Abstract: The reliability evaluation of hybrid energy storage systems (HESS) with different topologies. A reliability evaluation method based on Markov chain and Bayesian network is proposed. Firstly, the working mechanisms of hybrid energy storage system with five different topologies, the basic principles of Markov chain, and Bayesian network are introduced. Subsequently, reliability models for various topological structures of hybrid energy storage systems are established using Markov chain, and the failure rates of these hybrid energy storage systems are calculated using Bayesian network. Finally, by comparing the failure rates, a reliability assessment is conducted, revealing that the cascade structure with the battery in the middle and the parallel structure HESS exhibit the highest reliability.
1. Introduction
Energy storage components generally exhibit an inverse relationship between energy density and power density. Specifically, as energy density increases, power density decreases. For instance, power batteries are typically characterized by high energy density but low power density, whereas supercapacitors have high power density but low energy density. To address this contradiction and meet the dual demands of high energy density and high power density in pure electric vehicles, power batteries and supercapacitors can be combined through power converters. The combination of power batteries, supercapacitors, and power converters is defined as a Hybrid Energy Storage System (HESS).
Due to variations in the number and placement of power converters, the topological structures of hybrid energy storage system vary. Currently, scholars have conducted comparative studies on the complexity, maximum power output capacity, and control flexibility of hybrid energy storage system with different topologies. However, there is limited research on the reliability assessment of hybrid energy storage system. High reliability is a critical issue in the design and manufacture of vehicular HESS. Therefore, comparative research on the reliability assessment of different topological structures of hybrid energy storage system is of great significance.
2. Basic Principles of Markov Chain and Bayesian Network
2.1 State Transition of Markov Chain
A Markov chain can clearly describe the transition process between different states and matches the transition probabilities after each state change.
2.2 Bayesian Network
The advantage of a Bayesian network lies in its ability to simulate human reasoning processes and accurately calculate the probabilities of conditional events.
When combining Markov chain and Bayesian network for reliability assessment of different topological structures of hybrid energy storage system, the Markov chain is used to describe various failure states of the hybrid energy storage system, while the Bayesian network is responsible for reasoning and simplifying the ultimate conditions leading to failure, and accurately calculating the probability of failure occurrence, thus enabling more effective reliability assessment.
3. Reliability Evaluation of Hybrid Energy Storage System with Different Topologies
Five different topological structures of hybrid energy storage system are introduced, but due to fundamental defects, the passive structure hybrid energy storage system has no practical application value in the field of pure electric vehicles and will not be considered for reliability modeling in this paper.
3.1 Reliability Evaluation of Cascade Structure Hybrid Energy Storage System with Supercapacitor in the Middle
Table 1: Markov Chain State Transition Diagram for Cascade Structure Hybrid Energy Storage System with Supercapacitor in the Middle
| State | Description | Transition Rate |
|---|---|---|
| 1 | Initial state of all modules operating | – |
| 2 | Supercapacitor failure, hybrid energy storage system operates with reduced performance | λUC |
| 3 | Failure of battery, DC/DC converter 1, or DC/DC converter 2, system shutdown | λbatt, λBC1, λBC2 |
The failure rate P1 of this structure can be represented as:
P1=1−(1−λbatt)(1−λBC1)(1−λBC2)
3.2 Reliability Evaluation of Cascade Structure Hybrid Energy Storage System with Battery in the Middle
Similar to the previous section, the Markov chain state transition diagram and Bayesian network model are established for this structure.
3.3 Reliability Evaluation of Parallel Structure Hybrid Energy Storage System
Table 2: Markov Chain State Transition Diagram for Parallel Structure Hybrid Energy Storage System
| State | Description | Transition Rate |
|---|---|---|
| 1 | Initial state (normal state) | – |
| 2 | Failure of supercapacitor or DC/DC converter 1, hybrid energy storage system operates non-optimally | λUC, λBC1 |
| 3 | Failure of battery or DC/DC converter 2, system shutdown | λbatt, λBC2 |
The failure rate P3 of this structure can be derived similarly.
3.4 Reliability Evaluation of Multi-Input Converter Structure Hybrid Energy Storage System
Table 3: Markov Chain State Transition Diagram for Multi-Input Converter Structure Hybrid Energy Storage System
| State | Description | Transition Rate |
|---|---|---|
| 1 | Initial state | – |
| 2 | Supercapacitor failure, hybrid energy storage system operates normally | λUC |
| 3 | Failure of multi-input converter, system shutdown | λMIC |
The failure rate P4 for this structure is:
P4=1−(1−λbatt)(1−λMIC)
4. Reliability Comparison of Hybrid Energy Storage System with Different Topologies
For reasonable comparison, it is assumed that the failure rates of the same DC/DC converters in different topological structures of hybrid energy storage system are identical.
Based on the equations derived for the failure rates of the four different structural hybrid energy storage system, and considering that the failure rate of each module in the hybrid energy storage systemS is generally less than 50% for practical applications, the following comparison can be made:
P2=P3<P4<P1
Table 1: Reliability Ranking of Hybrid Energy Storage System with Different Topologies
| Topological Structure of Hybrid Energy Storage System | Corresponding Diagram | Failure Rate | Reliability Ranking |
|---|---|---|---|
| Cascade Structure with Supercapacitor in the Middle | Table 1, etc. | P1 | 4 |
| Cascade Structure with Battery in the Middle | Table 2, etc. | P2/P3 | 1 |
| Parallel Structure | Table 3, etc. | P3 | 1 |
| Multi-Input Converter Structure | Table 4, etc. | P4 | 3 |
5. Conclusion
This paper proposes a reliability evaluation method for vehicular hybrid energy storage systems with different topological structures based on Markov chain and Bayesian network. By briefly analyzing the working mechanisms of five different structural vehicular hybrid energy storage systems and evaluating their reliability, the following conclusions are drawn:
- The cascade structure hybrid energy storage system with the battery in the middle and the parallel structure hybrid energy storage system exhibit the highest reliability, followed by the multi-input converter structure hybrid energy storage system.
- The cascade structure hybrid energy storage system with the supercapacitor in the middle has the lowest reliability.
The reliability of different topological structures of hybrid energy storage system from a theoretical perspective. However, in actual circuits, there are other factors that affect reliability, such as voltage and current stress of different devices. Future work will involve analyzing a large number of actual circuits and conducting further assessments on the reliability of the top two-ranked topological structures after obtaining experimental data.