# 计算直线塔不平衡张力
# 新版输电线路大手册 P328

import math

# h_i 悬点高差
# l_i 悬点档距
# _alpha 导线膨胀系数  1/°C
# _elastic 弹性系数 N/mm2
# _t_e 架线时考虑初伸长的降温，取正值。单位°C
# lambda_i 计算不平衡张力时导线比载 N/(m.mm)
# sigma_i 计算不平衡张力时最低点水平应力 单位N/mm2
# t_i 计算不平衡张力时导线温度 单位°C
# _lambda_m 导线架线时时导线比载 N/(m.mm)
# _sigma_m 导线架线时时最低点水平应力 单位N/mm2
# _t_m 导线架线时时导线温度 单位°C


def delta_li(
    h_i: float,
    l_i: float,
    lambda_i: float,
    _alpha: float,
    _elastic: float,
    _t_e: float,
    t_i: float,
    sigma_i: float,
    _lambda_m: float,
    _t_m: float,
    _sigma_m: float,
) -> float:
    beta_i = math.atan(h_i / l_i)  # 高差角
    _delta_li = (
        l_i
        / ((math.cos(beta_i) ** 2) * (1 + (lambda_i * l_i / sigma_i) ** 2 / 8))
        * (
            (l_i * math.cos(beta_i)) ** 2
            / 24
            * ((_lambda_m / _sigma_m) ** 2 - (lambda_i / sigma_i) ** 2)
            + ((sigma_i - _sigma_m) / _elastic / math.cos(beta_i))
            + _alpha * (t_i + _t_e - _t_m)
        )
    )
    return _delta_li


# area 导线截面 单位mm2
# sigma_i 第i档内水平应力 单位N/mm2
# b_i 悬垂串沿线路方向水平偏移距离，沿大号方向为正，反之为负。 单位m
# length_i 第i基直线塔串长 单位m
# g_i 第i基直线塔串重 单位N
# h_i 悬垂串处千中垂位置时，,第 i 基对第 i-1 杆塔上导线悬挂点间的高差大号比小号杆塔悬挂点高者h本身为正值，反之为负值。
# lambda_i 第i档导线比载 N/(m.mm)
# h_i1 悬垂串处千中垂位置时，第 i+1 基对第 i 杆塔上导线悬挂点间的高差大号比小号杆塔悬挂点高者h本身为正值，反之为负值。
# lambda_i1
def fun_sigma_i1(
    area: float,
    sigma_i: float,
    b_i: float,
    length_i: float,
    g_i: float,
    h_i: float,
    l_i: float,
    lambda_i: float,
    h_i1: float,
    l_i1: float,
    lambda_i1: float,
):
    beta_i = math.atan(h_i / l_i)
    beta_i1 = math.atan(h_i1 / l_i1)
    _sigma_i1 = (
        (
            g_i / 2 / area
            + lambda_i * l_i / 2 / math.cos(beta_i)
            + lambda_i1 * l_i1 / 2 / math.cos(beta_i1)
            + sigma_i * h_i / l_i
        )
        + sigma_i / b_i * math.sqrt(length_i ** 2 - b_i ** 2)
    ) / (math.sqrt(length_i ** 2 - b_i ** 2) / b_i + h_i1 / l_i1)
    return _sigma_i1


# 求解循环。
def cal_loop():
    loop_end = 100000  # 最大循环次数
    # 架线时的状态
    # 取外过无风
    string_length = 9.2  # 串长 单位m
    string_g = 60 * 9.8  # 串重 单位N
    t_m = 15  # 导线架设时的气温。单位°C
    t_e = 20  # 架线时考虑初伸长的降温，取正值。单位°C
    alpha = 0.0000155  # 导线膨胀系数  1/°C
    elastic = 95900  # 弹性系数 N/mm2
    area = 154.48  # 导线面积 mm2
    lambda_m = 14.8129 / area  # 导线比载 N/(m.mm)
    # 取400m代表档距下
    sigma_m = 28517 / area  # 架线时，初伸长未释放前的最低点水平应力。单位N/mm2
    span_count = 3  # 几个档距
    # n个档距,n-1个直线塔
    h_array = [0, 0, 0]
    l_array = [400, 400, 400]
    t_array = [15, 15, 15]
    lambda_array = [lambda_m, lambda_m, lambda_m]
    loop_count = 1
    sigma_0 = sigma_m * 0.8
    while True:
        sigma_0 = sigma_0 + 0.001
        sigma_array = [sigma_0, 0, 0]
        b_i = 0
        delta_l_i_array = []
        for i in range(span_count - 1):
            h_i = h_array[i]
            l_i = l_array[i]
            lambda_i = lambda_array[i]
            t_i = t_array[i]
            sigma_i = sigma_array[i]
            _delta_l_i = delta_li(
                h_i,
                l_i,
                lambda_i,
                alpha,
                elastic,
                t_e,
                t_i,
                sigma_i,
                lambda_m,
                t_m,
                sigma_m,
            )
            delta_l_i_array.append(_delta_l_i)
            b_i += _delta_l_i
            length_i = string_length
            g_i = string_g
            h_i1 = h_array[i + 1]
            l_i1 = l_array[i + 1]
            lambda_i1 = lambda_array[i + 1]
            sigma_i1 = fun_sigma_i1(
                area,
                sigma_i,
                b_i,
                length_i,
                g_i,
                h_i,
                l_i,
                lambda_i,
                h_i1,
                l_i1,
                lambda_i1,
            )
            sigma_array[i + 1] = sigma_i1
        # print("第{loop_count}轮求解。".format(loop_count=loop_count))
        # print(b_i)
        loop_count += 1
        if math.fabs(b_i) < 1e-5:
            print("迭代{loop_count}次找到解。".format(loop_count=loop_count))
            print("悬垂串偏移累加bi为{b_i}".format(b_i=b_i))
            for i in range(span_count):
                print("第{i}档导线应力为{tension}".format(i=i, tension=sigma_array[i]))
            for i in range(span_count - 1):
                print("第{i}串偏移值为{bias}".format(i=i, bias=delta_l_i_array[i]))
            verify(
                area,
                h_array,
                l_array,
                string_length,
                string_g,
                sigma_array,
                delta_l_i_array,
                lambda_array,
            )
            break
        if loop_count >= loop_end:
            print("!!!未找到解。")
            print(sigma_array)
            print(b_i)
            break


# 检验等式。
def verify(
    area: float,
    h_array: [float],
    l_array: [float],
    string_length: [float],
    string_g: [float],
    sigma_array: [float],
    delta_l_i_array: [float],
    lambda_array: [float],
):
    # 用新版大手册p329页(5-61)最第一个公式校验
    for i in range(len(delta_l_i_array)):
        sigma_i = sigma_array[i]
        sigma_i1 = sigma_array[i + 1]
        left_equ = sigma_array[i + 1]
        _delta_l_i = delta_l_i_array[i]
        lambda_i = lambda_array[i]
        lambda_i1 = lambda_array[i + 1]
        h_i = h_array[i]
        h_i1 = h_array[i + 1]
        l_i = l_array[i]
        l_i1 = l_array[i + 1]
        beta_i = math.atan(h_i / l_i)
        beta_i1 = math.atan(h_i1 / l_i1)
        w_i = (
            lambda_i * l_i / 2 / math.cos(beta_i)
            + sigma_i * h_i / l_i
            + (lambda_i1 * l_i1 / 2 / math.cos(beta_i1) - sigma_i1 * h_i1 / l_i1)
        )
        right_equ = sigma_i + delta_l_i_array[i] / math.sqrt(
            string_length ** 2 - delta_l_i_array[i] ** 2
        ) * (string_g / 2 / area + w_i)
        if math.fabs(right_equ - left_equ) > 1e-4:
            print("!!!等式不满足")
            return
    print("等式满足。")


cal_loop()


print("Finished.")