Stochastic Programming-Based Fault Diagnosis in Power Systems Under Imperfect and Incomplete Information
Abstract
:1. Introduction
2. Chance-Constrained Programming
3. Analytic Model of Power System Fault Diagnosis Based on CPP
3.1. Modeling of Uncertain Factors
3.2. Analytic Model
3.3. Determination of the Expected States of PRs and CBs with Potential Malfunctions
3.3.1. PRs
- (a)
- If a fault occurred on , and both MP and BPB failed to operate, then should operate, i.e.,
- (b)
- If a fault occurred on the related device dj in the protection zone of ri, and all CBs along the related path from to were closed, i.e., the fault has not been cleared yet, then ri should operate. denotes the set of related sections in the protection zone, . So there is
3.3.2. CBs
3.4. The Final Expected States of PRs and CBs
4. Solving the Fault Diagnosis Problem
4.1. Constraint Checking
4.2. The Calculation of the Objective Function
- (a)
- The random variables are sampled times, and is calculated by using Equation (3) to obtain the sequence .
- (b)
- Set as the integer part of .
- (c)
- Select the smallest element in the sequence to be the objective value .
4.3. The Solving Procedure
5. Application Examples
- the number of chromosomes is set to 20;
- the times of Monte Carlo simulations is set to 1000;
- the initial value of confidence level is set to 0.3;
- is set to 0.7;
- the times of iterations is set to 1000;
- the probabilities of crossover and mutation are set to 0.5 and 0.3.
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclatures
PRs | Protective relays |
CBs | Circuit breakers |
ES | Expert system |
ANN | Artificial neural network |
FS | Fuzzy set |
CCP | Chance-constrained programming |
MP | Main Protection |
PBP | Primary Backup Protection |
SBP | Secondary Backup Protection |
BFP | Breaker Failure Protection |
GA | Genetic algorithm |
Vector of decision variables | |
Stochastic vector with a given probability density function | |
Objective function in CPP | |
Constraint function in CPP | |
Probability of the events in the set in CPP | |
Prescribed confidence levels of the constraints function in CPP | |
Prescribed confidence levels of the objective function in CPP | |
Minimum value of with the confidence level in CPP | |
Probabilities of the malfunction () of the ith PR () | |
Probabilities of the refusing () action of the ith PR () | |
Probabilities of the malfunction ()of the jth CB () | |
Probabilities of the refusing action () of the jth CB () | |
Probabilities of the false alarm ()of | |
Probabilities of the missing alarm () of | |
Probabilities of the false alarm () of | |
Probabilities of the missing alarm () of | |
Number of component in the outage area before the fault | |
Number of configured PRs connected to the outage components before the fault | |
Number of configured CBs connected to the outage components before the fault | |
Fault hypothesis in analytic model | |
Random vectors of the malfunctioning actions of the PRs and CBs | |
Random vectors of the refusing actions of the PRs and CBs | |
W | Random vectors of the false missing alarms |
Random vectors of the the missing alarms | |
Objective function of the analytic model | |
Actual states of PRs in analytic model | |
Expected states of PRs in analytic model | |
Actual states of CBs in analytic model | |
Expected states of CBs in analytic model | |
Probability of in analytic model | |
Initial value of in analytic model | |
Number of the iterations in analytic model | |
Maximum number of iterations set in analytic model | |
Minimum of the objective function with the confidence level | |
Expected states of the corresponding PR with considering the malfunctioning and other improper actions in analytic model | |
Expected states of the corresponding CB with considering the malfunctioning and other improper actions in analytic model | |
Final expected states of the corresponding PR in analytic model | |
Final expected states of the corresponding CB in analytic model | |
logic multiplication | |
logic summation |
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Timestamp (ms) | Substation | Alarms | Timestamp (ms) | Substation | Alarms |
---|---|---|---|---|---|
28 | Tangling | DP of L4335 operated | 665 | Tangling | Phase A of C18 was tripped |
31 | Jianshan | DP of L4335 operated | 665 | Tangling | Phase B of C18 was tripped |
75 | Tangling | Phase C of C10 was tripped | 666 | Tangling | Phase C of C18 was tripped |
79 | Jianshan | Phase C of C11 was tripped | 667 | Tangling | Phase A of C14 was tripped |
383 | Tangling | Acceleration Protection of C10 operated | 667 | Tangling | Phase B of C14 was tripped |
480 | Jianshan | DP of L4336 operated | 668 | Tangling | Phase C of C14 was tripped |
523 | Tangling | Phase A of C12 was tripped | 873 | Tangling | Phase A of C3 was tripped |
523 | Tangling | Phase B of C12 was tripped | 873 | Tangling | Phase B of C3 was tripped |
524 | Tangling | Phase C of C12 was tripped | 874 | Tangling | Phase C of C3 was tripped |
529 | Jianshan | Phase A of C13was tripped | 874 | Tangling | Phase A of C6 was tripped |
529 | Jianshan | Phase B of C13 was tripped | 875 | Tangling | Phase B of C6 was tripped |
529 | Jianshan | Phase C of C13 was tripped | 875 | Tangling | Phase C of C6 was tripped |
617 | Tangling | BFP of C10 operated |
L4333 | L4339 | L4335 | L4336 | B1-I |
---|---|---|---|---|
d0 | d1 | d2 | d3 | d4 |
L4333 | L4339 | L4335 | L4336 | B1-I | |
---|---|---|---|---|---|
MP | r0 | r1 | r2 | r3 | r4 |
PBP | r5 | r6 | r7 | r8 | — |
SBP | r9 | r10 | r11 | r12 | — |
BFP | C3 | C6 | C10 | C14 | C18 |
r13 | r14 | r15 | r16 | r17 |
C2 | C3 | C6 | C7 | C10 | C11 | C12 | C13 | C14 | C18 |
---|---|---|---|---|---|---|---|---|---|
c0 | c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 |
Alarm Type | MP | PBP | SBP | BFP | CB |
---|---|---|---|---|---|
Actual state | 00100 | 0000 | 0000 | 00100 | 0110011111 |
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Song, H.; Dong, M.; Han, R.; Wen, F.; Salam, M.A.; Chen, X.; Fan, H.; Ye, J. Stochastic Programming-Based Fault Diagnosis in Power Systems Under Imperfect and Incomplete Information. Energies 2018, 11, 2565. https://doi.org/10.3390/en11102565
Song H, Dong M, Han R, Wen F, Salam MA, Chen X, Fan H, Ye J. Stochastic Programming-Based Fault Diagnosis in Power Systems Under Imperfect and Incomplete Information. Energies. 2018; 11(10):2565. https://doi.org/10.3390/en11102565
Chicago/Turabian StyleSong, Huizhong, Ming Dong, Rongjie Han, Fushuan Wen, Md. Abdus Salam, Xiaogang Chen, Hua Fan, and Jian Ye. 2018. "Stochastic Programming-Based Fault Diagnosis in Power Systems Under Imperfect and Incomplete Information" Energies 11, no. 10: 2565. https://doi.org/10.3390/en11102565
APA StyleSong, H., Dong, M., Han, R., Wen, F., Salam, M. A., Chen, X., Fan, H., & Ye, J. (2018). Stochastic Programming-Based Fault Diagnosis in Power Systems Under Imperfect and Incomplete Information. Energies, 11(10), 2565. https://doi.org/10.3390/en11102565