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Formulae Sheet Mechanical power P= TXw Inertia of a solid cylinder Ion (Goin) dwm dwm T = Jeq dt = OM + D dt Relationship between torque, acceleration and inertia Kinetic energy stored in a motor-load system 1 W= = Um +Juwm? Gear ratios - Power factor, active, reactive and apparent power in a three-phase system, and their relationships пм TM ωι nu T2 WM P= V3 VL2114 | cos(6), or P = 3|Vp1|1p| cos(0) Q = 73|VL||4) sin(O). or Q = 3|vp||1p| sin(0) Q S = 3|Vp|lipl. = tan(O). pf = cos(0) Ni Hm = Im Ni Ni Bm = Am Hm = 4m ·= HOM, Im Permeability of air (po): Mo = 410 x 10-7 Field intensity along mean path Flux density (B) of ferromagnetic materials (henries ) m e(t) = No E Leap do Relationship between voltage, flux and current di hence also V = Nºw Magnetic reluctance Im Rm = Hm Am N2 L= Rm Inductance of a simple coil Electromagnetic torque in a generic motor DC machine induced electromagnetic torque and torque constant = DC machine induced electromotive force and voltage constant = Tem = 2B,(N 1)lr Tem = kria kr = C a dr) B; Ea = kęWm kg = Ca.r) B; Va = Eq + Rala = keWm + Rala Eloss = Pross At = 1,2R 4t Tem = kris NS k = 12V1B, DC machine equivalent circuit voltage DC machine electrical energy losses AC synchronous machine (2-pole) torque and AC machine torque constant
S = n-nsyn nsyn 3(Ira)?R Tem Wslip Induction motor slip relevant to the rotor and synchronous speeds (rpm) - NOTE: S is negative for motor, positive for generator Electromagnetic torque, as a function of slip and power loss (rotor resistivity / current) Space vector representation of current Space vector angles of current and flux density in a synchronous machine AC machine magneto-motive force (mm) space vector AC machine stator field density space vector AC machine magnetising current space vector = is(t) = ia(t)20° + ip(t) 120° + ic(t)/240° 0i, (t) = 0m(t) + 90° És(t) Ns is(t) p B (t) = MONS- T's(t) plg 3 īms(t) = zſm_wt Va kpwM Vtri) = = DC motor drive converter gain Electrical frequency, rotational speed (rpm) and number of pole-pairs in a synchronous machine nxp fel = 60