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

Wire, overcurrent protection, and disconnect sizing and selection

PV source circuit

If a wire size meets the current requirements determined in Phase 2 but fails to meet either the overcurrent protection requirements in Phase 3 or the voltage drop requirements in Phase 4, then the wire size will have to be increased.

Phase 1: Maximum circuit current

Maximum circuit current	= PV module Isc × Irradiance safety parameter
	= 4.85 A × 1.25 = 6.1 A

Phase 2: Wire ampacity

There will only be two current-carrying conductors in the conduit. The maximum ambient temperature is

The minimum wire size for a circuit can be determined by:

1. Determine the ambient temperature correction factor based upon the maximum ambient temperature for outdoor circuits and maximum indoor temperature for indoor circuits using the ambient temperature correction factor table. High temperatures increase the resistance of the wire and reduce its current carrying capacity.
   Note: Wires, nor conduit, should be located less than 2.25 cm from a roof surface in direct sunlight. This will increase temperatures as much as 33°C and can lead to the ampacity and temperature rating of wires to be exceeded.
2. Determine the conduit correction factor based upon the number of wires in the conduit using the conduit correction factor table. More than three wires - not including any wires related to the grounding system - in a conduit will reduce the current carrying capacity of each wires due to reduced cooling.
3. Determine the total wire correction parameter based upon the smaller of: the Ambient temperature correction multiplied by the conduit adjustment factor or .8 (a safety factor from the US National Electrical code).

Total wire correction parameter	= Smaller of (Ambient temperature correction factor (Step 1) × Conduit correction factor (Step 2)) or .8

4. Determine minimum wire ampacity. Divide the maximum circuit current by the total wire correction factor (Step 3)

Minimum wire ampacity	= Maximum circuit current ÷ Total wire correction parameter (Step 3)

5. Select a wire size with a maximum rated ampacity equal to or above the minimum wire ampacity calculated in the previous step using the allowable wire ampacities table. This table has three different temperature columns - 60°C, 75°C / 90°C – that correspond to different wire types. This temperature corresponds to the maximum temperature rating of the wire type, which should be labeled on the exterior of the wire and readily available from the product provider. Most wires have a dual rating of 60°C (wet)/75°C (dry), 75°C, or 90°C rating. If 60°C wire is used in the circuit, the 60°C column will have to be used.

Phase 3: Overcurrent protection and disconnects

Wiring diagram of a stand-alone PV system with a charge controller with DC lighting control and an inverter for AC loads. All potential overcurrent protection devices are labeled, but all may not be necessary.

Wiring diagram of a stand-alone PV system with a charge controller with DC lighting control and an inverter for AC loads. Equipment disconnects for PV modules provided by module connectors. All other required disconnects are labeled.

No wire should be exposed to current in excess of its rated capacity under the conditions of use. If a power source that a circuit is connected to can supply more current than the rated ampacity of a wire, then an overcurrent protection device must be used to prevent it from overheating and starting a fire. In off-grid systems overcurrent protection devices are also typically used as power source disconnects and equipment disconnects. Residual current devices should be sized using this same method if they are intended to function as an OCPD, if not they only need to be larger than the maximum current of the circuit to ensure that they do not accidentally trip.

Ground fault protection devices incorporate a breaker, but these GFPDs only come in a few sizes and it is common to use a GFPD with a breaker that is substantially larger than the ampacity of the wire for this reason. An additional breaker is therefore commonly used as the power source disconnect, because using the GFPD would mean that the DC system bond would be removed each time the breaker was used as a disconnect, which is not a safe practice.

There are some cases in which an overcurrent protection device is not required because another overcurrent protection device protects that circuit against excessive current or the power source cannot supply current that would exceed the rated capacity of the wire. Not all systems are wired the same - some designs will require additional OCPDs and others will require fewer.

Circuit
(1) PV source circuit OCPD	Required if the system has more than two parallel strings of PV modules. Can also serve as the required power source disconnect - see (10) in the image.
(2) PV output circuit OCPD	A power source disconnect - typically a breaker - is required for the PV source. If the PV source circuits have breakers they can meet this need if they are located near the charge controller. Can also serve as the required power source disconnect - see (10) in the image.
(3) Charge controller output circuit OCPD	The wires between the charge controller and the energy storage system must be protected by an OCPD. There should also be a power source disconnect for the energy storage system and an equipment disconnect for the charge controller. Both of these requirements can be fulfilled by installing a breaker - see (11) in the image.
(4) Charge controller load circuit OCPD	The wires between the charge controller and any lighting/load only need to be protected by an OCPD if the charge controller can supply current that exceeds the rating of the wires. This is typically not the case.
(5) DC branch circuit OCPD	The wires between the charge controller and any lighting/loads only need to be protected by an OCPD if the charge controller can supply current that exceeds the rating of the wires. This is typically not the case.
(6) Inverter input circuit OCPD	The wires between the inverter and the energy storage system must be protected by an OCPD. There should also be a power source disconnect for the energy storage system and an equipment disconnect for the inverter. Both of these requirements can be fulfilled by installing a breaker - see (13) in the image.
(7) Inverter output circuit OCPD	The wires between the inverter and any loads only need to be protected by an OCPD if the inverter can supply current that exceeds the rating of the wires. This is often not the case with smaller inverters, especially those operating at 220V. It is recommended that a residual current device (RCD) with an integrated breaker is used on the output of the inverter to increase system safety or on each individual circuit. It should be located before the AC system bonding jumper to avoid accidental tripping (activation).
(8) AC branch circuit OCPD	The wires between the inverter and any loads only need to be protected by an OCPD if the inverter can supply current that exceeds the rating of the wires. This is often not the case with smaller inverters, especially those operating at 220V. If there is no residual current device (RCD) on the output circuit of the inverter, it is recommended that one be added to AC circuit or outlet.
(9) Energy storage circuit OCPD	The wires between the energy storage system and any other component must be protected by an OCPD - charge controllers, inverters, DC-DC converters, low voltage disconnects, DC appliances. There also must be a power source disconnect for the energy storage system. Both of these requirements can be fulfilled by installing a breaker or a fused disconnect - see (12) in the image. Larger systems are typically designed like in the wiring diagram with one single circuit running from the energy storage system to common DC busbars to reduce wire and OCPD costs - in this case there is an energy storage circuit. Smaller systems often connect the charge controller and inverter directly to the energy storage system independently - in this case there is no energy storage circuit.

The appropriate overcurrent protection device size can be determined by:

1. Overcurrent protection devices (OCPDs) are thermally (heat) activated. If an OCPD operates for an extended period of time, it will begin to generate heat that could potentially cause it to accidentally activate. Thus, if a circuit will operate for more than three hours continuously, which all circuits in an off-grid system likely will at some point, then the overcurrent protection device size will be increased to avoid any issues. The maximum circuit current calculated in Phase 1 is multiplied by the therefore multiplied by the continuous duty safety parameter of 1.25.

Minimum OCPD size	= Maximum circuit current (Phase 1) × 1.25

2. There are standard OCPD sizes that both the NEC and IEC recognize. The OCPD size should be the next largest size after the minimum OCPD size calculated in Step 1.
   • Standard international OCPD sizes: 1 A, 2 A, 4 A, 6 A, 10 A, 13 A, 16 A, 20 A, 25 A, 32 A, 40 A, 50 A, 63 A, 80 A, 100 A and 125 A.
     
   • Standard US OCPD sizes per US NEC: 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 110, 125, 150, 175, 200, 225, 250, 300, 350, 400, 450, 500, 600, 700, 800, 1000, 1200, 1600, 2000, 2500, 3000, 4000 5000, and 6000 A. Additional standard fuse sizes are 1, 3, 6, 10, and 601 A.
3. Verify that the chosen OCPD size from Step 2 will protect the wire size chosen in Phase 2 from excessive current under the conditions of use. The current rating of the chosen breaker size (Step 2) must be less than the calculated maximum current under conditions of use unless the calculated maximum current under conditions of use is between standard OCPD values, in this case the next largest breaker can be chosen.

   Maximum current under conditions of use	= Wire ampacity from allowable wire ampacities table × Total wire correction parameter (Phase 2).

   Example 1: Step 1,2 suggest a 30 A breaker. Phase 2 calculated a 10 AWG / 6 mm² for the circuit. The ampacity rating for this wire is 35 A at 75°C. The total wire correction parameter (Phase 2) is .65 Can the 10 AWG / 6mm² wire be used?

   Maximum current under conditions of use = 35 A × .65

   Maximum current under conditions of use = 22.75 A

   The next largest breaker is a 25 A breaker, but this breaker would be too small for the circuit. The wire size needs to be increased to the next largest size of wire 8 AWG / 10mm²

   
   Example 2: Step 1,2 suggest a 30 A breaker. Phase 2 calculated a 10 AWG / 6 mm² for the circuit. The ampacity rating for this wire is 35 A at 75°C. The total wire correction parameter (Phase 2) is .8 Can the 10 AWG / 6mm² wire be used?

   Maximum current under conditions of use = 35 A × .8

   Maximum current under conditions of use = 28 A

   The next largest breaker is a 30 A breaker, which was the suggested breaker size (Step 1,2). 10 AWG / 6mm² and a 30 A breaker is acceptable.

Phase 4: Voltage drop

All wires should be sized to make sure that the resistance of the wire will not create an excessive voltage drop that can lead to lost PV production, improper battery charging, and loads that do not function properly. If the voltage drop for the wire chosen in Phase 2 for a particular circuit is not within the recommended values, then using a larger sized wire should be considered. Increasing the wire size will not affect any other part of this process; the calculated OCPD size can remain the same.

The formula for calculating voltage drop is:

Voltage drop	= 2 x Circuit current x One-way circuit length (m) x Resistance (Ω/Km) ÷ 1000

The most important value is the percentage voltage drop for the circuit. This is calculated using the formula:

Percentage voltage drop	= Voltage drop ÷ Circuit operating voltage x 100

Recommended circuit voltage drop values

The table below has recommended maximum voltage drop values for various circuits. It is important to note that other components in a circuit - terminals, fuses, breakers - add resistance and will increase voltage drop as well, therefore it is important to be conservative.

Note: Not all PV systems are wired the same. These voltage drop values are for total circuit length between one component and another. It is common to have DC busbars that have one single set of wires that runs to the energy storage system and connect to a positive and negative DC busbar that serve as a point of connection for the inverter and charge controller. In this case it is necesary to calculate the total voltage drop between the charge controller and the energy storage system, rather than just to the busbar.

Circuit	Maximum recommended voltage drop
PV source to charge controller	2%
Charge controller to energy storage	1.5%
Energy storage to inverter	1.5%
DC lighting circuits	5%
DC load circuits	3%
AC load and lighting circuits	2%

Phase 5: Terminal temperature ratings

The maximum temperature rating of the any breaker terminals or crimped terminals used in the circuit must be considered. Most terminals are rated for 60°C/75°C or 75°C. 60°C and 90°C terminals are not very common. This information should be printed on the component or be available from the manufacturer or provider. If a wire with a higher temperature rating than that of the terminals in the system, then it must be verified that the OCPD device will still protect the terminals under conditions of use. For example:

• If the circuit is being sized for use with 90°C rated wire and terminals with 75°C rating - a very common scenario - then the calculations below will have to be performed.
• If the circuit is being sized for use with 75°C rated wire and terminals with a 75°C rating, then the calculations below do not need to be performed.

The calculation is the same as the calculation performed in Phase 3 of the OCPD sizing entitled - Maximum current under conditions of use - but is instead performed with the ampacity of the chosen wire taken from the column of the allowable wire ampacities chart at the lower temperature rating of the terminals.

Step 1: Maximum current considering terminal temperature rating

Maximum current considering terminal temperature rating	= Wire size (Phase 2) ampacity at terminal temperature rating from allowable wire ampacities table × Total wire correction parameter (Phase 2).

Step 2: Verify OCPD protection considering terminal temperature rating

Verify OCPD size and derated wire ampacity under conditions of use including terminal temperature rating	= Maximum current considering terminal temperature rating (Step 1) must be greater than Chosen OCPD size (Phase 3)

If the wire is not protected by the OCPD at the temperature rating of the terminals in the circuit, then the wire size must be increased until the circuit passes this test. No other calculations need to be performed again. Increasing the wire size will have the added benefit of reducing voltage drop.