A single DC machine on the flywheel shaft serves as both motor and generator, but on a fixed-voltage battery bus it will only drive the wheel until its back-EMF equals the bus voltage and only generate above that speed. A machine that produces 48 V at 1,500 rpm on a 24 V bus therefore floats the wheel at 750 rpm, where it holds 154 Wh of the 617 Wh the same wheel holds at full speed. Never use a series-wound motor on a flywheel, because with no load it races without limit.
Part of Flywheel Energy Storage
Using one motor-generator on a flywheel shaft: how the electrical mode is decided by speed, what a fixed bus does to the usable range, and which machines to avoid.
The Mode Is Decided By Speed Against Voltage
From Motor-Generator Duality: a DC machine has a terminal voltage V = E ± I × R, where E is its internal EMF, proportional to speed (and field). When the bus voltage is higher than E, current flows into the machine and it motors; when E is higher than the bus, current flows out and it generates. No rewiring is needed, and the machine does not “know” which mode it is in.
That has a direct consequence for a flywheel. If the machine sits on a bus of fixed voltage V, the wheel is driven toward the speed at which E = V, and cannot be driven above it. Above that speed the machine returns power to the bus.
Worked Example: A 48 V Machine On A 24 V Bus
Inputs: permanent-magnet or fixed-field machine with E = 48 V at 1,500 rpm (ω = 157.1 rad/s), so E = 0.3056 V·s/rad × ω; bus 24 V; wheel I = 180 kg·m².
- Float speed where E = 24 V: ω = 24 ÷ 0.3056 = 78.5 rad/s = 750 rpm.
- Energy at float speed: ½ × 180 × 78.5² = 554.6 kJ = 154 Wh.
- Energy at 1,500 rpm: ½ × 180 × 157.1² = 2,221 kJ = 617 Wh.
So a motor on a 24 V bus can raise the wheel only to 750 rpm, one quarter of the full-speed energy. To store the full 617 Wh the machine has to be supplied at 48 V, from a higher-voltage source, a boost stage, or two batteries in series. On discharge the machine feeds the 24 V bus only above 750 rpm, which uses the top 75% of the energy, 463 Wh, and below that it cannot deliver. This is why Variable Speed Drive matters.
Starting Current And Control
DC Motors says that at standstill there is no back-EMF to limit the current, which can reach 5 to 15 times the rated value, so start through a series resistor or a ramped supply. A flywheel is a heavy load to start; the machine and its supply carry the spin-up current for as long as the spin-up lasts. Spin-up energy of 2.2 MJ at a 2 kW supply is 2,221,000 ÷ 2,000 = 1,110 s, about 18 min.
Machine Types
- Shunt-wound or permanent magnet. The corpus: speed nearly constant with load (shunt) and proportional to applied voltage (PM). This is what a flywheel wants, since the no-load speed is capped by the supply.
- Series-wound. DC Motors warns that a series motor at low load has weak field flux and very high speed, and that it should never run unloaded. A flywheel is a large inertia but little steady load: once up to speed, only bearing and air drag oppose the motor, so a series machine keeps accelerating. Do not use one.
- Induction motor. Induction Motor runs from a rotating field with no brushes. Its drive speed is capped near the synchronous speed set by the supply frequency, 1,500 rpm for four poles at 50 Hz (the alternator page’s own number). Driven faster by the wheel it generates back into the supply.
Common Mistakes
- Connecting a machine whose top-speed EMF exceeds the bus voltage and expecting full storage. It floats at the speed where E equals the bus.
- Starting without current limiting. The inrush can burn the commutator and brushes.
- Using a series motor because it has plenty of torque. It also has no top speed.
Safety
A runaway motor drives a flywheel through its burst speed
A series-wound motor, or any motor on a supply that can deliver more voltage than the design assumed, can push the wheel past the speed calculated in Burst Energy Calculation. Use a machine whose no-load speed is capped by the supply voltage, add an overspeed trip as described in Speed Limiting, and remember the machine cannot stop the wheel.
What’s Next
- Learn next: Clutch & Gearing — matching speeds and disconnecting the load
- Combine with: Generators and Motors — the machines themselves