CN110580387A - Entropy weight method based mixed Weibull reliability evaluation method for direct current protection system - Google Patents
Entropy weight method based mixed Weibull reliability evaluation method for direct current protection system Download PDFInfo
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Abstract
the invention relates to a mixed Weibull reliability evaluation method of a direct current protection system based on an entropy weight method, which comprises the following steps: obtaining index data of the defects of the direct current protection system according to the historical data; verifying the defect interval time accumulation to determine whether the defect interval time accumulation meets Weibull distribution; determining the weight coefficient of the defect index by using an entropy weight method so as to obtain the weight coefficient of various devices of the direct current protection system; the method comprises the steps of establishing single Weibull models of various devices based on defect interval time accumulated data by utilizing a maximum likelihood method, obtaining a mixed Weibull model of defect data of the high-voltage direct-current power transmission protection system by combining weight coefficients of the various devices in the defect data, and analyzing the reliability of the high-voltage direct-current protection system by utilizing the mixed Weibull model. The method can evaluate the reliability of the direct current transmission protection system by utilizing the operation defect information of the high-voltage direct current transmission protection equipment, and provides an important reference basis for the operation maintenance work of the direct current transmission protection system equipment.
Description
Technical Field
The invention relates to the technical field of power system reliability research, in particular to a mixed Weibull reliability evaluation method of a direct current protection system based on an entropy weight method.
Background
The direct-current transmission protection system is a first defense line for safe and reliable operation of a direct-current transmission system and is an important guarantee for safe and stable operation of direct-current engineering. In recent years, the problem of shutdown or lockout of the direct current system due to faults of the direct current transmission protection system occurs occasionally, wherein the direct current lockout is more than 10% caused by measurement faults of the protection system, board faults and faults of the protection host, and the safe and stable operation of the direct current system is seriously influenced. Therefore, the reliability of the direct-current power transmission protection system is important.
In the aspect of the reliability evaluation index of the existing protection system, the protection correct action is mainly used as the evaluation index, the reliability evaluation index of a protection method, a protection configuration scheme and protection equipment is researched, the action samples of the direct current protection system are few, the reliability of the evaluation result is low due to the fact that the existing indexes such as the correct action rate, the misoperation rate, the rejection rate and the like are adopted to evaluate the reliability of the direct current protection system, and meanwhile, the indexes are multi-purpose in evaluating the inherent reliability of the system and are difficult to evaluate the use reliability of the system; meanwhile, because the number of direct current protection samples is small, the reliability of an evaluation result of the traditional reliability evaluation method is low, and the practicability is poor. Therefore, the reliability evaluation is carried out on the defect data of the direct current protection system, the running state of the direct current protection system can be reflected, and an important reference basis is provided for the running maintenance work of the direct current protection system equipment.
Disclosure of Invention
The invention aims to provide a mixed Weibull reliability evaluation method of a direct current protection system based on an entropy weight method, which is used for evaluating the reliability of the direct current transmission protection system by utilizing the operation defect information of high-voltage direct current transmission protection equipment, provides an important reference basis for the operation maintenance work of the direct current protection system equipment, and is also suitable for the reliability evaluation of an alternating current/direct current system based on the defect data and the fault information of the alternating current/direct current system.
The purpose of the invention is realized by the following technical scheme:
a mixed Weibull reliability evaluation method of a direct current protection system based on an entropy weight method comprises the following steps:
the method comprises the following steps: classifying the direct current protection system according to different positions of the defects by combining the characteristics of the direct current protection system, collecting historical data of the defects of the direct current protection system, and obtaining index data of the defects of the direct current protection system according to the historical data;
Step two: checking the defect interval time accumulation of the high-voltage direct-current transmission protection system, and executing a third step after determining that the defect interval time accumulation conforms to Weibull distribution;
step three: determining the weight coefficient of the index data of each direct current protection system defect by using an entropy weight method, and further obtaining the weight coefficient of various devices of the direct current transmission protection system in the defect data;
step four: the method comprises the steps of establishing single Weibull models of various devices based on defect interval time accumulated data by utilizing a maximum likelihood method, obtaining a mixed Weibull model of defect data of the high-voltage direct-current power transmission protection system by combining weight coefficients of the various devices in the defect data, and analyzing the reliability of the high-voltage direct-current protection system by utilizing the mixed Weibull model.
Further, the specific implementation process of the step one is as follows:
(a) the characteristics of the direct current protection system are combined, and the defects of the direct current protection system are divided into the following five types according to different positions of the defects: measuring equipment defects, measuring interface device defects, direct current protection device defects, two-out-of-three device defects, tripping outlet and secondary circuit defects, and when the defect rate of a host type protection device, a device type protection device and an independent type protection device is high, calculating the host type protection device, the device type protection device and the independent type protection device as a type;
(b) collecting historical data of defects of a plurality of converter stations direct current protection systems in recent years;
(c) obtaining three index data of the defects of the direct current protection system according to historical data: component failure free time rate, component mean repair time rate, and component defect rate;
Further, the specific implementation process of the step two is as follows:
(a) accumulating the defect interval time of the high-voltage direct-current transmission protection system in ascending order;
(b) Checking the defect interval time accumulation of the high-voltage direct-current transmission protection system, and judging and determining whether the defect interval time accumulation conforms to Weibull distribution by using KS detection:
The Weibull probability distribution for both parameters is:
Wherein t is time, beta is a shape parameter, and eta is a scale parameter;
Assuming that the unary linear regression equation is y ═ BX + a, linear transformation is performed on the two-parameter weibull function to obtain:
xi＝lnti (9)
in the expressions (7) to (9), i is a defect interval time accumulated serial number, n is the number of samples accumulated in the defect interval time of the high-voltage direct-current transmission protection system, and tiaccumulating defect interval time of the high-voltage direct-current transmission protection system;
Through calculation, regression systems A and B in a unitary linear regression equation of y ═ BX + A are obtained, and further a shape parameter beta and a scale parameter eta are obtained:
β＝B (11)
Judging the correctness of defect distribution by KS inspection, and performing difference on the values of the formula (6) and the formula (8) to obtain the maximum value of the absolute values of the differences in all data, wherein the maximum value is the observed value Dmaxit is compared with an empirical threshold Dnand if the accumulated data does not conform to the Weibull distribution, the data accumulated by the defect interval time needs to be re-judged, and certain defects possibly have missing filling or wrong filling, and the data is re-improved and then is judged.
further, the specific implementation process of the step three is as follows:
(a) normalizing the defect index obtained in the step one, and obtaining a relation matrix (x)ij)m×nConverting into standard matrix, and performing polarization treatment according to reverse index formula (13) to obtain standard matrix (a) because index data are all reverse indexesij)m×nM is the number of defect types, and n is the number of evaluation indexes;
in formula (13), xmaxDenotes the maximum value, x, of each columnminRepresents the minimum value of each column;
(b) According to the standard matrix, the characteristic weight P of the j index of the i equipment is calculatedij：
When P is presentijWhen 0, it makes no sense to calculate the entropy value, so for PijModified to define as
(c) Calculating the entropy of the jth index as
(d) The entropy weight of the jth index is
(e) the weight coefficients of various elements of the direct current transmission protection system in the defect data are as follows:
(f) And further solving the weight coefficients of various devices of the direct current transmission protection system in the defect data according to the weight coefficients of various elements.
further, the specific implementation process of the step four is as follows:
(a) the defect interval time accumulation of five types of equipment of the high-voltage direct-current transmission protection system is arranged in ascending order, and the shape parameter beta and the shape parameter eta of the equipment are respectively estimated by utilizing a maximum likelihood estimation method:
for a two-parameter Weibull distribution, the likelihood function is constructed as:
partial derivatives are calculated for each parameter in the above equation (19) to obtain the equation system:
The formula (20) is an transcendental equation set, parameters can not be directly obtained, parameters beta and eta of various devices are solved on MATLAB by using a Newton-Raphson iterative method, and then a Weibull reliability function R of the various devices is obtainedi(x)：
In the formula (21), betaiis a shape parameter of the i-th class element, ηiIs a scale parameter of the i-th class element.
(b) establishing a mixed Weibull model R (x) of defect data of the high-voltage direct-current transmission protection system to obtain a reliability curve of the high-voltage direct-current transmission protection system;
R(x)＝P1R1(x)+P2R2(x)+…+PnRn(x) (22)
P＝P1+P2+…+Pn＝1 (23)
In the formula, n is the number of device types.
(c) analyzing the reliability of a high voltage direct current protection system
The independent variable of the hybrid Weibull model is defect interval time accumulation, the independent variable can be considered as the normal operation time of the equipment from the occurrence of the first defect, the larger the normal operation time is, the lower the reliability of the system is, the hybrid Weibull model curve (namely the reliability curve of the high-voltage direct-current power transmission protection system) can be considered as the normal operation time of the equipment from the occurrence of the first defect, in the case of the operation time being as long as possible, the higher the reliability is, the better the reliability is, and the expected value of the reliability is made to be the standard value RiFirst standard value R10.95, the corresponding operating time T is obtained from the mixed Weibull model curve1The standard value R of the subsequent timei＝Ri-1x 0.95, from the curve TiFrom this, T over a period of time can be obtainediAnd averaging the values to obtain an average value T, wherein the value can be regarded as the optimal maintenance time of the direct current protection system. If the reliability of certain equipment is to be analyzed independently, the optimal maintenance time of various equipment can be obtained by using the reliability function of various equipment and adopting the same method as the reliability analysis of the mixed Weibull model.
Comparing the average value T with the defect time interval of the high-voltage direct-current transmission protection system of each station, when the defect time interval of the system is larger than the average value T, the reliability of the system is higher, otherwise, the reliability of the system is judged to be lower, at the moment, the equipment maintenance time is adjusted according to the average value T, or measures such as replacing part of equipment are taken, so that the reliability of the system is in a higher level; according to the historical data of each station and the average value T of the mixed Weibull model, the interval time average value of the historical defects is larger than the average value T of the mixed Weibull model, and the larger the interval time average value of the historical defects is, the higher the reliability of the DC protection system of the station is, the longer the interval of the next defect of the system is, and the fewer the defects appear in the same time period; the historical defect interval time average value is smaller than the mixed Weibull model average value T, and the smaller the historical defect interval time average value is, the lower the reliability of the DC protection system is, the time interval of the system for the next defect is short, and the number of defects in the same time period is large.
The method obtains the mixed Weibull model of the direct current protection system based on the entropy weight method, further obtains the optimal maintenance time of the system and the optimal maintenance time of various devices, evaluates the direct current protection system of each converter station by combining the actual conditions of each converter station, provides important guidance for the operation and maintenance of the direct current protection system, and can obtain the mixed Weibull model curve of the converter station by adopting the method under the condition that defect samples of each station are complete for analyzing the reliability, the defect occurrence rate and the like of the direct current protection system of the converter station. The use effect of the invention can be obtained through a specific implementation scheme, the scheme verifies the effectiveness of the invention, provides the optimal operation and maintenance time of the converter station direct-current protection system, and provides an important operation and maintenance time basis for equipment operation and maintenance units. The invention is also suitable for analyzing the defect or fault data of the AC/DC system.
drawings
Fig. 1 is a block diagram of a high voltage direct current transmission system according to the invention;
FIG. 2 is a diagram of a hybrid Weibull model R (x) and R of various devices according to an embodiment of the present inventioni(x) The graph is schematic.
Detailed Description
The present invention will be further described with reference to specific examples to fully understand the objects, features and effects of the present invention.
in the embodiment, the data are from defects of the high-voltage direct-current transmission protection system in the Hubei power grid 2014 to 2018.
The entropy weight method-based mixed weibull reliability evaluation method for the direct current protection system in the embodiment includes the following steps:
the method comprises the following steps: combining the characteristics of the direct current protection system, classifying the direct current protection system according to different positions of the defects, collecting historical data of the defects of the direct current protection system, and obtaining index data of the defects of the direct current protection system according to the historical data: component non-failure time rate, component mean time to repair rate, and component defect rate.
According to the technical scheme, 173 defects of the high-voltage direct-current transmission protection system in the 2014-2018 of the Hubei power grid are obtained based on historical data, 56 defects of measuring equipment, 43 defects of measuring interfaces, 58 defects of host type direct-current protection, 6 defects of independent type direct-current protection and 10 defects of device type direct-current protection are obtained, and the host type protection device, the device type protection device and the independent type protection device can be independently used as one type for calculation when the defect rate of the host type protection device, the device type protection device and the independent type protection device is high, and if some equipment or elements are not defective, the main type protection device, the device type protection device and the independent type protection device do not participate in statistics.
the index data of the defects of the direct current protection system are shown in the following table:
Step two: checking the defect interval time accumulation of the high-voltage direct-current transmission protection system to determine whether the defect interval time accumulation meets Weibull distribution, wherein the second step specifically comprises the following steps:
(a) Accumulating the defect interval time of the high-voltage direct-current transmission protection system in ascending order;
(b) And verifying the defect interval time accumulation of the high-voltage direct-current transmission protection system, and judging and determining whether the high-voltage direct-current transmission protection system conforms to Weibull distribution by using KS (hue-saturation-value) inspection.
Obtaining accumulated data of defect interval time according to defect data of the high-voltage direct-current power transmission protection system, obtaining an unary linear regression equation of y-1.1049 x-7.4195, further obtaining beta-1.1049, eta-824.5367 and Dmax0.0883, wherein β is the shape parameter, η is the scale parameter, DmaxFor the maximum absolute value of the difference in all data, i.e. the observed value Dmax。
obtaining an empirical threshold from a KS test chartn is the sample volume 172, and D is obtainedn＝0.1037，DmaxBelow an empirical threshold, it may be determined that the defect interval time accumulation follows a weibull distribution.
step three: and determining the weight coefficient of each defect index by using an entropy weight method, and further obtaining the weight coefficient of various equipment of the direct current power transmission protection system in the defect data. The third step is specifically as follows:
(a) Normalizing the index to obtain a relation matrix (x)ij)m×nConverting into standard matrix, and performing polarization treatment according to reverse index formula (1) to obtain standard matrix (a) because index data are all reverse indexesij)m×nM is the number of defect types, and n is the number of evaluation indexes.
in the formula (1), xmaxdenotes the maximum value, x, of each columnminThe minimum value of each column is indicated.
(b) According to the standard matrix, the characteristic weight P of the j index of the i equipment is calculatedij：
When P is presentijWhen 0, it makes no sense to calculate the entropy value, so for PijModified to define as
(c) calculating the entropy of the jth index as
(d) The entropy weight of the jth index is
(e) The weight of each element of the direct current transmission protection system in the defect data is as follows:
(f) And further calculating the weight of the direct current transmission protection system equipment according to the weights of the various elements.
The entropy weights of the three indexes obtained by the method are shown in the following table:
| Index quantity | ratio of time without failure | average maintenance time ratio | ratio of element defects |
| Entropy weight of index quantity | 0.6188 | 0.1815 | 0.2067 |
The weights for each type of device, as calculated according to equation (6), are shown in the following table:
| All kinds of equipment | Weight (P) |
| Measuring device | 0.1596 |
| measurement interface | 0.2502 |
| Independent protection | 0.1829 |
| Host type protection | 0.3023 |
| Device type protection | 0.1049 |
Step four: the method comprises the steps of establishing single Weibull models of various devices based on defect interval time accumulated data by utilizing a maximum likelihood method, obtaining a mixed Weibull model of defect data of the high-voltage direct-current power transmission protection system by combining weight coefficients of the various devices in the defect data, and analyzing the reliability of the high-voltage direct-current protection system by utilizing the mixed Weibull model.
(a) and accumulating defect interval time of five types of equipment of the high-voltage direct-current transmission protection system in ascending order, and respectively estimating parameters beta and eta of the equipment by utilizing a maximum likelihood estimation method.
For a two-parameter Weibull distribution, the likelihood function is constructed as:
Calculating partial derivatives of the parameters in the above formula (7) to obtain an equation system:
Equation (8) is a transcendental system of equations and cannot be directly parameterized. Solving on MATLAB by using a Newton-Raphson iterative method to obtain parameters beta and eta of various devices, and further obtaining F of various devicesi(x)。
the parameters β and η of each type of equipment obtained by using MATLAB to the five types of equipment by using a maximum likelihood estimation method are shown in the following table:
| All kinds of equipment | Parameter beta | Parameter eta |
| measuring device | 1.4017 | 912.6431 |
| Measurement interface | 1.1336 | 720.7997 |
| independent protection | 2.0353 | 1131.0011 |
| Host type protection | 1.0240 | 595.8380 |
| Device type protection | 2.8301 | 1416.5968 |
(b) establishing a mixed Weibull model R (x) of defect data of the high-voltage direct-current transmission protection system to obtain a reliability curve of the high-voltage direct-current transmission protection system;
R(x)＝P1R1(x)+P2R2(x)+…+PnRn(x) (9)
P＝P1+P2+…+Pn＝1 (10)
A mixed weibull model is established by equations (9) and (10) as follows:
R(x)＝P1R1(x)+P2R2(x)+…+PnRn(x) The method is a hybrid Weibull model of defect data of the high-voltage direct-current transmission protection system. R1(x) As a function of the reliability of the measuring device, R2(x) For measuring the reliability function of the interface, R3(x) As a function of the reliability of the independent protection, R4(x) Reliability function for host type protection, R5(x) Mixing Weibull model R (x) and R of various types of equipment as reliability function of device type protectioni(x) The curves are shown in fig. 2:
(c) Analyzing the reliability of a high voltage direct current protection system
the mixed Weibull model curve can be regarded as the normal operation time of the equipment when the first defect occurs, and in the case of the operation time being as long as possible, the higher the reliability is regarded as better, and the expected value of the reliability is made to be the standard value Rifirst standard value R1Obtaining the corresponding operation time T according to a mixed Weibull model curve (namely a reliability curve of the high-voltage direct-current transmission protection system) as 0.951The standard value R of the subsequent timei＝Ri-1x 0.95, from the curve Tifrom this, T over a period of time can be obtainedithe average value T was found to be 31.97 days. The average value of various devices can be obtained in the same way, and the specific data are shown in the following table:
| Device or system name | Average value T |
| Measuring device | 32.75 |
| measurement interface | 31.79 |
| Independent protection | 28.08 |
| Host type protection | 29.62 |
| Device type protection | 29.28 |
| Direct current protection system | 31.97 |
According to the historical defect data of each converter station, the time average value of the historical defect interval from 2014 to 2018 of each station can be obtained as follows:
As can be seen from the table, the Longquan converter station has short defect interval time, and the mixed Weibull model average value T is combined to suggest that the equipment maintenance work of the Longquan converter station is enhanced. According to the historical data of each station and the average value T of the mixed Weibull model, the time average values of the historical defects of the Kudzuvine dam converter station, the Jiangling converter station, the Tuoling converter station and the Yidu converter station are all larger than the average value T of the mixed Weibull model, but the time average value of the historical defects of the Jiangling converter station is not greatly different from the average value T of the mixed Weibull model, and the equipment maintenance work of the Jiangling converter station is also enhanced. The time average value of the historical defect interval of the Longquan converter station is smaller than the average value T of the mixed Weibull model, which shows that the reliability of the DC protection system of the station is low, the time interval of the next defect of the system is short, and the number of the defects in the same time period is large.
Through the analysis, the number of the defects of the Longquan converter station is the largest, the defect interval time is the shortest, the difference between the average value of the historical defect interval time of the Longquan converter station and the average value of the measuring equipment and the measuring interface equipment is the largest, the number of the defects is increased, in order to verify the validity of the invention, the actual defects of the Longquan converter station in 2019 are both the measuring equipment and the measuring interface equipment by combining actual defect data of each converter station in 2019, the number of the defects is more than twice of the number of the defects of other stations, and the validity of the invention is verified.
The method obtains the mixed Weibull model of the direct current protection system based on the entropy weight method, further obtains the optimal maintenance time of the system and the optimal maintenance time of various devices, evaluates the direct current protection system of each converter station by combining the actual conditions of each converter station, provides important guidance for the operation and maintenance of the direct current protection system, and can obtain the mixed Weibull model curve of the converter station by adopting the method under the condition that defect samples of each station are complete for analyzing the reliability, the defect occurrence rate and the like of the direct current protection system of the converter station.
Claims (5)
1. A mixed Weibull reliability evaluation method of a direct current protection system based on an entropy weight method is characterized by comprising the following steps: comprises the following steps
the method comprises the following steps: classifying the direct current protection system according to different positions of the defects by combining the characteristics of the direct current protection system, collecting historical data of the defects of the direct current protection system, and obtaining index data of the defects of the direct current protection system according to the historical data;
Step two: checking the defect interval time accumulation of the high-voltage direct-current transmission protection system, and executing a third step after determining that the defect interval time accumulation conforms to Weibull distribution;
step three: determining the weight coefficient of the index data of each direct current protection system defect by using an entropy weight method, and further obtaining the weight coefficient of various devices of the direct current transmission protection system in the defect data;
Step four: the method comprises the steps of establishing single Weibull models of various devices based on defect interval time accumulated data by utilizing a maximum likelihood method, obtaining a mixed Weibull model of defect data of the high-voltage direct-current power transmission protection system by combining weight coefficients of the various devices in the defect data, and analyzing the reliability of the high-voltage direct-current protection system by utilizing the mixed Weibull model.
2. the entropy weight method-based mixed Weibull reliability evaluation method for the direct current protection system according to claim 1, characterized in that: the specific implementation process of the first step is as follows:
(a) The characteristics of the direct current protection system are combined, and the defects of the direct current protection system are divided into the following five types according to different positions of the defects: measuring equipment defects, measuring interface device defects, direct current protection device defects, two-out-of-three device defects, tripping outlet and secondary circuit defects, and when the defect rate of a host type protection device, a device type protection device and an independent type protection device is high, calculating the host type protection device, the device type protection device and the independent type protection device as a type;
(b) Collecting historical data of defects of a plurality of converter stations direct current protection systems in recent years;
(c) Obtaining three index data of the defects of the direct current protection system according to historical data: component failure free time rate, component mean repair time rate, and component defect rate;
3. The entropy weight method-based mixed Weibull reliability evaluation method for the direct current protection system according to claim 1, characterized in that: the concrete implementation process of the second step is as follows:
(a) Accumulating the defect interval time of the high-voltage direct-current transmission protection system in ascending order;
(b) Checking the defect interval time accumulation of the high-voltage direct-current transmission protection system, and judging and determining whether the defect interval time accumulation conforms to Weibull distribution by using KS detection:
the Weibull probability distribution for both parameters is:
Wherein t is time, beta is a shape parameter, and eta is a scale parameter;
Assuming that the unary linear regression equation is y ═ BX + a, linear transformation is performed on the two-parameter weibull function to obtain:
xi＝ln ti (9)
In the expressions (7) to (9), i is a defect interval time accumulated serial number, n is the number of samples accumulated in the defect interval time of the high-voltage direct-current transmission protection system, and tiAccumulating defect interval time of the high-voltage direct-current transmission protection system;
Through calculation, regression systems A and B in a unitary linear regression equation of y ═ BX + A are obtained, and further a shape parameter beta and a scale parameter eta are obtained:
β＝B (11)
Judging the correctness of defect distribution by KS inspection, and performing difference on the values of the formula (6) and the formula (8) to obtain the maximum value of the absolute values of the differences in all data, wherein the maximum value is the observed value DmaxIt is compared with an empirical threshold DnAnd if the accumulated data does not conform to the Weibull distribution, the data accumulated by the defect interval time needs to be re-judged, and certain defects possibly have missing filling or wrong filling, and the data is re-improved and then is judged.
4. The entropy weight method-based mixed Weibull reliability evaluation method for the direct current protection system, according to claim 1 or 2, characterized in that: the concrete implementation process of the third step is as follows:
(a) Normalizing the defect index obtained in the step one, and obtaining a relation matrix (x)ij)m×nConverting into standard matrix, and performing polarization treatment according to reverse index formula (13) to obtain standard matrix (a) because index data are all reverse indexesij)m×nM is the number of defect types, and n is the number of evaluation indexes;
In formula (13), xmaxdenotes the maximum value, x, of each columnminrepresents the minimum value of each column;
(b) According to the standard matrix, the characteristic weight P of the j index of the i equipment is calculatedij：
When P is presentijwhen 0, it makes no sense to calculate the entropy value, so for Pijmodified to define as
(c) Calculating the entropy of the jth index as
(d) The entropy weight of the jth index is
(e) the weight coefficients of various elements of the direct current transmission protection system in the defect data are as follows:
(f) and further solving the weight coefficients of various devices of the direct current transmission protection system in the defect data according to the weight coefficients of various elements.
5. The entropy weight method-based mixed Weibull reliability evaluation method for the direct current protection system according to claim 1, characterized in that: the concrete implementation process of the step four is as follows:
(a) the defect interval time accumulation of five types of equipment of the high-voltage direct-current transmission protection system is arranged in ascending order, and the shape parameter beta and the shape parameter eta of the equipment are respectively estimated by utilizing a maximum likelihood estimation method:
for a two-parameter Weibull distribution, the likelihood function is constructed as:
partial derivatives are calculated for each parameter in the above equation (19) to obtain the equation system:
The formula (20) is an transcendental equation set, parameters can not be directly obtained, parameters beta and eta of various devices are solved on MATLAB by using a Newton-Raphson iterative method, and then a Weibull reliability function R of the various devices is obtainedi(x)：
In the formula (21), betaiIs a shape parameter of the i-th class element, ηiIs a scale parameter of the i-th class element.
(b) Establishing a mixed Weibull model R (x) of defect data of the high-voltage direct-current transmission protection system to obtain a reliability curve of the high-voltage direct-current transmission protection system;
R(x)＝P1R1(x)+P2R2(x)+…+PnRn(x) (22)
P＝P1+P2+…+Pn＝1 (23)
In the formula, n is the number of device types.
(c) Analyzing the reliability of a high voltage direct current protection system
The independent variable of the hybrid Weibull model is defect interval time accumulation, the independent variable can be considered as the normal operation time of the equipment from the occurrence of the first defect, the larger the normal operation time is, the lower the reliability of the system is, the hybrid Weibull model curve (namely the reliability curve of the high-voltage direct-current power transmission protection system) can be considered as the normal operation time of the equipment from the occurrence of the first defect, in the case of the operation time being as long as possible, the higher the reliability is, the better the reliability is, and the expected value of the reliability is made to be the standard value RiFirst standard value R10.95, the corresponding operating time T is obtained from the mixed Weibull model curve1The standard value R of the subsequent timei＝Ri-1x 0.95, from the curve TiFrom this, T over a period of time can be obtainediAnd averaging the values to obtain an average value T, wherein the value can be regarded as the optimal maintenance time of the direct current protection system. If the reliability of certain equipment is to be analyzed independently, the optimal maintenance time of various equipment can be obtained by using the reliability function of various equipment and adopting the method the same as the reliability analysis of the mixed Weibull model;
Comparing the average value T with the defect time interval of the high-voltage direct-current transmission protection system of each station, when the defect time interval of the system is larger than the average value T, the reliability of the system is higher, otherwise, the reliability of the system is judged to be lower, at the moment, the equipment maintenance time is adjusted according to the average value T, or measures such as replacing part of equipment are taken, so that the reliability of the system is in a higher level; according to the historical data of each station and the average value T of the mixed Weibull model, the interval time average value of the historical defects is larger than the average value T of the mixed Weibull model, and the larger the interval time average value of the historical defects is, the higher the reliability of the DC protection system of the station is, the longer the interval of the next defect of the system is, and the fewer the defects appear in the same time period; the historical defect interval time average value is smaller than the mixed Weibull model average value T, and the smaller the historical defect interval time average value is, the lower the reliability of the DC protection system is, the time interval of the system for the next defect is short, and the number of defects in the same time period is large.
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