2023地下电缆群温升计算导则转移矩阵法

地下电缆群温升计算导则——转移矩阵法1 范围本标（本分本导性术件规了。本标（本分本导性术件适于。2 规范引文件下列件于文的用是不少是期的用件仅日版本用本件。凡是注期引文，其新本包所的修单适于文。JB/T10181《电缆载流量计算》IEC60287 Electriccablescalculationofthecurrentrating3 术语定义下列语定适于文件。3.1transfermatrix电缆群中电缆自身热导系数和与相邻电缆间热导系数所构成的矩阵。3.2flux单位时间通过某一面积的热能。3.3电缆从线芯到外表面的整体导热系数。3.4将整体模型划分为有限个单元并开展微分方程计算。3.5指电缆敷设周围的土壤或者其他物体。4 符号代和略语下列号代和略适用本件。T：Tm：转移矩阵H：热流矩阵5 步骤5.1有限元建模(1)5.2 有限元计算5.3 计算转移矩阵Tm*T=H(2)5.4 矩阵参数估算5.5 转移矩阵迭代附 录 A（资料性录）A.1 计算对象计算对象为六回直埋电缆，排列方式见图A.1。图A.1 建模对象A.2 计算过程A.2.1 有限元建模所建模型如图A.1所示，本例中各电缆23.3W/m2*K。A.2.2 有限元计算取边界1为对流散热系数为rand（0,1）*15W/m2*K，温度为30+rand（0,1）*20摄氏度，边界2、3、4均设为温度30摄氏度。在保证工况正交化的条件下，重复若干次计算，即可获得，以下结果汇总，如附表A.1所示。附表A.1稳态计算结果汇总环温差（K）导热系数（W/m2*K）散热系数（W/m2*K）H1（W）H2（W）H3（W）H4（W）H5（W）H6（W）T1（W）T2（K）T3（K）T4（K）T5（K）T6（K）16.940.76.8630.4654.3542.248.5166.560.2628.7342.2335.946.9659.130.1416.940.76.8636.8225.1462.2345.754.575.532.6327.644.2546.7850.6732.4116.940.76.8627.268.8341.5877.6749.5911.8529.8218.1534.2663.4246.1935.2316.940.76.8660.6143.5437.4963.1365.669.2845.6637.3936.2458.9258.8136.9616.940.76.8659.5856.0246.384.9728.871.7338.8839.2335.9624.4537.425.5116.940.76.8635.5766.1724.9748.2160.8555.5333.0949.4433.0851.5361.2659.7616.940.76.867.5945.4830.114.681.7636.5512.4931.0925.820.522.2437.8816.940.76.8642.992.813.8549.6556.3131.3133.6314.2116.7148.8348.9641.2116.940.76.8658.7667.870.9449.0839.410.9241.0244.717.548.7644.193216.940.76.8620.8971.2124.5238.1155.3439.4723.6950.2730.0142.6656.6948.8413.460.96.1119.8626.1677.9945.5171.1737.6721.4425.7643.4139.9251.8743.0413.460.96.1175.8527.6962.719.2621.1614.6338.2820.4434.8624.2726.0926.9413.460.96.1145.052.3462.0130.8916.7431.1428.1810.5633.8132.6223.1733.3513.4848.161.0949.5320.2870.8911.1627.6314.0438.7929.1948.5413.460.96.1162.1974.8550.9330.9778.253.1534.9143.2734.3833.6355.7228.6613.460.96.1133.8736.7773.7965.9219.482.1926.524.2438.9646.7326.1425.2113.4930.7542.033.3876.1643.0712.0925.827.918.3452.5139.4913.460.96.1144.116.3515.0465.518.410.4427.548.7215.1844.9516.6322.7113.4524.6940.9771.5158.6714.1515.0921.472747.1342.7630.0513.460.96.1165.8260.1361.5930.5473.758.8836.8737.8138.2234.3653.331.19171.114.747.8634.52.296.1542.9451.3822.1119.8812.1620.5732.5334.76171.114.721.9637.7732.6113.855.7352.1915.119.6620.0822.2320.2934.51171.114.771.7751.218.1762.6453.5155.8134.3927.3921.0143.1838.9241.9171.114.714.9645.7738.0420.2625.575.3812.2722.3120.0222.0925.5920171.114.751.213.6660.2536.6322.0540.4526.610.7729.1832.2924.6933.88171.114.720.644.6465.7212.494.354.0614.148.6426.519.8316.1518.51171.114.720.9129.3254.2926.0231.1332.9415.9318.8726.6426.3628.5830.73171.114.711.5875.6441.6650.3810.6924.2313.893223.6933.7923.5828.3241.7272.7542.760.2237.2313.0821.8232.2531.9619.232.45239.1778.1240.520.8140.9511.5921.2933.8231.1819.5333.7264.0430.5440.856.8849.7268.927.6318.1623.4335.6431.3640.0218.5158.6467.5566.1935.3812.1314.5623.6826.5232.6124.5921.3235.24.2151.5412.4668.2153.716.3611.1222.5417.1934.0431.6255.8720.7851.855044.1367.4825.0615.2425.2732.6728.7338.624.637.7131.2973.6164.1212.0210.0618.4816.6733.3532.0520.6271.2568.8973.6756.8242.3815.8729.1827.7330.633.6928.7425.0236.5816.3468.7943.2149.844.8417.6212.5225.2524.9726.044.7219.3874.0519.7734.750.0225.9911.7227.3814.3221.3129.5122.5232.2229.739.4471.3932.0734.417.1614.2611.5434.5421.2825.0259.3647.3362.5912.2843.7140.0823.0821.5926.2918.192828.20.2833.9236.8571.0563.3314.2312.7920.3320.6343.4542.9533.670.1169.177557.2844.4519.7431.129.9732.8947.4342.640.642.9728.6612.865.9947.5166.3618.7118.1915.7224.1838.642.441.3576.7227.4366.9914.1430.0622.5527.3219.8545.4628.30.532.6976.8861.1213.6973.269.5120.6435.4531.5933.5158.7355.577.963.6154.0238.5277.6513.1930.8630.1828.1339.8153.3438.550.8663.248.755.8139.2515.319.2824.621.4319.6132.926.060.3636.4133.5851.8543.3550.2727.721.3423.145.1140.2645.866.973.5942.3434.41.840.0823.015.4816.1626.539.970.536.3238.2474.6470.726.5814.9322.4919.8429.4146.8630.6133.92A.2.3 计算转移矩阵以环温差=16.94K，导热系数=0.7W/m2*K，散热系数=6.86W/m2*K的工况为例说明转移矩阵的求取。H矩阵：H=30.4636.8227.2660.6159.5835.577.5942.9958.7620.8954.3525.148.8343.5456.0266.1745.482.8167.8771.2142.262.2341.5837.4946.3824.9730.113.850.9424.5248.5145.777.6763.134.9748.214.6849.6549.0838.1166.5654.5749.5965.6628.8760.851.7656.3139.455.340.265.511.859.281.7355.5336.5531.3110.9239.47T矩阵：T=42.2327.618.1537.3939.2349.4431.0914.2144.750.2742.2335.944.2534.2636.2435.9633.0825.816.7117.530.0135.946.9646.7863.4258.9224.4551.5320.548.8348.7642.6646.9659.150.6746.1958.8137.461.2622.2448.9644.1956.6959.130.1432.4135.2336.9625.5159.7637.8841.2132.048.8430.1416.9416.9416.9416.9416.9416.9416.9416.9416.9416.9416.94转移矩阵：Tm=2.060-0.007-0.200-0.338-0.007-0.095-0.120-0.0082.060-0.200-0.008-0.338-0.094-0.120-0.201-0.2012.120-0.095-0.094-0.280-0.070-0.338-0.008-0.0951.844-0.010-0.251-0.973-0.008-0.338-0.095-0.0101.844-0.251-0.972-0.094-0.095-0.280-0.251-0.2511.933-0.861A.2.4 矩阵参数估算根据转移矩阵的定义，将参数划分为三类：电缆自身影响因素，电缆间影响因素与外部散热条件影响因素。a.自身影响因素（以电缆1对自身为例）根据转移矩阵，整理数据可得：附表A.2自身影响参数汇总导热系数(W/m2*K)散热系数(W/m2*K)Tm110.76.862.04371.34.723.89根据传热学原理，提出：Tm11=k1*导热系数利用最小二乘法可得：k1=2.9353。附表A.3拟合结果汇总No计算值拟合值12.062.054548822.6462.641562833.2373.228576743.8173.815590754.394.4026047b.电缆间影响因素（以电缆1对电缆2为例）根据转移矩阵，整理数据可得：附表A.4相邻电缆影响参数汇总导热系数(W/m2*K)散热系数(W/m2*K)Tm120.76.86-0.0070.96.11-0.011.114.7-0.0121.34.72-0.0141.50.5-0.016根据传热学原理，提出：a12=k2*导热系数利用最小二乘法可得：k2=-0.0107。附表A.5拟合结果汇总No计算值拟合值1-0.007-0.0075212-0.01-0.009673-0.012-0.0118194-0.014-0.0139675-0.016-0.016116c.外部散热条件影响因素（以电缆1对外界为例）根据转移矩阵，整理数据可得：附表A.6外部条件影响参数汇总导热系数(W/m2*K)散热系数(W/m2*K)a100.76.86-0.1200.96.11-0.1421.114.7-0.1991.34.72-0.1641.50.5-0.039根据传热学原理，提出：a10=1/(k3/导热系数+k4/散热系数)利用最小二乘法可得：k3=-4.698，k4=-11.306。附表A.7拟合结果汇总No计算值拟合值1-0.12-0.1168262-0.142-0.1379753-0.199-0.1960034-0.164-0.1784735-0.039-0.036984综合以上过程，可得到转移矩阵各因素拟合公式为：a11=2.9353*导热系数；a22=2.9353*导热系数；a33=3.0262*导热系数；a44=2.6229*导热系数；a55=2.6232*导热系数；a66=2.7400*导热系数；a12=-0.0107*导热系数；a13=-0.2875*导热系数；a14=-0.5179*导热系数；a15=-0.0126*导热系数；a16=-0.1445*导热系数；a23=-0.2877*导热系数；a24=-0.0128*导热系数；a25=-0.5280*导热系数；a26=-0.1442*导热系数；a34=-0.1445*导热系数；a35=-0.1446*导热系数；a36=-0.4116*导热系数；a45=-0.0236*导热系数；a46=-0.3842*导热系数；a56=-0.3840*导热系数；a10=-1/（4.6769/导热系数+11.3660/散热系数）；a20=-1/（4.5935/导热系数+12.1736/散热系数）；a30=-1/（6.9629/导热系数+27.6160/散热系数）；a40=-1/（0.5522/导热系数+1.6590/散热系数）；a50=-1/（0.5521/导热系数+1.6582/散热系数）；a60=-1/（0.6005/导热系数+2.0779/散热系数）A.2.5 转移矩阵迭代当导热系数与散热系数变化时，利用估算公式获得新的矩阵参数。如当导热系数为1.0W/m2*K，对流散热系数为9.46W/m2*K时，根据A.2.4中总结的拟合公式，可得转移矩阵为：Tm1=2.935-0.011-0.287-0.518-0.012-0.144-0.170-0.0112.935-0.288-0.012-0.528-0.144-0.170-0.287-0.2883.026-0.144-0.144-0.412-0.101-0.518-0.012-0.1442.622-0.022-0.383-1.374-0.012-0.528-0.144-0.0222.623-0.384-1.375-0.144-0.144-0.412-0.383-0.3842.740-1.219有限元直接计算所得转移矩阵为：Tm2=2.942-0.011-0.287-0.484-0.011-0.135-0.169-0.0112.942-0.287-0.011-0.483-0.1