A flywheel delivers a steadily falling speed, voltage and frequency as it discharges, so the usable energy depends on how wide a speed range the load can accept: a 2:1 range yields 75% of the stored energy, 1.5:1 yields 56% and 1.25:1 only 36%. Hold the output steady with a battery bus and a regulator, field control on a DC machine, or a mechanical variable-ratio drive, and design for the speed at which the load stops working, not for the speed at which the wheel stops.
Part of Flywheel Energy Storage
What the discharge does to a flywheel’s output and how to make that output usable: the usable energy as a function of speed range, and the ways to regulate it.
Usable Energy Is A Function Of The Speed Range
Energy goes as speed squared. If the load works from full speed ω_max down to ω_max ÷ r, the fraction of the stored energy it can take is 1 − 1 ÷ r².
| Speed range r | Lowest usable speed (from 1,500 rpm) | Usable fraction | Usable from the 617 Wh wheel |
|---|---|---|---|
| 1.25:1 | 1,200 rpm | 36% | 222 Wh |
| 1.5:1 | 1,000 rpm | 56% | 343 Wh |
| 2:1 | 750 rpm | 75% | 463 Wh |
| 3:1 | 500 rpm | 89% | 549 Wh |
Check, 1.5:1: 1 − 1 ÷ 2.25 = 0.556; 0.556 × 617 = 343 Wh. A wider range gets more of the energy out, but each step down demands more from the regulator or the load, because the torque for a given power rises in proportion to the range.
What Changes As The Wheel Slows
- DC machine or alternator voltage. The internal EMF is proportional to speed. At half speed the open-circuit voltage is half.
- AC frequency. For an alternator, frequency follows speed. Alternator Design gives a 4-pole machine as 1,500 rpm for 50 Hz, so at 750 rpm it makes 25 Hz. Transformers and motors built for 50 Hz run badly at 25 Hz.
- Torque for constant power. T = P ÷ ω. Halving the speed doubles the torque and the current in the machine.
Ways To Hold The Output Steady
- Battery bus. Rectify the machine’s output onto a battery. Current flows only while the machine’s rectified EMF exceeds the battery voltage, so the battery fixes the lowest usable speed, and the load sees a steady supply from the battery. The flywheel becomes a short-term buffer in front of the battery. A charge controller of the shunt type (Charge Controller) gives a source that always has a load.
- Field control on a DC machine. Raise the field current as the wheel slows so that the EMF (speed × flux) stays near the bus voltage. The range is limited by magnetic saturation of the iron; this page has no sourced limit, so test your machine, and expect something like the 1.25:1 to 1.5:1 rows of the table, not 3:1.
- Variable-ratio mechanical drive. A belt on cone pulleys (Belt Drives) can shift ratio in steps to hold the output shaft speed as the wheel slows. It needs the pulleys and a belt-shifter, and each step has a power limit that the belt’s slip sets.
- Accept the range. Resistive loads such as heaters work at any voltage, and a heating element does not care what the speed is.
Worked Example: A 2:1 Range Into A Battery Bus
Inputs: the 500 kg, 617 Wh wheel; a machine with E = 48 V at 1,500 rpm onto a 24 V battery bus (see Motor-Generator Set).
- Output starts when E exceeds 24 V, i.e. above 750 rpm.
- At 1,500 rpm the surplus EMF is 24 V; at 1,125 rpm it is 36 − 24 = 12 V, and at 750 rpm it is zero. Current, and so power, falls linearly toward zero near the bottom.
- The usable energy is 463 Wh from 1,500 to 750 rpm, but the power delivered at the bottom of the range is almost nothing. Real working range is therefore narrower than 2:1 unless a regulator boosts the voltage.
A boost regulator needs semiconductor or vibrating-contact parts the village may not have. If not available, accept a 1.5:1 range and 343 Wh.
Common Mistakes
- Quoting the stored energy as the delivered energy. Multiply by the usable fraction, then by the machine efficiency.
- Feeding a 50 Hz motor from a falling-frequency alternator. It overheats.
- Designing for full speed and ignoring the bottom of the range. The low-speed end sets the current rating.
Safety
Regulation failure speeds the wheel up, not down
If the load is lost, or a regulator or controller fails open, the wheel’s source keeps driving it; the corpus Load Control page notes that a generator with its load removed overspeeds within seconds. When any part of the regulation chain can fail open, add an independent overspeed trip; see Speed Limiting.
What’s Next
- Learn next: Burst Energy Calculation — what the top speed must not exceed
- Combine with: Power Regulation — voltage and frequency regulation for hydro sets