Multi-Objective Optimization Control for the Aerospace Dual ... - MDPI

energies Article

Multi-Objective Optimization Control for the Aerospace Dual-Active Bridge Power Converter Tao Lei 1, *, Cenying Wu 2 and Xiaofei Liu 1 1

2

*

Key Laboratory of Aircraft Electric Propulsion Technology, Ministry of Industry and Information Technology of China, Northwestern Polytechnic University, Xi’an 710072, China; [email protected] Shenyang Aircraft Design and Research Institute, Shenyang 110034, China; [email protected] Correspondence: [email protected]

Received: 27 March 2018; Accepted: 25 April 2018; Published: 7 May 2018

Abstract: With the development of More Electrical Aircraft (MEA), the electrification of secondary power systems in aircraft is becoming more and more common. As the key power conversion device, the dual active bridge (DAB) converter is the power interface for the energy storage system with the high voltage direct current (HVDC) bus in aircraft electrical power systems. In this paper, a DAB DC-DC converter is designed to meet aviation requirements. The extended dual phase shifted control strategy is adopted, and a multi-objective genetic algorithm is applied to optimize its operating performance. Considering the three indicators of inductance current root mean square root (RMS) value, negative reverse power and direct current (DC) bias component of the current for the high frequency transformer as the optimization objectives, the DAB converter’s optimization model is derived to achieve soft switching as the main constraint condition. Optimized methods of controlling quantity for the DAB based on the evolution and genetic algorithm is used to solve the model, and a number of optimal control parameters are obtained under different load conditions. The results of digital, hard-in-loop simulation and hardware prototype experiments show that the three performance indexes are all suppressed greatly, and the optimization method proposed in this paper is reasonable. The work of this paper provides a theoretical basis and researching method for the multi-objective optimization of the power converter in the aircraft electrical power system. Keywords: double active bridge converter (DAB); multi-objective optimization; evolution and genetic algorithm

1. Introduction The aerospace industry is promoting the use of more electrical technology to enhance the performance and increase the reliability of aircraft power systems and secondary power subsystems instead of hydraulic, pneumatic systems. High voltage DC systems (HVDCs) are very popular in aircraft electric power systems because of their simpler equipment and significant energy savings. This technology requires high power density, reliable DC-DC converter for the application of battery storage power supplies to mission critical aerospace situations, e.g., actuators and avionics. DAB converters, as the interface of energy storage devices, have become a research hotspot [1,2]. The DAB converter has been popular among researchers over the last ten years due to its high performance, high efficiency, galvanic isolation and soft-switching property [3,4]. A DAB converter’s topology is shown in Figure 1. Because of the extra power switching devices, the pressure and flow capacity of the power switching are strong, so a larger power can be transmitted [5], but there are also some shortcomings [6], such as the increase of the inductance current value will increase the switching loss and switching stress make the switching device become damaged easily. In addition, there is a Energies 2018, 11, 1168; doi:10.3390/en11051168

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loss and switching stress make the switching device become damaged easily. In addition, there is a negative power power transmission transmission in in the the DAB DAB converter, converter, the the circulation circulation loss loss is is large, large, so so the thetransmission transmission negative power peak in the circuit is increased, and the weight and volume of the transformer will be power peak in the circuit is increased, and the weight and volume of the transformer will be increased, increased, is not acceptablecontext. in aerospace context. The frequency saturation transformers of high frequency which is notwhich acceptable in aerospace The saturation of high will be transformers will be caused by the DC bias component existing in the inductance current under the caused by the DC bias component existing in the inductance current under the load transient variation, load transient variation, therefore, it how to optimize the dual active bridge DC-DC converter in therefore, it how to optimize the dual active bridge DC-DC converter in aircraft electrical power aircraft electrical power systems has important practical significance. systems has important practical significance. +

S1

SD1 S3

SD3

Forward iL

Q1 L

QD1 Q3

C2 V2

V1

Vin C1

SD2 S2 -

QD3 +

S4

SD4

1:n

Backward

Q2

QD2 Q4

Vo R

QD4 -

Figure Figure 1. 1. The The topology topology of of aa DAB DAB converter. converter.

At present, present, there thereare arefour fourmain mainDAB DABconverter convertertopologies: topologies:single-phase/three-phase single-phase/three-phase voltage voltage At source, single-phase current source, and single-phase resonant type. Control methods mainly focus source, single-phase current source, and single-phase resonant type. Control methods mainly focus on the phase shift control strategy, including single phase shift, double phase shift, expansion on the phase shift control strategy, including single phase shift, double phase shift, expansion double double phase shift, triple phase shiftwidth plus modulation pulse width modulation (PWM)strategy, hybrid phase shift, triple phase shift,phase phaseshift, shift plus pulse (PWM) hybrid control control strategy, and model predictive control methods [7–13]. The single phase shift control and model predictive control methods [7–13]. The single phase shift control strategy is simple and easy strategy simple and easy to realize, the range outputpower powerexists. is narrow and phase-shifting reverse power to realize,isbut the range of output powerbut is narrow andofreverse Multiple exists. methods Multiple have phase-shifting control methods increased control and the control increased control variables, andhave the combination selectionvariables, and calculation of combination selection and calculation of multivariable is the key points to controlling the multivariable is the key points to controlling the performance of DAB converters. performance of DAB converters. So far, many efforts have been made to improve the performance of DAB converters. Nevertheless, So far, many efforts havefrequency been made to converter improve transformers the performance of DAB converters. design considerations for high DAB are primarily concerned Nevertheless, design considerations for high frequency DAB converter transformers areconcept primarily with core material, loss minimization, and suppression of DC bias components. The of concerned withcondition core material, minimization, andinsuppression of the DCclosed bias components. The global optimal (GOC)loss equations is proposed [14] to derive form of analytic concept of global optimalmodulation condition (GOC) equations is proposed [14] to derive the closed form of expressions of an optimal scheme that makes the DAB in converter operate with minimized analytic expressions of an optimal modulation scheme that makes the DAB converter operate with root-mean-square (RMS) current during whole power range with different operating modes. Aiming to minimized root-mean-square (RMS) current during whole power range with different operating improve the performance features of conventional two-level DAB converters, reference [15] presented Aiming to improve the performance conventional DAB converters, amodes. three-level neutral-point-clamped (NPC) DABfeatures DC-DCof converter. A set two-level of decoupled optimization reference is [15] presentedas a three-level (NPC)degrees DAB DC-DC converter. A set of problems formulated a function neutral-point-clamped of the available modulation of freedom to minimize decoupled optimization problems is formulated as a function of the available modulation degrees of the predominant converter losses. A current-stress-optimized switching strategy is applied in [16] freedom to minimize the predominant converter losses. A current-stress-optimized switching based on Isolated Bidirectional DC-DC Converter (IBDC) to minimize the current stress, improve strategy is applied in [16] on system Isolatedpower Bidirectional DC-DCcapability, Converterand (IBDC) minimize the the system efficiency, and based increase transmission thesetoperformances current stress, improve the system efficiency, and increase system power transmission are particularly effective for operation conditions with high voltage conversion ratio and capability, light load. and model these predictive performances arealgorithm particularly effective for operation conditions with high voltage The control is used to improve the efficiency of DAB converter in [17]. conversion ratio and light load. The model predictive control algorithm is used to improve the A unit prediction horizon binary search-based nonlinear model predictive control (MPC) of phase efficiency of DAB converter in [17]. A unit prediction horizon binary search-based nonlinear model shift full-bridge DC-DC converter is presented in [18], which offers faster optimization solution for predictive control (MPC)high of phase shiftoperation full-bridge DC-DC converter is output presented in [18], which MPC, thereby facilitating frequency of the converter, thus the voltage regulation offers faster isoptimization solution for MPC, thereby of facilitating high frequency of the the performance improved. By investigating the influence the perturbation of controloperation variables on converter, thus the output voltage regulation performance is improved. By investigating the transferred power and the RMS value of the inductance current, a global optimal condition is deduced influence of the perturbation of controlroutine variables on the transferred power and thethe RMS value of the in [19]. A multi-objective optimization is proposed to systematically assess concepts with inductance current, a global optimal condition is deduced in [19]. A multi-objective optimization respect to the efficiency, power density, and the costs with the 3 and 5-Level DAB converter in [20]. routine is power proposed systematically assess the concepts respect power A detailed loss to model of a DAB converter was derivedwith in this paper, to butthe theefficiency, dynamic control density, and theon costs with the 3are andnot 5-Level DABAconverter in [20]. detailed power loss modelfor of methods based optimization regarded. minimized RMSAcurrent operation methods a DAB converter was derived in this paper, but the dynamic control methods based on the dual active half-bridge (DAHB) DC-DC converters is presented in [21]. In this paper, closed-form optimizationcorresponding are not regarded. minimized RMSare current operation methods RMS for the dual active expressions to twoAcontrol strategies derived which minimize value must be half-bridge (DAHB) DC-DC converters is presented in [21]. In this paper, closed-form expressions corresponding to two control strategies are derived which minimize RMS value must be consistent

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consistent value of transformer current at a given power with and without zero voltage switching Energies 2018, 11, x FOR PEER REVIEW 3 of 21 (ZVS) operation. The other optimal objectives are not discussed in this paper. A novel which can achieve thepower multi-objective for the performance in DAB value of method transformer current at a given with and optimization without zero voltage switching (ZVS) converters is proposed this paper. Using optimization methods based on the operation. The otherin optimal objectives arethis not genetic-algorithm discussed in this paper. A novel method the which can achievefeatures the multi-objective optimization performance dual phase shift control, performance of DAB converters suchforasthe high efficiency, in low dc DAB converters is proposed in this paper. Using this genetic-algorithm optimization methods based bias component and low stress to switching device can be realized considering the constraints such as the dual phase shift control, the performance features of DAB converters such as high efficiency, ZVS on conditions in DAB converter. low dc bias component and low stress to switching device can be realized considering the This paper is organized as follows: Section 2 introduces the operating principle of the DAB constraints such as ZVS conditions in DAB converter. converter, from two aspects of steady state and transient state, and some power characteristic formulas This paper is organized as follows: Section 2 introduces the operating principle of the DAB are derived. Section the multi-objective is established the basis of the converter,Infrom two 3, aspects of steady state optimization and transient model state, and some poweron characteristic Section 2, andare thederived. geneticInalgorithm is used to solve the optimal control variable for the power formulas Section 3, the multi-objective optimization model is established on the basismode of DAB converter. Simulation and hard in loop (HIL) experimental results for optimization on the of the Section 2, and the genetic algorithm is used to solve the optimal control variable for the power platform of software platform MATLAB/Simulink 2012 (The MathWorks Ltd, Natick, MA, USA) mode of DAB converter. Simulation and hard in loop (HIL) experimental results for optimization on and platform of software MATLAB/Simulink MathWorksverification Ltd, Natick, is MA, USA) HIL the platform typhoon 600 platform are delivered in Section 4.2012 The(The experimental described in and5.HIL platform typhoon 600 are our delivered in Section 4. The experimental verification is described Section Finally, Section 6 presents conclusions. in Section 5. Finally, Section 6 presents our conclusions.

2. The Establishment of Optimization Model 2. The Establishment of Optimization Model

In the DAB converter’s power transmission process, the coupled inductor L plays a very important In the DAB converter’s power transmission process, the coupled inductor L plays a very role, transmitting power either from the low voltage side to the high voltage side of the converter, important role, transmitting power either from the low voltage side to the high voltage side of the or from the high side to the low side, it uses of an inductance L is needed as the power transmission converter, or from the high side to the low side, it uses of an inductance L is needed as the power medium. Therefore, the inductance has a great influence on the operating of the DAB transmission medium. Therefore,selection the inductance selection has a great influence on ability the operating converter. The research on the input and output characteristics of the DAB converter will start with the ability of the DAB converter. The research on the input and output characteristics of the DAB analysis of the will inductance current iL . Figure 2 is inductance the main circuit waveform iL in acircuit switching converter start with the analysis of the current iL. Figureincluding 2 is the main L in the a switching The VH1and and secondary VH2 are theside primary sideofvoltage and cycle.waveform The VH1including and VH2 iare primary cycle. side voltage voltage high frequency secondary side voltage of high frequency transformers in Figure 2. Align equations and symbols transformers in Figure 2. Align equations and symbols D2Ts D1Ts

Ts

S1

t

S2

t

S3

t

S4

t

Q1(Q4)

t

Q2(Q3)

t nV1

VH1

t

-nV1 V2

VH2

t

-V2 nV1+V2

VL

V2

nV1-V2

t

-V2

-nV1+V2 -nV1-V2 t

iL

t

P t1' t0 t1 t2

t3

t4' t4 t5

t6

Figure 2. The main circuit waveform in one cycle.

Figure 2. The main circuit waveform in one cycle.

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2.1. Steady State Performance Analysis According to the principle of current ampere second equilibrium, the average of the inductance current is 0 within a switching period: Z 2T S 0

i L (t)dt = 0

(1)

The peak current of each time point can be derived from Figure 2:  i0 = i L ( t0 )      i1 = i L ( t1 )    i =i t 2 L( 2)  i3 = i L ( t3 )     i = i L ( t4 )    4 i5 = i L ( t5 )

= = = = = =

Ts 2L ( nV1 D1 − nV1 − 2V2 D2 + V2 ) Ts 2L ( nV1 D1 − nV1 + 2V2 D1 − 2V2 D2 + V2 ) Ts 2L (− nV1 D1 + 2nV1 D2 − nV1 + V2 ) Ts 2L (− nV1 D1 + nV1 + 2V2 D2 − V2 ) Ts 2L (− nV1 D1 + nV1 − 2V2 D1 + 2V2 D2 − V2 ) Ts 2L ( nV1 D1 − 2nV1 D2 + nV1 − V2 )

(2)

Because the magnitude of the effective current of inductor current directly affects the copper consumption of transformer and the state loss of semiconductor device [22], it is necessary to derive the expression of the RMS value square of inductance current as follows:

i2L(rms)

! !   nV1 D1 − nV1 D2 nV1 D1 + 2nV1 D2 − 3nV1   D1   −V2 D2 +2V2 D1 − 4V2 D2 + 3V2   ! !     nV1 D1 − nV1 + V2 D1 nV1 D1 − 2nV1 D2    + D2 Z2Ts −2V2 D2 + V2 +nV1 − 2V2 D1 − V2 1 Ts2  2 !2 !2 = i L (t)dt = 2  2Ts 6L  −nV1 D1 + 2nV1 D2 −nV1 D1 + nV1 1  0  +2[ +   −nV1 + V2 +2V2 D2 − V2   ! !     −nV1 D1 + 2nV1 D2 −nV1 D1 + nV1   ]  + −nV + V +2V D − V 1

2

2

2

2

               

(3)

              

In order to reduce the loss of the converter, the minimum RMS value of inductance current was chosen as one of the optimization objective functions. The average output power can be calculated as follow: 1 PO = Ts

ZTs

VH1 i L (t)dt =

0

nV1 V2 Ts 2D1 D2 − 2D22 + 2D2 − D12 − D1 2L

(4)

and it can be concluded that, when D1 = 0, D2 = 0.5, the maximum average output power is: Pmax =

nV1 V2 8 fs L

(5)

When the output load is R, PO can also be expressed as: V22 R

(6)

nV1 R 2D1 D2 − 2D22 + 2D2 − D12 − D1 4 fs L

(7)

PO = Combining with Equation (4) we can obtain: V2 =

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I2 =

nV1 2D1 D2 − 2D22 + 2D2 − D12 − D1 4 fs L

(8)

Because the DAB converter requires 28 V DC voltage output, V 2 = 28 V will be one of the constraints of this optimization model. 2.2. Reverse Power and Transient DC Bias Component Analysis It can be seen from Figure 2 that in the power transmission process, negative power has a reverse power flow direction. The negative power is a kind of reactive power, it increases the apparent power of the power transmission process in the circuit, meanwhile the losses of the circuit and devices are also increased. The increase of the power loss of the whole power converter can further reduce the efficiency of power transmission of the DAB converter. When the reverse negative power decreases, the peak value of the transmitted power also decreases, which reduces the switching stress of the power switching device and reduces the demand for the high frequency transformer capacity and thus reduces the power volume of the transformer under design. Therefore, in order to improve the performance of the converter, it is necessary to reduce the reverse negative power of the converter as much as possible. Deduce the time t10 of the inductance current iL is 0, that is: nV1 + V2 0 t1 − t1 + i ( t1 ) = 0 L We obtain: t10 =

(nV1 D1 + nV1 + 2V2 D2 − V2 ) Ts 2(nV1 + V2 )

(9)

(10)

The reverse negative power can be obtained from this: 0

P− avg

1 = Ts

Zt1

nV1 |i L (t)|dt

(11)

t1

Bring Equation (10) into Equation (11) and can be obtained: P− avg =

nV1 Ts [nV1 (1 − D1 ) + V2 (2D2 − 2D1 − 1)]2 8L(nV1 + V2 )

(12)

It can be seen that we can suppress the reverse negative power by optimizing the combination of D1 and D2 , thus we choose P− avg minimum as one of the optimization objective functions. In the circuit operating process, because of the difference of the parameters of the components or the asymmetry of circuit layout, the on-state voltage drop is not equal , the difference of the turn off time when the power switch is turned off, the power transistor trigger factors of pulse signal is asymmetric, and the current waveform of the high frequency transformer in the DAB converter cannot have ideal symmetry, therefore, the dc bias becomes a practical issue because of the inconsistency between theory and practice. According to these factors, the magnetization curve of the iron core is not symmetric about the origin of coordinates, and the magnetization curve is usually a nonlinear curve, so when there is very serious dc bias current, iron core will enter a saturation state, causing the magnetizing current to increase significantly, thus increasing the loss of the converter and even causing damage to the switching device [23–25]. Therefore, it is necessary to analyze and suppress this bias component. According to [16], the expression of DC bias is deduced to be used for subsequent suppression. The converter in positive mode (in buck mode), using a sudden increase in output power as an example, as shown in Figure 3, t0 moments ago, the converter stability and inductor current waveform were symmetrical, at time t0 ,

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are D1aand D2, surge, respectively, after theinternal power mutation, theshift converter internal and the external duty with power if the converter and external duty noted before powershift surge are D1 and D2 , respectively, D after the power mutation, the converter internal and external shift duty ratio ′ D′ 0 < D1 < D1′ and 0 < D2 < D2′ , then, with the ratio are refreshed0 to 1 0 and 2 respectively, are refreshed to D1 and D2 respectively, 0 < D1 < D1 0 and 0 < D2 < D2 0 , then, with the increase of increase of phase angle, the maximum value of the inductor current increases, and the DC bias phase angle, the maximum value of the inductor current increases, and the DC bias component will component will exist for even a few cycles. exist for even a few cycles.

Actual waveform of power stability Actual waveform of power sudden increase Ts ′

D 2 TS

D2Ts D1Ts

′

D1 TS

nV1

t

-nV1

t

V2 -V2

t

I dc

iL

t0 t1 t2

t3 t4 t5

t6

Figure3.3.Basic Basicwaveforms waveformsbefore beforeand andafter afterpower powerchanging changingdynamically. dynamically. Figure

DC DCbias biascomponent componentcan canbe becalculated calculatedaccording accordingto tothe the first first cycle cycle of: of: 2Ts

Z2Ts1 i t d = 2Ts−nV D' − D + 2V 2 D2' − D2 0 (13) 1Idc = 2Ts  1 1 0 1 L( )  2 T L Idc = isL (0t)d = −nV1 D1 − D1 + 2V2 D2 − D2 (13) 2Ts L 0 After the analysis above, this paper will select the minimum Idc as one of the optimization objective functions. After the analysis above, this paper will select the minimum Idc as one of the optimization In order to realize the high frequency, high efficiency and low loss operation for the converter, objective functions. soft switching technology oftenfrequency, used. Thehigh requirements thelow DAB converter to for implement ZVS In order to realize theishigh efficiencyof and loss operation the converter, are: soft switching technology is often used. The requirements of the DAB converter to implement ZVS are:

(

ii(( tt11))≤≤00  ii((t22)) ≥≥00

)

(

)

(

(14) (14)

SubstitutingEquation Equation(2) (2)into intoEquation Equation(14), (14),and andthe thefollowing following simplification simplification can can be be obtained: obtained: Substituting ( nV + 2V 2V22D 2V2V +2V2+≤V02 ≤ 0 nV D11D −1 −nV D1 1−− 1nV 2 D22 D 1 1+ (15) (15)  − nV D + 2nV D − nV + 2 ≥0 1 1D 1 1 + 2nV11D22− nV1 +1V2 ≥V0  −nV Equation(15) (15)will willbe beconsidered consideredas asthe theconstraint constraintcondition condition of of the the optimization optimization model. model. Equation Accordingto tothe therequirements requirements of of Table Table 1, 1, some function 3-D diagrams are drawn as follows. According

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Table 1. Circuit parameters in the rated state converter. Table 1. Circuit parameters in the rated state converter. Parameter Name Rated Value Parameter NameV1 Rated Value270 V High voltage side voltage Low voltage side voltage V2 V1 High voltage side voltage 270 V 28 V Low voltage side voltageCV 28 V 10 μF 1 2 High voltage side capacitance High voltage side capacitance 10 µF 1000 μF Low voltage side capacitance C2 C1 Low voltage side capacitance C2 1000 µF Transformer ratio n 270:80 Transformer ratio n 270:80 Coupled inductor L Coupled inductor L 12 µH 12 μH Load Load resistance R R resistance 1.568 Ω 1.568 Ω equivalent resistance 0.1 Ω 0.1 Ω Input Input equivalent resistance RS RS switching frequency 40 kHz 40 kHz switching frequency fS fS

D1 < D2 < 1 , the closer the D1 and D2 FromFigure Figure4a, 4a,ititcan canbe beseen seen that that under under the premise of From the premise of D 1 < D2 < 1, the closer the D1 and iL2(irms 2 ) Dare, are, the smaller the is. This result can be used as one of screening bases for D the D1 and 2 is.) This result can be used as one of the the screening bases for the 1 and D2 the smaller the L(rms Dcombination. 2 combination. A2

W

(a)

(b) A2

A

W

(c)

(d) 2

D1 − D2 − iL rms 2 Figure according to to Table Table 1.1. (a) (a)Function Functiondiagram diagram ; rms) Figure4.4.Function Function 3-D 3-D diagrams diagrams according of of D1 − D2 (− i) L; ((b) (b) Function diagram of D D1−−DD−2 P − P0 ; (c) Function diagram of D D1−− D − I ; (d) Function diagram of 2 dc D2 − I dc ; (d) Function diagram of 2 0 ; (c) Function diagram of 1 Function diagram of 1 P0 − i2L(2rms) . P0 − iL( rms )

.

Figure 4b proves that when D1 = 0, D2 = 0.5 Figure 4b proves that when D1 = 0, D2 = 0.5 nV1 V2 Pmax = nVV = 583W (16) Pmax = 8 f 1s L2 = 583W (16) 8 fs L It can be seen in Figure 4c, that when 0 < D1 < 0.6, 0.1 < D2 < 1, Idt is smaller this range can be It one can be seenscreening in Figurecriteria. 4c, that when 0 < D1 < 0.6 , 0.1 < D2 < 1 , I dc is smaller this range can be used as of the used as one of the screening criteria.

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As can be seen from Figure 4d, each PO corresponds to many i2L(rms) , so it is necessary to limit i2L(rms) . According to the rightmost point of the image, i2L(rms) should not exceed 1000 when solving the optimization model. This result will be used as an additional constraint. 3. The Optimal Solution of Power Model of DAB Converter Based on the above analysis, the optimization model of the DAB converter based on the extended phase shift control can be obtained according to the above analysis. Design variables: the interior angle x1 = D1 , and the external angle x2 = D2 , where: k1 = TS = 1/80000, k2 = 1.2e − 5, k3 = nV1 = 80, k4 = V2 = 28, k5 = P0 = 500. Objective function:       k x + 2k x 3 3 2  1   k2     f 1 ( x1 , x2 ) = 6k1 2 x1 (k3 x1 − k3 x2 − k4 x2 ) −3k3 + 2k4 x1    2      −4k!4 x2 + 3k4  !     k3 x1 − 2k3 x2 k 3 x1 − k 3 + k 4 x1   + x2   −2k4 x2 + k4 +k3 − 2k4 x1 − k4     !2 !2        −k3 x1 + 2k3 x2 − k 3 x1 + k 3    + min    −k3 + k4 +2k4 x2 − k4  1   ! !  +2      −k3 x1 + 2k3 x2 − k 3 x1 + k 3       +    − k + k + 2k x − k  3 4 4 2 4   " #  2   k 3 (1 − x1 )  k3 k1   f 2 ( x1 , x2 ) = 8k (k +k )  2 3 4  +k4 (2x2 − 2x1 − 1)     f ( x , x ) = 2k1 −k x 0 − x + 2k ( x 0 − x ) 3 1 3 1 2 2 1 4 2 k

(17)

2

Constraints:

 0 < x1 < x2 < 1       f 1 ( x1 , x2 ) < 1000 −k3 x1 + 2k3 x2 − k3 + k4 ≥ 0    k 3 x1 − k 3 + 2k 4 x1 − 2k 4 x2 + k 4 ≤ 0    k3 k4 k1 2x1 x2 − 2x22 + 2x2 − x12 − x1 = k5 2k

(18)

2

Genetic algorithm is an adaptive probability optimization algorithm that solves complex system optimization problems with the help of biological genetics and evolutionary ideas. It does not depend on the research object. Using the multi-objective genetic algorithm in the MATLAB genetic algorithm toolbox, the above models are solved, and a set of internal and external phase shift angles corresponding to the variation of load power are obtained, which is shown in Table 2. The Toolbox’s configuration is shown in following: Solver: gamultiobj; Population size: 1000; Pareto front population fraction: 0.02; Generations: 1000; Function tolerance: 1e-8; Constraint tolerance: 0.01. All the variables and parameters must be normalized. The Pareto front curve for the rated conditions is shown in Figure 5a. The terms f 1 and f 2 respectively correspond to the optimized objects. That is the optimization result, which is an important basis for our subsequent simulation and experiments. According to the Table 2, the basic relationship between the load power and phase shift angle D1 , D2 can be as shown in Figure 5b,c.

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Table 2. Optimization results. Table 2. Optimization results. No. Power Power (W)(W) 550550 1 500500 2 3 450450 4 400400 5 350350 6 300300 7 250250

No. 1 2 3 4 5 6 7

DD 11

D2

D2

0.215 0.215 0.33 0.33 0.456 0.456 0.52 0.52 0.568 0.568 0.617 0.617 0.746 0.746

0.548 0.58 0.726 0.654 0.645 0.645 0.865

0.548 0.58 0.726 0.654 0.645 0.645 0.865 D1

f1

0.8

0.7

D1

0.6

0.5

0.4

0.3

0.2 250

300

350

f2

400

450

500

550

P (W)

(a)

(b) D2 0.90 0.85 0.80

D2

0.75 0.70 0.65 0.60 0.55 0.50 250

300

350

400

450

500

550

P (W)

(c) Figure 5. (a) Pareto front on rated condition (b) Relation curve of D1 and power (c) Relation curve of Figure 5. (a) Pareto front on rated condition (b) Relation curve of D1 and power (c) Relation curve of D2 and power. D2 and power.

4. Simulation Verification 4. Simulation Verification 4.1. MATLAB Simulation Verification 4.1. MATLAB Simulation Verification According to the parameters in Table 1, a DAB converter model based on MATLAB/Simulink is According to s,the parameters in Table 1, a DAB converter model onΩMATLAB/Simulink fully run for 0.1 whereby the load resistance increases from 1.568 Ω based to 3.136 at 0.05 s, and the is fully run for 0.1 s, whereby the load resistance increases from 1.568 Ω to 3.136 Ω at 0.05 indexes s, and the transmission power is changed from the rated 500 W to 250 W, comparing the performance transmission power in is changed from the rated 500 W to 250integration W, comparing the performance indexes of DAB converter, contrast to the traditional proportion differentiation (PID) control of mode. DAB converter, in contrast to the traditional proportion integration differentiation (PID) control The closed-loop control blocks for the DAB converters can be realized by the look-up table mode. The closed-loop control blocks for the DAB converters can be realized by the look-up table from the control variable of Table 2 under the different load situations by the offline optimization from the control of Table 2 under thealgorithm differentcan load byclose-loop the offlinecontroller optimization method, so the variable linear extrapolation methods besituations used for the in method, the linear extrapolation methods algorithm can beload usedpower for the close-loop controller look-upsotable to meet the power demand between the given points in Figure 2. The in controltable block the DAB converter based on theload optimal in look-up to diagram meet the of power demand between the given powercontrol pointsmethods in Figureis2.shown The control Figure 6a andofthe of thebased control is shown Figure 6b. From Figure 6a,6a theand block diagram theflow DABchart converter onalgorithm the optimal controlin methods is shown in Figure

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the flow chart of the control algorithm is shown in Figure 6b. From Figure 6a, the offline optimal phaseoffline shift variables D1 and Dvariables the load power computation. The control algorithm 2 can be selected optimal phase shift D1 and Dby 2 can be selected by the load power computation. The basedcontrol on thealgorithm Figure 6bbased is very and efficiency. It ishigh very easily realized the digital signal on simple the Figure 6bhigh is very simple and efficiency. It is veryineasily realized processing (DSP) signal controller platform. in the digital processing (DSP) controller platform.

(a)

(b) Figure 6. (a) Proposed control block diagram; (b) The flow chart for the algorithm.

Figure 6. (a) Proposed control block diagram; (b) The flow chart for the algorithm.

4.1.1. Transient Output Characteristics

4.1.1. Transient Output Characteristics

The output voltage, current waveform and local magnification diagram of the two control mode

methods arevoltage, shown incurrent Figure 7. The output waveform and local magnification diagram of the two control mode methods are shown in Figure 7.

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V 28.6

V/A 30 25 20 Energies 2018, 11, x 15 FOR PEER REVIEW

V/A 30 0 25 20 15 V/A

28 11 of 21

27 V 28.6 0

t

0.05

(a)

0.05

t

28

V

30 20

27 28

010

t

0.05

0

t

0.05

(a) 27

0.05 t 0.05 0.052 t V 0.048 V/A 0 (b) 30 Figure 207. Output waveform and its amplification. (a) 28Optimal control mode; (b) Traditional control

Figure 7. Output mode. waveform and its amplification. (a) Optimal control mode; (b) Traditional 10 control mode. 27

One can get from the figures, on the optimal control model, that the response time of the 0 0.05 t 0.048 0.05 0.052 t converter is 6 ms, output voltage is stable at 28 V, output current is about 17.86 A, power is 500 W, (b) One can getthefrom the figures, on the optimal control model, that the response system has no overshoot during start-up, voltage ripple is less than 0.1 V, and the rippletime ratio isof the converter Figure 7.0.36%. Output waveform and its amplification. (a)voltage Optimal control mode; (b) Traditional control less than When the load mutates, the output has a 0.1 V overshoot with a rate of is 6 ms, output voltage is stable at 28 V, output current is about 17.86 A, power is 500about W, the system has mode. 0.3%, then settles at 27.7 V, about 1% error, ripple about 0.06 V, with a rate of about 0.2%. In the no overshoot during start-up, voltage ripple is less than 0.1 V, and the ripple ratio is less than 0.36%. traditional control mode, when the load is suddenly changed, the output voltage fluctuates rapidly One can get from on has the optimal model, that ratio the response timewhich of0.3%, the then settles between 27.6 V–28.3 V.the Thefigures, ripple peak value 0.7 V, and the ripple is about When the load mutates, the output voltage a reaches 0.1 Vcontrol overshoot with a rate of 2.5%, about seriously the stability of the converter converter is 6affects ms, output voltage is stable at 28output. V, output current is about 17.86 A, power is 500 W,

at 27.7 V, about 1% error, ripple about 0.06 V, with a rate of about 0.2%. In the traditional control mode, the system has no overshoot during start-up, voltage ripple is less than 0.1 V, and the ripple ratio is 4.1.2. RMS Value of Inductor Current and Bias voltage Current Component when the load suddenly changed, the output voltage fluctuates rapidlywith between 27.6 V and 28.3 V. lessis than 0.36%. When the load mutates, theDC output has a 0.1 V overshoot a rate of about 0.3%, then settles at 27.7 V, about 1% error, ripple about 0.06 V, with a rate of about 0.2%. In the In the two control modes, the waveforms of the inductance current are as shown in Figure 8. The ripple peak value reaches 0.7 V, and the ripple ratio is about 2.5%, which seriously affects the traditional control mode, when the load is suddenly changed, the output voltage fluctuates rapidly stability of the converter output. between 27.6 V–28.3 A V, and the ripple ratio is about 2.5%, which A V. The ripple peak value reaches 0.7 seriously affects the stability of the converter output.

30 30 Current and DC Bias Current 4.1.2. RMS Value of Inductor Component 4.1.2. RMS Value of0Inductor Current and DC Bias Current Component 0

In the two control modes, the waveforms of the inductance current are as shown in Figure 8. In the two control modes, the waveforms of the inductance current are as shown in Figure 8. 30

A

0

0.05 (a)

t

30 0

A

0.05

t

(b)

30 control mode; (b) Traditional control mode. Figure 8. 30Inductance current waveform of (a) Optimal 0 value of inductance current increases from 0 from the above diagrams that the peak It can be seen 60 A to 65 A in the traditional control mode when the load is changed. The inductance current 30 30 waveform is shifted upwards, the forward amplitude is about 40 A, and the negative amplitude is t t 0 0.05 about −25 A, and no longer has positive and negative0 symmetry. In0.05 the optimal control mode, the (a) (b) current waveform of the inductor still shows positive and negative symmetry, the peak-to-peak value decrease obviously, fromwaveform 60 A to 40 the positive and negative amplitude is about Figure 8. Inductance current of A, (a) and Optimal control mode; (b) Traditional control mode.20 A. At the same time, through the MATLAB/Simulink module solution, the RMS of the inductor Figure 8. Inductance current waveform of (a) Optimal control mode; (b)value Traditional control mode. current of traditional control mode is 19.91that A, the bias component is aboutcurrent 1.146 A, and for from the It can be seen from the above diagrams theDC peak value of inductance increases optimal control mode, the RMScontrol value of the inductor current A, theThe DC inductance bias component is A to 65 A in the the traditional mode whenthe the load isis16.86 changed. current It can be60 seen from above diagrams that peak value of inductance current increases about 0.4893 A, and one can the see that the two indexes is of about the RMS of the the negative inductor current and is waveform is shifted upwards, forward amplitude 40 value A, and amplitude biasthe component are significantly mode improved in optimal controlismode compared with the from 60 A to about 65DC A−25 in traditional when the load The inductance current A, and no longer hascontrol positive and negative symmetry. In the changed. optimal control mode, the traditional PI control.

waveform iscurrent shifted upwards, forward amplitude is negative about 40 A, and negative amplitude waveform of the the inductor still shows positive and symmetry, thethe peak-to-peak value decrease obviously, from 60 A to 40 A, and the positive and negative amplitude is about 20 A.control mode, is about −25 A, and no longer has positive and negative symmetry. In the optimal At the same time, through the MATLAB/Simulink module solution, the RMS value of the inductor the current waveform of the inductor shows and negative the current of traditional control modestill is 19.91 A, thepositive DC bias component is about symmetry, 1.146 A, and for thepeak-to-peak optimal control mode, value inductor is 16.86 the DC biasamplitude component isis about 20 A. value decrease obviously, fromthe60RMS A to 40ofA,theand the current positive andA,negative about 0.4893 A, and one can see that the two indexes of the RMS value of the inductor current and At the same time, through the MATLAB/Simulink module solution, the RMS value of the inductor DC bias component are significantly improved in optimal control mode compared with the current of traditional traditional PIcontrol control. mode is 19.91 A, the DC bias component is about 1.146 A, and for the optimal control mode, the RMS value of the inductor current is 16.86 A, the DC bias component is about 0.4893 A, and one can see that the two indexes of the RMS value of the inductor current and DC bias component are significantly improved in optimal control mode compared with the traditional PI control. 4.1.3. Reverse Negative Power The waveform of the transient power of the low voltage side of the transformer under two control modes is shown in Figure 9.


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4.1.3. Reverse Negative Power

Energies 2018, 11, 1168 The waveform of the transient power of the low voltage side of the transformer under two

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control modes is shown in Figure 9.

W 3000

W 3000

0 -2000

0 -2000

0

t

0.05

0

(a)

t

0.05 (b)

Figure 9. The waveform of the transient power of the low voltage side of the transformer. (a) Optimal

Figure 9. Themode; waveform of themode. transient power of the low voltage side of the transformer. (a) Optimal (b) Traditional mode; (b) Traditional mode. It can be clearly seen that under optimizing control mode, negative power was inhibited to almost 0, while under the traditional control mode, the negative power did not fall, therefore, the beindex clearly seen that under optimizing control mode, negative power was inhibited of negative power is also significantly improved under optimal control.

It can to almost 0, while under the traditional control mode, the negative power did not fall, therefore, the index of 4.1.4.isComparison and Summary of the Changes negative power also significantly improved under optimal control. The other situations are similar to the result of figure 7a,b. In Table 3, we directly give the ② is the traditional control mode.

comparison three indexes, is the optimization control mode, and 4.1.4. Comparison andofSummary of①the Changes

The other situations are similar to the result of Figure 7a,b. In Table 3, we directly give the Table 3. Comparison of indexes under each transient DAB model. 1 is the optimization control mode, and 2 is the traditional control mode. comparison of three indexes, 500 W ⟶ 250 W

iL( rms ) (A)

丨I 丨 (A)

P−avg (W)

dc Table 3. Comparison of indexes under each transient DAB model.

① ②

16.86 0.4893 19.91 1.146 ⟶ 300 500W W→ 500 250WW

iL( rms ) (A)

① ② 1

2

① ②

1

2

① ②

i L(rms) (A) 16 20.04 16.86

丨Idc丨 (A)

| Idc | (A)

0.677 1.126 0.4893 500W ⟶ 350W

19.91 1.146 iL( rms ) (A) Idc丨 (A) 500 W → 300丨W 17.41 0.6871 i L(rms)20.17 (A) | Idc | (A) 0.9325 500W ⟶ 400W

16 0.677 iL( rms ) (A) 丨Idc丨 (A) 20.04 1.126 18.28 0.6143 500W → 350W 20.29 0.6808

i L(rms) (A)500W ⟶|450W Idc | (A) 1 ① 2 ②

iL( rms ) (A)

17.41 0.6871 20.06 0.6302 20.17 0.9325 20.41 0.9902 ⟶ 550W 500W → 500W 400W iL rms (A)

① ② 1

2

) i L(rms)( (A)

21.51 22.54 18.28

20.29

1

2

20.06 20.41

丨I 丨 (A)

dc | Idc | (A)

0.7485 1.116 0.6143

0.6808 500W → 450W

i L(rms) (A) 1

2

丨Idc丨 (A)

| Idc | (A)

0.6302 0.9902 500W → 550W

−0.1567 −225

P−avg (W)

P− avg (W)

−1.058

−209 −0.1567 −225

P−avg (W) −9.099

P− avg (W) −194.4

−1.058 P−avg −209

(W)

−27.74 −180.3

P− avg (W)

P−avg (W)

−9.099 −79.41 −194.4 −165.9

P−avg (W)

P− avg (W)

−160

−257.2 −27.74 −180.3

P− avg (W)

−79.41 −165.9

i L(rms) (A)

| Idc | (A)

P− avg (W)

21.51 22.54

0.7485 1.116

−160 −257.2

Three contrastive curves are drawn in Figure 10 from Table 3: (the transverse axis indicates a transient variation from the rated power of 500 W to the corresponding power).

Three contrastive curves are drawn in Figure 10 from Table 3: (the transverse axis indicates a transient variation from the rated power of 500 W to the corresponding power). Energies 2018, 11, x FOR PEER REVIEW

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Energies 2018, 11, 1168contrastive curves are drawn in Figure 10 from Table 3: (the transverse axis indicates a 13 of 21 Three

transient variation from the rated power of 500 W to the corresponding power).

(a)

(b) (a)

(b)

(c) (c)

Figure 10. Three contrastive curves according to Table 3. (a) Comparison of RMS value of inductor Figure 10. Three contrastive curves according to Table 3. (a) Comparison of RMS value of inductor Figure 10. contrastive curves to Table 3. (a) Comparison of Comparison RMS value ofofinductor current; (b)Three Comparison of DC biasaccording component of inductance current; (c) reverse current; (b) Comparison of DC bias component of inductance current; (c) Comparison of reverse current; (b) Comparison of DC bias component of inductance current; (c) Comparison of reverse negativenegative power.power. negative power. The comparison in Figure showsthat, that,under under the power, the the indicators of the of twothe kinds The comparison in Figure 10 10 shows therated rated power, indicators two kinds of control modes are similar, but when the load changes, the performance index of the optimized The comparison in Figure 10 shows that, under the rated power, the indicators of the two kinds of of control modes are similar, but when the load changes, the performance index of the optimized control mode is obviously superior to the traditional control mode. control modes similar, but when to thethe load changes,control the performance index of the optimized control control mode isare obviously superior traditional mode. mode is obviously superior to the traditional control mode. 4.2. Typhoon Hard-in-Loop Simulation Verification

4.2. Typhoon Hard-in-Loop Simulation Verification Typhoon HIL system provides a complete solution to engineers doing research and design 4.2. TyphoonThe Hard-in-Loop Simulation Verification ofTyphoon power electronics systems on one a system (platform) for engineering project design, real-time The HIL system provides complete solution to engineers doing research and design The Typhoonverification HIL system provides atesting. complete solution engineers research design simulation, andon real-time Figure 11a for is to the hardware doing block diagram ofand the of power electronics systems one system (platform) engineering project design, real-time of power electronics systems Typhoon HIL system [26]. on one system (platform) for engineering project design, real-time simulation, verification and real-time testing. Figure 11a is the hardware block diagram of the main circuit ofreal-time the systemtesting. is built on the Typhoon platform, as shown in Figure 11b,of and simulation, The verification and Figure 11a is the hardware block diagram thetheTyphoon Typhoon HIL system [26]. semi physical simulation experiment is carried out in combination with the control program in the HIL system [26]. The main circuit of the system is builtDallas, on theTX, Typhoon platform, as shown in Figure DSP28335 (Delfino, Texas Instruments, USA). Like the MATLAB simulation, the11b, load and the The main circuit of the system is built on the Typhoon platform, as shown in Figure 11b, and the semi physical simulation experiment carried combination withpower the control program resistance increases from 1.568 Ω tois3.136 Ω at out 0.05 in s, and the transmission is changed from in the semi physical simulation is carried out in combination withvariation. the control program in the the rated 500 WTexas to 250experiment W. Observe the performance theLike load transient DSP28335 (Delfino, Instruments, Dallas, TX,under USA). the MATLAB simulation, the load DSP28335 (Delfino, Texas Instruments, Dallas, TX, USA). Like the MATLAB simulation, the load resistance increases from 1.568 Ω to 3.136 Ω at 0.05 s, and the transmission power is changed from resistance increases from 1.568 Ω to 3.136 Ω at 0.05 s, and the transmission power is changed from the the rated 500 W to 250 W. Observe the performance under the load transient variation. rated 500 W to 250 W. Observe the performance under the load transient variation.

(a)

(a) Figure 11. Cont.

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(b) Figure 11. 11. (a) HIL system; based converter converter Figure (a) The The hardware hardware block block diagram diagram of of the the Typhoon Typhoon HIL system; (b) (b) Typhoon Typhoon based virtual hardware circuit in software platform. virtual hardware circuit in software platform. (b)

4.2.1. Output Voltage Performance 4.2.1. Output Voltage Performance Figure 11. (a) The hardware block diagram of the Typhoon HIL system; (b) Typhoon based converter virtual hardwareiscircuit in softwarewith platform. The DAB converter connected pure resistive load in accordance with the parameters The DAB converter is connected with pure resistive load in accordance with the parameters given given in Table 1. The waveform at the output terminal of DAB converter is shown in Figure 12a in Table 1.4.2.1. TheOutput waveform the output terminal of DAB converter is shown in Figure 12a under Voltage at Performance under the rated steady state. The red waveform represents the output voltage. The green one is the rated steady state. The red represents theload output voltage.with The one is output The DAB converter is waveform connected with pure resistive in accordance thegreen parameters output current waveform. given in Table 1. The waveform at the output terminal of DAB converter is shown in Figure 12a current waveform. It is shown that the converter response time is about the 7 ms, there is no overshoot and output under the rated state. The red waveform output voltage. green one and is It is shown that thesteady converter response time represents is about 7 ms, there is noThe overshoot output voltage is output stablecurrent at 28 waveform. V, ripple voltage is about 0.04 V, the ripple ratio is 0.14%, output current is voltage is stable at 28 V, ripple voltage isresponse about 0.04 V, the ripple ratioisisno 0.14%, output current is about is shown that the converter about ratio 7 ms, is there overshoot and output about 17.86 A,Itthe current ripple is about 0.04 A,time the isripple 0.22%, output power reaches 500 W, 17.86 A, the current ripple is about 0.04 A, the ripple ratio is 0.22%, output power reaches 500 W, voltage is stable at 28 V, ripple voltage is about 0.04 V, the ripple ratio is 0.14%, output current is reached the requirements. about 17.86 A, the current ripple is about 0.04 A, the ripple ratio is 0.22%, output power reaches 500 W, reached the requirements. After the load is abruptly changed, the output voltage and current waveform are shown in the requirements. Afterreached the load is abruptly changed, the output voltage and current waveform are shown in Afterthe theload load transient is abruptly variation, changed, thethe output voltage and slightly, current waveform are shown in 28 V, the Figure 12b. After voltage drops but it remains near Figure 12b. After the load transient variation,the the voltage drops slightly, but it remains near 28 V, the load voltage current is Figure about12b. 8.86After A, and thetransient powervariation, is about 250 W. drops slightly, but it remains near 28 V, the the currentcurrent is about 8.868.86 A, A, and about is about andthe the power power isis about 250 250 W. W.

V 28.04 V 28 28.0427.96

28 27.96

0.027

A 17.88 17.86 17.84

A 17.88 17.86 17.84

0.027 0.027

0.028

t

t

0.028 0.029

t

(a)

Figure 12. Cont.

0.027

0.029 (a)

t

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(b) Figure 12. Output waveform. (a) output voltage, current waveform and local magnification diagram

(b) Figure 12. under Output waveform. (a) output voltage, current waveform and local magnification diagram optimal control mode; (b) Output waveform in the case of load transient variation. underFigure optimal control mode; (b) Output waveform in the case of load transient variation.diagram 12. Output waveform. (a) output voltage, current waveform and local magnification

4.2.2. Realization of Soft Switching under optimal control mode; (b) Output waveform in the case of load transient variation. The of operation of switch Q1 & S1 is shown in Figure 13. Figure 13a is the turn on waveform of S1. 4.2.2. Realization Soft Switching Under rated of working conditions, the voltage VDS when the switch is off is 270 V, and the drive 4.2.2. Realization Soft Switching The operation of switch shown in1 opening, Figure the 13.S2Figure is the turn on waveform of voltage of switch, VGS is Q 1 V. At S the moment of S has been13a turned off, the inductance 1 & 1 is The operation of switch Qanti-parallel 1 & S1 is shown in Figure 13. Figure 13a is the turn on waveform of S1. current is negative, and the diode of S 1 , S D1 is used to continue the current, thus, theand zero the drive S1 . Under rated working conditions, the voltage VDS when the switch is off is 270 V, Undervoltage rated opening working conditions, the The voltage VDS when theswitching switch iswaveform off is 270 V, andS1the conditions are met. red waveform is the of device anddrive voltage of switch, VGS is 1 V. At the moment of S1 opening, the S2 has been turned off, the inductance voltage ofThe switch, GS is V.waveform At the moment of S1 opening, Q1. greenVone is 1the of inductance current. the S2 has been turned off, the inductance

current is negative, andand thethe anti-parallel diode usedtoto continue current, the zero D1isisused current is negative, anti-parallel diodeofofSS11,, S SD1 continue thethe current, thus,thus, the zero voltage opening conditions are met. The red waveform is the switching waveform of device S1 and Q1. voltage opening conditions are met. The red waveform is the switching waveform of device S1 and The green one is the waveform of inductance current. Q1. The green one is the waveform of inductance current.

(a)

(a)

(b) Figure 13. Realization of soft switch (a); turn on waveform of S1 (b) turn on waveform of Q1.

Figure 13b is the open waveform of Q1. Under rated working condition, the voltage VDS when the switch is off is 28 V, and the drive voltage of switch, VGS is 1 V. At the moment of Q1 opening, the Q2 has been turned off, the inductance current is negative, and the anti-parallel diode of Q1, QD1 is (b) opening conditions are meet. The other switches used to continue the current, thus, the zero voltage areFigure similar13. to the above waveforms, and(a); therefore omitted here. Realization of soft switch turn onare waveform of S1 (b) turn on waveform of Q1.

Figure 13. Realization of soft switch (a); turn on waveform of S1 (b) turn on waveform of Q1 . 4.2.3. Coupled Inductor Related Waveforms

Figure 13b is the open waveform of Q1. Under rated working condition, the voltage VDS when Figure 14 is waveform, is in agreement with themoment theoretical Figure 13b the waveform ofvoltage Q1 . Under rated the voltage VDS when the switch isisoff is open 28anV,inductive and thevoltage drive of which switch, Vworking GS is 1 V. condition, At the ofanalysis. Q1 opening, the Q2 has been turned off, the the inductance current is negative, and diode of 1, Qopening, the switch is off is 28 V, and drive voltage of switch, VGS is the 1 V.anti-parallel At the moment ofQQ 1 D1 is to continue the current, thus, the zero voltage opening conditions are meet. The other switches the Qused has been turned off, the inductance current is negative, and the anti-parallel diode of Q1 , QD1 is 2 are similar to the above waveforms, and therefore are omitted here. used to continue the current, thus, the zero voltage opening conditions are meet. The other switches

are similar to the above waveforms, and therefore are omitted here. 4.2.3. Coupled Inductor Related Waveforms

FigureInductor 14 is an inductive waveform, which is in agreement with the theoretical analysis. 4.2.3. Coupled Related voltage Waveforms

Figure 14 is an inductive voltage waveform, which is in agreement with the theoretical analysis.

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Figure Inductancevoltage voltage waveforms. Figure 14.14. Inductance waveforms. Figure 14. current Inductance voltage waveforms. Figure 15a,b are the inductance waveforms of the steady-state and load abrupt

Figure 15a,b which are theareinductance current waveforms ofwaveforms. thewaveforms steady-state and load abrupt moments, same with the low voltage side current of transformer. As canmoments, be Figure 14. Inductance voltage Figure 15a,b are the inductance current waveforms of the steady-state and load abrupt seen fromwith Figure 15a, thevoltage current side waveform of the inductor is of in transformer. agreement withAs thecan theoretical which are same the low current waveforms be seen from moments, which areseen same with the low voltage side current waveforms of transformer. As current can be analysis. As can be from Figure 15b, after the load is abruptly changed, the inductance Figure 15a,b are the inductance current waveforms of thewith steady-state and load abrupt As can Figure 15a, the current waveform of the inductor is in agreement the theoretical analysis. seen from Figure 15a, the current waveform ofafter the inductor is in s,agreement withand the peak theoretical is restored to positive and negative symmetry about 0.0004 and the peak value which15b, are same with the low sidechanged, current waveforms of transformer. As is can be be seenmoments, from Figure after the load is voltage abruptly thechanged, inductance current restored to analysis. As can±30 be V seen from Figure 15b, afterthe theRMS loadvalue is abruptly the inductance current decrease from to ±20 V. By calculation of the inductor current is 16.88 A, and seen from Figure 15a, the current waveform of the inductor is in agreement with the theoretical positive is and negative symmetry after about 0.0004 s, and the peak and peak value decrease from ± 30 V restored to positive and negative symmetry after about 0.0004 s, and the peak and peak value the DC bias component about 0.4903 A.after the load is abruptly changed, the inductance current analysis. As can be seen is from Figure 15b, decrease from ±30 V to RMS ±20 V.value By calculation the RMScurrent value of is the16.88 inductor current is 16.88 A,component and to ±20 V. By calculation the of the inductor A, and the DC bias is restored to positive and negative symmetry after about 0.0004 s, and the peak and peak value the DC bias component is about 0.4903 A. is aboutdecrease 0.4903 A. from ±30 V to ±20 V. By calculation the RMS value of the inductor current is 16.88 A, and the DC bias component is about 0.4903 A.

(a) (a) (a)

(b) Figure 15. Inductance current waveforms (b) on (a) Steady state; (b) transient state. Figure 15. Inductance current waveforms (b) on (a) Steady state; (b) transient state. 4.2.4. Transformer Related Waveform Figure 15. Inductance current waveforms on (a) Steady state; (b) transient state. 15. Inductance current on (a) Steady (b) transient state. 16Figure is the voltage waveform ofwaveforms the low voltage side ofstate; the transformer, with an amplitude 4.2.4.Figure Transformer Related Waveform of ±80 V, andRelated the waveform is consistent with the theoretical analysis. 4.2.4. Transformer Waveform 4.2.4.Figure Transformer Related Waveform 16 is the voltage waveform of the low voltage side of the transformer, with an amplitude of ±80 V, and the waveform is consistent with the theoretical analysis. Figure Figure 16 is the waveform ofofthe side transformer, with an amplitude 16 isvoltage the voltage waveform thelow low voltage voltage side of of thethe transformer, with an amplitude of ±80 V, waveform is consistent theoreticalanalysis. analysis. of and ±80 V,the and the waveform is consistentwith withthe the theoretical

Figure 16. Voltage waveform of low voltage side of transformer. Figure 16. Voltage waveform of low voltage side of transformer. Figure 16. Voltage waveformof of low low voltage side of transformer. Figure 16. Voltage waveform voltage side of transformer.

Figure 17 is the power waveforms of the low voltage side of the transformer at the steady-state and load abrupt variation moments.


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Energies 2018, 11, 1168 17 is the power waveforms of the low voltage side of the transformer at the steady-state 17 of 21 Figure

and load abrupt variation moments.

(a)

(b) Figure 17. The power waveforms of the low voltage side of the transformer on (a) Steady state; (b)

Figure 17. The power waveforms of the low voltage side of the transformer on (a) Steady state; transient state. (b) transient state.

Due to the role of the external phase angle D2, the phase of the transformer's current and voltage is not synchronous in Figures 15a and 16, which results in a negative value of the instantaneous Due to theofrole of the external ofphenomenon. the transformer's current voltage is power the transformer, thatphase is, the angle reverseDnegative power However, fromand Figure 2 , the phase 16, we canin seeFigures that because of the of D1, the voltage has of zero time. In this not synchronous 15a and 16,presence which results in aoutput negative value theoutput instantaneous power of period, the negative power has changed to 0, which reduces the size of negative power and the transformer, that is, the reverse negative power phenomenon. However, from Figure 16, we can see improves the efficiency of energy transmission. It can be seen from Figure 17b that the reverse that because of the presence of D1 , the output voltage has zero output time. In this period, the negative negative power is suppressed after the load mutation, and after 12 cycles, about 0.3 ms, the negative power has changed to 0, which reduces the size of negative power and improves the efficiency of power is almost 0 W.

energy transmission. It can be seen from Figure 17b that the reverse negative power is suppressed Verification of Experiment Prototype after the5.load mutation, and after 12 cycles,Hardware about 0.3 ms, the negative power is almost 0 W. A prototype DAB converter was designed for verification of the proposed scheme. A 200–600 W

5. Verification of Experiment Prototype Hardware scaled down DAB converter has been developed. The schematic layout of experimental set-up is presented in Figure 18. During thedesigned experimentation, an aerospace high voltage DC source A (270 V A prototype DAB converter was for verification of the proposed scheme. 200–600 W DC) was used for power supply. In the DAB converter, the power switching device in high voltage scaled down DAB converter has been developed. The schematic layout of experimental set-up is side was a International Rectifier-MOSFET IRF460P (Infineon Technologies AG, Neubiberg, presented in Figure the experimentation, an aerospace high voltage DC source (270 V DC) Germany), and18. onDuring the low voltage side it is an IRF150P. was used forThe power supply. verification In the DABofconverter, the power switching device in highDSP voltage side was experimental DAB converter is carried out by using a DSP28335 digital controller, All the control algorithms downloaded into thisAG, controller. The results of the and on a International Rectifier-MOSFET IRF460Pwere (Infineon Technologies Neubiberg, Germany), areit shown in Figure 19. From Figure 19a, the steady state characteristic for the output the low experiments voltage side is an IRF150P. voltage can be achieved by the proposal controlling methods based on the multi-objective The experimental verification of DAB converter is carried out by using a DSP28335 DSP digital optimization. In Figure 19b,c, it is can been seen that the inductance current can charge and controller, All the control algorithms were downloaded into this controller. The results of the discharge following the control logic signal under the optimization methods. The power experiments are shown Figure according 19. FromtoFigure the steady state characteristic the output transmission can beinachieved Figure 19a, 19c. When the input voltage is 273 V, thefor output voltage can be achieved byorder the proposal controlling methods based on algorithm, the multi-objective optimization. voltage is 27.9 V. In to verify the transient ability of the control the transient load variation out, with experimental results shown in Figure 19d, and thedischarge output voltage In Figure 19b,c, was it iscarried can been seenthe that the inductance current can charge and following can be quickly kept at reference voltage of 28 V. the control logic signal under the optimization methods. The power transmission can be achieved according to Figure 19c. When the input voltage is 273 V, the output voltage is 27.9 V. In order to verify the transient ability of the control algorithm, the transient load variation was carried out, with the experimental results shown in Figure 19d, and the output voltage can be quickly kept at reference voltage of 28 V.

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Figure 18.The Theexperimental experimental prototype Figure 18. prototypediagram. diagram. Figure 18. The experimental prototype diagram. Figure 18. The experimental prototype diagram.

(a) (a) (a)

(b) (b) (b)

(c) (d) (c) (d) Figure 19. (a) The steady state waveform of input and output voltage; (b) The MOSFET gate driving (c) (d) signal inductor current waveform; (c)of Output characteristic waveform of power andgate voltage; (d) Figureand 19. (a) The steady state waveform input and output voltage; (b) The MOSFET driving Figure 19. (a) The steady state waveform of input and output voltage; (b) The MOSFET gate driving Figure 19. (a) The steady waveform inputload and output voltage; (b) The MOSFET driving The transient waveform ofstate output voltage under variation. signal and inductor current waveform; (c)of Output characteristic waveform of power andgate voltage; (d) signalsignal and and inductor current waveform; (c)Output Output characteristic waveform of power and voltage; inductor current waveform; (c) characteristic The transient waveform of output voltage under load variation. waveform of power and voltage; (d) In order to verify the capability ofvoltage the proposed method to decrease the reverse negative power (d) The ofoutput outputvoltage under variation. Thetransient transient waveform waveform of under loadload variation.

In order to the capability of thewas proposed to decrease reversemethods, negativefor power transmission, a verify comparative experiment carriedmethod out under the twothe control the In order to verify the capability of the proposed method to decrease the reverse negative power transmission, a comparative experiment was carried out under the two control methods, for traditional double phase shift and the proposed method, respectively. It can be seen from Figure 20 In order to verify the capability of the proposed method to decrease the reverse negativethe power transmission, a negative comparative experiment was carried out under thethat two control methods, for are the traditional double phase shift and the proposed method, respectively. It can be seen from Figure that the reverse power can be greatly reduced. It is verified the proposed methods transmission, a comparative experiment was carried out under the two control methods, 20 for the traditional double phase shiftfor and the method, It can be seen from Figure 20 that the reverse negative can be greatly reduced. Itrespectively. is verified that thebe proposed methods are valid and reliable enough use inproposed the DAB converter in an aircraft electric power system traditional double phase shiftpower and the proposed method, respectively. It can seen from Figure 20 that that the reverse negative power can be greatly reduced. It is verified that the proposed methods are valid and reliable enough for use in the DAB converter in an aircraft electric power system background. the reverse negative power can be greatly reduced. It is verified that the proposed methods are valid valid and reliable enough for use in the DAB converter in an aircraft electric power system background. and reliable enough for use in the DAB converter in an aircraft electric power system background. background.

(a) (b) (a) (b) Figure 20. The waveform of transmission power in (a) Traditional control methods (b) The proposed (a) (b) methods. Figure 20. The waveform of transmission power in (a) Traditional control methods (b) The proposed Figure 20. The waveform of transmission power in (a) Traditional control methods (b) The proposed methods. Figure 20. The waveform of transmission power in (a) Traditional control methods (b) The methods.

proposed methods.

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According to the different performance index testing methods, the aerospace DAB converter’s According to the different performance index testing methods, aerospace experimental result comparison under different control methods can the be showed in DAB Figureconverter’s 21. From experimental result comparison under different control methods can be showed Figure 21. Figure 21, the DAB converter’s performance features such as the inductance current in RMS can be From Figure 21, the converter’s performance features such as the inductance RMS can minimized based on DAB the optimization control method. The DC-bias current for thecurrent high frequency be minimized based on the optimization control method. The DC-bias current for the high frequency transformer can be suppressed greatly to avoid the saturation of the iron core of the transformer. transformer can be suppressed to avoid the saturation of the iron core of the transformer. The reverse negative power was greatly also greatly reduced based on the optimization control methods, The reverse negative was also greatly reduced based on the optimization controlthe methods, which can improve thepower efficiency of DAB converter. The experimental result can match result which can improve the efficiency of DAB converter. The experimental result can match the result from from the simulation result. the simulation result.

(a)

(b)

(c) Figure Figure 21. 21. Experimental Experimentalresult resultfor forcomparison comparisonbetween betweenthe theoptimization optimizationcontrol controland and traditional traditional control controlmethods methods(a) (a)RMS RMSvalue valueofofinductance inductancecurrent current(b) (b)DC DCbias biasfor fortransformer transformercurrent current(c) (c)Reverse Reverse negative power. negative power.

6. Conclusions 6. Conclusions Based on requirements of aviation, this paper designs a dual active bridge DC-DC converter Based on requirements of aviation, this paper designs a dual active bridge DC-DC converter with with an extended phase shifting control strategy. The interior and external phase angle are used as an extended phase shifting control strategy. The interior and external phase angle are used as the the design variables, taking three indexes—the inductor current RMS, transformer reverse negative design variables, taking three indexes—the inductor current RMS, transformer reverse negative power power and DC bias component—as the optimization goal. The optimization model is established and DC bias component—as the optimization goal. The optimization model is established with soft with soft switching as the main constraint. The genetic algorithm optimization toolbox in MATLAB switching as the main constraint. The genetic algorithm optimization toolbox in MATLAB is used to is used to solve the optimal control variable of the DAB converter optimization model. According to solve the optimal control variable of the DAB converter optimization model. According to the results the results of simulation and experiments based on the MATLAB/Simulink platform, the Typhoon of simulation and experiments based on the MATLAB/Simulink platform, the Typhoon HIL platform HIL platform and a hardware prototype, the three indexes have been effectively improved, and the and a hardware prototype, the three indexes have been effectively improved, and the rationality of rationality of the optimization method is verified. The next step for this research topic is to analyze the optimization method is verified. The next step for this research topic is to analyze the relationship the relationship between the different optimal objects, and simplify the optimal power model for the between the different optimal objects, and simplify the optimal power model for the DAB converter. DAB converter. Based on this, the aim is to explore the real-time selection method of the optimal Based on this, the aim is to explore the real-time selection method of the optimal solution and realize solution and realize online optimization control of the DAB converter. online optimization control of the DAB converter. Author Contributions: Tao Lei and Cengying Wu proposed the Multi-objective optimization control strategy; Cengying Wu build the simulation model for the DAB converter; Xaiofei Liu and Tao Lei performed the

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Author Contributions: Tao Lei and Cengying Wu proposed the Multi-objective optimization control strategy; Cengying Wu build the simulation model for the DAB converter; Xaiofei Liu and Tao Lei performed the experiments for DAB converter; Cengying Wu and Tao Lei analyzed the simulation and experimental data; Tao Lei, Cengying Wu, and Xaiofei Liu wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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