Chapter 3

Powering through Electricity Basics

IN THIS CHAPTER

Understanding current, voltage, and resistance

Getting to know Ohm’s Law

Differentiating between power and energy

Calculating series, parallel, and series-parallel connections

When you discuss electricity with someone, you tend to get one of two responses: the bobblehead response and the know-it-all response. The bobblehead is the person who just nods at everything you say because he has no knowledge about electricity so he can’t challenge any of it. The know-it-all is the person who’s just waiting for you to slip up so he can correct you.

You, as a PV system designer and installer, need to become the person somewhere between these two extremes. You absolutely must be educated in your language and understanding of the basic electrical terms and concepts. Some people will never catch you when you use the wrong term in conversation (it happens to the best of us), but if you continually mix up your terminology, you’ll lose your credibility before you can even finish speaking.

In this chapter, I take you through the fundamental electrical terms and topics for PV systems. (Although I’m sure you probably have a concept of the majority of the terms, a quick review never hurts.) Then I show you how to apply those terms in a few important calculations. I wrap it up by covering the ways you’ll configure PV arrays when you’re out working with these systems.

Going with the Flow: Current

Electrical current is typically viewed as the flow of electrons through a conductor (wire). Although this process is more properly described as the charge that’s flowing through the conductor, most people can get onboard with the thought of electrons moving from one point to another and doing work along the way.

If you want to dive into the electrical theory aspects of current, by all means do. Plenty of resources exist, but I don’t cover the topic any further here. I don’t mean to belittle the importance of the concept of flowing charges versus electrons. It’s certainly valuable to understand, but this topic is really beyond the scope of what most PV designers need to know.

In this section, I introduce you to the unit used to describe current, present the two different kinds of current, and explain how to measure current.

Understanding amps

The International System of Units (SI) describes current through the term ampere (A), or amp for short. Current is also represented by the symbol I, particularly in Ohm’s Law (which I cover later in this chapter). Ampere represents a flow, or a rate of electron movement. The fact that this is a rate is very important because you have to measure and predict the amps flowing throughout your systems.

The base units for an ampere are coulombs per second. A coulomb contains approximately 6.24 × 10¹⁸ electrons, which means an ampere represents a whole mess of electrons passing a point every second.

To better understand current, think of cars on a highway. Each car represents an electron, and the number of cars passing a single point over a period of time is the traffic flow. As long as all the drivers do their jobs, traffic flows smoothly, and the number of cars passing that point isn’t restricted.

The other point to note here is that the electrons don’t go anywhere after they do their work, meaning they aren’t used up. They continue in the circuit and are pushed along by the electrons behind them. So what does this fact mean in terms of understanding amps? Well, after the electrons have done their work, they continue flowing and go back “home.” This is an important fact to remember when you’re sizing conductors based on the current flow.

Distinguishing between direct current and alternating current

PV modules create a flow of current that’s described as direct current (DC) because the electrons move in just one direction. As sunlight strikes the PV cells, the electrons move off the cells and through a load (any piece of electrical equipment) before heading back to the cells, all while staying in a straight line.

DC is also the form of electricity stored by and delivered from batteries. This characteristic is very convenient when charging batteries from PV modules, but it’s rather inconvenient when you want to use a standard electrical load that runs on AC power. In Chapter 9, I detail the different inverters appropriate for battery-based systems.

One of the main drawbacks of DC electricity is the limited distance it can be transmitted before significant losses make it too inefficient. In PV systems, these losses can be overcome by using larger conductors to carry the current, but this solution is costly and has some limitations. (I show you how to calculate losses associated with PV wiring in Chapter 13.)

The other form of electricity that’s present in PV systems is alternating current (AC). In AC, which is the form of electricity delivered from utilities to homes and businesses, the electrons move in a back-and-forth pattern. So how does AC work in a PV system? In Chapter 2, I provide a basic description of the inverters that are connected in PV systems. These devices take the DC electricity in the PV array (in a grid-direct system) and batteries (in a battery-based system) and turn it into a form that the typical household loads can use, which is often AC.

AC differs from DC mainly in the sense that the current alternates in flow at a specific interval of time. The process of alternating the direction of current flow can be viewed graphically, as shown in Figure 3-1. Notice the sine wave shape of the AC current flow curve? It indicates the back-and-forth movement of the electrons. In contrast, the DC current flow is represented by a line that remains straight over time.

FIGURE 3-1: AC and DC current flow versus time.

Measuring current with a meter

As you install a PV system, you must measure the DC output of an individual module (or sometimes even the entire array) in order to troubleshoot an issue or verify performance. You may also need to measure the AC output of the inverter in order to troubleshoot the inverter. In either case, to measure current correctly you must have a good, hand-held current meter (also known as an ammeter) that can read both AC and DC. In the sections that follow, I describe types of ammeters and explain how to use one safely and effectively.

Many inverters have a way to meter the AC side of the system. These meters generally report the power output (I delve into the details of power in the later “Pondering Power and Energy” section). Although this isn’t the same as metering the current, it’s generally helpful. As you discover in the later “Relating power to current, voltage, and resistance with the power equation” section, you can take the reported power value and calculate the current value.

Checking out different kinds of ammeters

Two types of hand-held ammeters are available: inline and clamp.

• The inline meter (shown in Figure 3-2a) requires current to flow through the meter in order to be read. So to obtain a proper current reading with an inline meter, you have to place the meter in the circuit.

  Only use an inline meter when you fully understand how the current is flowing through the system and the proper ways to disconnect and safely collect the current measurement. Without a firm grasp on this knowledge, you can really hurt yourself when using an inline meter.

• The other (and better) option is the clamp meter, shown in Figure 3-2b. Clamp meters have a “jaw” on the top that opens when you press a lever on the side of the meter. To measure current with one, place a conductor in the middle of the open jaw and release the lever, allowing the meter to determine the amount of current flowing through the conductor without exposing any portion of it.

  A digital multimeter (DMM) is a device that can measure multiple electrical components such as current, voltage, and resistance. Because clamp meters can encompass all the features of a DMM listed, investing in a good clamp meter is wise.

FIGURE 3-2: Inline and clamp meters.

A lot of meters can handle AC without any issue but are limited when it comes to measuring DC. When shopping for a meter, look for one that, at a minimum, can measure both AC and DC voltage and current values (I cover voltage in full detail later in this chapter). Also, make sure the meter has the ability to read DC levels that are high enough for the work you plan to do. I recommend a meter that can read at least 100 amps direct current (ADC). Many meters are limited to 10 ADC, which hinders your ability to measure many arrays.

Walking through the measurement process

Typically, you measure DC current on a single module when you suspect that the module isn’t working properly or on an array when you want to verify the proper power output. (For the full scoop on array commissioning and maintenance methods, flip to Chapter 18.)

On the AC side, if you suspect that the inverter is underproducing, then you need to check the AC current levels. Another common scenario for checking current on the AC side is to see what an individual load is pulling; this information can be especially useful in battery-based systems where you need to know how many amps each load needs.

As I explain in the preceding section, I recommend using a clamp meter when you measure current. Here’s how to properly use one:

1. Put on personal protective equipment (PPE) such as insulating gloves and safety glasses.

   Measuring the current of a PV module can be very dangerous work. Electrons are flowing, and the probability of shocking yourself is high. Before conducting any current measurements, make sure you have all the proper safety gear in place and are correctly connecting and disconnecting the circuit to reduce electrical hazards. Yes, using a clamp meter helps keep you safer during the testing process, but you still have to safely stop the current flow. (Refer to Chapter 15 for full details on staying safe during installation work.)

2. Verify that you can safely place the meter’s clamp around the conductor you want to measure.

   These conductors will often be in boxes with tight clearances, so make sure you don’t come into contact with any live parts, such as wire terminations, fuse holders, or exposed conductors.

   Always expect that power is present and that a shock hazard exists.

3. Set the meter’s dial to read the appropriate range of DC current.

   Some meters are autoranging, meaning they set themselves to the proper range. If yours doesn’t, verify the amount of current you expect to see and set the dial to a value greater than that. For most PV modules, this amount is in the 10 ADC range.

4. Zero the meter reading.

   Many ammeters register a small value even if the meter isn’t measuring anything. By zeroing out the meter, you give it a baseline that increases the accuracy of the reading. To zero out the meter, refer to the manufacturer’s instructions that came with the meter.

5. Open the meter’s clamp and place it around a single conductor.

   Be careful not to place multiple conductors in the meter. If you do, the meter will read the sum of the currents, and you won’t get an accurate reading.

6. Read and record the current value from the meter.
7. Remove the meter from the conductor.

Never use an ammeter to connect the two terminals of a battery. At best, you’ll ruin both objects by creating a short circuit between the two terminals. At worst, you’ll place yourself in unnecessary danger.

May the (Electromotive) Force Be with You: Voltage

The amount of push that the electrons have behind them is known as voltage (V); voltage is measured in volts (how about that?) and represented by the letter E in equations. Another way to describe voltage is as electromotive force. In the following sections, I explain the basic concept of voltage, define nominal and operating voltage, and tell you how to measure voltage.

Grasping the concept of voltage

You can view voltage as the electrical pressure that encourages electrons to move; in other words, voltage makes current (the flow of electrons) happen. Very often you see voltage referred to as voltage potential because there must be a difference between the source of power’s voltage and the load’s voltage so that current can exist. For example, if you want to use a PV array to charge a battery, the PV array (the source of power) needs to have a greater voltage than the battery (the load). If the PV array has a voltage equal to or less than that of the battery, it can’t push the current into the battery, which means the battery can’t get charged.

Both DC and AC voltages are present in PV systems. The concepts and properties for both types of voltage are the same. You just need to make sure you’re thinking about and using the correct one depending on which side of the PV system you’re working on. Common convention (and what I use in this book) designates the differences by giving a numerical value followed by VDC (for volts DC) or VAC (for, you guessed it, volts AC).

Getting a grip on nominal voltage and operating voltage

A term you often hear as a PV system designer and installer is nominal voltage. This number represents a baseline for measuring voltage. Here’s an example: Way back at the dawn of the modern PV industry (the turn of the 21st century), PV modules were available in one of two nominal voltages, 12 V and 24 V, because most PV modules at the time were being used to charge batteries that generally came in 6 V and 12 V nominal voltages. (Remember: PV modules have to produce a voltage greater than batteries, or else there’s no current.) So the actual voltage put out by the modules had to be higher than the battery nominal voltage to effectively charge the batteries.

That output voltage is called the operating voltage; it’s the voltage value when the module is pushing current into a load. A typical 12 V nominal PV module has an operating voltage of 17 V to 18 V. In other words, it has 36 cells inside it that are wired to produce the 17 V to 18V. This allows the module to produce enough voltage to push the current into the battery under all conditions. So when you hear someone talking about a 12 V module, you know he’s referring to the nominal voltage.

The nominal voltages of PV modules have little meaning in grid-direct PV systems (although you still hear references to 12 V or 24 V modules). Where the distinction between nominal and operating voltages really comes into play is when you’re installing a small PV array to charge a battery bank. In this case, you need to make sure the PV array’s voltage is always high enough to charge the batteries. The easiest way to do this is to have an array nominal voltage that’s equal to the batteries’ nominal voltage.

The growth of the grid-direct, utility-interactive market has limited the demand for battery-charging PV modules. In fact, many of today’s modules have no relation to the battery-charging systems of old. This move away from modules that are designed to charge batteries has given module manufacturers a greater amount of flexibility in terms of the number of cells they put in each module. The result? PV modules with a wide variety of voltage ranges.

Measuring voltage

It’s your job to be prepared to properly measure the DC voltage for individual PV modules and an entire array, which means you need to know how to use a digital multimeter (DMM). This is typically the same meter used to measure current (that is, if you’re not using a dedicated ammeter; see the earlier “Checking out different kinds of ammeters” section for details on this tool).

When you take the voltage measurement of a module, there shouldn’t be any load on the PV system. Without a load to power, there’s no current, and the modules are at open-circuit voltage (Chapter 6 details the different voltages associated with PV modules). This value represents the voltage potential that can be delivered from the module; knowing this number is important because it allows you to verify the proper voltage levels in your system before you start flipping switches.

Figure 3-3 shows a typical DMM that has been set up for reading DC voltages on a PV module. To make the measurement:

1. Put on personal protective equipment (PPE), including insulating gloves and safety glasses.

2. Make sure the disconnects are in the off position.

   Performing this step stops any current from flowing, which keeps you from accidentally touching something that has current flowing through it.

   Don’t give yourself a false sense of safety when making a voltage measurement. PV modules should be considered live as soon as they’re in the sun; just because current isn’t flowing doesn’t mean you aren’t at risk of getting shocked. See Chapter 15 for details on staying safe during installation work.

3. Make the location where you want to take the voltage measurement accessible by removing the lids to the proper boxes, opening disconnect covers, or accessing the connectors on the backs of the modules.

   You can take the reading off of an individual module or inside electrical equipment.

4. Place the black meter lead in the connection point labeled Common on the meter.

5. Place the red meter lead in the connection point labeled V on the meter.

   Commonly, this point is also labeled Ω, indicating the ability to also measure resistance. (I cover resistance in detail later in this chapter.)

6. Set the meter’s dial to read the appropriate range of DC voltage.

   The appropriate range of DC voltage is the estimated voltage you expect to see. You can arrive at this estimate by looking at the modules’ ratings and where you’re at in the system.

   When in doubt, set the meter to the highest range and adjust it down if you need to. (Note that autoranging meters will set themselves to the proper range without any help from you.)

7. Place the black lead on the negative terminal for the PV module.
8. Place the red lead on the positive terminal for the PV module.
9. Read the voltage measurement on the meter’s screen.

10. Switch the meter leads on the PV module and note the presence of the negative symbol.

    This negative symbol is your indication of reverse polarity, which means the voltage from the source is backward to the meter (the meter expects that the positive terminal is connected to the red lead and that the negative is connected to the black lead).

    This ten-second test can save you a lot of time and heartache in troubleshooting, which is why I strongly suggest you perform it every time you check DC voltages. Although some equipment claims to be reverse-polarity-protected, you can’t rely on this “guarantee.” If the equipment isn’t able to protect itself, it’ll let you know by releasing some smoke.

11. Remove the leads from the module and pull them from the meter.

    I suggest removing the leads from the meter each time you’re finished. Doing so forces you to think about the measurement you’re about to take each time you go to use the meter. This is especially helpful if the meter can be used as an inline current meter. If you use an inline meter to check current and then go to check voltage without resetting the meter leads, you may be in for quite a surprise — namely, you’ll allow current to flow through the meter when you don’t expect it. Not a good thing.

FIGURE 3-3: Measuring a PV module’s voltage with a DMM.

Making a Stop: Resistance

In the context of DC electricity, the term resistance (represented in equations as R) means resisting the flow of current. It’s not much different than the resistance you encounter at home when you try and push that plate of broccoli in front of your child. You push the plate toward him, and he resists by pushing it back. In the next sections, I explain the unit of measurement for resistance and walk you step by step through the process of measuring resistance.

For AC circuits, the correct terminology for opposition to current flow is impedance. The calculations for impedance can get complex quickly and are beyond what I think you need to focus on. So for the purpose of the discussion here, I refer only to resistance.

Introducing ohms

In electrical circuits, resistance is measured in ohms (Ω). The greater the number of ohms, the greater the resistance. You want the conductors in your PV systems to have little resistance so current can flow through them as efficiently as possible, but it’s unreasonable to think there won’t be any resistance. The best you can do is keep that resistance to a minimum.

The size of the conductor used in PV systems has the biggest effect on the overall resistance. The bigger the conductor, the more room the electrons have to move around, which equals less resistance. Think of the conductor as the highway that all the cars in your area are driving on. If the highway is just two lanes wide, only so many cars can move down it at a time, which leads to increased resistance. If the same number of cars were to travel on an eight-lane expressway, you’d have far less resistance. (Flip to Chapter 10 for the basics on conductors and other electrical and safety devices.)

Measuring resistance

When you install a PV system, you may need to check the resistance in a given PV circuit (by this, I mean you may need to determine the resistance in the conductors you run from the PV array down to the inverter and/or battery bank). You look at resistance for two reasons: to verify that the conductors used allow the current to move with little opposition and to make sure that the conductors are properly connected to the electrical equipment.

The easiest way to determine the resistance in a circuit is to find the total voltage drop across that circuit by using Ohm’s Law (which I present later in this chapter) to calculate the total resistance. When resistance is present in the conductors, the voltage at the source will be greater than the voltage at the load (which is at the end of the line). I explain how to calculate this voltage drop value in Chapter 13.

Another common way of measuring resistance is to perform a continuity test. The goal of a continuity test is to find very little resistance in the circuit, indicating an easy path for the electrons to follow. A typical continuity test is to check the conductors connecting pieces of equipment. Think of two boxes mounted on a wall next to each other. You pull six conductors from Box 1 to Box 2, but after you’re done, you can’t tell which conductor in Box 1 is the same conductor in Box 2. Perform a continuity test by using a meter that’s set on measuring resistance to positively identify the two ends of the same conductor. When you touch the ends of the same conductor with your meter, there’ll be little to no resistance, and you’ll know for sure that you have the right conductor. (Note that using a meter to verify the points where each conductor is connected is far more reliable than using your fingers and eyes to trace the path of each conductor.)

Most DMMs have a resistance-measurement feature that incorporates an audible alarm. This alarm indicates that a low-resistance connection exists between the two points you’re touching. As soon as you remove one of the leads, the alarm shuts off, indicating a high amount of resistance between the two leads. This alarm helps you verify that the connections you made are correct before you turn on the power source(s).

Performing a continuity test doesn’t take very long and can save you a lot of time during the commissioning process that I describe in Chapter 18. To use a DMM to measure resistance and check continuity between various components, just follow these steps (and take a look at Figure 3-4):

1. Put on personal protective equipment (PPE) such as insulating gloves and safety glasses.

   Flip to Chapter 15 for the how-to on staying safe during installation work.

2. Switch the AC and DC disconnects to the off position to remove any power sources present.

3. Make the location where you want to take the continuity measurement accessible.

   You generally take the reading inside electrical equipment, which means you have to open the covers to the disconnects and inverter(s).

4. Place the black meter lead in the connection point labeled Common on the meter.

5. Place the red meter lead in the connection point labeled Ω.

   Commonly, this point is also labeled V, indicating the ability to also measure voltage. (I explain how to measure voltage earlier in this chapter.)

6. Set the meter’s dial to read the circuit’s resistance.

   Always start with the highest resistance values on your meter. If you need more precision on the readings, you can always turn the dial to the smaller numbers (unless of course you’re using an autoranging meter that sets itself to display the proper scale automatically).

7. Place the black lead on the first connection point.

   This connection point is typically found inside a disconnect.

8. Place the red lead on the second connection point.

   This point is typically the other end of the conductor on which you placed the black lead.

9. Read the resistance measurement on the meter’s screen or listen for the alarm that indicates a low-resistance connection.

   If the alarm doesn’t ring when you expect it to, you’ve either made the connection in the wrong location or placed the meter leads in the wrong spot. Investigate further by repositioning the leads from your meter to the points inside one of the boxes until you determine where the connections are being made.

10. Remove the leads from the module and pull them from the meter.

FIGURE 3-4: Measuring resistance with a DMM.

Connecting Current, Voltage, and Resistance with Ohm’s Law

As a PV designer and installer, you use three main electrical components in all of your calculations: current, voltage, and resistance. Knowing how these components relate to each other is critical to the success of your PV system designs. Consequently, you need to have a good understanding of Ohm’s Law, which relates current, voltage, and resistance to one another. You’ll use this formula in a variety of ways, from gauging conductor sizes and determining voltage drops to calculating power (I explain how to do that later in this chapter).

Ohm’s Law can be stated in many ways:

• Volts = Amps × Resistance (E = I × R)
• Amps = Volts ÷ Resistance (I = E ÷ R)
• Resistance = Volts ÷ Amps (R = E ÷ I)

So, for example, to determine the resistance in a circuit for a PV array that’s operating at 120 DC volts and 10 amps, perform the following calculation:

• Resistance = 120 DC volts ÷ 10 amps (or R = E ÷ I)
• Resistance = 12 ohms (R = 12 Ω)

Pondering Power and Energy

The value that everyone in the PV world likes to talk about is the power value, but what most folks don’t realize is that power and energy are closely related. In the next sections, I set you straight on the differences between power and energy and then relate those concepts to commonly used formulas.

Recognizing the differences between power and energy

One of the most important concepts to keep straight in your head is the difference between power and energy. Even though these terms are misused everywhere, the differences between them are basic and even obvious, as you discover in the sections that follow. Using these terms correctly is crucial to your success as a PV system designer and installer.

Power is a rate

Power is measured in watts (W), and 1,000 watts equals 1 kilowatt (kW). A watt is the measurement of the flow of energy, just like current (covered earlier in this chapter) measures the flow of charges. Simply stated, power is a rate; it’s an instantaneous value. If you’re talking to someone and he says his PV array produces 1,000 kilowatts per year, that makes as much sense as you telling him that you drive your car 65 miles per hour per year.

Part of the problem with the term watts is the lack of a time value, which people tend to associate with rates. They’re used to seeing a rate given in terms of a quantity per rate of time: miles per hour, gallons per second, kilobytes per second, and so on. Truth be told, watts have a time value to them. You just don’t see it.

One watt is equal to one joule of energy per second (that’s your time value).

Energy is a quantity

Energy is the measurement of power multiplied by time; it’s measured in kilowatt-hours (not kilowatts per hour). This is the number that your utility charges you for and, if you could hold it in your hand, the quantity of energy a load consumes.

In PV systems, the power value (wattage) gets the spotlight even though the energy value (kilowatt-hours) is the value that makes the real difference. The energy value is the one you should concern yourself with the most because it’s what people are consuming and you’re selling. All PV projects are driven by a budget, and kilowatt-hours can be directly converted into dollars and cents. For example, if a PV array is installed in a location that doesn’t allow it to produce enough energy (kilowatt-hours) on a consistent basis, the owner of that system will have to continue buying energy from someone, generally the utility. If that array were in a great location, it could produce a lot of energy, and the system owner would benefit from lower energy bills from the utility.

Relating power to current, voltage, and resistance with the power equation

The power equation is relatively simple and much like Ohm’s Law (which I present earlier in this chapter). In fact, it’s really an extension of Ohm’s Law because it relates voltage, current, and power.

You use the power equation when determining the power output of your PV array when you’re given the voltage and current specifications and when you want to figure out the amount of current your inverter will produce when the operating voltage and power value are known. You can also use the power equation to figure out voltage.

I like to present the power equation as you see it in Figure 3-5. Power is represented by P, current by I, and voltage by E. You need to know two of the values in order to calculate the third. See? Easy as pie.

FIGURE 3-5: A diagram of the power equation.

The easiest way to use Figure 3-5 is to cover up the value you want to find. What you’re looking at tells you how to do the math. For example, if you want to find power, cover the P and you have I next to E. Mathematically, you can view this as follows:

Power = Current × Voltage (P = I × E)

If you’re after current, cover the I and you have P over E, or mathematically:

Current = Power ÷ Voltage (I = P ÷ E)

And, of course, if you want to figure out voltage, cover the E and you get P over I, which looks like this:

Voltage = Power ÷ Current (E = P ÷ I)

Figure 3-6 is a common graphic used to relate current, voltage, resistance, and power; it combines Ohm’s Law and the power equation. To use this chart, choose the value you want to calculate from the four options at the center of the circle. Using your two known values, apply the calculation shown to obtain your answer.

FIGURE 3-6: Ohm’s Law and the power equation combined into one.

For example, if you want to determine current flow (amps) through the wires in a 3,000 watt (3 kilowatt) PV system that operates at 200 volts, just check out Figure 3-6 to see that you need to divide power by voltage:

3,000 watts ÷ 200 volts = 15 amps (P ÷ E = I)

You can also use Figure 3-6 to determine the amount of power any load in a home will consume. For example, if a television requires 120 AC volts and draws 3 amps, consult Figure 3-6 to determine that you can calculate the power draw by multiplying voltage by current:

120 volts × 3 amps = 360 watts (V × I = P)

Calculating energy in terms of watt-hours

After you know the number of watts a PV array can produce or the number of watts various loads will consume, keeping in mind that wattage is a rate, you can determine the energy production or consumption, which is measured in watt-hours (Wh). To do that, you need to know the number of hours the PV array will be operating or the load will be in use. Multiply this time value by the power draw to find the quantity of energy. Here’s the equation:

Power in watts or kilowatts (W or kW) × Number of hours = Energy in watt-hours or kilowatt-hours (Wh or kWh)

So if I say that my PV array is rated at 3,000 watts (3,000 watts = 3 kilowatts = 3 kW) and the sun is out for 6 hours, then the energy produced would be:

3 kilowatts (kW) × 6 hours = 18 kilowatt-hours (kWh)

There’s a big difference between watt-hours (Wh) and kilowatt-hours (kWh), so be sure to always keep your units straight. If you’re in too much of a hurry, you’ll inevitably confuse the two and end up with some very funny numbers.

Note: This example is a big-picture view, but it’s not entirely accurate because no system losses have been taken into account.

You can also calculate energy in terms of watt-hours in order to figure out what various loads consume each day. For instance, if a television draws 360 watts and the screen is on 2 hours a day (regardless of whether anyone is really watching it), then the television will consume

360 watts (W) × 2 hours = 720 watt-hours (Wh)

I show you how to take these energy calculations and apply them to sizing grid-direct systems in Chapter 11 and battery-based systems in Chapter 12.

Introducing amp-hours, a companion to watt-hours

If you’re using batteries, you should know that they’re rated in terms of amp-hours (Ah) rather than watt-hours because you’re focusing on the current flow. As I explain in the earlier “Understanding amps” section, the term amps represents a flow of electrons at a certain rate. By multiplying that rate by a certain amount of time, you get the following formula:

Amps (A) × Hours = Amp-hours (Ah)

Amp-hours describe a quantity just like watt-hours do. Current is a rate, just like power, so all the term amp-hour means is the quantity of electrons that are available to do some work.

The conversion between watt-hours and amp-hours is a pretty simple one. Simply divide the watt-hours value by the voltage value to find the amp-hours value. The answer lies in the power formula that I describe earlier in this chapter.

If you’re wondering why I want you to use the power equation for finding amp-hours, which is an energy value, allow me to explain. Amp-hours aren’t truly an energy measurement; only watt-hours are because they include a voltage component. What you know from the power equation is the relationship of power, voltage, and current. So to switch between watt-hours and amp-hours, you need to know the voltage. By dividing watt-hours by a voltage value, you wind up with the amp-hours you’re looking for. Here’s the equation:

Watt-hours (Wh) ÷ Voltage (V) = Amp-hours (Ah)

Technically this equation isn’t the same as the power equation, but you’re applying the same principles, so it makes sense to think of using the power equation as the way of calculating amp-hours.

Wrapping Together Current, Voltage, Resistance, Power, and Energy

Don’t read this section until after you’ve digested all the terms in the previous sections. Why? Because this section is intended to serve as an all-encompassing review of electricity basics, not an introduction to the concepts. In this section, I use multiple analogies to help convey electrical concepts because thinking about things you can touch and feel is generally easier than thinking about something as intangible as electricity. Well, what are you waiting for? A list of helpful analogies awaits.

Imagine that you’re taking a long road trip with your buddies. Like any good traveler, you decide to push the limits of both the car and everyone in it. Naturally, you run out of gas short of the next gas station. And just to add to the fun, you’re out of cellphone range and have to push the car to the next station. You can apply the electrical terms from the previous sections to the process of pushing the car:

• The voltage is the pressure you exert on the back of the car to move it down the road.
• The amperage is the number of steps you take every minute.
• The resistance is the number of people who are sitting in the car refusing to help push — after all, it was your fault. (Yes, the resistance would also include friction, but just play along with me for now.)
• The wattage is the car’s rate of speed creeping down the road.
• The watt-hours is the total distance traveled after pushing the car for some time.
• The amp-hours is the number of steps you take in an hour.

You can apply Ohm’s Law and the power equation to this scenario to see how all of these values play a role in getting the car to the gas station. If five people are in the car and you’re the only one who’s pushing initially, Ohm’s Law states that the amperage is equal to the voltage divided by the resistance. So with only one person pushing and four people sitting, the amperage will be small:

• I = E ÷ R
• I = The pressure of 1 person pushing ÷ The resistance of 4 people sitting

As your friends begin to realize that they’re going nowhere fast, they get out of the car (reducing resistance) and start pushing (increasing voltage). This in turn increases the number of steps taken each minute (amperage).

Now that you have a voltage and amperage value, you can calculate how fast the car is moving (wattage) by multiplying the two together (thanks to the power formula). If you time yourself, you can figure out how far you moved the car (watt-hours). And if you really want to impress your buddies later, you can tell them all how many steps they took (amp-hours) because you know how many steps were taken each minute and how many minutes everyone pushed.

Another Electricity Concept: Circuit Configurations

When you’re wiring up a PV array (or battery bank), you must configure it in a way that the delivered voltage and current values are at the levels you need. I walk you through the process of determining these values in Chapters 11 and 12. In the following sections, I help you understand how voltages and current levels are affected based on the wiring configuration used, with a little assistance from the power formula I provide earlier in this chapter.

Note: To keep things simple, I focus on the DC side of the systems here and show you both PV modules and batteries. The values I use are for reference only; they aren’t absolutes by any means.

Series

Series connections are made by connecting the positive wire from one module to the negative wire of the next module. By taking a group of modules and placing them all in a series, you create a series string of modules.

Many people like to refer to creating series connections as daisy chaining the modules. A more common, industry-accepted way of describing this process is to say you’re stringing the modules together.

These series strings, or simply strings, can be as few as 2 modules or greater than 20. The exact number depends on the PV modules, the components they’re connected to, and the restrictions from the National Electrical Code^® (NEC^®). If I were to take five modules and place them all in series, I’d call the result one string of five.

When making series connections, the voltage values are additive, and the current values remain the same. If you look at Figure 3-7, you see five modules all wired in series. Each one is rated at 12 V and 4 A. If I were to put my DMM on the positive end of the first module and the negative end of the last one, I’d get a reading of 60 V (5 modules × 12 V per module). If current was flowing from the PV array and I placed my amp meter in the circuit, I’d see 4 A on my meter.

FIGURE 3-7: Five PV modules wired in series.

Now that you know the voltage and current vales for the string, you can calculate the power output with the help of the power formula I provide earlier in this chapter:

60 volts (V) × 4 amps (A) = 240 watts (W)

Parallel

The number of modules that can be placed in series will be limited at some point, so if you need to create more power than one string can provide, you must place strings parallel to each other. Parallel connections are complementary to series connections: The positive wire from one module is connected to the positive wire of the next module; likewise, the negative wires are connected to each other.

The electrical characteristics for parallel connections also complement those of series connections. When modules are placed in parallel, the voltage remains constant, and the current values are additive. See Figure 3-8 for an example of five modules wired in parallel.

FIGURE 3-8: Five PV modules wired in parallel.

The modules in Figure 3-8 are the same as the modules used in the series example in the preceding section — each module is rated at 12 V and 4 A. If you were to take your DMM and measure the total voltage output, you’d see 12 V on your meter. If you then switched and checked the current value, you’d see 20 A (5 modules × 4 A per module). The power output in parallel is the same as it was in series (as you find out with the help of the power formula):

12 volts (V) × 20 amps (A) = 240 watts (W)

So which type of connection is better: series or parallel? It really just depends. The voltage and current ratings of the components you connect the modules to dictate the configurations, and the performance issues round out the decision-making. In terms of which is better for power output, it doesn’t matter. Five modules in series and five modules in parallel, for example, produce the exact same amount of power.

Series-parallel

Most PV systems boast a combination of series- and parallel-connected arrays. Figure 3-9 shows how a sample PV array would be connected if you wanted two strings of five modules in parallel.

FIGURE 3-9: PV modules wired in a series-parallel configuration.

First, the strings of modules are wired together in series to increase the voltage. After that, the two strings are wired in parallel in order to increase the current output. The result is an array with the following characteristics (based on the power equation):

• 5 modules in series × 12 volts per module = 60 volts
• 2 strings in parallel × 4 amps per string = 8 amps
• 60 volts (V) × 8 amps (A) = 480 watts (W)