Page 624 - Mechatronics with Experiments

610 MECHATRONICS
Therefore, the remainder of the regenerative energy must either be returned to the supply
line through a voltage regulating inverter or dissipated as heat at the regenerative resistor
and the motor winding.
Let us neglect the energy dissipated to heat at the motor winding. Hence, the remaining
energy must be dissipated at the “regen” resistors. The peak and continuous power rating
of the regenerative resistors can be calculated from

E reg − E cap
P peak = (8.22)
t dec
P = R ⋅ i 2 (8.23)
peak reg
2
V reg
= (8.24)
R reg
V 2 reg
R ≤ (8.25)
reg
P
peak
where P are peak, power dissipation capacity used to determine the regen resistor size
peak
R , E regenerative energy to be stored, V is the nominal DC bus voltage over which
reg cap reg
the regenerative circuit is active (i.e., a value between the nominal DC bus voltage and
maximum DC bus voltage, V , V ), to determine the regenerative storage capacitor
nom max
size C . In some applications, the regenerative power may be so small that the DC bus
cap
capacitor is large enough to store the energy without the need for dissipating it as heat over
resistors. Notice that the capacitor (or battery) is sized based on maximum energy, whereas
the resistor is sized based on maximum power.

8.1.2 Electric Fields and Magnetic Fields
There are two types of fields in electrical systems: electric fields and magnetic (also called
electromagnetic) fields. Although we are primarily interested in electromagnetic fields for
the study of electric motors, we will discuss both briefly for completeness. Electric fields
( ⃗ E) are generated by static charges. Magnetic fields ( ⃗ H, also called electromagnetic fields)
are generated by moving charges (current).
An electric field is a distributed vector field in space whose strength at a location
depends on the charge distribution in space. It is a function of the static location of charges
and the amount of charges. By convention, electric fields start (emitted) from positive
charges and ends (received) in negative charges (Figure 8.5a). Capacitors are commonly
used to store charges and generate electric fields. The smallest known charge is that of an
electron (negative charge) and a proton (positive charge) with units of Coulomb,C,

−
+
|e | = |p | = 1.60219 × 10 −19 C (8.26)
The electric field ⃗ E at a point in space (s) due to n many charges (q , q , … , q ) at various
1 2 n
locations can be determined from (Figure 8.5b),
n
∑ q
⃗ E(s) = k i ⋅ ⃗ e N∕C or V∕m (8.27)
e 2 i
i=1 r i
9
2
2
where k = 8.9875 × 10 N ⋅ m ∕C is called the Coulomb constant, r is the distance
i
e
between the location of charge (i) and the point in space considered (s), ⃗ e is the unit vector
i
between each charge location and the point s, q is the charge at location i. For negative
i
charges, the unit vector is directed towards the charge, for positive charges it is directed