An off-grid PV system has a constant daily energy demand of 100[Wh] . The system is equipped with two batteries of 12[V] and 70[Ah] . After two years of use, the capacity of the battery bank is reduced to 90% of the original value. Moreover, the minimum allowable SoC for the battery bank is 20% . Using this information answer the following questions:
A) What was the autonomy of the system when the batteries were new? Give the answer in [days] and with one decimal place.
B) What is the autonomy of the system after two years? Give the answer in [days] and with one decimal place.
To answer these questions, we need to calculate the autonomy of the system both when the batteries were new and after two years. Autonomy is defined as the number of days a system can operate without any input from the PV system.
First, let's calculate the autonomy when the batteries were new (question A):
Step 1: Calculate the total energy capacity of the battery bank.
The energy capacity of a battery bank can be obtained by multiplying the battery bank's voltage (V) by its ampere-hour capacity (Ah). Therefore, the energy capacity of the battery bank is:
Energy Capacity = Voltage (V) × Ampere-hour Capacity (Ah)
Given:
Voltage (V) = 12V
Ampere-hour Capacity (Ah) = 70Ah
Energy Capacity = 12V × 70Ah = 840Wh
Step 2: Calculate the usable energy capacity of the battery bank.
The usable energy capacity is the initial energy capacity reduced by 10% (as the question states the capacity after two years is reduced to 90% of the original value). Therefore:
Usable Energy Capacity = Energy Capacity × 90% = 840Wh × 0.9 = 756Wh
Step 3: Calculate the autonomy.
Autonomy = Usable Energy Capacity / Daily Energy Demand
Given:
Daily Energy Demand = 100Wh
Autonomy = 756Wh / 100Wh = 7.56 days
Therefore, the autonomy of the system when the batteries were new is approximately 7.6 days.
Now let's calculate the autonomy after two years (question B):
Step 1: Calculate the usable energy capacity after two years.
The usable energy capacity after two years is reduced to 90% of the original capacity. Therefore:
Usable Energy Capacity = Usable Energy Capacity (when new) × 90% = 756Wh × 0.9 = 680.4Wh
Step 2: Calculate the autonomy.
Autonomy = Usable Energy Capacity / Daily Energy Demand
Given:
Daily Energy Demand = 100Wh
Autonomy = 680.4Wh / 100Wh = 6.8 days
Therefore, the autonomy of the system after two years is approximately 6.8 days.