(1) Define the following fault types and provide an example of how each fault could occur in a microgrid: overcurrent, overvoltage, undervoltage, under-frequency, and high impedance faults. Microgrids introduce unique protection challenges due to the presence of distributed energy resources (DERs). Discuss with a diagram of a grid-connected microgrid how bidirectional power flow and varying fault current magnitudes impact the reliability of conventional overcurrent relays (OCRs). (2) Given a household with an average daily electricity consumption of \( 18-\mathrm{kWh} \) and a \( 6-\mathrm{kW} \) solar PV system that produces 26 kWh per day, determine the required battery capacity if \( 50 \% \) of the consumption occurs during daylight hours considering \( 90 \% \) depth of discharge (DoD) and \( 85 \% \) round-trip efficiency. Discuss the factors that influence battery sizing decisions.