Detailed DC system design

Design will be completed in January 2021

Physical evaluation

Location: Pampachiri, Apurimac, Peru
GPS coordinates: 14°11'37.65"S 73°32'31.73"W
Altitude: 3378m
Description: A two story adobe home in the Peruvian Andes with only DC power needs.

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  Photo of the home.

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  Location of the home.

Load evaluation

Step 1: Fill out DC load chart

						April - September			October - March
#	Load	Quantity	Watts	Total watts	Duty cycle	Hours per day	Days per week	Average daily DC watt-hours	Hours per day	Days per week	Average daily DC watt-hours
1	5 W LED	6	5 W	30 W	1	3 hours	7 days	90 Wh	3 hours	7 days	90 Wh
2	Radio	6 W	1	6 W	1	5 hours	7 days	30 Wh	5 hours	7 days	30 Wh
3	Cell phone	10 W	2	29 W	1	1 hours	7 days	20 Wh	1 hours	7 days	20 Wh

• Load: The make and model or type of load.
• Quantity: The number of the particular load.
• Watts: The power rating in watts of the load.
• Total watts = Quantity × Watts
• Duty cycle = Rated or estimated duty cycle for the load. If the load has no duty cycle a value of 1 should be used. A load with a duty cycle of 20% would be inputted as .2
• Hours per day: The maximum number of hours the load(s) will be operated per day. If the load has a duty cycle 24 hours should be used.
• Days per week: The maximum number of days the load(s) will be operated per week.
• Average daily DC watt-hours = Total watts × Duty cycle × Hours per day × Days per week ÷ 7 days

Step 2: Determine DC energy demand

Total average daily DC watt-hours (April - September)	= sum of Average daily DC watt-hours for all loads for April - September
	= 140 Wh

Total average daily DC watt-hours (October - March)	= sum of Average daily DC watt-hours for all loads for October - March
	= 140 Wh

Total average daily energy demand

The total energy demand for the system is the added Average daily DC-watt hours and Average daily AC watt-hours for each time period.

Average daily watt-hours required (April - September)	= Total average daily DC watt-hours (April - October) + Total average daily AC watt-hours (April - September)
	= 140 Wh

Average daily watt-hours required (April - September)	= Total average daily DC watt-hours (October - March) + Total average daily AC watt-hours (October - March)
	= 140 Wh

Weather and solar resource evaluation

Maximum ambient temperature = 23°C
Minimum ambient temperature = 2°C
Maximum indoor temperature = 20°C
Minimum indoor temperature = 10°C

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  Retrieving PVGIS monthly insolation data.

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  Retrieving PVGIS monthly insolation data.

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  Retrieving PVGIS weather data.

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  Retrieving PVGIS weather data.

Load and solar resource comparison

Step 1: Determine monthly ratio of energy demand to solar resource

Month	Average monthly insolation	Total average daily energy demand	Ratio
January	193.85 kWh/m²	140 Wh	.722
February	162.2 kWh/m²	140 Wh	.86
March	179.81 kWh/m²	140 Wh	.78
April	174.98 kWh/m²	140 Wh	.8
May	214.31 kWh/m²	140 Wh	.65
June	200.05 kWh/m²	140 Wh	.7
July	210.35 kWh/m²	140 Wh	.67
August	229.96 kWh/m²	140 Wh	.61
September	126.87 kWh/m²	140 Wh	1.1
October	214.82 kWh/m²	140 Wh	.65
November	212.91 kWh/m²	140 Wh	.66
December	176.98 kWh/m²	140 Wh	.79

• Month: The month of the year.
• Average monthly insolation: Solar resource data obtained for the location from Weather and solar resource data sources.
• Total average daily energy demand for the month from the load evaluation.
• Ratio = Total average daily energy demand ÷ Average monthly insolation

Step 2: Determine design values

Design daily insolation	= Average monthly insolation from month with the highest ratio ÷ 30
	= 126.87 kWh/m² ÷ 30 = 4.23 kWh/m²

Design daily watt-hours required	= Total average daily energy demand from month with the highest ratio
	= 140 Wh

Design parameters

System voltage parameter = 12 V

• The system, based upon the load evaluation, will be relatively small. A 12 V system makes the most sense.

Irradiance safety parameter = 1.25

• The irradiance safety parameter is always the same.

Continuous duty safety parameter = 1.25

• The continuous duty safety parameter is always the same.

Low voltage disconnect parameter = 11.5 V

• A simple charge controller with a pre-programmed low voltage disconnect will be used.

Energy storage sizing and selection

Step 1: Determine depth of discharge parameter
For this project a depth of discharge of .5 (40%) is a good compromise.

• Depth of discharge = .5

Step 2: Determine days of autonomy parameter
The home is used daily and providing lighting is very important, but at the same time the budget for the project is limited. The users are willing to adjust their consumption during periods of poor weather according to the state of charge of the energy storage system.

• Days of autonomy = 2

Step 3: Determine battery temperature correction factor
The minimum indoor temperature was determined to be 10°C. An AGM battery will be used to avoid regular maintenance.

• Battery temperature correction factor = 1.08

Correction factors for various battery types:

Temperature	FLA	AGM	Gel
25°C	1.00	1.00	1.00
20°C	1.06	1.03	1.04
15°C	1.13	1.05	1.07
10°C	1.19	1.08	1.11
5°C	1.29	1.14	1.18
0°C	1.39	1.20	1.25
-5°C	1.55	1.28	1.34
-10°C	1.70	1.35	1.42

Step 4: Calculate total Ah required

Total Ah required	= Average daily Watt-hours required ÷ System voltage parameter × Battery temperature correction factor (step 3) × Days of autonomy parameter (Step 2) ÷ Depth of discharge parameter (Step 1)
	= 140 Wh ÷ 12 V × 1.08 × 2 days ÷ .4 = 43 Ah

Step 5: Calculate number of batteries in series
A 12 V battery is ideal for a system of this size.

Batteries in series	= System voltage parameter ÷ Chosen battery voltage
	= 12 V ÷ 12 V
	= 1 × 12 V battery is sufficient

Step 6: Calculate number of batteries in parallel
In Peru 12 V AGM batteries are widely available in 40 Ah, 55 Ah and 75 Ah sizes. 55 Ah is too small, so a 75 Ah battery will have to be used.

Batteries in parallel	= Total Ah required (step 4) ÷ Chosen battery Ah rating
	= 43 Ah ÷ 55 Ah = .78
	= Round up to 1 × 55 Ah battery.

https://www.mkbattery.com/application/files/2715/6158/6466/8A22NF-DEKA_Spec_Sheet.pdf

Step 7: Calculate final Ah capacity

Final Ah capacity	= Number of batteries in parallel (Step 7) × Chosen battery Ah rating
	= 1 battery in parallel × 55 Ah = 55Ah

Minimum PV source size

Step 1: Deteremine PV source loss parameters

The PV module(s) will be mounted on a pole mount system.

• Module degradation parameter = .94
• Shading loss parameter = .95
• Soiling loss parameter = .97
• Wiring loss parameter = .96
• Module mismatch parameter = 1
• Mounting system temperature adder = 20°C for a pole mount
• PV source temperature loss parameter = -.48%/°C

PV source temperature loss parameter	= 1 + (Maximum ambient temperature + Mounting system temperature adder - 25°C) x Temperature coefficient of max power %/°C ÷ 100
	= 1 + (23°C + 20°C - 25°C) x -.48%/°C ÷ 100 = .91

Total PV source loss parameter	= Module degradation parameter × Shading loss parameter × Soiling loss parameter × Wiring loss parameter × Module mismatch parameter × PV source temperature loss parameter
	= .94 × .95 × .97 × .96 × 1 × .91 = .76

Step 2: Charge controller efficiency parameter

All charge controllers lose a certain percentage of all energy that is produced as heat as it is transferred to the energy storage system and loads. For both PWM and MPPT charge controllers a value of .98 (98% efficient) can be used.

Step 3: Energy storage efficiency parameter

The system will use an AGM battery, which is a VRLA battery.

• Valve-regulated lead acid (VRLA) battery efficiency = .85 (85% efficient)

Step 4: Deteremine minimum size of the PV source

Minimum PV source size	= Design daily watt-hours required ÷ Design daily insolation ÷ Total PV source loss parameter (Step 1) ÷ Charge controller efficiency parameter (Step 2) ÷ Energy storage efficiency parameter (Step 3)
	= 140 Wh ÷ 4.23 kWh/m² ÷ .76 ÷ .98 ÷ .85 = 52 W

Step 5: Determine charge controller type

A PWM charge controller is a reliable, low-cost option for a small system like this.

PWM charge controller sizing and selection

Step 1: Determine PV module power rating

The chosen System voltage limits the choices of modules and configurations that are possible with a PWM charge controller. A 12 volt system requires 1 ×36-cell module per string. The minimum size was determined to be 52 W. A 80 W polycrystalline PV module will be used for the design.

PV module power rating	= 80 W

Number of modules in series	= 1 module

Step 2: Determine proposed module configuration

This calculation will give a minimum number of PV modules - the result should always be rounded up. Different modules sizes and configurations can be explored to find the optimal design.

Minimum number of PV modules	= Minimum PV source size ÷ PV module power rating (Step 1)
	= 52 W ÷ 80 W = .65
	= 1 × 80 W module.

Minimum number of modules in parallel	= Minimum number of PV modules ÷ Number of modules in series (Step 1)
	= 1 ÷ 1 = 1

Step 3: Verify excess production

Proposed PV source low insolation production	= PV module power rating (Step 1) × Minimum number of PV modules (Step 2) × Total PV source loss parameter × Design insolation × Charge controller efficiency parameter × Energy storage efficiency parameter
	= 80 W × 1 × .76 × 4.23 kWh/m² × .98 × .85 = 214 Wh

Daily excess production in Ah	= (Proposed PV source low insolation production - Average daily watt-hours required) ÷ System voltage parameter
	= (214 Wh - 140 Wh) ÷ 12 volts = 6.2 Ah

Ah used at full depth of discharge	= Final Ah capacity × Depth of discharge parameter
	= 55Ah × .5 = 27.5 Ah

Time to reach full state of charge	= Ah used at full depth of discharge ÷ Daily excess production in Ah
	= 27.5 Ah ÷ 6.2 Ah = 4.4 days

The battery will be able to reach full state of charge while using loads in 4.4 days, which is less than the maximum of 7 days. The design is okay.

Step 4: Verify charging current

This system will use an AGM battery, so its charge current should be between .05 (5%) and .2 (20%) of its C/20 rating.

Minimum required charge current	= Final Ah capacity × .05
	= 55 Ah × .05 = 2.75 A

It is necessary to check the minimum required charge current against the available charge current from the proposed PV source power rating.

Available charging current	= Maximum power current (Imp) × Minimum number of PV modules in parallel
	= 4.4 A × 1 = 4.4 A

Percentage of C/20 rate	= Available charging current ÷ Final Ah capacity
	= 4.4 A ÷ 55 Ah = .08

The PV source can supply .08 (8%) of the C/20 current rating of the energy storage system, which is more than .05 (5%) and less than .2 (20%). The PV source configuration is okay.

Step 5: Determine final number of PV modules

Determine a final number of modules and a series/parallel configuration that can meet the requirements of Step 1, Step 2, Step 3, and Step 4.

Final number of PV modules	= 1

Final number of PV modules in series	= 1

Final number of PV modules in parallel	= 1

Step 6: Total PV source current

This calculation will give a minimum current rating to use as a basis for selecting the charge controller. The Isc rating of the PV module can be found on its specifications sheet.

Total PV source current	= Final number of PV modules (Step 5) × Isc rating of chosen module (Step 1) × Irradiance safety parameter
	= 1 × 4.85 A × 1.25 = 6.1 A

Step 7: Select a charge controller

The final chosen charge controller should:

1. Function at the system voltage.
2. The charge controller(s) should have a total current rating that is larger than the minimum current rating (Step 6).

The result of the following equation should always be rounded up.

Number of charge controllers	= Total PV source current (Step 6) ÷ Chosen charge controller current rating
	= 6.1 A ÷ 10 A = .61 = 1 (rounded up to 1 charge controller)

Step 8: Determine final PV source power rating

PV source power rating	= PV module power rating (Step 1) × Final number of PV modules in parallel (Step 5)
	= 80 W × 1 = 80 W