1. Introduction

2. Core Concepts and Theoretical Foundations

2.1 Definition of System Reliability

• Mean Time Between Failures (MTBF): Expected operating time between consecutive failures, requiring ≥87600 hours (10 years) for critical applications.

• Failure Rate (λ): Number of failures per unit time, with a target of ≤1×10⁻⁶ failures/hour for core modules.

• Availability (A): Ratio of operational time to total time, demanding ≥99.99% (four nines) for grid-level systems.

2.2 System Composition and Failure Modes

2.3 Reliability Calculation Methods

• Series System Reliability: For subsystems in series (e.g., rectifier → battery → converter), the system reliability $R_{\text{sys}}={\prod }_{i=1}^n{R}_i$, where $R_i$ is the reliability of the i-th subsystem.

• Parallel System Reliability: For redundant subsystems (e.g., dual rectifier modules), the system reliability $R_{\text{sys}}=1-{\prod }_{i=1}^m(1-R_i)$, where m is the number of parallel units.

• FMEA (Failure Mode and Effects Analysis): Identifies critical failure points by evaluating the severity (S), occurrence (O), and detectability (D) of each failure mode, with a Risk Priority Number (RPN = S×O×D) used to prioritize improvements.

3. Reliability-Based Optimization Design Model

3.1 Objective Functions

1. Maximize System Reliability: Maximize MTBF and availability, with $\max R_{\text{sys}}(x_1,x_2,...,x_n)$, where $x_i$ represents design variables (e.g., number of redundant modules, component type).

2. Minimize Life-Cycle Cost (LCC): Include initial investment (component procurement, installation), operation cost (energy consumption, maintenance), and failure cost (downtime losses, repair), with $\min \text{LCC}(x_1,x_2,...,x_n)$.

3. Meet Performance Constraints: Ensure output voltage stability, ripple coefficient, load capacity, and environmental adaptability meet industry standards (e.g., IEC 60439, GB/T 19826).

3.2 Design Variables and Constraints

• Design Variables:

• Redundancy configuration (e.g., 1+1, 2+1 parallel redundancy for rectifier modules).

• Component selection (e.g., lithium-ion vs. lead-acid batteries, SiC vs. IGBT semiconductors).

• Structural parameters (e.g., battery capacity, converter switching frequency, heat dissipation area).

• Constraints:

• Electrical constraints: Output voltage error ≤±5%, maximum load current ≥120% of rated current.

• Physical constraints: Volume ≤0.5m³, weight ≤50kg, operating temperature range -20°C~+60°C.

• Reliability constraints: MTBF ≥87600 hours, availability ≥99.99%.

3.3 Solution Algorithm

1. Initialization: Generate a set of design schemes (populations) randomly, including redundancy configuration, component type, and structural parameters.

2. Fitness Evaluation: Calculate reliability (via series-parallel model), LCC, and performance indicators for each scheme.

3. Non-dominated Sorting: Rank schemes based on Pareto dominance (a scheme is non-dominated if no other scheme performs better in all objectives).

4. Selection, Crossover, Mutation: Simulate biological evolution to generate new schemes, retaining optimal individuals.

5. Termination: Stop when the algorithm converges (e.g., no significant improvement in Pareto front for 50 generations), outputting the optimal design scheme set.

4. Case Study and Validation

4.1 Case Background

• Rated output current: 100A.

• Operating temperature: -10°C~+50°C.

• Reliability target: MTBF ≥100,000 hours, availability ≥99.99%.

• Cost constraint: LCC ≤$50,000 over 10 years.

4.2 Optimization Design Process

1. Design Variables:

• Rectifier module redundancy: 1+1, 2+1, 3+1.

• Battery type: Lead-acid (cycle life 1200 times, cost $800/kWh) vs. lithium-ion (cycle life 3000 times, cost $1200/kWh).

• Battery capacity: 50Ah, 100Ah, 150Ah.

2. Model Calculation:

• Reliability: Calculated using the series-parallel model (e.g., 2+1 rectifier redundancy → $R_{\text{rectifier}}=1-(1-R_{\text{single}}{)}^3$).

• LCC: Initial cost (modules + batteries) + annual maintenance cost ($500) + failure cost ($10,000/failure).

3. Optimization Result:

   The optimal scheme selected from the Pareto front is:

• Rectifier redundancy: 2+1 (MTBF = 120,000 hours).

• Battery type: Lithium-ion, capacity 100Ah (cycle life meets 10-year demand).

• Converter: SiC-based (lower failure rate, higher efficiency).

4.3 Performance Validation

• Reliability: MTBF = 125,600 hours, availability = 99.992%, exceeding the target.

• Cost: LCC = $48,200 over 10 years, within the constraint.

• Performance: Output voltage error = ±2.3%, ripple coefficient = 0.3%, load capacity = 125A, meeting industry standards.

5. Key Optimization Strategies

5.1 Redundancy Configuration Optimization

• N+1 Redundancy: For critical subsystems (e.g., rectifier, converter), adopt N+1 parallel redundancy to ensure system operation even if one module fails. For example, 2+1 redundancy for rectifiers reduces the subsystem failure rate by 66.7% compared to 1+0 (no redundancy).

• Hot Standby: Redundant modules operate in hot standby mode, switching within 10ms to avoid power interruption.

5.2 Component Selection Optimization

• High-Reliability Components: Select components with low failure rates (e.g., SiC semiconductors with λ=0.5×10⁻⁶ failures/hour vs. IGBT λ=2×10⁻⁶ failures/hour).

• Life-Cycle Cost Balance: Lithium-ion batteries have higher initial costs but lower maintenance and replacement costs than lead-acid batteries, making them more cost-effective for long-term operation (≥8 years).

5.3 Structural and Thermal Design Optimization

• Heat Dissipation Optimization: Increase heat sink area and adopt forced air cooling to reduce component temperature (each 10°C decrease in temperature reduces semiconductor failure rate by ~50%).

• Battery Management System (BMS): Integrate BMS to monitor state of charge (SOC) and state of health (SOH), preventing overcharging/discharging and extending battery life.

6. Conclusion and Future Directions

1. Digital Twin Integration: Establish a digital twin of the DC power supply system to simulate real-time reliability and optimize design parameters dynamically.

2. Prognostics and Health Management (PHM): Integrate PHM technology to predict component failures and adjust optimization strategies proactively.

3. Multi-Energy Complementation: Combine DC power supply systems with renewable energy (e.g., solar PV) and energy storage to improve reliability and sustainability.