Detailed DC system design

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.

DC load evaluation

#	Load	Quantity	Watts	Total watts	Duty cycle	Hours per day	Days per week	Average daily DC watt-hours
1	Cree 5 W LED	6	5 W	30 W	1	3 hours	7 days	90 Wh
2	Retekess radio	6 W	1	6 W	1	5 hours	7 days	30 Wh
3	Samsung cell phone	2	10 W	20 W	1	1 hour	7 days	20 Wh
Total average daily DC watt-hours								140 Wh

• Load: The make and model or type of load.
• Quantity: The number of of that 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
• Total average daily DC watt-hours = sum of Average daily DC watt-hours for all loads

Average daily watt-hours required

Average daily watt-hours required	= Total average daily DC watt-hours + Total average daily AC watt-hours
Average daily watt-hours required	= 140 Wh

Weather and solar resource evaluation

Maximum ambient temperature = 23°C
Minimum ambient temperature = 2°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

Month	Average daily insolation	Average daily Watt-hours required	Ratio
January	193.85 kWh/m² / 30 = 6.46 kWh/m²	140 Wh	21.67
February	162.2 kWh/m² / 30 = 5.41 kWh/m²	140 Wh	25.90
March	(179.81 kWh/m² / 30 = 6.00 kWh/m²	140 Wh	23.36
April	174.98 kWh/m² / 30 = 5.83 kWh/m²	140 Wh	24.00
May	214.31 kWh/m² / 30 = 7.14 kWh/m²	140 Wh	19.60
June	200.05 kWh/m² / 30 = 6.67 kWh/m²	140 Wh	20.10
July	210.35 kWh/m² / 30 = 7.01 kWh/m²	140 Wh	19.97
August	229.96 kWh/m² / 30 = 7.67 kWh/m²	140 Wh	18.26
September	126.87 kWh/m² / 30 = 4.23 kWh/m²	140 Wh	33.10
October	214.82 kWh/m² / 30 = 7.16 kWh/m²	140 Wh	19.55
November	212.91 kWh/m² / 30 = 7.10 kWh/m²	140 Wh	19.73
December	176.98 kWh/m² / 30 = 5.90 kWh/m²	140 Wh	23.73

• Month: The month of the year.
• Average daily insolation: Solar resource data from PVGIS.
• Average daily Watt-hours required from load evaluation.
• Ratio = Average daily Watt-hours required ÷ Average daily insolation

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

A flowchart depicting the primary inputs and outputs of the energy storage sizing and selection process.

The energy storage system is sized based upon the average daily energy requirements for the system and the design parameters. The first 5 steps of this process output a suggest Ah size for the energy storage system, but then it is necessary to determine a series and parallel configuration based upon the available battery voltages and sizes.

Step 1: Determine depth of discharge parameter For this project a depth of discharge of .4 (40%) is a good compromise.

• Depth of discharge = .4

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
10°C	1.19	1.08	1.11
0°C	1.39	1.20	1.25
-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 = 63 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
	= 63 Ah ÷ 75 Ah = .84
	= Round up to 1 × 75 Ah battery.

Step 7: Calculate final Ah capacity

Final Ah capacity	= Number of batteries in parallel (Step 7) × Chosen battery Ah rating
	= 1 battery in parallel × 75 Ah = 75Ah

Minimum PV source size

The size of the PV source, which is determined based upon the load evaluation and weather and solar resource evaluation will determine the necessary size of the charge controller. The charge controller must be selected at the same time as the PV source as the charge controller type - PWM or MPPT - will also determine the possible configurations of PV modules.

In this phase of the design process, more than in any other phase, it is necessary to explore different designs using PV module, series and parallel wiring configurations, and charge controllers in order to achieve the highest performance at the lowest cost possible. This phase may have to be performed several times.

An off-grid PV system that depends upon the PV as its single charging source requires an array that is sufficiently sized to be able to generate sufficient energy to both meet the energy needs of the users and to recharge the energy storage system under less than ideal conditions. Any sizing decisions should therefore lean towards an oversized PV source.

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
• PV source temperature loss parameter = -.48%/°C
• Mounting system temperature adder = 20°C for a pole mount

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: Determine charge controller type

A Pulse width modulation (PWM) charge controller is an good economical option for a small DC system.

Step 3: Charge controller efficiency parameter

• Pulse width modulation (PWM) charge controller efficiency: .99 (99% efficient)

Step 4: 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 5: Deteremine minimum size of the PV source

Minimum PV source size	= Average daily Watt-hours required ÷ Design insolation ÷ Total PV source loss parameter (Step 1) ÷ Charge controller efficiency parameter (Step 3) ÷ Energy storage efficiency parameter (Step 4)
	= 140 Wh ÷ 4.23 kWh/m² ÷ .76 ÷ .99 ÷ .85 = 51.75 W

PWM charge controller sizing and selection

This system will use a PWM charge controller. The charge controller and PV source must be sized together.

Step 1: Determine PV module power rating

This system will use 1 × 36-cell module per string. The minimum size was determined to be 51.75 W. We will proceed with an 80 W polycrystalline PV module.

Step 2: Determine proposed number of PV modules

This calculation will give a minimum number of PV modules. 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)
	= 51.75 W ÷ 80 W = .65.
	= 1 × 80 W module.

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 module × .76 × 4.23 kWh/m² × .99 × .85 = 216 Wh

Daily excess production in Ah	= (Proposed PV source low insolation production - Average daily Watt-hours required) ÷ System voltage parameter

Ah used at full depth of discharge	= Final Ah capacity × Depth of discharge parameter

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

If the time to reach full state of charge is less than 7 days, then the size of the PV source should be increased until it is below 7 days.

Step 4: Verify charging current

Lead acid batteries last longer and perform better when they are regularly recharged with a current in a certain range - typically between .05-.13 (5-13%) of their C/20 rating. If a system uses many loads during the day, this will limit the available charging current for the energy storage system and should be taken into account by increasing the PV source size. The maximum charging current for most lead acid batteries is between .13 (13%) and .2 (20%) of the C/20 rate. Most designs should have a charge rate between 5-10% - closer to 10% if the system is used heavily during the day. It is necessary to consult the manual or manufacturer for recommended maximum and minimum charging currents.

Minimum required charge current	= Final Ah capacity × .05

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 (Step 2) × Charge controller efficiency parameter × Module degradation parameter × Soiling loss parameter

Percentage of C/20 rate	= Available charging current ÷ Final Ah capacity

If the number of PV modules does not meet the recommendations outlined above, increasing the PV source in size should be considered.

Step 5: Final number of PV modules

A final number of modules should be chosen that can meet the requirements of Step 2, Step 3, and Step 4.

Step 6: Determine minimum current rating of charge controller

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.

Minimum current rating of charge controller	= Final number of PV modules (Step 5) × Isc rating of chosen module (Step 1) × Irradiance safety parameter

Step 7: Select a charge controller

The final chosen charge controller should:

1. Function at the system voltage.
2. Have a current rating that is larger than the minimum current rating (Step 6).

Step 8: Determine final PV source power rating

The total power rating of the PV source can be calculated by multiplying the power rating of the chosen PV module by the final number of PV modules (Step 5).

PV source power rating	= PV module power rating (Step 1) × Number of PV modules (Step 5)