Modeling Magnetic Fields from a DC Power Cable Buried Beneath San Francisco Bay Based on Empirical Measurements

The Trans Bay Cable (TBC) is a ±200-kilovolt (kV), 400 MW 85-km long High Voltage Direct Current (DC) buried transmission line linking Pittsburg, CA with San Francisco, CA (SF) beneath the San Francisco Estuary. The TBC runs parallel to the migratory route of various marine species, including green sturgeon, Chinook salmon, and steelhead trout. In July and August 2014, an extensive series of magnetic field measurements were taken using a pair of submerged Geometrics magnetometers towed behind a survey vessel in four locations in the San Francisco estuary along profiles that cross the cable’s path; these included the San Francisco-Oakland Bay Bridge (BB), the Richmond-San Rafael Bridge (RSR), the Benicia-Martinez Bridge (Ben) and an area in San Pablo Bay (SP) in which a bridge is not present. In this paper, we apply basic formulas that ideally describe the magnetic field from a DC cable summed vectorially with the background geomagnetic field (in the absence of other sources that would perturb the ambient field) to derive characteristics of the cable that are otherwise not immediately observable. Magnetic field profiles from measurements taken along 170 survey lines were inspected visually for evidence of a distinct pattern representing the presence of the cable. Many profiles were dominated by field distortions unrelated to the cable caused by bridge structures or other submerged objects, and the cable’s contribution to the field was not detectable. BB, with 40 of the survey lines, did not yield usable data for these reasons. The unrelated anomalies could be up to 100 times greater than those from the cable. In total, discernible magnetic field profiles measured from 76 survey lines were regressed against the equations, representing eight days of measurement. The modeled field anomalies due to the cable (the difference between the maximum and minimum field along the survey line at the cable crossing) were virtually identical to the measured values. The modeling yielded a pooled cable depth below the bay floor of 2.06 m (±1.46 std dev), and estimated the angle to the horizontal of the imaginary line connecting the cross-sectional center of the cable’s two conductors (0.1143 m apart) as 178.9° ±61.9° (std dev) for Ben, 78.6°±37.0° (std dev) for RSR, and 139.9°±27.4° (std dev) for SP. The mean of the eight daily average currents derived from the regressions was 986 ±185 amperes (A) (std dev), as compared to 722 ±95 A (std dev) provided by Trans Bay Cable LLC. Overall, the regressions based on fundamental principles (Biot Savart law) and the vectorial summation of cable and geomagnetic fields provide estimates of cable characteristics consistent with plausible expectations.

跨海湾电缆（Trans Bay Cable, TBC）是一条±200千伏（kV）、额定容量400兆瓦（MW）、全长85公里的高压直流（High Voltage Direct Current, DC）埋地输电线路，穿越旧金山湾，连接加利福尼亚州匹兹堡与旧金山（SF）。该电缆走线与多种海洋物种的洄游路线平行，包括绿鲟、奇努克鲑以及硬头鳟。

2014年7月至8月期间，研究人员在旧金山湾内四个横跨电缆走线的测区，使用安装于测量船后方的水下拖曳式Geometrics磁力计（两台），开展了大范围磁场测量。这四个测区分别为：旧金山-奥克兰海湾大桥（San Francisco-Oakland Bay Bridge, BB）区域、里士满-圣拉斐尔大桥（Richmond-San Rafael Bridge, RSR）区域、贝尼西亚-马丁内斯大桥（Benicia-Martinez Bridge, Ben）区域，以及圣巴勃罗湾（San Pablo Bay, SP）一处无桥梁覆盖的区域，测量航线沿横跨电缆路径的剖面布设，共计170条。

本文采用理想状态下的基础公式，将高压直流电缆产生的磁场与背景地磁场进行矢量叠加（假设无其他扰动源干扰环境磁场），以此推导无法直接观测的电缆特性参数。研究人员对沿170条测量航线获取的磁场剖面进行目视检查，以寻找表征电缆存在的独特信号模式。但多数剖面的磁场畸变主要由桥梁结构或其他水下物体引起，与电缆无关，因此无法识别出电缆产生的磁场信号。其中，旧金山-奥克兰海湾大桥区域的40条测量航线因上述原因未获得有效数据。这类无关磁异常的强度最高可达电缆产生磁异常的100倍。

最终，研究人员对76条测量航线获取的可识别磁场剖面进行了方程拟合，数据覆盖8天的测量工作。基于电缆产生的磁场异常（即测线穿越电缆处的磁场最大值与最小值之差）构建的模型结果，与实测值几乎完全一致。

本次建模整合所有测区数据后，得到电缆相对于湾底的整体埋深为2.06米（±1.46倍标准偏差）；同时估算出连接电缆两根导体（间距0.1143米）横截面中心的假想直线与水平线的夹角：贝尼西亚-马丁内斯大桥区域为178.9°±61.9°（标准偏差），里士满-圣拉斐尔大桥区域为78.6°±37.0°（标准偏差），圣巴勃罗湾区域为139.9°±27.4°（标准偏差）。

通过拟合得到的8次日平均电流均值为986±185安培（A，标准偏差），而跨海湾电缆有限责任公司（Trans Bay Cable LLC）提供的官方实测电流均值为722±95安培（标准偏差）。

总体而言，基于基础物理定律（毕奥-萨伐尔定律）以及电缆磁场与地磁场的矢量叠加开展的拟合分析，所得到的电缆特性参数估算结果符合合理预期。