Petri Net Model and Reliability Evaluation for Wind Turbine Hydraulic Variable Pitch Systems
Abstract
:1. Introduction
2. Petri Net Theory
2.1. Definition of the Basic Petri Net
2.2. Basic Properties of a Petri Net
2.3. Analytical Method of the Petri Net
2.3.1. Reachable Marking Graph and Coverable Tree
f : E → T, f(Mi, Mj) = tk
2.3.2. Incidence Matrix and Invariant
2.3.3. Linguistics Analysis Method
2.3.4. Computer Simulation Analysis
2.3.5. Structural Analysis
3. Modeling of a Hydraulic Variable Pitch System Based on the Petri Net
3.1. Working Process of a Hydraulic Variable Pitch System
3.2. Basic Petri Net Model of a Hydraulic Variable Pitch System
4. Modeling Based on the Fault Petri Net of a Hydraulic Variable Pitch System
4.1. Difference between Fault Tree and Fault Petri Net
Logical Relationship | Fault Tree Model | Petri Net Model |
---|---|---|
Logic OR Gate | | |
Logic AND Gate | | |
Logic BAN Gate | | |
Logic NOT Gate | | |
4.2. Fault Diagnostic Principle Based on Fault Petri Net
4.3. Modeling of the Fault Petri Net of a Hydraulic Variable Pitch System
Positions of Bottom Events | Meaning of Positions | Middle Positions | Meaning of Middle Positions |
---|---|---|---|
P1 (0.0005) | Hydraulic pump provides less oil | P12 | Pressure of return circuit is not enough, when brake is loosed |
P2 (0.0005) | Pressure of accumulator is not enough | P13 | The failure of loosing brake |
P3 (0.06) | Sealing is not good after valve 0 is charged with electricity | P14 | The fault of irreversible pitch on the process of start-up |
P4 (0.036) | Valve 1 is not charged with electricity or 19.1 leaks oil | P15 | The fault of increasing power or reversible pitch |
P5 (0.01) | Piston is seriously abraded | P16 | The fault of decreasing power or irreversible pitch |
P6 (0.036) | Valve 2 is not charged with electricity or 19.2 leaks oil | P17 | The fault of variable pitch for hydraulic variable pitch system |
P7 (0.05) | The state fault of valve 1 with electricity | ||
P8 (0.06) | The fault of valve 4 set on shoot-through | ||
P9 (0.05) | The state fault of valve 2 with electricity | ||
P10 (0.02) | Valve 3 leaks oil or double 23 is fault | ||
P11 (0.06) | The state fault of valve 4 set on the cross-modality |
5. Reliability Analysis of a Fault Petri Net
5.1. Qualitative Analysis of a Fault Petri Net
- (1)
- In the incidence matrix, find out the line which contains only 0 s and 1 s without −1 s. Then the library corresponding to that line is the top library. Start to search from this top library.
- (2)
- From 1 in the corresponding line of top library, −1 can be searched by column. Then the library which is represented by the corresponding line of −1s is an input library of the top library. If the column has multiple −1 s, the same transition will have multiple input libraries and these input libraries have an “AND” relationship.
- (3)
- According to the −1 which is searched by step (2), continue to search 1 by line. If there is a 1, the corresponding library is a middle library. Continue to search circularly as in step (2), until no 1s are found in the line. If there is no the line of 1s, the library will be a bottom library called basic event. If there are multiple 1s in a corresponding line, the corresponding library will have multiple transitions. From the corresponding line of 1 as step (2), find out the lines of −1 s. The corresponding libraries of these lines have the relationship of “OR”.
- (4)
- Continue to search as step (2) and step (3), until the most bottom libraries are found.
- (5)
- According to the above relationship of “AND” and “OR”, spread these bottom libraries and then get all cut sets.
- (6)
- Obtain minimum cut sets through Boolean absorption law, idempotent law and prime number method.
- (1)
- Define a planar array to express the incidence matrix;
- (2)
- Transfer recursive function to search −1 by column and 1 by line;
- (3)
- Use a loop statement to express the relationship among cut sets.
5.2. Quantitative Calculation of the Fault Petri Net
6. Conclusions
Acknowledgements
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Yang, X.; Li, J.; Liu, W.; Guo, P. Petri Net Model and Reliability Evaluation for Wind Turbine Hydraulic Variable Pitch Systems. Energies 2011, 4, 978-997. https://doi.org/10.3390/en4060978
Yang X, Li J, Liu W, Guo P. Petri Net Model and Reliability Evaluation for Wind Turbine Hydraulic Variable Pitch Systems. Energies. 2011; 4(6):978-997. https://doi.org/10.3390/en4060978
Chicago/Turabian StyleYang, Xiyun, Jinxia Li, Wei Liu, and Peng Guo. 2011. "Petri Net Model and Reliability Evaluation for Wind Turbine Hydraulic Variable Pitch Systems" Energies 4, no. 6: 978-997. https://doi.org/10.3390/en4060978