If you are interested in off grid power systems and/or already rely on them – as we all do more or less here on Great Barrier Island – you may ask: ‘How much do I need to know about things like photovoltaics, wind-power, batteries and electricity?’

The answers are straight-forward. You don’t need to know anything, a tradesman/-woman will sort you out and** you can know as much as you want about these topics**. It is 2013 folks, just type what you don’t know into a search engine and you will be presented with brief and exhaustive explanations.

My intention here is to provide you with a conceptual understanding – if you will a foundation or framework that allows you to build up further knowledge – and to also give you some rudimentary examples and calculations. I’m not an electrician and am also not in the business of providing off grid power solutions. My motivation is to share with you what I know and obviously also to continue learning via this process.

Independent of whether you are planning an entirely new off grid power system for your home or if you want to know how to properly maintain what you have and to possibly expand or upgrade your running system, you will need to establish knowledge about the following:

- What is my demand and how much am I likely to consume?
- What options do I have to generate off grid power?
- How can I store (electrical) energy and what factors influence this storage?
- Do I need to compromise and if so, how do I go about it?

These are simple but necessary questions to ask. Instead of jumping to conclusions by researching the net to find answers to these questions, I sincerely believe that the only way to get properly involved with this subject is to go a step back and ask yourself what these physical quantities actually mean:

- Energy, Power, Voltage, Current, Resistance, Charge, DC and AC

We have encountered these quantities in some way or another and kind of know that they all contribute towards the term electricity. What I observe in general is that these quantities are mixed up all the time. Their definitions and even conceptual meanings are not understood – not looked up either – and arguably most importantly their units are either mixed up or entirely omitted.

**Omitting the unit of a physical quantity or getting it wrong must be avoided, otherwise all conclusions and calculations are rendered meaningless, illogical and nonsensical. **

In the following, I will provide you with the definitions and units of the above-mentioned quantities and prove to you that in order to convert units and to calculate their relationships you only need primary school mathematics knowledge. (Note, I looked the definitions up on Wikipedia. You can do this to.)

**Energy = the capacity of a system to perform work**. It cannot be created nor destroyed, but it can be changed into different forms. It’s unit is the Joule [J], other common units are calorie [cal] and the one that we will be using here is [kWh].**Power = is the rate at which electric energy is transferred by an electric circuit**. Unit is Watt [W]. 1 W = 1 J/s (Energy per time).**Voltage = electric potential energy per unit charge.**Unit being Volt [V] i.e. [J/C = V] (Joules per Coulomb).**Electric current = is a flow of electric charge**. Given in Ampere [A].**Electric resistance = is the inverse quantity of electrical conductance**. Think of a piece of metal and a piece of wood. Its unit is Ohm [Ω]. Further, [V] = [Ω] times [A].**Electric charge = is the physical property of matter that causes it to experience a force when close to other electrically charged matter**. Unit being Coulomb [C], which is 1 A*s [1 Ampere times 1 second, current times time].**Direct current (DC) = the unidirectional flow of electric charge**. Think batteries.**Alternating current (AC) = the flow of electric charge periodically reverses direction**. Think 120 V and 240 V, think power plugs and sockets in homes.- Here is a link to the relationships between power, resistance, volts and current.
- The analogy of DC circuits with water kind of visualizes these quantities and their relationships.

It is paramount to note that you will always be able to look the definitions of these quantities and their units up. Stating that your battery stores 500 Ah of energy is just as wrong as saying that you are 5 kg long. It is nonsensical.

You already know that the unit of a distance [metre] can be expressed in various distance related units, such as feet, inch, yard, kilometre, centimetre, millimetre, lightyear and so forth. All these units describe a distance, hence they can be converted into one another via multiplication with a factor. Simple!

The same is obviously true for the units we just learned, a charge can be given in ampere seconds [As], ampere hours [Ah] in milliampere hours [mAh] or in Coulomb [C] which is the same as ampere seconds.** However, it must be clear by now that a charge cannot be converted into kWh, because this is a unit of energy and not charge**. In analogy, you cannot convert a metre into years.

- How do I know which unit describes which quantity?

You can always look it up and with time, and an understanding of the quantity itself, you will know which unit is physically correct and which not. Again, you must note the difference in saying stuff like :’My dad is 2000 cm tall’ or ‘My dad is 2 years tall.’ The first statement contains a mistake, no dad is 20 m tall, but a dad could be 2 m tall. The latter statement, however, is meaningless.

When you look at the label on the back of your electrical appliance, it will not state a unit for power like [J/s], it will instead say [W]. Hence, I provide you in the following with the most commonly used units for these quantities (note ‘k’ is always kilo, stating to multiply with 1000; ‘<->’ means equivalent) and also mention equivalent units which will help you better understand the respective definitions:

- Energy in [kWh] <-> 1 kWh = 3600 kJ (you obtain this by working out how many seconds an hour has and by understanding that 1 [W] = 1 [J/s])
- Power in [W] <-> 1 [W] = 1 [J/s]
- Voltage in [V] <-> 1 [V] = 1 [J/C] = 1 [J/(As)]
- Current in [A]
- Resistance in [Ohm]
- Charge [Ah]
- Voltage [V] times current [A] = power [W]
- Power [W] times time [s] = energy [J] ; Power [W] times time [h] = energy [Wh]

Time to use our knowledge to perform some calculations. Let’s start with a 12 V DC off grid power system, consisting of two 6 V deep-cycle batteries (we’ll discuss batteries in Off Grid Power System III – Batteries) and one 200 W 12 V solar panel. In this scenario the batteries are wired in series, i.e. resulting in a voltage of 12 V. There is a label on these batteries stating in this case 400 Ah @ 6V.

- If one battery stores a charge of 400 Ah, how much total charge do I have when I use two?

Answer: at 6 V you’d have 800 Ah (in parallel), at 12 V (in series) you have 400 Ah.

- Let’s say the sun has been shining ‘in ideal conditions’ onto the solar panel for 5 hours during a day. How much energy did the solar panel generate?

Answer: Unit of energy is kWh, our answer must hence have this unit –> 200 W * 5 h = 1000 Wh = 1 kWh

- The batteries are fully charged (400 Ah @ 12 V) and you wonder how long you can operate a 12 V light which draws 24 W of power.

Answer: We need to figure out how many Ampere the appliance is drawing. 1 [W] / 1 [V] = 1 [A]; here 24 W / 12 V = 2 A. The light hence draws 2 A current at 12 V. Theoretically, you could draw 2 A for 200 hours, with every hour resulting in reducing the total charge of the batteries by 2 Ah. However, we will see in ‘Off Grid Power Systems III – Batteries’ that every battery has different discharge rates, depending on the amount of current being drawn and on its duration. With this additional knowledge we can obtain a much more practical answer.

- Let’s get back to the example with 5 hours of ‘ideal conditions’ sunlight on the 200 W 12 V panel. The question being, would this time be enough to charge the batteries completely.

Answer: Again, we must assume a few things here because we don’t know how batteries work yet. We assume hence, that they are totally discharged, ie 0 Ah and we want to obtain the fully charged state 400 Ah. 200 [W] / 12 [V] = 16 [A]. After 5 hours, the batteries would have received a charge of 80 Ah. To obtain the full 400 Ah, we require 5 times longer. Therefore, it would require 25 hours to fully charge the batteries. If you are using a calculator, you should obtain 24 hours to fully charge the batteries from initially 0 Ah to 400 Ah.

- Our final question. With the battery bank being fully charged, ie 400 Ah at 12 V. What do these figures mean in terms of energy, in terms of kWh?

Answer: 400 [Ah] x 12 [V] = 4800 [Ah*V] = 4800 [Ah*J/(As)] = 4800 [J/s * h] = 4800 [Wh] = 4.8 kWh

Once you worked out that [A] times [V] equals [W], you can do this calculation in your head and don’t need to check the units along each step.

A few words on resistance. If you know the voltage and the wattage of an appliance, these figures are printed on the sticker on the back or bottom of your appliance, you also know the resistance of it. 1 [V] = 1 [Ohm] x 1 [A]

Actually, the resistance is something worthwhile to think about but at the same time it is something that doesn’t show up in practical, everyday calculations in terms of power, charge and energy. It doesn’t show up because it is a constant loss in terms of energy and in most cases you cannot reduce this unless in investing in better conducting materials. However, the greater the resistance, the more electrical energy will be lost in form of heat.

Okay, our next question is not only important from a practical point of view, but will also clear up a thing or two about resistance.

- Question: What DC power system should I run, 24 V or 12 V? And for that matter should I buy 12 V or 24 V solar panels?

If you can afford it, get everything in 24 V. If you can’t, I would always buy 24 V solar panels even if you are (temporarily) running a 12 V DC system (there are charge controllers that can take an input of say 24 V and charge a battery bank with 12 V. We’ll discuss charge controllers later). There are at least two mainly practical reasons for this and I will explain them now.

Let’s start with the solar panels. Yes, you can connect two 12 V solar panels in series and thus charge up your 24 V battery bank. This is, however, not ideal because a 24 V solar panel will generate more than 24 V even if it is partly covered with shade. Two 12 V panels, hooked in series, however, will generate a potential difference equal or sometimes even less than 24 V if one of these panels is partly covered.

Another reason why it isn’t ideal to operate two 12 V solar panels to charge a 24 V system up is that two 12 V panels will require much more space compared to one 24 V at an equal wattage. Two panels will therefore also be more prone to being partly covered than one. Remember, two 12 V panels each having the capacity to generate 200 W power will generate 200 W at 24 V, not 400 W.

The final reason that I can come up with is the thickness of the cables/wires that need to be used. Any wire that you use for your off grid power system must be able to handle the current that is forced through. Let’s say you’ve got copper wires with a cross section of 5 squared mm and the manufacturer states that it can be used with a current of up to 10 A. Now, if more current is being forced through that wire, its resistance will increase, meaning that you have proportionally more loss in terms of energy and worse it will eventually heat up, burn through the plastic insulation and create a short. If you didn’t use the recommended 10 A fuse, you will damage your off grid power system and you could start a fire and lose your home, and worse.

Remember, 24 V with a current of 10 A yields 240 W. To obtain 240 W with 12 V, the current has to be 20 A. More current means thicker wires (which are not cheap) and also because of that it means that the potential for losing current in form of heat is higher.

I suppose, you’ve got a few questions now. What are charge controllers, what types exist? How do batteries work, what types exist, which ones do I need? How much electrical energy does a regular household require per day? How is DC converted into AC, what are the practical differences?

In Off Grid Power Systems Part II, I will raise some important points about the common and practical means of generating off grid power and discuss things you should be aware of.

P.S. If you are scratching your head and stating that you are confused with things like Joule, Watt, Coulomb, Ampere etc., I will ask you why. You will answer that you don’t understand what they mean, and I will reply that you do at least a little bit now and that you don’t know how a second or a meter is defined either but have no problems working seconds into minutes and hours, etc.

Interesting read and good coverage of the basics. Bring on the next parts of the series and please do go into details!

On a side note, the definitions could use some more easy to understand explanations and it would be helpful to highlight the differences when connecting batteries in series or parallel in depth (you touch this point twice in the text but it might not be clear to every reader).

Cheers Lars, I’ll provide equivalent definitions using an example with flowing water through a pipe, and touch up on series vs. parallel in the battery section. Details are usually better explained by others on Wikipedia etc., but I suppose it all comes down to defining details. Let’s see what I come up with anyway; there are a few (exciting) things happening here at the moment…

Brilliant! I’ll be following this closely as it will be applicable to my motorhome. Already the advice to use 24v panels is useful. Keep at it. But go fishing too! L&K Paul xxxxx

I could tell you that I saw a kingi at the Cape, a good meter long and pretty fat. Also that I have been scouting; north side of Whangapoua beach, Waikaro point looks very interesting.