Reliability analysis of ultra-large-scale LTD power source
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摘要: 超大规模直线型变压器驱动源作为Z箍缩装置中最为关键且复杂的系统，可靠性评估是装置设计方案论证的核心问题。基于功率源的基本组成器件（开关、电容器等），建立了开关自击穿与电容器失效的概率模型；采用自上而下的层级分析方法，依次构建基本放电支路层、LTD模块层及LTD支路层的可靠性模型，提出故障域边界计算方法。基于性能裕量的可靠性理论，利用蒙特卡洛仿真实现了系统级可靠性量化评估。研究结果表明：当LTD模块层与支路层允许的故障个数均大于1时，忽略LTD开关纳秒时间内同时故障（极小概率）和多个相邻LTD模块同时故障的特殊情况，系统可靠度不超过IVA次级和故障隔离开关的可靠度乘积；单次开关意外放电产生的耦合电压会使得本模块的其他开关的故障概率几乎翻倍，对其他模块开关可靠度的影响为10−4量级，对电容器的影响为10−6量级，只有当LTD模块层与支路层允许的故障个数大于1时，该耦合效应在计算系统可靠度时才可忽略；随着器件可靠度的提升，开关在可靠度低于
0.9996 时进行提升对系统的可靠度影响显著，电容器的可靠度也只有在开关可靠度较低时进行提升才对系统的影响比较明显。Abstract:Background Linear Transformer Driver (LTD) are among the most critical and complex systems in Z-pinch device, and reliability assessment is a central issue in the demonstration of device design schemes.Purpose This study aims to establish a probabilistic model for switch self-breakdown and capacitor failure based on the basic components of the power source, and to propose a hierarchical analysis method for system-level reliability quantification.Methods Probability models for switch self-breakdown and capacitor failure were developed based on fundamental components such as switches and capacitors. A top-down hierarchical analysis approach was adopted to construct reliability models for the brick layer, LTD cavity layer, and LTD branch layer, along with a fault-domain boundary calculation method. System-level reliability was quantified using Monte Carlo simulations based on performance-margin reliability theory.Results The results indicate that when the allowable number of faults in both the LTD cavity layer and the branch layer is greater than one—and neglecting special cases such as simultaneous nanosecond-scale switch failures (extremely low probability) and multiple adjacent cavity failures—the system reliability does not exceed the product of the reliability of the IVA secondary and the fault-isolation switch. A single unintended switch discharge coupling voltage nearly doubles the failure probability of other switches within the same cavity, while its impact on switches in other cavities is on the order of 10−4 and on capacitors about 10−6. This coupling effect can be ignored in system reliability calculations only when the allowable number of faults in both the cavity and branch layers exceeds one. As component reliability improves, enhancing switch reliability below0.9996 significantly affects system reliability, whereas improving capacitor reliability only noticeably influences the system when switch reliability is relatively low.Conclusions The proposed hierarchical reliability modeling and Monte Carlo simulation approach provides a systematic framework for evaluating ultra-large-scale LTD systems in Z-pinch devices. The findings highlight the conditional negligible effects of coupling voltages and offer guidance for prioritizing component reliability improvements in engineering design. -
图 1 50 MA装置概念设计中的LTD功率源
Figure 1. LTD power source in conceptual design of 50 MA device
图 7 低气压下的开关自击穿实验概率分布Q-Q图
Figure 7. Probability distribution Q-Q diagram of switch self breakdown experiment under low pressure
图 8 一只开关自击穿对在本模块内产生的耦合电压
Figure 8. Coupling voltage generated in this cavity by self-breakdown of a switch
图 9 耦合电压对LTD模块和LTD支路的影响
Figure 9. Influence of coupling voltage on LTD cavity and LTD branch
图 10 不同位置的LTD模块中开关故障对其余模块的影响
Figure 10. The effect of switch failure in LTD cavities at different positions on the rest of the cavities
图 11 耦合电压叠加造成的故障概率变化
Figure 11. Changes in fault probability caused by coupling voltage superposition
图 12 求解得到的故障域边界值最小值组合
Figure 12. Combination of minimum values of boundary values in fault domain
图 13 器件可靠度提升对功率源可靠度影响
Figure 13. Effect of device reliability improvement on power source reliability
表 1 同一模块内开关故障产生耦合电压对可靠度的影响
Table 1. Influence of coupling voltage generated by switch fault in the same cavity on reliability
Number of faulty switches coupling voltage (kV) switch reliability capacitor reliability brick reliability 0 0 0.99953 0.99991 0.99935 1 4.7 0.99880 0.99990 0.99860 2 9.4 0.99712 0.99989 0.99690 
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表 2 功率源系统可靠度的95%置信区间
Table 2. 95% confidence interval of power source system reliability
Reliability m 0 1 2 3 z=0 0±0 0±0 0.00451 ±0.000212 0.30068 ±0.001450 z=1 0.48282 ±0.001580 0.91407 ±0.000886 0.91677 ±0.000874 0.91784 ±0.000868 z=2 0.91434 ±0.000885 0.91828 ±0.000866 0.9165 ±0.000875 0.91796 ±0.000868 z=3 0.91681 ±0.000873 0.91772 ±0.000869 0.91596 ±0.000877 0.91705 ±0.000872
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