛Ⅰ线雷电防护性能研究 公式 3-10
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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(
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i_curt, u_ph, rc_x, rc_y, rs_x, rs_y, rg_x, rg_y, ground_angel, rg_type
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): # 暴露弧的投影面积
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theta1, theta2 = intersection_angle(
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rc_x, rc_y, rs_x, rs_y, rg_x, rg_y, i_curt, u_ph, ground_angel, rg_type
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) # 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, rc_y, u_ph, typ=rg_type)
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theta_segments = int((theta2 - theta1) / theta_fineness)
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if theta_segments < 2:
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return 0
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theta_sample, d_theta = np.linspace(theta1, theta2, theta_segments, retstep=True)
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if len(theta_sample) < 2:
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return 0
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vec_calculus_bd = np.vectorize(calculus_bd)
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calculus_bd_np = vec_calculus_bd(theta_sample, rc, rs, rg, rc_x, rc_y, rs_x, rs_y)
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r_bd = np.sum(calculus_bd_np[:-1] + calculus_bd_np[1:]) / 2 * d_theta
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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
|
||
# f(k)=(k*x1-y1-k*x0+y0)**2-R**2*(k**2+1) x1,y1是圆心
|
||
# 已考虑两个解的判别
|
||
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
|
||
max_iteration = 30
|
||
for bar in range(0, max_iteration):
|
||
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
|
||
# 解决数值稳定性
|
||
if bar == max_iteration - 1:
|
||
if abs(math.atan(k)) * 180 / math.pi > 89:
|
||
k_candidate[ind] = k
|
||
# 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，通过雷暴日计算
|
||
if para.ng > 0:
|
||
r = para.ng
|
||
else:
|
||
r = 0.023 * (td**1.3)
|
||
return r
|
||
|
||
|
||
# 圆和地面线的交点，只去正x轴上的。
|
||
def circle_ground_surface_intersection(radius, center_x, center_y, ground_surface):
|
||
# 最笨的办法，一个个去试
|
||
x_series = np.linspace(0, radius, int(radius / 0.001)) + center_x
|
||
part_to_be_squared = (
|
||
radius**2 - (x_series - center_x) ** 2
|
||
) # 有可能出现-0.00001的数值，只是一个数值稳定问题。
|
||
part_to_be_squared[
|
||
(part_to_be_squared < 0) & (abs(part_to_be_squared) < 1e-3)
|
||
] = 0 # 强制为0
|
||
y_series = center_y - part_to_be_squared**0.5
|
||
ground_surface_y = ground_surface(x_series)
|
||
equal_location = np.abs(ground_surface_y - y_series) < 0.5
|
||
r_x = x_series[equal_location][0]
|
||
r_y = ground_surface(r_x)
|
||
return r_x, r_y
|
||
|
||
|
||
# u_ph是相电压
|
||
# insulator_c_len绝缘子闪络距离
|
||
def arc_possibility(rated_voltage, insulator_c_len): # 建弧率
|
||
# 50064 中附录给的公式
|
||
# TODO 需要区分交直流
|
||
# _e = rated_voltage / (3**0.5) / insulator_c_len #交流
|
||
_e = abs(rated_voltage) / (1) / insulator_c_len # 直流
|
||
r = (4.5 * (_e**0.75) - 14) * 1e-2
|
||
return r
|