#essay{:title        "Grug's Guide to Solar",       :date         #inst "2024-12-22",       :reading-time "19 min"}

Grug's Guide to Solar

2024-12-22 · 19 min read ·

Work-in-progress. H/T: Grug Brain

caveman grug explains solar for young grug learns how trap sun-spirit to keep cave lit and hi-fi pumping during loadshedding

by Petrus Theron

Introduction

grug see many caves go dark when sky-fire hide behind clouds
grug tired of paying wolf skins to evil chief for sun-spirit while grug wait for sky-fire to return
so young grug learns how build sun trap to capture sun-spirit and keep cave lit

sun magic deep like cave. old grug spend many long winter study electron magic

but young grug no fear – old grug teach sun magic simple for young grug
if young grug learn only 3 equation, young grug know pretty much all of electron magic

old grug used to earn wolf skins by building remote scrying and over-air firmware update for LiFePO4 crystal rock battery to store sun-juice

but grug not sun shaman, so if grug make mistake, wise grug please correct grug. grug very sleepy after writing long post on stone tablet 😴

Table of Contents

  1. Introduction
  2. Solar Components
  3. Loads: How Much Sun-Juice Grug Need?
  4. Energy & Power: Grug Explain Sun-Juice
  5. Voltage & Current: Electron Magic
  6. Ohm's Law: Resistance / Impedance
  7. Electron Magic Equations
  8. Grug Explain Joules vs. Watt-hours
  9. Peak Power vs. Continuous Power
  10. Cold & Cranky
  11. Typical Load
  12. Battery Chemistry

Solar Components

(grug make cave drawing later)

grug learn to appease sun goddess with 7 things:

  1. Battery – stores sun-juice for later
    • traps electron magic in crystal rock, give DC power, e.g. 12V, 24V or 48V
    • battery have chemistry like lead-acid, or lithium
    • grug dinorider use 12V lead-acid battery
    • modern cave battery mostly 24V or 48V lithium (LiFePO4)
  2. Battery charger – keeps crystal battery full by turning AC power into DC power, also called AC-to-DC converter
    • battery charger output same voltage as battery for safe charging
  3. Solar panel – obsidian tablet traps sun-spirit as DC electron magic, also called PV panel
    • PV short for photovoltaic. special silicon in PV crystal turn photon into electron
    • solar panel voltage change depend on time of day, or cloud
    • grug can think of solar panel as DC current source, either give DC power or get hot
  4. Solar charger – safely guides sun-spirit into battery, also called DC-to-DC converter
    • solar charger match battery voltage for safe charging
    • solar charger match impedance of solar panel to trap sun-spirit faster
    • solar charger can be cheap pulse-width modulated controller (PWM) or Maximum Power-Point Tracker (MPPT) – MPPT cost more wolf skins, but work better than PWM
  5. Inverter – magic electron box turn DC electron magic into AC electron magic to power grug bar fridge, also called DC-to-AC converter
  6. Cables – metal vines connect all parts. cables rated for current based on thickness, e.g. 15A for most cave extension lead
  7. Circuit breaker – click rocks break circuit, open when too much sun-juice flow
    • too much sun-juice power melts metal vines like lava, burn down cave – grug wife not happy
    • once big current start to flow, it want keep going like bison
    • so breaker have electromagnet + wide metal contactor to stop current without plasma arc
    • plasma chew on metal vines like baby t-rex, so breaker also save cables

sometimes many smart rocks combine in one big electron box called “inverter.” grug explain each part

Loads: How Much Sun-juice Grug Need?

first thing sun shaman ask grug: “what cave appliance grug wife want to power and how long?”
grug must know:

  1. which magic rock drink sun-juice,e.g. cold box, hot rock or light rock
  2. how fast magic rock drink sun juice, in Watts
  3. how long magic rock drink sun-juice, in hours

but first grug explain scary numbers like Watts
young grug no run away – old grug make simple for young grug

Energy & Power: Grug Explain Sun-Juice

sun-juice Energy measured in Joules [J], or Watt-hours [Wh]:

grug wife buy many cave appliance that drink sun Power in Watts; how fast they drink sun-juice?

now grug learn most important equation for sun magic:

grug give example:

young grug remember:

so if grug want know sun-juice Energy in Watt-hours,
grug simply multiply Power & Time, get Energy in Watt-hours [Wh]

most important discovery of sun magic. remember well, young grug use every day. from this sun magic equation, young grug also see that:

now old grug test young grug brain:

young grug recall Time = Energy / Power

grug divide sun-juice trapped in battery called Energy, by speed of sun-juice called Power:

hmm, 20 hours not that long; grug might need bigger battery keep wife happy

now young grug learn electron magic

Electron Magic (Voltage & Current)

electron magic flow like water in river, fast or slow
grug elders no like water analogy, but good for young grug learn electron magic:

grug ask why volt-ampere [VA] same as Watts? this go deep into electron magic. involve capacitors & inductors. but for now, young grug brain relax, only think in Watts [W], not volt-ampere [VA]

young grug remember: Power in Watts mean rate of flow of sun-juice Energy

Ohm's Law: Resistance / Impedance

grug watch over prairie many summer night and ponder why skyfire rain down on savanna, called lightning. grug know from water analogy:

grug learn same is true of electron magic, called Resistance, measured in ohms (Ω) like buddha:

grug elders think long and hard on this, but one day big-brained grug named Georg Ohm discover why river current flow strong during storm, even though valley narrow

young grug now learn most ancient equation that tell grug how much Current [I] will flow based on Voltage [V] (“electron pressure”) and Resistance [R] (“width of valley”)

this equation called Ohm’s Law:

from Ohm’s Law, young grug can compute third value even if only know two:

best way for grug to think of Ohm’s Law is that Current [I] will flow to satisfy V/R, until current stop

young grug see that as long Resistance high, smol current flow

but if voltage very high, can overcome high resistance (like high water pressure during storm) and big current will still flow

indeed, this why skyfire lightning travel through air despite high resistance (2×1016Ω⋅m): because electron skyfire very high voltage (100kV)

because I = V/R, given a fixed resistance R:

in reality, resistance not fixed because depend on frequency of voltage & current, but grug only think about simple loads today

now grug give example using Ohm’s Law:

how much current flow through metal vine in kettle?

grug know metal vine will melt when current too high, so is this safe?

grug test young grug brain
young grug recall that P = VI

how much power in Watts will cave kettle drink?

that is lot of power. hot rock very expensive to run on battery, this why grug prefer gas
better save sun magic for cold box and light box

Impedance vs. Resistance

impedance mean same as resistance, but more complex. related to deep electron magic that involve capacitor and inductor. grug ignore this for now; young grug only care about Resistance, measured in ohms

Electron Magic Equations

young grug now learns 3 most important equations in all of electron magic:

using these 3 equation, young grug can design all components of sun trap and appease sun goddess

grug do one last example to test young grug brain:

how fast energy flow out of battery called Power, measured in Watts?

lastly, if battery trap 2,000Wh sun-juice Energy, how long until battery empty?

Grug Explain Joules vs. Watt-hours

(keep this part? move to appendix probably)

grug can also count sun-juice in Joules, but more hard:

now grug test young grug brain with big number:

grug recall Energy = Power * Time

Peak Power vs Continuous Power

electron magic appliances have average power rating, but electron magic appliances drink more sun-juice when turning on, called peak power

peak power can be 2-10 times more than average
even if peak very short – just few seconds – breakers will trip if too much current flow

so grug must plan sun trap to handle peak loads, not just average loads

good example is cold box: cold box have compressor, drinks ~7 times more current when turn on, magnetise coil in compressor that make gas cold

this why grug battery struggle to run fridge

=== rest is todo

(grug is still writing this part, very tired)

Electrical loads are typically rated in terms of their average voltage [V] and average current [A] demands. We can calculate a load’s average electrical power demand by multiplying its rated voltage [V] and current [A] to arrive at volt-amperes [VA] or Watts [W], e.g.:

Power Demand [in Watts]
= Voltage [V] * Current [A]
= 12V * 5A
= 60W, or 60J.s-1.

…however, average power consumption (in Watts) only tells half the story: dynamical systems frequently exhibit nonlinear behaviour during transients like startup and shut down (that’s where the excitement is in life). For example:

OK, that’s enough theory for now - let’s design a system for a light electronic load.

Cold & Cranky {#cold-&-cranky}

To kickstart a petrol car engine with a 12V lead-acid battery costs 400A for ~4 seconds. This is called “cold-cranking amps.” Let’s calculate how much power that is:

P = V * I
= 12V * 400A
= 4,800W
= 4.8kW

How much energy is that in Joules? Recall, Energy = Power * Time:

E = Power * Time
= 4,800W * 4 seconds
= 4,800J.s-1 * 4s
= 19,200J.s.s-1
= 19,200J.s0
= 19,200J
= 19.2kJ.

How many times can you start a car before the battery runs flat?

Not all loads are made equal; we need to understand peak demands to design our plant.

Typical Load

What kind of battery and inverter setup do we need to power a laptop, a lamp and two hand-held radios for 12 hours a day? Our loads:

Total Average Power Demand: 120W.
Daily Demand: 120W * 12 hours = 1,440Wh [Watt-hours].

Hmm, sounds like all we need is a 120W solar panel and a 1440Wh battery, right?

Unfortunately, no system is 100% efficient - especially low-voltage systems. Lower voltage means higher currents and thermal losses grow exponentially as current rises. We need to compensate for losses:

Can’t we just add 10% to our spec? Not so fast! Draining our batteries down to 0% State of Charge (SoC) every day damages them and will cause them to fail in just a few short months. So we need to add a buffer so we do not exceed the optimal Depth of Discharge (DoD) for our battery. Optimal DoD depends on battery chemistry.

Battery Chemistry

There are two common battery technologies in 2024 used in home setups:

  1. Lead-acid, and
  2. Lithium, specifically lithium-ferrous phosphorus (LiFePO4).

Battery life is measured in cycles and Depth of Discharge (DoD) - not years. Deeper discharge = shorter life, depending on chemistry, so DoD is your main consideration for capacity planning. Batteries do not fail suddenly: their capacity erodes over time until voltage dips below a usable level.

If you can afford it, get LiFePO4. Here are the key differences:

Lead-acid Lithium
Chemistry PbSO4 & H2SO4 LiFePO4
Mass ~18kg/kWh (Heavy) 10kg/kWh (Light)
Cost ~R3,000/kWh ~R10,000/kWh
Lifetime (cycles) 6,000 cycles at 10% DoD 2,200 cycles 25% DoD 1,000 cycles @ 50% DoD 250-500 cycles @ 90% DoD 460 cycles @ 100% DoD 5000 cycles @ 50% DoD 3000 cycles @ 80% DoD 2000 cycles @ 100% DoD
Depth of Discharge (without losing significant capacity) 50% 70%
Battery Management Simple Complex
Ideal Storage Level (State of Charge or SoC) 100% ~70%
Self-Discharge Rate 3-8% per month <3% per month

To maximise the lifetime of our batteries, we need to store more energy than we’re going to use.

Lithium costs more, but it will last longer. Lead-acid is used in cars for their cold-cranking ability to provide high surge currents without deteriorating. They’re heavy and well-understood.

(here go into more detail on options with real-world choices)

Viva la Resistance {#viva-la-resistance}

Eskom transmits electricity over long distances at high voltages (20kV, 220kV or 400kV) because the same power can be transmitted at lower currents. Lower currents mean thinner, cheaper cables with fewer losses. Recall that:

As voltage goes up, current can come down proportionately without losing power. But why do losses scale exponentially with current flow?

Various materials conduct electricity and exhibit unique phenomena when they do. E.g.

Whenever an electrical component converts or stores electrical power, we will see a voltage drop over that component. This voltage drop will depend on the current that flows through the component. Now let us learn about the concept of Resistance.

Resistance is measured in Ohms and denoted by the Greek letter Ω (omega), so 10Ω means 10 ohms. There are plenty of water analogies floating around to explain electricity like “pressure vs. flow” for “voltage vs. current,” but liquid flow and electron flow are not the same. Better to focus on measurable behaviour like voltage, current and power transfer.

(todo work here)

Resistance is defined as…. The best-known electrical component is the resistor.

Remember, that since P = V*I, then if either V or I is zero, no power is dissipated by that component. Current can flow, but unless there is a voltage drop, P=0.

If power is being transferred, there must be a voltage drop over the component, or power was not being absorbed.

Therefore, if a wire heats up when we apply a voltage to it, that wire is converting electrical energy into heat. Heat, or kinetic energy, is dissipated at a certain rate, or power.

We can measure the rate heat is dissipated at using a super-sensitive temperature probe. Resistance as a concept is defined in terms of this rate of dissipation. Typically, resistance scales linearly with voltage and current, but not always. If you apply 1 Volt over the ends of a wire and the wire heats up to dissipate exactly 1W of power, then we say that wire has a resistance of exactly 1Ω (1 ohm).

(This section is unfinished)

This is evident from P = VI (todo diagram)

e apply a voltage to a component, you can be sure current is flowing because P must equal V * I. If either V or I are

= V*I, so if a wire heats up when we apply voltage, P = V*I. current

there will be a voltage drop over We can measure this with a multimeter like so (show diagram of voltage drop over LED when on).

Current can pass through a conductor without flows but there Electrical energy can pass through a component (like a wire) without transferred power

If current flows, but no

As long as current flows and there’s a voltage drop, we can calculate the power lost / transferred / converted in that component based on P(loss)= V * I. As long as current flows current flows

…

Battery C-Ratings

![][image1]

Ideal Battery C-ratings

C-Rate Rated Capacity (Ah) Average Current (A) Charge (or discharge) Time
5C 50 Ah 250 A 12 min
2C 50 Ah 100 A 30 min
1C 50 Ah 50 A 1 hour
.5C (aka C/2) 50 Ah 25 A 2 hours
.25C (aka C/4) 50 Ah 12.5 A 4 hours
.1C (aka C/10) 50 Ah 5 A 10 hours

(detail nonlinear discharge rates at various currents & temperatures)

Series vs Parallel {#series-vs-parallel}

Kirchoff’s Current Law? {#kirchoff’s-current-law?}

Detailed Components

Todo.

Battery {#battery}

Either lead acid or lithium (LiFePO4 means lithium ferrous phosphorus).

May contain a battery management system (BMS).

Solar Charger {#solar-charger}

This is essentially a DC-to-DC converter…

This will be either a PWM controller or MPPT (Maximum Power-Point Tracker)

Battery Charger {#battery-charger}

Overcharging or undercharging a battery is fatal. The main job of a battery charger is to limit charging current and stop charging when the battery is full so it doesn’t catch fire.

How do you know when a battery is fully charged? It’s complicated, but we’ll get into it. Consider that if you connect a fully charged battery to a discharged battery without a, maximum

Circuit Breakers {#circuit-breakers}

How do you stop a truck? Big brakes. And big brakes get hot when you dump energy on them. Electricity doesn’t like to stop flowing, so circuit breakers are kind of like brakes for your circuits. They are idealised switches that consist of a lever and a metal contactor that can be flipped with enough mechanical force to break the current flowing “all-at-once” without electrons arcing across the gap (“look ma, I’m welding!”).

Breakers are important to disconnect your battery from loads when more current starts flowing than your battery or cables can handle without starting a braai in your garage.

(to be continued…)