IEEE Electrification Magazine - December 2017 - 64

architecture are the dc/dc con-
verter and the dc/ac converter.
iin(t )
ac Power
io(t )
The CPL behavior of the loads
System
+
Electrical
ac/dc
dc/dc
vo(t )
dc Filter vin(t )
interfaced with these two types of
Load
Converter
Converter
-
PE converters is presented in this
Pin
article for illustration.
(Constant)
Controller
The dc/dc converter is common-
to Regulate
vref
ly
used
to supply certain avionics
Voltage
dc loads (Moir and Seabridge 2011)
(Figure  2). Power system applica-
Figure 2. A dc voltage regulator behaving as a CPL to the ac power supply.
tions for the dc/dc converter
require the output voltage v o to
remain fairly constant despite
perturbations in the input line volt-
ac Power
iin(t )
age and step changes in load cur-
System
+
PM
ac/dc
dc/ac
rents. This is achieved by having a
dc Filter vin(t )
Motor
Converter
Converter
-
compensator in the negative feed-
T
Pin
back loop of the converter, which
(Constant)
Controller
automatically adjusts the duty
wr
to Regulate
wr∗
cycle under various conditions of
Speed
disturbances, to keep the output
voltage v o constant and close to
the reference voltage v ref (Erick-
Figure 3. An actuator system behaving as a CPL to the ac power supply.
son and Maksimovic 2011). Since the
electrical load as well as the output
(EMAs) (Wheeler and Bozhko 2014). Further, flight control
voltage is constant in a steady-state condition, the power
systems and flight control actuation are expected to be PE
supplied to the load is constant. With the converter efficiency
based. Many of these functions are already implemented
considered unvarying, the input power Pin drawn from the
on current aircraft, such as the Boeing 787 Dreamliner
source is also constant.
(Moir and Seabridge 2011). The Boeing 787 has a total of
Another key component of the aircraft EPS is the dc/ac
1 MW of PE loads, as shown in Figure 1 (Karimi 2007).
converter. It is employed to drive loads such as flight con-
trol actuators (Moir and Seabridge 2011). Figure 3 depicts a
System Stability
system in which the controller regulates the speed w r of a
One key drawback to PE-driven loads is that they
permanent magnet (PM) machine such that it follows the
are prone to instability. As the aircraft electrical net-
reference speed w )r (Areerak 2009). Since the speed w r as
work becomes larger and more complex, the mul-
well as the torque T are constant at a given operating
titude of PE-based loads can challenge the stability of
point, the power supplied to the load is constant. Consider-
the electrical power system (EPS) (Areerak et al. 2012,
ing that the losses of the motor and converter are constant,
Barruel et al. 2005). This is because the loads interfaced
the input power Pin drawn from the source is also constant.
through PE converters exhibit constant power load (CPL)
The aforementioned examples of PE-driven loads
behavior under fast controller actions (Areerak et al.
exhibit CPL behavior. Under infinitely fast controller
2008, Jusoh 2004). They are seen in the network as nega-
actions, they can mathematically be represented as a volt-
tive impedances (Jusoh 2004). It is the negative imped-
age controllable current source, as shown in Figure 4. At
ance of the PE-based loads that may drive the system to
any given operating point, the input voltage and input cur-
instability. Two important components in the MEA
rent to the converter system may be represented by dc val-
ues (Vin, I in), as shown in Figure 5. If the voltage increases
by dv in (t), the input current has to decrease by di in (t) to
keep the input power Pin constant ( Jusoh 2004). Hence,
Pin (Constant)
while the instantaneous impedance Vin /I in is positive, the
i
(t
)
ac Power
in
System
incremental impedance given by dv in (t) /di in (t) is negative,
+
Pin
ac/dc
dc Filter vin(t )
as shown in Figure 5.
Converter
vin(t )
-
The ideal CPL can be represented by a linearized model
Zo Zin Ideal CPL
about a given operating point and is given by the negative
impedance - R cpl connected in parallel with a current source
I cpl, as depicted by Figure 6. At any arbitrary operating point,
Figure 4. An ideal CPL representing tightly controlled power
conversion systems.
shown as E qo in Figure 5, the system currents and voltages

64

I E E E E l e c t r i f i cati o n M a gaz ine / DECEMBER 2017



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