Your Restaurant in Brooklyn: Math! Darn Math! And Statistics!

We’re back again to your restaurant in Brooklyn once again. Let’s review what has occurred so far.  In week 1, you opened the restaurant only to discover that it had no electricity.  In week 2, you corrected the problem by installing a diesel generator.  In week 3, you starting seeing the downsides of having a generator – the smell, the black smoke, the sound, and the potential to run out of fuel.  Week 4 was a slight detour from the story to look at the impact of Hurricane Sandy, and see what would have happened if your restaurant were operating on a micro-grid at the time the storm hit.  In week 5, we started getting into the design of the micro-grid, and determine the size of the PV system that could fit on the roof of your restaurant. And, in week 7, we determined the size of the generator, and equipment we were going to us as the “brains” of the micro-grid (SMA Sunny Island) and how many of them we were going to need.

And, here we are in week 8 (It’s so true!  Time flies when you’re having fun!). We’ve gotten to the last piece of the initial design – sizing the battery bank. I’m sure you’re really excited to just dive right in are start crunching the numbers (I know; I am too!). But, it’s always good at this point to take a step back and think about what we want to accomplish with this battery bank. What are the loads for which we want to be able to provide back-up power?  How long do we want to be able to provide back-up power?  And, are there any other requirements that we want to meet?

Goals of the Battery Bank

The easiest place to start is to take a look at all of our equipment and see if there are any minimum requirements for batteries. Sure enough, the SMA Sunny Islands require that you have at least a 100 Ah battery bank per cluster, and that each battery bank puts out 48 V. Battery banks are sized in Ah, or amp-hours. For the time being, we’re just going to carry this value forward as we set out the high level requirements for our battery bank.  Once we start crunching the numbers, I’ll provide a thorough explanation of what Ah stands for, and how to convert that into our standard kW and kWh. We have two clusters of SMA Sunny Islands, with 3 Sunny Islands in each cluster.  So, we need at a minimum two 100 Ah battery banks.

The next piece is to look at our sources of electricity. Let’s start with the PV system. Don’t worry; we’ll get to the electrical grid and the generator soon enough. (You could start with the grid or the generator, but my experience is telling me we’re going to learn more from starting with the PV system than we will from starting with the others.) Does the PV system production have any influence on how you’re going to size the battery bank? The answer is that it could. If your PV system ever produces more electricity than you need at that moment in time, you want to be able to capture it. If you don’t use the electricity or store the electricity right when it’s being produced, you’re going to lose it, and thus part of the value of your PV system. In the case where the grid is very stable, you can send it back to the electrical grid and spin your meter backwards. It’s a process called net-metering. You end up using the electrical grid as your battery bank. The price to do this is extremely cheap – typically less than $100 to file the paperwork – so I highly recommend this method if your electrical grid is stable enough. In your case, the grid is only operation 30% of the time, so this isn’t going to work. So, our design requirement for this is that the battery bank needs to be sized large enough so that any excess electricity produced by the PV system can be stored in the batteries for use at a later time.

What about the generator? Do I need to capture the excess electricity it produces when we don’t need it? Generators operate differently than a PV system. PV systems produce electricity when the sun shines, while generators produce electricity by burning fuel. You can’t really control when the sun is going to shine, but you can control when you burn the fuel in your generator. So, the generator will only run when you can use the electricity. Because a generator can be turned on and off when needed, it is called a dis-patchable form of electricity. The sun doesn’t always shine, and when it does shine, it can be of varying intensity (leading to varying amounts of electricity being produced). This leads to PV systems and other types of similar systems to be termed intermittent, since the amount of electricity produced at a given time isn’t guaranteed. No impact of the generator on you battery bank design.

What about the electrical grid? From an energy source point of view, it has the same characteristics as the generator – it will only “produce” as much electricity as you need at a given time.  So, there’s also no impact from the electrical grid on your battery bank design.

The next item you have to consider is your uses of electricity, or electrical loads. Below are all the electrical loads in your restaurant, along with how much max power they’re going to draw, and how many hours out of the day they’re going to operate:

If all of your sources of electricity (PV system, electrical grid, and generator) are fully operating, all of these electrical loads will also be operating. To understand how you want your local electrical system to behave, you need to run some high-level scenario analysis on what will happen as your various sources of electricity trip off-line. If we go one by one, you’ll start to get a better understanding of how all the sources of electricity interact with each other and your loads, and how the batter bank (technically another source of electricity) allow the electrical system’s operation to be optimized to your needs.

First, let’s start with the PV system. What happens when the PV system goes off-line? Well, PV systems tend to be very robust, and will rarely malfunction to a point where the entire PV system is not operational. (Understanding how critical PV system operation is to the overall electrical infrastructure allows you to make some different decisions from a design point of view. There are ways to design PV systems with multiple redundant systems that greatly diminishes the chance of a mass failure of the PV system. More on this in a future article as we get into the nitty-gritty details of PV system design.) But, the electricity production of the PV system will change with the intensity of the sun, and will be zero between sunset and sunrise. So, between sunrise and sunset part to all of the electricity for your electrical loads will come from the PV system, but you’re going to need some other source of electricity overnight.

How about the electrical grid? Well, near your restaurant, the electrical grid is very unstable, and very unpredictable. You can never really count on getting your electricity from the grid at any given time. This is why you installed a generator in the first place. But, if the grid is operational, the electricity you get from it is cheaper than buying diesel to run your generator. So, when the PV system is operating, and the electrical grid is operating, the electrical grid will provide the shortfall electricity demand between what the PV system is producing and what the electrical loads are requesting. When the PV system is off-line, and the electrical grid is operating, the electrical grid will provide all of the needed electricity.

Now, let’s take a look at the generator. In these scenarios, the generator is only going to turn on when the grid is not operating, and when the PV system is not producing enough electricity to fully supply the electrical loads. The generator is dis-patchable, and controlled by the SMA Sunny Island, so it’s only going to turn on when it’s needed. But, when is the generator not going to work? And how likely is that failure? The number one cause for a generator not turning on in a micro-grid system is lack of fuel. And, at your restaurant, you have experienced at least one instance where you didn’t get the diesel you needed in time. So, I would say this is a scenario we need to look at a little deeper.

The SMA Sunny Island will turn on the generator only when the PV system is not producing all of the required electricity, and when the electrical grid is not operating. (If the electrical grid is operating, you’ll never run your generator anyway, so you don’t need to think about that scenario.) If the generator does not turn on, this is where you can get your restaurant into trouble. The problem will escalate quickly if the PV system is producing very little electricity or no electricity at that time. So, this possible scenario is going to happen in the early evening and the condition will persist until the sun comes up in the morning, and the PV system begins producing electricity again. The last and only source of electricity you have at this point is the battery bank.

Now time for the difficult decisions – what electrical loads are absolutely critical to you in this scenario? All of a sudden, a number of those items on the previous lists start to fall away, and only a few critical loads begin to stand out. So, here’s the short list of the critical loads – refrigerator, freezer, outdoor security, indoor AC unit, and some minimal lights in the sitting area. (The lights in the sitting area are only required if this happens during operating hours, and could ultimately be replaced by emergency lights that have their own integrated battery back-up.)

That was a tough process to go through, but you now have some parameters for your battery bank. So, here are the requirements we’ve come up with:

1.)   At least two 100 Ah battery banks (one battery bank per cluster)

2.)   Large enough to store all of the excess electricity produced by the PV system

3.)   Large enough to be able to power the critical loads until the PV system turns backs on (and can power those loads) and you can get diesel fuel delivered to run the generator

So, those are our guidelines.  Now let’s turn them into an actual battery bank

Turning the Guidelines into a Real Battery Bank

If you went to your local battery guy with this list of requirements, he’d laugh at you. Without more information, there’s no way to figure out just how many batteries you’re going to need, and of what size.  The first guideline has a hard number associated with it (a 200Ah 48V battery bank), but you need to put some numbers around the other two design requirements.

Let’s start with the PV system requirement first. In order to put some numbers to this, we’re going to need to know just how much electricity your restaurant uses, and when during the day you use it. Luckily, you followed my advice from the previous article. You installed some CTs on the main feeders in your electrical panel and collected hourly load data for three days. Now, you know what the hourly electricity usage looks like in your store:

The next part is determining just how much electricity the PV system will produce on an hourly basis. A few weeks ago, I wrote about some tools to use to determine the amount of electricity that can be produced by the PV system. The same PV Watts tool also provides an average hourly production value for the PV system, if you know where to look. At the bottom of the PV Watts output page there is a button that allows you to “Output Hourly Performance Data”. This will give you the data you’re going to need answer the battery sizing question for part 2. And here’s a small sample of what a day’s worth of data looks like:

“Year”, “Month”, “Day”, “Hour”, “AC Power (W)”
1991, 1, 1, 01:00, 0
1991, 1, 1, 02:00, 0
1991, 1, 1, 03:00, 0
1991, 1, 1, 04:00, 0
1991, 1, 1, 05:00, 0
1991, 1, 1, 06:00, 0
1991, 1, 1, 07:00, 0
1991, 1, 1, 08:00, 148
1991, 1, 1, 09:00, 355
1991, 1, 1, 10:00, 533
1991, 1, 1, 11:00, 649
1991, 1, 1, 12:00, 709
1991, 1, 1, 13:00, 667
1991, 1, 1, 14:00, 573
1991, 1, 1, 15:00, 531
1991, 1, 1, 16:00, 353
1991, 1, 1, 17:00, 136
1991, 1, 1, 18:00, 1
1991, 1, 1, 19:00, 0
1991, 1, 1, 20:00, 0
1991, 1, 1, 21:00, 0
1991, 1, 1, 22:00, 0
1991, 1, 1, 23:00, 0
1991, 1, 1, 24:00, 0

It’s important at this time to spend a little time understanding the data that we have to answer this question, and make sure that we understand the limitations of that data. Firstly, you only collected load data for your restaurant for three days. We are making the assumption that this data is representative of your electrical draw throughout the remainder of the year and into the future. If this data was collected on an “abnormal” day, like the warmest three days on record in the last 50 years, then your data is going to be a little off. Secondly, the data from PV Watts is also making a few assumptions. The hourly data from PV Watts is “meteorologically typical” for the site. This means that for the given hour, and the given day, this is roughly the average electricity production you can expect.  Over a long period of time, you can expect the electricity production from a PV system to closely match the values from PV Watts, but the shorter the period of time you will have more variance from this average. PV Watts explains that for any given year, the actual production of a PV system will be + or – 10% from the PV Watts estimate. If you look at the monthly actual production values compared to the PV Watts estimate, these could be + or – 40%. They don’t provide an estimate for the daily or hourly estimates, but judging by published errors over the year and month estimates, I figure it’s pretty high.

Think of it this way.  In my hometown, Chicago, there are on average 189 sunny days – a little over 50% of the days are sunny, so I can think about it like flipping a coin. If I flip a coin once, it’s either going to 100% head or 100% tails – much different than my 50 / 50 heads / tails average. If I flip it twice, I get 4 outcomes – 100% heads will happen 25% of the time, 50 / 50 heads / tails will happen 50% of the time, and 100% tails will happen 25% of the time. And, as I increase the number of times that I flip the coin, my measured outcome will get closer and close to the average.

So for the PV system production, we’re making the assumption that most of the time the PV system is going to produce close to the average. But, knowing that the actual production could be significantly higher or significantly lower than our model, we can make some adjustments to the design based on this knowledge. For instance, we don’t want to waste excess electricity produced by the PV system above and beyond our electrical load. So, we can take that into consideration when sizing the battery bank.

Let’s dig into the data, and figure out how big this battery bank needs to be to fulfill your second design requirement.  So here’s the math:

Electrical Load (in kWh) – PV System Production (in kWh) = Net Load (in kWh)

So, what are the results of this equation telling us? Well, for a given hour, you’re determining how much of the electricity needed is being delivered by the PV system. If the net load is positive, there’s a shortfall of electricity, which will need to be made up by either the electrical grid or the generator. If the net load is negative, it means the PV system is putting out more electricity than is currently needed, and this electricity will need to be stored in the battery bank. You’re going to need to do this calculation for every hour of the year – 8760 times in all.  (I highly recommend using a spreadsheet for this.) You’ll need to sum all consecutive hours where the net load is negative. (You can assume that the battery bank will provide some electricity overnight to serve loads, since it’s less expensive to use the PV system than to run the generator.) The highest amount you get will be the most you’ll ever be pushing to the battery bank on any given day. The amount is 12,868 kWh in September.

Awesome – you need at least a 12,868 kWh battery bank to store extra electricity from the PV system. But wait aren’t battery systems sized in Ah and not kWh?  How do I make the conversion?  It’s going to require use to take a look back at our power formula from last week (

P = I x V

Power (P) = Current (I) x Voltage (V)

The power into the battery bank has to be equal to the power being produced by the PV system, minus any losses experienced in the conversion. And, if you look at the spec sheet for our SMA Sunny Islands, the round trip conversion rate is 95% and the battery bank voltage is 48 V. Here’s what the math looks like:

P (PV System) = V x I (battery bank)

12.868 kWh x (1 kW / 1000 Wh) = 12,868 Wh

12,868 Wh x 97.5% conversion = 48 V x Y Ah

Y Ah = 261.4 Ah

So, now for part C, where we determine how much electricity we need to power our critical loads until you can get diesel for the generator. First, let’s start by looking at just how much electricity our critical loads are going to draw on an hourly basis. Here’s a table of all our critical loads:

Let me point out a couple things before we proceed. The values of “draw” for the critical loads are those values that are present on their electrical information tags. These values are for the most power that these pieces of equipment will draw at any given time, but may not be completely representative of how much energy they will use over time. (Think of your refrigerator at home. The “draw” written on the tag reflects the amount of power the refrigerator will require when the compressor kicks on. You can hear when the compressor kicks on. It’s not always on, is it?) I’m okay with these values because I know that these values are conservative, and because measuring more “accurate” values for these would require much more time and effort. (It might make sense if the load you’re measuring is down the hall or down the street. In my case, it’s halfway around the world. So, the values I have are good enough.)

The next question to answer is just how long do I want to provide electricity to these critical loads?  If you look at the extremes, the PV system goes off before 7pm at night and turns back on a little after 7am in the morning. (Lagos, Nigeria is 5 degrees north of the equator, so I don’t really have to make any corrections for seasonality. However, if you’re planning a system like this in Brooklyn, make sure you take account the shorter winter days in your calculations.) Let’s start with 12 hours of critical load electricity just to give us an idea of where we stand. And, now to the math:

 P (critical loads) x hours = V x I (battery bank)

4,672 W x 12 hours = 48 V x Y Ah x 97.5% conversion

Y Ah = 1,197.9 Ah

 So, from experience I know that’s a fairly large battery bank (which is going to get fairly expensive). But, at least you now have a range for the size of the battery bank – 260 Ah being on the aggressive side, and 1,200 Ah being on the very conservative side.

I always like to run the calculations the other way, just so I know what I’m dealing with. This way I’ll know just how much back-up capacity I’ll have if I install my very aggressive 260 Ah battery bank.  Here’s the math:

P (critical loads) x hours = V x I (battery bank)

4,672 W x Y hours = 48 V x 260 Ah x 97.5% conversion

Y hours = 2.6 hours


A battery bank that small isn’t going to work for this application, but it’s good to know.

Battery Basics

A couple more useful tidbits about batteries before you nail down your exact battery bank size.  You’re really going to have to spend some time thinking about how often you’re going to be cycling (charging and dis-charging) these batteries. Each battery is good for a number of cycles, but the more deeply you discharge that battery, the faster the battery will degrade, and the fewer cycles you’re going to get out of it. Below is a cycles versus life graph with cycles on the right and depth of discharge on the bottom.  Each battery manufacturer will have these for each of their battery types.

If you look at the graph, you’ll notice how much depth of discharge has on the battery life.  For your restaurant with a 260 Ah battery bank, you’re going to discharge it 100% every night, because you don’t ever want to waste excess energy being produced by the PV system. Because you’re discharging it 100% every night, your battery will only last 350 cycles, or 1 year. But, if you triple the size of the battery bank to 800 Ah, you’re only going to be discharging the battery about 33% every day. That means that your battery bank will last about 1,800 cycles, or 4.9 years. Given what we know about your system, and about batteries, the new range for your battery bank is 800 Ah to 1200 Ah.

(There are also some temperature correction factors that also need to be taken into account when finalizing the size of the battery bank. The warmer it is, the shorter the batter life and vice versa.  We’ll leave this until we’re specifying the exact equipment we’re going to use for the PV system.

The Wrap-Up

A lot has happened over the last few weeks. We’ve managed to go from an initial thought behind a micro-grid to actually sizing the major components of the system. So, here’s our system:

PV system:                                                       22 kW (88 solar panels)

Generator:                                                      30 kW

Sunny Islands (the brain):                  30 kW (six 5048 units)

Battery bank:                                                      800 Ah to 1200 Ah

Congratulations! That’s a lot of design work that you just completed. If I were you, I’d go home and crack open a beer. You’ve earned this one.

Next week, you’re going to take a hard look at your existing restaurant building and see if everything you’ve designed is going to work the way you expect it.  For me that means travelling to Lagos, Nigeria and confirming all the specifications and details I have been sent over the last few months regard the installation at which I’m looking.  I’m sure I’ll have a few store to share.

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