Glossary
Short definitions of the terms used in the simulators, with symbols, units and formulas. Every term links to the simulators where you can see it at work.
156 terms
The real power that does useful work or is delivered to the grid, in watts; it is the part of the apparent power in phase with the voltage.
↑ Increasing it: It grows with load or with the shaft power supplied; a lower power factor needs more current for the same active power.
In a linear induction motor the air gap g is the distance between the stator face and the reaction plate. It is large compared with a rotary motor, typically several millimetres to a few centimetres, because the vehicle has to run freely, so the magnetising current is high and the power factor low. A smaller gap raises flux, thrust and goodness factor but demands tighter mechanical tolerances.
↑ Increasing it: Coupling to the plate weakens: thrust, power factor and efficiency fall, and the goodness factor drops in proportion (G ∝ 1/g).
The anode-cathode voltage VAK is the voltage you apply across the device and the horizontal axis of its I-V curve. Positive values forward-bias the junction; the current stays negligible until VAK approaches the forward voltage and then grows exponentially. Negative values reverse-bias it: only a tiny leakage flows until the breakdown voltage is reached. In a real circuit the supply and series resistor set it, so the diode voltage seldom equals the supply voltage.
↑ Increasing it: Moving from reverse toward forward bias, the current stays near zero until about VF is reached and then rises steeply.
Current in the armature winding, the part of the machine that carries the load current and produces (or absorbs) the torque.
↑ Increasing it: Torque is proportional to armature current, so heavier loads draw more of it; too much heats the winding and, in a motor, stresses the commutator.
Armature resistance is the DC resistance of the armature winding plus brush contact. In a motor the supply must overcome the back-EMF plus the drop I·Ra, so a larger Ra means more speed droop under load. In a generator it makes the terminal voltage fall as load current rises, and all the I²R loss turns into heat.
↑ Increasing it: More voltage is lost inside the winding: the motor slows more under load and runs hotter.
An autotransformer starter feeds the motor from a tap that gives only a fraction k of the line voltage, typically 50, 65 or 80 %. The motor current is proportional to k and its torque to k squared, and the transformer ratio makes the current drawn from the line fall with k squared as well. A 65 % tap therefore gives about 42 % of the direct-start torque. Unlike star-delta, the tap can be chosen to suit the load, at the cost of a bulkier and more expensive device.
↑ Increasing it: The motor sees more voltage, so the starting torque and the starting current drawn from the line rise with the square of the tap.
The auxiliary (start) winding is a second stator winding placed 90 electrical degrees from the main winding. Fed through a capacitor or a resistance, its current is shifted in phase from the main current, so that the two windings together create a rotating field and a starting torque. Without it a single-phase induction motor has only a pulsating field and no torque at standstill, although it keeps running if it is spun up. Many motors disconnect it with a centrifugal switch after starting.
↑ Increasing it: Adding it gives the motor a rotating field and starting torque; without it a single-phase induction motor cannot start by itself.
Every motor is also a generator: its rotating field induces a voltage in the windings that opposes the supply. This back-EMF is proportional to speed, E = Ke · ω, so the current is I = (V - E) / R and falls as the motor speeds up. At no load the speed rises until the back-EMF nearly equals the supply voltage.
↑ Increasing it: The voltage left to push current falls, so the motor draws less current and its torque drops.
Angle to which the blades are rotated about their long axis; pitching changes how much wind power the rotor captures.
↑ Increasing it: Increasing the pitch angle reduces Cp and captured power, which is how the turbine limits power and speed above rated wind speed.
The slip at which an induction motor reaches its maximum (breakdown) torque; beyond it the torque falls as the motor slows down.
↑ Increasing it: It is proportional to rotor resistance: adding external resistance moves the peak toward standstill and raises starting torque, but the maximum stays the same.
The bulk series resistance RS is the ohmic resistance of the neutral semiconductor regions and the metal contacts, in series with the ideal junction. At low current its drop I · RS is negligible and the exponential junction law dominates. At high current the drop becomes large, so the total voltage is V = Vjunction + I · RS and the curve approaches a straight line of slope 1 / RS. Power diodes keep it to milliohms, small-signal diodes have a few ohms.
↑ Increasing it: At high current the voltage drop and heating grow, and the forward curve turns into a flatter, more resistive line.
The generator circuit breaker connects the machine to the grid and can disconnect it again, also under fault conditions. Closing it with unequal voltages, frequencies or phase angles drives a large equalising current between the machine and the grid and a torque shock on the shaft. For this reason the breaker is closed only when the synchroscope shows the generator in phase with the grid. Right after closing, the generator floats on the grid, delivering almost no power until the turbine power is raised.
↑ Increasing it: Closing it connects the generator to the grid: with a good match it takes load smoothly, with a mismatch it causes a current surge and a mechanical shock.
The commanded speed is the reference value that the speed loop of the drive tries to track. The controller compares it with the speed measured by the encoder and adjusts the voltage and current to remove the error. The motor can follow the command only while the supply voltage can overcome the back-EMF and the required torque stays within the current limit; above that the actual speed lags behind the command.
↑ Increasing it: The controller demands more speed and raises voltage and current until the speed is reached or a supply or torque limit stops it.
A brushless DC motor has no brushes, so the drive does the commutating electronically. In six-step commutation, each electrical cycle is split into six 60° sectors; in each one the inverter connects two of the three phases to the DC link while the third floats. Hall sensors (or the back-EMF) tell the drive in which sector the rotor is, so the current always flows in the pair of phases that gives the most torque. The order of the six steps sets the direction of rotation.
↑ Increasing it: Switching to another order or shifting it against the rotor makes torque fall and ripple rise; reversing the order reverses the rotation.
The conduction factor kn, also called the transconductance parameter, combines the electron mobility, the gate-oxide capacitance per unit area and the channel width-to-length ratio W / L: kn = µn · Cox · W / L. In saturation the simulator uses ID = ½ · kn · (VGS − Vth)², so doubling kn doubles the current. A wide, short channel gives a large kn, which is why power MOSFETs consist of thousands of cells in parallel.
↑ Increasing it: The drain current for the same overdrive grows in proportion, and the MOSFET becomes a stronger, lower-resistance switch.
In a DFIG the stator is connected directly to the grid, and only the rotor circuit goes through the back-to-back converter. The rotor carries just the slip power, which is approximately the slip times the stator power. A converter of 25–35 % of rated power therefore allows a speed range of about ±30 % around synchronous speed. This is the main advantage of the DFIG over a full-converter machine, which must pass all the power through the converter.
↑ Increasing it: A larger converter can handle more slip power, which widens the allowed speed range around synchronous speed, but it costs more.
Magnetic flux per unit core area; it follows the voltage, B = V / (4.44 · f · N · A), and the core saturates when it gets too high.
↑ Increasing it: It rises with supply voltage and falls with frequency; near saturation the magnetizing current jumps and the core heats.
The coupling coefficient k is the fraction of the flux produced by one winding that also links the other, with k = M / √(L1 · L2). An ideal transformer has k = 1. In a real one some flux leaks through the air and links only one winding, which appears as leakage inductance (1 − k) · L and causes a voltage drop under load. Iron-core power transformers reach 0.95 to 0.99, while air-core coils and loosely coupled coils, as in wireless charging, have much lower values.
↑ Increasing it: More of the flux links both windings, so there is less leakage inductance and the output voltage sags less under load.
A shunt generator excites itself: residual magnetism gives a small voltage, which drives field current, which raises the flux and the voltage. This only works if the field-resistance line is less steep than the slope of the magnetisation curve at the origin. The critical field resistance is the resistance at which the two coincide; above it the voltage collapses to the residual value, below it the voltage builds up to the point where the line crosses the saturation curve.
↑ Increasing it: Self-excitation becomes easier only if the actual field resistance stays below this value; a higher value widens the safe range.
Lowest speed at which a self-excited DC generator can build up voltage for a given field resistance; below it the voltage stays near zero.
↑ Increasing it: A larger field resistance raises the critical speed; if the prime mover runs below it, the generator fails to build up.
The angle of the stator current vector measured from the d-axis; it sets how the current is shared between flux and torque production.
↑ Increasing it: Near 45° gives the most torque per ampere; a smaller angle favours flux, a larger one raises torque demand and the stator voltage needed.
At low speed the back-EMF of a switched reluctance motor is small, so the current in a phase would rise very quickly and exceed safe values. The drive therefore chops: it switches the phase voltage off when the current reaches the reference and on again when it falls a little. This keeps the current close to the set limit and the torque controlled, at the price of switching losses and acoustic noise.
↑ Increasing it: The phase current is allowed to grow larger, giving more torque at low speed but also more heating.
The stator current split into a d-axis part, which builds the flux, and a q-axis part, which produces the torque, in the rotor's rotating frame.
↑ Increasing it: Torque is proportional to the product id·iq, so for a given current magnitude it peaks when the two are about equal (45° current angle).
The DC link is the DC bus, fed by a rectifier or a battery, from which the inverter builds the phase voltages. A motor's back-EMF grows with speed, and when it approaches the bus voltage the current can no longer be forced into the windings, so the DC-link voltage sets the top speed. It also sets how fast the current can change, di/dt = (V - e) / L, which matters for torque at high speed.
↑ Increasing it: The inverter can drive the motor to a higher top speed and change the current faster, but the winding and the switches carry more voltage stress.
The current flowing through the channel from drain to source; it is the MOSFET's output current and is controlled by the gate voltage.
↑ Increasing it: It is zero below the threshold voltage, then grows with VGS and, in the ohmic region, with VDS; in saturation it stays nearly flat.
The drain-source voltage VDS is the voltage across the channel and the horizontal axis of the output characteristic. As long as VDS is smaller than the overdrive VGS − Vth the MOSFET is in the ohmic (linear) region and behaves like a voltage-controlled resistor. Beyond that the channel pinches off at the drain end, the device enters saturation and the current is set almost only by VGS, which is how a MOSFET works as an amplifier. As a switch it is driven hard so that VDS stays small.
↑ Increasing it: In the ohmic region the drain current rises with VDS; once VDS exceeds VGS − Vth it saturates and stays almost constant.
Dynamic resistance rz = ΔV / ΔI is the slope of the V-I curve at the operating point, not the ratio V / I. For a Zener in breakdown it is typically a few ohms to a few tens of ohms, so a change ΔI in current moves the voltage by only rz · ΔI. The smaller it is, the stiffer the regulated voltage; it is lowest at moderate currents above the knee and is why output ripple is never exactly zero.
↑ Increasing it: The voltage regulation gets worse: the same change in current causes a larger change in the diode voltage, and ripple passes through more.
Efficiency is the ratio of useful output power to input power. The difference is lost as copper loss (I²R), iron loss (hysteresis and eddy currents), mechanical friction and windage. Motors are most efficient close to rated load and noticeably worse at light load, so an oversized motor wastes energy.
↑ Increasing it: More of the input power reaches the shaft, so less heat is produced and the machine runs cooler.
Frequency of the phase currents and back-EMF; it equals the pole-pair count times the mechanical speed in revolutions per second.
↑ Increasing it: It rises in proportion to speed, and with more pole pairs the same shaft speed needs a higher electrical frequency from the drive.
In island operation the generator is the only source, so the consumers decide how much active power it must deliver. A greater load tends to slow the rotor, because the electrical torque exceeds the turbine torque, and the speed governor must open the turbine to restore the frequency. The load current also causes a voltage drop in the stator impedance, which the automatic voltage regulator compensates by raising the excitation. A load beyond the rated power overheats the machine or exceeds the turbine capacity.
↑ Increasing it: In island operation, speed and frequency fall unless the turbine power is raised, and the voltage falls unless the excitation is increased.
An incremental encoder produces a fixed number of pulses per shaft revolution, and the drive counts them to know the position. With quadrature decoding the two output channels give four counts per pulse, so a 1000 ppr encoder resolves 4000 counts per revolution, or 0.09°. A finer resolution allows more accurate positioning and a better speed estimate at low speed, where only a few pulses arrive per sample, but the pulse rate and the processing demand grow with it.
↑ Increasing it: Position is measured in finer steps, so accuracy and low-speed feedback improve, but the controller must handle a higher pulse rate.
A rotary motor's field closes on itself, but a linear motor has a beginning and an end. As the plate moves through, eddy currents are created at the entry edge and cannot die out instantly, so a drag wave distorts the flux and reduces thrust and efficiency. The effect gets worse with speed and with a small goodness factor, and the simulator shows thrust with and without it.
↑ Increasing it: Thrust and efficiency fall further below the ideal value, most noticeably at higher speed.
An equivalent circuit replaces the windings, iron and air gap by a few resistors and reactances so that currents, torque and losses can be calculated with ordinary circuit analysis. The induction motor's per-phase model has stator resistance and leakage, a magnetising branch and a rotor branch whose resistance is Rr / s. The simulators solve these models; they assume linear iron and constant parameters.
↑ Increasing it: Not a single knob: each element of the circuit (resistance, reactance) changes current, torque or losses in its own way.
Voltage induced in the armature windings by the rotating field flux; it is the internal source voltage behind the machine's own impedance.
↑ Increasing it: It rises with field current and speed. Its size against the terminal voltage sets the reactive power and, with the load angle, the active power.
In a wound-rotor induction motor, resistors connected through the slip rings add to the rotor resistance R2. The slip at which breakdown torque occurs is proportional to R2, so a larger resistance moves the peak towards standstill and gives high starting torque with lower starting current, while the peak value of the torque stays the same. The price is a larger slip at load and slip power lost as heat in the resistors, so the resistance is cut out as the motor accelerates.
↑ Increasing it: Starting torque rises and starting current falls (up to the breakdown torque), but slip grows at load and more power is lost as heat in the resistors.
The field current magnetises the rotor (or the pole system) of a machine with a wound field. It sets the internally generated EMF, so in a generator it raises the terminal voltage. In a synchronous machine it also steers reactive power: under-excited it absorbs, over-excited it delivers; the V-curve shows the armature current against field current.
↑ Increasing it: The flux and the internal EMF grow, so a generator's terminal voltage rises and a synchronous motor shifts toward leading reactive power.
In a separately excited generator the field winding is fed from an independent DC source, so the flux does not depend on the armature voltage. In a shunt (self-excited) generator the field is connected across the armature terminals and the machine must build up its own voltage from residual magnetism. Self-excitation saves the extra source, but the voltage falls more under load, because a lower terminal voltage also weakens the field.
↑ Increasing it: Switching from separate to shunt excitation makes the voltage depend on the armature itself: it can fail to build up and drops more under load.
Field excitation is how the main magnetic flux of a DC motor is produced. A permanent magnet gives a fixed flux. A shunt field is connected in parallel with the armature, so flux and speed stay nearly constant. A series field carries the armature current, so torque grows with the square of current and speed drops sharply with load, with a risk of runaway at no load. A compound motor combines shunt and series fields. With a wound field, a rheostat can weaken the flux to raise the speed.
↑ Increasing it: Switching it changes how speed and torque vary with load: permanent-magnet and shunt motors hold speed, series motors slow sharply but start with high torque.
The field rheostat is a variable resistor in series with the shunt field winding. Raising its resistance reduces the field current and therefore the flux, so the generated EMF drops, and a shunt motor must run faster to produce the same back-EMF. In a self-excited generator the total field resistance must also stay below the critical value, otherwise the voltage collapses to the residual level.
↑ Increasing it: Flux and EMF fall: a generator's terminal voltage drops (and may fail to build up), while a shunt motor speeds up.
Back-EMF grows with speed and flux, and above base speed it would exceed what the inverter or supply can deliver. Field weakening cuts the flux (in a synchronous reluctance or PM machine by injecting negative d-axis current) so speed can keep rising. The price is torque: output torque falls roughly with 1/speed while power stays about constant.
↑ Increasing it: Speed can climb above base speed, but the available torque falls roughly as 1/speed.
Difference between the commanded position and the actual shaft position; the controller acts on it to drive the motor.
↑ Increasing it: It grows with faster commands, heavier loads and lower loop gain; a small following error means accurate tracking.
The forward voltage is the drop across a conducting diode or LED. For silicon it is about 0.6 to 0.7 V, for a Schottky diode around 0.3 V, and for LEDs it depends on the colour, from about 1.8 V for red to over 3 V for blue and white. Because it is nearly constant, a series resistor is what actually sets the current: R = (Vsupply - VF) / I.
↑ Increasing it: The diode or LED needs a higher supply before it conducts, and less current flows for the same supply and resistor.
The gate-source voltage VGS is the control input of a MOSFET. The gate is insulated by a thin oxide, so it draws practically no DC current and only its capacitance must be charged. Below Vth the device is off; above it the overdrive VGS − Vth sets the channel conductivity and, in saturation, the current ID = ½ · kn · (VGS − Vth)². The gate oxide limits VGS, typically to about ±20 V, and logic-level devices are fully on at 4.5 to 5 V.
↑ Increasing it: Nothing flows below the threshold; above it the channel opens and the drain current grows roughly with the square of VGS − Vth.
A wind-turbine rotor turns slowly, often 10–20 rpm, whereas a generator with a 50 Hz stator needs roughly 1000–1800 rpm. The gearbox bridges the gap with a step-up ratio, typically around 1:80 to 1:120 in several stages. The ratio, together with the rotor speed range, decides where the generator runs relative to synchronous speed, and thus how large the slip power through the converter becomes. Gearless designs avoid the gearbox but need a very large multi-pole generator.
↑ Increasing it: For the same turbine speed the generator shaft turns faster, shifting the DFIG toward super-synchronous operation (negative slip).
The goodness factor G, introduced by Laithwaite, combines frequency, pole pitch, air gap and the conductivity and thickness of the reaction plate. A high G means a strong magnetising field, low slip losses and good efficiency; a small G gives a weak, lossy machine. Because the pole pitch enters squared, long-pitch machines are inherently better.
↑ Increasing it: The motor couples to the plate better, so thrust, efficiency and top speed improve.
The grid voltage is the line-to-line voltage at the point of connection. A grid is so large that it holds this voltage almost unchanged whatever one generator does. Before the breaker is closed, the generator voltage is matched to it with the excitation; afterwards a change in excitation no longer changes the voltage but only the reactive power exchanged. In the wind-turbine DFIG the stator is tied directly to the grid, so the grid voltage also fixes the stator flux.
↑ Increasing it: The generator must be excited to a higher voltage before closing; a mismatch at closing drives a large reactive current.
Holding torque is the largest external torque that can be applied to a stepper at standstill, with its windings energised at rated current, before the shaft is pulled out of position. It is the main size figure of a stepper: a small NEMA 17 motor holds about 0.4 N·m. It is not the same as the torque available while turning, which is lower and falls as the step rate rises. Holding the position uses full current even though no work is done, so the motor warms up.
↑ Increasing it: The motor can resist a larger load torque at standstill without losing position, but it needs more current and runs hotter.
The ideality factor n appears in the Shockley equation I = IS·(eV / nVT − 1), where VT ≈ 26 mV at room temperature. It is close to 1 when diffusion dominates, as in many silicon junctions at moderate current, and approaches 2 when carrier recombination in the depletion region dominates, typically at low current. Real diodes and LEDs often sit between 1 and 2. A larger n stretches the exponential, so each tenfold current increase needs n times 60 mV instead of 60 mV.
↑ Increasing it: The forward curve becomes less steep: a larger voltage is needed for the same current, so the diode seems to turn on later.
The power the machine takes in: electrical power from the supply for a motor, or shaft power from the prime mover for a generator.
↑ Increasing it: Input power grows with load; the part not turned into output is lost as heat, so a larger gap between input and output means lower efficiency.
Temperature of the semiconductor junction itself; it equals ambient plus dissipated power times thermal resistance.
↑ Increasing it: More dissipated power raises it; exceeding the rated maximum shortens life or destroys the device, and for an LED it also lowers light output.
The knee current IZK is the lowest Zener current at which the breakdown region is still sharp. Below it the V-I curve rounds off, the dynamic resistance grows and the output voltage drops below VZ. In a shunt regulator the current through the diode is (Vsupply − VZ) / Rs − Iload, so the series resistor must be chosen so that it stays above IZK even at the lowest supply voltage and the highest load current.
↑ Increasing it: The Zener holds regulation down to a higher current only, so the series resistor must pass more current and more power is wasted.
A bank of lamps is a convenient resistive load: each lamp switched on is another resistor in parallel, so the total resistance falls and the load current rises. The armature current rises with it, and the terminal voltage drops by the armature resistance drop and the armature reaction. In a shunt generator the lower terminal voltage also reduces the field current, which makes the voltage fall further than in a separately excited machine.
↑ Increasing it: Each added lamp draws more current, so the terminal voltage sags further; in a shunt generator the weaker field makes the drop larger.
The colour of an LED is set by the band gap of the semiconductor, since a photon is emitted with energy close to Eg and wavelength λ ≈ 1240 / Eg (nm, with Eg in eV). Red LEDs use AlGaInP or GaAsP with a gap near 1.9 eV, green and blue use InGaN with about 2.5 to 3.0 eV, and white is usually a blue LED with a phosphor. A wider gap means a larger forward voltage, from about 1.8 V for red to above 3 V for blue, so the series resistor must be recalculated when the colour changes.
↑ Increasing it: Choosing a shorter wavelength (red to blue) raises the forward voltage, so a higher supply is needed and less current flows with the same resistor.
In a synchronous machine the rotor does not slip; instead it lags (motor) or leads (generator) the stator field by the load angle δ. Torque is proportional to sin δ, so it peaks at 90° electrical in a round-rotor machine (earlier in a salient-pole one). Beyond that the machine loses synchronism and pulls out, and the stability margin is the distance left to that limit.
↑ Increasing it: The machine carries more torque or power, until the stability limit near 90° is reached.
Load inertia is given as a multiple of the motor's own rotor inertia Jmotor. The acceleration is α = (Tmotor − Tload) / (Jmotor + Jload), so a large inertia, such as a flywheel or a big fan, makes the start slow but also smooths out speed changes. The kinetic energy stored, ½ · J · ω², is mostly dissipated as heat in the rotor during starting, so a very high inertia can overheat the motor even when the steady load is small.
↑ Increasing it: Run-up takes longer and speed reacts more slowly to load changes; starting current flows for longer and the winding heats more.
The power factor of the load tells how much of the current is reactive. An inductive (lagging) load, such as motors, draws lagging reactive power from the generator, and its demagnetising armature reaction makes the terminal voltage fall much more than a resistive one, so the excitation must be raised to hold the voltage. A capacitive (leading) load does the opposite and can even raise the voltage above its no-load value. Hence the voltage regulation of a synchronous generator depends as much on the power factor as on the load current.
↑ Increasing it: A power factor closer to 1 means less reactive current, so the voltage drops less and less excitation is needed to hold it.
The load resistance RL is the resistor connected to the output that stands for the consumer. For a given output voltage the current is I = V / RL and the power P = V² / RL, so a smaller RL is a heavier load. A real source or transformer has internal resistance and leakage reactance, so heavier loading makes the output voltage sag. Maximum power is transferred when RL equals the source resistance, but efficiency is then only 50 %.
↑ Increasing it: The load draws less current and power, and the output voltage of a real source or transformer sags less.
A load step suddenly changes the load torque by a given percentage of rated torque while the simulation runs. It shows the dynamic response: speed dips and the current jumps, then both settle at the new operating point after a time set by the inertia and the slope of the torque-speed curve. If the new load exceeds the breakdown torque, the motor cannot recover and its speed collapses.
↑ Increasing it: The sudden change in speed and current is larger; the motor settles at a new operating point, or stalls if the step exceeds the pull-out torque.
The load type describes how the resisting torque or force depends on speed. Constant-torque loads such as conveyors and hoists ask the same torque at every speed, fans and pumps follow T ∝ n², constant-power loads such as winders have T ∝ 1/n, and viscous loads grow linearly with speed. Aerodynamic drag on a linear-motor vehicle grows with v². On a synchronous generator the load type is electrical instead: an inductive (lagging) load lowers the terminal voltage, while a capacitive (leading) load can raise it.
↑ Increasing it: Changing it changes how load torque follows speed, so the operating point and run-up time shift; on a generator it changes the voltage regulation.
Brightness of the LED in a given direction; it is roughly proportional to the forward current and is shown here as a percentage of its rated value.
↑ Increasing it: More forward current makes the LED brighter, until heating and the current rating limit it; a hotter junction emits somewhat less light.
The maximum drain current ID(max) is the largest current the MOSFET is rated for, limited by bond wires, metallisation and, above all, heating. The continuous rating assumes the case is held at 25 °C, so in practice usable current is lower and falls with temperature. Short pulses may be several times higher. In the simulator the drain current is clipped to this value, which is how the current ceiling of a real device appears.
↑ Increasing it: The MOSFET can be used with heavier loads before the current limit is reached, but a larger device is usually costlier.
The maximum forward current IF(max) is the highest continuous current at which the junction temperature stays within its limit. Heat in the diode is mainly VF · IF, so the limit follows from the thermal resistance and the ambient temperature. Short pulses may exceed it, as given by a separate surge rating. A small-signal diode is rated for tens to hundreds of milliamperes, a typical 5 mm LED for 20 to 30 mA and a power rectifier for several amperes.
↑ Increasing it: The diode can carry more continuous current, so a smaller series resistor is allowed before it overheats.
The maximum power dissipation PD(max) is the heat the device can give off to its surroundings without the junction exceeding its temperature limit, usually 150 °C. It follows from PD(max) = (Tj(max) − Ta) / Rth, so it is quoted at a given ambient temperature and must be derated as that temperature rises. In a Zener the dissipated power is VZ · IZ, which sets the largest allowed current; in a MOSFET it is ID² · RDS(on) plus switching loss.
↑ Increasing it: The device can handle more heat, so a larger current or voltage drop is allowed before it overheats.
Mechanical load is the torque that the driven machine, such as a pump, fan or conveyor, asks from the shaft; here it is given as a percentage of rated torque. The motor settles where its own torque equals the load torque: an induction motor does so by slipping, a DC motor by drawing more armature current, and a synchronous motor by increasing its load angle. Above 100 % the motor is overloaded and heats up, and beyond its pull-out or stall torque it stops.
↑ Increasing it: The motor draws more current and heats up; speed falls slightly (slip rises in an induction motor) and a synchronous motor's load angle grows.
Speed of the vehicle or mover along the track; it always stays below the synchronous speed vs = 2 · pole pitch · supply frequency.
↑ Increasing it: A larger pole pitch or a higher supply frequency raises the synchronous speed and so the achievable vehicle speed; a heavier load increases slip.
Maximum torque per ampere splits the stator current into a flux part (id) and a torque part (iq) so that torque is largest for the current drawn. For a synchronous reluctance machine this means a current angle near 45° from the d-axis. It minimises copper loss and drive rating below base speed; above base speed field weakening takes over.
↑ Increasing it: Switching it on lets the drive pick the best current angle, so torque per ampere is highest.
The force perpendicular to the direction of travel, pulling the primary toward the reaction rail (attraction) across the air gap.
↑ Increasing it: It does no useful work but loads the guide and bearings; it is much larger than the thrust and grows as the air gap shrinks.
In island operation the generator alone supplies the consumers, so the load decides the power, the speed governor holds the frequency and the excitation holds the voltage. In parallel operation the generator is tied to a grid so large that it fixes voltage and frequency. Turbine power then sets the active power delivered, and excitation sets the reactive power. To go from one mode to the other, the generator must first be synchronised with the grid.
↑ Increasing it: Moving from island to grid fixes voltage and frequency at the grid's values; turbine and excitation then set the power, not the load.
The opposing force is the constant resistance the thrust has to overcome before the vehicle can accelerate: rolling friction, a slope (m · g · sin α) or a towed load. The vehicle reaches a steady speed where the thrust equals this force, and if the opposing force exceeds the standstill thrust it does not move at all. Because an induction motor's thrust falls towards zero near synchronous speed, a larger opposing force means a larger slip at steady speed and more loss in the plate.
↑ Increasing it: The net force that accelerates the vehicle shrinks, so it accelerates more slowly and settles at a lower speed, with more slip, where thrust equals the load.
The useful power leaving the machine: electrical power at the terminals of a generator or mechanical power at the shaft of a motor.
↑ Increasing it: Output power is input power minus losses, so efficiency is output divided by input; it rises with load until the rating is reached.
Current in one winding (phase) of the stator; its size tracks the torque and sets the copper losses and the drive rating.
↑ Increasing it: More load torque or a lower power factor raises it; copper loss grows with its square, so the winding heats faster than the current rises.
The phase sequence is the order in which the three phase voltages reach their positive peaks: A-B-C (positive) or A-C-B (negative). The stator field rotates from the phase that peaks first towards the next one, so exchanging any two supply wires reverses the rotation of an induction or synchronous motor. For a generator the sequence must match the grid, together with voltage, frequency and phase angle, before the breaker is closed.
↑ Increasing it: Swapping two phases (ABC to ACB) reverses the rotating field, so the motor turns the other way; a generator then no longer matches the grid.
The reaction plate is where the travelling field induces the eddy currents that produce thrust. A thin plate's surface conductivity is its conductivity times its thickness, σ · d, and the goodness factor is proportional to it, so a thicker plate gives a higher goodness factor and better efficiency. Thick plates cost more and weigh more, and beyond the depth to which the field penetrates, extra thickness hardly helps.
↑ Increasing it: The plate conducts better (more σ · d), so the goodness factor, thrust and efficiency improve, with diminishing returns for thick plates.
Polarity tells which of the two supply terminals is positive. The torque of a DC motor depends on the product of field flux and armature current, so reversing the armature current while the field stays the same reverses the torque and the rotation. Here the switch stands for reversing the armature connection; in a real shunt or series machine, swapping only the supply leads reverses both field and armature, so the direction stays the same.
↑ Increasing it: Switching the polarity reverses the direction of rotation and of the torque; the speed magnitude stays the same.
The pole count is the number of north and south poles the stator winding creates, always an even number. Together with the supply frequency it fixes the synchronous speed. More poles give a lower speed and, at the same power, a higher torque, which is why slow machines such as wind generators use many poles.
↑ Increasing it: The field turns more slowly, so speed drops while torque for the same power rises.
A machine with p pole pairs has 2p poles. For every mechanical revolution the field passes p north-south pairs, so the electrical frequency is f = p · n / 60 with n in rpm. Synchronous speed follows as ns = 60 · f / p, which is why a four-pole machine (p = 2) on 50 Hz turns at 1500 rpm. BLDC and servo controllers use p to convert the measured shaft angle into the electrical angle they need for commutation.
↑ Increasing it: At the same shaft speed the electrical frequency is higher, and for a given supply frequency the field turns slower.
The pole pitch τ is the distance between the centres of two adjacent poles along the stator. The magnetic field travels along the motor at the synchronous speed vs = 2 · τ · f, so for a given frequency a larger pitch means a faster field and a faster vehicle. Because the goodness factor is proportional to τ², a long pitch also couples the field to the plate well, whereas a short pitch suits low-speed, short-stroke applications.
↑ Increasing it: Synchronous speed rises in proportion (vs = 2 · τ · f) and the goodness factor grows with τ², but the stator gets longer.
In a servo, the position loop turns the position error, the difference between the target and the encoder reading, into a speed command: the larger the gain, the more speed is requested for the same error. The gain roughly sets the bandwidth of the loop, and the following error during motion at constant speed is the speed divided by the gain. Raising the gain stiffens the axis and reduces the error, but delays in the speed loop and the mechanics eventually make it overshoot and oscillate.
↑ Increasing it: The axis responds faster and tracks the command more tightly, but with too much gain it overshoots and oscillates.
Fraction of the wind's kinetic power the rotor captures; it can never exceed the Betz limit of 16/27 ≈ 0.593.
↑ Increasing it: A higher Cp means more of the available wind power becomes mechanical power; it depends on tip-speed ratio and blade pitch angle.
Electrical power converted into heat in the component, P = V · I; it must stay below the rated power or the part overheats.
↑ Increasing it: It grows with the square of the current (or voltage across a resistor), so doubling the current quadruples the heat.
The power factor is real power divided by apparent power. A value below one means part of the current only magnetises the machine and swings back and forth, loading the supply without doing work. Induction motors run at a lagging power factor, worst at light load; overexcited synchronous machines can run at a leading one.
↑ Increasing it: Less of the current is wasted as reactive current, so the supply carries less current for the same real power.
The power rating Pmax is the largest power a resistor can turn into heat continuously at its rated ambient temperature, typically 70 °C. The actual dissipation is P = I² · R = V² / R, which must stay clearly below the rating, and a margin of 50 % or more is good practice. Above the rated temperature the allowed power must be derated. Common axial resistors are rated 1/8, 1/4, 1/2 and 1 W, and a larger rating means a physically larger body.
↑ Increasing it: The resistor can dissipate more heat continuously, so it can take a higher current or voltage without overheating.
The number of primary turns N1 sets how much flux the core needs for a given voltage. By Faraday's law the peak flux is Φ = V1 / (4.44 · f · N1) for a sinusoidal supply, so more turns mean a lower flux density and less risk of saturating the core. Together with the secondary turns it fixes the output voltage, V2 = V1 · N2 / N1. More turns also add copper resistance and leakage inductance, and need a larger winding window.
↑ Increasing it: The core flux and magnetising current fall for the same voltage, and the output voltage drops if the secondary turns stay unchanged.
The primary voltage V1 is the AC voltage applied to the primary winding. The secondary voltage follows it through the turns ratio, V2 = V1 / a. The core flux is proportional to V1 / f, since Φ = V1 / (4.44 · f · N1). Operating well above the rated voltage, or at a lower frequency than rated, pushes the core into saturation, where the magnetising current rises sharply and distorts, causing heating. That is why a 60 Hz transformer should not be supplied from a 50 Hz grid at its full rated voltage.
↑ Increasing it: The output voltage rises in proportion, but the core flux and magnetising current also grow, bringing the core closer to saturation.
The prime mover, a turbine or an engine, turns the generator shaft. The induced EMF is proportional to the flux and the speed, so at fixed excitation a faster shaft gives a higher voltage. In a synchronous generator the frequency is also tied to speed through f = p·n / 60 (p pole pairs), which is why a generator alone on an island must hold its speed accurately, and why it must be brought to synchronous speed before it is connected to the grid.
↑ Increasing it: The EMF rises in proportion to speed, and in an AC generator so does the frequency.
Maximum load torque a synchronous motor can carry; beyond it the rotor loses synchronism with the stator field and stalls.
↑ Increasing it: Raising the field current (and so the internal EMF) increases the pull-out torque and the margin before the motor falls out of step.
Pulse-width modulation switches the DC link on and off thousands of times per second. The duty cycle D is the fraction of each period during which the switch is on, so the average voltage is D times the DC-link voltage. The motor inductance smooths the current, which responds to the average rather than to the individual pulses. At 100 % the motor sees the full bus voltage, and at 0 % none.
↑ Increasing it: The motor sees a higher average voltage, so its speed and torque rise, and so does the current.
RDS(on) is the resistance of the channel when the MOSFET is fully turned on. In the ohmic region the device behaves like a resistor of this value, so the voltage drop is ID · RDS(on) and the heat generated is ID² · RDS(on). Datasheets give it at a specified VGS and junction temperature; it rises with temperature, which must be allowed for when sizing the heat sink.
↑ Increasing it: Conduction loss and heating grow, and the voltage drop across the switch rises with current.
The ramp time is how long a soft starter takes to take the voltage from its initial value to full voltage; a drive uses the same idea to raise frequency. A long ramp gives gentle acceleration and lower stress on the supply and the mechanics. If it is too long, the motor may not develop enough torque to accelerate during the early part of the ramp and then stays at low speed with a high current, which heats the windings.
↑ Increasing it: Voltage or frequency climbs more slowly, so acceleration is gentler and current peaks are lower, but reaching full speed takes longer.
Apparent power S is the product of voltage and current, S = √3 · U · I for three phases and S = U · I for a single phase, and it is measured in volt-amperes. Generators and transformers are rated in kVA instead of kW because their heating depends on current, not on the power factor of the load. The active power available is P = S · cos φ, and the rest is reactive power.
↑ Increasing it: The machine or transformer can carry more current at rated voltage, so it can supply more active and reactive power before it overheats.
Rated current is the line current at rated voltage, frequency and load, and it sets the heating of the windings. Starting current of a direct-on-line induction motor is typically five to eight times higher, which is why starters exist. Protective devices are chosen relative to this value.
↑ Increasing it: Higher continuous load is allowed and the overload warning triggers later.
Rated frequency is the supply frequency at which the nameplate values hold. It fixes the synchronous speed together with the pole count. Running at a lower frequency with the same voltage raises the magnetic flux and can saturate the core; drives therefore keep the voltage-to-frequency ratio constant.
↑ Increasing it: Synchronous speed rises; at the same supply voltage the flux falls and torque weakens.
Rated power is the shaft output printed on the nameplate, the power the manufacturer guarantees without overheating. It is mechanical output, not electrical input, so the supply must deliver more by the amount of the losses. Running above it for long periods shortens insulation life.
↑ Increasing it: The motor is treated as larger: more torque is available and the rated current and torque scale up.
The rated power factor links the apparent power to the active power on the nameplate, Pn = Sn · cos φn. Synchronous generators are usually rated at 0.8 to 0.95 lagging, because grids and their loads are mostly inductive and need reactive power. A lower rated power factor means a larger machine with a stronger field winding for the same active power.
↑ Increasing it: The rated active power rises for the same kVA, while the reactive power the machine is built to supply falls.
Rated speed is the shaft speed when the motor delivers rated power at rated voltage and frequency. For an induction motor it is always below synchronous speed, and the gap between the two gives the rated slip. The simulator uses it to work out the rated torque and the rotor parameters.
↑ Increasing it: The nameplate slip shrinks, so the motor reaches closer to synchronous speed at full load.
Rated torque is the torque the shaft delivers at rated power and rated speed, Tn = Pn / ωn with ωn = 2π · nn / 60. It is limited by heating, so the motor may exceed it briefly as peak torque but not for long. Datasheets of servo and stepper motors usually list the continuous torque and the higher peak torque separately.
↑ Increasing it: The motor is rated for more continuous load; at the same speed that means proportionally more shaft power, P = T · ω.
Rated voltage is the supply voltage at which the machine reaches its rated flux, torque and efficiency. For three-phase machines it is the line-to-line voltage, and the winding connection (star or delta) must match it. Too low a voltage cuts torque quickly, too high a voltage saturates the iron and overheats the machine.
↑ Increasing it: The motor is designed for a higher voltage, so the same supply now under-excites it and torque falls.
The rated wind speed is where the turbine first delivers its rated power, typically 11–14 m/s. Below it the rotor is run at its best efficiency and the power follows the cube of the wind speed. Above it, extracting all the available power would overload the generator and the drive train, so the blades are pitched out of the wind to hold the power at its rated value. A turbine designed for a lower rated speed needs a larger rotor per kilowatt and produces rated power more often.
↑ Increasing it: The turbine reaches rated power later: below the new value it produces less, and full power needs stronger wind.
The reaction plate is the conductor in which the travelling field induces eddy currents; their interaction with the field produces the thrust. Aluminium (about 35 MS/m) is light, cheap and the usual choice, while copper (about 58 MS/m) conducts roughly 1.6 times better. Higher conductivity raises the goodness factor, so the same stator gives more thrust at lower slip, at the price of higher cost and weight.
↑ Increasing it: Copper instead of aluminium conducts about 1.6 times better, which raises the goodness factor, thrust and efficiency.
Power that swings back and forth between source and magnetic or electric fields without doing work; it sets the voltage level and loads the wires.
↑ Increasing it: Over-excited machines deliver reactive power and raise the voltage; under-excited ones absorb it. More reactive power means more current and loss.
Ferromagnetic iron keeps a little magnetisation after the field current has been switched off, typically a few percent of rated flux. Spinning the armature in this flux induces a small EMF, which is the starting point of self-excitation in a shunt generator. If the iron has lost its remanence, for example after being demagnetised, the generator does not start until the field is flashed from an external DC source.
↑ Increasing it: A stronger remanent flux gives a larger starting voltage, so the generator builds up more easily and from a higher initial value.
Resistance R is the ratio of the voltage across a component to the current through it, R = V / I (Ohm's law), measured in ohms. In a resistor it comes from collisions of the charge carriers with the lattice and it turns electrical energy into heat: P = I² · R = V² / R. It depends on material, length and cross-section as R = ρ · l / A and changes a little with temperature. Common values run from fractions of an ohm to several megohms.
↑ Increasing it: The current drops for the same voltage, while the voltage across the resistor and the power it dissipates at a given current rise.
The reverse breakdown voltage VBR is the reverse bias at which the current rises steeply because of avalanche multiplication or Zener tunnelling. In an ordinary rectifier diode this is a failure limit: the junction is damaged if the current is not limited. A Zener diode is designed to operate there, with the voltage held nearly constant. Rectifier diodes are rated from tens of volts up to over a thousand volts.
↑ Increasing it: The diode withstands a higher reverse voltage before it conducts heavily, so it is safe in higher-voltage circuits.
The direction is set by the order in which the windings are energised or by the polarity of the supply. A stepper motor reverses when its phase sequence is reversed, a brushed DC motor when the armature voltage changes sign, and a single-phase induction motor when the connection of the auxiliary winding is swapped, because the main winding alone has no preferred direction. Drives usually treat the two directions as positive and negative speed.
↑ Increasing it: Switching it makes the shaft turn the other way; reversing at speed first brakes the rotor and draws a high current.
Frequency of the currents in the rotor circuit, equal to the slip times the supply frequency; it is zero at synchronous speed.
↑ Increasing it: It grows with the distance from synchronous speed. In a doubly-fed generator the converter must supply exactly this frequency to the rotor.
The rotor speed is the mechanical speed of the shaft, as opposed to the speed of the rotating stator field, which is the synchronous speed. Their relative difference is the slip. A plain induction generator must run just above synchronous speed, but in a DFIG the converter lets the rotor run both below it (sub-synchronous, the rotor absorbs slip power) and above it (super-synchronous, the rotor delivers slip power to the grid). This lets the turbine follow the wind speed to extract the maximum power.
↑ Increasing it: Slip falls as speed rises; in a DFIG, passing synchronous speed makes it negative and the rotor circuit feeds power into the grid.
A single-phase winding alone produces a pulsating field, not a rotating one. A capacitor in series with the auxiliary winding makes its current lead the main-winding current, and when the two are about 90° apart in time and space the field rotates almost circularly. A start capacitor is large and switched out after starting; a run capacitor is smaller and stays in circuit to improve torque, efficiency and power factor.
↑ Increasing it: Torque and efficiency improve until the field is nearly circular; beyond that optimum the auxiliary current grows too large and the field turns elliptical.
The saliency ratio ξ = Ld / Lq compares how easily flux passes along the rotor's d-axis with the q-axis. A synchronous reluctance motor makes torque only from this difference, so ξ decides its torque density. It also caps the power factor at (ξ - 1) / (ξ + 1), which is why designers push the rotor barriers to raise ξ.
↑ Increasing it: Reluctance torque and the power-factor ceiling both rise, so the same current gives more torque.
The saturation current IS is the scale factor of the Shockley equation I = IS·(eV / nVT − 1) and, for a large negative voltage, the tiny reverse current of the ideal diode. For a given forward current, the voltage is V = nVT·ln(I / IS), so a larger IS means a lower forward voltage. It depends on the semiconductor and the junction area and roughly doubles for every 5 to 10 °C rise in temperature, which is why the forward voltage falls by about 2 mV per kelvin.
↑ Increasing it: The forward curve shifts to lower voltage, so the diode turns on earlier; the reverse leakage is also larger.
Current that the load draws from the secondary winding; it is reflected to the primary divided by the turns ratio.
↑ Increasing it: A lower load resistance draws more current, which raises the primary current, the copper loss and the voltage drop in the windings.
The number of secondary turns N2 determines the output voltage: with a fixed primary, V2 = V1 · N2 / N1, so the voltage per turn is the same in both windings. Doubling N2 doubles the open-circuit output voltage, while the current the winding can supply is limited by the conductor cross-section, so a high-voltage secondary uses thin wire and many turns. Taps on the secondary give several output voltages from one winding.
↑ Increasing it: The output voltage rises in proportion, and the output current for a given power falls.
Voltage delivered by the secondary winding to the load; with no load it equals the primary voltage times the turns ratio.
↑ Increasing it: It follows the primary voltage and turns ratio, and sags slightly under load because of the winding resistance and leakage inductance.
A shunt generator feeds its own field winding from its output; residual magnetism starts the voltage, which then builds up on its own.
↑ Increasing it: Voltage builds up only if residual flux exists, the field is connected with the right polarity, and field resistance and speed are within the build-up limits.
A shunt generator can only build up if the field current produces flux in the same direction as the residual flux, so each increase in voltage strengthens the flux. If the shunt winding is connected the wrong way round, the field current opposes the residual flux and the generator loses even that small voltage. The usual remedy is to reverse the field leads, or to flash the field with a DC source in the right direction.
↑ Increasing it: Flipping the polarity so the field opposes the residual flux cancels it, and the voltage collapses instead of building up.
Slip is the difference between the speed of the rotating magnetic field and the rotor speed, divided by the field speed. An induction motor needs slip: only a rotor that lags the field has currents induced in it and so produces torque. Slip is 100 % at standstill, close to zero at no load and typically a few percent at rated load.
↑ Increasing it: The rotor runs slower relative to the field, so torque and rotor current rise until the load is met.
The fraction s of the air-gap power that crosses to the rotor circuit as electrical power at slip frequency instead of becoming shaft power.
↑ Increasing it: A motor with a rotor resistor burns it as heat, lowering efficiency at high slip; a doubly-fed generator instead sends it through the converter to the grid.
A soft starter uses thyristors to apply a voltage that rises from an initial value to full voltage over the ramp time. The initial voltage must be high enough for the torque, which varies with its square, to overcome the load's breakaway torque; if it is too low, the motor hums without turning until the ramp has risen far enough. If it is too high, the benefit is lost, because the starting current and mechanical shock approach those of a direct start.
↑ Increasing it: The motor starts on more voltage, so starting torque and inrush current rise and the start becomes less gentle.
The speed command is the target speed of the drive, given as a percentage of base speed, the speed at which the motor reaches rated voltage. Below base speed the drive raises voltage and frequency together, so the flux and the maximum torque stay constant. Above 100 % the voltage is limited and the drive applies field weakening: the available torque falls roughly as 1/n and the power stays about constant, until the pull-out limit is reached.
↑ Increasing it: The drive asks for more speed; above 100 % the flux is weakened and the torque available falls.
The power coefficient of a rotor is highest at one tip-speed ratio, the ratio of blade-tip speed to wind speed. In MPPT mode a tracker sets the rotor speed so that the ratio stays at this optimum as the wind changes, within the slip limits the converter can handle. In manual mode the user sets the rotor speed inside the slip window; away from the optimal ratio the turbine captures less power than it could. Above rated wind speed, pitch control limits the power in both modes.
↑ Increasing it: Switching from manual to MPPT moves the operating point onto the optimal tip-speed-ratio curve, so more power is captured below rated wind.
Largest power a synchronous machine can exchange with the grid (at load angle 90°); the margin shows how far the operating point is from it.
↑ Increasing it: Higher excitation raises the limit and the stability margin; a heavier load shrinks the margin and pushes the load angle toward 90°, where synchronism is lost.
The stack width is the width of the laminated stator core, measured across the direction of travel. The stator area facing the reaction plate is this width times the stator length, so thrust and power scale roughly with it while the speed does not change. A wider stack gives more force from the same pole pitch and frequency, at the cost of more iron, copper and weight, and the plate must be at least as wide to avoid transverse edge effects.
↑ Increasing it: Thrust rises roughly in proportion to the width, and so do the magnetising current and the input power at the same voltage.
Large capacitor in series with the auxiliary winding during starting; a centrifugal switch removes it once the motor is near full speed.
↑ Increasing it: A larger value raises starting torque and current, but too large a value overheats the auxiliary winding. Unlike the run capacitor, it acts only at start.
A rotor starter divides the external resistance into a number of steps. Each step is shorted after a set time, which lowers the rotor resistance and moves the operating point to a new torque-speed curve. With few steps each switching causes a visible torque and current jump; with many steps the start approaches smooth, stepless acceleration. The step time sets how long each resistor stays in circuit.
↑ Increasing it: The resistance is cut out in smaller steps, so torque and current change more smoothly at each switching moment.
Direct-on-line starting applies full voltage at once: the motor draws five to eight times its rated current but delivers its full starting torque. Star-delta, autotransformer and soft-starter methods start on a reduced voltage, which lowers the inrush current; because torque falls with the square of the voltage, the starting torque drops as well. A variable-frequency drive avoids this trade-off by raising voltage and frequency together, so it can give good torque at low current.
↑ Increasing it: Moving from direct to a reduced-voltage method cuts the starting current but also lowers the starting torque.
Torque the motor develops at standstill (zero speed); it must exceed the load torque or the shaft will not start turning.
↑ Increasing it: A higher starting torque lets the motor accelerate heavier loads, but it usually comes with a higher starting current.
The stator is connected to the grid, but the converter feeds the rotor and so controls the magnetising of the machine. If the rotor supplies only the magnetising current, the stator exchanges no reactive power (unity power factor). By adjusting the rotor current component that magnetises the machine, the converter can make the stator deliver reactive power to the grid (positive, like an over-excited alternator) or draw it from the grid (negative). This lets a wind farm support the grid voltage without extra capacitor banks, within the current limit of the converter.
↑ Increasing it: The turbine delivers more reactive power to the grid and supports its voltage, at the cost of more rotor current and converter loading.
A switched reluctance motor has salient poles on both stator and rotor, and the two numbers are written stator/rotor, for example 6/4. The stator has two poles per phase, so 6/4 is a three-phase machine and 8/6 a four-phase one. The rotor has fewer poles than the stator, so only some of the rotor poles line up at a time, and the phases take turns. The stroke angle is 360° divided by the number of phases times the rotor poles: 30° for 6/4 and 15° for 8/6. More phases and poles give smoother torque but need more power electronics.
↑ Increasing it: Choosing a larger combination (for example 8/6 instead of 6/4) adds a phase and shortens the step angle, giving smoother torque with more switches.
The step angle is how far the shaft turns for each pulse sent to the driver. Typical hybrid steppers have 1.8° (200 steps per revolution) or 0.9° (400 steps), set by the number of rotor teeth. Microstepping divides the full step further by shaping the winding currents, which gives smoother motion and finer positioning, though the extra resolution does not add the same amount of accuracy or torque. At a given step rate, a larger step angle means a faster shaft.
↑ Increasing it: Each pulse turns the shaft further, so resolution gets coarser and motion less smooth, but the same step rate gives a higher speed.
The step rate f is how many pulses per second the driver receives, and the shaft speed follows it directly: n = 60 f / N revolutions per minute for N steps per revolution, so 1000 pps on a 200-step motor gives 300 rpm. As the rate rises, the winding current has less time to build up against the inductance and the back-EMF grows, so the available torque falls. If the load torque exceeds it, or the rate changes too abruptly, the rotor misses steps; a ramp is therefore used to accelerate.
↑ Increasing it: The motor turns faster in proportion, but torque falls with rate and above a limit the rotor misses steps.
Supply frequency f sets how fast the stator field rotates, ns = 120 · f / p. In induction and synchronous motors the shaft speed follows it, which is how variable-frequency drives control speed. Raising the frequency without raising the voltage lowers the flux (the V/f ratio falls) and the available torque, and the winding reactance X = 2π · f · L grows. On a grid the frequency is common to all machines and reflects the balance between generation and demand.
↑ Increasing it: The field and motor speed rise in proportion, while reactance grows and the flux (V/f) falls unless the voltage is raised too.
A universal motor has its field and armature windings in series, so reversing the current reverses both fluxes and the torque keeps its direction. It can therefore run from DC or from AC. On AC the current and torque pulsate at twice the supply frequency, the winding reactance limits the current and the brushes spark more; on DC the torque is steady and the speed is higher for the same voltage. On AC a phase-angle controller such as a triac can regulate the speed.
↑ Increasing it: Going from DC to AC adds reactance and torque pulsation at twice the line frequency, so speed is lower and power factor drops at the same voltage.
Supply voltage is what the source applies to the motor terminals. In a DC motor the speed is roughly proportional to it, n ≈ (V − I · Ra) / (Ke · Φ). In an AC induction motor the torque scales with V², so a low voltage reduces the pull-out torque and raises the current for the same load, while the speed stays close to synchronous speed. Running well above rated voltage saturates the iron and overheats the winding.
↑ Increasing it: Current and torque rise (on an AC induction motor torque grows with V²) and a DC motor's speed rises roughly in proportion.
A star-delta or autotransformer starter first runs the motor on reduced voltage, then switches to full voltage after a set time. The switch should happen when the speed is close to its final value: then the current jump and the torque transient are small. Switching too early gives a large second current peak, almost like a direct start; waiting too long may leave the motor stalled at a speed where its reduced-voltage torque only just equals the load torque.
↑ Increasing it: The motor stays longer on reduced voltage and reaches a higher speed before the switch, which makes the current jump at switchover smaller.
Synchronous speed is how fast the stator field rotates: 120 times the supply frequency divided by the number of poles. A synchronous machine runs exactly at this speed, while an induction motor runs a little below it. Doubling the pole count halves the speed, which is why a 4-pole motor on 50 Hz turns at about 1500 rpm.
↑ Increasing it: The rotating field and, with it, the motor's no-load speed rise in proportion.
The synchroscope shows the phase angle between the generator voltage and the grid voltage. If the generator is slightly faster than the grid, the angle keeps growing, so the pointer rotates in one direction; if it is slower, it rotates the other way. The aim is to adjust the speed until the pointer turns very slowly, then close the breaker as it passes through zero. Closing at a non-zero angle gives a current surge and a torque jolt until the machine has pulled into step.
↑ Increasing it: A larger angle means the voltages are further out of phase, so closing the breaker then would cause a bigger current and torque shock.
Voltage measured across the machine's terminals, the one the load or supply actually sees.
↑ Increasing it: In a generator it drops below the internal EMF as load current flows through the winding resistance and reactance, and armature reaction weakens the field.
The threshold voltage Vth is the gate-source voltage needed to invert the semiconductor under the gate and form a conducting channel. Below it the MOSFET is in cut-off and only leakage flows. Above it, the drain current grows with (VGS - Vth)², so a larger overdrive gives more current and a lower channel resistance.
↑ Increasing it: More gate voltage is needed to turn the MOSFET on, so at a given gate voltage the drain current drops.
The linear force the primary exerts on the reaction rail along the direction of travel; the linear-motor equivalent of torque.
↑ Increasing it: Thrust is highest near standstill and falls as the vehicle nears synchronous speed; it accelerates the vehicle only while it exceeds the load force.
Ratio of the blade-tip speed to the wind speed, λ = ωR / v; it sets how efficiently the rotor extracts power from the wind.
↑ Increasing it: Power coefficient peaks at one optimal λ; faster or slower rotation than that optimum, at the same wind speed, captures less power.
The tolerance is the largest allowed deviation of the actual resistance from its nominal value, given in percent and also shown by the last colour band (gold 5 %, silver 10 %, brown 1 %). A 1 kΩ resistor with 5 % tolerance may measure anywhere from 950 Ω to 1050 Ω. Tighter tolerances cost more and matter in dividers, filters and measuring circuits, while a current-limiting resistor for an LED rarely needs better than 5 %. Standard values follow the E-series: E12 for 10 %, E24 for 5 %, E96 for 1 %.
↑ Increasing it: The real resistance may stray further from the marked value, so currents and voltages in the circuit become less predictable.
Torque is the turning effect of a force about the shaft axis, T = F · r, measured in newton-metres. It is produced in the air gap by the interaction of the stator and rotor magnetic fields, and in most motors it is proportional to the current times the flux. Mechanical power is P = T · ω, so at a given power a slower machine has more torque. The load demands a torque, and the motor settles at the speed where its torque equals that of the load.
↑ Increasing it: The shaft can deliver more turning force: at the same speed the mechanical power rises, and the motor draws more current.
The torque constant links current to torque: T = Kt · I. For permanent-magnet and separately excited DC machines it is set by the flux and winding, and in SI units it has the same numerical value as the back-EMF constant Ke in V·s/rad. A high Kt gives more torque from less current but a higher back-EMF, so a lower no-load speed.
↑ Increasing it: Each ampere gives more torque, but the back-EMF also rises, so the no-load speed falls.
Torque ripple is the difference between the highest and lowest instantaneous torque, relative to the mean. In a switched reluctance motor it comes from the phase-by-phase commutation, in a single-phase AC universal motor from the power pulsating at twice the line frequency. High ripple excites mechanical resonances and audible noise, and makes smooth speed control harder.
↑ Increasing it: Vibration, noise and speed fluctuation grow noticeably.
The track length is the distance along which stator sections are installed, so thrust acts only over this length. The simulator reports the time to reach the track end and the speed there. On a short track the vehicle leaves with whatever speed it has gained, v = √(2 · a · L) for constant acceleration; on a long track it approaches the steady speed where thrust equals the opposing force, which lies below synchronous speed.
↑ Increasing it: The vehicle has more distance to accelerate: the speed at the end of the track is higher, but the run takes longer.
How much the drain current changes per volt of gate-source voltage; it measures the MOSFET's gain as an amplifier.
↑ Increasing it: It is zero in cutoff and rises with the overdrive VGS − Vth, so a harder-driven MOSFET amplifies more but also conducts more current.
The firing angle is the delay, measured from the zero crossing of the AC voltage, at which the triac is triggered. Until it fires, the motor receives no voltage; afterwards the triac conducts until the current falls to zero. At 0° the motor sees the full sine wave, and as the angle grows the RMS voltage falls (about 70 % at 90° for a resistive load). The chopped waveform adds harmonics and torque ripple, which is the price of this cheap speed control.
↑ Increasing it: The triac conducts for a shorter part of each half-cycle, so the effective voltage, torque and speed all decrease.
The turbine converts the energy of steam, water, gas or wind into mechanical power on the shaft. Minus the losses, this is the active power that the generator can send into the grid or to its load. When the turbine power is higher than the electrical power taken, the surplus accelerates the rotor; when it is lower, the rotor slows down. Connected to a stiff grid, the speed is fixed by the grid, so more turbine power shows up as a larger load angle and more delivered power.
↑ Increasing it: More mechanical power is fed to the shaft: on the grid the generator delivers more active power; on an island it speeds up unless the load grows.
The turn-off angle is the rotor position at which the phase voltage is removed. After that the current does not vanish at once: it decays through the freewheeling diodes while the winding inductance resists the change. If the current is still flowing when the rotor passes alignment and the inductance starts to fall, it produces negative (braking) torque. The turn-off angle must therefore be early enough for the tail current to die away, yet late enough to use as much of the rising-inductance region as possible.
↑ Increasing it: The phase conducts longer, adding torque at first, but current may still flow when negative torque begins, which cuts efficiency.
In a switched reluctance motor a phase produces positive torque while its inductance is rising, as the rotor pole approaches alignment with the stator pole. The turn-on angle is the rotor position where the phase starts to be energised. Switching on early gives the current time to build before the pole arrives, which matters at high speed when the back-EMF opposes the rise. Too early, however, and the current flows for longer than needed, adding losses without much torque.
↑ Increasing it: The phase switches on later, so less current builds before the poles align, giving less torque and a lower peak current.
The turns ratio a = N1 / N2 compares the turns of the primary and secondary windings. For an ideal transformer the voltages scale with it, V1 / V2 = a, the currents inversely, I1 / I2 = 1 / a, and the power stays the same. A load impedance seen from the primary is a² times larger than at the secondary, which is why transformers also match impedances. Step-down transformers have a > 1, step-up transformers a < 1.
↑ Increasing it: With more primary than secondary turns, the output voltage is lower and the output current higher; the opposite for a ratio below 1.
The vehicle mass m is the total mass the motor has to accelerate, load included. Newton's second law gives the acceleration a = (thrust − load force) / m, so a heavy vehicle accelerates slowly and needs a longer track to reach the same speed. The mass does not change the thrust the motor produces, which depends on the field and the slip; it only sets how long it takes to get to the steady speed.
↑ Increasing it: Acceleration falls (a = F / m), so the vehicle needs more time and track length to reach a given speed.
How much the terminal voltage falls from no load to full load, as a percentage of the full-load voltage; lower is a stiffer source.
↑ Increasing it: Heavier load raises the drop across armature resistance or synchronous reactance, so regulation worsens; a lagging power factor makes it worse still.
The power in the wind is ½ρAv³: it grows with the cube of the wind speed, so doubling the speed gives eight times the power. The turbine can extract only a fraction of it, limited by the power coefficient, which never exceeds the Betz limit of 59 %. A turbine starts at the cut-in speed of about 3 m/s, reaches rated power at around 11–14 m/s, and is shut down at the cut-out speed of about 25 m/s to protect it.
↑ Increasing it: The available power rises with the cube of the speed, so the turbine produces much more until it reaches rated power.
Winding reactance X = 2π · f · L is the opposition of the winding inductance to alternating current. In a universal motor the field and armature windings are in series, so on AC the supply voltage divides between the resistance, the reactance and the back-EMF. A larger reactance lowers the current and torque for a given voltage and makes the current lag the voltage, which reduces the power factor. On DC the inductance has no steady effect, which is why a universal motor runs faster on DC than on AC at the same voltage.
↑ Increasing it: The AC current drops and the power factor falls, since more of the voltage appears across the inductance; on DC the reactance has no effect.
Winding resistance R is the DC resistance of one phase winding, as measured with an ohmmeter, and for copper it rises by about 0.4 % per kelvin of warming. It sets the stall or starting current, I = V / R, and causes the copper loss I² · R that heats the motor. In small BLDC, stepper and universal motors it is often the main loss, and the voltage drop across it reduces the speed under load.
↑ Increasing it: The voltage drop I · R and copper loss I² · R rise, so speed drops under load, efficiency falls, and the stall current V / R is lower.
The Zener voltage is the reverse voltage at which the diode breaks down in a controlled way and clamps its terminal voltage, specified at a test current. It makes the Zener a simple shunt regulator: a series resistor feeds it from a higher supply and the diode absorbs whatever current the load does not need. The value drifts slightly with temperature and rises a little with current because of the dynamic resistance.
↑ Increasing it: The regulated output voltage rises to the new value, and a higher supply is needed to keep the diode in breakdown.
