### Critical design analysis

A PV system cannot generate constant energy for the entire year, but a stand alone PV system should be able to supply loads during any month of the year, and since solar energy generation varies by month, a PV designer should take into account the critical design value for the PV system. For example, if the application requires more energy during the winter, where low insolation occurs, then the PV system should be sized to meet the load requirement of that specific month or season.

#### Critical design month:

When the PV system needs to meet different load requirements throughout the year, the month with the highest design ratio is referred to as the critical design month. It is taken into account the worst-case scenarios associated with the lowest insolation and highest load demand. We can analyze this design ratio at three tilt angles: Lattitude, Lattitude +15, and at Lattitude -15 degrees. As we said the highest ratio value will be the critical ratio and the month associated with it is the critical desighn month.

#### Considerations:

Since array orientation has a significant impact on generated energy, the orientation should be chosen to match the critical design month. For example, if a 15° tile produces more energy during the critical design month when compared to a 25° tile, a designer should consider the 15° to optimize the system design as long as it doesn’t affect other design months' values. The cost associated with the lower tilt is another factor to take into account when selecting the racking materials.

### System design voltage

PV system DC voltage link is determined by the battery bank in stand-alone systems. As we discussed earlier, battery voltage can be 12V, 24V, or 48V. The voltage level changes depending on system size. As a rule of thumb, small PV systems are usually 12V systems, and larger systems are preferred to be 48V to handle more current. Some very large systems can be 120V, but that is considered a special case.

### System Availability

Since the solar irradiance is not always available, stand-alone systems need to be sized to meet load demand for the entire year, and that is expressed by **system availability,** which is the percentage of time that a stand-alone system can meet the load demand within the period of a year. It is determined by isolation and autonomy. **Autonomy** is the amount of time the load will be supplied from the battery bank by itself and is expressed in days. For example, 95% availability (3 days of autonomy assumung PSH is around 5.0 for that location) means that the system cannot meet the load demand for 5% of the time.

#### Note:

This figure illustrates that local sun hours for any location along with the desired sytem availability determine the system autonamy (in days). It is also important to know that the system availability depends on how critical the load application is. For critical loads, 99% is considered acceptable (10 days of autonomy if your average PSH is around 4.0)

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You can refer to chapter 9 in textbook to read more.

### Battery Sizing

After we learned in Lesson 3 about the main parameters of batteries, we established that batteries are used to store energy for later use. A stand-alone system is a perfect application.

#### Battery bank required output capacity

Considering the daily energy demand during critical design month and desired days of autonomy, the batteries should be able to provide energy to the load for all of the autonomy days.

#### Example:

The required battery capacity is calculated as follows:

$${B}_{out}=\frac{{E}_{crit}\times Ta}{{V}_{sdc}}$$ WhereB

_{out}is the required battery bank output capacity (Ah)

E

_{crit}is the required daily system energy demand for the critical month (Wh/day)

T

_{a}is the days of autonomy

V

_{sdc}is the nominal DC-system voltage

#### Battery bank rated capacity

As we established in Lesson 3, no battery can be completely discharged, and that is referred to as allowable DOD that a battery cannot exceed. It ranges from 20%-80% depending on battery type. Also, the operating temperature affects the available capacity the battery can deliver. Low temperature with high DOD can reduce the available battery capacity. Finally, the discharge rate is a main factor that determines the available battery capacity at certain temperature. This is expressed as a derating factor to the available capacity.

#### Example:

To put all factors together, we can write:

$${B}_{rated}=\frac{{B}_{out}}{DO{D}_{a}\times {C}_{t,rd}}$$Where:

B_{rated} is the battery bank rated capacity (Ah)

B_{out} is the required battery bank output capacity (Ah)

DOD_{a} is the allowable depth of discharge

C_{t,rd} is the temperature and discharge -rate derating factor

### Array sizing

A PV array should be sized to supply enough energy the meet the load demand at the critical design month while accounting for the system losses. This will ensure that system availability is high and the battery bank is charged.

#### Rated array output

Similar to grid-connected systems, array size can be determined using the peak sun hours of the location. However, since we have different DC system voltage depending on the system, it is more desirable to calculate the array current. Furthermore, off-grid systems include batteries. These batteries are not 100% efficient, so this should be taken into account.

#### Example:

$${I}_{array}=\frac{{E}_{crit}}{{\eta}_{batt}\times {V}_{sdc}\times {T}_{PSH}}$$Where:

I_{array} is the required maximum power current [A]

E_{crit} is the required daily system energy demand for the critical month (Wh/day)

η_{batt} is the battery efficiency

V_{sdc} is the nominal DC-system voltage

T_{PSH} is peak sun hours for the critical design month (hr/day)

There are factors that reduce the output of any PV array.

#### Note:

This section is thoroughly covered in Chapter 9 in the required reading textbook.