Detailed DC system design

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Design will be completed in January 2021

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.

  • Photo of the home.

  • Location of the home.

DC 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

  • Retrieving PVGIS monthly insolation data.

  • Retrieving PVGIS monthly insolation data.

  • Retrieving PVGIS weather data.

  • Retrieving PVGIS weather data.

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

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

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 .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:[1]

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

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
  • 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 = Average daily Watt-hours required ÷ Design 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

There are two different charge controller types - pulse width modulation (PWM) and maximum power point tracking (MPPT) - each of which has advantages and disadvantages that are are detailed in Charge controller types. Two separate designs may be performed with each type of charge controller to determine the best system design. The current and voltage rating of the charge controller will be determined when in either PWM charge controller sizing and selection or MPPT charge controller sizing and selection.

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

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

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

During periods of poor weather or low solar resource, an off-grid PV system is designed to discharge the battery to a certain depth of discharge which can leave the energy storage system depleted. It is important that the energy storage system is brought back up to a full state of charge in short period of time or the cycle life of the batteries will be reduced. The PV array therefore must be sized to generate sufficient excess energy, while continuing to meet all of the power needs from the Load evaluation. OSSP recommends that the array be sufficiently sized to reach a full state of charge within a week or that the system incorporate a generator to ensure adequate charging.

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

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.[2] 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.[3] 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.

These calculations are performed with the Ah rating of the total energy storage system.

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

A single charge controller is the simplest and cheapest option, but for larger systems multiple charge controllers often are used in parallel. 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

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


Notes/references

  1. ↑ Trojan Battery Company - Battery Sizing Guidelines https://www.trojanbattery.com/pdf/TRJN0168_BattSizeGuideFL.pdf
  2. ↑ Trojan Battery Company - User's Guide https://www.trojanbattery.com/pdf/TrojanBattery_UsersGuide.pdf
  3. ↑ Rolls Battery - Battery User Manual https://rollsbattery.com/public/docs/user_manual/Rolls_Battery_Manual.pdf
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