Reliability prediction and its validation for nuclear power units in service

Abstract

In this paper a novel method for reliability prediction and validation of nuclear power units in service is proposed. The equivalent availability factor is used to measure the reliability, and the equivalent availability factor deducting planed outage hours from period hours and maintenance factor are used for the measurement of inherent reliability. By statistical analysis of historical reliability data, the statistical maintenance factor and the undetermined parameter in its numerical model can be determined. The numerical model based on the maintenance factor predicts the equivalent availability factor deducting planed outage hours from period hours, and the planed outage factor can be obtained by using the planned maintenance days. Using these factors, the equivalent availability factor of nuclear power units in the following 3 years can be obtained. Besides, the equivalent availability factor can be predicted by using the historical statistics of planed outage factor and the predicted equivalent availability factor deducting planed outage hours from period hours. The accuracy of the reliability prediction can be evaluated according to the comparison between the predicted and statistical equivalent availability factors. Furthermore, the reliability prediction method is validated using the nuclear power units in North American Electric Reliability Council (NERC) and China. It is found that the relative errors of the predicted equivalent availability factors for nuclear power units of NERC and China are in the range of –2.16% to 5.23% and –2.15% to 3.71%, respectively. The method proposed can effectively predict the reliability index in the following 3 years, thus providing effective reliability management and maintenance optimization methods for nuclear power units.

Keywords

nuclear power units in service / reliability / reliability prediction / equivalent availability factors

Introduction

Generally, the reliability prediction of generators is conducted according to the statistical analysis of historical operation data, such as the USA standard of ANSI/IEEEStd762 [ 1] and the Chinese Standard of Reliability Evaluation Procedure for Power Generation Equipment (DL/T793) [ 2]. In these standards the reliability statistics are obtained by analyzing the historical operation data in the past one or several years. Besides, in the Generating Unit Statistical Brochure used by North American Electric Reliability Council (NERC) and the China Electric Reliability Management Annual Report offered by the China Electric Reliability Management Center, reliability predictions are both conducted with the historical operation data used. The reliability prediction method for nuclear power units used today focuses on dealing with the operation data. However, this method does not pay much attention to the outage scheduler in the future. Moreover, it cannot obtain the equivalent availability factor in the next few years. Therefore, a new reliability prediction method for the next few years is of great importance to nuclear power units in service. It can play an important role in reliable management, and safe and economic operation of nuclear power units.

Reliability index of nuclear power units

Calculations of equivalent availability factor and planed outage factor

The equivalent availability factor E_AF and planed outage factor P_OF are the main reliability index for nuclear power units [ 1, 2], which are defined as

(1) E_{\mathrm{AF}}={\displaystyle \frac{t_{\mathrm{AH}}-t_{\mathrm{EUNDH}}}{t_{\mathrm{PH}}}}\times \mathrm{100}\%={\displaystyle \frac{t_{\mathrm{AH}}-t_{\mathrm{EUNDH}}}{t_{\mathrm{AH}}+t_{\mathrm{UH}}}}\times \mathrm{100}\%={\displaystyle \frac{t_{\mathrm{AH}}-t_{\mathrm{EUNDH}}}{t_{\mathrm{AH}}+t_{\mathrm{UOH}}+t_{\mathrm{POH}}}}\times \mathrm{100}\%,

(2) P_{\mathrm{OF}}={\displaystyle \frac{t_{\mathrm{POH}}}{t_{\mathrm{PH}}}}\times \mathrm{100}\%,

where t_AH is the available hours, which is the sum of service hours and reserve shutdown hours. t_EUNDH is the equivalent unit derated hours, t_POH is the planed outage hours, t_UOH is the un-planed outage hours, t_PH is the period hours which can be expressed as t_PH = t_AH + t_UH = t_AH + t_UOH + t_POH, and t_UH is the unavailable hours which is the sum of t_UOH and t_POH.

The unavailable hours of nuclear power units consist of the planed outage hours and un-planed outage hours. t_UOH is a measure of the impact of unplanned outage event caused by equipment failure on the reliability of nuclear power units, and t_POH measures the impact of maintainability on the unit operation. A larger t_UOH corresponds to a lower reliability, and a larger t_POH corresponds to a worse maintainability. Besides, for the nuclear power units in service, a larger E_AF indicates a higher reliability. Traditionally, Eq. (1) is for calculating the equivalent availability factor E_AF, and the planed outage hours t_POH is considered in the denominator. For a single nuclear power unit, in the year with A class repair, the values of t_POH and P_OF are relatively higher, and that of E_AF is relatively lower. The value of t_POH has a notable effect on E_AF.

Calculation of equivalent availability factor deducting planed outage hours from period hours

To eliminate the effect of planed outage, an equivalent availability factor deducting planed outage hours from period hours E_AP is proposed. E_AP can be used as the reliability evaluation index for nuclear power units in service, which can be expressed as

(3) E_{\mathrm{AP}}={\displaystyle \frac{t_{\mathrm{AH}}-t_{\mathrm{EUNDH}}}{t_{\mathrm{PH}}-t_{\mathrm{POH}}}}\times \mathrm{100}\%={\displaystyle \frac{t_{\mathrm{AH}}-t_{\mathrm{EUNDH}}}{t_{\mathrm{AH}}+t_{\mathrm{UOH}}}}\times \mathrm{100}\%={\displaystyle \frac{E_{\mathrm{AF}}}{\mathrm{1}-P_{\mathrm{OF}}}}\times \mathrm{100}\%.

The difference between Eq. (1) and Eq. (3) is the deduction of planed outage hours t_POH in the denominator. E_AP can effectively indicate the effect of unplanned outage event caused by the equipment failure on the reliability of nuclear power units, which is the inherent reliability evaluation index. In practical applications, the inherent reliability of nuclear power units in service varies in a certain extent. The planed outage hours are arranged by 3 years in advance. As a result, the planed outage factor P_OF can be determined in advance. By determining the variation of inherent reliability E_AP, the variation of E_AF can be obtained. According to Eq. (3), E_AF can be expressed as

(4) E_{\mathrm{AF}}=(\mathrm{1}-P_{\mathrm{OF}})\times E_{\mathrm{AP}}.

Calculation of maintenance factor

In the study by Shi et al. [ 3], a maintenance factor r was proposed to express the variation of equivalent availability factor deducting planed outage hours from period hours E_AP, which is defined as

(5) \rho ={\displaystyle \frac{t_{\mathrm{UOH}}+t_{\mathrm{EUNDH}}}{t_{\mathrm{AH}}-t_{\mathrm{EUNDH}}}}.

The relationship between maintenance factor r and E_AP can be expressed as

(6) \rho ={\displaystyle \frac{\mathrm{1}-E_{\mathrm{AP}}}{E_{\mathrm{AP}}}},

(7) E_{\mathrm{AP}}={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+\rho }}.

Substituting Eq. (3) into Eq. (6), there is

(8) \rho ={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}-E_{\mathrm{AF}}}{E_{\mathrm{AF}}}}.

For a nuclear power unit in service, the values of E_AF, E_AP and P_OF are different in different years, and the maintenance factor r varies with the year t_i. The value of r(t_i) can be expressed as

(9) \rho （t_i）={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}（t_i）-E_{\mathrm{AF}}（t_i）}{E_{\mathrm{AF}}（t_i）}},

where E_AF(t_i) is the statistical equivalent availability factor in the year t_i, and P_OF(t_i) is the statistical planed outage factor in the year t_i.

Numerical model of reliability

Numerical model of maintenance factor

In the study by Shi [ 4], a reliability growth model was proposed, and it is reported that the maintenance factor can be expressed as a power function. Power function, polynomials, exponential function and Weibull distribution are all used for the curve fitting of statistical reliability data. However, it is found that the curve fitting with the power function used shows the best agreement with the maintenance factor. The function of r(t) can be expressed as

(10) \rho (t)={\eta }_i{t}^{-m_i},

where t is the operating years of nuclear power units in service, h_i is the scale parameter, and m_i is the growth factor.

Numerical model of equivalent availability factor deducting planed outage hours from period hours

Substituting Eq. (10) into Eq. (7), the equivalent availability factor deducting planed outage hours from period hours can be obtained.

(11) E_{\mathrm{AP}}(t)={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{\eta }_i{t}^{-m_i}}}.

Numerical model of equivalent availability factor

After obtaining the numerical models of equivalent availability factor deducting planed outage hours from period hours E_AP(t) and planed outage factor P_OF(t), Eq. (11) can be substituted into Eq. (4) to get the equivalent availability factor E_AF(t)

(12) E_{\mathrm{AF}}(t)={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}(t)}{\mathrm{1}+{\eta }_i{t}^{-m_i}}}.

Reliability prediction method for nuclear power units

The first step for reliability prediction of the nuclear power units is to analyze the multiple power units and the single power unit history data of nuclear power units to present the inherent-reliability change of nuclear power units. The next step is to determine the parameters m and h, so as to predict the equivalent availability factor deducted planed outage hours from period hours E_AP of nuclear power units. The third step is to predict the equivalent availability factor E_AF of power units based on the arrangement of planed repair days in advance.

Statistical analysis of operation data

For the nuclear power units in service, the maintenance factor r(t_i) can be calculated according to Eq. (9) with the statistical value of E_AF(t_i) and P_OF(t_i), which can be obtained using the historical reliability data in the past n years (n≥3). The scale parameter h_i and the growth factor m_i in Eq. (10) can be obtained using the least squares method [ 4, 5].

Equivalent availability factor deducting planed outage hours from period hours E_AP

The numerical model of E_AP can be obtained with the historical reliability data in the past n years. Given t = n + 1, n + 2 and n + 3, the value of E_AP in the very year (t = n + 1), the next year (t = n + 2) or two (t = n + 3) can be expressed as

(13) E_{\mathrm{AP}}(n+\mathrm{1})={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{\eta }_i{(n+\mathrm{1})}^{-m_i}}},

(14) E_{\mathrm{AP}}(n+\mathrm{2})={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{\eta }_i{(n+\mathrm{2})}^{-m_i}}},

(15) E_{\mathrm{AP}}(n+\mathrm{3})={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{\eta }_i{(n+\mathrm{3})}^{-m_i}}}.

Prediction of planed outage factor P_OF

The maintenance plan of the nuclear power units in service is conducted according to the standard of DL/T8384 (Guide of Maintenance for Power Plant Equipment) [ 6]. The planned maintenance days M₁ in the very year can be determined at the beginning of the year, and the planned maintenance days in the following one and two years can also be obtained. According to Eq. (2), the planed outage factor P_OF in the very year and the next one and two years can be written as

(16) P_{\mathrm{OF}}(n+\mathrm{1})={\displaystyle \frac{\mathrm{24}\times M_{\mathrm{1}}}{\mathrm{8760}}},

(17) P_{\mathrm{OF}}(n+\mathrm{2})={\displaystyle \frac{\mathrm{24}\times M_{\mathrm{2}}}{\mathrm{8760}}},

(18) P_{\mathrm{OF}}(n+\mathrm{3})={\displaystyle \frac{\mathrm{24}\times M_{\mathrm{3}}}{\mathrm{8760}}}.

Prediction of equivalent availability factor E_AF

After obtaining the equivalent availability factor deducting planed outage hours from period hours E_AP and the planed outage factor P_OF, the equivalent availability factor E_AF in the next few years can be obtained using Eq. (4).

(19) E_{\mathrm{AF}}(t)=[\mathrm{1}-P_{\mathrm{OF}}(t)]\times E_{\mathrm{AP}}(t).

Based on the value of E_AP(n + l), E_AP(n + 2), and E_AP(n + 3) and P_OF(n + 1), P_OF(n + 2), and P_OF(n + 3), the equivalent availability factor E_AF in the next few years can be obtained by using

(20) E_{\mathrm{AF}}(n+\mathrm{1})=[\mathrm{1}-P_{\mathrm{OF}}(n+\mathrm{1})]\times E_{\mathrm{AP}}(n+\mathrm{1})=\left(\mathrm{1}-{\displaystyle \frac{\mathrm{24}\times M_{\mathrm{1}}}{\mathrm{8760}}}\right)\times {\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{\eta }_i{(n+\mathrm{1})}^{m_i}}},

(21) E_{\mathrm{AF}}(n+\mathrm{2})=[\mathrm{1}-P_{\mathrm{OF}}(n+\mathrm{2})]\times E_{\mathrm{AP}}(n+\mathrm{2})=\left(\mathrm{1}-{\displaystyle \frac{\mathrm{24}\times M_{\mathrm{2}}}{\mathrm{8760}}}\right)\times {\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{\eta }_i{(n+2)}^{m_i}}},

(22) E_{\mathrm{AF}}(n+\mathrm{3})=[\mathrm{1}-P_{\mathrm{OF}}(n+\mathrm{3})]\times E_{\mathrm{AP}}(n+\mathrm{3})=\left(\mathrm{1}-{\displaystyle \frac{\mathrm{24}\times M_{\mathrm{3}}}{\mathrm{8760}}}\right)\times {\displaystyle \frac{\mathrm{1}}{\mathrm{1}+{\eta }_i{(n+3)}^{m_i}}}.

Reliability prediction method for nuclear power units

Validation method for the predicted value

By statistically analyzing the historical reliability data of the nuclear power units in service, the statistical value of equivalent availability factor E_AF(t_i) and planed outage factor P_OF(t_i) in a certain year can be obtained. There are certain differences between the statistical planed outage factor of the nuclear power units in service and the predicted value using Eqs. (16) to (18). As a result, the validation for the reliability prediction cannot be conducted based on the comparison between the E_AF(t) obtained from Eqs. (20) to (22) and the statistical value of E_AP(t_i). However, during the operation of nuclear power units, the prediction of equivalent availability factor E_AFi (t) can be conducted with the predicted value of E_AP(t) obtained from Eqs. (13) to (15) and the statistical value of P_OF(t_i) used. Under the condition of using the same planed outage factor P_OF(t_i), the validation for the reliability prediction of nuclear power units in service can be realized based on the comparison between the predicted value of E_AFi (t) and the statistical value of E_AF(t_i).

Prediction of the equivalent availability factor

According to Eq. (4), the predicted value of equivalent availability factor E_AFi(t) in a certain year can be written as

(23) E_{\mathrm{AF}i}(t)=[\mathrm{1}-P_{\mathrm{OF}}(t_i)]\times E_{\mathrm{AP}}(t),

where E_AP(t) is the predicted value of equivalent availability factor deducting planed outage hours from period hours using Eqs. (13) to (15), and P_OF(t_i) is the practical statistical value of planed outage factor for nuclear power units.

The statistical value of planed outage factor in the year t_i is P_OF(t_i). The predicted value of equivalent availability factor E_AFi(n + 1) in the year t_i using the scale parameter h_i and the growth factor m_i in the year t_i–1 can be expressed as

(24) E_{\mathrm{AF}i}(n+\mathrm{1})=[\mathrm{1}-P_{\mathrm{OF}}(t_i)]\times E_{\mathrm{AP}}(n+\mathrm{1})={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}(t_i)}{\mathrm{1}+{\eta }_i{(n+\mathrm{1})}^{-m_i}}}.

The predicted value of equivalent availability factor E_AFi(n + 2) in the year t_i using the scale parameter h_i and the growth factor m_i in the year t_i‒2 can be expressed as

(25) E_{\mathrm{AF}i}(n+\mathrm{2})=[\mathrm{1}-P_{\mathrm{OF}}(t_i)]\times E_{\mathrm{AP}}(n+\mathrm{2})={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}(t_i)}{\mathrm{1}+{\eta }_i{(n+\mathrm{2})}^{-m_i}}}.

The predicted value of equivalent availability factor E_AFi(n + 3) in the year t_i using the scale parameter h_i and the growth factor m_i in the year t_i‒3 can be expressed as

(26) E_{\mathrm{AF}i}(n+\mathrm{3})=[\mathrm{1}-P_{\mathrm{OF}}(t_i)]\times E_{\mathrm{AP}}(n+\mathrm{3})={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}(t_i)}{\mathrm{1}+{\eta }_i{(n+\mathrm{3})}^{-m_i}}}.

Relative error of the reliability prediction

The absolute errors of the predicted and statistical equivalent availability factor D₁ and D₂ can be written as

(27) {\Delta }_{\mathrm{1}}=\max \left\{\begin{array}{l}[E_{\mathrm{AF}}(n+\mathrm{1})-E_{\mathrm{AF}}(t_j)],\\ [E_{\mathrm{AF}}(n+\mathrm{2})-E_{\mathrm{AF}}(t_j)],\\ [E_{\mathrm{AF}}(n+\mathrm{3})-E_{\mathrm{AF}}(t_j)]\end{array}\right\},

(28) {\Delta }_{\mathrm{2}}=\min \left\{\begin{array}{l}[E_{\mathrm{AF}}(n+\mathrm{1})-E_{\mathrm{AF}}(t_j)],\\ [E_{\mathrm{AF}}(n+\mathrm{2})-E_{\mathrm{AF}}(t_j)],\\ [E_{\mathrm{AF}}(n+\mathrm{3})-E_{\mathrm{AF}}(t_j)]\end{array}\right\}.

At {\Delta }_{\mathrm{1}}>\mathrm{0} and \left|{\Delta }_{\mathrm{1}}\right|\ge \left|{\Delta }_{\mathrm{2}}\right| , the relative error E_r can be expressed as

(29) E_r={\displaystyle \frac{{\Delta }_{\mathrm{1}}}{E_{\mathrm{AF}}(t_i)}}\times \mathrm{100}\%.

At and , the relative error E_r can be expressed as

(30) E_r={\displaystyle \frac{{\Delta }_{\mathrm{2}}}{E_{\mathrm{AF}}(t_i)}}\times \mathrm{100}\%.

Maintenance optimization

In the reliability prediction of nuclear power units, the planned maintenance days are suggested to be the ceiling value in the standard DL/T838 (Guide of Maintenance for Power Plant Equipment). If the predicted value of equivalent availability factor is not up to the required target value, the lower limit of planned maintenance days should be gradually reduced according to the rules of DL/T838. Reliability prediction can be conducted using the method introduced in this paper until the predicted equivalent availability factor of the nuclear power unit meets the required reliability target value.

For example, for a 1000 MW nuclear power unit, it takes 70 to 80 days to conduct A class repair in the rules of DL/T838, while it takes 35 to 50 days, 26 to 30 days and 9 to 15 days, respectively to perform B, C, and D class repair. The planned maintenance days can be optimized by using the reliability prediction method proposed in this paper. In this way, the reliability management can be realized and the reliability index of the nuclear power units will be under control.

If the planned maintenance days of a nuclear power unit are in the range of the rules of DL/T838 introduced above, the un-planed outage hours t_UOH will not increase with the decreasing planned maintenance days. The original maintenance plan needs to be changed, and a more efficient maintenance schedule can be obtained.

Reliability prediction and validation examples of multiple nuclear power units

For application examples of multiple nuclear power units, reliability prediction error could be validated based on the reliability history data from NERC.

Statistical reliability data of NERC nuclear power units

The statistical data of E_AF(t_i) and P_OF(t_i) for nuclear power units in 2004 and 2013 are listed in Table 1, which is provided by the North American Electric Reliability Council (NERC) [ 7]. In 2004 totally 103 units were statistically analyzed, including 62 pressurized water reactor (PWR) units and 30 boiling water reactor (BWR) units. In 2013 totally 104 units were statistically analyzed, including 65 PWR units and 33 BWR units.

Reliability prediction and validation examples of multiple nuclear power units

The statistical data of equivalent availability factor E_AF(t_i) and planed outage factor P_OF(t_i) in 2004 and 2013 provided by NERC are tabulated in Tables 1 and 2. Given that t_i = 1 in 2004 and t_i = 10 in 2013, the growth factor m_i and scale parameter h_i (Table 2) can be obtained by using the statistical reliability data in the past n years. Besides, the predicted E_AF(n + 1), E_AF(n + 2) and E_AF(n + 3) and the relative error E_r for the very year (t = n + 1) and the following years are also presented in Table 2.

The predicted equivalent availability factor E_AFi(n + 3) in 2013 can be obtained by using the growth factor m_i and scale parameter h_i in 2010 (n = 7) used.

E_{\mathrm{AF}i}(n+\mathrm{3})=[\mathrm{1}-P_{\mathrm{OF}}(t_i)]\times E_{\mathrm{AP}}(n+\mathrm{3})={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}(\mathrm{10})}{\mathrm{1}+{\eta }_i{(n+\mathrm{3})}^{-m_i}}}={\displaystyle \frac{\mathrm{1}-\mathrm{0.0639}}{\mathrm{1}+\mathrm{0.058300}\times {\mathrm{10}}^{-\mathrm{0.151293}}}}=\mathrm{89.91}\%.

With the growth factor m_i and scale parameter h_i in 2011 (n=8) used, the predicted equivalent availability factor E_AFi(n+2) in 2013 can be obtained as

E_{\mathrm{AF}i}(n+\mathrm{2})=[\mathrm{1}-P_{\mathrm{OF}}(t_i)]\times E_{\mathrm{AP}}(n+\mathrm{2})={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}(t_i)}{\mathrm{1}+{\eta }_i{(n+\mathrm{2})}^{-m_i}}}={\displaystyle \frac{\mathrm{1}-\mathrm{0.0639}}{\mathrm{1}+\mathrm{0.054965}\times {\mathrm{10}}^{-\mathrm{0.072899}}}}=\mathrm{89.45}\%.

With the growth factor m_i and scale parameter h_i in 2012 (n=9) used, the predicted equivalent availability factor E_AFi(n+1) in 2013 can be obtained as

E_{\mathrm{AF}i}(n+\mathrm{1})=[\mathrm{1}-P_{\mathrm{OF}}(t_i)]\times E_{\mathrm{AP}}(n+\mathrm{1})={\displaystyle \frac{\mathrm{1}-P_{\mathrm{OF}}(t_i)}{\mathrm{1}+{\eta }_i{(n+\mathrm{1})}^{-m_i}}}={\displaystyle \frac{\mathrm{1}-\mathrm{0.0639}}{\mathrm{1}+\mathrm{0.049651}\times {\mathrm{10}}^{\mathrm{0.04978}}}}=\mathrm{88.67}\%.

The statistical equivalent availability factor in 2013 provided by NERC is E_AF(t_i) = 87.66%, thus D₁ = 89.91%–87.66% = 2.25%, D₂ = 88.67%–87.66% = 1.01%. The relative error of the predicted equivalent availability factor is

E_r={\displaystyle \frac{{\Delta }_{\mathrm{1}}}{E_{\mathrm{AF}}(t_i)}}\times \mathrm{100}\%={\displaystyle \frac{\mathrm{2.25}}{\mathrm{87.66}}}\times \mathrm{100}\%=\mathrm{2.57}\%.

According to Table 2, the relative error of the predicted equivalent availability factor varies in the range of –1.32% to 5.13%. The error of reliability prediction of year 2012 is relatively big which is related to a large un-planed outage hours for NERC nuclear power units in that year.

Reliability prediction and validation examples of 800–999 MW nuclear power units

The statistical data of E_AF(t_i) and P_OF(t_i) of 800–999MW nuclear power units in 2004 and 2013 are listed in Tables 1 and 3, respectively. Given that t_i = 1 in 2004 and t_i = 10 in 2013, the growth factor m_i and scale parameter h_i (Table 3) can be obtained by using the statistical reliability data in the past n years. The predicted E_AF(n + 1), E_AF(n + 2) and E_AF(n + 3), and the relative error E_r for the very year (t = n + 1) and the following years are also given in Table 3. It is found that the relative error of the predicted equivalent availability factor for 800–999MW nuclear power units varies in the range of –2.16% to 5.23% since 2007. The error of reliability prediction of year 2011 is relatively big which is related to a large un-planed outage hours for NERC 800–999 MW nuclear power units in that year.

Reliability prediction and validation examples of 1000 MW nuclear power units

The statistical data of E_AF(t_i) and P_OF(t_i) for 1000 MW nuclear power units in 2004 and 2013 are presented in Tables 1 and 4, respectively. Given that t_i = 1 in 2004 and t_i = 10 in 2013, the growth factor m_i and scale parameter h_i can be obtained by using the statistical reliability data in the past n years, as given in Table 4. The predicted E_AF(n + 1), E_AF(n + 2) and E_AF(n + 3), and the relative error E_r for the very year (t = n + 1) and the following years are also listed in Table 4. It is found that the relative error of the predicted equivalent availability factor for 1000MW nuclear power units has been varying in the range of –0.52% to 4.53% since 2007. The error of reliability prediction of year 2012 is relatively big which is related to a large un-planed outage hours for NERC 1000 MW nuclear power units in that year.

Reliability prediction and validation examples of a single nuclear power unit

For application examples of the single nuclear power unit, reliability prediction error could be validated based on the reliability history data from China Electric Reliability Management Annual Report (CERMAR) .

Reliability prediction and validation examples of 1000 MW nuclear power units in China

Two 1000MW PWR units [ 8] in China are studied. Units 1 and 2 began their commercial operation days on May 17, 2007 and Aug. 16, 2007, respectively. Tables 5 and 6 lists the statistical data of E_AF(t_i), P_OF(t_i), m_i, and h_i, the predicted E_AF(n + 1), E_AF(n + 2), and E_AF(n + 3), and the relative error E_r of Units 1 and 2, respectively. It can be found that the relative error of the predicted equivalent availability factors for Units 1 and 2 vary in the range of –0.04% to 0.95% and –0.07% to 1.11%, respectively, indicating that the prediction accuracy for equivalent availability factors is high.

Reliability prediction and validation examples of 990 MW nuclear power units in China

Two 990MW PWR units [ 8] in China are studied. Units 1 and 2 began their commercial operation days on May 28, 2002 and Jan. 8, 2003, respectively. Tables 7 and 8 give the statistical data of E_AF(t_i), P_OF(t_i), m_i, and h_i, the predicted E_AF(n + 1), E_AF(n + 2), and E_AF(n + 3), and the relative error E_r of Unit 1 and 2, respectively. As observed, the relative error of the predicted equivalent availability factors for Units 1 and 2 vary in the range of –0.23% to 2.66% and –0.23% to 2.66%, respectively, indicating that the prediction accuracy for equivalent availability factors is also high.

Reliability prediction and validation for 700 MW nuclear power units in China

Two 700MW CANDU units [ 8] in China are studied. Units 1 and 2 began their commercial operation days on Nov. 19, 2002 and Jun 12, 2003, respectively. Tables 9 and 10 list the statistical data of E_AF(t_i), P_OF(t_i), m_i, and h_i, the predicted E_AF(n + 1), E_AF(n + 2), and E_AF(n + 3), and the relative error E_r of Units 1 and 2, respectively. As observed the relative error of the predicted equivalent availability factors for Units 1 and 2 vary in the range of –0.55% to 1.72% and –0.27% to 0.96%, respectively, indicating that the prediction accuracy for equivalent availability factors is high.

Reliability prediction and validation example of a 310 MW nuclear power unit in China

A 310MW PWR unit (Unit 1) [ 8] is studied. Unit 1 began its commercial operation day on Dec. 15, 1991. Given t_i = 1 in 1992 and t_i = 13 in 2004, the statistical data of E_AF(t_i), P_OF(t_i), m_i, and h_i, the predicted E_AF(n + 1), E_AF(n + 2), and E_AF(n + 3), and the relative error E_r of Unit 1 are given in Table 11. As observed, the relative error of the predicted equivalent availability factor for Unit 1 varies in the range of –0.03% to 0.78%, indicating that the prediction accuracy for equivalent availability factors is high.

Reliability prediction and validation example of a 984 MW nuclear power unit in China

A 984MW PWR unit (Unit 1) [ 8] is studied. Unit 1 began its commercial operation day http://www.nerc.com/on Feb. 1, 1994. However, the statistical reliability data in 1995 and 1998 is not available. Given t_i = 2 in 1996 and t_i = 19 in 2013, the statistical data of E_AF(t_i), P_OF(t_i), m_i, and h_i, the predicted E_AF(n + 1), E_AF(n + 2), and E_AF(n + 3), and the relative error E_r of Unit 1 are tabulated in Table 12. It is found that the relative error of the predicted equivalent availability factor for Unit 1 varies in the range of –1.03% to 2.52, indicating that the prediction accuracy for equivalent availability factors is high.

Conclusions

In this paper, a novel method for reliability prediction of nuclear power units in service is proposed. The equivalent availability factor in the next 3 years can be obtained by using the historical equivalent availability factor E_AF(t_i) and planed outage factor P_OF(t_i) in the past n years (n≥3) and the planned maintenance days in the next 3 years.

The relative errors of the predicted equivalent availability factors for nuclear power units of NERC are in the range of –2.16% to 5.23%. For the 8 nuclear power units in China, the relative errors vary in the range of –2.15% to 3.71%.

If the predicted value of equivalent availability factor is not up to the required target value, the lower limit of planned maintenance days should be gradually reduced according to the rules of DL/T838 until the predicted equivalent availability factor of the nuclear power unit meet the required reliability target value.

The new reliability prediction method proposed in this paper can effectively predict the equivalent availability factor in the next few years, which is of great importance to nuclear power units in service. By optimizing the planned maintenance days, it can effectively satisfy the predicted equivalent availability factor, thus providing a safe and economic reliability management method for nuclear power units.

References

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[3] Shi J Y, Yang Y, Wang Y. Theory and Method of Reliability Prediction and Safe Operation of Large Generating Units. Beijing: China Electric Power Press, 2014 (in Chinese)

[4] Shi J Y. Study on reliability boost of power plant equipment. Power Engineering, 1991, 11(5): 51–53 (in Chinese)

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