Wire Sizing Tools and Resources

Hello ladies and gentlemen!  To wrap up my extended series on wire sizing and voltage drop in solar systems, I want to share some wire sizing tools/resources for calculating voltage drop that can help make your life easier.
Online Wire Sizing Configurators
This is an extremely simple voltage drop calculator that assumes no conditions of use similar to my examples for voltage drop in the previous post.  It allows you to input any voltage into it, which makes it unique among the free online voltage drop calculators I checked out.  It’s simple but easy to use and understand.
This calculator lets you select from a long list of preset voltages, and gives you the choice of DC, AC, or AC three phase.  The issue with this calculator is the list of voltages is very arbitrary, there are “holes” in its selection that prevent it from being a comprehensive tool.  Other than that, it lets you adjust conductor temperature to include derating due to conduit fill and ambient temperatures.  It also lets you select your conduit type.  All in all, it’s a very good calculator for AC voltage drop and an OK calculator for DC.
Online Wire Sizing & Voltage Drop Information Resources
These are some of the resources I have used in the past for learning about voltage drop and wire sizing.  The information in these articles is extremely useful and in-depth.  I owe a great deal of my knowledge on this subject to them.

http://en.wikipedia.org/wiki/Voltage_drop#How_to_calculate_voltage_drop

Episode 5 pt 3: Voltage Drop and Wire Sizing for Solar

Voltage drop and wire size are important considerations when designing and installing solar PV systems.  Voltage drop occurs in any electrical circuit carrying power. A percentage of the power running through the conductors will be lost as heat.  This amount is dependent on the size of the wire along with the voltage and current of the load, and some environmental factors as well (circuit length, temperature, conductor material).  This post will cover selecting the correct wire size based on your maximum solar current and calculating the voltage drop based on that.  I will be heavily referencing the NEC 2011 codebook throughout this post.
Conditions of Use
Before getting into selecting wire sizes, I want to cover conditions of use.  These are factors that need to be applied to the maximum current we calculated earlier based on environmental conditions.  The most obvious condition of use is ambient temperature, found in Table 310.15(B)(2)(a).  Based on most sources, the average high temperature for the location should be used.  This can be obtained from the ASHRAE handbook (the 2% value) or determined from weather data available online.  The other conditions of use are more complicated.  Conduit fill is an important consideration for large systems and long conduit runs, it is found in Table 310.15(B)(3)(a).  This is because wiring will generate heat during operation and the hotter it gets inside the conduit the worse the voltage drop will get.  Conduit distance above roof for roof mounted systems is very important as well, and can make the conductors even hotter, reference Table 310.15(B)(3)(c) for more information.  For the purpose of this post, conduit fill and conduit distance factors will both be assumed as 1 for power production.  Ambient design temperature will be fixed at 85° F, which gives a modifier of 1 on our current calculation for simplicity.
Wire Sizing
From my previous submission, maximum DC solar current is based on the solar panel’s Isc rating multiplied by 1.56.  The maximum AC solar current is the inverter’s maximum continuous current multiplied by 1.25.  Taking these maximum calculated currents, proper wire sizes for them can be selected using NEC 2011 wire sizing methods and tables.  These methods will assume conductors and terminals are rated for 75° C.  The first table to reference is 310.15(B)(16), where the 75° C Copper column will be used to select wire size based on the maximum calculated current.  For example, for a solar panel Isc rating of 8.5A, our maximum DC current is 13.26A.  Using table 310.15(B)(16), the minimum wire size #14 AWG.  For a solar inverter with a rated current of 25A, maximum AC current will be 31.25A.  This results in #8 AWG wire.  Conditions of use, if we had them, would be applied here to the overall ampacity of the wire to derate it and check against our maximum calculated current.  Conveniently, all of our conditions of use for this example are fixed at “1”.
Now that the wire size has been found for the maximum calculated current, it needs to be checked against worst case voltage drop in the conductor for the designed length of the circuit.  If the voltage drop would be too high the wire has to be upsized to the next size to correct for it.  The maximum voltage drop is 1.5% for DC and 1.5% for AC circuits based on my previous post.
Calculating Voltage Drop
The heart of voltage drop calculations is Ohm’s law, which reads V (Voltage) = I (Current) x R (Resistance). The units are Volts, Amps, and Ohms, respectively.  Voltage drop calculations are based on values for Resistance (Ohms) per 1000 feet found in NEC tables in Chapter 9, Table 8 or 9 (DC circuits Table 8,  AC circuits Table 9). The value we need is for stranded, uncoated copper conductors.  This changes the formula from V = I x R to Voltage Change = I x (R / 1000’) x Total Circuit Length
Written another way, it can be expressed in terms of 1-way circuit length and converted into a percentage value:
 Equation for Voltage Drop based on NEC 2011 Chaper 9 Tables 8 & 9

Going back to my example in Wire Sizing, let’s consider a DC and an AC wire run for a 100 foot distance and calculate the voltage drop for each.  For DC, we have:
#14 AWG Wire  300V String         I = 13.26A            L = 100 feet         R = 3.26 (NEC Chapter 9 Table 8)
VD = 2 x 100 x 13.26 x 3.14 / 1000 = 8.33V               8.33V / 300V = 2.78% Voltage Drop
Based on our maximum desired DC voltage drop of 1.5%, this obviously will not do.  We need to upsize the wire to get a better voltage drop.  Rerunning the numbers for a #12 wire gives:
VD = 2 x 100 x 13.26 x 1.98 / 1000 = 5.44V               5.44V/ 300V = 1.75% Voltage Drop
Close, but not quite what we wanted.  Obviously a #10 AWG wire is the way to go, but just to be sure:
VD = 2 x 100 x 13.26 x 1.24 / 1000 = 3.42V               3.42V / 300V = 1.10% Voltage Drop
That’s got it right there!  A #10 AWG wire will give us ~1.1% voltage drop for a 300V circuit over 100 feet (In general, I’ve found that a #10 wire is best for solar string wiring for most roofs).  Now that we’ve figured out DC voltage drop, AC voltage drop is pretty simple.  Using Table 9 of Chapter 9, we need to use the values in the column labeled “Alternating-Current Resistance for Uncoated Copper Wires”.  Going back to our earlier example:
#8 AWG Wire     240V AC               I = 31.25A            L = 100 feet         R = 0.78 (NEC Chapter 9 Table 9)
VD = 2 x 100 x 31.25 x .78 / 1000 = 4.875V               4.875V / 240V = 2.03% Voltage Drop
Again, we’re close but not quite where we want to be for this AC wire run.  Upsizing the wire to #6 results in:
VD = 2 x 100 x 31.25 x .49 / 1000 = 3.06V 3.06V / 240V = 1.28% Voltage Drop
Based on our examples, a #10 wire will give us a 1.1% voltage drop for a 300V, 8.5A string of solar panels over 100 feet.  A #6 wire will give us a 1.28% voltage drop for a 240V, 25A solar inverter over 100 feet.
Wire sizing and voltage drop calculations are an extremely important consideration for any solar designer or installer, and it’s essential to understand the fundamentals behind them.  The calculations and examples in this post have been kept simple on purpose, the subject can get complicated in a hurry when multiple conditions of use need to be applied.  In my next post, I will share some of my favorite tools and rules of thumb for calculating wire size and voltage drop.
References

NEC 2011
Conditions of Use: 310.15(B)(2), 310.15(B)(3)
Wire Ampacity: Table 310.15(B)(16)
Wire Resistance: Chapter 9 Tables 8 & 9

Episode 5 pt 2: Voltage Drop and Wire Sizing for Solar

Voltage drop and wire size are important considerations when designing and installing solar PV systems.  Voltage drop occurs in any electrical circuit carrying power. A percentage of the power running through the conductors will be lost as heat.  This amount is dependent on the size of the wire along with the voltage and current of the load, and some environmental factors as well (circuit length, temperature, conductor material).  Today I’m going to go over how to calculate your maximum current for a designed voltage drop in a solar system.
Based on last week’s article, the amount of voltage drop to design for in a solar PV system is usually around 3% unless otherwise specified.  This should be split between the DC and the AC conductors, so 1.5% maximum DC and AC voltage drops are the end goals.  If microinverters are being used, there are no DC conductors that need to be sized.  In that case, the AC voltage drop should still be kept below 1.5% to help with grid synchronization.  Now, it’s time to break out the NEC 2011 codebook and start figuring out how to size our wires.
Current Calculations
Before getting into voltage drop and circuit distances, the first thing we need to figure out is how much current to design for.  Looking at solar panel and inverter data sheets, there’s a few different values for current we can use.  On the DC side, our starting point will always be the solar panel’s Isc current rating at STC.  This is based on NEC article 690.8, Circuit Sizing and Current.  We are concerned with 690.8(A)(1) and 690.8(B)(1)(a) for DC current calculations, which state:
690.8(A)(1): The maximum current shall be the sum of parallel module rated short-circuit currents multiplied by 125 percent.
690.8(B)(1)(a): Overcurrent devices, where required, shall be rated to carry not less than 125 percent of the maximum current calculated in 690.8(A).
While these talk about overcurrent devices, our circuits will have to be sized based on these same requirements.  Now, looking at the solar panel’s Isc rating, it has to be multiplied by 125% per 690.8(A)(1).  Then to size wire for it, an additional 125% multiplier needs to be added per 690.8(B)(1)(a).  Taken together, the DC current multiplier for wire sizing is 1.56 times Isc.
On the AC side, the inverter’s rated continuous current (make sure it’s for the correct AC voltage!) needs to be used for wire sizing calculations.  Like on the DC side, there’s a factor that needs to be applied to find our AC wire sizing current.  Looking at the same NEC article, the inverter output circuit current can be found using 690.8(B)(1)(a) and again referencing 690.8(B)(1)(a), which together state:
690.8(A)(3): The maximum current shall be the inverter continuous output current rating.
690.8(B)(1)(a): Overcurrent devices, where required, shall be rated to carry not less than 125 percent of the maximum current calculated in 690.8(A).

Unlike on the DC side, only one 125% multiplier needs to be applied on the AC current to find our maximum current for wire sizing.  The final AC current multiplier for wire sizing is 1.25 times rated continuous current.  Next, we’ll select wire sizes and calculate voltage drop based on our solar current calculations.  To keep post length down, I’m breaking it up into multiple submissions.

Episode 5 pt 1: Voltage Drop and Wire Sizing for Solar

Voltage drop and wire size are important considerations when designing and installing solar PV systems.  Voltage drop occurs in any electrical circuit carrying power. A percentage of the power running through the conductors will be lost as heat.  This amount is dependent on the size of the wire along with the voltage and current of the load, and some environmental factors as well (circuit length, temperature, conductor material). Today I’m going to look at designing for voltage drop and how to design for it so your solar array functions properly.
The maximum voltage drop you should design for in a system is not set in stone.  For commercial systems, it can be specified in the bid documentation, but for smaller systems you are usually left trying to figure out the best value that will deliver the most energy without breaking the bank on wire.  While the National Electric Code (NEC 2011) does not explicitly provide a maximum permissible voltage drop for solar PV systems, you can find a reference point in Articles 210 and 215 in fine print notes.  They state that overall voltage drop should not exceed 3% for branch or feeder circuits and 5% overall.  Based on this, most solar systems are designed to never exceed 3% overall voltage drop as a feeder circuit, with no more than 1.5% voltage drop on the AC side.
The reasons you want to keep voltage drop low in your solar system are multiple.
First, the obvious reason is wasted energy and wasted dollars. A solar array is a major investment, and if an upgrade from #12 to #10 wire will provide a significant decrease in voltage drop it will pay for itself throughout the life of the system.  A difference between 1% and 2% voltage drop between your inverter and the interconnection is a difference of 50W for a 5000W system, and it quickly adds up the larger it gets.
On the DC side of the inverter, you need to hit a defined voltage window.  If you size your solar strings to the lower end of that range, a high voltage drop could put you outside of the maximum power point tracking window of the inverter. This is at its worst in hot weather, when voltages are already low and the inverter is hot.  This is also some of the best production time for solar PV systems all year, optimum performance is critical and your DC wiring needs to be sized with that in mind.
AC voltage drop is possibly more important than DC for solar PV systems.  The issue is one with the electric grid and your inverter.  Your service voltage can vary depending on several conditions including weather and time, and the inverter is constantly working to match up with that voltage.  This is why on inverter data sheets you see an AC voltage range the inverter is capable of producing, typically -12% / +10%.  For a 240V inverter, this gives an upper voltage limit of 264V.  Grid voltages as high as 250V or higher have been seen for 240V services. iIf your AC wire was sized with a 5% voltage drop your inverter would see 262.5V, almost its limit and at risk of going into fault.  This is why low AC voltage drop is extremely important, and most commercial bids and lease agreements require 1% or less.

Now that you have a guideline for how much voltage drop you want to design for in your solar system, how do you do it?  Next week I’ll be digging into the NEC 2011 codebook for wire sizing methods and solar current calculations.  I’ll also share some of my favorite online/mobile tools and rules of thumb to help make this as smooth and painless as possible.  Happy New Year!

Residential System Design and Installation Episode 4: Connecting to the grid without violating the National Electric Code

I want to cover an issue that seems to always pop up, performing the tie-in on a grid tied solar system.  Navigating the rules and regulations for connecting solar to the grid can be a challenge for any designer or installer.  The National Electric Code (NEC 2011) is open to interpretation by your inspector, and local jurisdictions often have their own requirements.  Local rules and regulations regarding interconnection of solar arrays will always take precedence over the methods I present here, but these are guidelines that will give you a code-compliant interconnection 95% of the time.
Connecting to the grid without violating the National Electric Code
First, I’ll reference and explain the relevant NEC 2011 articles and terms that are “proof” these methods are safe and suitable for solar:
230.82(6) – “Only the following equipment shall be permitted to be connected to the supply side of the service disconnecting means… (6) Solar Photo voltaic systems, fuel cell systems, or interconnected electric power production sources.”
If you find yourself being questioned by your inspector for connecting the solar system upstream of the main distribution panel (often called a “line side tap”), this article outlines the different systems that are allowed per NEC 2011.  Solar is included here because it can operate in parallel with the electrical service as long as the Utility service conductors are sized appropriately.
705.12 – “The output of an interconnected electric power source shall be connected as specified in 705.12(A – D).
A & D are the relevant sections for this discussion; B & C are for larger systems with advanced power and safety controls and doesn’t apply to residential and light commercial system interconnection.
(A) “Supply Side. An electric power production source shall be permitted to be connected to the supply side of the service disconnecting means as permitted in 230.82(6).  The sum of the rating of all over current devices connected to power production sources shall not exceed the rating of the service.”
Section A talks about interconnections upstream of the main service disconnect (line side taps).  At this point, the only power production source with an over current device is the solar array, so you can connect a system as large as the service, in parallel with your electrical service without modifying anything inside the Main Distribution Panel if desired.
(D) “Utility-Interactive Inverters”  The output of a utility-interactive inverter shall be permitted to be connected to the load side of the service disconnecting means of the other source(s) at any distribution equipment on the premises.  Where distribution equipment including switchboards and panel boards is fed simultaneously by a primary source(s) of electricity and one or more utility-interactive inverters, and where this distribution equipment is capable of supplying multiple branch circuits or feeders or both, the interconnecting provisions for the utility-interactive inverter(s) shall comply with D(1 – 7).”
Section D is all about connecting your solar system inside the Main Service Panel using a circuit breaker.  With 7 sub-sections, it’s easily the most complicated section in article 705.12 Point of Connection.  We are mainly concerned with D2, the rest are pretty self-explanatory but I will cover them briefly.
D2 “Bus or Conductor Rating” – “The sum of the ampere ratings of over current devices in circuits supplying power to a busbar or conductor shall not exceed 120 percent of the rating of the busbar or conductor.”
This seems to confuse people the most when they attempt to connect a solar system in their Main Panel.  Essentially, the solar circuit breaker represents a power source feeding the busbar.  Almost always, the only other source of power feeding the Main Panel busbar is utility power via the Main Panel Breaker.  For most Main Panels, the busbar rating is equal to the Main Breaker rating.  Based on these assumptions (which hold true for the vast majority of grid tied solar installs), an equation for determining if the Main Panel will accept a solar circuit breaker can be made.
Main Busbar Rating * 1.2 – Main Breaker Rating = Maximum Solar Circuit Breaker Rating
For most new homes, there’s a 200A Main Panel and 200A Main Breaker.  Using our equation, the largest solar circuit breaker would be 200A * 1.2 = 240A – 200A = 40A solar circuit breaker.  Dividing by 1.25 (NEC required over current protection factor) gives a maximum solar AC current of 32A for a 200A panel.
D1 “Dedicated Over current and Disconnect” – Connect your solar system with a dedicated circuit breaker that has been installed solely for that task.  No double duty, tandem breakers with solar and other loads can be used.
D3 “Ground Fault Protection” – Today’s grid tied inverters include integrated ground-fault protection equipment so this isn’t an issue.
D4 “Marking” – Make sure the solar circuit breaker is properly identified at the point of connection.
D5 “Suitable for Back feed” – As long as the solar circuit breaker is not marked “line” or “load”, it is suitable for this application.
D6 “Fastening” – Usually when you back feed circuit breaker in an AC distribution panel you are required to provide additional fasteners for the circuit breaker on the busbar.  This is not the case for circuit breakers from utility-interactive solar inverters, the fastener can be omitted without issue.
D7 “Inverter Output Connection” – This states that you always need to install the solar circuit breaker at the opposite end of the busbar from the Main Panel Breaker.  For situations where you have a “center-fed” busbar with the Main Breaker in the middle, choose one end of the busbar to install the solar circuit breaker.  You want the power sources feeding the busbar at opposite ends for proper flow of electricity.  It also talks about panel boards connected in series (Sub panels being fed from the Main Panel).  If you connect solar in a sub panel, you only need to make sure you aren’t violating the 120% rule for that sub panel’s busbar and conductors.
Specific requirements for fastening, marking and labeling your system will come from your Utility/AHJ (Authority Having Jurisdiction, usually the local municipality).
Based on these NEC articles and our experiences in the industry, here’s a summary of guidelines for interconnecting solar systems:
Circuit Breaker – Follow the 120% rule for sizing the circuit breaker to ensure the electrical panel (Main or Sub) is large enough to handle your proposed solar system.  A quick rule of thumb is a 200A panel can handle a 40A solar circuit breaker, 150A can do a 30A solar breaker, and 100A will allow a 20A solar breaker.  Remember to divide by 1.25 to find the maximum allowable current from the utility interactive solar inverter.  Install the circuit breaker at the opposite end of the busbar from the Main Breaker, and make sure it’s marked/labeled properly.
Derate the Main Breaker – Sometimes you have a situation where you want to land your solar circuit breaker in the panel, but it would violate the 120% rule.  Rather than resorting to a line side tap immediately, you can derate the main breaker which frees up more capacity for solar by reducing the other power source feeding the panel.  While it adversely affects the overall capacity of the Main Panel, many people aren’t fully utilizing their service which can give you some added solar capacity.
Line Side Tap – There aren’t many rules regarding line side taps.  As long as the over current device for your system is less than or equal to the rating of the service, you can tap the conductors coming into the Main Panel.  A service-entrance rated solar disconnect (over current + load break protection) should be installed adjacent to this connection.  Line Side Taps can be accomplished one of a few ways.
Insulation Piercing Tap Conductors – These devices (pictured below, typical) can be used to make a “hot connection” to the conductors coming into the Main Panel without needing to turn off the electrical service with the Utility.  They can be used in a variety of locations in addition to the Main Panel, including exterior wiring gutters or disconnects.
 Figure 1: Insulation Piercing Tap Conductors by Ilsco

Double-Lugged Panels – Sometimes you have a Main Panel that has a double set of lugs for the incoming Utility conductors.  If one set of lugs is open, you can use those to perform a line side tap.
Parallel Main Panels – Even though it may be rated twice as high, it’s still contained in separate panels with only half the rating.  Each panel has to be treated as its own separate entity, the overall service capacity cannot be used as the service rating.
Old Panels – Sometimes you have a panel that’s been in service for so many years, it’s gone out of code or the brand doesn’t exist anymore.  Sourcing breakers for these panels is a major challenge, they have to be UL-listed as a replacement breaker for the obsolete panel.  Some panels will be red-tagged by your inspector if you land your breaker in it.  In these cases, you will have to do a line side tap or upgrade the equipment.
References:
NEC 2011 230.82(6)

NEC 2011 705.12

Residential System Design and Installation Episode 3: Battery Based Solar System Sizing

This is Affordable Solar’s blog series on best practices, tips, and tricks to being a successful solar designer or installer.  My inspiration for these entries is pulled from my years of experience working in solar photovoltaics, from shipping to sales to design and drafting, and from my work with installers around the country.  I am not the ultimate authority, but we have had a track record of success and I want to share that with you.

For my third post, I am looking at battery based solar arrays and the things you need to keep in mind when designing them.  Before reading, I would recommend checking out my previous post “Simple Sizing of Grid Tied Solar Arrays“, especially it’s section on Sun Hours.

Battery Based Solar System Design

One of the biggest challenges in modern solar system design is how to properly design a system that includes batteries.   Unlike a pure grid-tied system, a solar system with batteries consists of three separate systems all working together to create, store, and deliver energy for your electric loads.  You need to ensure each component is properly sized for your specific energy needs and environmental conditions.  This will explore sizing a stand-alone solar system based on an average daily load in watt hours that will be calculated from your usage habits or pulled from electric bills.

For every load you want to include in your calculations, there needs to be an estimate of the average number of hours per day it will be turned on and drawing power and its power draw in watts.  By multiplying watts times hours, you get the total amount of energy you need to run that load for a day.  For an entire house, there are a lot of things drawing power at once, a lot of calculations that need to be done to determine the total amount of energy required.  A good way to keep track of everything in is to use Affordable Solar’s Off-Grid Load Estimator.  This online tool lets you enter any number of loads into the calculation, their size in watts, and hours/day in use.  It sums them up and gives you the total watt-hours per day that your solar array and battery bank will be sized for.
 Figure 1: Affordable Solar’s Off Grid Load Estimator

If the power/energy of an electric load is unknown, it can be determined using a “Kill A Watt” electricity usage monitor (or equivalent).   The “Kill A Watt” monitor can be used to find out how much energy is being used over time in watt hours.  It is an excellent tool for finding appliance’s average daily load, and highly recommended for any battery based system sizing.
 Figure 2: The Kill A Watt EZ, available in most major hardware stores

While they may sound similar, ‘Power’ and ‘Energy’ describe two different things.  Power is the amount of electricity being used or created at any moment in time, while Energy is the amount of electricity that is used over time.  Watts are used to describe Power, and Watt-hours describe Energy.  This difference is important for sizing the three distinct components of a battery-based solar system.  The solar array and battery components are both sized based on the amount of energy (watt-hours) required per day, while the inverter and power panel are sized based on the maximum amount of power (watts) that will be used at once.

Solar Array Sizing:
To size your solar array based on the average daily electric load (either calculated or converted from monthly electric bills), you will need to know how much sunlight hits your site on a daily basis.  If you have not read “Simple Sizing of Grid Tied Solar Arrays”, I would recommend you check out the section titled “Sun Hours” for help in finding this information.

PVWatts can be used to find the available solar resource for a location for any orientation.  Calculating the number of sun hours your site will receive, PVWatts outputs a table of results with values for every month as well as an average for the year.  At this point, you will need to know if you plan on using a source of back-up power in addition to the solar array.  An example of a source of back-up power would be a generator or the grid.  This greatly affects the eventual size of the solar array.  If you are using a source of back-up power for your system, then you can size the solar array based on the average daily solar radiation (sun hours) for the entire year just like a grid tied solar array.  If there are no power source besides the solar array, you need to use the month that has the lowest value of sun hours for the year (in most cases December).

 Figure 3: PVWatts results table showing monthly and annual values for solar radiation (sun hours)

Having back-up power lets you get away with a much smaller solar array.  If you don’t have anything backing up the solar system, then the only thing keeping the batteries charged are the solar panels.  Since the batteries are the critical component of any off-grid system, it is very important that their charge be maintained or you risk over cycling them, drawing them down too far, or otherwise overworking them so that they prematurely age and require replacement in 2-5 years rather than 10-15 years.  Without an additional source of power to bail out the solar system when the sun hours are short, you need to size the solar array for the absolute worst case scenario or you’ll end up with a dead battery bank that requires complete replacement.

With the daily load in watt hours and the solar resource in sun hours, the solar array size can be calculated.  The equation, from “Simple Sizing of Grid Tied Solar Arrays”, is:
System Size (Watts) = ((Watt hours) * η) / (sun hours)
The system efficiency factor η is usually estimated between 0.65 – 0.7 for stand-alone systems (0.55 – 0.6 for systems with a non-MPPT charge controller).  You may notice that this is much lower than the ones used for sizing grid tied solar arrays.  This is mainly due to the addition of a battery bank and charge controller, and the difference in inverter efficiency between grid tied and off-grid systems.  Battery-based inverter/chargers typically have efficiencies in the range of 88 – 93% versus 94 – 98% for grid tied inverters.
Battery Bank Sizing:
Sizing the battery bank for your daily electric load is very simple.  The equation is:

If the average daily load in Watt hours has been calculated already (from the “Load Estimation”), the only factors that need to be determined are the days of autonomy and the maximum depth of discharge.

The days of autonomy represents the longest amount of time the solar array will have to deliver power for your loads while you are unable to charge the batteries from any source.  This is mostly due to cloud cover that can block the sun for days at a time.  With a grid tied solar array, there wouldn’t be any issues because the electric grid is almost always available.  However, with a battery system, the batteries have to be sized to handle the possibility that there won’t be any other power available for days at a time.  For most systems, 3 days will cover almost all scenarios and give you a sufficiently large battery bank.  If you have reliable grid power available for backup, a smaller battery bank can be considered.  However, if you live somewhere with consistent cloud cover or a long winter, you may want a battery to store enough energy for 4 days or longer.
The maximum depth of discharge of a battery bank can be tricky thing to figure out.  Its roots are in the properties of deep cycle lead-acid batteries used in renewable energy applications.  A complicated discussion on these properties could follow here, but suffice to say that the less you use batteries, the longer they last.  By setting an arbitrary point for when you stop draining batteries, you help preserve them and they will hold a charge for longer than if you fully discharge them.  The longest-lasting and most robust battery banks are never discharged more than 20-30%.  Most systems are designed to a 50% depth of discharge, which is enough to give you 7-10 years of effective life from your batteries if cycled and charged properly.
Another reason to set a maximum depth of discharge is the chemistry of deep cycle batteries.  As you drain a battery, the acid in each cell becomes less and less acidic, and its freezing point rises.  A fully charged lead-acid battery might not freeze in 0 degree weather, but a fully discharged one most certainly will because the “electrolyte” inside the battery is mostly water at that point.

 Figure 4: Depth of Discharge vs. Electrolyte Freeze Point

As a consequence of this, you need to be aware of where you plan on locating the batteries for a stand-alone system.  If they will be somewhere where it could reach 0 degrees or less and if they are discharged below 60% charge they can freeze and you will have to buy a whole new bank of batteries.  For more information on battery banks and their maintenance, check out “Extending Battery Life” in our learning center for an in-depth look.
Inverter Sizing:
Sizing a battery-based inverter for a stand-alone solar system is a simple question.  Unlike a grid tied solar array, a battery-based inverter is physically providing all of the power for your backed up electric loads.  So, if you have 3000 watts of lights you need to run at once with your stand-alone system, you will need an off-grid inverter rated for 3000 watts or higher or there won’t be enough AC power to run all of them.  When sizing an inverter for your loads, it’s best to come up with a “worst case scenario” where the most appliances, lights, and other loads will be running at once.  The inverter needs to be able to handle your highest planned continuous power load.
In addition to continuous loads, there can be “surge loads” that your inverter should be sized for.  A surge load occurs when starting an electric motor or pump, usually for air conditioning units, well pumps, or shop tools.  These power surges can be 2-5 times higher than the continuous load, and the inverter has to have the extra capacity to start it or risk being overloaded.  Fortunately, most modern battery-based solar inverters have a “surge rating” for 1-10 seconds that is twice as high as their continuous rated output, allowing for some flexibility in determining how much AC power you should include.  In the end, more AC power is better and you should always err on the side of caution when looking at how much you need for your battery based solar array.

Residential System Design and Installation Episode 2: Calculating Tilted Array Spacing

This is Affordable Solar’s blog series on best practices, tips, and tricks to being a successful solar designer or installer.  My inspiration for these entries is pulled from my years of experience working in solar photovoltaics, from shipping to sales to design and drafting, and from my work with installers around the country.  I am not the ultimate authority, but we have had a track record of success and I want to share that with you.

For my second installment, I am sharing the equations and resources I use to calculate tilted array spacing and solar panel spacing from obstructions.  Without further ado…

Calculating Tilted Array Spacing

When you’re designing a solar array, shading is the enemy.  Most locations for solar projects tend to get around 5 to 6 net sun-hours per day, so anything that obstructs that sunlight needs to be avoided at all costs.  Shading just one corner of a module can cut production in half, so avoiding shade on the array is important.  This is mainly an issue on ground mounts and some flat roof mounts, where rows of solar panels need to be optimally spaced to best use the available space.  With limited solar resource and steep penalties for failure, properly determining correct shade spacing is a critical calculation in solar system design.
 Figure 1: Side View of Tilted Array Showing Solar Altitude Angle
The procedure for calculating shadow spacing starts with the sun’s position in the sky on the winter solstice, December 21st.  You need to obtain the minimum solar altitude angle α, which is the minimum angle the sun makes with the ground in your shade-free solar window (figure 1).  For a 4 ho­­ur solar window, you want to obtain the sun’s altitude angle at 10 AM or 2 PM on December 21st, because that is when the sun will be lowest in the sky.  For a 5 hour window, you will need the sun’s altitude at 9:30 AM or 2:30 PM instead.  When you find this angle, you will most likely also be able to get the suns azimuth angle, ψ.  This is how far off true south the sun’s position is (figure 2), and will be needed to obtain the minimum allowable row spacing.
 Figure 2: Top View of Tilted Array Showing Solar Azimuth Correction
Finding values for local Solar Azimuth and Altitude angles on the winter solstice can be a challenge.  Luckily for the modern solar designer, there are tools available that greatly simplify the process.  The tool I have selected is the NOAA Solar Calculator, available for free online at http://www.esrl.noaa.gov/gmd/grad/solcalc/.  By clicking a location on the map, you are given coordinate and time zone information, and by entering the date for the winter solstice, December 21, the “worst case” position of the sun is easily obtainable.  The procedure for using NOAA’s Solar Calculator has been visually outlined on the webpage below.
 Figure 3: NOAA Solar Calculator showing workflow and relevant data
Step 1: Red – Enter your initial project inputs.  This is your location in coordinates, the time zone, and December 21st.  Select a city in your time zone that has a marker on the map to find your time zone value.  As easy way to find coordinates is to go to itouchmap.com/latlong.html and put the pointer on your location.
Step 2: Blue – Find Solar Noon based on your location, time zone, and the date.  If you are located in the western half of your time zone, this value is typically later than local time.  For the eastern half of a time zone, it will be earlier than local time.
Step 3: Green – Enter in the earliest time in the day on December 21st that the solar array should be without shading.  If you are designing for a shade-free solar window in the middle of the day, take the overall length of the solar window in hours and divide by two.  Subtract this value in hours from Solar Noon and enter it for Local Time.
Step 4: Orange – Obtain your worst-case Solar Azimuth and Altitude angles at Local Time, which will be used in the shading calculations to determine the minimum spacing.  The top value is the Solar Azimuth angle, while the bottom is the Solar Altitude angle.  Using the morning sun position, the Solar Azimuth angle should always be less than 180 degrees, and the Solar Altitude angle should be between 15 and 35 degrees for most locations in the United States.
After finding the Solar Altitude and Azimuth angles, the calculations to determine row spacing can begin.  For most ground and roof mounted systems where row spacing is a concern, the height (h) of the obstruction can be directly obtained from the dimensions of the solar panel and the array tilt.  Alternately, it can be measured as the difference in height between the bottom/leading edge of one row and the maximum height of the next row south of it, or a direct measurement of whatever obstruction you want the array to avoid (figure 1).  Using this height, the maximum shadow distance can be obtained.  The shadow distance is found through using simple trigonometry.  The equation:
D’ = h / tan (α)
From here, just one more calculation gives the minimum inter-row spacing needed to avoid shade within your solar window.  This is called the “Solar Azimuth Correction” (figure 2).  Using the morning sun position, the equation is:
D = D’ * cos (180 – ψ)
Using NOAA’s solar position calculator, the only information you need to quickly and painlessly determine shadow spacing is the height of the row or obstruction, your desired shade-free solar window, and the location in decimal-degree coordinate form.  With this method, you can accurately determine your solar panel spacing from obstructions with only a few simple steps.
Appendix: Variables/Equations for Calculating Tilted Array Spacing
• α = solar altitude angle
• ψ = solar azimuth angle
• h = height of obstruction              x = tilted module length                                θ=tilt angle
• h = x * sin(θ)
• D = Minimum array row spacing­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­
• D’ = Maximum shadow length (morning/afternoon)
• D’ = h / tan (α)             D = D’ * cos (180 – ψ)(morning)            D = D’ * cos (ψ – 180)(afternoon)

Residential System Design and Installation Episode 1: Simple Sizing of Grid Tied Solar Arrays

This is Affordable Solar’s blog series on best practices, tips, and tricks to being a successful solar designer or installer.  My inspiration for these entries is pulled from my years of experience working in solar photovoltaics, from shipping to sales to design and drafting, and from my work with installers around the country.  I am not the ultimate authority, but we have had a track record of success and I want to share that with you.

We’re going to kick this series off by revisiting some articles I have written in the past for our website. Ladies, Gentlemen, Solar Pros and Amateurs alike, I present to you…

Simple Sizing of Grid Tied Solar Arrays

Correctly sizing grid tied solar arrays is critical in today’s solar market.  Most utility rebate programs only pay back for the total amount of energy used at the site, and money that could have been earned from over-producing is lost.  Because of this, the penalty for over-sizing a solar array is a less cost-effective system and a longer payback.  In an industry where every penny per watt is important, it is very important that the solar array be sized accurately to the site-specific electric usage, array orientation, and the type of equipment used.
There are three variables in a basic array sizing calculation, the equation is:

System Size (Watts) = ((Watt hours) * η / (sun hours)

Where η is the DC to AC system efficiency, Watt hours are obtained from your utility bill, and sun hours are found using an online calculator from the National Renewable Energy Laboratory (NREL).  All of these factors are described and expanded on, so there is a clear understanding of everything that affects the size of the solar array, and more accurate system sizes can be calculated.  Once values for all three are obtained, it’s a simple matter of plugging and playing to get the solar array size in watts.

Watt hours:

Watt-hours are a unit of energy that is calculated just like you would think, by multiplying watts of power with hours in use.  Most of the time, the electric power utility will have values for this, and the only thing that needs to be obtained is the average daily load in watt hours.  Utilities will bill their customers per “kWh”.  This stands for “kilowatt-hour” and represents 1000 watt-hours.  The site usage in kilowatt-hours per month/year can be converted to watt-hours per day in order to get correct values using one of the following equations:

Watt hours/Day = (Kilowatt hours / Month) * (1 Month / 30 Days) * (1000 Watt hours / 1 Kilowatt hours)
Watt hours/Day = (Kilowatt hours / Year) * (1 Year / 365 Days) * (1000 Watt hours / 1 Kilowatt hours)
Often you will have more than one year of data to work with.  It is important that a time period that best represents the future electrical usage of the site be selected.  In most cases this is the most recent year’s usage at the site.  However, in many cases there are “outlier” months where a weather disaster or special event causes a spike in usage that the solar array doesn’t need to take into account.  In these cases, it is important to substitute data from the same month in previous years or take an average of other months’ usage data instead.  Creating an accurate estimation of the site’s future electrical energy use is the first step in determining what size solar array will offset that usage.

Sun hours:

Sun hours can be a confusing term.  It calls to mind the number of hours sunlight is hitting the solar array, which would correspond to average hours of daylight.  The reality is more complicated.  Sun hours are derived from the total amount of sunlight a given site receives, factored in with its intensity, the amount of particulate matter in the air, temperature, and other environmental factors that affect the amount of the light that reaches the solar array on the ground.  Solar panels are tested and rated to a specific solar intensity and environment.  The sun hours at any proposed site are equivalent to the number of hours a solar panel would produce rated power under these test conditions.  Additionally, the number of sun hours a site receives is dependent on the orientation of the solar array or how it tracks the sun.  Because of the factors that affect sun hours, it is best to use values for sun-hours obtained through analysis by NREL (National Renewable Energy Lab).  For the entire United States, and many international sites, NREL has done testing to determine the average number of sun-hours a given location will receive.

To find data for your location, the most popular method is to use NREL’S PVWATTS solar design tool (http://pvwattsbeta.nrel.gov/).   By entering your zip code, address, or coordinates, the viewer will locate your site on the map and give you the option to “Go to System Info”.  There are a few editable fields.  To determine the number of sun-hours, only the Array Type, Array Tilt, and Array Azimuth should be modified.  The Array Type is the type of mounting structure you are using, whether a fixed system or one that tracks the sun on one or two axes.  The Array Tilt is the tilt angle from horizontal that the solar panels will be at.  The Array Azimuth is the solar array’s orientation with respect to True South at 180 degrees (An array pointing north would be at 0 degrees, east corresponds to 90 and west is 270 degrees).

Figure: Using PVWATTs solar calculator to find sun hours for a specific orientation
After entering the proposed orientation of the solar array in the orange boxes, hit “Calculate” and you can see the sun hours for your site specific conditions.  This is found in the Results table, under the column “Solar Radiation”.  There is an average value for each month, which corresponds to a daily average for the month, as well as a daily average for the year.  The green box highlights the DC to AC system efficiency and its individual factors, and will be explored in the next section.

DC to AC System Efficiency (η):

The DC to AC system efficiency is a value that is estimated from the various efficiencies in the system from the solar panels to the point of interconnection with the electric grid.  The standard in past years was to assume a value between 75 – 80%.  Nowadays, with better equipment and installation standards, values higher than this can be safely used to get more accurate sizing of the solar array with less over-production.  For understanding solar system efficiency and the specific efficiencies that make it up, NREL’s PV Watts solar calculator is an excellent resource.   Within the same tool used to obtain a site’s sun-hours, there is a field that can be modified called “DC to AC Derate Factor”.  This can be adjusted as is, but the real magic happens when you go into “Derate Factor Help” and bring up a detailed list of everything that affects it.  See the green box in Figure 2.  All of the factors may look intimidating, but for the most part only 2-4 will ever need to be modified.  The other values can be changed if you know your site will receive some shading or significant snow-cover in winter.  Otherwise it’s best to leave them alone.

For PV module nameplate DC rating, the default value is 0.95.  This value is based on two things; the initial “burn-in” that can reduce module output once they’re installed, and the power tolerance manufacturers include with their solar panels (typically +/- 3 to 5 watts).  If you consider major brands, many solar panels on the market today have a positive-only power tolerance (+ 3 to 5 watts only), which means they will always produce rated power out of the box.  Because of this, if you are using a solar panel that has a positive-only power tolerance, this value can be changed to 0.98.

Inverter and Transformer represent the overall efficiency of the solar inverter that will be used.  The most accurate values for inverter efficiency have been obtained through testing by California’s Energy Commission (http://gosolarcalifornia.ca.gov/equipment/inverters.php).  These values are slightly lower than the maximum efficiencies for inverters found on data sheets.  However, they are typically much higher than the placeholder value, 0.92.  For example, a Power One 4.2 inverter is weighted at 96% efficiency at 240V, a 4-point gain in efficiency over the default value.

Mismatch arises from manufacturing tolerances within each solar panel.  Each one will produce a slightly different voltage and current under ideal conditions.  It’s not enough to grossly affect the output of a string of solar panels, but it is enough to introduce a loss in the system.  Standard string inverters are the only inverters affected by this value, because they depend on groups of solar panels wired together into strings to produce power.  Micro inverters and DC-DC optimizer systems are not affected by individual solar panel variance, because each inverter or optimizer is only concerned with maximizing the power output of their solar panel.  Because of this, the losses due to mismatch are completely marginalized; the factor can be modified to its maximum value of 0.995.

One added benefit of using a microinverter under each solar panel is the virtual elimination of any DC wiring losses.  Because of this, if you are using a microinverter as opposed to a DC-DC optimizer, the DC wiring losses can be minimized as well.

Enter the modified values into the calculator and hit “Calculate Derate Factor”, and the difference is clear.  For example, using a Hyundai or CSI solar panel and a Power One 4.2 inverter, the system efficiency is .828, or 83%.  It’s a pretty big gain from a 77% efficient solar array, and can make a huge difference when you size the solar array.  Even using a module with a negative power tolerance, like Astroenergy or Trina, you can see system efficiencies of 80% or higher.

 Power One String Inverter Enphase Microinverter Hyundai/CSI 82.8% 84.9% Astroenergy 80.3% 82.3%
Table: Sample values for η using different equipment

Appendix: Variables for Calculating Tilted Array Spacing

• Watt hours = Energy use obtained from your electric bill
• Watt hours = (Watts of power) * (Hours in use)
• Sun hours = Amount of solar energy available per day
• η = DC to AC system efficiency

Appendix: Equations for Calculating Tilted Array Spacing

• System Size (Watts) = ((Watt hours) * η / (sun hours)
• Watt hours/Day = (Kilowatt hours / Month) * (1 Month / 30 Days) * (1000 Watt hours / 1 Kilowatt hours)
• Watt hours/Day = (Kilowatt hours / Year) * (1 Year / 365 Days) * (1000 Watt hours / 1 Kilowatt hours)

SunPower buying Tenesol: beat me harder

Charles Manson said that you beat a man so long and after a while he gets to like the whip. What was SunPower thinking?  Do they want another whipping?  We have 50GW of cell manufacturing capacity in an 20GW world market. There are no financials on the Tensol deal so I’d be guessing if the \$165mm was well spent. On the plus side Tenesol has an integration business that might be bringing a backlog.  SunPower’s modules are beautiful and definitely worth a small premium but why pay \$0.50/w more than the current \$1/w?  Buying Tenesol does not seem like a solution for SunPower.

Conergy: it’s only hubris if you lose

Conergy is selling it’s inverter subsidiary; the giant is dying a death by a thousand cuts.  Conergy planned to parlay their street cred into a marquee brand, manufacture everything in house and capture the manufacturers margin in addition to the distributors margin. Double your money & double your fun.  Pity about the timing. The plan was conceived in a product constrained market when manufacturers could command almost any price.  By the time Conergy finished working out the manufacturing kinks, the global capacity exceeded supply and prices started to sink. Not enough customers wanted Conergy branded product.  Their brand was not strong enough to pull the company through a product surplus market. Conergy shut down the PV plants mid summer.  Now they are selling the inverter division.  Had Conergy succeeded, they would have been heroes. It’s only Hubris if you lose.

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