Power & Energy Fundamentals

Everything in power systems rests on one distinction that trips up almost everyone at first: power is not energy. Get this clear and the rest of L6 follows naturally.

Power is a rate; energy is a total

• Power is how fast energy is being used, measured in watts (W). A 100W bulb, a 5W phone charger, a 1500W kettle — these describe the rate of consumption at any instant.
• Energy is the total amount used over time, measured in watt-hours (Wh). It's power multiplied by how long: Energy = Power × Time.

A 100W load running for 10 hours uses 100 × 10 = 1000Wh (1 kWh) of energy.

The everyday analogy: power is like the speed of a car (how fast right now), and energy is the distance travelled (speed × time). A fast car driven briefly covers little distance; a slow car driven all day covers a lot.

Why this matters for a battery

A battery's job is to store energy. So a battery is rated in watt-hours. Solar generators carry ratings like 1024Wh — that's the total energy the pack holds.

A load draws power (watts). So the key question — how long will this battery run this load? — is just:

Runtime (hours) = Battery energy (Wh) ÷ Load power (W)

A 1024Wh battery running a 100W load:

1024Wh ÷ 100W ≈ 10 hours (before losses).

Run a heavier 500W load and it lasts only ~2 hours. Run a tiny 10W load and it lasts ~100 hours. Same battery — the runtime depends entirely on the power the load draws.

The trap to avoid

People constantly confuse the two. "This battery is 1000 watts" is meaningless as a capacity statement — watts is a rate, not a store. The right questions are:

• How much energy does it hold? → watt-hours (Wh).
• How fast can it deliver / how much can the load draw? → watts (W).

Keep "watts = rate, watt-hours = total" fixed in your mind. Every sizing calculation, every runtime estimate, every product spec in this module depends on it.

The next slide adds the other unit you'll see everywhere — amp-hours (Ah) — and why voltage is the bridge between Ah and Wh.

You'll see batteries rated two ways: in watt-hours (Wh) and in amp-hours (Ah). They're related, but only if you know the voltage. Mixing them up is the most common sizing mistake.

Amp-hours measure charge, not energy

Amp-hours (Ah) measure how much charge a battery holds — how many amps it can deliver for how many hours. A 20Ah battery can deliver 1A for 20 hours, or 2A for 10 hours, and so on.

But Ah alone doesn't tell you the energy. Why? Because energy depends on voltage too. The same 1A flowing at 48V carries four times the energy of 1A flowing at 12V.

Voltage is the bridge: Wh = V × Ah

To convert charge (Ah) into energy (Wh), multiply by the voltage:

Energy (Wh) = Voltage (V) × Charge (Ah)

So a 12V, 20Ah battery holds:

12 × 20 = 240Wh

And a 24V, 20Ah battery — same Ah — holds:

24 × 20 = 480Wh

Same amp-hours, double the energy, purely because of the higher voltage. This is why you can't compare batteries by Ah alone. A "100Ah" battery sounds big, but at 12V it's 1200Wh; at 48V the same 100Ah would be 4800Wh. Always convert to Wh to compare fairly.

Why higher-voltage systems are common

This is also why larger systems use higher voltages (24V, 48V) rather than 12V. To deliver a given power (watts), a higher voltage needs less current (P = V × I). Less current means:

• Thinner, cheaper wiring (current drives wire size).
• Lower losses (resistive loss rises with current squared — I²R).
• Smaller, cooler components.

That's a recurring theme in power engineering: when you can, push the voltage up to keep the current — and the losses — down.

Putting it together

For any battery, you now have the full picture:

• Ah → how much charge.
• V → the system voltage.
• Wh = V × Ah → the real energy, which (divided by load watts) gives runtime.

Solar generators are rated in Wh precisely because it's the honest, voltage-independent measure of what the customer actually gets — usable energy.

The next slide adds the final reality of every real system: efficiency losses, and the power budget that ties it all together.

The numbers on a battery's label are the ideal case. Every real system loses some energy along the way — and a good engineer budgets for those losses instead of being surprised by them.

Nothing is 100% efficient

Every time energy is stored, converted, or moved, a little is lost (mostly as heat):

• The inverter (DC → AC) is typically 85–90% efficient. Feed it 1000Wh of DC and you get ~870Wh of AC out.
• The battery round-trip (charge then discharge) loses a little too — LiFePO4 is good here, ~90–95%.
• Wiring and connectors lose a small amount to resistance, more if undersized.

These stack up. A 1024Wh battery driving AC appliances through an 85% inverter delivers, in practice, closer to ~870Wh of usable AC energy — not the full 1024Wh on the label. The label isn't lying; it's the stored DC energy. Real-world usable energy is always somewhat less.

The power budget: the core sizing tool

A power budget is simply an honest accounting of energy in vs energy out. You build one like this:

1. List every load with its power and how long it runs each day:

2. Add a margin for losses — divide by efficiency (or add ~15–30%). At 85% inverter efficiency, 980Wh of load needs ~1150Wh drawn from the battery.

3. Check the battery and solar can supply it. Does the battery hold enough for the run-time you need (e.g., overnight)? Can the solar recharge that much energy the next day?

Why this discipline matters

Skip the power budget and you get the two classic failures:

• Undersized: the battery dies before morning, or the solar never fully recharges it, and the customer is unhappy.
• Oversized: the customer pays for capacity they'll never use.

The power budget is what turns "I need backup power" into a specific, correct system. It's also the heart of the L6 P-Check — you'll build a real one. Every good solar recommendation starts here.

You now have the foundation: power vs energy, Ah vs Wh, efficiency, and the budget. The next lesson goes inside the battery itself — chemistry, and why LiFePO4 is the right chemistry for Nigeria.