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Conceptual Design and Weight Optimization of Aircraft Power Systems with HighPeak Pulsed Power Loads
Q.Li 1, B.Devarajan 2, X. Zhang 1, R.Burgos 1, D.Boroyevich 1, and P.Raj 2
1 Center for Power Electronics Systems
The Bradley Department of Electrical and Computer Engineering
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061 USA
2 Department of Aerospace and Ocean Engineering
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061 USA
Abstract— The more electric aircraft (MEA) concept has gained
popularity in recent years. As the main building blocks of
advanced aircraft power systems, multi-converter power
electronic systems have advantages in reliability, efficiency and
weight reduction. The pulsed power load has been increasingly
adopted--especially
in
military
applications--and
has
demonstrated highly nonlinear characteristics. Consequently,
more design effort needs to be placed on power conversion units
and energy storage systems dealing with this challenging mission
profile: when the load is on, a large amount of power is fed from
the power supply system, and this is followed by periods of low
power consumption, during which time the energy storage
devices get charged. Thus, in order to maintain the weight
advantage of MEA and to keep the normal functionality of the
aircraft power system in the presence of a high-peak pulsed
power load, this paper proposes a novel multidisciplinary weight
optimization technique. The presented weight optimization
method mainly focuses on comparing and evaluating the weights
among different power electronics system structures based on
subsystem weight models, including the gearbox, synchronous
generator, power electronic converters and supercapacitors.
Finally, through a case study, it is shown that a system weight
reduction of 11.9 % can be attained when applying the proposed
optimization method to down-select alternative system
configurations.
I. INTRODUCTION
The more electric aircraft (MEA) concept has continued
evolving with the development of new electrical power
converter technologies. Unlike conventional aircraft
architecture where the system’s secondary power is supplied
by a combination of hydraulic, pneumatic mechanical and
electrical sources, in the MEA the electrical power system is
used to drive the majority of the aircraft subsystems [1,2]. As
such, one of the main building blocks in advanced aircraft
power systems are multi-converter power electronics systems
that have demonstrated significant advantages in terms of
reliability, efficiency and weight reduction [2].
The power conversion units used in MEAs must provide
energy under challenging mission profiles, which includes
feeding pulsed-power loads, which have been increasingly
adopted in applications that demand high peak power from
these systems, particularly military applications. Due to the
nonlinear characteristic of a pulsed power load [4], when the
load is on it consumes large amounts of power in a short period
of time, which is subsequently followed by periods of low
power consumption. These power transients are significant,
affecting the mechanical system to the point where it could
impact its physical integrity if the generator-shaft mechanism
is not designed to sustain such a loading profile. Usually, in the
case of a high-peak pulsed power load, an energy storage
system is needed to provide instant power. However, the
charging process of the energy storage system during the
pulse-off periods (ranging from a few seconds to several
minutes) stresses the power distribution network.
Supercapacitors are commonly used with pulsed-power loads.
It has larger power density than a battery--usually above
500W/kg [5]; this is an important feature in the applications
which require a power supply with a high slew rate.
Meanwhile, the supercapacitors also outperform aluminum
electrolytic capacitors in respect to energy density: a
supercapacitor’s energy density usually reaches the amount of
0.5-15Wh/kg, compared with 0.01 to 0.3Wh/kg for the
aluminum capacitors [6].
In order to maintain the weight advantage of the MEA, as
well as to keep the normal functionality of the aircraft power
systems, it is highly desirable to apply multidisciplinary
optimization techniques to this electromechanical system
under the presence of high-peak pulsed power loads.
Traditionally, both the mechanistic approach and the
simultaneous approach are applied to aircraft power system
optimization [7]. The mechanistic approach is a simple
combination of optimized subsystems and may result in an
overdesigned system. The simultaneous approach involves all
the components in its optimization process, which requires
tremendous calculation efforts. The authors of [7] thus propose
a new sequential collaborative approach which combines the
benefits of both the mechanistic and simultaneous approaches.
In [8], the authors give a comprehensive explanation of
different system optimization methodologies, including the
simultaneous design method and the multi-level design
method; they also provide design examples concerning
electromechanical systems.
Along these lines, this paper introduces a novel
multidisciplinary weight optimization method for aircraft
power systems with high-peak pulsed-power loads. The focus
of this proposed optimization method will be on evaluating the
difference between power electronics system topologies. For
the targeted power system, a combination of various
mechanical and electrical subsystems are considered,
including the engine, gearbox, synchronous generator, power
electronic converters and energy storage devices. By
developing weight models for each of these subsystems, it
becomes possible to calculate, compare, and evaluate the
weights of the power systems with different architectures.
This paper is organized as follows: An introduction of the
targeted power system is given in the second section of this
paper. The third section will present subsystem’s weight
models and an illustration of the proposed multidisciplinary
optimization technique. A case study of two different powerconversion-unit topologies is shown in the fourth section; the
comparison results validate the proposed conceptual design
and weight optimization methodology. Conclusions and future
work is presented in the last section of the paper.
II. INTRODUCTION OF POWER SYSTEM
TABLE I
ELECTRICAL SPECIFICATIONS OF POWER SYSTEM TO BE DESIGNED
Input Specifications:
Nominal Input Voltage
230 V (rms, line-neutral)
Electrical Frequency
400 Hz
Output Specifications:
Output Power
500 kW
Pulse On Time
5s
Output Voltage
270 V± 6%
Pulse Duty Cycle
20%
Peak Load Current
2000 A
Pulse Rise time, Fall
time
5 ms
Current Ripple
0.5%
Fig. 1. Structure of the power system to be designed.
A. Introduction of Power System Structure
Figure 1 shows the structure of the power system to be
designed. The entire system consists of four parts, which are
the mechanical system, the synchronous generator, the
electrical system and the high-peak pulsed power load. The
mechanical system transmits generated mechanical power
from the engine. Through the workings of the gearbox, the
mechanical power is delivered to the synchronous generator.
The brushless synchronous generator will then transform the
mechanical power into electrical power with high efficiency.
The electrical power system functions as a power conversion
unit that transforms the AC output from the generator into
270V DC voltage and feeds the load when the pulse is on. The
mission profile of the pulsed power load is shown in Figure 1,
and as can be seen from Table I, when the pulsed power load
is on, it draws 500kW power instantly. During the pulse-on
period, the electrical power system needs to supply a total of
2500kJ of energy to the load with strictly enforced input and
output electrical specifications. To complete these tasks, two
different aircraft power system topologies are proposed,
evaluated and compared. The structures of these two
topologies are shown in Figures 2 and 3.
B. Introduction of Electrical Power System Topology and
Power Flow Charts
Different electrical power systems have different power
flow patterns, and the power rating of a subsystem is the key
factor in deciding the subsystem weight. As a result, a detailed
analysis of the power flow charts is conducted in this section
for the two topologies.
Fig. 2. Proposed System Topology 1.
Fig. 3. Proposed System Topology 2.
(1). TOPOLOGY 1
Pulse-on period (𝑇𝑜𝑛 ): A parallel-structured buck converter
is directly connected with the pulsed power load to supply
power when the pulse is on. In the meantime, when the buck
converter feeds the load, it produces a power loss denoted as
𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 in Figure 4. The exact value of 𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 depends on
the power rating as well as the input and output specifications
of the buck converter. In Topology 1, the power sources of the
electrical power system, which are the synchronous generator
and the supercapacitor bank, will together provide
(500kW+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 ) amount of power to the buck converter
and then to feed the load. Here it is assumed that between these
two sources, 𝑃𝑐 amount of power is supplied by the
supercapacitor bank. Then, the power ratings of the boost
rectifier and the generator are:
𝑃𝑏𝑜𝑜𝑠𝑡_1 =500kW+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 -𝑃𝑐
(1)
𝑃𝑔𝑒𝑛_1 =500kW+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 -𝑃𝑐 + 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡1
(2)
where 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡1 stands for the power loss from the boost
rectifier during 𝑇𝑜𝑛 time.
Pulse-off period (𝑇𝑜𝑓𝑓 ): The energy storage system--the
supercapacitor bank--needs to get charged during the pulse-off
time to prepare for the next pulse period, and this amount of
energy is provided again by the generator. From Table I, it can
be easily observed that the pulse-off time 𝑇𝑜𝑓𝑓 is four times the
value of the pulse-on time 𝑇𝑜𝑛 , which is 𝑇𝑜𝑓𝑓 = 4 𝑇𝑜𝑛 . By
assuming the same charging and discharging profiles for the
supercapacitor bank and defining the power efficiency of the
supercapacitor bank to be 𝜂𝑐 , the power ratings for the boost
rectifier and the generator during pulse-off time are:
𝑃𝑏𝑜𝑜𝑠𝑡_2 =
𝑃𝑔𝑒𝑛_2 =
𝑃𝑐
4𝜂𝑐2
𝑃𝑐
4𝜂𝑐2
+ 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡2
(3)
(4)
where 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡2 stands for the power loss from the boost
rectifier during 𝑇𝑜𝑓𝑓 time.
It is fair to assume that 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡1 = 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡2 , as the
power losses are small compared with the power ratings of the
subsystems. As a consequence, the power ratings of the boost
rectifier and thus the generator are determined by the larger
value of 𝑃𝑏𝑜𝑜𝑠𝑡_1 or 𝑃𝑏𝑜𝑜𝑠𝑡_2 :
When 𝑃𝑏𝑜𝑜𝑠𝑡_1 ≥ 𝑃𝑏𝑜𝑜𝑠𝑡_2 (condition 1), which equals to
0 ≤ 𝑃𝑐 ≤
500+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘
1
4𝜂2
𝑐
1+
1
4𝜂2
𝑐
1+
< 𝑃𝑐 ≤ 500 + 𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 , the power rating of the
boost rectifier is: 𝑃𝑏𝑜𝑜𝑠𝑡 =
generator is: 𝑃𝑔𝑒𝑛 =
𝑃𝑐
4𝜂𝑐2
𝑃𝑏𝑜𝑜𝑠𝑡 = 𝑃1 + 𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_1
(5)
𝑃𝑔𝑒𝑛 = 𝑃1 + 𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_1 + 𝑃𝑏𝑜𝑜𝑠𝑡_𝑙𝑜𝑠𝑠1
(6)
𝑃𝑐𝑎𝑝 =
500kW−𝑃1 +𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
𝜂𝑐
.
(7)
Pulse-off period (𝑇𝑜𝑓𝑓 ): The generator is used to charge the
supercapacitor bank during 𝑇𝑜𝑓𝑓 . The power losses through
Buck converter 1, Buck converter 2 and the boost rectifier are
labeled as 𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_2 ,
𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_2 and 𝑃𝑏𝑜𝑜𝑠𝑡_𝑙𝑜𝑠𝑠2 ,
respectively. The amount of power fed into the supercapacitor
bank during 𝑇𝑜𝑓𝑓 is calculated as:
𝑃𝑐𝑎𝑝_𝑟𝑒𝑞 =
500kW−𝑃1 +𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
4𝜂𝑐2
.
(8)
With the above analysis, the power ratings of buck converter
2, buck converter 1, the boost rectifier and generator are:
𝑃𝑏𝑢𝑐𝑘2 =
𝑃𝑏𝑢𝑐𝑘1 =
𝑃𝑏𝑜𝑜𝑠𝑡 =
500kW−𝑃1 +𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
(9)
4𝜂𝑐2
500kW−𝑃1 +𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
4𝜂𝑐2
500kW−𝑃1 +𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
4𝜂𝑐2
+𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_2
(10)
+𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_2 + 𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_2
(11)
, the power rating of the boost rectifier
is: 𝑃𝑏𝑜𝑜𝑠𝑡 =500kW+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 -𝑃𝑐 and the power rating of the
generator is: 𝑃𝑔𝑒𝑛 =500kW+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 -𝑃𝑐 + 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡 .
When 𝑃𝑏𝑜𝑜𝑠𝑡_1 < 𝑃𝑏𝑜𝑜𝑠𝑡_2 (condition 2), which equals to
500+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘
supercapacitor bank will feed the remaining part of the power
to the load. A buck converter with parallel structure is again
connected between the supercapacitor bank and the load for
voltage, current and power regulation purposes. With this
power flow configuration, the power rating of Buck converter
2 is 𝑃2 = 500kW-𝑃1 . As the power losses of Buck converter 1,
Buck converter 2 and the boost rectifier are labeled as
𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_1, 𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1 and 𝑃𝑏𝑜𝑜𝑠𝑡_𝑙𝑜𝑠𝑠1 , the power ratings of
the boost rectifier, the generator and the supercapacitor bank
(with power efficiency 𝜂𝑐 ) during 𝑇𝑜𝑛 are:
𝑃𝑐
4𝜂𝑐2
and the power rating of the
+ 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡2 .
With the above analysis, the power ratings for all the
electrical subsystems are obtained. The results are summarized
in Table II for convenient reference.
(2). TOPOLOGY 2
Pulse-on period (𝑇𝑜𝑛 ): With power system Topology 2,
when the pulsed load is on, the 500kW load power is supplied
by two power branches simultaneously, as shown in Figure 5.
The power source of the first branch is the generator. The
power generated from the generator will go through the boost
rectifier, the parallel-structured Buck converter 1 and finally
provides 𝑃1 power to the load. For Branch 2, the
𝑃𝑔𝑒𝑛 =
500kW−𝑃1 +𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
4𝜂𝑐2
+𝑃𝑙𝑜𝑠𝑠_𝑡𝑜𝑡𝑎𝑙
(12)
where 𝑃𝑙𝑜𝑠𝑠_𝑡𝑜𝑡𝑎𝑙 = 𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_2 +𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_2+𝑃𝑏𝑜𝑜𝑠𝑡_𝑙𝑜𝑠𝑠2 .
Following the same analysis procedure used for Topology
1, the power ratings of the generator, boost rectifier, Buck
converter 1, and Buck converter 2 can be obtained by
comparing their power ratings during the 𝑇𝑜𝑛 and 𝑇𝑜𝑓𝑓
periods. The resulted power ratings for all the subsystems are
𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
listed in Table III where condition 1 equals to 500𝑘𝑊+𝑃
≤
1+4𝜂𝑐2
500𝑘𝑊+𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
𝑃1 ≤ 500𝑘𝑊 and condition 2 equals to0 ≤ 𝑃1 ≤
.
1+4𝜂2
𝑐
TABLE III
POWER RATINGS OF THE SUBSYSTEMS IN TOPOLOGY 2
Subsystem
Name
Supercapacitor
Subsystem Power Rating
𝑃𝑐𝑎𝑝 =
𝑃𝑏𝑢𝑐𝑘2 =500 kW-𝑃1
Buck
Converter2
Buck
Converter1
Fig. 4. Power flow chart of Topology 1.
𝑃𝑐𝑎𝑝
Buck Converter
Condition 2
+𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_2
4𝜂𝑐2
𝑃𝑏𝑜𝑜𝑠𝑡 = 𝑃1 + 𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_1
𝑃𝑏𝑜𝑜𝑠𝑡
500 kW−𝑃1 +𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
4𝜂𝑐2
=
+𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_2+
Generator
Condition
1
𝑃𝑔𝑒𝑛 = 𝑃1 + 𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_1
+ 𝑃𝑏𝑜𝑜𝑠𝑡_𝑙𝑜𝑠𝑠1
𝑃𝑏𝑜𝑜𝑠𝑡 =500 kW+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 -𝑃𝑐
𝑃𝑏𝑜𝑜𝑠𝑡 =
Condition 2
Generator
𝑃𝑏𝑢𝑐𝑘1 =
500 kW−𝑃1 +𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
𝑃𝑏𝑢𝑐𝑘1𝑙𝑜𝑠𝑠_2
Boost Rectifier
Condition 1
Condition
2
Condition
2
𝑃𝑐
=
𝜂𝑐
𝑃𝑏𝑢𝑐𝑘 =500 kW
Condition 1
𝑃𝑏𝑢𝑐𝑘1 = 𝑃1
Boost Rectifier
Subsystem Power Rating
Supercapacitor
Bank
Condition
1
Condition
1
TABLE II
POWER RATINGS OF THE SUBSYSTEMS IN TOPOLOGY 1
Subsystem Name
500 kW − 𝑃1 + 𝑃𝑏𝑢𝑐𝑘2𝑙𝑜𝑠𝑠_1
𝜂𝑐
𝑃𝑐
4𝜂𝑐2
𝑃𝑔𝑒𝑛 =500 kW+𝑃𝑙𝑜𝑠𝑠_𝑏𝑢𝑐𝑘 -𝑃𝑐 +
𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡1
𝑃𝑔𝑒𝑛 =
𝑃𝑐
4𝜂𝑐2
+ 𝑃𝑙𝑜𝑠𝑠_𝑏𝑜𝑜𝑠𝑡2
III. SUBSYSTEM WEIGHT MODELS AND OPTIMIZATION
TECHNIQUE
A. Subsystem Weight Models
In order to estimate the weight of the entire power system,
weight models for each of the subsystems are constructed. As
indicated in Figure 6, we need to define the input and output
parameters to and from the weight model for each of the
subsystems. Then, a mathematical equation is developed to
describe their relationships. As the focus of the paper is to
propose a conceptual design method for system weight
optimization, even though some approximations are made
when deriving the subsystem weight models, the results will
provide a good description of the weight performance of the
subsystems for this purpose. Table IV lists the input and output
variables for all the subsystems.
Fig. 5. Power flow chart of Topology 2.
Fig. 6. General subsystem weight model diagram.
TABLE IV
TABLE V
LIST OF INPUT AND OUTPUT VARIABLES OF SUBSYSTEMS
WEIGHT AND POWER OF TYPICAL AIRCRAFT AC GENERATORS
Subsystem
Input Variables
Output Variables
Gearbox
Power rating
Subsystem weight
Generator
Power rating
Subsystem weight
Boost Rectifier
Power rating;
AC input voltage;
line frequency;
DC output voltage;
switching frequency;
inductor current ripple %
Subsystem weight
Power rating;
minimum terminal voltage;
maximum terminal voltage
Subsystem weight
Buck
Converter
Power rating;
input DC voltage;
output DC voltage;
switching frequency;
inductor current ripple %;
capacitor voltage ripple %
Subsystem weight
Heat Sink
Heat sink to ambient thermal
resistance.
Subsystem weight
Supercapacitor
𝑘𝑔
Rating (kVA)
Weight (kg)
30
30.71
60
47.63
40
36.70
6000 rpm
15
17.69
60
39.55
20
19.73
120
71.26
40
14.97
105
29.48
60
18.60
12000 rpm
The gearbox weight was derived in [12] using the NASA
document which was based on actual gearbox weight data
from over fifty rotorcraft, tiltrotors, and turboprop aircraft
[13]. A linear relationship between the mass of the gearbox and
the mechanical power of the generator is given below:
𝑘𝑊
Weight (kg)
8000 rpm
B. Gearbox Weight Model
𝑚𝑔𝑒𝑎𝑟𝑏𝑜𝑥 = 0.087 ∗ (
Rating (kVA)
) ∗ 𝑃𝑔𝑒𝑛 .
(13)
C. Generator Weight Model
In order to estimate the weight of the brushless synchronous
generator, information about the power rating and rotor speed
is needed. From reference [14], the synchronous generator
weight is related to the apparent power rating as:
𝑎
Generator Weight = K ∗ (𝑃𝑔𝑒𝑛 ) (kg).
(14)
Where 𝑃𝑔𝑒𝑛 stands for the apparent power rating of the
generator, K depends on the rotor speed and 𝑎 is 0.75. Several
values of generator weight, power and rotor speed were
obtained as given in [15].
From these values and equation (14), values of K for each
rotor speed was computed, averaged and a power law
relationship was developed relating the rotor speed and K:
K = 296.8 ∗ RPM −0.608 .
(15)
Equation (15) was used to compute K for a state of the art
generator rated at 24,000 rpm.
D. Boost Rectifier Weight Model
In the electrical power system, the boost rectifier regulates
the AC output voltage from the generator to DC voltage.
Figure 7 shows the circuit diagram of a boost rectifier. In order
to estimate the entire subsystem weight, we should first
estimate the weights of individual devices, including AC
inductor 𝐿𝑎𝑐 , switching devices 𝑆1−6 , and output capacitor C.
Inductor weight estimation: Figure 8 shows the inductor
weight estimation process. Based on the known electrical
parameters (power rating, input/output voltage, line frequency,
switching frequency, and modulation scheme), the required
AC inductance can be calculated as:
1
3
𝑣ln _𝑝𝑘
2
4
𝑓𝑠𝑤 𝐼𝑟𝑝𝑝
𝐿𝑎𝑐 = (1- M)
(16)
where M is the modulation index, 𝑣ln _𝑝𝑘 is the peak input
phase voltage, 𝑓𝑠𝑤 is the switching frequency, and 𝐼𝑟𝑝𝑝 is the
peak value of the input current ripple. Equation (16) shows the
calculation of 𝐿𝑎𝑐 based on the DPWM modulation scheme.
After the selection of core shape, core material, and wire
data, the dimensions of the inductor core will begin sweeping.
The resulting inductor designs will then go through four
constraint checks, which are the wire fitting check, air gap
thickness check, core saturation check, and temperature rise
check. The inductor with the lowest weight will be selected
from all the check-passed designs.
Switching device weight estimation: 1200V single-switch
IGBT modules from Infineon are chosen as the switching
devices in this application. The weights of different power
modules are listed in Table VI. After knowing the power rating
of the boost rectifier, together with its input and output
electrical specifications, one of these IGBT modules will be
selected as the switching device.
Output capacitor weight estimation: Selection of the DC side capacitor is based on worst case analysis [10]. When a
maximum amount of power is delivered to the load with no
input power to the boost rectifier at the same time, the
capacitor must feed the load itself, and this will result in a
voltage dip of ∆𝑈 across the capacitor. In this case, the output
capacitance can be calculated based on its energy storage
equation:
C=
𝑃𝑚𝑎𝑥
(17)
1
2
(𝑈0 ∆𝑈− ∆𝑈 2 )𝑓𝑠
where 𝑈0 is the average output DC voltage of the boost
rectifier.
In contrast, when the boost rectifier has the maximum input
power but no simultaneous output power, the output capacitor
needs to sustain voltage rise ∆𝑈 as well. In this case, the
capacitor needs to be larger than:
C=
𝑃𝑚𝑎𝑥
(18)
1
2
(𝑈0 ∆𝑈+ ∆𝑈 2 )𝑓𝑠
We can then select from the off-the-shelf capacitors based
on the calculated capacitance and get the weight information
from the device’s data sheet.
E. Supercapacitor bank weight model
The
supercapacitor
bank’s
terminal
voltages
(minimum/maximum voltage across the bank) as well as its
power rating will have a significant influence on its weight.
For a supercapacitor bank with a capacitance of C and terminal
voltage variation between 𝑉𝑐_𝑚𝑎𝑥 and 𝑉𝑐_𝑚𝑖𝑛 , the total energy
stored inside the supercapacitor bank can be obtained by
applying the capacitor energy storage equation:
1
𝐸𝑡𝑜𝑡𝑎𝑙 = C(𝑉𝑐_𝑚𝑎𝑥 2 -𝑉𝑐_𝑚𝑖𝑛 2 )
(19)
2
This amount of energy will be used to supply the pulsed
power load during the 𝑇𝑜𝑛 period. The power rating 𝑃𝑐𝑎𝑝 of the
supercapacitor is derived from the subsystem power rating
analysis in the previous section. Then the total energy provided
by the supercapacitor bank during the pulse-on period is:
𝐸𝑐𝑎𝑝 =𝑃𝑐𝑎𝑝 𝑇𝑜𝑛
(20)
By equating (19) and (20), the demanded capacitance of the
supercapacitor bank can be obtained:
𝐶𝑡𝑜𝑡𝑎𝑙 =
2𝑃𝑐𝑎𝑝 𝑇𝑜𝑛
A single supercapacitor cell has a capacitance of 𝐶𝑐𝑒𝑙𝑙 , a
nominal voltage of 𝑉𝑐𝑒𝑙𝑙 , and a weight of 𝑚𝑐𝑒𝑙𝑙 . Normally, the
supercapacitor bank is connected to a DC bus with terminal
voltage 𝑉𝑑𝑐 bigger than 𝑉𝑐𝑒𝑙𝑙 . Thus, 𝑁𝑠𝑒𝑟𝑖𝑒𝑠 number of the
same type of supercapacitor cells need to be connected in
series to satisfy the terminal voltage requirement, and 𝑁𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙
number of those series-connected supercapacitor branches
need to be in parallel to store enough energy.
Fig. 7. Boost rectifier circuit diagram.
𝑁𝑠𝑒𝑟𝑖𝑒𝑠 = ⌈
𝑉𝑑𝑐
𝑉𝑐𝑒𝑙𝑙
𝑁𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = ⌈
TABLE VI
INFINEON 1200V IGBT MODULES AND THEIR WEIGHT
Current Rating
⌉
(22)
𝐶𝑡𝑜𝑡𝑎𝑙 𝑁𝑠𝑒𝑟𝑖𝑒𝑠
𝐶𝑐𝑒𝑙𝑙
⌉
(23)
In this way, the total number of supercapacitor cells in the
supercapacitor bank is: N=𝑁𝑠𝑒𝑟𝑖𝑒𝑠 *𝑁𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 . As a result, with
a single cell weight of 𝑚𝑐𝑒𝑙𝑙 , the total weight of the
supercapacitor bank is:
Fig. 8. Inductor weight estimation process.
FZ400R12KE4
400 A
Weight/each
module
340 g
FZ600R12KE4
600 A
340 g
FZ900R12KE4
900 A
340 g
FZ1200R12HE4
1200 A
1300 g
FZ1800R12HE4_B9
1800 A
1900 g
FZ2400R12HE4_B9
2400 A
1900 g
Module Part Number
(21)
𝑉𝑐_𝑚𝑎𝑥 2 −𝑉𝑐_𝑚𝑖𝑛 2
Supercapacitor bank weight = N𝑚𝑐𝑒𝑙𝑙 =
⌈
𝑉𝑑𝑐
𝑉𝑐𝑒𝑙𝑙
⌉⌈
𝐶𝑡𝑜𝑡𝑎𝑙
𝐶𝑐𝑒𝑙𝑙
⌈
𝑉𝑑𝑐
𝑉𝑐𝑒𝑙𝑙
⌉⌉ 𝑚𝑐𝑒𝑙𝑙
(kg)
(24)
E. Buck Converter Weight Model
The buck converter is a commonly used DC-to-DC voltage
regulator and its circuit diagram is shown in Figure 9. Similar
to the weight model construction process of the boost rectifier,
single-device weight estimation will be carried out first.
Inductor weight estimation: For a buck converter working
in continuous conduction mode (CCM), the inductor current
ripple should be limited to ∆𝑖𝐿 . With this current ripple
restriction, the inductance of the buck inductor should satisfy
the following relationship:
L>
𝑉
(1− 𝑜 )𝑉𝑜 𝑇𝑠
𝑉𝑖𝑛
2∆𝑖𝐿
(25)
where 𝑉𝑖𝑛 is the input voltage of the buck converter, 𝑉𝑜 is the
output voltage of the buck converter, and 𝑇𝑠 is the circuit’s
switching period.
The design flow chart of the buck inductor is similar to that
of the AC inductor, as shown in Figure 8; the buck inductor,
however, has some unique features which should be taken into
consideration in the design process: the total power loss of the
buck inductor is dominated by DC copper loss; the flux density
needs to avoid saturation; and a core material with high
saturation flux density can also be considered in this
application.
Switching device weight estimation: Again, 1200V IGBT
modules should be used in this application, and the proper
switching devices can be chosen from Table VI based on the
power rating of the Buck converter and its terminal electrical
specifications.
Output capacitor weight estimation: DC output voltage
from the Buck converter should meet the electrical
specifications for the pulsed-power load; the DC voltage ripple
percentage is kept within 6%. Setting ∆V be the output DC
voltage ripple, the minimum required capacitance is calculated
through:
C>
∆𝑖𝐿 𝑇𝑠
8∆𝑉
(26)
We can then select the off-the-shelf capacitors based on the
calculated capacitance and get the weight of the capacitor.
Fig. 9. Buck converter circuit diagram.
F. Heat Sink Weight Model
The heat sink weight model is based on the thermal flow
equivalent circuit shown in Figure 10. Power loss Q can be
expressed as:
Q=
𝑇𝑗−𝑇𝐴𝑀𝐵
𝑅𝜃𝐽𝐶 +𝑅𝜃𝐶𝐻 +𝑅𝜃𝐻𝐴
(27)
where 𝑇𝑗 is the junction temperature, 𝑇𝐴𝑀𝐵 is the ambient
temperature, and 𝑅𝜃𝐽𝐶 , 𝑅𝜃𝐶𝐻 , and 𝑅𝜃𝐻𝐴 are the junction-tocase, case-to-heat sink, and heat sink-to-ambient thermal
resistance, respectively.
Power loss Q can be calculated by analyzing the system’s
working conditions. In this paper, only the power loss from the
switching network is considered when designing the heat sink.
𝑅𝜃𝐽𝐶 and 𝑅𝜃𝐶𝐻 can be easily found from the manufacturer’s
data sheet. The maximum junction temperature is set at 150°
for the semiconductor devices, and when operating in an
aircraft environment, 70 ° is the conventional ambient
temperature. With these facts, the only unknown parameter in
(27) is the heat sink-to-ambient thermal resistance 𝑅𝜃𝐻𝐴 , and
it can be calculated directly from the other parameters.
The heat sink weight is inversely proportional to 𝑅𝜃𝐻𝐴 [11].
Equation (28) is used to approximate this relationship:
Heat Sink Weight =
0.1171
𝑅𝜃𝐻𝐴
+ 2.093 (kg)
(28)
Fig. 10. Thermal flow equivalent circuit.
IV. INTRODUCTION OF SYSTEM OPTIMIZATION
METHODOLOGY
Figure 11 shows the proposed multidisciplinary weight
optimization method of the pulsed-power-load power supply
system. For both topologies, global optimization variables are
firstly selected for the electromechanical system. Then for
each of the subsystem, local optimization variables are defined.
During the optimization process, the global variables are swept
as the outer loop for subsystem designs. The local optimization
variables will then be used to locate and store the minimum
subsystem weight for each combination of the global variable
values. By adding up all the locally-optimized subsystem
weight under the same group of global variable values, finally,
weight optimization design of the entire power supply system
is achieved.
In this paper, two electrical system topologies of interest are
studied as presented in Figure 2 and 3. For Topology 1, the
power distribution between the generator branch and the
supercapacitor branch as well as the midpoint DC voltage
between the boost rectifier and the buck converter are chosen
as the global optimization variables of the power system.
Boost rectifier transforms the three-phase AC voltage from the
synchronous generator to DC output. Three local optimization
parameters, namely the modulation scheme, the converter
switching frequency, and the boost inductor current ripple
percentage, are selected for the boost rectifier subsystem.
Meanwhile, the parallel-structured buck converter has four
local optimization variables, which are the number of
paralleled converters, switching frequency, IGBT selections
and again the filter inductor current ripple percentage.
Same global optimization parameters are used for Topology
2 as for Topology 1. The boost rectifier and buck converter 1
in the generator power supply branch share the same local
optimization variables as their counterparts in Topology 1.
However, as the input side of buck converter 2 is directly
connected with the supercapacitor bank, the supercapacitor
bank output voltage variation is added as the fifth local
optimization variable for buck converter 2. Table VII
summarizes the global and local optimization variables for
different system topologies and subsystems.
TABLE VII
OPTIMIZATION VARIABLES FOR TOPOLOGY 1 AND 2
Topology 1
Global Optimization Variables
Power distribution; midpoint DC
voltage
Boost Rectifier Local
Optimization Variables
Modulation scheme; switching
frequency; inductor current ripple %
Buck Converter Local
Optimization Variables
Number of paralleled stages;
switching frequency; IGBT
selections; inductor current ripple %
Supercapacitor Bank Local
Optimization Variables
Maximum terminal voltage;
minimum terminal voltage
Topology 2
Global Optimization Variables
Power distribution; midpoint DC
voltage
Boost Rectifier Local
Optimization Variables
Modulation scheme; switching
frequency; inductor current ripple %
Buck Converter 1 Local
Optimization Variables
Number of paralleled stages;
switching frequency; IGBT
selections; inductor current ripple %
Supercapacitor Bank and Buck
Converter 2 Power Branch
Local Optimization Variables
Number of paralleled stages;
switching frequency; IGBT
selections; inductor current ripple %;
maximum terminal voltage;
minimum terminal voltage
V. SYSTEM WEIGHT OPTIMIZATION AND COMPARISON
In this part of the paper, weight optimization of the highpeak pulsed-power-load power supply system is carried out
applying the subsystem weight models and the proposed
multidisciplinary optimization method in the previous section.
In the optimization process, the electrical specifications listed
in Table I are followed. Based on the optimization results,
comparison and evaluation of different power system
topologies are carried out and the system topology with the
minimum weight is pointed out.
A. System topology 1
System topology 1, as shown in Figure 2, has a power
system that consists of three subsystems for weight
optimization purpose, which are the boost rectifier/mechanical
subsystem, the supercapacitor bank subsystem and the
parallel-structured buck converter subsystem. From the
analysis of the power flow and the subsystem power rating
conducted in the second section of this paper, it is known that
the parallel-structured buck converter has a power rating of
500kW. In order to meet the electrical specifications listed in
Table I, the input DC voltage of the buck converter, also being
one of the global optimization variables for this topology, is
set between 650V and 800V. The lower limit of this DC
voltage is decided by the boost rectifier operating principle: the
output DC voltage must be higher than the peak line-to-line
input AC voltage. And the upper boundary of this midpoint DC
voltage is limited by the voltage ratings of the semiconductor
devices. When the pulsed power load is on, the generator
power branch and the supercapacitor power branch will
together feed 500kW power to the load; the power distribution
between these two branches is the second global optimization
variable for Topology 1.
Figure 12 shows the proposed weight optimization
procedure for Topology 1. The global optimization parameters
are firstly selected based on the system topology. For each
subsystem, local optimization variables are defined and swept
to find the minimum subsystem weight under one group of the
global variable values; then, the total power system weight is
attained by adding up the optimized subsystems’ weight. After
sweeping all the global variable value combinations and
comparing the resulted power system weight, the optimized
value is selected and stored for the topology.
B. System Topology 2
Fig. 11. Proposed multidisciplinary weight optimization method.
The weight optimization procedure for Topology 2 is
presented in Figure 13. For different power system topologies,
choice of the optimization variables varies accordingly, but the
main analysis idea stays the same. Compared with the system
structure of Topology 1, in Topology 2, the supercapacitor
bank is removed from the high voltage DC bus between the
boost rectifier and the buck converter and is directly connected
to the pulsed load to provide power when the load is on. The
most intuitive influence of this system structure modification
is that an additional local optimization variable- supercapacitor
bank terminal voltage-is used during the weight optimization
process of buck converter 2. It will also be seen from the next
section that the entire system weight is reduced dramatically
due to this topology modification; when the supercapacitor
bank is connected across a high voltage bus, large numbers of
the supercapacitor cells are need to connect in series to sustain
the high voltage which results in smaller series capacitance and
heavier cap bank.
TABLE VIII
WEIGHT OPTIMIZATION RESULTS FOR TOPOLOGY 1 AND 2
Subsystem/ system
weight (kg)
Topology 1
Topology 2
Buck Converter 1
23.45
22.90
Buck Converter 2
N/A
25.07
Supercapacitor Bank
138.8
69.68
Boost Rectifier
122.42
121.70
Mechanical System
101.96
101.37
Total System Weight
386.63
340.72
Fig. 12. Proposed weight optimization procedure for Topology 1.
Fig. 14. Weight optimization results for Topology 1 and 2—column chart.
Fig. 13. Proposed weight optimization procedure for Topology 2
C. System Weight Comparison and Evaluation
Following the weight optimization procedures shown in
Figure 12 and 13, optimized power system weight is obtained
for both topologies. And the results are presented in Table VIII
and Figure 14.
For both topologies, the optimized system weight is attained
when the generator power branch provides 400kW power to
the pulsed load when it is on; and the remaining 100kW power
is supplied by the supercapacitor power branch. Meanwhile, in
both cases, the minimum system weight is achieved with a
midpoint DC voltage of 650 V. In Topology 1, five 100kW
buck converters are connected in parallel to get the minimum
subsystem weight. Also, the same parallel structure applies to
the 400kW buck converter 1 of Topology 2.
As demonstrated in Table VIII and Figure 14, the
supercapacitor bank weight is the key factor that influences the
total power system weight. In Topology 1, the supercapacitor
bank is connected across the high DC voltage bus (650V). A
total number of 253 supercapacitor cells are connected in
series to sustain this high voltage. In order to provide more
flexibility to the terminal voltage of the supercapacitor bank,
in Topology 2, the supercapacitor bank is removed from the
midpoint DC voltage bus and is connected directly to the
pulsed power load through a buck converter. With this system
schematic modification, the nominal minimum terminal
voltage for the supercapacitor bank is reduced to 270V. This
analysis process is proved after calculating the minimum
weight for both topologies through the proposed optimization
method; a system weight reduction of 11.9 % is attained due
to the system topology modification.
VI. CONCLUSION AND FUTURE WORK
Within the concept of the more electric aircraft (MEA),
multi-converter power electronic systems have been
commonly adopted in advanced aircraft power systems.
Because of this, the authors propose a novel conceptual
multidisciplinary weight optimization methodology focusing
on different power-conversion-unit structures based on
subsystem weight models of the gearbox, synchronous
generator, the power electronic converters, the supercapacitors,
and the heat sink. For the two proposed power system
topologies, first a power flow analysis is conducted. Based on
this analysis, the power ratings of each of the subsystems are
discussed and calculated. Weight models are then constructed
for each of the electrical subsystems. Finally, following the
proposed weight optimization procedure, it is shown that
system weight reductions in the order of 11.9 % can be attained
after analyzing the weight breakdown diagrams of the
subsystems and applying the proposed optimization method to
down-select alternative system configurations.
The proposed power system weight model in this paper does
not include the subsystem weight models for the packages, the
wires, and the circuit breakers. Modeling of these subsystems
will be the focus of our future work and a more complete
weight optimization process can be expected.
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