A Dual-Channel-Enhanced Power Generation Architecture With Back-to-Back Converter for MEA Application

This article proposes an improved power generation architecture (PGA) for future more electric aircraft applications. In the proposed architecture, a starter/generator is connected to the high-pressure (HP) shaft, and a generator is connected to the low-pressure (LP) shaft. Their outputs supply a common dc bus via active power converters. A back-to-back (B2B) converter is deployed to link the ac terminals of the two generators. The proposed topology embraces three main advantages. First, with the B2B converter, the HP generator can operate at a high speed without flux weakening; thus, the magnitude of stator current will be decreased when output same active power. This will lead to the reduction of power losses on the generators and the active rectifiers. Second, the proposed PGA allows power transfer from the LP and to the HP shafts. This can potentially reduce the fuel consumption and increase aircraft engine compressor surge margins when the engine is at low-speed setting. Third, the B2B converter provides an additional power flow path to the generators under converter fault scenarios, hence improving the postfault operation ability. For the proposed PGA, engine benefits, modeling, control design, and efficiency improvements are illustrated in detail. The control performances of the proposed PGA, engine performance improvement by transferring power from the LP to HP shaft, and power loss reduction are verified via simulations and experimental results collected from a twin-shaft aircraft power generation test rig.


I. INTRODUCTION
T HE more electric aircraft (MEA) concept is one of the major trends toward the modern aerospace industry for gas emission reduction, decreased fuel consumption, low maintenance cost, etc. [1]. Existing pneumatic, hydraulic, and mechanical actuators are substituted by their electrical counterparts on MEA. Consequently, the onboard installed electrical power increases significantly and this results in high electrical power demand. For a twin-shaft engine, the LPT drives the fan and LPC via the LP shaft, and the HPT drives the axial and radial HPCs via HP shaft. Traditionally, electrical generator is driven by a gearbox linked to the HP shaft of the engine. This is due to the desirable HP shaft characteristics, such as high and relatively constant speed, which enables engineers to decrease the size and weight of HPG. Nevertheless, extracting the high amount of power from the HP shaft could have a negative impact on the performance of the engine system. In [2] and [3], it has been proved that there is a limit on the amount of power off take from HP shaft, where if exceeded will cause compressor surge a critical threat to the engine. This can be addressed by oversizing the HPT or excessive bleedings, whereas those actions will either increase the fuel consumption or lead to undesirable thrust [4].
An alternative way is to use the LP shaft as an additional power source, i.e., using the LP shaft to drive another electrical generator. Because of the wide speed range of the two shaft drives, the easiest way concerning power electronic devices is to supply the electric power to one common dc bus, as dc bus configuration can reduce weight and does not need reactive power compensation component compared with ac bus. This gives a two-generator single-dc-bus structure. So far, several publications have dedicated on designing proper power generation architectures (PGAs) with different types of electrical machines 0093-9994 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information.  1. PGA with two PMGs and a single dc bus in [9] and [10]. and converters. For example, in [5] and [6], a switched reluctance starter/generator (SRSG) controlled by a bidirectional drive unit performs as HP machine and LP machine is a permanent magnet generator (PMG) controlled by a unidirectional unit. In [7], two wound-field synchronous machines (WFSMs) are adopted, where the HP machine is controlled with an active rectifier (AR), and the LP machine is regulated by a passive 12-pulse rectifier. The induction generator (IG) based ac/dc hybrid electric power generation system is also proposed in [8].
Compared with SRSG, WFSM or IG, PMGs are preferable options due to the advantages in power density, volume, and weight, which are crucial for aerospace applications. Therefore, in [9] and [10], two PMGs are connected to the turbine shafts and can operate in variable speed mode. The structure is illustrated in Fig. 1. In this configuration, the two generators can take power from the main engine through HP shaft and LP shaft in different conditions such as climb, cruise, and descent, guaranteeing an efficient exploitation of the power generated by the engine. Theoretical analysis and experimental results confirm the superiority of the PGA, as shown in Fig. 1, in terms of stability and efficiency, making it a competitive candidate of PGA for future MEA [9], [10].
However, the PGA, as shown in Fig. 1, has some drawbacks that undermine the feasibility in practical application. The first issue is related to the flux-weakening (FW) operation of the generator coupled to the HP shaft. At full thrust settings, the rotary speed of HP shaft can reach 20 000 r/min [11]. Therefore, FW control should be applied to HPG to decrease the flux density in the stator core and back EMF. Great amount of defluxing current is constantly injected into the HPG without outputting active power in most of the flight conditions, leading to significant power losses, and the power rating of HP AR has to be increased to conduct larger current.
Another issue is the poor fault tolerance ability. For the existing PGA in Fig. 1, if the contingency occurs to rectifiers, the system performance will be deteriorated and may lead to instability. For example, if an open-switch fault occurs to the HP rectifier, which is caused by thermal cycling high collector current and gate driver fault, the current will distort and can generate secondary problems [17]. In this case, stopping the operation of the HP rectifier is an effective solution. However, for the PGA in Fig. 1, if there are no redundant rectifiers, the HP generator has to be cutoff from the power generation system and hence the power supply ability will be greatly impaired.
To resolve the aforementioned issues of the PGA in Fig. 1, a new PGA containing a back-to-back (B2B) converter is proposed, as shown in Fig. 2. The additional B2B converter will bring various benefits including the following.
1) Enabling the HPG to operate without FW at high speed.
2) Better fault tolerance performance as an additional power flow channel is provided when the converters associated with HPG or LPG are shutdown. 3) Enabling power transfer between LPG and HPG. This will increase the compressor margin and its overall efficiency. The rest of the article is organized as follows. Details of the proposed PGA and the basics of the engine will be described in Section II. Section III illustrates the modeling and controller design of the whole system, including a voltage controller, powersharing method, inductor selection, power-transfer control, etc. Section IV compares the power loss of the proposed PGA and the existing PGA in Fig. 1. In Section V, control performances of the proposed PGA and benefits to engine performance when transferring power from the LP to HP shaft as well as power loss reduction using the proposed PGA are validated. Section VI makes a conclusion of the whole article.

A. Proposed PGA With a B2B Converter
The diagram of the proposed PGA is shown in Fig. 2. Two electrical generators (HPG and LPG) are supplying a common dc bus (270 V) through its own dedicated converter. A B2B converter is used to connect the HPG and LPG. When the modern engine is moving toward more electric and with high-bypass ratio, the electrical power that can be extracted from the HP shaft will become further limited. Thus, it is considered that LPG generally outputs more power than HPG [3], [10]. In this case, the B2B converter is mainly used to transfer power from the LP side to the HP side. Therefore, the converter connected to the LPG within the B2B converter is denoted as B2B Rectifier and the other is denoted as B2B Inverter . Besides, it is worth to note that the intermediate voltage V mid in the B2B converter can be set to a value much higher than 270 V, as it does not supply onboard loads directly. Two groups of inductors, denoted as L 1 and L 2 , respectively, are deployed to separate voltage sources, i.e., LP converter and B2B Rectifier , and HP converter and B2B Inverter . To the best knowledge of authors, this is the first time to present this kind of PGA. The main contributions of the proposed PGA are highlighted as follows.
1) HPG could operate at a high speed without FW due to high V mid in the B2B converter. Hence, the magnitude of the stator current will decrease. This will help to reduce the power losses in HPG and power converters. 2) The proposed PGA has the postfault operation ability when any of the HP or LP converters shut down under fault scenarios since the B2B converter provides an additional power flow path to both LPG and HPG.
3) The power of LP shaft can be transferred to HP shaft electrically via the B2B converter by controlling HP machine in motoring mode. This will not only improve the fuel efficiency but also increase the compressor surge margin (SM) at low-speed settings. Details of this advantage are explained in Section II-B.

B. Basics of Turbofan Engine
In this part, the basics of turbofan engine will be introduced and the reason why power transfer from the LP to HP shaft is beneficial to engine performance will also be explained.
High-bypass ratio turbofan is considered as the dominant source of propulsion for most of the civil aircraft. The schematic diagram of a two-spool high-bypass turbofan engine with an unmixed exhaust is shown in Fig. 2. The major engine components of a turbofan can be named as fan, booster (LPC), HPC, combustion chamber, HPT, LPT, and discharge nozzles. The HPT drives the HPC on the HP shaft and the LPT drives the fan and LPC on the LP shaft.
In order to study the effect of the proposed power-transfer method on engine performance, an aircraft engine model has been developed with the article presented in [2] and [3] by our group. The model contains the nonlinear thermodynamic behavior of a multispool engine for the whole range of operation. In this article, it is proved that by transferring power from the LP to HP shaft, the fuel consumption will be reduced and compressor SM will be expended. To make the advantages more understandable, the basics of compressor surge and the relationship between fuel consumption and power transfer are given as follows.

1) SM Enlargement by Power Transfer:
The surge effect is a critical threat to the engine. If the downstream pressure of the compressor keeps increasing, at some point, the pressurized air will act as a blockage, causing total breakdown of the airflow and stall all over the compressor blades, accompanied with the reversal of the airflow. This phenomenon is referred to as surge. Surge can lead to mechanical damage to the compressor blades and the thrust bearings due to the large fluctuations of airflow and direction of the forces on the rotor. Until now, multispool and variable geometry compressors have been the main solutions to overcome the surge phenomenon [14].
By electric power transfer from the LP to HP shaft at lowspeed settings of the engine, the swallowing capacity of HPC increases. This widens the SM of LPC and HPC. SM is referred to as the margin between the operating line and surge line on the compressor map (see Fig. 3).
2) Fuel Consumption Reduction by Power Transfer: The engine efficiency is higher at a higher core pressure ratio. In this case, power transfer from LP to HP shaft can move the operating line to higher pressure ratios at low-speed settings of the engine. With a higher pressure ratio, the fuel consumption is reduced. Hence, with the proposed PGA, the desirable amount of power can be transferred from LP to the HP shaft via the B2B converter by controlling the HPG as a motor. This will increase compressor SM and efficiency.

III. MODELING AND CONTROLLERS DESIGN
Since the proposed PGA contains two ARs, one B2B converter, two PMGs with distinct speeds, and two groups of inductors, the modeling and controller design is complex and challenging. In this article, different controllers are tailored for controlling the LP, HP, and B2B converters to achieve power and voltage control. The controller gains are adaptive to keep a constant closed-loop bandwidth. Droop control is utilized for power sharing between the sources. The criteria of inductor L 1 selection are derived from the phase diagram analysis and gradient descent method.
In Fig. 2, there are four power converters: LP converter, HP converter, B2B Rectifier , and B2B Inverter . They can be further classified according to their positions: LP converter and B2B Rectifier are the LP-side converters, and HP converter and B2B Inverter belong to the HP-side converters. The control methods design of the LP-and HP-side power converters, the selection of inductors, and how to control the system in the converter fault scenario are illustrated as follows.

1) Voltage Control for LP Converter:
The overall control diagram of the LP converter is shown in Fig. 4. It can be seen from Fig. 2 that the HP converter and LP converter are parallel connected to supply a common dc bus; therefore, measures  should be taken to realize the output power sharing between two converters. Here, the current-mode droop method presented in [9] is adopted to fulfill power sharing. Its aim is to control individual dc current to follow the reference computed from the droop characteristic, which is shown as where g LP is the droop gain of the LP converter. The dynamic equations for PMG in generator mode in dq frame are given as follows: where u d and u q are the dq axes stator voltages for LPG; i d and i q are the dq axes stator currents for LPG; L d and L q are the dq axes stator inductance of LPG; R s is the stator resistance; ψ f is the flux linkage of permanent magnet; and ω e is the electrical rotor speed. For the surface-mounted PMG used in this article, Since LPG is connected to the LP shaft, which has a large moment of inertia, the mechanical constant can be treated as much slower than the electrical constant. Then, the linearized q-axis voltage can be derived as The linearized active power of the LP converter can be expressed at operating point (indicated with "o") as follows: where i dso and i qso are obtained from LP-side main branch currents i aLs , i bLs , and i cLs in Fig. 5; and P LP is the output power of the LP converter.
Assume that the ratio between the power generated by LPG and the power transferred to B2B Rectifier is n:1; hence, i q :i qs = n:(n − 1). Consider the situation that LPG operates with i d = 0, the linearized active power of the LP converter in a small-signal manner can be written as where ρ = (n−1):n. Since the active power in a small-signal manner can also be represented as ΔP LP = V dc Δi dcLP , the transfer function between Δi dcLP and Δi q can be obtained as Considering i dc = P/V dc , the following relationship in a smallsignal manner can be derived as: In the Laplace domain, (7) can be rewritten as Assume that the power-sharing ratio between the LP converter and HP converter is k:1, then the ratio of corresponding droop gains is 1:k. Then, the following relationship can be derived as: where σ = (k + 1)/k. Using (6)-(9), the control block diagram of the LP converter can be constructed in Fig. 6. Using the zero of voltage-loop proportion-integration (PI) controller to eliminate the pole of forward path, the expression of PI controller can be given as where k vp and k vi are the proportion and integration gains of PI controller, ω c is a factor related to the closed-loop bandwidth. Equation (10) reveals that k vp and k vi should be adaptive according to different operation conditions, such as P o and V dc . By tuning factor ω c instead of k vp and k vi , desirable transient and steady performance of dc voltage loop can be obtained. From Fig. 6, the closed-loop transfer function of voltage loop can be derived as eq. (11) shown at the bottom of this page. where g LP is the droop gain.
dc C, m 0 = P, and n 0 = V 2 dc σ. System parameters are given in Table I. In this article, the HP and LP converters account for the same power, i.e., σ = 2. By comparing the characteristic equation in (11) with the desired second-order system, ω c can be obtained by the pole placement technique [15]. In this article, the desired poles are placed at −300 ± j 810, which guarantee the stability and closed-loop bandwidth at 200 Hz simultaneously.
The closed-loop bode diagram when total power P changes from 20 to 60 kW is shown in Fig. 7. As can be seen from Fig. 7, in the low-frequency region, the magnitude is smaller than 0. This can be explained by the feature of droop control: the actual dclink voltage is smaller than the reference in heavy load condition due to the droop characteristic. Moreover, at around 200 Hz, the magnitude damps −3 dB compared with the initial value in the low-frequency region. This proves that the bandwidth of the designed voltage loop is set to around 200 Hz, no matter how P changes by choosing the factor ω c using the pole placement idea.
2) Selection of Inductor L 1 : From Fig. 5, the LP-side circuit is derived as Fig. 8(a), where U aCon represents a phase voltage generated by the LP converter, U aRec is the voltage generated The inductor L 1 is important because of two main reasons: First, it separates U aCon and U aRec , and adjust U aRec according to load profiles; Second, it filters high-frequency pulsewidth modulation (PWM) harmonics. Therefore, the optimal value of L 1 should be carefully selected. If the value is too large, the weight and size of the core of L 1 will increase. If the value is too small, it cannot fulfill the function to filter the high-frequency PWM harmonics.
The following voltage equation can be obtained from Fig. 8(a) using Kirchhoff voltage law: The relationship shown in (12) is also valid for b and c phases. Multiplying T = [1, e j(2π/3) , e j(4π/3) ] with the a, b, and c phase voltage equations, the voltage vectors can be obtained, as exhibited in Fig. 8(b), where According to the cosine theorem, the following equation can be obtained from the relationship in Fig. 8(b): Since | V L1 | = jωL 1 | I Rec |, cosθ = sinϕ, (14) can be rewritten as Choose L 1 as the variable, then L 1 can be obtained as The phase diagram of LPG is demonstrated in Fig. 9, considering that LPG operates in i d = 0 mode. The expressions of LP-side variables can be given as follows: where ω eLP , i qLP , and P LP are the speed, q-axis current, and output power of LPG, respectively. The ratio between the power generated by LPG and the power transferred to B2B Rectifier is assumed to be n:1. ϕ is the phase-shift angle between voltage vector U Con and current vector I Rec . As will be pointed out in Section III-A.3, i xL and i xRec (x = a, b, c) are controlled in phase.
Therefore, from Fig. 9, the relationship of ϕ and γ is Considering the modulation technique applied to the B2B Rectifier is space vector PWM, the largest modulation index (MI) is √ 3/3; hence, the following expression regarding | U Rec | can be derived considering both largest MI and phase diagram in Fig. 8(b): Substituting (17)- (19) into (16), the value of L 1 can be expressed as the function of ω eLP , P LP , and n as follows: where The expression of J(Θ) min is straightforward, and the minimum value of J(Θ) max denoted as min(J(Θ) max ) with respect to the variation of ω eLP , P LP , and n should be derived. Here, the gradient descent method shown in (21) is utilized for solving this multivariable optimization problem The operation region for LPG is speed: 2000-10 000 r/min, P LP : 10-60 kW, and n: 5-7. Hence, the maximum value of J(Θ) min should be n max * L q = 0.7 mH. And min(J(Θ) max ) can be obtained by solving the iterative equation in (21). The result within the given operation region is 1.5 mH.
For further validating this result, the relationships of J(Θ) max and ω eLP , P LP , and n are also plotted in Fig. 10. Here, two main findings can be summarized.
1) From Fig. 10(a), it can be seen that min(J(Θ) max ) is almost independent of the LPG speed ω eLP . This means that the selection of L 1 does not rely on ω eLP . 2) From Fig. 10(b), it shows that min(J(Θ) max ) locates on the point of the maximum power of P LP and minimum power ratio n. This indicates that the value of L 1 is very sensitive to P LP and n. The result in Fig. 10(b) matches with that from the iterative equation, both with 1.5 mH. Hence, the value of L 1 should be chosen between 0.7 and 1.5 mH. In the latter validations, the value of L 1 is set as 1.0 mH.
3) Controller Design of B2B Rectifier : Since the phase terminals of LPG and B2B Rectifier branches share the same junctions, as shown in Fig. 5, an effective way to control the transferred power to B2B Rectifier is to control the phase currents of LPG (i xL ) and B2B Rectifier (i xRec , x = a, b, c) [see Fig. 11] in phase. Hence, the ratio of the phase current magnitude is proportional to the ratio of power.
Apart from regulating currents in phase, the B2B Rectifier controller is also responsible to control the intermediate dc voltage V mid . However, if adopting the conventional control structures in applications, such as active frontend [18] or flywheel energy storage system [19], the output of outer voltage controller, which is the reference of active power or active current, will not be able to control i xRec and i xL in phase. To cope with this problem, a new method is proposed aiming to realize the following two major functions: 1) dc voltage V mid regulation; 2) controlling currents i xRec and i xL in phase, x = a, b, c.
The block diagram of B2B Rectifier controller is shown in Fig. 11. Compared with the conventional control structure in [18] and [19], where active current reference equals to the output of voltage controller, in the proposed control structure, current references come from the product of the LPG dq axes currents and a gain m. Obviously, in this way, the phase currents i xRec and i xL can be controlled in phase if i xRec and i xL conduct abc/dq transformation using same frame. And the value of m comes from the voltage loop. When V mid is smaller than its reference, m should increase so that more current can be pumped into dc link and V mid will increase, and vice versa. Therefore, with such control method, V mid can be stabilized and i xRec can be controlled in phase with i xL .

B. Modeling and Control Design for HP-Side Converters
1) Controller Design of B2B Inverter : As can be seen in Fig. 2, terminals of HPG are directly connected to the B2B Inverter . Therefore, the operation of HPG is controlled by the B2B Inverter . The rotary speed of HPG is imposed by the HP shaft of the engine and is denoted as ω mHP . Hence, for properly controlling the power of HPG, the core is to control the torque for a surface-mounted permanent magnet (PM) machine is to control the q-axis current. Hence, the q-axis current reference can be obtained as follows: where P HP and p are the power and pole pairs of HPG.
Since the dc voltage V mid is set high enough, the HPG is able to operate at high generation speed without FW. Hence, i ref dH is set as 0 to maximize efficiency.
2) Control Design for HP Converter: The equivalent circuit of a phase at HP side is presented in Fig. 12. The electrical  dynamics in dq axes can be derived as where the direction of the voltage vector U Inv generated by the B2B Inverter is selected as d-axis, which means u dInv = U Inv and u qInv = 0. The position of U Inv is obtained by implementing a phase-locked loop to voltages U aInv , U bInv , and U cInv . Besides, u dCon and u qCon are the dq axes' voltages generated by the HP converter; i dHs and i qHs are the dq axes currents of HP-side main branches; and P HP_Con is the active power of HP converter.
Next we discuss how to acquire dq current reference. As aforementioned, the power sharing of LP and HP converters is fulfilled by droop control. Therefore, the active current reference comes from the droop controller. It should be noted that the magnitude of U Con is smaller than U Inv ; hence, the reactive current cannot be 0 as what usually do to control the grid-connected AR [13].
Here, the reactive current command is obtained from the required power of HP converter. Assume that the power sharing ratio between LP and HP converter is k:1. Based on (23), the reactive current reference can be derived as where P is the total power demand. The overall control diagram of the HP converter is shown in Fig. 13. In Fig. 13, g HP is the droop gain; the decoupling terms in the current loop are obtained from (23).

C. Postfault Operation When HP Converter Shuts Down
One of the main advantages of the proposed PGA over the existing one in Fig. 1 is the postfault operation ability. For In this case, there are three converters left in the system, B2B Inverter , B2B Rectifier , and LP converter. The structures of their controllers are discussed in the following text but the details are not given since this is not the main focus of this article.
1) For the controller of B2B Inverter , there should be two cascaded loops, the outer loop is responsible for stabilizing the voltage V mid , and the inner loop should be the current loop to control the dq axes currents of the HPG. 2) For the controller of B2B Rectifier , there should be two major functions. The first one is to make sure the phase current of LPG and the phase current of L 1 in phase. The second is to manipulate the magnitude ratio of the phase currents of LPG and the phase current of L 1 to transfer a given amount of power via the B2B converter. 3) For the controller of the LP converter, an outer voltage loop is required for controlling the main dc bus voltage to 270 V. And the inner loop is supposed to control the dq axes currents of LPG.

D. Power Control of the System
Here, the power control method for HP and LPGs, HP and LP converters, and B2B converter is summarized. The power of HPG is independently controlled by B2B Inverter , and power sharing between the LP and HP converter is realized by a droop method. Hence, the power transferring via the B2B channel is self-tuned by the difference between the powers of HPG and HP converter.

IV. EFFICIENCY IMPROVEMENTS
In this section, the power losses of generators and power converters of the existing PGA (denoted as PGA 1 ) and the proposed PGA (denoted as PGA 2 ) are discussed. As a starting point, the expressions of generator losses are given.
The copper loss of the PMG is given as follows: where R s is the stator resistance and I is the peak value of the phase current. The iron loss density P iron is modeled approximately as where P h and P e are the hysteresis and the eddy current loss, respectively. k h is the hysteresis constant, k e is the eddy current constant, B is the magnetic flux density, and β is the Steinmetz constant.
Here, the operating trajectories of HPG under different speeds are presented in Fig. 15. As can be seen in Fig. 15 that with a 270 V dc bus voltage, the HPG has to work in the FW region in most of the time of the generation mode at high speed. While with an increased dc bus voltage 400 V, the d-axis current can be allowed to be 0 at high speed, hence greatly decreasing the current magnitude when generating the same active power. Based on (25) and (26), some conclusions regarding the generator loss can be derived.
1) From (25), it can be concluded that compared with PGA 2 , the existing PGA 1 will lead to large copper loss due to large FW current, or d-axis current.
2) The FW effect caused by large d-axis current in PGA 1 will help to diminish the flux density B in the stator core, as a consequence from (26), the iron loss would be a bit smaller than that of PGA 2 at the same speed. Here, HPG losses are studied with a finite-element analysis (FEA) tool MagNet and validated by experiments. The details of the main findings are given in Section V-C. Apart from the machine loss, attention is also paid to the converter loss. The conduction loss of one IGBT and diode is given as where V t and V f are the built-in voltages of the IGBT and diode, while R ce and R ak are the differential resistances of the IGBT  and diode, respectively. M is the MI. ϕ is the displacement angle between the fundamental of the voltage and the current. Since the proposed PGA 2 helps to reduce the magnitude of phase current I compared with PGA 1 ; thus, from (27), it can be expected that the conduction loss of HP converter can be significantly reduced when using PGA 2 than PGA 1 .

V. VALIDATIONS
An overall control block diagram of the proposed PGA is demonstrated in Fig. 16, where the connections of various components and control structures of LP, HP, and B2B converters are presented. A test rig for mimicking the LP and HP shafts of a twin-shaft engine is constructed, as shown in Fig. 2. It is composed of two PMGs and two induction machines as prime movers. Two bidirectional three-level neutral point clamped (NPC) converters are used as the interfaces between the LP and HP generators and dc bus. Experiments of power transfer from the LP to HP shaft and power loss analysis are done on this rig, which verifies the improvements in engine performance and power loss reduction using the proposed PGA. Simulations of the control performance of the proposed PGA are also conducted.

A. Proposed PGA in Dual-Generator and Power-Transfer Modes
In the dual-generator mode, HP and LP machines both perform as generators. The results are shown in Fig. 17(a)-(e). In the power-transfer mode, the HP machine performs as a motor providing power to the HP shaft. The results are shown in Fig. 17(f). In the dual-generator mode, there are three different The currents of LPG and HPG are shown in Fig. 17(a) and (b). In Fig. 17(b), i dHP is controlled to 0 due to high dc voltage V mid . This confirms that the proposed PGA allows HPG to operate without FW even at high speed of 20 000 r/min. However, with the existing PGA in Fig. 1, in this case i dHP will be over 100 A [11]. As will be shown in Section V-C, this benefits to improve the efficiency.
The dc voltages of main bus V dc and V mid inside the B2B converter are demonstrated in Fig. 17(c). V dc remains stable throughout the whole process. This confirms the effectiveness of the voltage controller and droop method in Section III-A. V mid also remains stable with a slight deviation from reference, since only proportional (P) control is adopted in Fig. 11. As it does not supply power to the onboard load directly, it is acceptable that V mid slightly declines. And P control is useful enough as well as easy tuning. If the system requires a stable V mid , a PI controller can be applied.
The output powers in dual-generator mode are exhibited in Fig. 17(d). At stages 1 and 2, LP power is twice and thrice of HP power, respectively. This confirms the effectiveness of the proposed PGA to realize precise power control between sources with the proposed control methods.
The currents of i aL , i aRec , and i aLs are shown in Fig. 17(e), where i aL , i aRec , and i aLs are tightly kept in phase, which confirms the effectiveness of B2B Rectifier controller in Fig. 11. And the ratio of their current magnitudes is proportional to the ratio of the powers at different stages.
The output powers in the power-transfer mode are presented in Fig. 17(f). HP machine performs as a motor, which output 10 kW power to the HP shaft. While LPG on the one hand supplies power to the loads on main dc bus, whereas on the other hand, it supplies power to the HP machine. This confirms the feasibility of transferring power from the LP to HP shaft using the proposed PGA and controllers.

B. Engine Performance Improvement With Power Transfer
To transfer some power from the LP to HP shaft, the LPG should output a certain amount of power and HPG should work in motoring mode to absorb power generated from LPG. The experimental results when LPG generating 11.3 kW power and HPG absorbing 11.2 kW power are shown in Fig. 18.
As can be seen in Fig. 18(a), the speeds of LPG and HPG are controlled to 10 000 and 13 000 r/min by two induction machines, which perform as prime movers. The dq axes currents of LPG and HPG are exhibited in Fig. 18(b), where a negative i q of LPG indicates that it is working in generator mode and a positive i q of HPG indicates motoring mode. i d of HPG is negative for the purpose of FW. The dc bus voltage is shown in Fig. 18(c), which is 270 V as required in the standard [12].
The powers of LPG and HPG are shown in Fig. 18(d) and (e), respectively. LPG generates 11.3 kW power to the dc bus and HPG absorbs 11.2 kW power from the dc bus. No other loads are connected to the dc bus. It means 11.3 kW mechanical power of the LP shaft is converted into electric power by LPG and this amount of power is transferred to the HP shaft by controlling the HP machine in motoring mode. The line-to-line voltage and phase current of HPG are also shown in Fig. 18(f), where five voltage levels can be observed due to the nature of the NPC converter. The peak value of the phase current is around 50 A, which is consistent with the dq axes currents in Fig. 18(b). And the frequency of phase currents is 650 Hz, which is consistent with the speed of HPG, 13 000 r/min.
The data in this power-transfer experiment are used to feed the engine's model, as mentioned in Section II-B. Here, the flight idle mode is selected as an example of the low-speed setting of the engine. Results for flight idle mode at 20 000 ft are presented in Table II. They reflect that in flight idle mode, as some amount of the power is transferred from the LP to HP shaft, the reduction of fuel consumption and the increase of available compressors SM can be achieved.

C. Comparison of Power Losses of Different PGAs
In this section, the existing PGA in Fig. 1 is denoted as PGA 1 , and the proposed PGA is denoted as PGA 2 . The results of dc bus voltage, HPG phase currents, and line-to-line voltages with different PGAs at 13 000 r/min are exhibited in Fig. 19(a) and (b). As can be seen in Fig. 19(a) that with PGA 1 , the magnitude of phase current is 65 A. While Fig. 19(b) shows that the magnitude of the phase current with PGA 2 is reduced compared with that in Fig. 19(a). The operating point moves from E 1 to E 2 , as shown in Fig. 15. Hence, the great reduction of copper loss can be achieved, as analyzed in Section IV. The data of phase currents are imported into the FEA model of HPG. Corresponding magnetic fields and losses are given in Fig. 19(c) and (d). The copper loss is reduced from 103.3 to 52.3 W. In Fig. 19(c), the flux density of the stator core with PGA 1 is 0.85T due to the FW effect. While the flux density with PGA 2 increases to 1.1T as no FW action is applied with high V mid . Hence, the iron loss with PGA 2 (169.1 W) is higher than that with PGA 1 (130.8 W). The total loss of HPG with PGA 2 is smaller than with PGA 1 .
The power loss of PGA 1 and PGA 2 is further compared considering the entire HP channel, including HPG and HP converter. The results are given in Fig. 20. The generated active power is fixed to 4.2 kW for both PGAs. The speed of prime mover is controlled to be 13 000 r/min. With PGA 1 , the torque of prime mover is 3.607 N·m, while that of PGA 2 is 3.507 N·m, which means when outputting the same active power, less power of prime mover is consumed when using the proposed PGA 2 . Hence, it can be concluded that compared with PGA 1 , the proposed PGA 2 is able to reduce the power loss of HPG and HP converter, hence improving efficiency by eliminating the FW operation of HPG due to an increased dc bus voltage from 270 to 400 V.
To further compare the efficiency with the two PGAs, performances at high-speed high-load condition (15 000 r/min, 10.3 kW, indicating the cruise mode), and low-speed light-load condition (9500 r/min, 2.2 kW, indicating the taxiing mode) are demonstrated in Figs. 21 and 22, respectively.
In Fig. 21, the generated power is 10.3 kW for both PGAs. The speed is fixed to be 15 000 r/min to emulate the high-speed  condition at cruise mode. With PGA 1 , the torque of prime mover is 7.592 N·m, while that of PGA 2 is 7.199 N·m. This means that when generating the same active power, prime mover needs to provide relatively less power with the proposed PGA 2 . As discussed above, this improvement comes from the elimination of the FW operation of HPG. As can be seen from Fig. 21(a), with PGA 1 , the magnitude of phase current is around 100 A because of a high defluxing current component. In Fig. 21(b), the magnitude of phase current is only 50 A since there is no defluxing component when using PGA 2 .
In Fig. 22, the generated power is 2.2 kW for both PGAs and the speed is 9500 r/min to emulate the low-speed light-load condition when the aircraft is taxiing on the ground. From the prime mover side, the torque with PGA 1 is 2.669 N·m and that with PGA 2 is 2.700 N·m. In this case, the efficiency with PGA 2 is slightly lower than with PGA 1 . This can be explained by the characteristics of HPG. HPG is designed for high-speed operation, hence with low inductance and low back EMF coefficient as can be seen from Table I. Therefore, at a low speed 9500 r/min, the MI is low, leading to undesirable current harmonics. Current harmonics can be further degraded as dc voltage increase from 270 to 400 V. Therefore, the current waveform in Fig. 22(b) with PGA 2 is worse than Fig. 22(a) with PGA 1 . Large current harmonics will cause power loss in both generator and power converter.
However, in the main operation modes, such as cruise, the proposed PGA 2 is advantageous in terms of efficiency.

VI. CONCLUSION
In this article, a new PGA for the MEA application is proposed. Two PMGs are attached to the LP and HP shafts feeding a 270 V main dc bus. A B2B converter is used to transfer power between the LP side and HP side. Modeling, controller design for each individual converter, and the criterion for inductor selection are given. Power sharing between the LPG and HPG, as well as the output power sharing between the LP and HP converters, could be effectively controlled. The main contributions that have been experimentally validated can be highlighted as follows.
1) Fuel consumption can be reduced and compressor SM can be expanded by transferring power from the LP to HP shaft at low-speed settings.
2) The HPG could operate at a high speed without FW, reducing the magnitude of stator current of HPG. This will help to reduce the overall power losses. Furthermore, the proposed PGA also has the postfault operation ability when any of the HP or LP converters shut down under fault scenarios since the B2B converter provides an additional power flow path for the generators. Details of this characteristic will be investigated in the future study.

ACKNOWLEDGEMENT
The author Xiaoyu Lang also thanks the stipend funding from China Scholarship Council (CSC).