CN112507516B - Reliability-based preventive maintenance optimization method and device for electrical equipment - Google Patents

Reliability-based preventive maintenance optimization method and device for electrical equipment Download PDF

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CN112507516B
CN112507516B CN202011205594.1A CN202011205594A CN112507516B CN 112507516 B CN112507516 B CN 112507516B CN 202011205594 A CN202011205594 A CN 202011205594A CN 112507516 B CN112507516 B CN 112507516B
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徐攀腾
朱博
宋述波
陈海永
李倩
郑星星
樊友平
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Guangzhou Bureau of Extra High Voltage Power Transmission Co
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Abstract

The invention discloses a reliability-based preventive maintenance optimization method and device for electrical equipment, wherein the method comprises the following steps: (1) defining preventive maintenance types and calculating corresponding influences on the reliability of the electrical equipment; (2) modeling a fault process of the electrical equipment according to a non-uniform poisson process; (3) constructing a preventive maintenance optimization model of the electrical equipment by taking the minimum total maintenance related cost as a target and the reliability of the electrical equipment as a constraint; (4) and solving the optimal solution of the preventive maintenance optimization model of the electrical equipment based on a simulated annealing algorithm. According to the method, the available resources of the electrical equipment and the minimum reliability requirement are used as decision variables, the total maintenance cost is minimized to serve as an optimization target, a preventive maintenance optimization model of the electrical equipment is established, the method is more consistent with the actual situation, the accuracy is improved, the maintenance cost is reduced as far as possible, and therefore the utilization rate of the electrical equipment is improved.

Description

Reliability-based preventive maintenance optimization method and device for electrical equipment
Technical Field
The invention relates to the field of power systems and automation thereof, in particular to a reliability-based preventive maintenance optimization method for electrical equipment.
Background
The safety of the electrical equipment is related to the national civilization, the reliability of the electrical equipment is an important performance index, and the electrical equipment has a profound influence on the economy and the safety of a power grid system. The performance of electrical devices depends on the reliability of critical components of the electrical devices, which are closely related to the service life and applied maintenance strategies, generally decreasing with the degradation of the critical components. In order to keep the reliability of the electrical equipment at a desired level, appropriate maintenance measures have to be performed.
According to the maintenance mode, the electrical equipment maintenance can be divided into two major categories: corrective maintenance and preventative maintenance. Corrective maintenance is usually carried out after a failure of the electrical equipment, preventive maintenance corresponding to the operation of the electrical equipment still within the operating plan, which aims to maintain a certain reliability of the electrical equipment by improving the condition of critical components. In general, preventive maintenance is more advantageous because it can prevent serious loss of electrical equipment due to unexpected malfunction, and is generally performed at a predetermined time point to maintain reliability of electrical equipment at a desired level.
Disclosure of Invention
The invention aims to provide a reliability-based preventive maintenance optimization method for electrical equipment, which enables the electrical equipment to select a reasonable maintenance mode within constraint conditions, reduces the maintenance cost as much as possible and ensures the safe and stable operation of a power system.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a reliability-based preventive maintenance optimization method for electrical equipment, comprising the following steps:
defining preventive maintenance types and calculating the corresponding influence on the reliability of the electrical equipment;
modeling the fault process of the electrical equipment according to the non-uniform poisson process;
step three, constructing a preventive maintenance optimization model of the electrical equipment by taking the minimum total maintenance related cost as a target and the reliability of the electrical equipment as a constraint;
and fourthly, solving the optimal solution of the preventive maintenance optimization model of the electrical equipment based on the simulated annealing algorithm, and outputting a maintenance scheme.
The invention also provides a reliability-based preventive maintenance optimization device for electrical equipment, which comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes the steps of the optimization method when executing the program.
The invention also provides a computer-readable storage medium, in which a computer program is stored, which computer program, when being executed by a processor, carries out the steps of the above-mentioned optimization method.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the method, the available resources and the minimum reliability requirements of the electrical equipment are used as decision variables, the total maintenance cost of equipment maintenance is minimized to serve as an optimization target, a preventive maintenance optimization model of the electrical equipment is established, the variables comprise maintenance cost and resource constraints, and the maintenance cost and the resource constraints are more consistent with actual conditions.
2. The selection of the maintenance scheme of the electrical equipment relates to a plurality of nonlinear decision variables, and the simulated annealing algorithm is adopted, so that the size and the structure of the equipment can be not limited, and a good solution can be provided within reasonable search time.
Drawings
FIG. 1 is a flow chart of an electrical equipment preventive maintenance optimization method of the present invention.
FIG. 2 is a flow chart of the optimal solution of the method for optimizing preventive maintenance of electrical equipment based on simulated annealing algorithm according to the present invention.
FIG. 3 is a schematic diagram of an exemplary converter valve cooling apparatus.
FIG. 4 is a schematic diagram of the convergence curve during the optimization of the simulated annealing algorithm.
Fig. 5 is a schematic view of the reliability level of the converter valve cooling arrangement under initial and optimal preventive maintenance.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, a method for optimizing preventive maintenance of electrical equipment based on reliability includes the following steps:
step one, defining a preventive maintenance type and calculating the corresponding influence on the reliability of the electrical equipment, and specifically comprises the following substeps:
(1) the invention is characterized in that key components of the electrical equipment are checked in equal time intervals, and in each check, preventive maintenance is carried out based on the degradation state of the components and the effect of the degradation state on the reliability of the electrical equipment, and the preventive maintenance is divided into the following three maintenance types:
1) and (4) checking: this type of maintenance, which generally inspects the different components of the electrical apparatus, only performs simple services, such as lubrication, adjustment/calibration, tightening of loose parts, etc., generally requires less resources and tools and does not increase the reliability of the electrical apparatus;
2) low-level maintenance: this type of maintenance is mainly used to replace some simple parts, such as springs, seals, belts and bearings, etc., low level maintenance generally improving the reliability of the electrical equipment, but not making it "as good as the new electrical equipment";
3) high-level repair (replacement): this type of maintenance, which is the highest level of maintenance, mainly involves replacement with a new critical component of the electrical equipment, is generally adopted in order to avoid serious damage to the entire electrical equipment due to random failure of such a component, which would bring the component to a perfect condition.
(2) The reliability of an electrical equipment component at the start of a task is equal to the reliability of the component at the end of the previous period plus the reliability increased by maintenance of the current period, as determined by the following equation:
Figure BDA0002756952440000031
wherein R isi,0,nFor the reliability of the i-th component at the beginning of the nth checking period of the electrical apparatus, Ri,f,n-1Reliability of the ith component at the end of the n-1 th inspection cycle of the electrical apparatus, m2An impact factor one for preventive maintenance is determined according to the type of maintenance, reflecting the impact of the performed preventive maintenance operation on the reliability of the assembly, and m2≤1。
(3) Substituting the reliability of the ith component at the beginning of the nth cycle into equation (2) to obtain the reliability function of the ith component in the nth cycle:
Figure BDA0002756952440000032
wherein R isi,n(t) reliability of the ith component in the nth cycle of the electrical apparatus, β, σ are shape and scale parameters of the Weibull distribution, tpFor the time interval between two examinations, m1An impact factor of two for preventive maintenance, determined by the failure rate function of the component, and m1≥0，m1The specific determination process of (2) is as follows:
from the relationship between reliability and failure rate, the failure rate function of a component can be expressed as:
Figure BDA0002756952440000033
wherein h isn(t) is the failure rate of the component in the nth cycle, Rn(t) is a reliability function of the assembly.
In conjunction with equations (2) and (3), the failure rate of the nth cycle component can be expressed as:
Figure BDA0002756952440000034
wherein h is0,nIs the initial failure rate of the component in the nth cycle, the failure rate function through the componentNumber of times parameter m can be determined1The value of (c).
Step two, modeling the fault process of the electrical equipment according to the non-uniform poisson process, and specifically comprising the following substeps:
(1) establishing a mathematical model of the non-uniform poisson process according to the intensity function and the random variable:
Figure BDA0002756952440000041
wherein { N (t), t ≧ 0} is a non-uniform Poisson process and N (0) ═ 0, h (t) is an intensity function; when τ → 0, P { N (t + τ) -N (t) ≧ 2} ═ o (τ), P { N (t + τ) -N (t) ≧ 1} ═ h (t) τ + o (τ); h (t + s) -H (t) obeys a Poisson distribution and
Figure BDA0002756952440000042
(2) establishing a fault process model of the electrical equipment by utilizing the cumulative distribution function according to the service life of the electrical equipment and the relevant probability density function:
the average of the poisson process of N (t + s) -N (t) is:
H(t+s)-H(t)＝-logR(t+s)-logR(t) (6)
where n (t) is the number of faults occurring within [0, t ], and the intensity function h (t) ═ f (t)/{1-f (t) }; when t is not less than 0, R (t) is 1-F (t);
wherein, f (t) is the related probability density function of the electrical equipment, F (t) is the cumulative distribution function of the electrical equipment, and R (t) is the reliability function of the electrical equipment.
Step three, taking the minimum total maintenance related cost as a target and the reliability of the electrical equipment as a constraint, and constructing a preventive maintenance optimization model of the electrical equipment, wherein the preventive maintenance optimization model specifically comprises the following substeps:
(1) establishing an objective function of the total maintenance cost of the electrical equipment according to the maintenance cost, the replacement cost, the random failure cost of the electrical equipment and the shutdown cost of the electrical equipment of each component:
Figure BDA0002756952440000043
wherein the decision variable XinAnd YinIf the ith component is maintained in the nth period, the value is 1, otherwise, the value is 0, and a decision variable W is determinednIf the electrical equipment stops running due to preventive maintenance in the nth period, the value is 1, otherwise, the value is 0;
Figure BDA0002756952440000044
for the maintenance cost of the ith module,
Figure BDA0002756952440000045
for the replacement cost of the ith component, C[f]For the cost of random failure of electrical equipment, CdDue to the cost of down-time of the electrical equipment due to preventive maintenance.
(2) Establishing a constraint function according to the resources required by component maintenance, the resources required by replacement and the reliability of the electrical equipment:
Figure BDA0002756952440000046
Figure BDA0002756952440000047
Figure BDA0002756952440000057
wherein the content of the first and second substances,
Figure BDA0002756952440000051
in order to repair the resources required for the ith module,
Figure BDA0002756952440000052
to replace resources required by the ith component, EnFor the total resources available during the nth check,
Figure BDA0002756952440000053
for electrical equipment reliability during the nth cycle,
Figure BDA0002756952440000054
for minimum reliability required by the electrical equipment within the planning range, N is the number of inspection cycles within the planning range, I is the total number of key components in the electrical equipment, wherein Λ (N) is time [ t [ t ] ]n-1,tn]Average value of internal random fault number and
Figure BDA0002756952440000055
step four: solving an optimal solution of the preventive maintenance optimization model of the electrical equipment based on a simulated annealing algorithm, performing simulation through temperature parameters, generating a new test solution by using a sample of the generated solution, starting to move from the current solution, and reducing the temperature according to a specified cooling schedule, if the new solution is improved, adopting the new solution, as shown in fig. 2, specifically comprising the following substeps:
(1) randomly generating an initial solution, and calculating a target function;
(2) generating a new solution by disturbance, and calculating a target function;
(3) calculating the difference value of the two objective functions, if the difference value is less than 0, adopting a new solution, otherwise, adopting a new solution generated by the Metropolis criterion, wherein the expression is as follows:
Figure BDA0002756952440000056
Ti＝αT i-10<α<1 (12)
wherein p iscurrFor current preventive maintenance programs, pcandFor a new preventive maintenance program, Δ C, generated using Metropolis guidelinesiFor preventive maintenance cost changes between the current solution and the candidate solution in the ith iteration, TiIs the temperature in the ith iteration, and α is the cooling rate in the simulated annealing algorithm;
(4) repeating (2) and (3) to enable the iteration number to reach a preset value;
(5) and judging whether the output meets the constraint condition, if so, determining the output is an optimal solution, otherwise, slowly reducing the temperature, and resetting the iteration times.
The optimization method of the present invention is further explained below by taking the converter valve cooling device of the converter station as an example:
the converter valve cooling device of the converter station consists of 11 key components including a raw water pump, a raw water tank, a water replenishing pump, an ion exchanger, a first filter, an expansion tank, a nitrogen gas bottle, a degassing tank, a main circulating pump, an air cooler and a second filter, wherein the code numbers are respectively 1-11, and the structural schematic diagram is shown in figure 3.
In order to realize the optimal preventive maintenance scheme of the equipment, the simulation is carried out by utilizing a simulated annealing algorithm under matlab software.
Assuming a converter valve cooling plant consisting of a series-parallel connection of 11 individual components with negligible probability of at least two failures within a period, a two-year planning period at monthly check interval (k 24) was designed, the input parameters for preventive maintenance are provided in table 1, and the available resource E for all n time intervalsnAnd the converter valve cooling equipment minimum reliability requirements are set to 10 units and 90%, respectively. From multiple simulation experiments, the optimal initial temperature and cooling rate were found to be 50,000 and 0.99, respectively.
TABLE 1 input parameters for preventive maintenance in converter valve cooling plant
Figure BDA0002756952440000061
FIG. 4 shows a schematic diagram of the convergence curve during the optimization of the simulated annealing algorithm. According to fig. 4, the initial oscillation is due to high temperature, indicating that further optimization convergence is required at this stage, and as the search progresses and the temperature is gradually reduced, the simulated annealing algorithm converges and the curve tends to be smooth. After a search time of about 1000s, the algorithm converges to the final solution without any optimization improvement thereafter. It turns out that given sufficient runtime, the algorithm can determine the optimal repair type for each component to minimize the total preventive repair cost.
Fig. 5 is a schematic view of the reliability level of the converter valve cooling arrangement under initial and optimal preventive maintenance. As shown in fig. 5, the constraint that the reliability of the converter valve cooling arrangement determines the optimal preventive maintenance is to keep the converter valve cooling arrangement reliability always above the required 90% level. This demonstrates that the preventive maintenance can ensure safe and stable operation of the converter valve cooling device while reducing the total maintenance cost of the converter valve cooling device as much as possible.
Simulation results verify that the converter valve cooling equipment adopts a simulated annealing algorithm to simulate to obtain an optimal preventive maintenance scheme, can select a plurality of nonlinear decision variables in the maintenance scheme of the electrical equipment, is not limited to the size and the structure of the equipment, provides a good solution within reasonable search time, and ensures the safe and stable operation of a system on the basis of reducing the total maintenance cost of the electrical equipment as much as possible.
In addition, all or part of the flow in the method according to the embodiments of the present invention may be implemented by a computer program, which may be stored in a computer readable storage medium and used by a processor to implement the steps of the embodiments of the method. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), etc.
The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention accordingly, and not to limit the protection scope of the present invention accordingly. All equivalent changes or modifications made in accordance with the spirit of the present disclosure are intended to be covered by the scope of the present disclosure.

Claims (6)

1. A reliability-based preventive maintenance optimization method for electrical equipment is characterized by comprising the following steps: the optimization method comprises the following steps:
defining preventive maintenance types and calculating the corresponding influence on the reliability of the electrical equipment; the method comprises the following steps:
(1) checking critical components of the electrical equipment at equal time intervals, and performing preventive maintenance based on the degradation state of the components and the role thereof in the reliability of the electrical equipment in each check;
(2) the reliability of an electrical equipment component at the start of a task is equal to the reliability of the component at the end of the previous period plus the reliability increased by maintenance of the current period, as determined by the following equation:
Figure FDA0003281773990000011
wherein R isi,0,nFor the reliability of the i-th component at the beginning of the nth checking period of the electrical apparatus, Ri,f,n-1Reliability of the ith component at the end of the n-1 th inspection cycle of the electrical apparatus, m2The impact factor for preventative maintenance, one, reflects the impact of the performed preventative maintenance operation on the reliability of the assembly, and m2≤1；
(3) Substituting the reliability of the ith component at the beginning of the nth cycle into equation (2) to obtain the reliability function of the ith component in the nth cycle:
Figure FDA0003281773990000012
wherein R isi,n(t) reliability of the ith component in the nth cycle of the electrical apparatus, β, σ are shape and scale parameters of the Weibull distribution, tpBetween two examinationsTime interval, m1An impact factor of two for preventive maintenance, determined by the failure rate function of the component, and m1≥0；
Modeling the fault process of the electrical equipment according to the non-uniform poisson process;
step three, constructing a preventive maintenance optimization model of the electrical equipment by taking the minimum total maintenance related cost as a target and the reliability of the electrical equipment as a constraint;
and fourthly, solving the optimal solution of the preventive maintenance optimization model of the electrical equipment based on the simulated annealing algorithm, and outputting a maintenance scheme.
2. The reliability-based preventive maintenance optimization method for the electrical equipment as claimed in claim 1, wherein: the second step comprises the following steps:
(1) establishing a mathematical model of the non-uniform poisson process according to the intensity function and the random variable:
Figure FDA0003281773990000013
wherein { N (t), t ≧ 0} is a non-uniform Poisson process and N (0) ═ 0, h (t) is an intensity function; when τ → 0, P { N (t + τ) -N (t) ≧ 2} ═ o (τ), P { N (t + τ) -N (t) ≧ 1} ═ h (t) τ + o (τ); h (t + s) -H (t) obeys a Poisson distribution and
Figure FDA0003281773990000021
(2) establishing a fault process model of the electrical equipment by utilizing the cumulative distribution function according to the service life of the electrical equipment and the relevant probability density function:
the average of the poisson process of N (t + s) -N (t) is:
H(t+s)-H(t)＝-logR(t+s)-logR(t) (6)
where n (t) is the number of faults occurring within [0, t ], and the intensity function h (t) ═ f (t)/{1-f (t) }; when t is not less than 0, R (t) is 1-F (t);
wherein, f (t) is the related probability density function of the electrical equipment, F (t) is the cumulative distribution function of the electrical equipment, and R (t) is the reliability function of the electrical equipment.
3. The reliability-based preventive maintenance optimization method for the electrical equipment as claimed in claim 2, wherein: the third step comprises:
(1) establishing an objective function of the total maintenance cost of the electrical equipment according to the maintenance cost, the replacement cost, the random failure cost of the electrical equipment and the shutdown cost of the electrical equipment of each component:
Figure FDA0003281773990000022
wherein the decision variable XinAnd YinIf the ith component is maintained in the nth period, the value is 1, otherwise, the value is 0, and a decision variable W is determinednIf the electrical equipment stops running due to preventive maintenance in the nth period, the value is 1, otherwise, the value is 0;
Figure FDA0003281773990000023
for the maintenance cost of the ith module,
Figure FDA0003281773990000024
for the replacement cost of the ith component, C[f]For the cost of random failure of electrical equipment, CdThe cost of electrical equipment down due to preventive maintenance;
(2) establishing a constraint function according to the resources required by component maintenance, the resources required by replacement and the reliability of the electrical equipment:
Figure FDA0003281773990000025
Figure FDA0003281773990000026
Figure FDA0003281773990000027
wherein the content of the first and second substances,
Figure FDA0003281773990000028
in order to repair the resources required for the ith module,
Figure FDA0003281773990000029
to replace resources required by the ith component, EnFor the total resources available during the nth check,
Figure FDA00032817739900000210
for electrical equipment reliability during the nth cycle,
Figure FDA00032817739900000211
for minimum reliability required by the electrical equipment within the planning range, N is the number of inspection cycles within the planning range, I is the total number of key components in the electrical equipment, wherein Λ (N) is time [ t [ t ] ]n-1,tn]Average value of internal random fault number and
Figure FDA00032817739900000212
4. a reliability-based preventive maintenance optimization method for electrical equipment according to claim 3, characterized in that: the fourth step comprises:
(1) randomly generating an initial solution, and calculating a target function;
(2) generating a new solution by disturbance, and calculating a target function;
(3) calculating the difference value of the two objective functions, if the difference value is less than 0, adopting a new solution, otherwise, adopting a new solution generated by the Metropolis criterion, wherein the expression is as follows:
Figure FDA0003281773990000031
Ti＝αTi-1 0<α<1 (12)
wherein p iscurrFor current preventive maintenance programs, pcandFor a new preventive maintenance program, Δ C, generated using Metropolis guidelinesiFor preventive maintenance cost changes between the current solution and the candidate solution in the ith iteration, TiIs the temperature in the ith iteration, and α is the cooling rate in the simulated annealing algorithm;
(4) repeating (2) and (3) to enable the iteration number to reach a preset value;
(5) and judging whether the output meets the constraint condition, if so, determining the output is an optimal solution, otherwise, slowly reducing the temperature, and resetting the iteration times.
5. A reliability-based preventive maintenance optimization device for electrical equipment, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the program, implements the steps of the optimization method according to any one of claims 1 to 4.
6. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the optimization method according to any one of claims 1 to 4.
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