sizing - off grid photovoltaics for agricultural...

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2016Sizing - Off Grid Photovoltaics for Agricultural Systems

Practice Worksheets for Teachers

ContentReference Equations 2

I / Definitions ..........................................................................................................................................2

II / Main Equations ..........................................................................................................................................2

III / Supplementary Equations.........................................................................................................................................2

IV / NREL Solar Insolation Map for Oahu.........................................................................................................................2

V / The Engineering Design Process (EDP).......................................................................................................................3

VI / Worksheets ..........................................................................................................................................4

Example 1:...................................................................................................................................................................4

Example 2:...................................................................................................................................................................6

Example 3:...................................................................................................................................................................8

Example 4:.................................................................................................................................................................11

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In this manual, you will practice using the principles covered for sizing photovoltaic systems for hydroponic and aquaponics gardening systems.

VA Load:

Battery Capacity:

Battery Energy=AmpHours×Voltage

Apparent Power:

Continuous Load:

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Power Factor:

PV Size:

Battery Size:

Reference Equations

I / Definitions

II / Main Equations III / Supplementary Equations

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Continuous Load: Average power draw of system over each one-hour period of the day.PV Size: Total size in watts of the PV system.Sun Hours: A measure of solar irradiance. The solar insolation which a particular location

would receive if the sun were shining at its maximum value for a certain number of hours. *Refer to Section 4

Derating Factor: Estimated percent efficiency of the total system. Usually 70%.Battery Capacity: Total amount of energy able to be stored in the battery system. Usually

measured in watt hours.Energy: The ability to do work. Usually measured in joules or watt hours.Power: Rate of energy usage. Usually measured in watts.Actual Power: The rate of active power usage by a device.Apparent Power: The rate of active and reactive (imaginary) power usage by a device.Power Factor: The ratio of actual power to apparent power (device efficiency).

PV ¿≥ Continuous Load×24HoursSun Hours

× 1Derating Factor

Amps×Voltage=VA load rating

IV / NREL Solar Insolation Map for Oahu

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V / The Engineering Design Process (EDP)

The engineering design process developed by the Museum of Science, Boston is a five step process. Ask, Imagine, Plan, Create and Improve. In the Ask step students are encouraged to ask many questions to better understand the problem statement or design challenge. Imagine is where students brainstorm ideas that can solve the problem or design challenge. Next students are expected to Plan their idea from the Imagine step by listing out all the materials they need and also to put together a schedule to complete their design. Then the students will Create their design following their plan. Finally, the students will evaluate their design, analyze their results and can Improve their design based on their findings. This is also a good step to share and communicate with their other students.

Source: http://www.eie.org/overview/engineering-design-process

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VI / Worksheets

Example 1:System Usage: AquaponicsPump: On 100% of timePump nameplate load: 100 WattsSun Hours for Area: 5 hoursDerating factor: Assume 70% for most systems

1. Find the minimum size of PV system that will work for your system:a. What is the continuous load for the equipment?

Continuous load = ____________________________________

b. Calculate the minimum PV size for the system:

Minimum PV size = ____________________________________

2. Find the recommended capacity of the battery bank:

Recommended capacity of battery bank = ____________________________________

3. Battery options:

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PV ¿≥ Continuous Load×24HoursSun Hours

× 1Derating Factor

ݐݐݐݐݐݐݐݐݐݐݐݐݐݐ�� ܮ ൈ�Ψ ݐݐݐݐݐݐݐݐݐݐݐݐݐ ݐ ൌ�� ݏ� ݑ ݐݐݐݐݐݐݐݐݐݐݐݐݐݐݑ � �

You have batteries which are rated at 12 volts and 50 Amp hours each. What is the minimum number of these batteries that you would need to create this battery bank? (Hint: Amp hr * V = W)

Minimum number of cells = ____________________________________

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Example 2: A generous philanthropist has donated a hydroponic kit to your school. You open your kit to find this specification sheet:

The box containing the pump indicates that it is a 400 gallon per hour pump. Additionally, the kit contains a timer which will activate the pump for 15 minutes every hour for 24 hours a day. Your school is located in Waipahu, HI. Refer to the NREL solar insolation map for Oahu.

Summary:Pump: 400 GPHActive time on per hour: 15 minutesSun Hours for Area: 5 hoursDerating factor: Assume 70%

1. Find the minimum size of PV system and recommended battery bank for this kit:Show your reasoning and calculations:

a. What does the specification sheet say for the load rating of this pump?

Pump rated load = ____________________________________

b. What is the continuous load for this system?

Continuous load = ____________________________________

c. What is the minimum size of PV system to run this kit?

Minimum size PV = ____________________________________

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2. Calculate the recommended battery bank capacity for these conditions:

Recommended battery capacity = ____________________________________

3. Given battery cells rated at 6 volts and 35 amp hours, what is the minimum number of cells?


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Example 3:You wish to apply some ingenuity and convert the kit in example 2 into an aquaponics setup. Initially you use the engineering design process to determine that you can eliminate the timer and run the water pump 100% of the time through a biological filter to solve your problem. You move on to the planning stage so that you can create your system.

Calculate the new ratings based on these changes:

1. What is the continuous load for this system?

Continuous load = ____________________________________

2. What is the minimum size of PV system to run this kit?

Minimum size PV = ____________________________________





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Using the engineering design process, you ask yourself how you could improve upon this system. You ask what might allow you to use less energy. You imagine a system that runs the water pump just for 15 minute intervals every hour, and an added low power air pump which will run 100% of the time to maintain the fish. In planning for this solution you must recalculate the new system ratings to see if this is an improvement.

The sticker on the air pump says:

5. What is the apparent power of the air pump?

Apparent power = ____________________________________

6. What is the continuous load of the air pump? (Use apparent power for load)

Continuous load of air pump = ____________________________________

7. What is the continuous load of the water pump?

Continuous load of water pump = ____________________________________

8. What is the total continuous load of all parts in the system?

Total continuous load =____________________________________9

Super Duper Aquarium Air Pump

Output: 400 liters/hour

Power Factor: 0.6

Power: 5 Watts

a. What is the minimum size of PV system to run this kit?

Minimum size PV = ____________________________________b. Calculate the recommended battery bank capacity for these conditions:

Recommended battery capacity = ____________________________c. Given battery cells rated at 12 volts and 35 amp hours, what is the minimum number of cells?


9. Is this an improvement over the previous system?

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Example 4:You have two hydroponics systems and wish to power it using an off-grid photovoltaic system. You have a Kill-a-Watt measuring device which is able to measure the power of devices plugged into it so you decide to measure the power of each component to make an informed choice about system sizing.

Figure 1: Kill-a-Watt measuring device.

You take the following readings for each piece of powered equipment:

Device 1: 400 GPH water pump

Duty cycle: On for 15 minutes every hour

Actual power: 39 Watts

Voltage: 118 Volts

Power Factor: 0.6

Apparent Power: 65 VA

Device 2: 160 GPH water pump

Duty cycle: On for 15 minutes every hour


Voltage: 118 Volts

Power Factor: 0.65

Apparent Power: 15.4 VA

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Device 3: Circulation fan

Duty cycle: On all the time


Voltage: 118 Volts

Power Factor: 0.85

Apparent Power: 5.88 VA

1. What is the continuous load for this system?

Continuous load = ____________________________________

2. What is the minimum size of PV system to run this kit?

Minimum size PV = ____________________________________





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