Note that the navigation is two-dimensional, with both left-right arrows and up-down arrows on some slides in order to move
vertically deeper into some topics.
Students will learn the principles of home energy conservation and off-grid energy production for the purposes of installing or
competently hiring a contractor to install a system in their home to free them from dependence on the electrical grid.
Syllabus
Schedule:
Class 1 (Thursday, 09/19): Duration 2 hours: Familiarization with the concepts of off-grid systems, reasons why one might
want to go the off-grid route (and how convince others likewise). Crash course in electrical theory, voltage, amperage,
resistance, inductance, fuses/breakers, wire gauge, grounding, sources/generators, etc.
Class 2 (Thursday, 09/26): Duration 2 hours: Fundamental principles of home electrical systems, types of loads, and how
to estimate home electrical energy and power requirements. Energy conservation methods, types and examples of alternative
energy sources, cost/benefit calculations for upgrading loads for better efficiency versus generating more power.
Class 3 (Thursday, 10/03): Duration 2 hours: System components: power sources, batteries, charge controllers, inverters,
off-grid vs grid-interconnected, DC-DC converters, and other equipment needed to build a functional off-grid system.
Class 4 (Thursday, 10/10): Duration 2 hours: Putting it all together to design and implement an off-grid energy system.
What is "Off-Grid"?
Providing substantially all of your own needs, including electricity, heat, water, sanitation, and food. Electricity is often
instrumental to providing most of these other needs, e.g.: pumping water, circulating heat, and refrigerating food.
Excess production is stored on-site for times of deficit. For electricity, that generally means batteries, but could also
include supercapacitors, hydrogen (via electrolysis), or pressurized water.
Self-sufficient and independent of civilization, but still enjoy modern comforts and conveniences.
Off-grid is NOT synonymous with minimalist, primitive living. Off-grid electrical systems can power all of today's
advanced automation, entertainment, and communication devices.
Motivations for Going Off-Grid
Reliability and Availability
Keep lights and refrigerators and communications up and running during storms that knock out grid power for a few hours or days.
Aging grid infrastructure makes catastrophic failures more likely. According to the American Society of Civil Engineers (ASCE),
"most electric transmission and distribution lines were constructed in the 1950s and 1960s with a 50-year life
expectancy," meaning half of the grid is at least two decades older than what it was designed to last.
An EMP or CME could crash the entire national electric grid for years. The major transformers, some bigger than
a building, cost millions of dollars, are made in China, and have a lead time of several years to produce.
Motivations for Going Off-Grid
Rising Costs
Changes in supply & demand due to severe summer heat, winter cold, fuel disruptions, among other
reasons, may cause price surges.
Government may add onerous new energy taxes at any time.
Carbon caps and environmental regulations place artificial scarcity and costs on fuel use.
Global geopolitical instability means that sanctions or war may break out at any time, adding a
risk premium.
Monetary policy may drive steep inflation, like the stagflation of the 1970s or worse, like
Zimbabwe or Venezuela.
Motivations for Going Off-Grid
Privacy & Security
Utility companies are installing smart meters, occupancy sensors, and other smart grid technology throughout the country. These devices...
Track your personal behavior patterns in the name of optimizing energy production and usage.
This will include determining when people are home and which individual appliances are running.
Turn off certain appliances remotely during peak load times.
Perform real-time surveillance for government agencies, who don't even need a warrant under FISA.
Data mine to profile you for targeted marketing, insurance premium calculation, law enforcement
dragnets, creditworthiness, and other purposes.
Open you up to risk of identity theft or targeted home invasion if the utility company servers
are hacked.
Motivations for Going Off-Grid
Privacy & Security
Load Signature Analysis
Motivations for Going Off-Grid
Investment
Off-grid systems are a capital investment which provide tax-free non-monetary dividends.
Not only do you not pay income taxes on these returns, you don't have to pay the sales taxes and smart meter rider fee
and other charges associated with purchasing them. You may even get tax rebates or credits.
And if you earn less money because you don't need to spend as much, you'll be in a lower tax bracket. Thus your cost of living is
significantly reduced.
Being less dependent on a paycheck makes you resilient to recessions. It's better than unemployment insurance. Even if you
lose your job, you know your power cannot be shut off.
Motivations for Going Off-Grid
Insurance & Stability
You don't need a huge nest egg in order to have a long and secure retirement. Your living costs won't exceed your fixed income
because you'll have no utility bills to worry about.
Becoming financially independent – without needing to be rich – enables you to retire or cut back your hours and focus more on
family, hobbies, education, starting a business, etc.
Greater quality of life is made possible by eliminating expenses and work and the stress of paying bills.
Freedom from home carrying costs enables long-term planning, such as vacation travel.
Basic Physics
Force, Work, and Energy
Basic Physics
The Work Energy Principle
Basic Physics
Power
Electrical Power Primer
The purpose of having electricity is to do work, typically measured in kilowatt hours (kWh) for electricity, but
also possibly measured in therms or BTUs for heat output or horsepower hours for motors.
The watt (W) is a measure of power defined as 1 joule of work per second, or 1 Wh/h. Power is the rate at which
energy is produced or consumed to do work. 1 kilowatt (kW) = 1,000 W = 1.34102 HP = 3,412.142 BTU/hr
Electricity flows in a circuit, made of a conductor (usually copper wire, but also integrated circuit boards and semiconductor chips),
transferring energy to various devices which convert the electrical power to heat, light, motion, sound, or chemical reactions to do
useful work.
Using 10 watts of power for 1 hour does the work of 10 Wh. So does 1 W for 10 hours or 60 W for 10 minutes. 10 Wh is also the
same as 0.01 kWh.
Electrical Circuits and Systems
Electrical Charge
The fundamental force at the heart of all circuits is the electrical charge, which is the attraction between protons (+) and
electrons (-) or atoms with an unbalanced number of protons and electrons. The flow of electrons from a
negatively charged object or substance toward a positively charged one is electricity.
Electrical Circuits and Systems
Conductors & Insulators
Electrical Circuits and Systems
Semiconductors
Electrical Circuits and Systems
Voltage & Current
Voltage (volts) is the potential energy between two charged objects. It's like water pressure in a
pipe where the water has a gravitational pull or a mechanical pump driving it down the pipe. In an electrical circuit, a
conductive wire is the pipe between two charges that want to cancel each other out.
Voltage is always relative to a reference point, called ground or common, which is zero volts. Sometimes it's
literally a grounding rod in a home electrical system. But ground can also be some other reference point such as a battery terminal
or car chassis.
When electric charges flow through a conductor due to a voltage, they become a current (measured in amperes, or
amps for short). When referenced in electrical formulas, current is usually represented by the letter I (for intensity).
Electrical Circuits and Systems
Voltage, Current, & Power
The relationship between voltage, current, and power is known as Watt's Law:
Power (watts) = Current (amps) * Voltage (volts)
Or stated differently:
Current (amps) = Power (watts) / Voltage (volts)
Or:
Voltage (volts) = Power (watts) / Current (amps)
Electrical Circuits and Systems
Circuits
A circuit is a loop of conductive wire (or printed circuit board or semiconductor) between a voltage source and ground on which is placed
at least one or many loads. A load is any device which consumes electric power (causing a drop in voltage) in order to do work.
The work that is done causes resistance to current flow. Resistance is measured in Ohms (usually represented by an omega,
Ω). The relationship between voltage, current, and resistance is known as Ohm's Law:
Voltage (volts) = Current (amps) * Resistance (ohms)
Or stated differently:
Current (amps) = Voltage (volts) / Resistance (ohms)
Electrical Circuits and Systems
Direct Current (DC) is a type of circuit where the electricity flows from a source (S) to the ground (G). The ground may
literally be the Earth itself or some other sink such as the opposite pole of a battery. You can think of the source as pushing
electrons away and the ground or sink pulling electrons toward it because they are opposite charges.
As an analogy, electricity in a DC circuit is like water flowing through a pipe. The amount of water in the pipe is the
amperage while the pressure of the water or force with which it comes out is the voltage.
The total power is the amperage times the voltage, as per Watt's Law. E.g. 12 Volts * 10 Amps = 120 Watts. Like with water,
either more volume or higher pressure results in more work done, such as if the water is directed through a water wheel or turbine or
electricity is sent through a motor or heating coil.
Electrical Circuits and Systems
All electronics are DC circuits. Batteries are also always DC.
Battery-based DC systems found in buildings and vehicles typically use a nominal voltage that's a multiple of 12 volts.
12 VDC is the voltage of most automobiles, RVs, and yachts. 24 VDC is common in commercial trucks and industrial control applications.
Electrical Circuits and Systems
Circuit Diagrams
Circuits are represented in schematic diagram form using a standard set of symbols. Schematics do not have wire lengths to scale and do
not match the exact physical positioning of real-world components, but are drawn to be most easily understood. The circuits that are built
from them are laid out according to economy of connections and access to interactive components.
Electrical Circuits and Systems
Resistors
Circuit components called resistors are used to convert a voltage or amperage (by Ohm's Law) into one more suitable
for a component, such as a light-emitting diode (LED) which might require a lower voltage or amperage than the circuit it's on. It's like
kinking a garden hose to prevent from washing away your seedlings. Resistors are electric insulators that dissipate electrical power as heat.
Electrical Circuits and Systems
Series & Parallel Circuits
A series circuit is when voltage sources or loads are daisy chained from positive to negative ends.
A parallel circuit is when voltage sources or loads are connected to common ends on the same leg.
Electrical Circuits and Systems
Series & Parallel Resistance
Resistances in series behave similar to voltage sources, but in parallel are quite different:
Electrical Circuits and Systems
In an Alternating Current (AC) circuit, electricity flows back and forth at some frequency, or number of times per second.
AC is usually produced by a coil of wire spinning in a fixed magnetic field (generator) or a magnet spinning in fixed
coils of wire (alternator). These can be powered by a steam turbine, such as in a coal or nuclear power
plant, or wind turbine, engine, or anything else which produces rotation. Output is a sine wave.
Electrical Circuits and Systems
AC can also be produced from DC current via an inverter, which is a solid-state (no moving parts) electronic device. Some inverters
produce what's called a square wave. Others produce a modified sine wave. The most expensive will replicate a pure sine wave.
Any non-perfectly sinusoidal waveform will introduce harmonics which have the potential to cause malfunctioning of equipment and
protective devices as well as inefficiency.
Electrical Circuits and Systems
Resistance loads (heaters, incandescent lights, etc) tend to do fine on square waves or modified sine waves, however...
Square wave or modified sine wave inverters may:
Cause AC motors to overheat, produce less torque, and buzz or whine due to eddy currents, magnetostriction, radial deflection, and vibration
Create excessive heat and noise from power transformers for similar reasons
Cause fluorescent and LED lights to flicker and hum
Create interference and noise with audio and video reception and output
Disrupt timers and digital clocks, including washing machine and oven controls
Damage battery chargers or batteries, especially for rechargeable power tools
Damage high end audio and electronic equipment
Produce higher currents on the neutral wire of the electrical system than it's designed to accommodate
Cause electrical control equipment to act erratically, such as tripped breakers
Void warranty coverage on appliances, electronic equipment, and computers
Harmonic loads -- such as AC/DC drive systems, induction heaters, arcing devices, switch mode power supplies, and rectifiers --
operating on the same system as a harmonic source such as a square wave inverter, may amplify harmonic resonance and increase
the risk of damage.
Electrical Circuits and Systems
AC can also be converted to DC current with a rectifier, which is a diode which allows half of the AC wave to flow and prevents the
other half that flows in the opposite direction. Multiple diodes in a bridge rectifier are able to capture both directions of the AC
wave, reversing half of it so that the final current is DC in the same direction. A resistor-capacitor filter is used to smooth the ripples
in the output.
Electrical Circuits and Systems
The national electric grid uses AC current at very high voltages, while the power in grid-connected houses is transformed down to
120 VAC at a frequency of 60 Hz. In a household electric panel, two phases of grid power can be combined to produce 240 VAC.
Any household loads that include electronics are converted from 120 VAC to 12 VDC or 5 VDC with a power converter that includes
transformers and rectifiers. These are sometimes referred to as "wall warts" or "power bricks" or are internal to an appliance. Conversions
between AC and DC in either direction are not 100% efficient, but generally suffer 10-20% losses as heat.
Electrical Circuits and Systems
Efficiency & Safety Considerations
Besides your intended loads, resistance is also caused by less than perfect efficiency of conduction through wires or conversion of
electricity to desired work. This is known as electrical losses. Larger diameter wires (lower gauge) have less resistance just like
larger pipes in plumbing systems have less resistance to water flow. Wire sizes should be chosen so as to avoid unacceptable (and possibly
dangerous) resistance.
Nominal or rated voltages do not always equal real-world voltages due to inefficiencies in the circuit, partially discharged
batteries, aged components, more or less current draw, etc. For example, a 12 V system may have an actual voltage range from 10 V to 14 V.
A short circuit is caused when current is inadvertently allowed to flow freely between a voltage source and ground without
passing through the intended loads and resistors. This can cause fires, damage to electronics, and personal injury. Shorts can be caused
by frayed wires (broken insulation), a conductive object or liquid falling on components, defective components, or human error in making
connections.
Circuits should be designed to catch and safely handle over-current, over-voltage, under-voltage, and other anomalous conditions.
How the Electrical Grid Works
How the Electrical Grid Works
How the Electrical Grid Works
How the Electrical Grid Works
Home Circuit Layout
Home Circuit Layout
Home Circuit Layout
Home Circuit Layout
Types of Home Electrical Loads
Resistance Heating (1,000 to >20,000 W) - range, toaster, dryer, water heater, baseboards
Compressors (500 to 6,000 W) - refrigerators, air conditioners, dehumidifiers, heat pumps
Pumping (20 to 5,000 W) - well water, septic, heating circulator pumps, sump pumps
Motors (1 to 500 W) - ventilation fans, power tools, washer
Lighting (1 to 100 W) - incandescent, fluorescent, CFL, LED
Electronics (<1 to 300 W) - computers, TVs, DVRs, clocks, thermostats, security system
Phantom (<1 to 15 W) - small persistent loads such as power indictor lights; remote standby power; wall warts;
trickle charging batteries; home automation sensors; switch resistive losses; device settings stored in volatile memory
Energy Usage Estimation
Electric Utility Statement
Energy Usage Estimation
Energy Guide Sticker
Wattage Label
Appliance Manual
Manufacturer Website
Energy Usage Estimation
Kill-a-Watt Meter
Energy Usage Estimation
Multiply device wattages by a conservative estimation of how long they will be on each day.
Energy Conservation
Conservation is almost always less expensive than generation.
Scaling up an off-grid system doesn't merely involve more solar panels or a bigger wind turbine.
Higher system wattage means more/bigger charge controllers, fuses, wires, inverters, batteries, etc., often in a more complex arrangement.
It also usually implies more maintenance and a more expensive replacement cycle.
Reduce the loads to the minimum wattage necessary to provide the service you desire.
Sometimes that means upgrading appliances. Other times it might involve moving to a different energy source than electricity.
Energy Conservation
Eliminate All Resistance Heating Loads
With wattages from 1 kW to 20+ kW, resistance heating is the least efficient use of electricity. Thankfully, there are lots of
alternatives to resistance heating.
Propane (or natural gas) is an easy replacement for electric ranges, ovens, dryers, hot water, and space heaters.
Passive solar is the most efficient off-grid energy technology. It can provide significant space heating.
Solar thermal is the next most efficient. It can take over virtually all space and water heating.
A wood stove will provide plenty of space heating and also can pick up some cooking tasks and even water heating.
Solar ovens and dehydrators can do some cooking.
A clothes line can replace a clothes dryer.
Energy Conservation
Reduce or Upgrade Compressors and Pumps
It would be quite an inconvenience to do without a refrigerator or freezer, but these appliances can be upgraded to more efficent
models. Also, adequate ventilation helps.
The need for air conditioning can be significantly reduced with more insulation and thermal mass as well as the implementation of
some passive solar principles.
Reduce well & septic pumping by adding a hot water recirculation loop to your washing machine & bathrooms.
Limit heating system pump time by upgrading insulation and thermal mass.
Add a graywater diversion valve to send some sinks, clothes washer, etc., to the garden.
Energy Conservation
Minor Loads can be Low Hanging Fruit
Replace any incandescent bulbs with CFL or LED bulbs instead.
Put lights on motion sensors and timers.
Switch from a desktop computer to a laptop (or high-efficiency desktop with a mobile chip).
Put DVRs on timers so that they only need to be on during prime-time.
Turn off televisions and electronics completely with the use of a power strip.
Set your thermostat more conservatively (wear a sweater if necessary).
Energy Conservation
Advanced Methods
Replace old windows with low-emissivity (low-e) alternatives.
Replace baseboard or forced air heating with hydronic radiant floor heating.
Install heat-recovery ventilators in place of normal vent fans.
Add solar tubes for daylighting areas where you use lights during the daytime.
Convert some of your lighting and appliances to DC.
Set up a home automation system to shut off lights and appliances when not in use.
Collect rainwater in a cistern for toilet flushing and other purposes.
Cost-Benefit Analysis
Conserve vs Generate
After estimating home energy usage, price out the energy generating system needed to make that much power
When you get over the price shock, target the largest energy users for upgrade or replacement; then the low-hanging fruit
What remains will be moderate energy users; upgrade anything fairly old or that comes with additional benefits from upgrading, such
as a high-def flatscreen or nicer fridge
Batteries will be one of the least long-lived investments, so minimizing battery size requirements is a high priority
Inverter output will also be a limiting factor
Consider targeting a lower peak threshold before you'll resort to running an on-demand generator, at least until you can upgrade
some appliances or add more capacity
System Components
Off-Grid Power Sources
The energy needed to power your home's loads needs to come from somewhere. Most people are familiar with simply
plugging into grid power, which comes mostly from coal, gas, and nuclear power plants tens or hundreds of miles away. In an off-grid
system, we'll need a different set of tools to generate that voltage. Preferably several to provide redundancy.
System Components
Gasoline, Diesel, Propane, or Hydrogen Fuels
The most common off-grid voltage source is a gas generator, as most people have these for when the grid
goes down, such as during a storm.
For low-energy or high-demand times to supplement other sources
Too expensive to size a renewable system for worst case peak demand times, so on-demand
generation picks up the slack
When plugging these into a battery-centered system, they can be drastically scaled down from the
whole-house standby generators usually used because they don't need to power peak loads, but only charge batteries.
System Components
Gasoline, Diesel, Propane, or Hydrogen Fuels
Fuels are high energy density -- store easily and are portable
Propane is cleaner and more stable than gasoline or diesel
Biomethane can be created renewably on-site in a digester
Hydrogen can be produced by electrolysis of water with excess electricity from peak production times
May also use a hydrogen fuel cell (possibly with propane/nat gas reformer)
System Components
Wind Power
Similar in principle to a gas generator, but with much fewer moving parts are wind turbines and microhydro turbines.
Like gas generators, these spin an alternator or generator to create voltage, but using renewable resources without the need to
burn fossil fuels in complicated, failure-prone engines.
Low-cost energy, if you have the resource at your location
With few moving parts, there's very little maintenance
Excellent for combination with solar in a hybrid system – wind is usually stronger when overcast and
in winter
Abundant in PA – largely class 3 or 4 - but need to be at high elevation
Feasible with average wind speeds of 5 – 25 MPH
System Components
Micro-hydro Power
Very low-cost energy in some circumstances
Few moving parts – only occasional maintenance
Obviously, you need a creek or river on your property
May be seasonal though
Environmental permitting issues
System Components
Photovoltaic Panels
Photovoltaic solar panels are even less complicated and more robust because they have no moving parts at all, but are
entirely solid state, i.e. composed of semiconductor transistors. They produce energy reliably for decades whenever the
sun is shining.
Plentiful energy source, even in northern latitudes
Most widely available alternative energy – any southern exposure
Great in a hybrid system
Cost has come down drastically in the past decade ~ under $1 per Watt!
Energy inflation will make any PV investment worthwhile over the course of its rated lifespan
System Components
Photovoltaic Panels
60-cell panels are optimized for grid-intertie.
72-cell panels are optimized for off-grid battery charging.
STC = Standard Test Conditions = idealized (1000 W/m2, 25°C/77°F, etc).
NOCT = Nominal Operating Cell Temperature =
more real-world assumptions. Irradiance is
800 W/m2, because PV modules don't
always face the sun and because atmospheric and
geographic conditions vary. Panels also heat up
considerably during operation, so the temperature
considered is about 45°C/113°F. A windspeed of
1 m/s is considered, with air at 20°C/68°F.
For off-grid, it's best to mount low and steep (around 60°)
to point at the winter sun, shed snow easily, and pick up
reflected light off the snow.
Monocrystalline panels are up to about 20% efficient.
Polycrystalline panels are about 15% efficient.
Thin film panels are about 9% efficient.
System Components
Thermoelectric Power
Similar to photovoltaics, thermoelectric generators (TEGs) are solid-state chips that turn temperature gradients into a
DC electrical voltage.
On-demandrenewable power source
Reliable – no moving parts
High cost per watt, but can run 24/7
Combined heat and power (CHP) makes it super efficient
Some even have thermoelectric generators for charging mobile devices
Passive solar - solar tube lights, clothes line, dehydrator, garden
System Components
Human Power
It's possible to hook up an alternator to a bicycle or other human-powered machine
Manual well pump along side an electric pump
Hand-crank flashlights and battery chargers
Hand-crank kitchen and power tools (mixer, can opener, lathe, drill, etc)
System Components
Batteries
Batteries are the heart of any off-grid system. They store the energy of various power sources. And they are the voltage
source that powers every load.
Batteries come in many different chemistries and are engineered for different purposes. Off-grid energy systems require deep
cycle batteries as opposed to automobile starter batteries, because they're built to withstand a much deeper state of discharge
on a daily basis.
System Components
Battery Types
Light, expensive batteries like lithium-ion are best suited for electric cars and mobile devices. Stationary installations are best
served by lead acid batteries. They're inexpensive and longer-lived, but very heavy.
Flooded lead acid (FLA) batteries off-gas hydrogen while charging due to electrolysis and therefore require topping off the electrolyte
with distilled water every few months, but they're very robust and long-lived (up to 20 years).
Gelled electrolyte or absorbed glass mat (AGM) batteries do not require refilling of electrolyte and do not off-gas (as much). They also
cannot spill and are more freeze-resistant. This makes them suited for mobile applications like forklifts, scooters,
etc., and in living spaces such as for uninterruptible power supplies (UPS). But they're usually shorter lived (3-7 years) and more
expensive per amp-hour.
System Components
Battery Banks
Batteries are organized into banks of cells, usually both in series and parallel so as to produce the ideal nominal voltage and amp-hours.
The amp-hours times the nominal voltage provides the rated watt-hours of work that the system is capable of providing. You can't
directly compare amp-hours of batteries at different nominal voltages. E.g. a 10 Ah12 V battery has 120 Wh of energy while a
20 Ah4 V battery has only 80 Wh of energy. As you should recall, this is due to
Watt's Law.
System Components
Battery Cells
At full state of charge (SoC), each lead acid battery cell has a nominal voltage of about 2.14 V. At 50% depth of
discharge (DoD), they'll be about 2.03 V. Fully discharged, they'll be about 1.75 V, at which point there's risk of
permanent damage.
2.14 V + 2.14 V + 2.14 V + 2.14 V + 2.14 V + 2.14 V = 12.84 (SoC 100% / DoD 0%)
2.03 V + 2.03 V + 2.03 V + 2.03 V + 2.03 V + 2.03 V = 12.18 (SoC 50% / DoD 50%)
1.75 V + 1.75 V + 1.75 V + 1.75 V + 1.75 V + 1.75 V = 10.50 (SoC 0% / DoD 100%)
Discharging a 12 V battery to 10.5 V is like keeping a pot on the stove until all of the
water has boiled off. At that point you're at high risk of destroying your cookware and maybe your kitchen.
To help batteries last as long as possible, they should not exceed 80% DoD and they should be
desulfated (sharp spikes of voltage) and equalized (higher than normal charging voltage) every few months, after which
the electrolyte should be topped up. This is only possible for FLA batteries, not gel or AGM or other chemistries.
Water-saver vent caps can help retain water in between maintenance cycles.
System Components
Battery Capacity
The faster batteries are drawn down, the less amp-hours they can provide in total. This is known as Peukert's Law.
H is the rated discharge time (h). Batteries are usually advertised at their 20-hour discharge rate.
C is the rated capacity at that discharge rate (Ah)
I is the actual discharge current (A)
k is the Peukert constant (dimensionless). For different lead-acid rechargeable battery technologies, it
generally ranges from 1.05 to 1.15 for AGM batteries, from 1.1 to 1.25 for gel, and from 1.2 to 1.6 for flooded
batteries. It also generally increases (gets worse) with age.
t is the actual time (h) to discharge the battery given these conditions
System Components
Battery Capacity
For example, let's say we have a 12V 100 Ah FLA battery (20-hr), and want to run a 100 A (1200 W) load...
20 h (100 Ah / (100 A * 20 h))^1.4 = 0.30 h = 18 min 6 sec
For a 10 A (120 W) load on the same battery...
20 h (100 Ah / (10 A * 20 h))^1.4 = 7.58 h = 7 hours 35 min
For a 1 A (12 W) load on the same battery...
20 h (100 Ah / (1 A * 20 h))^1.4 = 190.37 h = 7 days 22 hours
This does not take into consideration temperature, age, or self-discharge, which also affect capacity.
System Components
Battery Capacity
The actual effective capacity given a true discharge rate can be calculated by:
H is the rated discharge time (h). Batteries are usually advertised at their 20-hour discharge rate.
C is the rated capacity at that discharge rate (Ah)
I is the actual discharge current (A)
k is the Peukert constant (dimensionless)
Ce is the effective capacity of the battery given these conditions
System Components
Battery Capacity
So again, let's use a 12V 100 Ah FLA battery (20-hr), and run a 100 A (1200 W) load...
100 Ah (100 Ah / (100 A * 20 h))^0.4 = 30.2 Ah
For a 10 A (120 W) load on the same battery...
100 Ah (100 Ah / (10 A * 20 h))^0.4 = 75.8 Ah
For a 1 A (12 W) load on the same battery...
100 Ah (100 Ah / (1 A * 20 h))^0.4 = 190.4 Ah
System Components
Battery Capacity
Lead acid batteries do not have a "memory" and do not need to be fully discharged before recharging. Regularly charging after a 20% to 50%
DoD is good practice while only occasionally allowing up to 80% DoD. That will maximize lifespan.
As batteries age, their capacity will slowly be lost. Unless mistreated, they won't fail instantaneously, but will simply hold less
energy when fully charged as they get toward the end of their life.
System Components
Battery Lifespan
Also, although deeply discharging batteries regularly shortens their life expectancy, they do like to be cycled at least
a little -- keeping them always fully charged is also not good.
Batteries also behave differently in varying temperatures.
Rated amp-hours are given at room temperature.
Very high temps will increase the total capacity of the battery, but at the cost
of shorter lifespan.
Low temps do the opposite, except to the point where the battery freezes solid and destroys
the housing.
A charged battery (full of sulfuric acid) will not freeze anywhere near the
freezing point of water.
But a discharged flooded lead acid battery holds mostly just water and will freeze.
System Components
Charge Controllers
Batteries need to be charged up to their rated voltage from an energy source that can supply the needed voltage. Although current
carries the energy, a constant current source at the wrong voltage will not charge a battery.
Think of it like trying to fill up a gallon jug using either a firehose or a drinking straw. Too much pressure and you'll destroy the
vessel. Too little and you either won't force any charge into it at all or at such a slow rate that it's not worthwhile.
A charge controller is a device that assesses your current battery voltage and the voltage of your source. It then uses circuitry that
essentially applies Ohm's Law to convert between current and voltage to provide the ideal charging voltage.
System Components
Charge Controllers
There are primarily two types of charge controllers...
Pulse-width modulation (PWM) charge controllers rapidly turn on and off
the source current to control the voltage. They tend to be cheaper but must operate near the nominal battery voltage and are less
efficient in most conditions.
Maximum Power Point Tracking (MPPT) charge controllers use DC-to-DC converters to accurately match
voltages from source to battery, including wildly higher or lower, and on average tend to be up to about 30% more efficient. But also
generally twice as expensive.
System Components
Charge Controllers
Charge controllers typically use a 3-stage charge cycle...
BULK: voltage gradually rises while batteries draw maximum current
ABSORB: voltage is maintained at peak charging voltage while current tapers off
FLOAT: voltage is lowered to a safe maximum maintenance level
System Components
Charge Controllers
Charge controllers also occasionally provide a fourth stage...
EQUALIZE: raise voltage 10% above typical peak voltage to boil the cells to desulfate and destratify and balance the specific gravity
Solar charge controllers are typically not built to handle the rapid fluctuations in voltage produced by a wind turbine.
System Components
Inverters
Inverters convert a direct current voltage source into an alternating current and step up the voltage to standard house voltage.
Inverters provide either a square wave, modified sine wave, or pure sine wave. Most AC electric motors and
compressors work better and last longer on a pure sine wave.
Inverters are typically between 85% and 95% efficient, losing the rest as heat.
System Components
DC-DC Converters
Sometimes it's necessary to step up or down a DC voltage, such as from 24 to 12, or 12 to 5 (USB) for certain loads, or from 12
to 24 to transmit power over smaller wires for some distance without as much voltage loss.
Switch mode converters use inductors, transformers, capacitors, and field-effect transistors (FETs) to achieve up to 98%
efficiency.
Non-transformer step-down converters are called "buck" converters, while step-up converters are "boost" converters.
Always check whether a converter is a dividing/multiplying or constant voltage output source.
System Components
Wire Gauge
Wire gauge or thickness is important for two reasons:
Exceeding the amperage for which a wire is rated can result in a fire or other destructive
outcomes. With low system voltages, it requires more amps to deliver the same wattage.
Smaller wires (higher gauge numbers) result in greater voltage loss due to resistance. At
low system voltages, even a small loss over the length of a wire can result in loads being unable to function.
System Components
Wire Gauge
Choosing an appropriate wire gauge is primarily a function of amperage and distance.
System Components
Wire Gauge
But the absolute ampacity of the selected wire may differ from the voltage drop limits.
System Components
Wire Gauge
Factors to
consider include conductor metal (copper, aluminum), type of wire insulation and jacket, solid or stranded (and if stranded, how many
conductors), ambient temperature, temperature rating of the wire, whether it's in the open, in a chase, or in conduit, whether it has
oxidation or kinks, peak current vs continuous current, etc. Charts can only give you an estimate -- you should read the manufacturer's
ampacity rating on the product you actually purchase to be used in the environment you intend and not exceed that.
System Components
Fuses & Breakers
Fuses are sacrificial devices that will blow out, creating an open circuit (infinite resistance) to save wires and devices on the
circuit from over-amperage conditions. Circuit breakers are like fuses, but resettable.
Fuses or breakers should be sized to protect the weakest rated component in a circuit.
Some other electronic devices such as charge controllers, inverters, and DC converters may also protect
against over-current, over-voltage, under-voltage, ground-fault, etc.
System Components
Fuses & Breakers
System Components
Grounding
Not all off-grid electrical systems need to be grounded, but it can alleviate RF noise problems and safety issues.
Because metal frames are often used as the "common" or "ground" in electrical systems, a voltage difference between that frame
and the literal Earth may cause electric shocks. Providing a conductive path eliminates that risk.
Grounding can also safely discharge a short circuit that might otherwise cause injury or property damage. It can also shunt lightning
strikes and other unintended discharges away from people and property.
An electrical system should only be grounded in one place. If grounded in multiple places, a voltage may develop between them. Multiple
grounds will usually cause a ground-fault error condition in inverters.
Although it doesn't strictly matter whether positive or negative are grounded, the negative is conventionally the grounded side. The battery
or circuit breaker panel is a good place to make the ground connection.
General System Layout
General System Layout
General System Layout
General System Layout
Putting It All Together
How to Size Your Components
Based on your load estimate, determine the Ah of batteries needed to
power you for the period you're comfortable not needing to switch to an on-demand source (generator).
Typically, this should be at least 20 hours in order to meet the 20-hour discharge rate by which
batteries are measured.
First convert energy per day (kWh) to average power (Wh/h).
Then use Watt's Law multiplied by the discharge
period to get Ah
For example, if your home requires 15 kWh/day, and you're using 12 V batteries, and you
want to plan for a 20-hr rate of discharge, then
15,000 Wh/24 h = 625 Wh/h = 625 W
625 W/12 V = 52 A, 52 A * 20 h = 1040 Ah
But this is an idealized, perfect-world estimate. In reality, there will be losses from inefficiencies.
You could try to calculate all of the losses in your wires and components, or just apply an average 8-15%... e.g.
1040 Ah / 90% efficiency = 1156 Ah
And you don't want to exceed 80% depth of discharge...
1156 Ah / 80% DoD = 1445 Ah
Putting It All Together
How to Size Your Components
We can do a sanity check by applying Peukert's Law...
The calculated capacity is higher than the rated capacity because we're drawing it down in greater than
20 hours.
Temperature, age, self-discharge, and other adverse conditions are covered by our efficiency buffer that
we built in previously.
Putting It All Together
How to Size Your Components
You'll then have to shop around for the right combination of batteries that will meet your amp-hour requirements, your
system voltage requirements, your chemistry, maintenance, & mobility requirements, and your budget.
For example, to make a 24V system voltage, you may find that you can create 2 parallel strings of
four 6-volt batteries.
But remember that 1445 Ah * 12 V = 2890 Ah * 6 V = 723 Ah * 24 V in order to give you the same
amount of energy in Wh. So when you compose strings of lower voltage batteries, you need to do the conversions to ensure
you're meeting your energy requirements.
Putting It All Together
How to Size Your Components
To compare cost between different amp-hour and voltage batteries, first normalize to watt-hours, e.g.
$1760 / (6 * 140 Ah * 12 V)
= $1760 / 10,080 Wh
= $0.175 / Wh
$240 / (1 * 109 Ah * 12 V)
= $240 / 1,308 Wh
= $0.183 / Wh
$200 / (2 * 215 Ah * 6 V)
= $200 / 2,580 Wh
= $0.078 / Wh
Don't forget to make sure the Ah being advertised are all at the same rate of discharge, e.g. 20 hour.
Other factors to consider include the rated lifespan, acceptable DoD per cycle, warranty, chemistry, etc.
A battery that costs twice as much per Wh, but has three times the lifespan, is a good deal.
Putting It All Together
How to Size Your Components
Once you have a battery bank estimate, you can size a PV array such that you can charge it reasonably
in one sunny day. As a rule of thumb, I use 8 hrs to charge 100%. Though many days
you won't get 8 hours of full sun, your batteries also won't be totally depleted, so this generally works.
So if your batteries are 1400 Ah @ 12 V, you need to generate...
(1400 Ah * 12 V) / 8 hours = 2,100 W
Recall that the nameplate rating on solar panels is STC; you need to
look at the NOCT value for a realistic output
To be safe, you should also derate it by about 15% system losses, so if you're looking at 350 W panels (NOCT 256 W), then
2,100 W / 0.85 / 256 W/panel = 9.65 panels
Since you can't have a fraction of a panel, you need to round either up or down. Rounding up would be safer. But you did
factor in a buffer already, so rounding down could be okay. If you need two parallel strings in order to accomodate
your charge controller(s), then coming out to an even number will be an important consideration.
Putting It All Together
How to Size Your Components
Charge controllers are rated in amps to your batteries. So if you need to push 2560 W into batteries at 24V,
2560 W / 24 V = 106.67 A
MPPT charge controllers (like you'll want) are typically rated at 60 A and 80 A, so in this case, you could put two
series strings of 5 panels on two 60 A charge controllers.
If you chose to use a 12 V system voltage, you'd have twice the amperage, so need twice the charge controllers. So this is
something to think about before deciding on a system voltage.
Putting It All Together
How to Size Your Components
For AC output, you might want to consider whether you'll have a single (or two) central inverter(s), or possibly multiple,
smaller, point-of-use inverters distributed to where they're needed, such as one for a refrigerator and another for shop tools
and another for audio-video equipment.
For a central inverter, you may want to match the brand and family with your charge controller(s) and meter/remote,
as this can give you good organization of system monitoring and control, with such features as generator auto-start,
unified logging, control from a smart phone or laptop, and internet monitoring.
An important element of sizing the inverter(s) is estimating the peak simultaneous loads. If you think you might be running
a 2,000 W well pump and 1,500 W toaster at the same time, then you'll need a 3,500 W inverter.
Putting It All Together
How to Size Your Components
The balance of your system will consist of wires, connectors, fuses, breakers, load centers, battery switches, DC-DC
converters, communications, battery boxes, ventilation, etc., depending on your setup.
Wires must be sized to carry at least the peak amps needed for each component. E.g. on a 24 V system, the wires
between the batteries and a 4 kW inverter must carry 4000 W / 24 V = 167 A. And you must place a breaker or fuse on that circuit rated less
than the peak wire amperage. E.g. if you choose a wire gauge rated at 180 A, then putting a 200 A fuse on the circuit will NOT protect the
wire. On the other hand, choosing a 200 A capable wire and protecting it with a 180 A fuse would work fine. The fuse would blow before the
wire is imperiled.
