Study on Reliability Evaluation Model for the Reactor Protection System Shutdown Function Considering Self-diagnostics
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摘要: “在线自诊断”作为数字化仪控系统的重要特征，对核电厂反应堆保护系统（RPS）停堆功能的可靠性分析具有重要作用。通过分析自诊断对人因、定期试验等因素的影响，建立设备级误动模型；以典型RPS TX为例，通过马尔科夫方法建立动态的TX序列级和系统级模块误动模型；利用系统级模块误动模型定量计算TX停堆功能可靠度与自诊断的关系。通过定性分析与定量计算论证了综合考虑自诊断对RPS停堆功能可靠性分析的必要性，为后续国内RPS停堆功能的可靠性评价提供了借鉴。Abstract: As an important feature of digital instrument control system, online self-diagnostics plays an important role in the reliability analysis of shutdown function of reactor protection system (RPS) in nuclear power plant. By analyzing the influence of self-diagnostics on human factors and periodic testing, the component-level spurious actuation model was established. Taking a typical RPS TX as an example, the dynamic TX sequence-level and system-level module spurious actuation models are established by Markov method. The relationship between TX shutdown function reliability and self-diagnostics is quantitatively calculated by using the system-level module spurious actuation model. Through qualitative analysis and quantitative calculation, the necessity of comprehensive consideration of self-diagnostics in RPS shutdown function reliability analysis is demonstrated, which provides a reference for the subsequent reliability evaluation of RPS shutdown function in China.
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图 2 序列级Level1模块误动故障可靠性框图
Figure 2. Sequence Level 1 Module Spurious Actuation Fault Reliability Block Diagram
图 3 序列级Level1模块误动故障Markov状态转移图
Δt—单位时间，1 h；O—模块的正常工作状态；E—模块失效的状态（吸收态），任一卡件失效则序列级Level1模块失效进入吸收态EL1；下标L1—序列级Level1模块
Figure 3. Sequence Level 1 Module Spurious Actuation Fault Markov State Transition Diagram
图 4 序列级Level2模块误动故障可靠性框图
Figure 4. Sequence Level 2 Module Spurious Actuation Fault Reliability Block Diagram
图 5 序列级Level2模块误动故障Markov状态转移图
KL2,1—4条RT和DO串联通路的其中任一条发生误动；KL2,2—属于同个CL的2个RT和DO串联通路均失效；EL2—单序列Level2模块3条RT和DO串联通路出现故障状态，为吸收态；下标m—RT和DO的串联通路；下标L2—序列级Level2模块
Figure 5. Sequence Level 2 Module Spurious Actuation Fault Markov State Transition Diagram
图 6 序列级Level3模块误动故障马尔科夫状态转移图
EL3—单序列Level3模块2个RTCB均发生误动，单序列Level3模块触发，为吸收态；KL3,1—1个RTCB发生误动；下标L3—序列级Level3模块
Figure 6. Sequence Level 3 Module Spurious Actuation Fault Markov State Transition Diagram
图 7 不考虑ASD的系统级Level模块误动故障马尔科夫状态转移图
KS1,1—2oo4逻辑TX的一个序列发生故障；下标S1—不考虑自诊断的系统级Level模块；下标L—序列级各Level模块
Figure 7. System-level Module Spurious Actuation Fault Markov State Transition Diagram without Considering ASD
图 8 考虑ASD的系统级Level模块误动故障马尔科夫状态转移图
KS2,1—仅ASD发生故障；KS2,2—在ASD故障的情况下TX的一个序列发生故障，此时TX未切换逻辑；KS2,3—2oo4表决逻辑TX的一个序列发生故障，此时ASD正常，自动切换成2oo3表决逻辑；KS2,4—2oo3表决逻辑TX的ASD发生故障；KS2,5—ASD故障条件下2oo3表决逻辑TX的一个序列发生故障；KS2,6—2oo3表决逻辑TX的一个序列发生故障，TX切换成1oo2表决逻辑；ES2,1—2oo4表决逻辑TX的2个序列发生故障，触发停堆；ES2,2—1oo2表决逻辑TX出现序列故障，触发停堆；ES2,3—2oo3表决逻辑TX的2个序列发生故障，触发停堆；$ {\mu }_{\mathrm{d}} $—ASD设备的修复率，考虑其平均修复率为0.2；下标S2—考虑自诊断的系统级Level模块
Figure 8. System-level Spurious Actuation Fault Markov State Transition Diagram Considering ASD
图 9 一个换料循环TX停堆功能可靠度变化
Figure 9. TX Shutdown Function Reliability Changes in a Refueling Cycle
表 1 RPS停堆子系统设备初始数据和计算结果
Table 1. Initial Data and Calculated Results of RPS Shutdown Subsystem Equipment
设备名称 λr/h−1 N Pd λS/h−1 λw/h−1 PI 1.20×10−5 6 0.9 1.200010×10−5 1.22×10−5 DI 1.25×10−6 6 0.9 1.250100×10−6 1.40×10−0 AI 1 3.66×10−5 6 0.9 3.660011×10−5 3.68×10−5 AI 2 3.58×10−6 6 0.9 3.580100×10−6 3.73×10−6 PM1(2) 1.31×10−5 6 0.99 1.310010×10−5 1.32×10−5 RT 1.31×10−5 2 0.99 1.310010×10−5 1.32×10−5 DO 1.39×10−6 2 0.9 1.390100×10−6 1.54×10−6 RTCB 1.00×10−6 2 0 1.000100×10−6 1.15×10−6 
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表 2 2种情况下序列级各Level模块故障率
Table 2. Failure Rate of Each Sequence-level Module under Two Conditions
故障率 考虑自诊断 不考虑自诊断 $ {\lambda }_{\mathrm{L}1} $/h−1 2.39526×10−4 2.41996×10−4 $ {\lambda }_{\mathrm{L}2} $/h−1 4.30211×10−9 8.72537×10−9 $ {\lambda }_{\mathrm{L}3} $/h−1 1.00019×10−11 1.33279×10−11
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表 3 TX单序列/停堆功能故障率与
$ {\lambda }_{\mathrm{d}} $ 和γ的关系Table 3. Relationship between the Failure Rate of TX Single Sequence/Shutdown Function and the
$ {\lambda }_{d} $ and γ条件 $ {(\lambda }_{\mathrm{L}1} $+$ {\lambda }_{\mathrm{L}2} $+$ {\lambda }_{\mathrm{L}3}) $/h−1 TX停堆功能故障率/h−1 不考虑自诊断, γ=0.002 2.420043×10−4 3.40549×10−6 不考虑自诊断, γ=0 2.395324×10−4 3.33801×10−6 $ {\lambda }_{\mathrm{d}} $=1×10−10 h−1, γ=0 2.395299×10−4 2.22161×10−9 $ {\lambda }_{\mathrm{d}} $=1×10−10 h−1, γ=0.002 2.395299×10−4 2.22162×10−9 $ {\lambda }_{\mathrm{d}} $=1×10−8 h−1, γ=0.002 2.396885×10−4 2.22608×10−9 $ {\lambda }_{\mathrm{d}} $=1×10−6 h−1, γ=0.002 2.555432×10−4 2.70362×10−9 $ {\lambda }_{\mathrm{d}} $=1×10−5 h−1, γ=0.002 3.996783×10−4 1.04573×10−8 $ {\lambda }_{\mathrm{d}} $=1×10−4 h−1, γ=0.002 1.841119×10−3 1.01053×10−6
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