DIY Solar-Powered PC
This is part three of the three part article. Part 1 is here.
DYI Solar-Powered PC Solar Components
Daniel Schuhmann
September 25, 2007 07:44
A Positional Tracking Solar Array
Our solar panels orient themselves automatically to the sun's position, and provide power for our solar-powered PC. A battery stores excess (or unused) power to provide juice for nighttime operation. In this third installment of our article series on a DIY solar powered PC, we explore and explain the construction of our solar array, describe necessary components and tools, work out the battery capacity and lifetime, and provide plenty of pictures of our experiment in installing and using solar power to drive our PC.
The total costs for our solar power delivery and storage system run in the neighborhood of $5,000.
Those readers who might like to start at the beginning of this series will find the first two installments here:
- Technical Foundations: DIY Solar-Powered PC [local copy on DotRose]
- Testing and Choosing Components: DIY Solar Powered PC [original copy at Tom's Hardware]
As you dig more deeply into solar power technology, you'll quickly come to understand that solar power for PCs or other electrical components are not readily available. That's why you shouldn't expect to pick up the gear (or even a suitable PC) at your neighborhood PC retailer. That said, we made sure to design and build our solar-powered PC as a normal desktop PC, even though it draws only 61 Watts, including the monitor.
Because nobody's done anything similar just yet, we can only assume this effort will spawn plenty of imitations. We were even able to achieve reasonable computing performance, thanks to the powerful yet energy-efficient dual-core AMD Athlon X2 BE-2350 we used in our system. Our extraordinarily low level of power consumption was only possible because we tested each and every candidate component carefully for efficiency: random selection of seemingly suitable components simply won't do. Our Munich test labs worried about every half-watt of power consumed, and designed this PC to run as long as possible, even when the sun isn't shining bright (or anywhere in sight).
In this third installment of our "DIY Solar Powered PC" series, we construct our solar array and position it on the roof of our Munich test lab. We'll show you which components we used and how to install each of them, step by step. Our most important observation in this regard is that the solar cells are constructed to orient themselves automatically to gather the sun's rays most efficiently. That's why we constructed the array so that manual adjustments aren't even necessary. That's also why we will briefly present all facets of the solar array's design and construction in a live Webcast very soon.
The solar-powered PC we described in Part 2 now runs entirely off solar power
As we put this project together, we needed components that don't normally appear in standard solar power installations, to make it suitable to drive our PC. Because this entire project is something of a research project as well as a feasibility experiment, we chose not to use materials designed for permanent or long-standing use. This enabled us to be more flexible about the experiments we conducted, and to work "on the cheap." But the electrical circuits we used in our project are standard and well-documented, so that others can follow in our footsteps with relative ease.
Solar modules on the roof of our Munich test labs
Our solar array delivers up to 260 Watts of power at maximum output. With the current that our solar generator produces we power our PC all day long, and take advantage of our storage battery to deliver additional power at night, when the solar cells aren't producing any power themselves. As we started down this road, we had to work our way through numerous initial attempts, before we came up with an approach that produced the results documented here. Along with numerous size and arrangements of power leads, to connect our arrays to our battery and then to the PC, we also had to conduct complex calculations of our energy budget. One primary goal of our project has been and remains our desire to communicate our findings, and to stimulate further development of power generation techniques for the future.
Mounting and installing our rooftop solar arrays begins with framing them out.
On our Internet forums, we've observed that energy consumption for computers is one of the most popular topics of discussion. We have succeeded in building a desktop PC system that runs completely and exclusively off solar power, so that all typical office applications and uses may be carried out.
Polycrystalline Solar Cells Produce 260 Watts
Of course, the most important component in any solar array is the solar modules themselves. These convert the energy in the sun's rays into direct current (DC).
Each solar panel delivers up to 130 Watts of electricity.
For our solar array we used two PX 130/6 solar modules, each of which produces a nominal maximum output of 130 Watts. We purchased these modules in advance from German manufacturer Sunset Solar; similar offerings from Kyocera and Sun Electronics are available in North America.
Specification tag from the solar module
To meet the values called for in the power output specs, the modules must be exposed in an area where incident solar energy achieves levels of at least 1,000 Watts/m2 at a radiation spectrum with an air mass (AM) of 1.5 (ozone value; see this explanation at Newport Corporation for all the related details) at a temperature of 77° F (25° C). Energy output from solar cells decreases as ambient temperature levels increase.
Because the efficiency of a solar converter decreases until it approaches the nominal maximum output during the first year of use, we purchased solar cells with about ten percent higher power output than we needed. That's why our solar cells also produce "extra power." Because we included two solar modules in our design, on peak sunshine days we have over 260 Watts at our disposal. For the polycrystalline silicon solar cells we chose for our installation, power conversion efficiency typically operates at about ten percent.
Over time, the position of the sun in the sky changes regularly. In Munich, it rises in the east, appears in the south at mid-day, and sets in the west. Because we wanted to collect as much solar power as possible, we positioned the solar cells for maximal efficiency, and set them up so they could orient themselves toward the sun automatically. Because the inclination of our arrays couldn't be completely optimal owing to technical installation issues, we were only able to collect 80% of the theoretical maximum from our arrays. Those who follow our lead will realize different levels of efficiency as well, simply because no real situation ever achieves theoretical perfection.
On those perfect sunny days where not a single cloud occludes the sky with between 8 and 18 hours of sunshine, we could theoretically accumulate up to 2.6 kWh of power. Assuming something less than perfection, particularly because of the ever-changeable weather, we assume that our actual collection will fall somewhere between 1 and 2 kWh less than that amount.
Attaching The Solar Modules
Because our solar array is a research tool, we didn't follow standard industry practice and enclose the solar modules within aluminum frames. Instead, we used lumber available at any home improvement store. This not only made it easy for us to build and set up our installation, it should also make it easy for us to change things up any time we like.
Measure twice...
Cut once...
... and drill out the lathes.
First version of the solar framework
Framework with solar panel installed
Complete framework, ready for mounting on the rooftop at our test lab
Photo Essay: Constructing The Solar Panel Framework
The motherboard and components from Part II, the Solar-Powered PC, which runs entirely from solar power.
Solar cells on the roof of our Munich test labs
Construction of our solar arrays for outdoor use
Our solar panels deliver 130 Watts of power.
Specifications tag from our solar panel.
Measuring the lumber for the solar panel frame.
Sawing
Tools and lumber for the solar panel framework
Using one trimmed piece to measure a second keeps lengths consistent.
Cutting a framing lathe
Short and long pieces, side-by-side.
Frame stock ready for assembly in background, assembled panel in foreground.
Constructing The Solar Panel Framework, Continued
Drilling pilot holes for wood screws to speed frame assembly
Cutting frame members
Checking measurements
Double-checking measurements
Screwing the solar panel framework together
Assembling the solar panel framework.
Holding a partially assembled frame
Both sides of frame now attached
Assembly of solar panel frame continues
More drilling required
Moving the frame
Pausing to enjoy partial fruits of their labors
Constructing The Solar Panel Framework, Continued
Let's drill this hole at an angle
Solar panel framework with solar panel attached
Detail of solar panel prior to mounting
Mating up the framework to the solar panel
Attaching the framework to the solar panel
Attaching the framework to the solar panel
Assembling the complete framework, including solar panel
Assembling the complete framework, including solar panel
Assembling the complete framework, including solar panel
Assembling the complete framework, including solar panel
Assembling the complete framework, including solar panel
Checking framework construction
Completed panels up on the rooftop, rear view
Completed panels up on the rooftop, front view
Tracking The Sun With Our Solar Arrays
After we finished framing up the solar panels and put them on the roof, we decided to make these arrays self-positioning, so they could track the sun across the sky. To that end, we built a solid platform for each framework using OSD (Oriented strand board, a special weather-resistant composite building material much like plywood). The solar panel framework is attached to one OSB platform, that rotates on an axle pivot and four rollers atop a second platform mounted on the rooftop.
After a few days in use we realized that the platform sagged in the center, probably because of the weight of the framework assembly it was supporting, and the effects of airborne humidity. We added a couple of additional slats to stiffen and strengthen the platform.
Photo Essay: Working On The Turntable Platform
Completed turntables, cabled up and ready for use.
Completed turntables, front view
Measuring the panels for turntable construction
Marking up platform panels for cutting
Sawing up the platform panels
Shorter panel goes on top and supports the solar panel framework.
Mounting the rollers and central pivot/axle.
Completed upper panel, ready for insertion into lower panel
Drilling the pivot hole in the lower panel
Mounting the pivot sleeve in the lower panel
Working On The Turntable Platform, Continued
Reinforcing the lower panel with firring strips.
Upper panel mated to lower panel, rotating freely
The top platform rotates atop the fixed lower platform
The top platform is the same width as, but slightly shorter than the lower platform.
The top platform rotates freely in either direction
Preparing to mount the solar array on the turntable platform (top platform anchored to framework, axle and rollers need proper positioning)
Lining up the upper and lower platforms
Upper platform mated to lower platform with solar array attached
Maneuvering the upper platform and framework.
Completed turntable in place on the roof
Working On The Turntable Platform, Continued
Rear view of completed turntable platform and solar module in situ
Front view of completed turntable platform in situ
Additional view of completed turntables in situ
Rear view detail for solar panel on turntable
Unscrewing rear member on solar panel framework
Unscrewing rear member on solar panel framework
Adding stiffening/strengthening members near turntable pivot point
Screwing in stiffening/strengthening members
Framework with strenthening/stiffening members attached on one end
Front view of completed frameworks on their respective turntables
Additional front view detail of strengthened turntables with solar arrays
Using Positioning Cables: The Pulley Principle
To turn the solar cells automatically to track the sun's progress through the heavens, we decided to use a set of positioning cables, with some help from a pulley and a counterweight. In our initial tests, we quickly learned that moving our turntables required more power than we could easily deliver. We turned to a construction that steered the central axles upon which the turntables pivot, and attached this assembly using a 10mm steel bolt.
This assembly let us change the orientation for both solar arrays in tandem about their axes. We were also able to put the coarse gravel with which our roof is covered to work for our counterweight as well.
Photo Essay: Cable Positioning For Solar Arrays
Mounting the pulley assembly on a nearby wall
Our first counterweight
The cabling stretches from the pulley to the nearest platform
Anchoring the cables to the platform
Contemplating effective use of building materials
Assembling the pulley framework
Attaching the pulley to the end of the framework
Mounting wooden blocks on the pulley arm
Mounting wooden blocks on the pulley arm
Cable Positioning For Solar Arrays, Continued
The completed pulley arm assembly
Pulley arm mounted to railing and nearby wall
Pulley arm detail to show railing mount
Double brass pulley attached to solar array framework
Double brass pulley attached to railing using polypropelene twine
Cabling (twine) routed through double brass pulley and atttached to solar cell framework
Constructing mounting blocks for pulley attachment
Back side of mounting blocks for pulley attachment
Cable Positioning For Solar Arrays, Continued
Mounting blocks attached to railing for pulley attachment
Double brass pulley attached to mounting block on railing
Solar arrays ready for cable attachment
Second view of solar arrays prior to cable attachment
Cabling up begins, using blue cord for final version
Pulley on framework cabled up to railing mount
Cabling from wall/corner pulley block (left) and railing mount (right)
Cabling detail at wall/corner pulley block
Cabling run from wall/corner pulley block to closest solar array
Cabling from right-side railing mount to far corner of nearest solar array
Photo Essay: Power Cable Drive
The principle of cable positioning is simple: both solar arrays are literally tied together using a cable, so that both turn in perfect tandem. A counterweight is mounted on one side of the cell.
The cable is positioned using a computer-driven battery-powered screwdriver, by winding it up and letting it out.
Disassembled battery powered screwdriver on the bench
Wiring up a controller circuit for the battery powered screwdriver
Detail: soldering leads to the controller board
Calibrating signals and voltages between controller and screwdriver
Leads attached to the screwdriver motor
The motor returns to its housing, leads attached
Top view of controller board, with leads attached
Power Cable Drive, Continued
A cable reel replaces more conventional bits on the screwdriver
Screwdriver shell elements prior to reassembly
Remounting the drive motor inside the screwdriver shell
Attaching the screwdriver to the railing pulley-mount plate
Screwdriver motor with positioning cables
Half of screwdriver shell, affixed to railing mount plate
Screwdriver shell with motor in place
Power Cable Drive, Continued
Cable wound up on cable spool attached to screwdriver
Rear view of screwdriver attached to railing mount plate
Initial test set up, with screwdriver lashed onto railing (note use of polypropelene twine for testing).
Detail of screwdriver lashed to railing for test
View from railing during test of screwdriver cable positioning
The motor pulls a cable through a pulley to change the angle of the solar cells in one direction as it takes cable up. The counterweight provides motion in the other direction when the motor turns in reverse and pays cable out. This is a simple, but effective solution that adds only a few watts per day to our overall energy budget.
Controller card for the battery-powered screwdriver motor
To enable remote computer control over our battery powered screwdriver we used an 8-channel controller card that could connect up through the parallel port to our PC. The desirable angles and timings are pre-programmed and run every day as a background application. At night, when the solar cells generate no power, the cells are set into the starting position for the next day.
The controller at work
Soldering leads to the controller
Component And Vendor Detail Listing
We used numerous components for the construction of our solar power generator.
All of these ingredients were used in our solar power generator.
We were ably and substantially assisted by Wagner & Co Solartechnik in the practical construction of this project. They also made a wide range of components available to use as we worked through the details.
In contrast to PCs, where individual components may be purchased separately and safely assumed to interconnect and interoperate, we learned that building a solar power generator is somewhat more difficult. To begin with, we performed numerous calculations to help us determine the proper types and power ratings for the battery, power cables, and voltage regulator we used.
It's also necessary to include protective components - for example, fuses - to make sure that variations in the power generation system don't deliver spikes or surges that might otherwise damage electrical components.
We used standard automotive fuses rated up to 25 A to protect our gear
Sizing Our Power Cables: Only 2.6% Energy Loss
Both of our solar arrays combine to produce a nominal maximum power output of 260 Watts with output voltage of around 16 volts. The distance between the solar panels on the roof and our desktop PC ran about 40 feet (12 meters). Because we need separate leads for positive and negative polarities, this doubles the transmission length to nearly 80 feet (24 meters). In this case the electrical resistance of the cable plays a major role in ensuring that as little power as possible is wasted from end to end. That's why we used heavy duty cable with a cross-section of nearly 0.024 in2 (16 mm2) which is approximately 5 gauge AWG cable; by contrast lamp cord (the type of cable used for many A/C appliances) is only 16 gauge with a cross-section of only 1.31 mm2.
Heavy-duty power cable is 12 times thicker than lamp cord
Our readers can't help but notice that the color of our wiring is green and yellow. This color coding is normally associated with ground wire (PE, protective earth) applications. For ferrying conventional solar power direct current, blue is used for minus and red for positive voltage. We decided to use the green-yellow coated cable because it's much more efficient at carrying current than cables in other colors. Otherwise, construction details remain the same, no matter what color your cables might be.
Laying our heavy duty power cable
If we had used ordinary 1.5 mm2 power cable for this application - it's probably what runs between the wall-sockets and the circuit box in your house - power loss from the cable alone would have amounted to 22.3%. For our particular installation, this would mean a significant power loss of 58 Watts.
Left, 2.5 mm2 power cable normally used for solar power; right, 16 mm2 power cable.
Solar power vendors typically won't tolerate energy losses greater than 3% from power cables. With our tenfold increase in thickness to 16 mm2 energy loss drops to 2.6% which amounts to 6.8 Watts for the current that this cable carries.
Modular Junctions For Maximal Cabling
To keep power losses in a modest 16 volt circuit to a minimum, heavy duty cabling with a large cross-section is required (not to be confused with the maximum current it can carry for safe use). According to our calculations, these losses only become tolerable for our distances when cross-section gets to 16 mm2 or higher. But we can't connect a 16 mm2 cable directly to our solar panels, because it's too thick. That's why we hooked up to the solar cells using the 4 mm2cable delivered along with those panels. We kept this portion of the cable plant as short as possible, and inserted a modular connection junction close to the two solar panels, and ran the 16 mm2 cable from the junction box indoors to the PC.
Special solar power cables have a 4 mm² cross-section.
Our 4 mm² cables are only a little more than 5.5 feet long. Because we used two solar panels in our design, each of these segments carried half the total power. At maximum load, we lose 1.93 Watts. On the subsequent 39-plus foot 16 mm² segment, we lose 6.81 Watts. The total power loss across all segments is thus 8.74 Watts, for a total of 3.9% of our total power capacity.
Junction box for the two solar panels
We used a junction box to attach the two solar panels to the 16 mm² cables.
Junction box
The junction box includes protective diodes to protect circuits from inverted polarity.
Connecting the cables
This junction box supports cable cross-sections of up to 32 mm².
Modular Junctions For Maximal Cabling, Continued
Junction box with solar cables attached.
When the junction box is screwed shut after the cables are connected, it becomes watertight. Both of our solar panels, each with 2 4 mm² cables are connected to two 16 mm² cables inside this device.
Cables are cut to precise lengths
Open junction box with all cables installed
Position of the junction box between the two solar cells
Routing the cables from the rooftop to the test lab area
Our green-and-yellow 16 mm2 cable (code H07V-K) is not designed for permanent outdoor use, and is employed only briefly during testing. Here's why we chose this type of cable: It's significantly cheaper than standard outdoor 16 mm2 cable normally used for ground wires. Because our construction is simply for research, this approach works for us. Those who want to make a permanent installation should use compatible outdoor cable with the required protective sheath instead. We recommend using red for the positive voltage, and blue for the negative voltage when working with direct current (DC).
Comparison: Standard 4 mm² solar power cable left, Kabel links, 16 mm² right.
Charge Controller: Battery Stores Excess Solar Energy
To make sue our PC and monitor always have sufficient power, we must use a charge controller. This device directs excess energy that the PC doesn't use into a storage battery. The stored energy from the battery is used when bad weather hampers power collection, or during night-time hours when no power is collected at all.
Morningstar ProStar-15 charge controller
We used the ProStar-15 solar charge controller, made available to us by the German company, Wagner Solar. As the product name is meant to indicate, it can load a battery with a maximum current of 15 Amperes. This entails around 190 Watts. Because our solar generator can deliver a maximum of 260 Watts, this leaves about 70 Watts left over. At idle, our solar-powered PC consumes about 61 Watts, which makes our 15 Amp charge controller and ideal fit for our setup. The energy output from the charge controller goes primarily to service the PC.
This device can also display the actual battery voltage, power delivered from the solar panels, or energy consumed by the computer, as the following photos attest.
Readings for battery voltage (top), solar amperage (middle), and load amperage (bottom).
The solar charge controller obtains its power from the battery, because when it's dark there would otherwise be no power available for its use (and no possibility of controller charge and discharge behavior). Because power regulation also entails energy loss, the rear side of the charge controller is bedecked with a heatsink, to dissipate related heat production.
Rear view of the charge controller
1.5 KWh Storage Battery
On rainy days when the solar panels produce only a small amount of power, and at night, when they produce no power at all, our solar-powered PC still needs juice to operate. We use a storage battery to provide this power, and use the charge controller to charge it up during the day. In our installation, this is a lead-acid battery that weighs in at nearly 75 lbs (32 kg).
Solar battery from the Sonnenschein (sunshine) company, made by Exide Technologies
Under optimal conditions, our solar array deliver up to 260 Watts of power. In idle mode, the solar-powered PC consumes 61 Watts, which leaves nearly 200 Watts available to charge the battery.
Our gel-filled lead-acid battery offers a capacity of 130 Ah. At 12 volts this produces 1560 Wh. With a full charge, our battery can run the PC for about 23 hours, without any input from the solar panels. But this is possible only during optimal conditions, which occur only seldom, if at all.
Terminal connectors for the lead-acid battery
Energy Distribution
To support a clear understanding of where and how much power is consumed in our solar powered installation, here's a block diagram of all the components with supporting details.
Power Expended For 24-hour Use
How much energy must the solar array collect during the day, to keep the computer running 24 hours a day?
The lead-acid battery operates at about 80% efficiency, which means that 20% of the stored energy is lost.
Power Collection: 10 Hours Per Day
We calculated an average of 10 hours of sunshine per day. During this time, the PC does not access the battery for energy, so we can forgo the 20% loss that battery use otherwise entails. This explains how we produce energy consumption of 610 Wh in the preceding figure (10 hours x 61 Watts = 610 Wh).
Battery Operation: 14 Nighttime Hours
The other 14 hours during which the solar cells deliver no power must be serviced by energy stored in the battery. This means a discharge of 855 Wh (14 hours x 61 Watts = 854 Wh, rounded to 855).
Because we must also factor a 20% energy loss from battery use into this equation, we require that the battery must store 1030 Wh (855 Wh + 20% = 1026 Wh).
Adding the daytime energy consumption to the nighttime consumption we come up with a total daily energy budget of 1636 Wh (610 Wh by day + 1030 Wh by night = 1636 Wh total).
The battery at work in our test installation
Together our two solar panels must deliver an average of 163 Watts during the day so that the PC is able to operate 24 hours a day. If we fail to attain this value, the PC will shut down in the middle of the night when it runs out of power.
Each solar cell produces 130 Watt under optimal conditions. Thus, our solar power rig must produce at least 62.9% of that value for at least 10 hours a day, to keep it running around the clock.
Solar Battery Energy Capacity: 1592 Wh
Because the solar cells experience regular voltage sags daily, primarily because of cloud cover diminishing or interrupting power collection, the battery also acts as a buffer to provide reserve energy when needed.
If our solar cells operate at 100% of their capability for 10 hours a day, with no clouds to interfere with collection, we can collect an additional 1990 Wh per day above and beyond what the PC consumes (10 hours x (260 Watts - 61 Watts for PC) = 1990 Wh) for storage.
After factoring out the 20% power loss from the battery itself, this produces a usable capacity of 1592 Wh. This means our battery, which has a rated capacity of
1560 Wh is perfectly sized to handle excess collection without losing appreciable energy.
But of course, these are gross totals, which fail to take power losses from other components into account.
A fuse on the battery protects components from short circuits.
Smaller fuses provide additional protection.
Because a lead acid battery of this capacity can produce extreme power spikes, we must protect all attached devices with fuses.
A wall-socket is a no-no for this PC: our first attempt at computing independent from the power grid.
Shopping List: Components And Prices
Because our solar-powered PC setup was first and foremost a research project, we didn't manage costs as a paramount concern. This affects our choice of solar panels most directly, along with related cabling, devices, and other components. Nevertheless we did attempt to keep costs as much under control during our construction as we could. Thus, this overview can also serve as a shopping list for interested potential users.
By themselves, costs for the solar collection and storage components came to $2,685. Including a little over $1,000 for the solar-powered PC with monitor, total project costs come to $3,796--$3,800 in round numbers. A direct copy of this project is only possible for those who can obtain the same components that we used ourselves; costs will certainly vary with the differences between our choices and those that others make. Our budget also includes measurement tools, so that builders can check voltage and current levels in their constructions.
Solar Power Rig | |
---|---|
Solar panels
Substitute Kyocera KC130TM 130W/12V panels |
$1,200
Substitute Monster 300 4 gauge PowerFlex cable (80 ft) |
16 mm2 cable | $220 |
4 mm2 cable
Substitute Monster 200 10 gauge power cable (25 ft) |
$25 |
2.5 mm2 cable
Substitute 12 gauge speaker wire 2 conductor (50 ft) |
$25 |
Battery | $470 |
Battery cables
Includes terminal clamps |
$20 |
Charge ctrlr | $150 |
Junction box | $150 |
Lumber | $85 |
Rope | $50 |
Screwdriver
Battery-powered Black&Decker model |
$35 |
8-chan ctrlr | $50 |
Hardware
screws, sheet metal, incidental parts |
$60 |
Pivot & rollers | $30 |
Lubricant | $5 |
OSB sheets | $50 |
Incidental parts | $50 |
Plexiglas | $10 |
Solar-Powered PC | |
Power supply | $90 |
CPU | $85 |
Motherboard | $95 |
RAM | $215 |
Hard disk | $56 |
DVD player | $45 |
Monitor | $400 |
Keyboard - Mouse | $35 |
TOTAL | ~$ 3,800 |
In the preceding list, incidental parts include solder, wire nuts, miscellaneous electrical components, conduit, and so forth. We also used various tools to complete this project, including drills and drill presses, battery-powered screwdrivers (to drive screws, not to handle the steering rope for the solar panels), saber saws, and all kinds of hand tools. A well-equipped workbench is a must for anybody who wants to tackle this kind of project for themselves.
Summary: On To The Live Test!
In a few weeks we will complete this effort with our fourth installment - a live test - to conclude this series of articles. Using our test equipment we will set up a Web site with 24-hour coverage of the solar powered PC so that visitors can come check it out online any time they like.
During the live test we will also share our experiences in building the project, observe whether the solar powered PC can maintain constant operation, measure the output of our solar panels, and keep tabs on how much energy we have at our disposal over time.
Those readers who might like to start at the beginning of this series will find the first two installments here: