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that don't have access to electricity? Well, primarily, it's in Sub Saharan Africa and villages like this. This is a village in Zambia, there's no power lines that make it to this village. And so this is endemic across the continent, Sub Saharan Africa, so 70% of the people without access to electricity live in Sub Saharan Africa, another 20% live in South Asia, and 10% live in the rest of the world. And in my work. In my work history, typically, you find that a lot of organizations, a lot of attention is focused on Sub Saharan Africa and South Asia and not that rest of the world slice. So it's important to not forget that even in places like the United States, and a lot of our tribal communities, there are homes that don't have access to electricity. Some estimates that I've seen in North America put the number of people without access to the grid to be somewhere north of 100,000 people, which is a significant amount, maybe even up to 200,000 depending on what you what you count as access and what you don't. So our webinar today is primarily going to focus on this, this electricity access on the Navajo Nation. And the challenges with that, but also the opportunities and and what we've learned from off grid electrification on the Navajo Nation. So let me just give you just a very brief background of the electricity access situation. In the United States, rural electrification really took off in the 1930s, with the intervention by the federal government that provided huge subsidies and loans to electrify rural areas. However, Navajo Nation, like many tribal communities, tribal lands in the United States were overlooked by that government intervention. So they didn't, they didn't receive the benefits.
Now reality of the situation is that to extend a power line, you know, usually cost somewhere between 20 to $40,000 per mile, it's quite expensive. On the Navajo Nation, some of the homes are so remote, that there may be 40 miles from the nearest power line. So you can think about how much it would cost to extend the power line to that one home that is 40 miles away, it would be over a million dollars. And it makes sense then that, you know, it's it's not the highest priority, or it's not really economically justifiable to spend a million dollars to connect one home. In addition, Navajo Nation and historically they've been raised sheep and goats and horses and so forth. And so it's a pastoral community, where they are used to having lots of land surrounding their homes with neighbors quite far away. So there's low population density. So you combine the remoteness, the sparse population, you put those together, and it's a perfect recipe for low electrification, it will require substantial subsidies to connect all the homes. So as a result, there's about 10,000, maybe even 20,000 homes that aren't connected to the grid on the Navajo Nation, progress as is being made, but it's still a substantial gap. And the Navajo Nation represents about, you know, the least electrified of all the US tribal reservations. So that's kind of a background. That's maybe why the situation is the way it is. And thankfully, the Navajo tribal utility authority has been making a lot of progress in in changing the situation. So let me turn it over to Derek here to talk a little bit more about NTU a. 

really interested in is how has consumption changed on the longer term. So what we did is we looked at the total consumption took the average of it of all the homes per month from inception. So this goes all the way up to about March of this year. And, you know, we do notice a couple of attributes here, right, we noticed that there is a seasonal profile here that tends to peak in the summer. This is interesting. There may be a couple of reasons why for this. One is that there could be some electricity that's used for cooling. We also think that there it could be attributed to work in school patterns which have a seasonality to IT people children might be or adults might be home during the summer, more people in the home usually means more electricity uses. It also could be related to the availability of the energy, sunnier in the summer, so maybe people know that they can consume more, more energy. One of the other things that we know is that there's actually from 2021 to 2022, a decrease in energy consumption. This is a little atypical from maybe your experience in Sub Saharan Africa where generally we see growth. There could be some reasons for that. One is that in 2021, the Navajo Nation, very much had COVID restrictions applied to it. So people were working from home. They stayed at home a lot more in 2021 than 2022. So as more people left the home and 2022 Maybe that had to do with the decrease. Maybe that was Despite the consumption decreased, it's also possible that the components made degraded from year 2021 to 2022, making less energy available. So we're doing some surveys and we're looking into this in more detail. But right now it's it's what the data is showing us that there is a decrease. Now, if we drill down, instead of looking at overall averages of all the homes, if we look at how much energy each home consumed on a particular day, and we plot the histogram of it, we get something that looks like this. So on the AC side, the average consumption was 3.58 kilowatt hours per day. But you can see from this distribution, there's a wide variety of that not every home consumed 3.58, right, there was a wide distribution, some consumed multiple times that some consumed far less than that. By the way, 3.5 kilowatt hours a day is is actually quite low, if you look at say New Mexico, their average for grid connected homes, it's more like 20 to 24 kilowatt hours per day. So this is still providing access to electricity, but it's not replicating the grid. And I think that's an important aspect. Now, if we look on the DC side of the system, the DC side of the inverter, the consumption is probably about five kilowatt hours a day. This is based on an estimated inverter losses. So that that jump from 3.58 to five has to do with the inverters, you know, its internal fans turning on its its keeping its own lights on etc. And that is actually more energy that that difference of about 1.5 kilowatt hours is about 15 to 20% of the homes actually consume less than that on the AC side. So it can be significant. And I know as a result of that, that understanding, NCUA is now installing systems with much smaller inverters to try to reduce those standby losses because eight kilowatts of consumption very rarely ever occurred. So this is what it looks like in form of a in the form of a histogram, if we wanted to look at it in a slightly different way. This is looking at the this is an empirical inverse cumulative distribution function where we can see the percentiles or quantiles, and how much they consumed. So as an example, if we look at the 50th percentile, that's the median. So half the homes essentially consumed more than 3.14 kilowatt hours a day half consumed less on either of the extremes, if we jump up to the 95th percentile, you know, then we get to 6.77 kilowatt hours a day. So 95% of the homes consumed no more than this. Understanding this curve is important in determining what's an appropriate size for your system. Generally speaking, we don't size around the maximum, we would design around maybe the 95th or 97th percentile, because we'll see, to meet the needs of everyone, you end up with a very, very large system. So you're if you want to as a little guide, this is how you would interpret that the 50th percentile, you draw a line straight up, and you would go to the left to see the consumption. Now homes consumed, generally had a wide variety and their daily consumption. So even within a home, there was a variety and consumption, some homes were a little more consistent than others, some exhibited a wide variety. So if you look at their average value, which is this dashed red line, some homes stayed, you know, within a multiple of it, some it was three or four or five times their average that they consumed on Sunday. So this could be days where maybe they had company over days at work was extremely hot or extremely cold, whatever the reason. And so this also this wide variety that that some of the homes exhibited makes it challenging to design the battery bank to figure out how many days of autonomy is actually provided. And, and it's important characteristic to look at on a per home basis, right, it's the variation that happened. Now just to provide a specific examples here are 25 homes and the box plot of their energy use. So what we see here is that little green horizontal line, that's the median daily consumption for that home, and then within the box, it's the 25th and 75th percentile. So it gives you an idea of the range that typically were exhibited by homes. You can see for most homes, the consumption is less than five kilowatt hours a day. Although there are some that is a bit higher, and some have small ranges, some have large ranges. One of the most important things to note here, if any of you are researchers that are trying to model off grid consumption is that the distributions aren't normal, they're not Gaussian distribution. So if you make that assumption that the day to day consumption follows a normal distribution, that's really not that accurate. These are these are, they don't follow any parametric distribution that I'm aware of, although maybe our future research tasks can be modeling, distribution functions to fit these. So they all exhibit sort of a Skewness in the positive direction with outliers. 

to the next. And you can see that it's fairly consistent with most seasons, sort of in the the the spring and summer months, you have more load that occurs during the day. But more or less, you see that two peaks that generally happen. So what does this all tell us in terms of design? Well, we looked at how the PV arrays are sized based upon the load that was actually recorded. So the first thing that we did in this research was to figure out how much energy could be, we could expect these PV panels to produce. And to do that we use the simple formulation, I don't think I'm gonna go into it in detail. But essentially, you can estimate the energy that that can be produced by PV array, based upon the average installation of the area, accounting for the tilt and the the latitude and longitude and the losses. And we picked 4.2 to be 4.5 kilowatt hours per meter squared per day, that's the January average installation for the homes that have the solar systems. And then from that, we said, well, we need to apply a right to load ratio of about 1.3. Because you have to oversize to some degree, make up for times when the consumption is a lot higher, or the battery charging profile doesn't let you consume as much energy as could be produced. So when we do that, we can take the two equations, and we can put them together, and you come up with a result that for every one kilowatt hour of dc side load requires three 385 watts of PV capacity. So based on those assumptions, for every kilowatt hour of dc side load, that's how much capacity you would need to serve it. And so what we did is we looked at the distribution then of dc side load has figured out how large of a PV array we would have needed now this is retro, I mean, we're looking, we have the benefit of having this data. So we're looking back, we didn't have this data, of course, during the design phase, but what it tells us is that because the consumption is fairly low, the we can serve about 50% of the homes with a 1.7 KW array. And I remember that the arrays themselves are somewhere around here, you know, 3.8 kW. So in some cases, in fact, many cases, the PV array could be made a lot smaller, and and still provide the homes, but it wouldn't be able to provide enough energy for all the homes, right. But it does suggest that an approach maybe in the future would be would be to offer maybe smaller arrays for, you know, maybe half the homes and then the other half could get these larger arrays. And that could be a way of saving money, if interested. A similar approach would be to look at the battery bank sizing, 

or we look at the days of autonomy and we do some calculations based upon that. And I think I'll go through this a little bit fast, but we make some assumptions on how the batteries are going to behave over time, how deeply they'll be discharged and what their charging efficiency would be and based upon on these reasonable assumptions, for for every kilowatt hour of dc side load, you need about six kilowatt hours of battery size. So we again can look at the actual DC size, load dc side load and see how large of a battery would need to meet, it took me three days of autonomy. And what we see is that the existing battery banks provide three days of autonomy for about 75% of the systems. So you might say, well, the target was three days of autonomy, this seems to, you know, you're only doing that for for three out of four homes. So maybe the design was off. But to really look at what it would take to provide three days autonomy for all systems, it would require more than doubling the battery bank capacity, which would result in gigantic battery banks. So here, we're highlighting the trade off, right, you know, if you're going to have one design that you stick with, where on this curve, where on this table Do you want to be. And I would argue that meeting 75% of the homes with three days of autonomy is probably a good trade off, the more homes that you serve, the larger the battery bank, you need to have for each home. So let me just point out a few things. Before we talk about future work. What we've kind of shown in this design case study of looking at having the benefit of having now historical data shows a few things. First of all, if you didn't have the data, estimating the size of the load, and the size of your components, it's very difficult, especially in contexts where there's not a lot of literature. also point out the NCUA when they rolled these systems out, we're less concerned about capital costs, and more concerned about getting them rolled out quickly. And having sort of a one size fits all for just efficiency on there. And, and then also, this, as Derek pointed out, the service costs are high getting out to some of these areas can take hours. So you'd rather have maybe your PV array larger than it needed to be if that meant one fewer trip that you had to take a year. So we shouldn't ignore the maintenance and service costs. Now that we're just sort of scratching the surface on the analysis that we can do here. We just like what I presented was just about electricity use, Muhammad is going to briefly talk about some of the future analyses that we're looking at. So go ahead and a holiday.
you Harry. So, our future analysis will include analyzing battery voltage profiles, in order to give us insight about the reliability of the system, as you can see here in the figure, which provide a typical voltage profile. So, a little after sunset, after sunrise, there is enough solar power for the batteries to recharge, which is evident by the battery voltage increasing rapidly. And this is called the bulk charging stage. And once the battery voltage increases to predefined set points, as you can see observed called the absorption voltage. It's usually for between 4546 to 50 volts depending on the temperature here it's above that then the charge controller regulates the battery voltage as such doesn't damage the battery by over over voltage. And this is called the absorption stage, which can be sold as a few minutes too long the longer hour several hours for example. And when the battery is fully charged battery is fully charged transmission to float stage. And the battery is maintained at a lower voltage. As you can see lasting from about 11am in this graph to 4pm. And this typically this profile just shows a typical behavior it doesn't happen always exactly like this one. But this is typical behavior show in over a year in multiple systems. So we'll be trying to investigate multiple multiple systems sample from system that we have over the year, and see how the behavior is showing in order to give us insight of derivative system. This next slide shows an example of a time series analysis for the battery. This is 10 days chunked in days in January. You can see most of the days where the absorption stage reached. However, there are some some days didn't it didn't reach the absorption. Or sometimes it's different times happen. For example, in January 1, the absorption stage was only reached late in the afternoon. It could mean that the battery was never fully recharged on that day. So we are now investigating if the timing of wind absorption stage is reached and how often it's reached it and also which will give us an insight about the relative system. Next slide. This graph shows the history RAM for the voltage, as you can see here in the system spent significant amount of time at around absorption voltage. So, between 40 and 56 volt. So this does indicate a higher reliability of the system. This graph shows the example of the time at which the absorption stage is first reach for for different unit, some get recharged earlier in the day, which again would suggest that the batteries are being fully recharged. So, now we are at this stage of analysis, we will try to get solicits at what time exactly the battery reach to the recharge to the fully absorption over the year for multiple systems. And we'll compare and see the reliability of the system across the year. So, this is a type of analysis that you can do if you have such data for off grid system. And hopefully we'll get more insight from there is that we have this futurism research.
on you for see to hear more about where you can see some of these questions and dressed and for snippets of this particular webinar. And we've shared the link to the webinar series that Henry generously provided previously, that includes a lot of detailed guidance on on how to load estimation amongst other topics. With that, I want to wish all of you a good morning and good evening or good afternoon, or looking forward to seeing you on another webinar soon. And thank you all so much for your attention, your time and your thoughtful questions today. It's been a fantastic conversation. Enjoy the rest of your day everyone. Take care. Thanks