following key components:

1. System Architecture and Design
   • A detailed block-level design of the DC microgrid is presented, consisting of a solar PV array, DC-DC converters, energy storage (battery bank), load centers, and a centralized control unit.
   • Load estimation methods based on rural household demand profiles are discussed.
2. Mathematical Modeling and Equations

   • PV Module Modeling: The solar panel is modeled using the single-diode equivalent circuit,

   • Energy Balance Equation:

   • Battery Sizing and State of Charge (SOC) Model:

   • Converter Efficiency Model: Used to account for losses in the DC-DC boost and buck converters.

3. Optimization of System Components
   • A multi-objective optimization approach is used to minimize cost and maximize reliability.
   • Techniques such as Linear Programming (LP) and Genetic Algorithms (GA) are applied to size PV capacity and battery storage optimally.
4. Simulation and Performance Analysis
   • The system is modeled in MATLAB/Simulink for dynamic simulations under varying solar irradiance and load conditions.
   • Performance metrics include Loss of Power Supply Probability (LPSP), battery autonomy, and system efficien

2.0 Equations:

• PV Module Modeling;

  

• Energy Balance Equation:

• Battery Sizing and State of Charge (SOC) Model:

  

• Converter Efficiency Model: Used to account for losses in the DC-DC boost and buck converters.

  

1. The high frequency switching loss is given by

   

2. Total power dissipation in the MOSFET (excluding the drive power) is expressed in..