Page 183 - Industrial Power Engineering and Applications Handbook

Static controls and braking of motors 6/163
List of formulae used Tb = braking torque in mkg

Speed control through phasor control Braking heat
j -71 - - (6.1) Hb=-. (N; - N:l) W.s
GD;
I - m +Im +I,
II = line current 730 (6.9)
I; = loss component Minimum braking torque
I,,, = magnetizing component
I, = active component
(6.10)
Field-oriented control
Electrodynamic or d.c. electric braking
T = k . I, . I, sin 8 (6.2)
8 = phasor displacement between I, and I, (electrical (6.11)
position of rotor field in space with respect to stator)
idc = braking current
= phase value of the starting current
To obtain variable V and f in IGBTs = IJ43
through PWM kl = factor to determine the equivalent ampere turns
for a particular configuration
CDF = t, + t2 + t3 + t4 + t, + t6 (6.3) TI = average load torque between running speed and
T the final speed
tl, t2 . . . t6 are the pulse widths in one half cycle Tb = average braking torque between running speed
T = one half of a cycle and the final speed
or v~,~,~ v2/CDF (6.4) Te, = braking torque of the external brakes, if provided;
=
otherwise this may be considered as zero
V = amplitude of output, voltage pulses T,, = starting torque of the motor
V,,,, = r.m.s. value of the output, a.c. voltage k2 = a factor to account for the average braking torque
To smooth output a.c. ripples Induction generator power output
dv
Q=C-
dt
GI = generator output at the same negative slip as for
Q = charge stored by the capacitor unit the motor
C = capacitance of the capacitor K = factor to account for the lower p.f. at higher
dv/dt = rate of voltage change or a.c. ripples in the d.c. negative slips, when working as an induction
link generator
IG = generator rated current in A
Current source inverter (CSI) to vary ZI and f cos @J = generator rated p.f.
di .
V = L - (ignoring R of the circuit)
dt Wind energy
V = voltage across the inductor P = 0.5 ' Cp. A ' p ' V3 (6.13)
L = large series inductor
di
- = a.c. ripples P = power generated by the windmill in watts
dt Cp = coefficient of performance
A = swept area of the rotor in m2
Computation of energy saving in a pump D = diameter of the rotor (blades) in m
p = air density = 1.225 kg/m3
V= velocity of wind at the site of installation, at the
height of hub in mts
P = shaft input in kW
Hd = head in bar Number of starts and stops
Q = discharge in m3/hour
d = specific gravity of the liquid in g/cm3 ZL = ZNL. x' (6.14)
KL
17 = efficiency of the pump Kb
Z, = number of starts and equivalent stops per hour on
Braking time load
ZNL = permissible number of starts per hour with free
GD; .N shaft
375 . Tb Kb = factor of braking
tb = ~ seconds(s)
N = N, - N,, (i.e. speed reduction in r.p.m.) KL = mean load factor