1. Energy, Power, and Electrical Basics

Learning objectives

By the end of this chapter you will be able to:

• Distinguish power from energy and use the correct units without confusion.
• State and apply Ohm’s law and the electrical power relationship.
• Explain the difference between DC and AC and why PV is natively DC.
• Read the basic electrical quantities off a component and reason about a simple circuit.

1.1 Why this chapter is non-negotiable

The single most common conceptual error in solar (made by customers, salespeople, and rushed installers alike) is confusing power with energy. A system isn’t “an 8 kW system that makes 8 kW a day.” It’s an 8 kW system that, on a good day in a sunny location, might make 30–40 kilowatt-hours. Power is a rate; energy is an amount. Get this straight now and a third of the field’s confusion evaporates.

1.2 Charge, current, and voltage

Electricity is the movement of electric charge (measured in coulombs). Three quantities describe it:

• Current (I): the rate of charge flow, measured in amperes (A). One ampere is one coulomb per second. Think of it as how much water moves through a pipe per second.
• Voltage (V): the electrical pressure or potential difference that pushes charge, measured in volts (V). Think of it as the pressure difference driving the water.
• Resistance (R): opposition to current flow, measured in ohms (Ω). Think of it as how narrow the pipe is.

The water analogy is imperfect but durable: voltage = pressure, current = flow rate, resistance = pipe restriction.

1.3 Ohm’s law

These three are bound by the most important equation in the trade:

V = I × R

Rearranged as needed: I = V / R and R = V / I.

Example 1.A: A PV source circuit pushes 40 V across a load with 8 Ω of resistance. Current = V/R = 40/8 = 5 A. Double the voltage to 80 V (same resistance) and current doubles to 10 A. This linear relationship is why voltage and current track together in resistive situations. PV, which is not a simple resistor, needs the more careful treatment we give it in Chapter 4.

1.4 Power: the rate of energy

Power (P) is the rate at which energy is delivered or consumed, measured in watts (W). For electrical circuits:

P = V × I

Combined with Ohm’s law this also gives P = I²R and P = V²/R.

Example 1.B: A module operating at 30 V and 10 A delivers P = 30 × 10 = 300 W. This is the instantaneous rate: how fast it’s doing work right now, under those conditions.

Common multiples you’ll use constantly:

• 1 kilowatt (kW) = 1,000 W
• 1 megawatt (MW) = 1,000 kW = 1,000,000 W

Residential arrays are sized in kW; commercial in kW to low MW; utility plants in MW to hundreds of MW.

1.5 Energy: power across time

Energy is power multiplied by the time it flows:

Energy = Power × Time

The trade’s unit is the kilowatt-hour (kWh): one kilowatt sustained for one hour. This is what utilities bill and what a PV system produces.

Example 1.C: A 5 kW array producing at full output for 4 hours generates 5 kW × 4 h = 20 kWh. The same array idling at night produces 0 kWh regardless of its kW rating. The kW rating is the system’s capacity; the kWh is its output. Sizing (Part IV) is fundamentally the art of turning a customer’s annual kWh need into the right number of kW of array.

⚠️ Field habit: whenever someone states a “solar number,” immediately ask yourself: is this a power (kW) or an energy (kWh) figure? Mislabeling one as the other produces designs that are off by the number of sun-hours in a day. The result is wildly wrong.

1.6 Direct current vs alternating current

• Direct current (DC): charge flows in one constant direction. Batteries and PV modules are inherently DC sources: sunlight liberates charge that flows one way.
• Alternating current (AC): charge reverses direction periodically (60 Hz in North America, 50 Hz in much of the world). The grid and household appliances run on AC.

Because PV is DC and the grid is AC, every grid-connected system needs an inverter to convert DC to AC (Chapter 6). This DC-to-AC boundary organizes much of the wiring, code, and safety logic in later chapters. The “DC side” and “AC side” of a system are governed by different rules and carry different hazards.

1.7 Series and parallel: a first look

How you connect sources changes the result:

• Series (end to end): voltages add, current stays the same. Wiring modules in series raises string voltage. This is how we build the high DC voltages inverters want.
• Parallel (side by side): currents add, voltage stays the same. Paralleling strings raises total current.

This single rule (series adds volts, parallel adds amps) is the basis of all array configuration (Chapter 15). We’ll return to it with PV-specific numbers once you can read a module datasheet.

1.8 Visualizing series and parallel

SERIES (voltages add, current same)        PARALLEL (currents add, voltage same)
                                           
 [+]──[Mod]──[Mod]──[Mod]──[−]              [+]──┬──[Mod]──┬──[−]
       30V    30V    30V                        │          │
   String V = 90 V,  I = 10 A                ├──[Mod]──┤
                                                │          │
                                                └──[Mod]──┘
                                             V = 30 V,  I = 30 A

Three 30 V / 10 A modules in series make a 90 V, 10 A string. The same three in parallel make a 30 V, 30 A source. Same modules, same total power (900 W), but very different voltage and current. That difference is the entire game in Chapter 15.

1.9 Putting it together: a worked chain

Example 1.D (multi-step): A small off-grid load draws 4 A at 24 V for 6 hours/day. (a) What power does it draw? (b) What daily energy? (c) If served by a 24 V battery, how many amp-hours does that represent?

• (a) P = V × I = 24 × 4 = 96 W
• (b) E = P × t = 96 W × 6 h = 576 Wh/day (0.576 kWh)
• (c) Energy ÷ voltage = 576 Wh ÷ 24 V = 24 Ah/day

This three-step move (power, then energy, then amp-hours for batteries) is the spine of off-grid load analysis in Chapter 13/17.

Example 1.E (catching the classic error): A salesperson says a home “needs a 30-kilowatt-hour system.” Is that a power or energy figure? It’s energy (kWh): a daily consumption, not a system size. At a 5 PSH site with 0.83 derate, the array needed is 30 ÷ (5 × 0.83) ≈ 7.2 kW (Chapter 14). Reading the “30” as kW of array would oversize the system roughly four-fold. Always label the unit before you act on the number.

Chapter 1 summary

Power (W, kW) is a rate; energy (kWh) is an amount, and Energy = Power × Time. Ohm’s law (V = I × R) and electrical power (P = V × I) are the two relationships you’ll use most. PV is DC and the grid is AC, so inverters bridge them. Series connection adds voltage; parallel adds current. Every later part leans on these.

Practice Problems: Chapter 1

1. A module operates at 38 V and 9.5 A. What is its power output?
2. A 7 kW array produces at full output for 5 hours. How many kWh does it generate that day?
3. A circuit carries 6 A through a 4 Ω resistance. What is the voltage across it, and the power dissipated?
4. Five 40 V / 11 A modules are wired in series. What are the string voltage and current?
5. Those same five modules are instead wired in parallel. Now what are the voltage and current?
6. A home uses 900 kWh in a 30-day month. What is its average power draw, in kW?
7. A 12 V appliance draws 60 W. What current does it pull, and how many Ah over 8 hours?

Solutions: Chapter 1

1. P = 38 × 9.5 = 361 W.
2. 7 kW × 5 h = 35 kWh.
3. V = IR = 6 × 4 = 24 V; P = I²R = 36 × 4 = 144 W (or P = VI = 24 × 6 = 144 W).
4. Series: V = 5 × 40 = 200 V, I = 11 A (unchanged).
5. Parallel: V = 40 V (unchanged), I = 5 × 11 = 55 A.
6. 900 kWh ÷ (30 days × 24 h) = 900 ÷ 720 = 1.25 kW average.
7. I = P/V = 60/12 = 5 A; 5 A × 8 h = 40 Ah.