Consider a 100[W] incandescent light bulb powered by an off-grid PV system. The bulb is on 14 hours per day, and the acceptable loss of load probability is 0.1 . What is the maximum number of hours per year that the system can fail to provide the power demanded by the load? Give the answer in [h⋅year−1] as an integer.
Oh, boy, let's shed some light on this! So, we have a 100W incandescent light bulb that runs for 14 hours a day. That means it consumes 100W x 14 hours = 1400 watt-hours per day. Now, to find the maximum number of hours per year that the system can fail, we need to figure out the annual energy demand.
1400 watt-hours per day multiplied by 365 days in a year gives us a total energy demand of 511,000 watt-hours per year. But wait, there's more! We need to take into account the acceptable loss of load probability, which is 0.1.
Since the acceptable loss of load probability is 0.1, we can multiply our annual energy demand by 0.1 to find out the maximum allowable loss. 511,000 watt-hours per year multiplied by 0.1 gives us 51,100 watt-hours.
Now, since we know the power capacity of the system is given in watts, we can convert our maximum allowable loss to watts for simplicity. So, 51,100 watt-hours divided by 365 days equals approximately 140 watts.
Now the moment of truth, drumroll, please... The maximum number of hours per year that the system can fail to provide the power demanded is 140 watts divided by 100 watts (the power of the light bulb), giving us 1.4 hours per year. But since we need our answer in hours per year as an integer, the maximum number of hours per year that the system can fail is 1 hour per year. Ta-da!
Just remember, this is all assuming that the sun doesn't pull any tricks on us and shine when we need it the most.
To find the maximum number of hours per year that the system can fail to provide the power demanded by the load, we can calculate the Loss of Load Hours (LOLH).
1. First, we need to calculate the total energy demand in watt-hours per day:
Energy demand = Power demand × Hours per day
Energy demand = 100 W × 14 hours = 1400 watt-hours per day
2. Next, we need to calculate the total energy demand in kilowatt-hours per year:
Energy demand per year = Energy demand × Days per year
Energy demand per year = 1400 watt-hours per day × 365 days = 511,000 watt-hours per year
3. Since the acceptable loss of load probability is 0.1, we can calculate the maximum LOLH:
LOLH = Energy demand per year × Loss of Load Probability
LOLH = 511,000 watt-hours per year × 0.1 = 51,100 watt-hours per year
4. Finally, to convert LOLH to hours per year, we divide by the power demand:
Hours per year = LOLH / Power demand
Hours per year = 51,100 watt-hours per year / 100 W = 511 hours per year
Therefore, the maximum number of hours per year that the system can fail to provide the power demanded by the load is 511 hours per year.
To calculate the maximum number of hours per year that the PV system can fail to provide the power demanded by the load, we first need to determine the total energy required by the light bulb in one day.
Since the bulb is powered for 14 hours per day, the energy consumed by the light bulb in one day can be calculated by multiplying its power (100 W) by the number of hours it is on (14 hours):
Energy consumed per day = Power × Time = 100 W × 14 hours = 1400 Wh or 1.4 kWh.
Next, we need to calculate the maximum energy that the PV system can generate in one day by considering the acceptable loss of load probability. The acceptable loss of load probability represents the probability of not meeting the energy demand of the load. In this case, it is given as 0.1 (10%).
To find the maximum energy generated by the PV system, we divide the energy consumed per day by the acceptable loss of load probability:
Maximum energy generated per day = Energy consumed per day / Acceptable loss of load probability = 1.4 kWh / 0.1 = 14 kWh.
Finally, we need to convert the maximum energy generated per day to hours per year. Assuming a year consists of 365 days, we can calculate the maximum energy generated in one year by multiplying the daily energy by 365:
Maximum energy generated per year = Maximum energy generated per day × 365 = 14 kWh/day × 365 days = 5110 kWh/year.
Since we want to find the maximum number of hours per year that the system can fail to provide power, we divide the maximum energy generated per year by the power of the light bulb:
Maximum hours per year = Maximum energy generated per year / Power = 5110 kWh / 0.1 kW = 51100 hours/year.
Therefore, the maximum number of hours per year that the off-grid PV system can fail to provide the power demanded by the load in this scenario is 51100 hours/year.