Solar Panels, Solar Power, and Solar Energy

(©) PV Solar and Wind Energy

Larry Neal Gowdy

Part 1 How to size solar panels for your home

How to estimate solar panels costs

How to Estimate PV Solar Panel Energy Systems for Your Home - Part 1

This article is condensed from the Energy chapter of my 1999 book Homesteading and Self-Reliance. The information is intended for individuals who are sincere in their interest of using photovoltaic (PV) solar panels for generating 100% of all electricity needs for an energy efficient home located on a well-planned homestead. The nature of the article is also purposefully narrowed to PV installations costing approximately $500.00 to $5,000.00. Larger PV systems are unnecessary and they exceed the sensibility of using solar energy for individual dwellings. The information can also be adapted for use in creating an emergency backup system for lighting and medical needs in city housing.

Unlike city electricity that can be consumed without the consumer having any knowledge of electricity, the use of a PV system requires that the owner knows at least a basic knowledge of electrical theory. Prior to purchasing solar panels, the owner must understand how much energy a PV can produce, how much energy can be stored in batteries, how much energy the owner will consume, and how much energy will be lost in the efficiency of wiring, batteries, and electrical devices.

This article provides basic electrical theory which should be sufficient for the reader to be able to mathematically estimate the necessary quantity of PV panels for a dwelling, but it is necessary that all future PV users invest additional time into the further study of electrical theory (specifically that of capacitance, inductance, magnetism, etc..) As a general rule of thumb, spending two hours with a competent electrician, plus another two hours with a competent electronics technician, will teach you more than what might be normal for a two year course. I had two years of electronics in high school, another two years in college, another two years through a correspondence course, plus being raised in a family where it was considered second-nature to service all types of electronics, and still I had to learn the vast majority of my knowledge through firsthand experience. In my opinion, formal training is nowhere near as effective as reading a book and then applying the knowledge on one's own. Bluntly, there are individuals graduating colleges with technical degrees that cannot make light with a battery, bulb, and wire: education is a waste of time if the student cannot think. Knowledge never has and never will be a suitable substitute for thinking. Just an FYI, but I was the top tech for three companies, in my own business I have had competitors call to solve problems they could not solve, and I have fixed twenty-year-old problems in industrial equipment that no other tech could. Except for basic Ohm's law (which I give below), my education literally taught me nothing useful, and so I promote independent thought, not the memorization of words.

Analogy for Beginners : Most everything in Nature functions with a similar behavior of pressure and quantity. An idea of how electricity flows is found by observing how water flows. A city water line maintains a relatively stable pressure, and the quantity of water that can be used to water a city lawn is dependent on the size of the lawn hose. It is obvious that a small 1/4" water hose allows only a small stream of water flow, while a 3/4" hose allows a greater quantity of water flow. The cause of the smaller hose restricting the quantity of water flow is termed "friction". Rubbing one’s hands together is also an example of friction, and friction creates heat.

The water hose analogy illustrates that when the pressure remains the same, then the quantity of water flow will decrease when more friction is applied, and the water flow will increase when less friction is present. In electrical theory, friction is termed "resistance". Under normal conditions, larger wire should allow for less resistance, and smaller wire should increase resistance. Like friction, increasing resistance results in an increase of heat. During PV installation it is important to use large diameter wiring to allow for the maximum quantity of electricity flow, as well as to prevent the wiring from heating. The use of small diameter wire will result in a loss of electricity as well as increase the danger of creating fires within the walls of houses.

It is a generally accepted theory that electricity predominately flows along the surface of a conductor. There are two main types of wiring; solid and stranded. The solid variety has one large wire, and it is similar to what is used in the walls of city housing for 120 volt Alternating Current (AC) electricity. (AC is used for long distance power lines due to there being less voltage drop in the lines themselves. Typical North American city home sine-wave AC travels from zero volts to about 120 volts positive, then goes back to zero volts and on down to a negative 120 volts, and then it goes back up to zero volts and repeats the cycle 60 times every second (60 hertz = 60 cycles per second)). The stranded variety has numerous small strands of solid wires combined together within a single insulator. Stranded wire is similar to what is used in automobiles for 12 volt Direct Current (DC) electricity. (DC is like the voltage from a battery that maintains the same polarity of positive and negative.) One advantage of using stranded wire is that it has more surface area, which theoretically means that it has less resistance, and thus it can usually carry more electricity while creating less heat. The actual temperature difference between solid and stranded wiring is negligible and is rarely needful of knowing, but the lower resistance is noticeable and should remain in mind while wiring a PV system. Although minor, the primary disadvantages of stranded wire is that it requires end-fittings (ring terminals) for proper connections, and that stranded wire is typically more expensive than single-strand wire.

A PV solar system located near the storage batteries will not be greatly affected if single solid-strand wire is used from the PV panels to the batteries. For house wiring, however, the longer distances do require stranded wire to maximize electricity flow, to maintain maximum voltages, and to prevent the heating of the wire itself.

AC Versus DC Electricity

Regardless of what anyone might claim, AC electricity is not good for an individual’s health. This article is being presented as a guide for sizing and living only with DC electricity. I will not promote the use of a known health danger.

Electrical Terminology

Conductor : Anything that has a sufficiently low resistance to electricity. Iron, steel, aluminum, water, brass, gold, silver, and many other materials easily conduct electricity. The most common conductor for housing electrification is copper wire.

Closed Circuit : Like attaching two garden hoses together to allow water to flow from one to the other, a closed circuit is one where two conductors are connected together. A light switch is "closed" when contacts within the switch are touching and the light bulb is illuminated.

Open Circuit : Like removing a garden hose between the faucet and lawn sprinkler, an open circuit is one where two conductors are disconnected. A light switch is "open" when contacts within the switch are not touching and the light bulb is not illuminated.

Short Circuit : A short circuit is a closed circuit in a location that prevents adequate electricity from flowing through the intended device. Most typically, a short circuit implies an unwanted closed circuit that has very little resistance, it causes a high flow of electricity through the short circuit, it causes electrical devices to not operate, it will rapidly deplete a battery’s stored voltage, and it has a high probability of burning the conductor in-two and starting a fire. For the home owner, shorts are a bad thing.

Ohm : Ohm is a measurement of electrical resistance. The higher the ohms, the higher the resistance. As a small garden hose may have twice the resistance of a larger hose, in electrical terms it would be said that the small hose has more ohms than the larger hose.

Continuity : Continuity simply refers to a conductor carrying electricity. A switch that is properly closed is said to have continuity. A switch that is open is said to have no continuity. Using an ohm meter, a wire that is tested from one end to the other, and discovered to have few ohms, is said to have continuity. If the ohm meter does not measure ohms between one end of the wire and the other end, then the wire is said to not have continuity. Continuity is a closed circuit. No continuity is an open circuit.

Voltage : As water pressure is the force that pushes water out of a hose, voltage is the pressure behind electricity. The higher the pressure, the higher the quantity of electricity can be produced. Voltage is also termed "potential".

Amperage : As oceans of water are quantity, so is amperage the quantity of electricity. Amperage is also commonly referred to as "current", "amperes", and "amps".

Wattage : Also termed "power", wattage is the combination of voltage-pressure and amperage-quantity. Increasing voltage or amperage will result in a higher wattage. Decreasing voltage or amperage will result in a lower wattage. Increasing the resistance of a circuit by using a smaller diameter wire will result in less voltage and less amperage, which results in less wattage to the electrical device.

Basic Electrical Formulas

Power (Wattage) is figured by multiplying voltage (E) by amperage (I). The formula is written W / ExI, or more easily remembered as W=ExI (watts = voltage times amperage). A 12 volt device using 10 amps will draw 120 Watts (12 volts (E) x 10 amps (I) = 120 watts (W)). If an appliance only states a wattage rating, the amperage is determined by dividing the wattage by the voltage. A 120 volt electric heater rated at 1,200 watts draws 10 amps (1,200 watts (W) divided by 120 volts (E) = 10 amps (I)). For a 12 volt electric heater to produce 1,200 watts it must draw 100 amps (12 volts (E) x 100 amps (I) = 1,200 watts (W) : 1,200 watts (W) divided by 12 volts (E) = 100 amps (I)). Very simple!

Ohms law is written E / I x R (E over I times R), or more easily remembered as E = I x R (E= voltage, I= amperage, R= resistance measured in ohms). E is determined by multiplying I by R; I is determined by dividing E by R; and R is determined by dividing E by I.

It is not very common to need to determine what a voltage is on a homestead since the owner should already be familiar with what voltages are being used, but it is common to need to know what amperage a resistance will draw at a certain voltage. A 2 ohm resistance at 12 volts will draw 6 amps (12 volts (E) divided by 2 ohms (R)). By multiplying the voltage by the amperage, it can then be known what the wattage is (12 volts x 6 amps = 72 watts). The 2 ohm resistance would create as much heat as a 72 watt light bulb, which is enough to melt plastic insulation from wiring and cause fires.

The formula for summing ohms in a series circuit is R+R=R total. 10 ohms plus 5 ohms equals 15 ohms. 10R + 10R + 80R = 100 ohms. Similar to connecting several garden hoses end to end, the total friction is increased and the water output is decreased.

The method for summing ohms in a parallel circuit is by adding the reciprocals and then taking the reciprocal of the sum: 1/R1 + 1/R2 = 1/R = R/1. A parallel circuit with 10 ohms in the first circuit and 10 ohms in the second is figured by adding the reciprocals 1/10 + 1/10, which sums to 2/10, and the reciprocal equals 10/2, which is 5 ohms. If three wires each had a resistance of 20 ohms, and the wires were connected in parallel, the total resistance would be approximately 6.6 ohms (1/20 + 1/20 + 1/20 = 3/20 = 20/3 or 6.6). The total resistance in a parallel circuit will always be lower than the lowest resistance of any one line in the circuit.

The primary advantage of knowing how to sum parallel resistance is that if there is a need to lessen the resistance in a long wire, it may be more reasonable to install two medium sized wires of low cost in parallel rather than install one large wire of high cost. As an example, if the distance from the PV storage batteries to a television is too long, there may be too great of a resistance in the wiring, and the television will not receive sufficient voltage to operate. By installing an additional wire of the same size in parallel, the resistance will be cut in half, and the voltage at the television will be increased. For 12 volt DC receptacles located a sizable distance from the storage batteries, it may be necessary to install two or three medium sized wires in parallel so as to maintain the highest possible amperage and voltage to the receptacle.

Using wire too thin can also reduce the output of PVs 50% or more. Always keep wires as short and large as possible, and if necessary, run multiple wires in parallel so that each wire can carry its share of the total amperage.

A 12 volt electric heater drawing 100 amps has an internal resistance of .12 ohms (12 volts divided by 100 amps). A 60 watt light bulb draws 5 amps at 12 volts and has an internal resistance of 2.4 ohms. Placing two each 2 ohm resisters in series makes the total resistance 4 ohms (2 ohms plus 2 ohms equals 4 ohms). Each resister, being equal, will each use half of the total voltage and cause the total amperage usage to drop in half.

If a wire has 2.4 ohms resistance, and a 12 volt 60 watt light bulb has 2.4 ohms, then in a series circuit the light bulb would receive 6 volts while the wire itself is wasting 6 volts as heat in the house walls. In such a scenario, the light bulb would be dim, and half of the output of the PV system would be wasted. It is cheaper and better to run properly sized wiring than to spend more money on twice as many PV panels and batteries. One properly installed PV panel can produce more useful energy than several improperly installed PV panels.

Preliminary Sizing of a Solar Panel System

Once an individual has an idea of the mathematical formulas behind electricity, it is then possible to begin estimating the quantity of PV panels needed for a dwelling. The next step is to write down on paper a full list of all electrically powered devices (including light bulbs) that are currently being used by the individual. Once the list is complete, beside each item is to be listed the item’s voltage, amperage, wattage, and hours of use each day. Multiply the wattage by the hours to sum the watt-hours of each item, and then add all watt-hours together to determine the total daily watt-hours. To verify that the estimates are close, the total watt-hours can be multiplied by 30 and then be divided by 1,000, which would be the monthly kilowatt-hours, and should be reasonably close to the kilowatt-hours listed on the monthly electric bill.

Device - Volts - Amps - Watts - Hours = Watt-hours

Bulb - 120 - .5 - 60 - 5 = 300

TV - 120 - 2 - 240 - 10 = 2400

PC - 120 - 2 - 240 - 5 = 1200

Oven - 240 - 10 - 2400 = 2 - 4800

DC TV - 12 - 3 - 36 - 2 = 72

Total = 8772

Strictly for fun, divide the total daily watt-hours used in your home by 125, and then multiply the result by $500.00. The total amount is roughly what it would cost to power your city home with PV panels in a sunny location. As an example, if a person pays about $200.00 a month on electricity at 10 cents a kilowatt-hour, then the person is consuming approximately 2,000 kilowatts a month, or about 66,666 watts daily. Dividing 66,666 by 125 equals about 533, and multiplied by $500.00 equals about $266,664.00, which is a ball-park figure of what it would cost to power the house solely with PV panels.

The 125 figure is based on a 75 watt PV panel producing 4 amps at 12.5 volts for an average of 5 hours per day in summer. The total average output per solar panel would be approximately 250 watt hours per day. Deducting efficiency losses of batteries, wiring, and cloudy days, the average output would be around 125 watt hours per solar panel per day. In winter, PV panel output will drop an additional 25-50% or more depending on your region’s location.

It is not rational to consider solar energy for powering a typical city house that uses common AC electrical devices. The $266,664.00 placed into a bank at only 3% interest would earn roughly $8,000.00 a year, which would more than pay for the electric bill. Also, the typical maintenance on such a large PV system would far exceed the typical electric bill. The popular hype about converting city homes to solar power is not based on reality.

The next step is to take the list of electrical devices and mark-off all that are unnecessary. Continue trimming the list until there are no other items that can be eliminated without causing undue discomfort. A typical house can easily reduce its electricity use by 50% or more simply by the owners discovering the purpose of the "off" button. Once the final list is complete, sum the watt-hours again as above, and recalculate the cost of PVs. The cost will likely still be unreasonably high, where even if the home owner eliminated 90% of electricity consumption, the PV cost would still be approximately $26,666.00.

Now subtract another 90% from the total cost to get an idea of the difference between using common 120 volt AC devices and the less common 12 volt DC devices. The cost of a PV solar energy system would now be approximately $2,666.00, which is at a reasonable level and is within the general goal of this series of articles; to produce 100% of all electricity needs of a home through the use of about five each 75 watt PV panels. Below is a quick comparison of common city 120 volt AC devices versus 12 volt DC devices that perform the same purpose. For convenience, the estimates are all based on each device being used five hours per day.

AC @ Watts = Watt-hrs | DC @ Watts = Watt-hrs

Bulb @ 60 = 300 / Bulb @ 30 = 150

TV @ 240 = 1200 / TV @50 = 250

PC @ 240 -=1200 / Laptop @ 24 = 120

Oven @ 2400 = 12000 / Small Oven @ 240 = 1200

Stereo @ 240 = 1200 / Stereo @ 12 = 60

Total = 15,900 for AC devices, 1,780 for DC devices.

As the table above illustrates, energy consumption can be decreased close to 90% by simply choosing common DC devices. Additional energy savings are easily attained by choosing specific types of devices that are more efficient than the average.

When estimating power output from a PV panel, always rely on the amperage rating, not the wattage rating. An 80 watt PV that outputs 4 amps at 20 volts will produce no more useful energy than a 60 watt PV that outputs 4 amps at 15 volts. Storage batteries require about 12.5 to 13 volts, and any voltage above that will be stopped by the voltage regulator. PV panels with high voltages have the advantage of being mounted at a further distance from the batteries (the voltage loss in the long wiring is compensated by the PV's higher voltage), and a high wattage PV will produce more energy if it is wired directly to an electric heater that can make use of the higher voltage, but neither reason is acceptable for a Green home. PV panels should be mounted near the storage batteries, and the savings of not having to pay for higher wattage PV panels will enable the home owner to purchase an additional smaller PV to increase the total amperage.

Beware of companies that advertise PV panels as wattage only without also giving the exact voltage and amperage ratings. Never ever buy any alternate energy device from anyone if the product is not advertised with all specifications. Legitimate and knowledgeable dealers will always list the specifications.

Also beware of companies that claim a homeowner can sell excess electricity back to a power company. In a best case scenario a 60 watt PV panel will average about 360 watt-hours per day. City electricity currently costs about 10 to 15 cents per kilowatt. At about 3 to 5 cents of electricity produced per day per 60 watt PV panel, it would take about 50 years for a PV panel to pay for itself, but when figuring in the additional costs of an inverter to convert the PV electricity to be used by the power company, never can a PV panel earn its cost back.

Better PV panels with high amperage and lower voltage cost approximately $85.00 per amp, while the low wattage models with similar voltage but lower amperage cost about $95.00 per amp. In the example above, the 1,780 watt-hours would equal about 148 amp-hours per day. In a sunny region during summer, with 6 hours of good sunlight, the 148 is divided by the 6 to sum about 25 amps needed for each of the 6 hours. The ball-park estimate then states that 25 amps multiplied by $85.00 is about a $2,150.00 cost for the PV panels. Approximately $150.00 per PV is also needed for storage batteries, wiring, mounts, and other hardware. Generally, the 1,780 watt-hour example would cost the home owner about $2,500.00 to $3,000.00 total.

I lived comfortably off the grid for over five years, and with only five 80 watt PV panels. Part two of the article covers specifics on which types of DC devices are suitable substitutes for common AC appliances. One topic is how to modify an inexpensive DC cooler to only use about 5% of the electricity that a normal AC refrigerator consumes. Other topics include solar storage batteries, inverters, and regulating systems. Part three includes very important information about wind power for the home.

Update May 09, 2016: my workload has not allowed me enough time to properly create the additional pages, and at present it does not appear that I will have the time for at least two more years. Also please note that the stated PV costs are from three to five years ago; some PVs can now be found at lower costs.