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A method to improve the efficiency of an electric aircraft propulsion system
Energy 140 (2017) 436e443
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Energy journal homepage: www.elsevier.com/locate/energy
A method to improve the efficiency of an electric aircraft propulsion system Shaohua Ma a, Shuli Wang a, b, Chengning Zhang c, Shuo Zhang c, * a
School of Electrical Engineering, Shenyang University of Technology, Shenyang, 110023, China General Aviation Laboratory, Shenyang Aerospace University, Shenyang, 110136, China c National Engineering Laboratory for Electric Vehicles, School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 10081, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 September 2016 Received in revised form 15 August 2017 Accepted 21 August 2017 Available online 24 August 2017
An electric aircraft propulsion system utilizes a high efficiency motor to generate thrust for electric aircraft. However, it can be challenging to maintain high efficiency for the fixed pitch propeller, which is commonly used in electric aircraft, through all phases of the flight. This paper investigates the power demands of the electric aircraft during the climb and the cruise phases according to the flight profile, and presents a model to estimate the energy consumption per flight. Simulation results suggest that the efficiency in the climb and the cruise phases can affect the energy consumption of an electric aircraft. Efficiency during the climb phase can have a significant effect on the capacity of the electric aircraft propulsion system. Based on the aforementioned results, this paper proposes a novel approach to achieve high efficiency, in which the optimal efficiency points of the electric aircraft propulsion system in the climb and the cruise phases can be obtained by solving an optimization problem with minimizing the energy consumption per flight as the object function and under the constraints that the climb and cruise phases must be successful. For testing purposes, the proposed method is adopted to the design of the electric aircraft propulsion system on a specific two-seater electric aircraft. Experimental results obtained from real flights suggest that the proposed method can reduce the energy consumption of the electric aircraft by over 10%, while reducing the capacity demand for the electric aircraft propulsion system. © 2017 Published by Elsevier Ltd.
Keywords: Electric aircraft propulsion system Efficiency in climb phase Efficiency in cruise phase Energy consumption
1. Introduction The electric aircraft is an environment-friendly aircraft in terms of cost, efficiency, safety and environmental protection [1]; therefore, many countries such as Europe, USA and China have been developing electric aircraft [2]. Nowadays, a variety of electric aircraft including electric model aircraft, electric unmanned aircraft and electric rotor aircraft, as well as electric glider, serve many fields including industrial production, agriculture, forestry, animal husbandry, education, entertainment [3]. However, there are still many unresolved issues for developing electric aircrafts [4]. The batteries are the power source of an electric aircraft [5]. Due to the limitation of battery energy-density, only a few types of batteries can be applied to electric aircrafts [6]. So far, three types of batteries: lithium batteries, air/metal batteries and graphene batteries are believed to be suitable for electric aircraft [7]. However,
* Corresponding author. E-mail address: [email protected] (S. Zhang). http://dx.doi.org/10.1016/j.energy.2017.08.095 0360-5442/© 2017 Published by Elsevier Ltd.
air/metal batteries and graphene batteries are still in the research stage [8]; therefore, only lithium batteries have been applied to electric aircraft. Although the energy density of lithium batteries can theoretically reach 300 W$h/kg [9], the actual practical capacity is much lower to satisfy the structure requirement [10]. For a twoseater electric aircraft, its power demand is about 20 kW during the cruise phase, and the weight of its equipped batteries is less than 100 kg [11]. In addition, given the limited batteries life, which is usually less than 1 h, the power demand during take-off, climbing and landing phases has to be taken into consideration as well [12]. To design high performance electric aircraft propulsion system (EAPS) for electric aircraft and to improve the endurance of electric aircraft, improvements must be made, such as choosing the motor with higher power and lighter weight [13]. Currently, there is still little research on improving the efficiency of the EAPS of electric aircraft and the EAPS is not utilized properly to fulfill its full potential [14]. The EAPS generates the thrust for an electric aircraft. An EAPS consists of a controller, a permanent magnet synchronous machine (PMSM), a propeller and a set of batteries [15]. The PMSM and the
S. Ma et al. / Energy 140 (2017) 436e443
controller have a wide high-efficiency operation range. In comparison, the fixed pitch propeller, which is usually used on a smallsize electric aircraft, has very limited operation range to achieve high efficiency throughout entire flight [16]. As the result, the propeller usually operates at its peak efficiency during the cruise phase to reduce the overall energy consumption [17]. However, peak efficiency during the cruise phase does not guarantee that the EAPS will be operating at high efficiency during climbing phase. The climbing phase demands large amount of power, which is at least 2.5 times of the power required in the cruise phase [18]; therefore, the capacity of the EAPS must take consideration of the power demand during the climb phase. Low efficiency during the climb phase results in additional capacity requirement for the EAPS, which increase the weight of the EAPS and by extension, increase the energy consumption [19]. This paper presents a novel approach to improve the efficiency of the EAPS. The power demands of an electric aircraft during the climb and the cruise phases, as well as the efficiency of the EAPS are analyzed. The best efficiency points of the EAPS during the climb and the cruise phases can be obtained by optimizing its energy consumption. The method presented in this paper is used to design the EAPS for manned electric aircraft. Experimental results show that the proposed method can effectively reduce the energy consumption of the EAPS and increase the battery-life of the electric aircraft [20]. The rest of this paper is organized as following: Section 2 discusses the energy consumption of the EAPS in different flight phases. The proposed method to achieve the best efficiency points of the EAPS is introduced in section 3. Section 4 presents experiments results obtained from the real flight tests. Section 5 presents the conclusion of this paper. 2. Energy consumption of EAPS 2.1. Flight profile of electric aircraft The flight profile of an electric aircraft is shown in Fig. 1, which can be separated into four phases: take-off (from 0 to 1 min), climbing (from 1 min to 4 min), cruising (from 4 min to 34 min) and landing (from 34 min to 38 min). Energy consumption varies from phase to phase. For instance, the take-off phase requires similar power output to the cruise phase. However, it only contributes to less than 2% of the total energy consumption due to its short interval (usually around 1 min). The climb phase, which usually last for 3 min, constitutes about 20% of the total energy consumption and its power requirement is 2.5 times of the cruise phase power. Despite of its relative lower power requirement comparing to the climb phase, the cruise phase still makes up more than 75% of the
437
total energy consumption for flights over 30 min. The landing phase consumes the least amount of energy at about 0.5% of the total energy consumption. Its power requirement is 40% of the cruise phase power. It can be concluded that, the take-off and landing phases combined are less than 2.5% of the total energy consumed due to their low power requirement and short operation time. Considering the limited impact from the take-off and the landing phases, the proposed model for analyzing power and energy consumption only involves the climb and the cruise phases [21]. 2.2. Principle of EAPS Unlike airplanes powered by internal combustion engines, an electric aircraft is powered by the EAPS. As shown in Fig. 2, the EAPS consists of the following components: the controller (which has a drive module and a control module), the motor, the power batteries, the user interface (power integrated display), the throttle stick, the auxiliary power and other miscellaneous components. During the flight, the pilot in the aircraft cockpit controls the throttle lever, which outputs an analog signal to the control module of the controller. The control module adjusts the output of the drive module according to the analog quantity. The drive module of the controller converts direct current (DC) supplied by the power batteries into alternating current (AC) to drive the motor and the motor rotates the propeller to generate thrust for the airplane. The power batteries are fully charged and installed before the flight and removed from the airplane for charging after the flight. Usually, an electric aircraft is equipped with two or more rechargeable batteries to guarantee sufficient energy. Batteries recharged more than 800 times or containing less than 85% of initial capacity are removed from service and recycled. The pilot can obtain information about the status of the motor, the controller, and the power batteries through the power integrated display on the front panel. The power integrated display and the control module of the controller are powered by a 24VDC lithium battery [22]. 2.3. Energy consumption of EAPS As mentioned in section 2.1, the climb and the cruise phases contributes to more than 95% of the total energy consumption. The other two phases are ignored for now [23]. The power requirement for climbing and cruise is determined by the propeller, which can be calculated as the product of the thrust of the propeller and the aircraft velocity. i.e.
Ppro ¼ T pro ,v
(1)
where, Tpro is the thrust generated by the propeller and v is the
Fig. 1. Flight profile of electric aircraft.
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S. Ma et al. / Energy 140 (2017) 436e443
Fig. 2. System block diagram of electric aircraft propulsion system.
aircraft velocity. Limited by its construction and weight, an electric aircraft usually uses fixed pitch propellers. The thrust generated from a fixed pitch propeller is [24]:
8 > prR4pro Ct 2 > > < Tpro ¼ npro 2 > > > : r ¼ 0:0034831Ap T
prR4 Ct
f
¼ kn2pro
f
Tpro
c
¼ kn2pro
c
Tpro f vf ðtÞdt Ztf
¼
kn2pro f
(5) vf ðtÞdt
0
(3)
Tpro
f
¼ 0
(2)
where, k ¼ 2pro . Climbing requires the highest power out of the entire flight; therefore, the propeller rotational speed is higher in the climb phase comparing to the cruise phase. Let npro_f denotes the propeller rotational speed during the climb phase and npro_c denotes the propeller rotational speed during the cruise phase, their corresponding thrusts can be calculated as:
(
Ztf Wpro
where, Rpro is the radius of the propeller, Ct is the tension coefficient of the propeller, npro is the rotational speed of the propeller,r is the air density, Ap is the atmosphere pressure and T is the absolute atmospheric temperature. It can be concluded from Eqn. (2) that the thrust generated by the propeller is proportional to the square of its rotational speed under constant temperature and pressure.
Tpro ¼ kn2pro
Tpro_c is the propeller thrust during the cruise phase. The work done by the propeller during the climb phase is:
(4)
where, Tpro_f is the propeller thrust during the climb phase and
¼ kn2pro f vf
av tf
where, Wpro_f is the work done by the propeller during the climb phase, tf is time for climbing, Tpro_f is the climb thrust generated by the propeller, vf(t) is the aircraft velocity during the climb phase, vf_av is the aircraft average velocity during the climb phase. The work done by the propeller during the cruise phase is:
Wpro
c
¼ Tpro c vc tc ¼ kn2pro c vc tc
(6)
where, Wpro_c is work done by the propeller during the cruise phase, tc is the cruise time, Tpro_c is the cruise thrust generated by the propeller, vc is the aircraft velocity during the cruise phase. The energy consumed by the EAPS during the climb phase is:
Qf ¼
Wpro
hf
f
¼
kn2pro
hf
f
,vf
av tf
(7)
where, hf is the efficiency of the EAPS during the climb phase. It can be observed from Eqn. (7) that the energy consumption during the climb phase is related to the rotational speed of the propeller, the climb time of the aircraft and the climb average velocity of the aircraft.
S. Ma et al. / Energy 140 (2017) 436e443
The energy consumption during the cruise phase is:
Qpro
c
¼
Wpro
hc
c
¼
kn2pro
hc
c
vc tc
(8)
where, hc is the efficiency of the EAPS during the cruise phase. From Eqn. (8), it can be concluded that the energy consumption during the cruise phase is related to the rotational speed of the propeller, the cruise velocity of the aircraft and the cruise time of the aircraft. Ignoring the energy consumption during the take-off phase and the landing phase given their limited impact, the energy consumed during one flight can be approximated as:
Q ¼k
n2pro
hf
f
,vf
av tf þ
n2pro
hc
! c
,vc tc
439
v is the aircraft velocity. The following equation describes the relation between the takeoff speed and the rotational speed of the propeller. It can be obtained from Eqn. (10) and Eqn. (4) [26]:
rSCd 2
vf ðtÞ2 þ m
dvf ðtÞ ¼ kn2pro dt
f
mg sin q
(11)
Leta ¼ m; b ¼ rSCd =2; c ¼ kn2pro f mg sin q, and if the initial speed of the aircraft is the vf0, the solution of Eqn. (11) is:
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi 1 þ b=cvf ðtÞ 1 þ b=cvf 0 a a pffiffiffiffiffiffiffiffi pffiffiffiffiffi ln pffiffiffiffiffiffiffiffi ¼t pffiffiffiffiffi ln 2 bc 1 b=cvf ðtÞ 2 bc 1 b=cvf 0
(12)
Thus, the climb velocity of the aircraft is:
(9)
where, Q is the energy consumption during one flight. It is shown in Eqn. (9) that the total energy consumption is related to the average climb velocity of the aircraft, the climb time of the aircraft, the cruise velocity of the aircraft, the cruise time of the aircraft, the rotational speed of the propeller during the climb and the cruise phases. In addition, the energy consumption can also be affected by the efficiency of the EAPS. Although the flying distance during the climb phase is limited comparing to the cruise phase, the propeller rotational speed is much higher; therefore, the energy consumption during the climb phase still contributes to a significant portion of the total energy consumption. On the other hand, the lower efficiency of the EAPS during the climb phase may require higher power motor and controller to compensate, which can increase the weight of the EAPS and consequently increase its energy consumption. To reduce the energy consumption of the EAPS, the rotational speeds of the propeller during the climb and the cruise phases can be determined under the constraint that the aircraft must stay airborne. In addition, the best efficiency points during the climb phase and the cruise phase should be determined to reduce the total energy consumption.
exp tþq t 1i vf ðtÞ ¼ h tþq p exp t þ 1 where,p ¼ q¼t
qffiffi b c
¼
(13)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rSCd ;t 2ðk1 npro mg sin qÞ f
¼
paffiffiffiffi 2 bc
m ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2rSCd ðknpro f mg sin qÞ
1þpv ln 1pvff 00 .
The climb speed of the aircraft v must always be greater than vset_f (the minimum climbing speed) to avoid aircraft stalling. During the cruise phase, the airplane travels at constant velocity horizontally. The cruise velocity of the aircraft can be obtained from Eqn. (14) and Eqn. (4):
sffiffiffiffiffiffiffiffiffiffi 2k n vc ¼ rSCd pro
c
(14)
The cruise speed of the aircraft cannot be less than vset_c (the minimum cruise speed) to prevent aircraft stalling.
3. Efficiency matching of EAPS 3.1. Speed and efficiency characteristics of EAPS
2.4. Propeller rotational speed requirements during climb and cruise phases
The efficiency of the EAPS is:
As shown in Eqn. (9), the energy consumption of the EAPS is proportional to the square of the rotational speed of the propeller during the climb and the cruise phases. However, low rotational speed of the propeller can decrease the speed of the aircraft, which may lead to accident due to insufficient flight height; therefore, the operating speed of the airplane and the propeller during the climb phase and the cruise phase cannot be too low. The minimal required speed of the aircraft during the climb and the cruise phases can be obtained from the tech specs of the aircraft model. Using the lowest operating speed available, it is possible to get the best efficiency points of the EAPS during the climb phase and the cruise phase by optimizing Eqn. (9). The velocity of the airplane can be calculated as [25]:
8 dv > > < Tpro ¼ Ad þ mg sin q þ m dt > r SC > d 2 :A ¼ v d 2
(10)
where, Ad is the air resistance, m is the mass of the airplane, g is acceleration of gravity, q is the climb angle of the aircraft, r is the air density, S is the area of the wing, Cd is the resistance coefficient and
h ¼ hco hmo hpro
(15)
where, hco is the efficiency of the controller, hmo is the efficiency of the motor, hpro is the efficiency of the propeller. To drive the motor, the controller transforms DC current generated by the batteries to AC. The DC to AC transformation also consumes energy at the controller and the amount of energy consumption is related to the rotational speed of the propeller [27]; therefore, the characteristic curve between the propeller rotational speed and the efficiency of the controller is nonlinear [28]. The motor directly drives propeller rotation. Its power is related to the rotational speed and the torque of the propeller; therefore, the characteristic curve between the propeller rotational speed and the efficiency of the motor is also nonlinear [29]. The design and selection of the controller and the motor must satisfy the power demand during the climb phase, since climbing phase demands the highest power. Additionally, to reduce the energy consumption of the EAPS, it is preferred to use PMSM and corresponding controller, since they can maintain high efficiency during the cruise and the climb phases [30]. The efficiency of the propeller satisfies the following set of equations [31]:
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S. Ma et al. / Energy 140 (2017) 436e443
8 60vfl > > > l¼ > > n Rpro pro > > > > > > Tpro > > CT ¼ 2 4 > > > rnpro Rpro > > < Ppro > CW ¼ 2 5 > > > r npro Rpro > > > > > > CT l > > > > hpro ¼ C > > W > > : Ppro ¼ 2pnpro Mpro
(16)
where, l is the propeller advance ratio, Ct is the thrust coefficient, Cw is the power coefficient, Rpro is the propeller radius, npro is the propeller rotational velocity, Tpro is the propeller thrust, vfl is the fluid velocity, Ppro is the propeller input power and Mpro is the propeller torque. It can be derived by Eqn. (16)
hpro ¼
30rvfl CT npro R4pro
pMpro
(17)
The propeller torque Mpro, is the same as the torque of the motor driving it. The torque of the motor is not linearly related to its velocity as shown in Fig. 3; therefore, the characteristic curve of the propeller efficiency is also non-linear. The propeller is usually utilized at its peak efficiency during the cruise phase to reduce the total energy consumption. However, it may cause two issues: (1) The climb phase demands the highest power and it limits the design and the selection of the EAPS. The lower efficiency during the climb phase requires higher capacity motor and controller to compensate and increases the weight, volume, and cost of the EAPS. (2) As the weight of the EAPS increases, the weight of the aircraft also increases. As the result, energy consumption increases. Although utilizing the propeller at its peak efficiency point during
Fig. 4. Performance of propeller.
the climb phase may reduce the cost of the motor and the controller in the EAPS while producing sufficient power for climbing, it unfortunately prevents the EAPS from high efficiency operation during the cruise phase and increases the overall energy consumption. As shown in the previous discussion, for an electric aircraft using fixed pitch propellers, utilizing the propeller between its peak efficiency points of the climb and the cruise phase can result the minimum energy consumption. This paper proposes the method to find the optimal energy consumption efficiency points of the EAPS
Fig. 3. Rpm, torque and power curve of the experimental motor.
S. Ma et al. / Energy 140 (2017) 436e443
Fig. 5. Aircraft ground test.
during the climb and the cruise phases by solving the minimum energy consumption of the EAPS. 3.2. Efficiency matching of EAPS Eqn. (9) shows that the energy consumed by the EAPS is related to the average velocity of climb, the time of climb and the rotational velocities of the propeller during the climb and cruise phases. The controller and the motor of the EAPS are designed to provide sufficient power and capable of operating at high efficiency during climbing and cruise. However, the fixed pitch propeller, which is commonly used in electric airplanes due to its small size, cannot maintain high efficiency for both cruise and climb phases. In addition, the lower EAPS efficiency could increase the weight of the airplane, since higher power motor and its controller are required to meet the power demand during climbing. This paper proposes a method to reduce the energy consumption for both climbing and cruise by optimizing the energy consumed by the EAPS [32]. The objective function describing the energy consumption of the EAPS is:
minf ppro f ; ppro c ; hf ; hc ¼ mink
n2pro
hf
f
,vf
av tf
s:t: 8 vf av vset f > > > > > > vc vset c > > > > > < hpro ¼ f1 npro ; Tmo > h ¼ f2 npro ; Tmo > > > mo > > > > > hco ¼ f3 npro ; Tmo > > : h ¼ hco hmo hpro
þ
n2pro
hc
! c
,vc tc
(18)
441
corresponding propellers. Propeller 1 is designed to operate at maximum efficiency during climb and propeller 2 is designed to achieve its peak efficiency during cruise as shown in Fig. 4. The thrust requirement during cruise is 75 kg and the propeller rotational velocity during climbing is 2200 rpm. Flight profile is shown as Fig. 1. The cruise distance is 50 km at 1 km flight height and the angle of climb during climbing is 0.12. The efficiency of the motor during both the climb phase and the cruise phase are 92%. Capacity of the batteries is 12 kWh. Experimental results show that the energy consumed of the EAPS using propeller 1 is 8.4 kWh. In comparison, design with propeller 2 consumes 9 kWh of energy after completing the same flight. The batteries residual quantity displayed on the power integrated display on the front panel are 30% and 25% respectively. By adopting the proposed method, the peak efficiency of the propeller obtained from Eqn. (18) using randomized search method is approximately 1700 rpm. The propeller rotational velocity during climbing is 2200 rpm and the propeller rotational speed is 1650 rpm during the cruise phase. At this speed, the aircraft is estimated to consume minimum energy per flight. This design is adopted to the EAPS with the double blade wooden propeller, the PMSM and the controller. Photos of the aircraft and the propeller are shown in Fig. 5 and Fig. 6 respectively. The test results are shown in Fig. 7. Data is obtained from experiments using wind tunnel test at 72 km/h air velocity. Propeller rotational velocities between 1300 rpm and 2200 rpm are tested, since only the climb phase and the cruise phase are considered. As shown in Fig. 7, as the propeller rotational velocity increases, the thrust generated by the propeller increases. The motor is operating at high efficiency once the propeller rotational velocity exceeds 1300 rpm, which is similar to the PMSM. Once the propeller rotational velocity exceeds 1300 rpm, the controller reaches its peak efficiency. However, the efficiency of the controller slightly decreases as the propeller rotational velocity increases further. Such phenomenon can be explained as the result of the increasing propeller current incurring larger switching losses at the controller. Finally, the peak efficiency for the propeller occurs at around 1720 rpm, which is extremely close to the estimated 1700 rpm. Considering the 75 kg thrust demand, the corresponding rotational velocities of the propeller are respectively 1650 rpm for cruising and 2200 rpm for climbing. The energy consumed per flight is 7.15 kWh. It leaves 4.85 kWh of energy remaining on the batteries with 12 kWh total capacity. Comparing to the previous
The aircraft velocities for climbing and cruise are related to its motor, which can be obtained through Eqn. (13) and Eqn. (14). Eqn. (18) describes an optimization problem with constraints, whose solution can be obtained with randomized search method. 4. Method validation To examine the proposed method, experiments were conducted on the two-seater electric aircraft with the following design requirements: the maximum take-off weight is 480 kg, the cruise speed is 100 km/h, the climb speed is 90 km/h, the angle of climb is 0.12, and the maximum flight height is 1 km. Its flight profile is: take-off (1 min), climbing (3 min), cruising (30 min) and landing (4 min) [33]. Two propulsion systems were designed for this aircraft with
Fig. 6. Propeller wind tunnel test.
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S. Ma et al. / Energy 140 (2017) 436e443
Fig. 7. Test results of EAPS.
systems, the proposed design saves 1.25 kWh and 1.85 kWh respectively. The batteries residual quantity displayed on the power integrated display on the front panel is 40% after completing the flight. 5. Conclusion This paper proposes a method to reduce the energy consumption of the electric aircraft based on the study on an electric aircraft propulsion system (EAPS)of a two-seater electric aircraft. The efficiency of the EAPS is related to the efficiency of the motor, the controller and the propeller. The motor and the controller are capable of high efficiency operation through the entire flight, while the propeller has a narrow high efficiency operating range. Therefore, the efficiency of the EAPS is largely affected by the efficiency of the propeller. The climb phase demands 2.5 times of power required for cruise and consume more than 20% of the total energy. The cruise phase consumes approximate 75% of the total energy. The capacity and energy consumption of the EAPS are related to the efficiency of the EAPS.
With the total energy consumption as the object function based on the flight profile, and under the constraint that guarantee safe climbing and cruise, the proposed method can obtain the optimized operating point of the EAPS to achieve high efficiency to greatly reduce the energy consumption of the EAPS on the electric aircraft. The proposed method is tested and verified with real flight tests. Experimental results demonstrate the effectiveness with more than 15% improvement compared to conventional configuration. References [1] Hu XS, Zou Y, Yang YL. Greener plug-in hybrid electric vehicles incorporating renewable energy and rapid system optimization. Energy 2016;111:971e80. [2] Hyderak. A century of aerospace electrical power technology. J Propuls Power 2003;19(6):1155e79. [3] Stoll Alex M. Drag reduction through distributed electric propulsion.14th AIAA aviation Technology. Integration, and Operations Conference; 2014. [4] Zhao CH, Chen LW. Technical progress of electric aircraft. Sci Technol Rev 2013;30(12):62e70. [5] Lawrence Dale A. Efficiency analysis for long-duration electric aircraft. American Institute of Aeronautics and Astronautics; 2015. [6] Takahashi Kenichiro, Fujimoto Hiroshi. Modeling of propeller electric airplane and thrust control using advantage of electric motor.AMC2014-Yokohama.
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A method to improve the efficiency of an electric aircraft propulsion system Shaohua Ma a, Shuli Wang a, b, Chengning Zhang c, Shuo Zhang c, * a
School of Electrical Engineering, Shenyang University of Technology, Shenyang, 110023, China General Aviation Laboratory, Shenyang Aerospace University, Shenyang, 110136, China c National Engineering Laboratory for Electric Vehicles, School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 10081, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 September 2016 Received in revised form 15 August 2017 Accepted 21 August 2017 Available online 24 August 2017
An electric aircraft propulsion system utilizes a high efficiency motor to generate thrust for electric aircraft. However, it can be challenging to maintain high efficiency for the fixed pitch propeller, which is commonly used in electric aircraft, through all phases of the flight. This paper investigates the power demands of the electric aircraft during the climb and the cruise phases according to the flight profile, and presents a model to estimate the energy consumption per flight. Simulation results suggest that the efficiency in the climb and the cruise phases can affect the energy consumption of an electric aircraft. Efficiency during the climb phase can have a significant effect on the capacity of the electric aircraft propulsion system. Based on the aforementioned results, this paper proposes a novel approach to achieve high efficiency, in which the optimal efficiency points of the electric aircraft propulsion system in the climb and the cruise phases can be obtained by solving an optimization problem with minimizing the energy consumption per flight as the object function and under the constraints that the climb and cruise phases must be successful. For testing purposes, the proposed method is adopted to the design of the electric aircraft propulsion system on a specific two-seater electric aircraft. Experimental results obtained from real flights suggest that the proposed method can reduce the energy consumption of the electric aircraft by over 10%, while reducing the capacity demand for the electric aircraft propulsion system. © 2017 Published by Elsevier Ltd.
Keywords: Electric aircraft propulsion system Efficiency in climb phase Efficiency in cruise phase Energy consumption
1. Introduction The electric aircraft is an environment-friendly aircraft in terms of cost, efficiency, safety and environmental protection [1]; therefore, many countries such as Europe, USA and China have been developing electric aircraft [2]. Nowadays, a variety of electric aircraft including electric model aircraft, electric unmanned aircraft and electric rotor aircraft, as well as electric glider, serve many fields including industrial production, agriculture, forestry, animal husbandry, education, entertainment [3]. However, there are still many unresolved issues for developing electric aircrafts [4]. The batteries are the power source of an electric aircraft [5]. Due to the limitation of battery energy-density, only a few types of batteries can be applied to electric aircrafts [6]. So far, three types of batteries: lithium batteries, air/metal batteries and graphene batteries are believed to be suitable for electric aircraft [7]. However,
* Corresponding author. E-mail address: [email protected] (S. Zhang). http://dx.doi.org/10.1016/j.energy.2017.08.095 0360-5442/© 2017 Published by Elsevier Ltd.
air/metal batteries and graphene batteries are still in the research stage [8]; therefore, only lithium batteries have been applied to electric aircraft. Although the energy density of lithium batteries can theoretically reach 300 W$h/kg [9], the actual practical capacity is much lower to satisfy the structure requirement [10]. For a twoseater electric aircraft, its power demand is about 20 kW during the cruise phase, and the weight of its equipped batteries is less than 100 kg [11]. In addition, given the limited batteries life, which is usually less than 1 h, the power demand during take-off, climbing and landing phases has to be taken into consideration as well [12]. To design high performance electric aircraft propulsion system (EAPS) for electric aircraft and to improve the endurance of electric aircraft, improvements must be made, such as choosing the motor with higher power and lighter weight [13]. Currently, there is still little research on improving the efficiency of the EAPS of electric aircraft and the EAPS is not utilized properly to fulfill its full potential [14]. The EAPS generates the thrust for an electric aircraft. An EAPS consists of a controller, a permanent magnet synchronous machine (PMSM), a propeller and a set of batteries [15]. The PMSM and the
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controller have a wide high-efficiency operation range. In comparison, the fixed pitch propeller, which is usually used on a smallsize electric aircraft, has very limited operation range to achieve high efficiency throughout entire flight [16]. As the result, the propeller usually operates at its peak efficiency during the cruise phase to reduce the overall energy consumption [17]. However, peak efficiency during the cruise phase does not guarantee that the EAPS will be operating at high efficiency during climbing phase. The climbing phase demands large amount of power, which is at least 2.5 times of the power required in the cruise phase [18]; therefore, the capacity of the EAPS must take consideration of the power demand during the climb phase. Low efficiency during the climb phase results in additional capacity requirement for the EAPS, which increase the weight of the EAPS and by extension, increase the energy consumption [19]. This paper presents a novel approach to improve the efficiency of the EAPS. The power demands of an electric aircraft during the climb and the cruise phases, as well as the efficiency of the EAPS are analyzed. The best efficiency points of the EAPS during the climb and the cruise phases can be obtained by optimizing its energy consumption. The method presented in this paper is used to design the EAPS for manned electric aircraft. Experimental results show that the proposed method can effectively reduce the energy consumption of the EAPS and increase the battery-life of the electric aircraft [20]. The rest of this paper is organized as following: Section 2 discusses the energy consumption of the EAPS in different flight phases. The proposed method to achieve the best efficiency points of the EAPS is introduced in section 3. Section 4 presents experiments results obtained from the real flight tests. Section 5 presents the conclusion of this paper. 2. Energy consumption of EAPS 2.1. Flight profile of electric aircraft The flight profile of an electric aircraft is shown in Fig. 1, which can be separated into four phases: take-off (from 0 to 1 min), climbing (from 1 min to 4 min), cruising (from 4 min to 34 min) and landing (from 34 min to 38 min). Energy consumption varies from phase to phase. For instance, the take-off phase requires similar power output to the cruise phase. However, it only contributes to less than 2% of the total energy consumption due to its short interval (usually around 1 min). The climb phase, which usually last for 3 min, constitutes about 20% of the total energy consumption and its power requirement is 2.5 times of the cruise phase power. Despite of its relative lower power requirement comparing to the climb phase, the cruise phase still makes up more than 75% of the
437
total energy consumption for flights over 30 min. The landing phase consumes the least amount of energy at about 0.5% of the total energy consumption. Its power requirement is 40% of the cruise phase power. It can be concluded that, the take-off and landing phases combined are less than 2.5% of the total energy consumed due to their low power requirement and short operation time. Considering the limited impact from the take-off and the landing phases, the proposed model for analyzing power and energy consumption only involves the climb and the cruise phases [21]. 2.2. Principle of EAPS Unlike airplanes powered by internal combustion engines, an electric aircraft is powered by the EAPS. As shown in Fig. 2, the EAPS consists of the following components: the controller (which has a drive module and a control module), the motor, the power batteries, the user interface (power integrated display), the throttle stick, the auxiliary power and other miscellaneous components. During the flight, the pilot in the aircraft cockpit controls the throttle lever, which outputs an analog signal to the control module of the controller. The control module adjusts the output of the drive module according to the analog quantity. The drive module of the controller converts direct current (DC) supplied by the power batteries into alternating current (AC) to drive the motor and the motor rotates the propeller to generate thrust for the airplane. The power batteries are fully charged and installed before the flight and removed from the airplane for charging after the flight. Usually, an electric aircraft is equipped with two or more rechargeable batteries to guarantee sufficient energy. Batteries recharged more than 800 times or containing less than 85% of initial capacity are removed from service and recycled. The pilot can obtain information about the status of the motor, the controller, and the power batteries through the power integrated display on the front panel. The power integrated display and the control module of the controller are powered by a 24VDC lithium battery [22]. 2.3. Energy consumption of EAPS As mentioned in section 2.1, the climb and the cruise phases contributes to more than 95% of the total energy consumption. The other two phases are ignored for now [23]. The power requirement for climbing and cruise is determined by the propeller, which can be calculated as the product of the thrust of the propeller and the aircraft velocity. i.e.
Ppro ¼ T pro ,v
(1)
where, Tpro is the thrust generated by the propeller and v is the
Fig. 1. Flight profile of electric aircraft.
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Fig. 2. System block diagram of electric aircraft propulsion system.
aircraft velocity. Limited by its construction and weight, an electric aircraft usually uses fixed pitch propellers. The thrust generated from a fixed pitch propeller is [24]:
8 > prR4pro Ct 2 > > < Tpro ¼ npro 2 > > > : r ¼ 0:0034831Ap T
prR4 Ct
f
¼ kn2pro
f
Tpro
c
¼ kn2pro
c
Tpro f vf ðtÞdt Ztf
¼
kn2pro f
(5) vf ðtÞdt
0
(3)
Tpro
f
¼ 0
(2)
where, k ¼ 2pro . Climbing requires the highest power out of the entire flight; therefore, the propeller rotational speed is higher in the climb phase comparing to the cruise phase. Let npro_f denotes the propeller rotational speed during the climb phase and npro_c denotes the propeller rotational speed during the cruise phase, their corresponding thrusts can be calculated as:
(
Ztf Wpro
where, Rpro is the radius of the propeller, Ct is the tension coefficient of the propeller, npro is the rotational speed of the propeller,r is the air density, Ap is the atmosphere pressure and T is the absolute atmospheric temperature. It can be concluded from Eqn. (2) that the thrust generated by the propeller is proportional to the square of its rotational speed under constant temperature and pressure.
Tpro ¼ kn2pro
Tpro_c is the propeller thrust during the cruise phase. The work done by the propeller during the climb phase is:
(4)
where, Tpro_f is the propeller thrust during the climb phase and
¼ kn2pro f vf
av tf
where, Wpro_f is the work done by the propeller during the climb phase, tf is time for climbing, Tpro_f is the climb thrust generated by the propeller, vf(t) is the aircraft velocity during the climb phase, vf_av is the aircraft average velocity during the climb phase. The work done by the propeller during the cruise phase is:
Wpro
c
¼ Tpro c vc tc ¼ kn2pro c vc tc
(6)
where, Wpro_c is work done by the propeller during the cruise phase, tc is the cruise time, Tpro_c is the cruise thrust generated by the propeller, vc is the aircraft velocity during the cruise phase. The energy consumed by the EAPS during the climb phase is:
Qf ¼
Wpro
hf
f
¼
kn2pro
hf
f
,vf
av tf
(7)
where, hf is the efficiency of the EAPS during the climb phase. It can be observed from Eqn. (7) that the energy consumption during the climb phase is related to the rotational speed of the propeller, the climb time of the aircraft and the climb average velocity of the aircraft.
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The energy consumption during the cruise phase is:
Qpro
c
¼
Wpro
hc
c
¼
kn2pro
hc
c
vc tc
(8)
where, hc is the efficiency of the EAPS during the cruise phase. From Eqn. (8), it can be concluded that the energy consumption during the cruise phase is related to the rotational speed of the propeller, the cruise velocity of the aircraft and the cruise time of the aircraft. Ignoring the energy consumption during the take-off phase and the landing phase given their limited impact, the energy consumed during one flight can be approximated as:
Q ¼k
n2pro
hf
f
,vf
av tf þ
n2pro
hc
! c
,vc tc
439
v is the aircraft velocity. The following equation describes the relation between the takeoff speed and the rotational speed of the propeller. It can be obtained from Eqn. (10) and Eqn. (4) [26]:
rSCd 2
vf ðtÞ2 þ m
dvf ðtÞ ¼ kn2pro dt
f
mg sin q
(11)
Leta ¼ m; b ¼ rSCd =2; c ¼ kn2pro f mg sin q, and if the initial speed of the aircraft is the vf0, the solution of Eqn. (11) is:
pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi 1 þ b=cvf ðtÞ 1 þ b=cvf 0 a a pffiffiffiffiffiffiffiffi pffiffiffiffiffi ln pffiffiffiffiffiffiffiffi ¼t pffiffiffiffiffi ln 2 bc 1 b=cvf ðtÞ 2 bc 1 b=cvf 0
(12)
Thus, the climb velocity of the aircraft is:
(9)
where, Q is the energy consumption during one flight. It is shown in Eqn. (9) that the total energy consumption is related to the average climb velocity of the aircraft, the climb time of the aircraft, the cruise velocity of the aircraft, the cruise time of the aircraft, the rotational speed of the propeller during the climb and the cruise phases. In addition, the energy consumption can also be affected by the efficiency of the EAPS. Although the flying distance during the climb phase is limited comparing to the cruise phase, the propeller rotational speed is much higher; therefore, the energy consumption during the climb phase still contributes to a significant portion of the total energy consumption. On the other hand, the lower efficiency of the EAPS during the climb phase may require higher power motor and controller to compensate, which can increase the weight of the EAPS and consequently increase its energy consumption. To reduce the energy consumption of the EAPS, the rotational speeds of the propeller during the climb and the cruise phases can be determined under the constraint that the aircraft must stay airborne. In addition, the best efficiency points during the climb phase and the cruise phase should be determined to reduce the total energy consumption.
exp tþq t 1i vf ðtÞ ¼ h tþq p exp t þ 1 where,p ¼ q¼t
qffiffi b c
¼
(13)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rSCd ;t 2ðk1 npro mg sin qÞ f
¼
paffiffiffiffi 2 bc
m ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2rSCd ðknpro f mg sin qÞ
1þpv ln 1pvff 00 .
The climb speed of the aircraft v must always be greater than vset_f (the minimum climbing speed) to avoid aircraft stalling. During the cruise phase, the airplane travels at constant velocity horizontally. The cruise velocity of the aircraft can be obtained from Eqn. (14) and Eqn. (4):
sffiffiffiffiffiffiffiffiffiffi 2k n vc ¼ rSCd pro
c
(14)
The cruise speed of the aircraft cannot be less than vset_c (the minimum cruise speed) to prevent aircraft stalling.
3. Efficiency matching of EAPS 3.1. Speed and efficiency characteristics of EAPS
2.4. Propeller rotational speed requirements during climb and cruise phases
The efficiency of the EAPS is:
As shown in Eqn. (9), the energy consumption of the EAPS is proportional to the square of the rotational speed of the propeller during the climb and the cruise phases. However, low rotational speed of the propeller can decrease the speed of the aircraft, which may lead to accident due to insufficient flight height; therefore, the operating speed of the airplane and the propeller during the climb phase and the cruise phase cannot be too low. The minimal required speed of the aircraft during the climb and the cruise phases can be obtained from the tech specs of the aircraft model. Using the lowest operating speed available, it is possible to get the best efficiency points of the EAPS during the climb phase and the cruise phase by optimizing Eqn. (9). The velocity of the airplane can be calculated as [25]:
8 dv > > < Tpro ¼ Ad þ mg sin q þ m dt > r SC > d 2 :A ¼ v d 2
(10)
where, Ad is the air resistance, m is the mass of the airplane, g is acceleration of gravity, q is the climb angle of the aircraft, r is the air density, S is the area of the wing, Cd is the resistance coefficient and
h ¼ hco hmo hpro
(15)
where, hco is the efficiency of the controller, hmo is the efficiency of the motor, hpro is the efficiency of the propeller. To drive the motor, the controller transforms DC current generated by the batteries to AC. The DC to AC transformation also consumes energy at the controller and the amount of energy consumption is related to the rotational speed of the propeller [27]; therefore, the characteristic curve between the propeller rotational speed and the efficiency of the controller is nonlinear [28]. The motor directly drives propeller rotation. Its power is related to the rotational speed and the torque of the propeller; therefore, the characteristic curve between the propeller rotational speed and the efficiency of the motor is also nonlinear [29]. The design and selection of the controller and the motor must satisfy the power demand during the climb phase, since climbing phase demands the highest power. Additionally, to reduce the energy consumption of the EAPS, it is preferred to use PMSM and corresponding controller, since they can maintain high efficiency during the cruise and the climb phases [30]. The efficiency of the propeller satisfies the following set of equations [31]:
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8 60vfl > > > l¼ > > n Rpro pro > > > > > > Tpro > > CT ¼ 2 4 > > > rnpro Rpro > > < Ppro > CW ¼ 2 5 > > > r npro Rpro > > > > > > CT l > > > > hpro ¼ C > > W > > : Ppro ¼ 2pnpro Mpro
(16)
where, l is the propeller advance ratio, Ct is the thrust coefficient, Cw is the power coefficient, Rpro is the propeller radius, npro is the propeller rotational velocity, Tpro is the propeller thrust, vfl is the fluid velocity, Ppro is the propeller input power and Mpro is the propeller torque. It can be derived by Eqn. (16)
hpro ¼
30rvfl CT npro R4pro
pMpro
(17)
The propeller torque Mpro, is the same as the torque of the motor driving it. The torque of the motor is not linearly related to its velocity as shown in Fig. 3; therefore, the characteristic curve of the propeller efficiency is also non-linear. The propeller is usually utilized at its peak efficiency during the cruise phase to reduce the total energy consumption. However, it may cause two issues: (1) The climb phase demands the highest power and it limits the design and the selection of the EAPS. The lower efficiency during the climb phase requires higher capacity motor and controller to compensate and increases the weight, volume, and cost of the EAPS. (2) As the weight of the EAPS increases, the weight of the aircraft also increases. As the result, energy consumption increases. Although utilizing the propeller at its peak efficiency point during
Fig. 4. Performance of propeller.
the climb phase may reduce the cost of the motor and the controller in the EAPS while producing sufficient power for climbing, it unfortunately prevents the EAPS from high efficiency operation during the cruise phase and increases the overall energy consumption. As shown in the previous discussion, for an electric aircraft using fixed pitch propellers, utilizing the propeller between its peak efficiency points of the climb and the cruise phase can result the minimum energy consumption. This paper proposes the method to find the optimal energy consumption efficiency points of the EAPS
Fig. 3. Rpm, torque and power curve of the experimental motor.
S. Ma et al. / Energy 140 (2017) 436e443
Fig. 5. Aircraft ground test.
during the climb and the cruise phases by solving the minimum energy consumption of the EAPS. 3.2. Efficiency matching of EAPS Eqn. (9) shows that the energy consumed by the EAPS is related to the average velocity of climb, the time of climb and the rotational velocities of the propeller during the climb and cruise phases. The controller and the motor of the EAPS are designed to provide sufficient power and capable of operating at high efficiency during climbing and cruise. However, the fixed pitch propeller, which is commonly used in electric airplanes due to its small size, cannot maintain high efficiency for both cruise and climb phases. In addition, the lower EAPS efficiency could increase the weight of the airplane, since higher power motor and its controller are required to meet the power demand during climbing. This paper proposes a method to reduce the energy consumption for both climbing and cruise by optimizing the energy consumed by the EAPS [32]. The objective function describing the energy consumption of the EAPS is:
minf ppro f ; ppro c ; hf ; hc ¼ mink
n2pro
hf
f
,vf
av tf
s:t: 8 vf av vset f > > > > > > vc vset c > > > > > < hpro ¼ f1 npro ; Tmo > h ¼ f2 npro ; Tmo > > > mo > > > > > hco ¼ f3 npro ; Tmo > > : h ¼ hco hmo hpro
þ
n2pro
hc
! c
,vc tc
(18)
441
corresponding propellers. Propeller 1 is designed to operate at maximum efficiency during climb and propeller 2 is designed to achieve its peak efficiency during cruise as shown in Fig. 4. The thrust requirement during cruise is 75 kg and the propeller rotational velocity during climbing is 2200 rpm. Flight profile is shown as Fig. 1. The cruise distance is 50 km at 1 km flight height and the angle of climb during climbing is 0.12. The efficiency of the motor during both the climb phase and the cruise phase are 92%. Capacity of the batteries is 12 kWh. Experimental results show that the energy consumed of the EAPS using propeller 1 is 8.4 kWh. In comparison, design with propeller 2 consumes 9 kWh of energy after completing the same flight. The batteries residual quantity displayed on the power integrated display on the front panel are 30% and 25% respectively. By adopting the proposed method, the peak efficiency of the propeller obtained from Eqn. (18) using randomized search method is approximately 1700 rpm. The propeller rotational velocity during climbing is 2200 rpm and the propeller rotational speed is 1650 rpm during the cruise phase. At this speed, the aircraft is estimated to consume minimum energy per flight. This design is adopted to the EAPS with the double blade wooden propeller, the PMSM and the controller. Photos of the aircraft and the propeller are shown in Fig. 5 and Fig. 6 respectively. The test results are shown in Fig. 7. Data is obtained from experiments using wind tunnel test at 72 km/h air velocity. Propeller rotational velocities between 1300 rpm and 2200 rpm are tested, since only the climb phase and the cruise phase are considered. As shown in Fig. 7, as the propeller rotational velocity increases, the thrust generated by the propeller increases. The motor is operating at high efficiency once the propeller rotational velocity exceeds 1300 rpm, which is similar to the PMSM. Once the propeller rotational velocity exceeds 1300 rpm, the controller reaches its peak efficiency. However, the efficiency of the controller slightly decreases as the propeller rotational velocity increases further. Such phenomenon can be explained as the result of the increasing propeller current incurring larger switching losses at the controller. Finally, the peak efficiency for the propeller occurs at around 1720 rpm, which is extremely close to the estimated 1700 rpm. Considering the 75 kg thrust demand, the corresponding rotational velocities of the propeller are respectively 1650 rpm for cruising and 2200 rpm for climbing. The energy consumed per flight is 7.15 kWh. It leaves 4.85 kWh of energy remaining on the batteries with 12 kWh total capacity. Comparing to the previous
The aircraft velocities for climbing and cruise are related to its motor, which can be obtained through Eqn. (13) and Eqn. (14). Eqn. (18) describes an optimization problem with constraints, whose solution can be obtained with randomized search method. 4. Method validation To examine the proposed method, experiments were conducted on the two-seater electric aircraft with the following design requirements: the maximum take-off weight is 480 kg, the cruise speed is 100 km/h, the climb speed is 90 km/h, the angle of climb is 0.12, and the maximum flight height is 1 km. Its flight profile is: take-off (1 min), climbing (3 min), cruising (30 min) and landing (4 min) [33]. Two propulsion systems were designed for this aircraft with
Fig. 6. Propeller wind tunnel test.
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S. Ma et al. / Energy 140 (2017) 436e443
Fig. 7. Test results of EAPS.
systems, the proposed design saves 1.25 kWh and 1.85 kWh respectively. The batteries residual quantity displayed on the power integrated display on the front panel is 40% after completing the flight. 5. Conclusion This paper proposes a method to reduce the energy consumption of the electric aircraft based on the study on an electric aircraft propulsion system (EAPS)of a two-seater electric aircraft. The efficiency of the EAPS is related to the efficiency of the motor, the controller and the propeller. The motor and the controller are capable of high efficiency operation through the entire flight, while the propeller has a narrow high efficiency operating range. Therefore, the efficiency of the EAPS is largely affected by the efficiency of the propeller. The climb phase demands 2.5 times of power required for cruise and consume more than 20% of the total energy. The cruise phase consumes approximate 75% of the total energy. The capacity and energy consumption of the EAPS are related to the efficiency of the EAPS.
With the total energy consumption as the object function based on the flight profile, and under the constraint that guarantee safe climbing and cruise, the proposed method can obtain the optimized operating point of the EAPS to achieve high efficiency to greatly reduce the energy consumption of the EAPS on the electric aircraft. The proposed method is tested and verified with real flight tests. Experimental results demonstrate the effectiveness with more than 15% improvement compared to conventional configuration. References [1] Hu XS, Zou Y, Yang YL. Greener plug-in hybrid electric vehicles incorporating renewable energy and rapid system optimization. Energy 2016;111:971e80. [2] Hyderak. A century of aerospace electrical power technology. J Propuls Power 2003;19(6):1155e79. [3] Stoll Alex M. Drag reduction through distributed electric propulsion.14th AIAA aviation Technology. Integration, and Operations Conference; 2014. [4] Zhao CH, Chen LW. Technical progress of electric aircraft. Sci Technol Rev 2013;30(12):62e70. [5] Lawrence Dale A. Efficiency analysis for long-duration electric aircraft. American Institute of Aeronautics and Astronautics; 2015. [6] Takahashi Kenichiro, Fujimoto Hiroshi. Modeling of propeller electric airplane and thrust control using advantage of electric motor.AMC2014-Yokohama.
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