Environmental Engineering Reference
In-Depth Information
and will be examined here for completeness. Consider again the hybrid vehicle on
level terrain and no wind. The propulsion power for this case is
1
2
r
C
d
A
f
V
3
P
ð
V
Þ¼
MV V
gMC
rr
V
ð
3
:
6
Þ
where
M
=(
M
v
+
M
pass
) and let
C
r
=
gMC
rr
and
C
a
=½
C
d
A
f
. Furthermore, note that
the propulsion system driveline power encounters at least three dissipative elements
to its flow, the losses due to electrical to mechanical energy conversion in the main
traction motor, MG1, the power inverter losses and the loss due to gear meshing in
the final drive. Accounting for these means that to sustain a constant regenerative
power,
P
b
, into the battery requires a power
P
v
at the wheels of
P
b
h
dl
h
mg
1
h
INV
P
v
¼
ð
3
:
7
Þ
Let the regen power be very modest, and within the M/G regeneration region
of Figure 3.6 at a level of
P
v
= 500W. Later in Example 4 the power will be
increased dramatically to illustrate the difference. For this case one must solve
(3.6), and this is challenging because there is no closed form solution. One
approach would be to refer to tables of integrals,
1
but this gives time as an implicit
function of velocity,
V
, which is the sought-after dependent variable. In this case
the usual approach is to employ numerical integration. A numerical solver for (3.6)
is shown in Figure 3.7 using the values for a Camry Hybrid listed earlier and for the
case of
P
v
= 500 W at the wheels.
The power set point for constant power regen is set in the lower right of
Figure 3.7 in the box showing an example case
P
v
= 29,200 to be discussed in the
V_Dot
Simulation of Camry Hybrid vehicle speed to regen 25 kW into NiMH battery
GAIN
1
Velocity and acceleration outputs
Cr_by_M
INTG1
SUM2
SUM1
Ve l
CONST
I
GAIN
1
29.06
0.0785
Mass
MUL1
MUL3
CONST
MUL2
1748.5
CONST1
CA_by_M
SUM3
CONST
CONST
0.2
MUL4
Reciprocal
0.000224
Regen power setpoint
Rec
Power_Val
Given: Driveline efficiencies:
eta_dl = 0.93
eta_mtr
CONST
=
0.95
29200
eta_INV
=
0.97
Figure 3.7 Numerical integration of (3.6) in Simplorer
1
See, for example, equation 2.172 in Reference 1.
