A Layered Fault Tree Model for Reliability Evaluation of Smart Grids
Abstract
:1. Introduction
2. Layered Fault Tree Model for Smart Grids
2.1. Fault Tree Analysis
2.2. The Layered Fault Tree
- With the introduction of DGs, new distribution systems become multi-power resources served networks, instead of traditional radial construction served by a single source, so the structures of the new distribution systems will be improved, in order to gain a better architecture to have DGs access.
- The uncertainty of the operating state of the new distribution systems increases greatly. The output power of renewable primary energy sources has great randomness, and no longer depends on users’ loads. Moreover, new distribution systems may be operating in islanded mode or grid-connected mode, which can reconfigure the new distribution systems to be bidirectional networks, with many small-scale DGs integrated.
- Control techniques and methods for the envisioned distribution systems are undergoing significant changes. Different from conventional distribution systems, it is difficult for the smart grids to use a single control center to regulate the whole system rapidly and efficiently. Control of the new distribution systems should base on local information as much as possible [1,18,19]. Therefore, the theory of distributed control for new distribution systems can be far more complicated than traditional control theory.
- 1
- The islanding strategy of a smart grid is intentional. It gives the possibility to imply the state changing process in the structure of the fault tree model and in the simulation process. Based on a specific architecture of smart grid, the research object should also be an integral potential islanded local framework, with one or more intelligent substations in it.
- 2
- In the local smart grid framework, power can be dispatched freely, and loads of low priority can be cut off from the system in order to guarantee power supply for more important loads if needed. The lines or buses in the distributed smart grid infrastructure also have enough capacity and won’t be overloaded when transmitting electricity. This assumption conforms to the designing and operational feature of smart grids, which increases the power distribution reliability.
- 3
- The intelligent control and protection systems of smart grids are not further analyzed and decomposed in this paper. These functions are usually incorporated in the intelligent substations in a specific smart grids architecture and will be achieved not only by devices but also through the intelligent control software. The consideration of these systems can make the models improved, but will increase the complexity additionally of the overall procedure.
2.2.1. Construction of the Primary Fault Tree
- Information subsystem failure.
- Communication subsystem failure.
- Intelligent substation failure.
- Protection subsystem failure.
- Power supply failure.
- Failures of other devices depending on the architecture.
2.2.2. Construction of the Secondary Fault Tree
2.3. Importance Measures
2.4. Simulation Strategy
- 1
- The fault tree constructed reflects the operational mechanism of smart grids. The change of two different power supply modes should be embodied in the reliability assessment process with the proposed fault tree.
- 2
- Start time of operation are different between devices in the two layers of fault tree, in that local supply is triggered by utility supply failure. Time requirement for islanded operation is not as high as for normal systems, so a short islanded operation time cycle should be integrated in the assessment.
- 3
- The proposed procedure for assessment of inadequacy judgment function for the secondary fault tree should be integrated in the reliability evaluation process.
3. Case Study
3.1. A Case of FREEDM System
Load point | Priority | Priority factor | Power demand (kW) |
---|---|---|---|
Load 1 | 1 | 1.000 | 5 |
Load 2 | 2 | 0.875 | 3 |
Load 3 | 3 | 0.750 | 5 |
Load 4 | 4 | 0.625 | 5 |
Load 5 | 5 | 0.500 | 2 |
Load 6 | 6 | 0.375 | 2.5 |
Load 7 | 7 | 0.250 | 5 |
Load 8 | 8 | 0.125 | 2.5 |
3.2. Reliability Assessment
No. | Basic Event | No. | Basic Event |
---|---|---|---|
1 | Community-level circuit breaker failure | 19 | Operation failure of diesel generator 1 |
2 | Circuit breaker 1 failure | 20 | Starting failure of diesel generator 1 |
3 | IFM cooperative isolation failure | 21 | Rectifier 2 failure |
4 | IEM cooperative control failure | 22 | Operation failure of diesel generator 2 |
5 | 12 kV AC bus failure | 23 | Starting failure of diesel generator 2 |
6 | 120 V AC bus 1 failure | 24 | DC/DC Converter 2 failure |
7 | Local communication failure | 25 | Intermittent output of battery 2 |
8 | Cross-system communication failure | 26 | Degraded output of battery 2 |
9 | 400 V DC bus 1 failure | 27 | Short of battery 2 |
10 | 400 V DC bus 2 failure | 28 | DC/DC Converter 4 failure |
11 | 400 V DC bus 3 failure | 29 | PV array failure |
12 | Circuit breaker 2 failure | 30 | DC/DC Converter 3 failure |
13 | Circuit breaker 3 failure | 31 | Intermittent output of battery 3 |
14 | DC/DC Converter 1 failure | 32 | Degraded output of battery 3 |
15 | Intermittent output of battery 1 | 33 | Short of battery 3 |
16 | Degraded output of battery 1 | 34 | Rectifier 3 failure |
17 | Short of battery 1 | 35 | Wind turbine failure |
18 | Rectifier 1 failure |
Load point | Reliability | Compound weight | Unreliability contribution |
---|---|---|---|
Load 1 | 99.9550% | 0.1667 | 7.50 × 10‒5 |
Load 2 | 99.9518% | 0.0875 | 4.22 × 10‒5 |
Load 3 | 99.9139% | 0.1250 | 1.08 × 10‒4 |
Load 4 | 99.4451% | 0.1042 | 5.78 × 10‒4 |
Load 5 | 99.3837% | 0.0333 | 2.05 × 10‒4 |
Load 6 | 99.3311% | 0.0313 | 2.09 × 10‒4 |
Load 7 | 86.4229% | 0.0417 | 5.66 × 10‒3 |
Load 8 | 85.9354% | 0.0104 | 1.47 × 10‒3 |
Component | NRAW+ | NRAW | Component | NRRW+ | NRRW |
---|---|---|---|---|---|
IEM | 71.9406 | 27.3848 | Diesel generator 1 | 1.2327 | 1.2198 |
12 kV AC bus | 71.9406 | 27.3848 | Diesel generator 2 | 1.2324 | 1.2196 |
Local communication | 71.9406 | 27.3848 | Wind turbine | 1.0320 | 1.0275 |
Cross-system communication | 71.9406 | 27.3848 | PV array | 1.0254 | 1.0225 |
PV array | 71.6585 | 64.4566 | IEM | 1.0067 | 1.0024 |
Wind turbine | 56.4163 | 49.7676 | Local communication | 1.0066 | 1.0024 |
120 V AC bus 1 | 37.7093 | 14.0423 | 12 kV AC bus | 1.0065 | 1.0024 |
400 V DC bus 1 | 33.9686 | 16.6568 | Cross-system communication | 1.0061 | 1.0022 |
Circuit breaker 1 | 22.7390 | 10.7413 | 120 V AC bus 1 | 1.0031 | 1.0011 |
Diesel generator 2 | 21.9213 | 21.2917 | 120 V AC bus 2 | 1.0014 | 1.0006 |
Diesel generator 1 | 21.7725 | 21.2584 | 120 V AC bus 3 | 1.0013 | 1.0005 |
120 V AC bus 3 | 19.6982 | 7.8285 | IFM | 1.0003 | 1.0001 |
120 V AC bus 2 | 16.5330 | 7.5141 | 400 V DC bus 1 | 1.0001 | 1.0000 |
IFM | 4.1946 | 1.8846 | Circuit breaker 1 | 1.0000 | 0.9962 |
Battery 1 | 2.6618 | 1.8156 | 400 V DC bus 3 | 1.0000 | 1.0000 |
IEM | Failure rate (failures/hour) | ||
---|---|---|---|
1.00 × 10‒8 | 1.00 × 10‒7 | 1.00 × 10‒6 | |
Unreliability of Load 1 | 4.50 × 10‒4 | 1.24 × 10‒3 | 9.13 × 10‒3 |
Unreliability of Load 8 | 1.41 × 10‒1 | 1.42 × 10‒1 | 1.49 × 10‒1 |
Communication | Failure rate (failures/hour) | ||
1.00 × 10‒8 | 1.00 × 10‒7 | 1.00 × 10‒6 | |
Unreliability of Load 1 | 4.50 × 10‒4 | 2.06 × 10‒3 | 1.79 × 10‒2 |
Unreliability of Load 8 | 1.41 × 10‒1 | 1.42 × 10‒1 | 1.55 × 10‒1 |
IFM | Failure rate (failures/hour) | ||
1.00 × 10‒8 | 1.00 × 10‒7 | 1.00 × 10‒6 | |
Unreliability of Load 1 | 4.50 × 10‒4 | 4.55 × 10‒4 | 8.42 × 10‒4 |
Unreliability of Load 8 | 1.41 × 10‒1 | 1.41 × 10‒1 | 1.42 × 10‒1 |
4. Conclusions
Acknowledgments
Author Contributions
Nomenclature
i | Identifier and the priority of load in the local smart grid framework |
NL | The number of all loads in the local smart grid framework |
j | Identifier of current simulation |
n | The number of basic events |
N | Total number of times of simulation |
k | Identifier of component in the local smart grid framework |
fp | Identifier of output flow path |
Nfp | The number of all output flow paths |
fpi | Identifier of DG connected to output flow path fp |
fp_N | The number of all DGs connected to output flow path fp |
Ki | Capacity of load i |
K | Total capacity of the local smart grid framework |
Pi | Priority factor of load i |
LOLP | Loss of load probability measure of the local smart grid framework |
LOLP* | Modified Loss of load probability measure of the local smart grid framework |
Risk achievement worth for component k corresponding to load i | |
Risk reduction worth for component k corresponding to load i | |
NRAWk | Power system risk achievement worth of component k |
NRRWk | Power system risk reduction worth of component k |
Modified smart grid risk achievement worth of component k | |
Modified smart grid reduction worth of component k | |
QGDi | Failure probability of power delivery to load i |
QGDi(QK = 1) | Failure probability of power delivery to load i when unreliability of component k is set to 1 |
QGDi(QK = 0) | Failure probability of power delivery to load i when unreliability of component k is set to 0 |
tk,j | Fault time of component k in the jth simulation |
tGDi,j | Occurrence time of the top event of load i in the jth simulation |
OFPfp(t) | State function for output flow path fp |
POWtot(t) | Total power generated by the DGs at time t |
POWfpi(t) | Power function for DG fpi connected to output flow path fp |
powDi(t) | Real-time power demand of load i |
powerfpi(t) | Real-time power generated of DG fpi |
X(t) | State variable of the system |
bk,j(t) | State function for basic event of component k in the jth simulation |
ϕ[X(t)] | Structure function of the fault tree |
Conflicts of Interest
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Song, G.; Chen, H.; Guo, B. A Layered Fault Tree Model for Reliability Evaluation of Smart Grids. Energies 2014, 7, 4835-4857. https://doi.org/10.3390/en7084835
Song G, Chen H, Guo B. A Layered Fault Tree Model for Reliability Evaluation of Smart Grids. Energies. 2014; 7(8):4835-4857. https://doi.org/10.3390/en7084835
Chicago/Turabian StyleSong, Guopeng, Hao Chen, and Bo Guo. 2014. "A Layered Fault Tree Model for Reliability Evaluation of Smart Grids" Energies 7, no. 8: 4835-4857. https://doi.org/10.3390/en7084835