Energy · Sector explainer

Explainer

Wind, sun and the wire between them.

A wind resource is measured before it is built; a feeder is watched after. Each chapter puts one energy deployment on the stage, lets you change the input that drives it, and computes the result: shear, the Betz limit, autonomy, path loss, sag and fire weather.

Chapters

7

Deployments

6

Readouts

28

Scale

1:1 metres

01 · Resource campaign

Formula

Measure at one height, bank at another.

A guyed met mast with anemometers on booms measures the wind for a year or more before a project is financed. The turbine hub sits higher than the top anemometer, so the speed is extrapolated with a shear exponent fitted from the mast’s own heights. Change the measured speed, the shear and the hub height.

Speed at hub (v·(h/80)^α)

7.93 m/s

Change from 80 m

+10.2 %

Power density ½ρv³ at hub

306 W/m²

Power density gain

+34 %

Shear profile v(h) = v₁(h/h₁)^α with α fitted across the mast’s own heights; air density 1.225 kg/m³. Campaigns follow IEC 61400-12-1 and use the measured speed distribution, since the mean of v³ exceeds the cube of the mean.

02 · Power curve

Formula

No rotor beats Betz.

A generic 4.2 MW turbine with a 130 m rotor. The wind carries ½ρAv³ through the swept area; no rotor can extract more than 16/27 of it. Move the wind speed: the rotor turns faster, the output follows the power curve to its rated limit, and the power coefficient shows how much of the available power is captured.

Power in the wind ½ρAv³

5.93 MW

Betz limit (16/27 of it)

3.51 MW

Turbine output

1.97 MW

Power coefficient Cp

0.333

State

Partial load

Swept area πD²/4 for a 130 m rotor, ρ = 1.225 kg/m³, Betz limit 16/27 ≈ 0.593. The curve rises with v³ from a 3 m/s cut-in to 11.5 m/s rated and stops at 25 m/s; a real curve comes from the IEC 61400-12-1 power performance test.

03 · Remote microgrid

Computed

Diesel hours you no longer burn.

A remote community microgrid: solar, storage and the diesel it reduces, with a weather station whose irradiance and temperature explain the solar yield. Size the array and the battery against the daily load and the sun: the share the diesel still supplies and the hours the battery can carry the load are computed.

Solar energy per day (PR 0.8)

1,024 kWh

Load met by solar

85 %

Diesel share

15 %

Battery carries average load

16.0 h

Solar per day = kWp × peak sun hours × 0.8 performance ratio; battery usable to 80% depth of discharge; average load = daily load ÷ 24. A full design runs the year hour by hour on measured irradiance.

04 · Grid-edge private LTE

Formula

One site, a whole feeder.

A utility’s own LTE site at the substation reaches reclosers, line sensors and meters along the feeder. How far it reaches starts with the band: lower frequencies lose less in free space. Pick a band and a distance to see the free-space loss and the range at which a given path-loss budget runs out.

Band

Free-space loss at that distance

107.4 dB

Margin left in the budget

27.6 dB

Free-space range at the budget

191.8 km

Range vs 3.5 GHz

5.0 ×

FSPL(dB) = 20log₁₀(d km) + 20log₁₀(f MHz) + 32.44 is the best case; terrain, clutter and foliage add tens of dB, which planning takes from elevation and land-cover data.

05 · Conductor sag

Formula

Hot wire, low wire.

A 300 m transmission span. As the conductor heats, from load, sun and still air, it lengthens and sags towards the ground and the trees beneath it. Line sensors report conductor temperature and sag so the operator can rate the line on the real weather. Heat the conductor and watch the span drop.

Conductor length

300.77 m

Mid-span sag

9.32 m

Change from 15 °C

+1.32 m

Clearance at mid-span (28 m attachment)

18.7 m

Parabolic span L = S + 8D²/(3S), so D = √(3S(L − S)/8), with thermal expansion L = L₀(1 + α(T − 15 °C)), α = 19.3 × 10⁻⁶ /°C for ACSR and 8 m sag at 15 °C. Sag-tension design adds elastic stretch and creep.

06 · Fire-weather stations

Computed

Dry, hot and windy, measured along the line.

Weather stations along a transmission corridor through forest and grass. A utility weighs dryness and wind before it de-energises a line in fire weather; dense stations show where the conditions actually are. Set temperature, humidity and wind to compute the Fosberg Fire Weather Index from them.

Equilibrium moisture content

3.4 %

Moisture damping η

0.794

Fosberg Fire Weather Index

66

Fosberg (1978): FFWI = η·√(1 + U²)/0.3002 with U in mph and η = 1 − 2(m/30) + 1.5(m/30)² − 0.5(m/30)³, where m is the Simard (1968) equilibrium moisture from temperature and humidity.

07 · Proof

Computed

The record a lender reads.

What a lender’s engineer asks to see, from the sector research. The report opens with data recovery: hours lost to a dead logger or an iced sensor are hours the energy estimate cannot use. Set the outage and the threshold your lender applies.

• Calibration from accredited laboratories
• Data recovery above the lender’s threshold
• Independent engineer sign-off

Hours in the year

8,760

Data recovery

97.0 %

Against the threshold

Meets it

Outage the threshold allows

876 h

Data recovery = valid hours ÷ hours in the period, against the threshold your lender sets.