energies Article
Backflow Power Optimization Control for Dual Active Bridge DC-DC Converters Fei Xiong *
ID
, Junyong Wu, Liangliang Hao and Zicheng Liu
School of Electrical Engineering, Beijing Jiaotong University, Haidian District, Beijing 100044, China;
[email protected] (J.W.);
[email protected] (L.H.);
[email protected] (Z.L.) * Correspondence:
[email protected] Received: 10 August 2017; Accepted: 6 September 2017; Published: 14 September 2017
Abstract: This paper proposes optimized control methods for global minimum backflow power based on a triple-phase-shift (TPS) control strategy. Three global optimized methods are derived to minimize the backflow power on the primary side, on the secondary side and on both sides, respectively. Backflow power transmission is just a portion of non-active power transmission in a dual active bridge (DAB) converter. Non-active power transmission time is proposed in this paper, which unifies zero power transmission and backflow power transmission. Based on the proposed index, an optimized control method is derived to achieve both the maximum effective power transmission time and minimum current stress of DAB at the same time. A comparative analysis is performed to show the limitations of the minimum backflow power optimization method. Finally, a prototype is built to verify the effectiveness of our theoretical analysis and the proposed control methods by experimental results. Keywords: dual active bridge (DAB); optimization control; backflow power; non-active power
1. Introduction In recent years, dual active bridge (DAB) dc-dc converter is an attractive application with the advantages of bidirectional power flow, electrical isolation, high power density, and high transfer efficiency. DAB converter is suitable for the applications in the areas of renewable energy power generation and power electronics applications, such as the battery energy storage systems, and electric vehicles, solid-state transformers [1–6]. The traditional single-phase-shift (SPS) control method [2] only uses one degree of freedom of DAB. As a result, SPS control is easy to implement on-chip. However, SPS control only provides high operation efficiency when the voltage conversion ratio d is close to 1. The current stress and current rms for SPS control will increase a lot and the range of soft-switching will decrease when the voltage conversion ratio d is far from 1. Therefore, SPS control is not highly efficient under wide voltage variation conditions. In order to improve the performance of DAB, various optimization methods have been proposed based on the optimal objectives of current stress and current rms. In [7,8], the extended-phase-shift (EPS) control and the dual-phase-shift control are proposed to reduce the current stress for DAB. Two degrees of freedom are utilized for optimization in EPS and DPS control. In order to obtain the minimum current stress for DAB, the global optimal method for current stress is derived in [9] based on the triple-phase-shift (TPS) control method. Similar to the optimized methods for current stress, a numerical method is used to find the optimal control parameters for minimum rms of transformer current in [10]. In [11,12], the analytical expressions of the optimal control parameters are derived for minimum rms of transformer current. As a result, the optimal control method can be implemented by on-line and on-chip calculation. These optimal methods above all take the current as the optimal objectives for DAB. Energies 2017, 10, 1403; doi:10.3390/en10091403
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In addition to current, many other optimal objectives also have been studied in the existing literature. Like the definition of reactive power in sinusoidal ac circuit, the reactive power is defined and minimized for a DAB converter in [13–15]. However, it is too complex to obtain the analytical expressions of the control parameters based on the optimal objective of reactive power. Only numerical solutions can be found for the optimal objective of reactive power in [13–15]. Furthermore, the physical significance for the reactive power in DAB is not clear enough. Therefore, this kind of optimal method has low practicability. Minimization of backflow power is another common optimal objective for DAB. The delivery direction of backflow power is contrary to the delivery direction of average power transmission in DAB. Thus, the backflow power indeed reduces the power transmission efficiency in DAB. In [16,17], a novel extended-single-phase shift (ESPS) control method and an easy-to-implement control method are proposed, respectively. These two control methods can eliminate (to zero) the backflow power on both sides of the DAB converter. However, these two references do not take all operation modes of DAB into consideration and no global optimal results are derived for the whole load range. As a result, these two control methods are just local optimal results and they can only be implemented under light and medium load range conditions. Reference [18] derives the dual-phase-shift control method to eliminate the backflow power in the input side of DAB. Reference [19] proposes a zero circulating current (ZCC) control method to eliminate the backflow power on the output side of DAB. These two control methods only use two degrees of freedom for optimization of backflow power, leading to local optimal results rather than global optimal results. Moreover, these two control methods eliminate the backflow power just on one side of DAB and the backflow power on both sides cannot be optimized at the same time. In [20], the sum of backflow power on both sides is minimized, so the backflow power on both sides can be reduced at the same time, however, the optimized control parameters are derived just when the voltage conversion ratio is equal to 1. Therefore, no global and complete control methods for backflow power are derived in existing research. Furthermore, the optimization performance of various optimized objectives of backflow power mentioned above (i.e., the backflow power on the primary side, the secondary side and on both sides) have not been compared to each other. In [21,22], the circulating current is defined as the transformer current during the period of time when no active power is transmitted on the output side of DAB. In [22], the circulating current is the transformer current during the period of time when backflow power and zero power (caused by vcd = 0) are transmitted on the output side of DAB. The optimal objective in [21,22] is to minimize the rms value of circulating current. Only the circulating current on the output side is considered in [21,22]. In [23], the concept of non-active power which is proposed in [24] is utilized to define a new optimization objective, i.e., non-active power loss. In [24], the non-active current is defined just for the SPS control method to be the result of backflow power transmission. However, the non-active current caused by zero power transmission is not considered in [23,24]. Similar to the optimized methods in [7–12], these optimized control methods in [21–24] are essentially still for current. In fact, the backflow power is just a portion of the non-active power transmission in DAB and the limitations of the backflow power control method are not presented. The complete non-active power transmission in DAB is supposed to be defined for the performance optimization. Firstly, this paper proposes optimized control methods for global minimum backflow power based on triple-phase-shift (TPS) control strategy. Three global optimized methods are derived to minimize the backflow power on the primary side, on the secondary side and on both sides, respectively. Compared to the existing backflow power optimization methods in the published literature, the backflow power is minimized by the three proposed control methods. A comparative analysis is carried out to evaluate the performance differences among these three control methods and SPS control. The comparative analysis results show however that the power transmission efficiency may not be improved in some cases by the backflow power optimization methods. Therefore, the concept of maximum non-active power transmission time is proposed in this paper and it unifies the zero power transmission and the backflow power transmission together. Then, a new
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optimal objective is defined as the maximization of the effective power transmission time ratio in the in the DAB converter. The derived optimized control method achieves both the maximum effective DAB converter. The derived optimized control method achieves both the maximum effective power power transmission time and minimum current stress of DAB at the same time. A comparative transmission time and minimum current stress of DAB at the same time. A comparative analysis is analysis is performed to show that the minimum non-active power optimization method has the best performed to show that the minimum non-active power optimization method has the best optimization optimization performance and also explain the limitations of the minimum backflow power performance and also explain the limitations of the minimum backflow power optimization method. optimization method. Finally, a prototype is built to verify the effectiveness of the theoretical analysis Finally, a prototype is built to verify the effectiveness of the theoretical analysis and the proposed and the proposed control methods by experimental results. control methods by experimental results.
2. Operation 2. Operation Principles Principles 2.1. DAB 2.1. DAB Converter Converter The DAB DAB converter converter is is shown shown in in Figure Figure 1. 1. A The A high-frequency high-frequency transformer transformer T T connects connects the the primary primary H-bridge (Q1 to Q4) and the secondary H-bridge (Q5 to Q8). The inductance L is the value which has H-bridge (Q1 to Q4) and the secondary H-bridge (Q5 to Q8). The inductance L is the value which beenbeen reflected to the primary side. L includes the the has reflected to the primary side. L includes theleakage leakageinductance inductanceofoftransformer transformerTT and and the additional complementary inductance. V 1 is the dc-bus voltage on the primary side (input voltage). additional complementary inductance. V 1 is the dc-bus voltage on the primary side (input voltage). V22 is dc-bus voltage voltage on on the thesecondary secondaryside side(output (outputvoltage), voltage),respectively. respectively. The turns ratio is set V is the the dc-bus The turns ratio n isn set to to 1 to simplify the analysis process. The electric quantities on the secondary side can be reflected to 1 to simplify the analysis process. The electric quantities on the secondary side can be reflected to the the primary side when n≠1. As a result, the analysis process is similar to the situation when n=1. primary side when n 6= 1. As a result, the analysis process is similar to the situation when n = 1.
iin
Primary side
D1 Q3
Q1
D3
L
iL
a
v1
vab
Q2
Secondary side
T
c vcd
b
D2 Q4
D4
Q6
iload
D7
D5 Q7
Q5
io
C d
D6 Q8
v2
D8
Figure 1. Topology of the DAB converter. converter.
2.2. Selected Modes of of Triple Triple Phase Phase Shift Shift Control Control 2.2. Selected Operating Operating Modes Due to to the the symmetry of DAB, based on on positive power flow flow is is enough, and analysis Due symmetry of DAB, the the analysis analysis based positive power enough, and analysis methods are similar to the situation when negative power flow is engaged. In [25], the operating methods are similar to the situation when negative power flow is engaged. In [25], the operating modes of of TPS TPS are are divided divided into into twelve twelve types. types. Only modes have have the the ability ability for for positive modes Only eight eight operating operating modes positive 0 power transmission, as presented in [25].The mode 1 and mode 1′ in [25] have the same transmission power transmission, as presented in [25].The mode 1 and mode 1 in [25] have the same transmission power capability. capability. However, However, the the backflow backflow power power in in mode mode 11′0 is is apparently apparently larger larger than than mode mode 11 due due to to power the opposite opposite polarity polarity between between vvab ab and in mode 1′.0 It means that the power cannot be transferred the and v vcd cd in mode 1 . It means that the power cannot be transferred from the primary side to the secondary side and from from the the secondary secondary side side to to the the load load side side at at the the same same from the primary side to the secondary side and 0 0 time in in mode time mode 1′. 1 . Similar Similar conclusions conclusions can can be be drawn drawn for for mode mode 2′ 2 and andmode mode4, 4,respectively. respectively. The The backflow backflow 0 power in mode 2′ is obviously larger than in mode 2, while the backflow power in mode 4 is obviously power in mode 2 is obviously larger than in mode 2, while the backflow power in mode 4 is obviously 0 , mode 0 , mode 0 , and larger than than in in mode mode 5. 5. The The rest rest of of the the operating operating modes modes in in [25], [25], i.e., i.e., mode mode 33′, mode 44′, mode 55′, and larger 0 mode 66′,, can mode can only only transfer transfer negative negative power. power. As As aa result, result, only only five five types types of of operating operating modes modes are are selected selected to achieve both positive transmission power from the primary side to the secondary side and small to achieve both positive transmission power from the primary side to the secondary side and small backflow power. These five modes are depicted in Figure 2. Based on these five modes, an optimized backflow power. These five modes are depicted in Figure 2. Based on these five modes, an optimized control strategy strategy could could be be derived derived in in Section Section 33 to to minimize minimize the the backflow backflow power power in in aa DAB DAB converter converter control when the transmission power is positive. when the transmission power is positive.
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Q1
D2Ths
Q2
Q4 Q6
Q3 Q5 Q8
vcd
D1Ths
Q4 Q6 Q7
iL
vcd
vab
t3 t4 t5 t6
(a)
t
Ths
t7 t8
t0 t1 t2 t3
vab
vcd
iL
D2Ths
D2Ths v cd
D1Ths
Ths
Ts
t
iL
iL Ts
t8
t0 t1 t2 t3
(d)
t4 t5 t6 t7 (e)
Ts
Ths
Ths
t5t6t7
vcd
vab
t
Ths
t8
(c)
D1Ths
t4
t4 t5 t6 t7
(b)
D2Ths
t1t2t3
Ts
D2Ths
t0 t1 t2
D1Ths
t0
iL
Ths
Ths
D2Ths
vab
vab
t
Ts
t
D1Ths
vcd Ts
Ths
Ths
Ths
D1Ths
vab
t
Ths
t8
t0 t1t2t3
t4t5 t6t7
t8
(f)
Figure2.2.Operating Operating waveforms of selected with TPS (a) control: (a) Definition of control Figure waveforms of selected modesmodes with TPS control: Definition of control parameters; parameters; (b) Mode 1; (c) Mode 2; (d) Mode 3; (e) Mode 4; (f) Mode 5. (b) Mode 1; (c) Mode 2; (d) Mode 3; (e) Mode 4; (f) Mode 5.
In Figure 2a, φ is defined as the outer phase shift ratio between the drive signals of Q1 (or Q2) In Figure 2a, φ is defined as the outer phase shift ratio between the drive signals of Q1 (or Q2) and and Q5 (or Q6). When the drive signal of Q1 is ahead of Q5, φ is positive. Otherwise, when the drive Q5 (or Q6). When the drive signal of Q1 is ahead of Q5, φ is positive. Otherwise, when the drive signal signal of Q1 lags behind Q5, φ is negative. D1 is defined as the inner phase shift ratio in the primary of Q1 lags behind Q5, φ is negative. D1 is defined as the inner phase shift ratio in the primary H-bridge H-bridge between the drive signals of Q1 (or Q2) and Q3 (or Q4). D2 is defined as the inner phase between the drive signals of Q1 (or Q2) and Q3 (or Q4). D2 is defined as the inner phase shift ratio in the shift ratio in the secondary H-bridge between the drive signals of Q5 (or Q6) and Q7 (or Q8). The secondary H-bridge between the drive signals of Q5 (or Q6) and Q7 (or Q8). The operation constraints operation constraints and transmission power of these five modes are listed in Table 1. K is denoted and transmission power of these five modes are listed in Table 1. K is denoted as the normalized as the normalized transmission power to the reference value AV1V2, i.e., k = PDAB/(AV1V2). A is the transmission power to the reference value AV 1 V 2 , i.e., k = PDAB /(AV 1 V 2 ). A is the constant coefficient constant coefficient Ths/(2L).The voltage conversion ratio d is defined as d = V2/V1. The maximum Ths /(2L).The voltage conversion ratio d is defined as d = V 2 /V 1 . The maximum transmission power of transmission power of DAB is k = 0.5 when D1 = 1, D2 = 1 and φ = 0.5. As shown in Figure 2, DAB is k = 0.5 when D1 = 1, D2 = 1 and φ = 0.5. As shown in Figure 2, understeady-state conditions, understeady-state conditions, the waveforms of vab, vcd and iL are symmetric in an adjacent half the waveforms of vab , vcd and iL are symmetric in an adjacent half switching period. Therefore, the switching period. Therefore, the following mathematical analysis is carried out only in half a following mathematical analysis is carried out only in half a switching period for simplification. switching period for simplification. Table 1. Operation constraints and transmission power for selected modes. Table 1. Operation constraints and transmission power for selected modes. Modes
Modes
Mode Constraints Mode (D D2 ≤ 1) 1 andConstraints
D2 ≤ 1) Mode 1 D1(D − 1Dand 2 ≤φ≤0 Mode 2 1 0 ≤Dφ1 ≤ D12 ≤ −φ D2≤ 0 Mode −D Mode 3 D1 ≤ φ ≤ 1 − D2 Mode 2 0 ≤ φ ≤ D1 − D2 Mode 4 max(D1 − D2 ,0) ≤ φ ≤ min(1 − D2 ,D1 ) Mode 3 −1D2 Mode 5 1 −DD1 2≤≤φφ≤≤1 D Mode 4 Mode 5
max(D1 − D2,0) ≤ φ ≤ min(1 − D2,D1) 1 − D2 ≤ φ ≤ D1
3. Global Minimum Backflow Power Control
Transmission Power k
Transmission power k k = D1 (D2 − D1 + 2φ)
D12(D (D2 − −D D11 ++ 2φ) 2φ) kk==D k = D1 D2 k = D2(D2 − D1 + 2φ) k = −D1 2 − φ2 + 2D1 φ + D1 D2 2 2 k =+ D 2 k = −D1 − D2 − 2φ2 + 2φ 2D1D 1 φ − 2D2 φ + D1 D2 + 2D2 − 1 k = −D12 − φ2 + 2D1φ + D1D2 k = −D12 − D22 − 2φ2 + 2φ + 2D1φ − 2D2φ + D1D2 + 2D2 − 1
3. Global Minimum Backflow Power Control 3.1. Backflow Power Under SPS Control Figure 3 Power showsUnder the operation waveforms of DAB under a single-phase-shift (SPS) control strategy. 3.1. Backflow SPS Control The phase shift time between the voltage vab and vcd is defined as φ·Ths , where Ths is a half switching Figure 3 shows the operation waveforms of DAB under a single-phase-shift (SPS) control strategy. The phase shift time between the voltage vab and vcd is defined as φ∙Ths, where Ths is a half
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switching period. The phase shift ratio between vab and vcd is φ. iin and io are the input current on the period. The phase shift ratio between vab and vcd is φ. iin and io are the input current on the primary primary side and the output current on the secondary side, respectively. side and the output current on the secondary side, respectively.
vab
φ· Ths
φ· Ths
φ· Ths
t
vcd iL
t
iin io
t t01’
t23’
t0 t1
t45’
t2 t3
t4 t5
t
Figure 3. 3. Operating Operating waveforms waveforms of of SPS SPS control. control. Figure
For simplification, simplification, only only the thepositive positivepower powerflow flowfrom fromthe theprimary primaryside sidetotothe the secondary side For secondary side is is analyzed in this paper. As can be seen in Figure 3, the transmission power of DAB flows back analyzed in this paper. As can be seen in Figure 3, the transmission power of DAB flows back to the 0 while the to the primary side (i.e., supply) power supply) DABt0 during t0 to t01t023′and t2 to primary side (i.e., power from thefrom DAB the during to t01′ and t2 to while thet23 transmission 0 transmission power of the DAB flows back to the DAB from the load side during t to t230 1 and 01 t23′ tto power of the DAB flows back to the DAB from the load side during t01′ to t1 and t3. The to t3 . The transmission power during these in this paper as the power. backflow power. transmission power during these periods is periods defined is in defined this paper as the backflow Backflow Backflow power is one type of the non-active power in DAB and it will reduce the power transmission power is one type of the non-active power in DAB and it will reduce the power transmission efficiency in 3, the backflow power on the side and secondary side areside defined efficiency inDAB. DAB.InInFigure Figure 3, the backflow power onprimary the primary side and secondary are by Equations (1) and (2), respectively. defined by Equations (1) and (2), respectively. Z 0 1 t01 ' Q pQ= 1 t01 vv1i|i Ldt|dt (1) (1) p Ths 1 L t t 0 Ths 0 11 QsQ= s T Thshs
Z t t1
t010 vv2i|i Ldt|dt 1
' t01
2
L
(2) (2)
where both Qp and Qs are positive values. where both Qp and Qs are positive values. 3.2. Minimum Backflow Power Conrtrol (MBPC) at Low Power Level 3.2. Minimum Backflow Power Conrtrol (MBPC) at Low Power Level Mode 1 to mode 4 in Figure 2 are the operating modes at low power level. Moreover, both the Mode 1 to mode 4 in Figure 2 are the operating modes at low power level. Moreover, both the backflow power on the primary side (i.e., Qp ) and these secondary side (i.e., Qs ) can be eliminated backflow power on the primary side (i.e., Qp) and these secondary side (i.e., Qs) can be eliminated simultaneously to zero in mode 1 to mode 4. Therefore, these modes have the minimum backflow simultaneously to zero in mode 1 to mode 4. Therefore, these modes have the minimum backflow power on both sides. Optimized control parameters in each operating mode can be derived as below power on both sides. Optimized control parameters in each operating mode can be derived as below based on the optimal object Qp = Qs = 0. based on the optimal object Qp = Qs = 0. MBPC in mode 1. In order to eliminate Qp and Qs , the current conditions iL (t0 ) ≥ 0, iL (t1 ) ≥ 0, iniLmode order be to eliminate p and Qs, the current conditions iL(t0) ≥ 0, iL(t1) ≥ 0, iL(t2) = iL (t2 )MBPC = 0 and (t3 ) =1.0Inshould satisfied toQobtain: 0 and iL(t3) = 0 should be satisfied to obtain: D1 = dD2 , ϕ = 0 (3) D1 dD2 , 0 (3)
Substituting Equation (3) into the expression of transmission power in Table 1, the optimized control parameters with its constraints in mode 1 can be solved: D1 d
k , D2 d (1 d )
k , when k ≥ 0 and d< 1 d (1 d )
(4)
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Substituting Equation (3) into the expression of transmission power in Table 1, the optimized control parameters with its constraints in mode 1 can be solved: s D1 = d
k , D2 = d (1 − d )
s
k , when k ≥ 0 and d < 1 d (1 − d )
(4)
Based on the constraints of mode 1 in Table 1, the maximum transmission power is: k1max = d(1 − d), when D1 = d, D2 = 1
(5)
MBPC in mode 2. Solving the current conditions iL (t0 ) = 0, iL (t1 ) ≥ 0, iL (t2 ) ≥ 0 and iL (t3 ) = 0 for the elimination of Qp and Qs we obtain: D1 = dD2 , ϕ = D1 − D2
(6)
Substituting Equation (6) into the expression of transmission power in Table 1, the optimized control parameters with its constraints in mode 2 can be solved: r D1 = d
k , D2 = d−1
r
k , when k ≥ 0 and d > 1. d−1
(7)
According to the constraints of mode 2 in Table 1, the maximum transmission power is: d−1 , when D1 = 1, D2 = 1/d. d2
k2max =
(8)
MBPC in mode 3. Solving the current conditions iL (t0 ) = 0, iL (t1 ) ≥ 0, iL (t2 ) ≥ 0 and iL (t3 ) = 0 for the elimination of Qp and Qs we can obtain: D1 = dD2 , D1 ≤ ϕ ≤ 1 − D2
(9)
This indicates that the elimination of backflow power in mode 3 is only determined by D1 and D2 . The outer phase shift ratio ϕ has no effect on it. However, in order to reduce the root-mean-square (RMS) current of iL as much as possible, ϕ is supposed to be D1 in this mode. Therefore, the period of time t1 to t2 can be eliminated to zero and RMS current can be reduced, as shown in Figure 2d. Substituting Equation (9) into the expression of transmission power in Table 1, the optimized control parameters of mode 3 can be calculated:
√ D1 =
r dk, D2 =
k , when k ≥ 0 d
(10)
The maximum transmission power in mode 3 is: k3max =
d
(1 + d )2
, when D1 = d/(1 + d), D2 = 1/(1 + d)
(11)
MBPC in mode 4. Solve the current conditions iL (t0 ) = 0, iL (t1 ) ≥ 0, iL (t2 ) ≥ 0 and iL (t3 ) = 0 to eliminate Qp and Qs : D1 = dD2 , max( D1 − D2 , 0) ≤ ϕ ≤ min(1 − D2 , D1 )
(12)
Substituting Equation (12) into the expression of transmission power in Table 1 to obtain: k = −( ϕ − dD2 )2 + dD2 2
(13)
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According to the quadratic curving relationship in Equation (13), it can be obtained that: ( k max =
D1 2 d , when 0 ≤ D1 −( d12 + 1d + 1) D1 2
≤ 1+d d and ϕ = D1 + 2(1 + 1d ) D1 − 1, when 1+d d < D1 ≤ 1 and ϕ = 1 −
D1 d
(14)
Therefore, the maximum transmission power in mode 4 is: d d2 + d d+1 7 of 28 , when D = , D2 = 2 (15) 1 2 2 d +d+1 d +d+1 d +d+1 Figure 4 presents the curves of kmax versus d for mode 1 to mode 4 according to Equations (5), (8), Figure 4 presents the curves of kmax versus d for mode 1 to mode 4 according to Equations (5), (8), (11) and (15). From Figure 4, we can conclude that k4max is larger than the other three modes under (11) and (15). From Figure 4, we can conclude that k4max is larger than the other three modes under different d. Especially when d is equal to 1, mode 1 and mode 2 will not be effective anymore while different d. Especially when d is equal to 1, mode 1 and mode 2 will not be effective anymore while k4max reaches its maximum value. This indicates that mode 4 has the widest power range for zero k4max reaches its maximum value. This indicates that mode 4 has the widest power range for zero backflow power on both the primary side and secondary side. As a result, mode 4 is the optimized backflow power on both the primary side and secondary side. As a result, mode 4 is the optimized operating mode at low power level. operating mode at low power level. Energies 2017, 10, 1403
k4max =
0.35
k4max
0.30 k1max
k2max
kmax
0.25 0.20
k3max
0.15 0.10 0.05 0
0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 d
Figure Maximum transmission power kmaxininmode mode1 1totomode mode4 4versus versusvoltage voltageconversion conversionratio ratiod.d. Figure 4. 4. Maximum transmission power kmax
Similar to the backflow power in mode 3, the elimination of backflow power in mode 4 is only Similar to the backflow power in mode 3, the elimination of backflow power in mode 4 is only dependent on D1 and D2. The outer phase shift ratio φ has no effect on it. For simplicity, φ is designed dependent on D1 and D2 . The outer phase shift ratio φ has no effect on it. For simplicity, φ is designed to be a linear relationship with D1 or D2 as shown below: to be a linear relationship with D1 or D2 as shown below: d D1 dD2 , d D1 D1 = dD2 , ϕ = d 1D1 d+1 The optimized control parameters of mode 4 can be solved as: The optimized control parameters of mode 4 can be solved as: dk d 1r dk dk D1 (r d 1) 2 , D2 , d r 2 2 dk d + 1 dk d d d 1 d d 1 d d dk 1 D1 = (d + 1) , D2 = , ϕ=d 2 2 d d +d+1 d +d+1 d2 + d + 1
(16) (16)
(17) (17)
3.3.Minimum MinimumBackflow BackflowPower PowerConrtrol ConrtrolatatMedium MediumPower PowerLevel Level 3.3. thetransmission transmission power exceeds k4max , theDAB DABconverter converterwill willoperate operateininmode mode5.5.However, However, If Ifthe power exceeds k4max , the QpQp andQQ s cannot be eliminated at the same time in mode 5 when k is larger than k4max. Mode 5 can be and s cannot be eliminated at the same time in mode 5 when k is larger than k4max . Mode 5 can further on the the current currentconditions conditionsofofi i.L.Due Duetotothe the be furthersubdivided subdividedinto intofive five operating operating modes modes based based on L symmetry of v ab, vcd and iL in the adjacent half switching period, only the current values in a half symmetry of vab , vcd and iL in the adjacent half switching period, only the current values in a half periodare are presented: period presented: (1) Mode 5A.When iL(t0) ≥ 0, iL(t1) ≥ 0, iL(t2) ≥ 0, and iL(t3) ≥ 0, Qp can be eliminated to zero, while Qs (1) Mode 5A. When iL (t0 ) ≥ 0, iL (t1 ) ≥ 0, iL (t2 ) ≥ 0, and iL (t3 ) ≥ 0, Qp can be eliminated to zero, cannot be eliminated, as shown in Figure 5a. while Qs cannot be eliminated, as shown in Figure 5a. (2) Mode 5B. When iL(t0) < 0, iL(t1) ≤ 0, iL(t2) ≥ 0, and iL(t3) ≥ 0,Qs can be eliminated to zero, while Qp cannot be eliminated, as shown in Figure 5b. (3) Mode 5C. When iL(t0) ≤ 0, iL(t1) ≥ 0, iL(t2) ≥ 0, both Qp and Qs cannot be eliminated to zero. However, it is the only operating mode to reach the maximum transmission power of DAB, i.e., k = 0.5 when D1 = 1, D2 = 1 and φ = 0.5, as shown in Figure 5c. (4) Mode 5D. When iL(t0) ≥ 0, iL(t1) ≥ 0, iL(t2) ≥ 0, and iL(t3) ≤ 0, both Qp and Qs are larger than that in
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(2) (3)
(4) (5)
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Mode 5B. When iL (t0 ) < 0, iL (t1 ) ≤ 0, iL (t2 ) ≥ 0, and iL (t3 ) ≥ 0, Qs can be eliminated to zero, while Qp cannot be eliminated, as shown in Figure 5b. Mode 5C. When iL (t0 ) ≤ 0, iL (t1 ) ≥ 0, iL (t2 ) ≥ 0, both Qp and Qs cannot be eliminated to zero. However, it is the only operating mode to reach the maximum transmission power of DAB, i.e., k = 0.5 when D1 = 1, D2 = 1 and φ = 0.5, as shown in Figure 5c. Mode 5D. When iL (t0 ) ≥ 0, iL (t1 ) ≥ 0, iL (t2 ) ≥ 0, and iL (t3 ) ≤ 0, both Qp and Qs are larger than Energies 10, 1403 8 of 28 that in2017, mode 5A under certain k. Therefore, this mode is not selected to be optimized below. Mode 5E. When iL (t0 ) ≤ 0, iL (t1 ) ≤ 0, iL (t2 )≤ 0, and iL (t3 ) ≥ 0, both Qp and Qs are larger than that power on the primary side and secondary side, respectively. Based on the two objectives, only two in mode 5B under certainare k. Therefore, this mode is also not selected to be optimized below. control degrees of freedom considered in [18,19]. D2Ths
D2Ths D1Ths
vcd
vab
D1Ths
iL
vab
D1Ths
iL Ts
Ts Ths
t
t
Ths
t'01
Ths
Ths
t4t5 t6 t7
t8
vcd
vab
iL
Ts Ths
t0 t1t2 t3
D2Ths
vcd
t0 t1
t2 t3
(a)
t4t5
t
Ths
t6 t7
t8
t0 t1t2t3
(b)
t4 t5 t6t7
t8
(c)
Figure 5. Operating waveforms of selected modes in mode 5: (a) Mode 5A; (b) Mode 5B; (c) Mode 5C.
Figure 5. Operating waveforms of selected modes in mode 5: (a) Mode 5A; (b) Mode 5B; (c) Mode 5C.
In this section, the two optimized objectives are modified to obtain a smaller backflow power on As analyzed above, only mode 5A, mode 5B and mode 5C are selected to be optimized as below. both sides with three control degrees of freedom. The optimized control parameters at medium There are two common optimal objectives in mode 5, i.e., Qp = 0 or Qs = 0, to eliminate the backflow power level are derived based on two modified objectives respectively as below: power on the primary side and secondary side, respectively. Based on the two objectives, only two Objective The objective 1 at medium control degrees of 1: freedom are considered in power [18,19].level is to eliminate the primary backflow power Qp with minimum secondary backflow power Qs: In this section, the two optimized objectives are modified to obtain a smaller backflow power on both sides with three control degrees of freedom. optimized control parameters at medium Qp 0The and min Qs (18)power level are derived based on two modified objectives respectively as below: The optimized objective in Equation (18) not only achieves zero backflow on the primary side, Objective 1: The objective 1 at medium power level is to eliminate the primary backflow power Qp but also gives consideration to the reduction of backflow power on the secondary side. Moreover, with minimum secondary backflow power Qs : when iL(t0), iL(t1), iL(t2), and iL(t3) are not smaller than zero, Qp can be eliminated to zero. Therefore, the optimized mode for objective 1 is mode 5A, as shown in Figure 5a. The secondary backflow power Q p = 0 and minQs (18) Qs in this case is:
(V1 D1achieves V2 D2 ) zero backflow on the primary The optimized objective in QEquation (18) not2 only (19) ] s A[V1V2 ( D2 1) 4 side, but also gives consideration to the reduction of backflow power on the secondary side. where when A is theiLconstant hs/(2L). Moreover, (t0 ), iL (tcoefficient iL (t3 ) are not smaller than zero, Qp can be eliminated to 1 ), iL (t2 ), Tand It can be seen from Equation Qs cannot eliminated zero when Qp is zero. However, zero. Therefore, the optimized mode(19) forthat objective 1 isbe mode 5A, astoshown in Figure 5a. The secondary the value beis: minimized based on appropriate control parameters. According to backflow powerofQQs sincan thisstill case 2
Equations (18), (19) and the transmission power in Table 1, the optimized control parameters are derived in Equation (20) (the detailed derivation process (isVpresented in Appendix A). D −V D )2 2
2
Qs = A[V1 V2 ( D2 + ϕ − 1)2 + 1 21 ] (19) d (2d 1) d1 d 4d (d 1)1 D1 , D2 1 1 , 2d 2 2d 1 2d 2 2d 1 where A is the constant coefficient Ths /(2L). (20) d 2 d (2d 2 2d 1)k It can be seen from Equation where 1 (19) that 2Qs cannot be eliminated to zero when Qp is zero. d d 1 based on appropriate control parameters. However, the value of Qs can still be minimized AccordingThe to optimized Equations (18), indicate (19) and the Table 1, the optimized control results that thetransmission value of iL(t0) ispower exactlyin equal to zero. That is to say, the optimized control parameters in Equation (20) are actually located at the boundary of mode 5A and parameters are derived in Equation (20) (the detailed derivation process is presented in Appendix A). mode 5C. The maximum transmission power is reached when α1 in Equation (20) is equal to zero:
D1 =
d(2d+1)+ dα1 2 2 d d , 2d +2d+1
k5 Amax
d2 + d ( d +1) α
1 2 D2 = 1 − α1 , ϕ2d= d2d2 +2d+1 q , when D , D 1 1 2 d2 +d−( 2d22d+22d 2d 2 2α d = 1 +21d)k 1 where 1 d2 + d +1
(21) (20)
Objective 2: The objective 2 at medium power level is to eliminate the secondary backflow power Qs with minimum primary backflow power Qp
Qs 0 and min Qp
(22)
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The optimized results indicate that the value of iL (t0 ) is exactly equal to zero. That is to say, the optimized control parameters in Equation (20) are actually located at the boundary of mode 5A and mode 5C. The maximum transmission power is reached when α1 in Equation (20) is equal to zero: k5Amax =
2d2 + d d2 + d , when D1 = 2 , D2 = 1 + 2d + 1 2d + 2d + 1
2d2
(21)
Objective 2: The objective 2 at medium power level is to eliminate the secondary backflow power Qs with minimum primary backflow power Qp Qs = 0 and minQ p
(22)
As long as the current conditions iL (t0 ) ≤ 0, iL (t1 ) ≤ 0, iL (t2 ) ≥ 0, and iL (t3 ) ≥ 0 are met, Qs can be eliminated to zero, as shown in Figure 5b. The primary backflow power Qp in this case is: 1 Q p = AV1 2 [( D2 + ϕ − 1)( D1 − D2 − (1 − d)( ϕ − 1)) + ( D1 − (d + 2) D2 + 2(1 − ϕ))2 ] 4
(23)
It can be seen from Equation (23) that Qp cannot be eliminated to zero when Qs is zero. However, the value of Qs can still be minimized based on appropriate control parameters. Based on Equations (22), (23) and the transmission power in Table 1, the optimized control parameters can be derived as below: 1+d+d2 −(1+2d+d2 )α2 d+2+dα2 , ϕ= d2 +2d +2 d2 +2d+2 q d+1−(d2 +2d+2)k where α2 = d2 + d +1
D1 = 1 − α2 , D2 =
(24)
Under the optimized control parameters in Equation (24), the value of iL (t1 ) is exactly equal to zero. Therefore, the optimized control method by in Equation (24) is actually located at the boundary of mode 5B and mode 5C. The maximum transmission power is reached when α2 in Equation (24) is equal to zero: k5Bmax =
d+1 d+2 , when D1 = 1, D2 = 2 d2 + 2d + 2 d + 2d + 2
(25)
3.4. Minimum Backflow Power Conrtrol at High Power Level Along with the increase of transmission power, k will exceed k5Amax or k5Bmax . In this case, the current value of iL (t0 ) is smaller than zero while the current value of iL (t1 ) is larger than zero. The DAB converter will operate in mode 5C, as shown in Figure 5c. The backflow power on both sides needs to be recalculated by Equations (26) and (27): V1 AV1 i L ( t0 )2 = (−V1 D1 − V2 D2 − 2V2 ϕ + 2V2 )2 4A(V1 + V2 ) 4(V1 + V2 )
(26)
V2 AV2 i L ( t1 )2 = (2V1 D2 − V1 D1 + V2 D2 − 2V1 + 2V1 ϕ)2 4A(V1 + V2 ) 4(V1 + V2 )
(27)
Qp = Qs =
Objective 1: Objective 1 at high power level is to eliminate the primary backflow power Qp : minQ p
(28)
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Substituting the expression of transmission power in Table 1 into Equation (26) to eliminate the variable φ, the optimized control parameters can be derived: ∂Q p
D1 = 1 − (1 + d)
q∂D1
∂Q p ∂D2
= 0,
1−2k , 2d2 +2d+1
= 0 at k ⇒
D2 = 1, ϕ =
1 2
−
1+2d 2
q
(29)
1−2k 2d2 +2d+1
Objective 2: Objective 2 at high power level is to eliminate the secondary backflow power Qs : minQs
(30)
Energies 10, 1403 control parameters can be derived as: Similarly, the 2017, optimized
∂Qs
D1 =
= 0,
∂Qs
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= 0 at k ⇒
∂D2 Qs Qs ∂D1 q 0, 0 at k 1−2k 1, = 1 − ( 1 + d ) ,ϕ DD D 1 2 2 d2 +2d+2
=
1 2
+
d 2
q
(31)
1−2k d2 +2d+2
(31) 1 2k 1 d 1 2k , As can be seen in Equations (28) to (31),d 2whether objective 2 is selected to be 2 2 d 21or 2d 2 objective 2d 2 D1 1, D2 1 (1 d )
optimized, three control of freedom are whether needed.objective It indicates that only single-side As can be seendegrees in Equations (28) to (31), 1 or objective 2 is selected to backflow be power (i.e., Q or Q ) can be optimized at high power level. p s optimized, three control degrees of freedom are needed. It indicates that only single-side backflow power (i.e., Qp (20) or Qsand ) can (29) be optimized at high level. Equations (17), constitute thepower “global minimum primary backflow power control Equations while (17), (20) (29) constitute the “global minimum primary backflowminimum power control method (GMPBPC)”, theand Equations (17), (24) and (31) constitute the “global secondary method (GMPBPC)”, while the Equations (17), (24) and (31) constitute the “global minimum backflow power control method (GMSBPC)”. secondary backflow power control method (GMSBPC)”.
3.5. Comparative Analysis of Global Minimum Backflow Power Control 3.5. Comparative Analysis of Global Minimum Backflow Power Control
3.5.1. Backflow PowerPower 3.5.1. Backflow The backflow powerpower of GMPBPC, GMSBPC traditional SPS control method are depicted The backflow of GMPBPC, GMSBPCand andthe the traditional SPS control method are depicted Figure 6. Itbecan be seen in Figure 6a,b thatGMPBPC GMPBPC and achieve minimum Qp andQp and in Figurein 6. It can seen in Figure 6a,b that andGMSBPC GMSBPC achieve minimum minimum Qs, respectively, as expected. Compared to to the the SPS method, thesethese two optimized minimum Qs , respectively, as expected. Compared SPScontrol control method, two optimized methods can reduce backflow power effectively, especially at lower power level. However, at higher methods can reduce backflow power effectively, especially at lower power level. However, at higher power level, the backflow power of optimized methods may be even larger than the backflow power power level, the backflow power of optimized methods may be even larger than the backflow power of the SPS control method. of the SPS control method. 180
500
160
450
500
400
140 120
GMPBPC 240W
350
SPS
80 60
Qsum(W)
100
250 200
GMSBPC
20
k4max
0
40W GMBPC
100
50 0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0
GMBPC
100 GMPBPC
k4max 0
k
240W
k
k
(b)
(c) 600 500
120
GMSBPC
Qs(W)
250 200 150
GMBPC
400
SPS
Qsum(W)
SPS
300
100 80
50
k4max 0
GMPBPC
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k
(d)
300
GMPBPC 40W
20 0
SPS
200
60 40
100
GMBPC
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
140
350
Qp(W)
0
160
400
0
0
180
GMSBPC
450
GMSBPC
k4max
GMSBPC
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
(a) 500
300 200
150
40
SPS
400
SPS
300
Qs(W)
Qp(W)
600 GMPBPC
k4max
0
100
GMPBPC
GMBPC
GMSBPC 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k4max 0 0
GMBPC
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k
k
(e)
(f)
Figure 6. The backflow power of GMPBPC, GMSBPC, GMBPC and traditional SPS control method;
Figure 6. The backflow power of GMPBPC, GMSBPC, GMBPC and traditional SPS control method; (a–c) are plotted for V1 = 60 V, V2 = 120 V; (d–f) are plotted for V1 = 120 V, V2 = 60 V. (a–c) are plotted for V 1 = 60 V, V 2 = 120 V; (d–f) are plotted for V 1 = 120 V, V 2 = 60 V. Under the condition when d = 2 (V1 = 60 V, V2 = 120 V), Qs of GMPBPC is much larger than Qs of other methods at higher power level. The maximum difference of Qs between GMPBPC and GMSBPC is about 240 W, as shown in Figure 6b. However, the maximum difference of Qp between GMSBPC and GMPBPC is only about 40 W, as shown in Figure 6a. As a result, GMPBPC has worse optimized results in comparison to GMSBPC when d is larger than 1. Similarly, GMSBPC has worse optimized results in comparison to GMPBPC when d is smaller than 1, as shown in Figure 6d,e. As analyzed above, the control method should be switched to GMPBPC when d is larger than 1 and switched to GMSBPC when d is smaller than 1, in order to ensure good optimized performance
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Under the condition when d = 2 (V 1 = 60 V, V 2 = 120 V), Qs of GMPBPC is much larger than Qs of other methods at higher power level. The maximum difference of Qs between GMPBPC and GMSBPC is about 240 W, as shown in Figure 6b. However, the maximum difference of Qp between GMSBPC and GMPBPC is only about 40 W, as shown in Figure 6a. As a result, GMPBPC has worse optimized results in comparison to GMSBPC when d is larger than 1. Similarly, GMSBPC has worse optimized results in comparison to GMPBPC when d is smaller than 1, as shown in Figure 6d,e. As analyzed above, the control method should be switched to GMPBPC when d is larger than 1 and switched to GMSBPC when d is smaller than 1, in order to ensure good optimized performance of DAB under different voltage conversion ratio d. However, the mode switching increases the complexity of the implementation in digital controller. In order to optimize the backflow power in both sides under arbitrary voltage conversion ratio d but without mode switching, an alternative optimal objective is to minimize the sum of backflow power in both sides as below. Objective 3: The objective 3 is to minimize the sum of primary and secondary backflow power, i.e., Qsum : minQsum , where Qsum = Q p + Qs (32) At low power level, the optimized control parameters has been derived in Section 3.2, i.e., mode 4, and Qsum is reduced to zero. At medium power level, Equations (18) and (22) are essentially equivalent to the optimal objectives “minimum Qsum ” in mode 5A and mode 5B, respectively. The optimized results are located at the boundary of mode 5C. At high power level, only mode 5C has the ability to reach the maximum power transmission of DAB. As a consequence, the global minimum Qsum can only be derived in mode 5C when transmission power k is larger than k4max . The optimized control parameters are derived based on Equations (26), (27) and (32) as shown below:
D1 = 1 −
q
∂Qsum ∂D1 1−2k , 1+ d2 + d4
D2 =
∂Qsum ∂D2 = 0 at k ⇒ q 1 − d2 1+1d−22k , ϕ = 12 + d4
= 0,
+
d2 − d −1 2
q
1−2k 1+ d2 + d4
(33)
The control method which consists of Equations (17) and (33), is called as “global minimum backflow power control (GMBPC)” in this paper. As can be seen in Figure 6a,b, the values of Qp and Qs in GMBPC are always between the values in GMPBPC and GMSBPC. It indicates that the optimal objective in Equation (32) is essentially a tradeoff between minimum Qp and minimum Qs . Moreover, as shown in Figure 6b, the optimized results of GMBPC are closer to the optimized results of GMSBPC when d = 2. This is because Qs accounts for the largest portion of Qsum (i.e., Qs >> Qp ) at higher power level when d = 2, GMBPC is prone to reduce Qs when d is larger than 1. Figure 6d–f show Qp , Qs , and Qsum at d = 0.5 (V 1 = 120 V, V 2 = 60 V) respectively. The optimized results in Figure 6d–f show the symmetry with respect to the optimized results when d = 2 (V 1 = 60 V, V 2 = 120 V) in Figure 6a–c. Therefore, GMBPC is prone to reduce Qp when d is smaller than 1. As a result, the optimized performance of GMBPC is similar to the optimized performance of mode switching between GMPBPC and GMSBPC. The mode switching can be avoided. In conclusion, GMBPC not only has nearly the same optimized performance as GMPBPC when d is smaller than 1 or as GMSBPC when d is larger than 1 without mode switching, but also has smaller Qsum than other methods. Therefore, GMBPC is supposed to have better performance than other two optimized methods. The optimized control parameters and the power range of the three derived methods above are listed in Table 2.
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Table 2. Control parameters and the power range of backflow power optimal control methods. Modes
GMPBPC
GMSBPC
GMBPC
dk d 1 dk dk Mode 4 : D1 (d 1) 2 , D2 , d 2 d d 1 d d 2 d 1 d d 1
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d 0k 2 Power Range Table 2. Control parameters and the power range of backflow optimal control methods. d dpower 1 Mode 5C : Mode 5 A : Mode 5 B : GMPBPC GMSBPC GMBPC 1 2k d (2 d 1) d1 D1 1 2 D1 1 q D1 q q 2 1 d2 d4 2 d 2 d 1 d + 1 dk dk Medium Power d 2 d Low Power Level Mode 4 : D1 = (d + 1D) d2 +d+1 , D22 = d , ϕ = d d2 +dkd+1 d2 + d +1 2 2 D2 1 1 1 2k d 2d 2 Level D2 1 d 2 d Power Range 1 d 2 d 4 d 2 d (d 1)1 1 0d ≤ dk2 ≤ (1d2+2dd+1 d 2 ) 2 2Mode d 2 2d5A 1: d 2 5B 2d: 2 1Mode d 2 5C d : 1 1 2k Mode q 1−2k d(2d+1)+dα1 2 1− 2 14 d 2 d 4 D1 = 1 − α2 D = 2 D = 2 1 2 1 d d 1 2d +d 2d+1 d d q1+d +d Medium Power Level 2 2+dα 1−α Power Range D = dk+ D k= 2 +2d + 22 D2 = 1 − d2 1+1d−22k d 2 d1+2d1+d2d−( d 2 d 2 d 1 2 d2 +2d(dd2+11)2αd 1 2d 2 q + d4 ϕ = 5C : d2 +12d++2d2+d )α2 ϕ := 2d2 +2d+1 1 2 Mode 5C Mode ϕ = 12 + d −2d−1 1+1d−22k + d4 2 d D21 d 1 ≤ k ≤ 2 d+1 Power Range ≤ k ≤ 12d2d2+k+2dd+1 d + d +1 d +2d+2 +1 d ) D1 d12 +d(1 2d 2 5C 2d: 1 1 2k Mode D2 1 (1Mode d ) 5C2 : High PowerLevel q D2 1 d 2d 2 1−2k D = 1 1 D1 = 1 − (1 + d) 2d2 +2d+1 q 1−2k High PowerLevel 1 1 2d D 1= 12k 1 d 1 2 k D = 1 − ( 1 + d ) 2 2 22 q q2d d2 +2d+2 2 2 21 d 2d 21 d2d 2d 11−2k 12+ 1−2k ϕ = 2 + 2 d2 +2d+2 ϕ= 2− 2 2d2 +2d+1
Modes
d 1 1 k 1 ≤ 2k ≤ 2 2
d2 d 1 2 k 1 2 d +d 2d2d 2 +22d d +11 ≤ k ≤2 2
Power Range Power Range
d
d 2 ≤ k ≤ 1k d2 +dd +1 d 1 2
d2+1 +22d d2d+2d
1 2
3.5.2. 3.5.2.Control ControlParameters Parameters According 1, 1 D, 2D , and φ versus k are depicted in According to toTable Table2,2,the theoptimized optimizedcontrol controlparameters parametersDD φ versus k are depicted 2 , and Figure 7 when d =d2=(V = 160= V, = 2120 V).V). AsAs cancan be be seen in in Figure 7,7,the in Figure 7 when 2 1(V 60 V V,2 V = 120 seen Figure thecontrol controlparameters parametersofofall all these methods are arepiecewise piecewisecontinuous continuousfunction function k. Only two subsections these three three control methods ofof k. Only two subsections (i.e.,(i.e., lowlow and and power in GMBPC, three subsections (i.e., low, medium highlevel) power highhigh power level)level) exist exist in GMBPC, while while three subsections (i.e., low, medium and highand power are level) are in and GMPBPC andMoreover, GMSBPC. D1 and D2 changeinmonotonically in GMBPC. in GMPBPC GMSBPC. D1 Moreover, and D2 change monotonically GMBPC. Therefore, GMBPC Therefore, is easier to be implemented compared to other two methods. is easier toGMBPC be implemented compared to other two methods. Mode 4
1.0
Mode 5A
Mode 5C
0.8
D1
D1 D2 φ
0.7
φ
0.6 0.5 0.4
0.6
φ
0.5
D2
0.2 0.1
0.4
0
k5Amax
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0.1 0
0.6
φ
0.5 0.4 0.3
D2
0.2
k4max
D1
0.7
0.3
0.3
Mode 5C
0.9
D1 D2 φ
D1
0.7
Mode 4
1.0
0.8
0.8
D1 D2 φ
Mode 5C
0.9
0.9
0
Mode 5B
Mode 4
1.0
0.2
k4max 0
k5Bmax
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
D2
0.1 0
k4max 0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k
k
k
(a)
(b)
(c)
Figure Figure7.7.Control ControlParameters Parametersof ofoptimized optimizedcontrol control methods methods under under V V11==60 60V, V,VV2 2==120 120V;V;(a) (a)GMPBPC; GMPBPC; (b) GMSBPC; (c) GMBPC. (b) GMSBPC; (c) GMBPC.
3.5.3. Current Stress and Current rms 3.5.3. Current Stress and Current rms In order to further study the performance differences of the three optimized methods, the In order to further study the performance differences of the three optimized methods, the current current stress and the current rms value of iL are compared in Figure 8. Compared to the traditional stress and the current rms value of iL are compared in Figure 8. Compared to the traditional SPS SPS control method, the current stress and current rms can be reduced effectively by all the three control method, the current stress and current rms can be reduced effectively by all the three optimized optimized methods especially at lower power level. However, as shown in Figure 8a, the current methods especially at lower power level. However, as shown in Figure 8a, the current stress of stress of GMPBPC becomes larger than with other control methods (even than SPS control method) GMPBPC becomes larger than with other control methods (even than SPS control method) at higher at higher power level when d is larger than 1. Similar situations can also be seen in Figure 8b where power level when d is larger than 1. Similar situations can also be seen in Figure 8b where the current the current stress of GMSBPC becomes larger than other methods when d is smaller than 1. A similar stress of GMSBPC becomes larger than other methods when d is smaller than 1. A similar phenomenon phenomenon has been seen and analyzed in Figure 6 in regard to backflow power Qp and Qs. As a has been seen and analyzed in Figure 6 in regard to backflow power Qp and Qs . As a result, the same conclusion can be drawn that GMPBPC has worse performance when d is larger than 1 while GMSBPC has worse performance when d is smaller than 1.
1 while GMSBPC has worse performance when d is smaller than 1. As shown in Figure 8c,d, the differences of current rms are smaller than the differences of current stress among the three optimized methods. However, current rms of the three optimized methods all becomes slightly larger than with the SPS control method at higher power level, which means larger Energies 2017, 10,losses 1403 arise in a higher power operation range by the optimized methods. 13 of 27 conduction 25
25
GMPBPC
20 GMSBPC SPS
15
GMBPC
10
Current Stress(A)
Current Stress(A)
20
GMSBPC
5
GMPBPC SPS
15
GMBPC
10
5
0 0
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k
k
(a)
(b) 16
16 GMPBPC
GMSBPC 14
12
GMSBPC GMBPC
10 SPS
8 6 4 2 0
Current RMS (A)
Current RMS (A)
14
12
GMPBPC GMBPC
10 SPS
8 6 4 2
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k
(c)
0 0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k
(d)
Figure8.8. Current Current stress methods; (a)(a) Current stress under V1 = Figure stress and and current currentRMS RMSofofoptimized optimizedcontrol control methods; Current stress under V, V2 = 120 V; (b) Current stress under V1 = 120 V, V2 = 60 V; (c) Current RMS under V1 = 60 V, V2 = V60 1 = 60 V, V 2 = 120 V; (b) Current stress under V 1 = 120 V, V 2 = 60 V; (c) Current RMS under V 1 = 60 V, 120 RMSRMS under V1 =V120= V, V2 = 60 V. V 2 = V; 120(d) V; Current (d) Current under 1 120 V, V 2 = 60 V.
In general, GMBPC has the best current performance compared to the other two optimized As shown in Figure 8c,d, the differences of current rms are smaller than the differences of current control methods. stress among the three optimized methods. However, current rms of the three optimized methods all becomes slightly larger than with the SPS control method at higher power level, which means larger 3.5.4. Switching Characteristics conduction losses arise in a higher power operation range by the optimized methods. the resonance duringperformance switching transition, generally InNeglecting general, GMBPC has theprocess best current comparedthe to soft-switching the other two is optimized determined by the polarity of the current at the switching moment. At low power level, all the control methods. optimized methods operate in mode 4 and the current satisfies the condition when iL(t0) = 0, iL(t1) ≥ 0, 3.5.4. iL(t2)≥Switching 0 and iL(tCharacteristics 3) = 0. Therefore, Q3, Q4, Q5 and Q6 are turned on at zero-voltage-switching (ZVS) while Q1, Q2, Q7 and Q8 are turned offduring at zero-current-switching (ZCS) mode 4. All the switching Neglecting the resonance process switching transition, the in soft-switching is generally devices can by achieve soft-switching at low power determined the polarity of the current at thelevel. switching moment. At low power level, all the At medium power level, the GMPBPC iL(t0) = 0, iLwhen (t1) > 0,i i(tL(t)2)=>0,0 and (t3)0,> optimized methods operate in mode 4 and themethod currentrequires satisfiesthat the condition iL (t1 )iL≥ L 0 Q3, Q4, Q5, Q6, Q7 and Q8 are turned on at ZVS while Q1 and Q2 are turned off at ZCS iL0.(tTherefore, 2 ) ≥ 0 and iL (t3 ) = 0. Therefore, Q3, Q4, Q5 and Q6 are turned on at zero-voltage-switching (ZVS) in mode 5. Similarly, Q1,are Q2,turned Q3, Q4, and Q6 are turned on at ZVSin while Q7 Q8 switching are turned while Q1, Q2, Q7 and Q8 offQ5 at zero-current-switching (ZCS) mode 4. and All the off at ZCS in mode 5 for the GMSBPC method. Thus, all the switching devices can achieve softdevices can achieve soft-switching at low power level. switching at medium At medium powerpower level,level. the GMPBPC method requires that iL (t0 ) = 0, iL (t1 ) > 0, iL (t2 ) > 0 and At high power level, optimized control methods operate 5Care under the iL (t3 ) > 0. Therefore, Q3, Q4, all Q5,three Q6, Q7 and Q8 are turned on at ZVS whileinQ1mode and Q2 turned conditions when i L(t0) < 0, iL(t1) > 0, iL(t2) > 0 and iL(t3) > 0. As a result, all the switching devices can be off at ZCS in mode 5. Similarly, Q1, Q2, Q3, Q4, Q5 and Q6 are turned on at ZVS while Q7 and Q8 turned onoff at ZVS at high power level. are turned at ZCS in mode 5 for the GMSBPC method. Thus, all the switching devices can achieve In conclusion, based on the comparative analysis above, GMBPC is a preferable choice to be a soft-switching at medium power level. tradeoff between Qp all bythree GMPBPC and min Qs bymethods GMSBPC. Compared to 5C GMPBPC andconditions GMSBPC, At high powermin level, optimized control operate in mode under the when iL (t0 ) < 0, iL (t1 ) > 0, iL (t2 ) > 0 and iL (t3 ) > 0. As a result, all the switching devices can be turned on at ZVS at high power level. In conclusion, based on the comparative analysis above, GMBPC is a preferable choice to be a tradeoff between min Qp by GMPBPC and min Qs by GMSBPC. Compared to GMPBPC and GMSBPC,
Energies Energies2017, 2017,10, 10,1403 1403
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GMBPC allows smaller current stress, smaller current rms value, easier implementation method and GMBPC allows smaller current stress, smaller current rms value, easier implementation method and wider ZVS range. wider ZVS range. 4. Non-Active Power Transmission in DAB Converter 4. Non-Active Power Transmission in DAB Converter 4.1. Non-Active Non-Active Power Power Transmission TransmissionTime TimeininDAB DABConverter Converter 4.1. The global backflow power optimization methods are derived in Section However, The globalminimum minimum backflow power optimization methods are derived in3.Section 3. the backflow power transmission is just a portion of the non-active power transmission in a DAB However, the backflow power transmission is just a portion of the non-active power transmission in The ideal maximum power transmission efficiency in DAB occurs positive is aconverter. DAB converter. The ideal maximum power transmission efficiency in DABwhen occurs when power positive transmitted from the primary side to the secondary side while positive power is also transmitted power is transmitted from the primary side to the secondary side while positive power is also from the secondary to the load the same time, e.g., the period to t3 inofFigure transmitted from theside secondary side side to theatload side at the same time, e.g., of thet2 period t2 to t9. 3 However, shown inasFigure the practical on the primary side of side DABofisDAB that in Figure 9.asHowever, shown 9a, in Figure 9a, the situation practical situation on the primary transmission power power flows back to back the primary side during 0 to ta and transmission power is zero on is that transmission flows to the primary sidetduring t0 to ta and transmission power the primary side during t 3 to t4. Therefore, non-active power transmission time on the primary side is zero on the primary side during t3 to t4 . Therefore, non-active power transmission time on the containsside twocontains portionstwo during t0 toduring ta (i.e.,t the backflow power) and t3 to t4 (i.e., the zero power) primary portions 0 to ta (i.e., the backflow power) and t3 to t4 (i.e., the zero respectively. A similar situation can also be seen on side of the DAB, as shown inshown Figure power) respectively. A similar situation can also be the seensecondary on the secondary side of the DAB, as 9b.Figure 9b. in
vcd
D2Ths D1Ths
D1Ths
vab
iL
tpez
iL tsez
Ts
ta' tb'
Ths
te
Ths
t0 t1t2t3
vab
tsez
tpz tatb
vcd
D2Ths
Ts
t ta
tsz te
t4 t5t6t7 (a)
t8 t0 t1t2t3
tc Ths
t
Ths
t4 t5t6t7
t8
(b)
Figure 9. 9. Non-active Non-active power power transmission transmission time time in in (a) (a) Primary Primary side; side; (b) (b)Secondary Secondaryside. side. Figure
However, the the factor factor of ofzero zeropower powertransmission transmission is is not not considered considered in in Section Section 33 with with the the optimal optimal However, objective of of backflow backflow power. power. Although backflow power is is minimized minimized by by the the methods methods derived derived in in objective Section 3, the time of zero power transmission may increase. As a result, the power transmission Section 3, the time of zero power transmission may increase. As a result, the power transmission efficiencymay maynot notbe beimproved improvedby bythe theoptimization optimizationof ofbackflow backflowpower. power. efficiency In order to transmission in DAB, the the concept of maximum nonIn to optimize optimizethe thenon-active non-activepower power transmission in DAB, concept of maximum active power transmission timetime is proposed in this section. Taking thethe operation mode in in Figure 9 as non-active power transmission is proposed in this section. Taking operation mode Figure 9 anan example, zero power transmission onon the t 4.t The duration of t 3 tto as example, zero power transmission theprimary primaryside sideoccurs occursduring duringt3tto to . The duration of 3 4 3 t4 is as as tpz.tThe backflow power Qp is backback to the primary sideside during t0 tot0ta.toThe to t4 denoted is denoted backflow power Qptransmitted is transmitted to the primary during ta . pz . The same amount of power which is also equal totoQQ p, pcan the The same amount of power which is also equal , canbebetransmitted transmittedfrom fromthe the primary primary side to the secondaryside sideduring duringtatato tottbb.. Therefore, Therefore, the the average averagepower powerduring duringt0t0to tottbb is is zero. zero. The The period periodof oftt00 to to secondary t b can be called the equivalent zero power transmission time, just like the zero power transmission tb can be called the equivalent zero power transmission time, just like the zero power transmission during tt33 to to tt44. However, the same amount of power power which which is is equal equal to to Q Qpp,, can can also also be be transmitted transmitted during from the primary side to the secondary side during other different time intervals, e.g., during ta’tato0 to tb’ from the the secondary side during other different time intervals, e.g., during 0 0 0 9a. 9a. TheThe duration of ta of to ttab is than the duration of ta’ tooftbt’adue average tin in Figure duration to longer tb is longer than the duration to tto duesmaller to the smaller b Figure b the current during a to tb. Therefore, t0 to tb istthe maximum equivalent zero power transmission time on average current tduring ta to tb . Therefore, to t is the maximum equivalent zero power transmission 0 b the primary side caused by backflow power Q p . The duration of t 0 to t b is denoted as t pez . As time on the primary side caused by backflow power Qp . The duration of t0 to tb is denoted as tpeza. consequence, the maximum non-active power transmission time on the primary side, i.e., tpna, can be defined to be the sum of tpz and tpez as given below:
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As a consequence, the maximum non-active power transmission time on the primary side, i.e., tpna , can be defined to be the sum of tpz and tpez as given below: t pna = t pez + t pz
(34)
The non-active power transmission time ratio (NTR) on the primary side is defined as γp . γp is the percentage of tpna to Ths . Therefore, the effective power transmission time ratio (ETR) on the primary side can be defined as δp = 1 − γp : δ p = (1 −
t pna ) × 100% = 1 − γ p Ths
(35)
Similarly, as shown in Figure 9b, the non-active power transmission time ratio on the secondary side, i.e., γs , is the percentage of tsna to Ths . The ETR on the secondary side can be defined as δs = 1 − γs . Nonactive power transmission time unifies the zero power transmission and the backflow power transmission together. The backflow power is converted to zero power transmission time equivalently. Therefore, δp indicates the active power transmission time efficiency on the primary side while δs indicates the active power transmission time efficiency on the secondary side. The active power transmission time efficiency for DAB is limited by the minimum transmission time efficiency either on the primary side δp or on the secondary side δs , i.e., min (δp , δs ). As a result, the active power transmission time efficiency for a DAB converter on both sides cannot be just denoted as the tradeoff between δp and δs , e.g., the summation of δp and δs . The effective power transmission time te for a DAB converter can be denoted as the time during which no non-active power on the primary side or on the secondary side is transmitted. In Figure 9, the period of t2 to t3 is the effective power transmission time. Therefore, it makes sense for te to indicate the power transmission time efficiency for DAB. For the purpose of minimizing the non-active power transmission time on both sides for DAB, a new optimal objective can be constructed in Equation (36) to maximize the effective power transmission time ratio (δe = te /Ths ): max δe
(36)
4.2. Minimum Non-Active Power Transmission Time Control (MNPC) at Low Power Level At low power level, GMPBPC, GMSBPC and GMBPC are all in mode 4 with the control parameters shown in Table 2. The time tpna , tsna and te can be calculated as: t pna = Ths (1 − D1 ), tsna = Ths (1 − D2 ), te = Ths ( D1 − ϕ) = Ths
p
D1 D2 − k
(37)
In this case, when D1 and D2 are selected to be their maximum values, γp and γs can be minimized. Moreover, as can be seen in Equation (37), the optimal objective “max δe ” is equivalent to the objectives “min γp ” and “min γs ” at the same time. Therefore, the effective power transmission time te can be maximized while the non-active power transmission time can be minimized in the meantime. The maximum values of D1 and D2 can be obtained based on the limitation condition of ϕ in Equation (12). Optimized results show that the MNPC method in mode 4 is located at the boundary of mode 1 and mode 4 when d < 1 or the boundary of mode 2 and mode 4 when d > 1. Moreover, it can be demonstrated that the control parameters of MNPC in mode 1 and mode 2 are the same as the results in Equations (4) and (7), respectively. Figure 10a,b show the simulation waveforms of MNPC and GMBPC at low power level respectively when d = 2. Although the backflow power in these two control methods is zero, the non-active power transmission time is different. Under certain transmission power k = 0.2, δp , δs , and δe of MNPC are 89.4%, 44.7%, and 44.7%, respectively, while δp , δs , and δe of GMBPC are 71.7%, 35.9%, and 23.9%, respectively. Apparently, the effective power transmission time ratio δp , δs , and
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vcd
vab tpz
0 t(10us/div)
iL
tsz
te
Ts
Ths
vab(t) vcd(t) iL(t) (50A/div) (50V/div) (50V/div)
vab(t) vcd(t) iL(t) (50A/div) (50V/div) (50V/div)
δe of MNPC are all larger than that of GMBPC. As a result, the optimized performance of MNPC is Energies 2017, 10, 1403 16 of 28 supposed to be better than optimized performance of GMBPC at low power level.
vcd
vab tpz tsz
te
0 t(10us/div)
iL
Ths
(a)
Ts
(b)
Figure10. Simulationwaveforms waveforms MNPC and GMBPC at low power under 1 = 60 V, V2 = 120 Figure 10. Simulation ofof MNPC and GMBPC at low power levellevel under V 1 =V60 V, V 2 = 120 V; V; (a) MNPC; (b) GMBPC. (a) MNPC; (b) GMBPC.
4.3.Minimum MinimumNon-Active Non-ActivePower PowerTransmission Transmission Time Control High Power Level 4.3. Time Control at at High Power Level high power level, the optimized control strategy willin work in mode Based on the AtAthigh power level, the optimized control strategy will work mode 5C. Based 5C. on the numerical numerical optimization results in B, Appendix B, the minimum power transmission time is optimization results in Appendix the minimum non-activenon-active power transmission time is always always reached in mode 5Ca when d > 1 or in mode 5Cd when d < 1. reached in mode 5Ca when d > 1 or in mode 5Cd when d < 1. mode5Ca, 5Ca,the thet tpna, ,t tsna and and tte can can be be calculated calculated as: as: InInmode pna
sna
e
2V V V i (t ) i (t1 )2 V1 V2 V1 V2 + ϕThs , te = Ths − tsna (38) (38) V2 −V1 Ths , te Ths tsna pna L 0 sna V1 V2 V V1 V V1 As shown in Figure A1a, tsna is2 larger than tpna in2 mode 5Ca. Therefore, the ETR on the secondary side (i.e., δs ) isA1a, smaller the ETR primary side (i.e.,the δp ).ETR Moreover, as can As shown in Figure tsna isthan larger than tpnaon in the mode 5Ca. Therefore, on the secondary beside seen in Equation (38), thethe maximization of δe is equivalent the minimization γs . Therefore, (i.e., δs) is smaller than ETR on the primary side (i.e., δpto ). Moreover, as can beofseen in Equation the minimization of minof (δpδ,e δiss )equivalent and the maximization of δe canofbeγsreached at the time. Theof (38), the maximization to the minimization . Therefore, thesame minimization optimized are derived below: min (δp, δcontrol s) and parameters the maximization of δeascan be reached at the same time. The optimized control parameters are derived as below: ∂tsna ∂D2 D =1 = 0 ⇒ q q tsna1 (39) 01 1−2k 1 1−2k d −2 D1 = 1, D = − ( d − 1 ) , ϕ = + , when d ≥ 1 2 2 2 2 2 D2 D 1 d −2d+2 d −2d+2 1 (39) k 1as: d 2 1 2k In mode 5Cd, the tpna , tsna and te can 1be 2 calculated D1 1, D2 1 (d 1) 2 , , when d 1 2 2 d 2d 2 d 2 2d 2 r t = − 2 L2L i (t ), t =LiLi L((tt0)) + t pna V1 +V2i L(t 0), t sna VL2 −0V1
L
2V2 V +V
LL
r
2 2V1 1 2 V2 −V1 2 21 0) + 0 V1 +V2 i L (t1 ) L V1 +V2 i L ( tL
V −V
i L (t1 )2 + V1 +V2 i L (t0 )2
2 2 Li L (t1 ) the tpna1, tsna Int pna mode and te1 can be calculated = −V5Cd, + + (1 − D1 +as: ϕ) Ths , tsna = V1 −V2 1 −V2
2V
2L V1 +V2 i L ( t1 ), te
= Ths − t pna
(40)
V V
2 2 L process iL (t1in )2 mode 1 5Ca, iL (t0the ) 2 optimized control parameters in mode 5Cd can Similar to the derivation V1 V2 V1 V2 LiL (t1 ) 2L (40) t pnabelow: (1 D1 )Ths , tsna iL (t1 ), te Ths t pna be derived as V1 V2 V1 V2 V1 V2 ∂t pna = 0 ⇒process in mode 5Ca, the optimized control parameters in mode 5Cd derivation Similar to∂Dthe 1 D 2 =1 q q (41) 2k 1 1 1−2k can be derived D1as=below: 1 − (1 − d) 1−12d−+ , D = 1, ϕ = − , when d < 1 2 2 2 2d2 1−2d+2d2
t pna 0simulation Figure 11a,b show the waveforms of MNPC and GMBPC at high power level, D 1 2 respectively, when d 1= D2. Under certain transmission power k = 0.4, δp , δs , and δe of MNPC (41) are 87.8%, 42.4%, and 42.4%, respectively, while δ , δ , and δ of GMBPC are 79.7%, 39.3%, and 35.4%, 1 2k 1e 1 1 2k p s D1 1 (1 d ) , D2 1, , when d 1 respectively. Both the zero power 1transmission 2 equivalent 2 1 2d 2zero 2d 2d 2 time and the d 2 power transmission time Figure 11a,b show the simulation waveforms of MNPC and GMBPC at high power level, respectively, when d = 2. Under certain transmission power k = 0.4, δp, δs, and δe of MNPC are 87.8%, 42.4%, and 42.4%, respectively, while δp, δs, and δe of GMBPC are 79.7%, 39.3%, and 35.4%, respectively. Both the zero power transmission time and the equivalent zero power transmission time
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tpez tpez tsz tsez
te
tsez
tsez tsz
te
tsez
0 t(10us/div) 0 t(10us/div)
Ths
Ts
Ths (a)
Ts
iL(t) iL(t) vcd(t) vcd(t)vab(t) vab(t) (50V/div) (50V/div) (50A/div) (50V/div) (50V/div) (50A/div)
iL(t) iL(t) vcd(t) vcd(t)vab(t) vab(t) (50V/div) (50V/div) (50A/div) (50V/div) (50V/div) (50A/div)
17 ofis 28 power of MNPC are smaller than that of GMBPC. As a result, power transmitted more efficiently in MNPC than in GMBPC at high power level. caused backflow power of MNPC are smaller that of As GMBPC. a result, power is caused byby backflow power of MNPC are smaller than thatthan of GMBPC. a result,As power is transmitted transmitted more efficiently in MNPC than in GMBPC at high power level. more efficiently in MNPC than in GMBPC at high power level.
tpez
tpz
tpez tsz tsez
te
tpz tsez
tsez
te
tsez
tsz
0 t(10us/div) 0 t(10us/div)
Ths
Ts
(b)Ths
Ts
Figure 11. Simulation waveforms of MNPC and GMBPC at high power level(b) under V1 = 60 V, V2 = 120 (a) V; (a) MNPC; (b) GMBPC. Figure11. 11. Simulation Simulation waveforms GMBPC at high power levellevel under V1 = 60 2 = 120 Figure waveforms of ofMNPC MNPCand and GMBPC at high power under V 1V,=V60 V, V; (a) MNPC; (b) GMBPC. VEquations (b) constitute GMBPC. the control parameters of MNPC when d is smaller than 1 while (4)MNPC; and (41) 2 = 120 V; (a)
Equations (7) and (39) constitute the control parameters of MNPC when d is larger than 1. Similar to Equations and (41) constitute the control parameters MNPC when d is smaller than 1while while (4)(4) and (41) parameters ofof MNPC when d is smaller the Equations GMBPC, MNPC also constitute has only the twocontrol subsections (i.e., low and high power level).than The1 control Equations(7)(7)and and (39)constitute constitutethe thecontrol control parameters of MNPC when d is larger than 1.Similar Similartoto Equations (39) parameters of MNPC when d is larger than 1. parameters are piecewise continuous function with k. More than that, according to the optimized theGMBPC, GMBPC,MNPC MNPC alsohas hasonly onlytwo two subsections(i.e., (i.e.,low low and high power level).The Thecontrol control the and high power level). control parameters inalso Equations (4), (7), subsections (39) and (41), MNPC method is exactly the same as the UTPS parametersare arepiecewise piecewisecontinuous continuousfunction functionwith with k.More Morethan thanthat, that,according according tothe the optimized parameters control method to minimize the current stress in k.whole load range in [9]. In to other optimized words, the control parameters in Equations (4), (7), (39) and (41), MNPC method is exactly the same as the UTPS control parameters Equations (7), (39) and (41), MNPC method is exactly the same asat the minimum current in stress and the(4), minimum non-active transmission time can be reached theUTPS same control method to minimize the current stress in whole load range in [9]. In other words, the control method to minimize the current stress in whole load range in [9]. In other words, the minimum time. minimum stress and the minimumtransmission non-active transmission time can at the same current stresscurrent and the minimum non-active time can be reached atbe thereached same time. time. 4.4. Comparative Analysis of Minimum Nonactive Power Transmission Time Control 4.4. Comparative Analysis of Minimum Nonactive Power Transmission Time Control The overall performance of MNPC, GMBPC and Transmission SPS is compared as follows. 4.4.The Comparative Analysis of Minimum Nonactive Time overall performance of MNPC, GMBPCPower and SPS is compared as Control follows. The overall performance of MNPC, GMBPC and SPS is compared as follows. 4.4.1.Backflow Backflow Power 4.4.1. Power The backflow powerofofMNPC, MNPC,GMBPC GMBPCand andSPS SPSversus versusk kisisplotted plottedininFigure Figure12. 12.The Thebackflow backflow 4.4.1. Backflow Power The backflow power powerininMNPC MNPCisisslightly slightlylarger largerthan thanthat thatininGMBPC. GMBPC.Moreover, Moreover, thebackflow backflowpower powerofofMNPC MNPCand and power The backflow power of MNPC, GMBPC and SPS versus k isthe plotted in Figure 12. The backflow GMBPC is much smaller than the backflow power of SPS control especially at lower power level. In GMBPC is MNPC much smaller than the than backflow power of SPS control the especially at power lower power level. power in is slightly larger that in GMBPC. Moreover, backflow of MNPC and general, GMBPC has a better performance than MNPC on the reduction of backflow power. InGMBPC general,isGMBPC has a better MNPC oncontrol the reduction of backflow power.level. In much smaller than performance the backflow than power of SPS especially at lower power general, GMBPC has a better performance than MNPC on the reduction of backflow power. 180 500 600 450
100 140 80 120 60 100 4080 2060 040 0 20 0
0
400 500 350 SPS 450 SPS 300 400 250 350 SPS 200 SPS 300 150 250 100 MNPC 200 k2max k4max k2max k4max MNPC 50 GMBPC 150 GMBPC 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 100 MNPC MNPC k2max k4max k2max k4max k k 50 GMBPC GMBPC 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Qs(W)
Qp(W) Qp(W)
120 160
Qs(W)
140 180
(a) k
(b)
k
500 600
SPS
400 500
Qsum(W) Qsum(W)
160
300 400
SPS
200 300
100 200
k4maxMNPC
k2max
GMBPC 0 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 100 MNPC
k2max k
0
0
k4max
GMBPC
(c)
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k
Figure12. 12.Backflow Backflow powerofofMNPC, MNPC,GMBPC GMBPCand andSPS SPSversus versusk kunder underVV1==60 60V,V,VV2==120 120 (a)QQ p; (a) power (b) (c)V;V;(a) Figure p; 1 2 (b) Q s; (c) Qsum. (b) Qs ; (c) Qsum . Figure 12. Backflow power of MNPC, GMBPC and SPS versus k under V1 = 60 V, V2 = 120 V; (a) Qp; Qs; (c) Q sum. 4.4.2. (b) Effective Power Transmission Time Ratio
4.4.2. Effective Power Transmission Time Ratio
between low power mode and high power mode. As shown in Figure 13a, δp in SPS is even larger than δp in MNPC and GMBPC at higher power level. However, δs in SPS is much smaller than δp in SPS. The operation performance is mostly determined by δe and the minimum value of δp and δs. Therefore, the performance of SPS is worse than that of MNPC and GMBPC. When d =1403 2(V1 = 60 V, V2 = 120 V), the maximum values of δp, δs and δe of MNPC are 100%, 50% Energies 2017, 10, 18 of 27 and 50%, respectively, while the maximum values of δp, δs and δe of GMBPC are 86%, 43% and 43%, respectively. Moreover, the δp, δs and δe in MNPC are always larger than that in GMBPC. Especially, 4.4.2. Power Transmission Time the δeEffective in MNPC is much larger than theRatio δe in GMBPC and SPS. As a result, MNPC has a better performance GMBPC reduction non-active power d reduces to As shownthan in Figure 13,on thethe maximum δp of and δs in MNPC andtransmission.When GMBPC occur at the boundary 1.5(V 1 = 80 V, V2 = 120 V), the δe in GMBPC, MNPC and SPS increases when d approaches to 1. between low power mode and high power mode. As shown in Figure 13a, δp in SPS is even larger than the increase rate of δe in GMBPC is smaller than that of MNPC and SPS control. Therefore, δHowever, p in MNPC and GMBPC at higher power level. However, δs in SPS is much smaller than δp in SPS. δ e in GMBPC is even smaller than δe in SPS control. It indicates that the performance of DAB may not The operation performance is mostly determined by δe and the minimum value of δp and δs . Therefore, be improved by GMBPC is close the performance of SPS is when worsedthan thattoof1.MNPC and GMBPC. 100
50 MNPC
70
35
60
30
50 40 30
20
20
5
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k
(b)
(c)
70
100 90
70
60
MNPC
MNPC
60 GMBPC
50
40 30
40 30 20
20
SPS
MNPC
50
δe ×100%
GMBPC
50
δs ×100%
70 60
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
0
k
(a)
80
SPS
10
SPS
k
δp ×100%
25
5 0
GMBPC
30
15
10
SPS
MNPC
35
25
10 0
40
MNPC
15
20
45
GMBPC
40
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Figure13. 13. Effective Effectivepower powertransmission transmissiontime timeratio ratioofof MNPC, GMBPC and SPS versus k under = 60 Figure MNPC, GMBPC and SPS versus k under V1 V =160 V, V2120 = 120 p; (b) δs; (c) δe and V1 = 80 V, V2 = 120 V; (d) δp; (e) δs; (f) δe. VV,2 = V; V; (a) (a) δp ; δ(b) δs ; (c) δe and V 1 = 80 V, V 2 = 120 V; (d) δp ; (e) δs ; (f) δe .
4.4.3. Current Stress and Current rms When d = 2(V 1 = 60 V, V 2 = 120 V), the maximum values of δp , δs and δe of MNPC are 100%, As shown in Figure 14a,b, the current stress and current MNPC GMBPC reduced 50% and 50%, respectively, while the maximum values of δrms δe ofand GMBPC areare 86%, 43% p , δsofand efficiently compared to that of SPS control when d = 2. Moreover, MNPC has the minimum current and 43%, respectively. Moreover, the δp , δs and δe in MNPC are always larger than that in GMBPC. stress and minimum currentisRMS to other methods. AsSPS. a result, a better Especially, the δe in MNPC muchcompared larger than the δe two in GMBPC and As aMNPC result, has MNPC has of current GMBPC. be seenpower in Figure 14c,d, when the voltage aperformance better performance thanthan GMBPC on theHowever, reductionas of can non-active transmission.When d reduces conversion ratio reduced 1.5,δethe stress andand current of GMBPC even larger than to 1.5(V 1 = 80 V, dVis 120 V),tothe in current GMBPC, MNPC SPS rms increases whenare d approaches to 1. 2 = that of SPSthe control. The same be drawn that of backflow power may However, increase rate of δconclusion is smaller than thatthe of optimization MNPC and SPS control. Therefore, δe e in GMBPCcan not ensure is the high-efficiency of DAB It when d is close in GMBPC even smaller thanoperation δe in SPS control. indicates that to the1.performance of DAB may not be improved by GMBPC when d is close to 1. 4.4.3. Current Stress and Current rms As shown in Figure 14a,b, the current stress and current rms of MNPC and GMBPC are reduced efficiently compared to that of SPS control when d = 2. Moreover, MNPC has the minimum current stress and minimum current RMS compared to other two methods. As a result, MNPC has a better performance of current than GMBPC. However, as can be seen in Figure 14c,d, when the voltage conversion ratio d is reduced to 1.5, the current stress and current rms of GMBPC are even larger than that of SPS control. The same conclusion can be drawn that the optimization of backflow power may not ensure the high-efficiency operation of DAB when d is close to 1.
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Figure14. 14.Current Current stress current of MNPC, GMBPC andcontrol SPS control method. (a) Current Figure stress andand current rmsrms of MNPC, GMBPC and SPS method. (a) Current stress stress under V 1 = 60 V, V2 = 120 V; (b) Current rms under V1 = 60 V, V2 = 120 V; (c) Current stress under under V 1 = 60 V, V 2 = 120 V; (b) Current rms under V 1 = 60 V, V 2 = 120 V; (c) Current stress under 1 = 80 V, V2 = 120 V; (d) Current rms under V1 = 80 V, V2 = 120 V. VV 1 = 80 V, V 2 = 120 V; (d) Current rms under V 1 = 80 V, V 2 = 120 V.
4.4.4.Switching SwitchingCharacteristics Characteristics 4.4.4. Asanalyzed analyzedininSection Section3.5.4, 3.5.4,all allswitching switchingdevices devicescan canachieve achievesoft-switching soft-switchingininGMBPC. GMBPC.At Athigh high As power level, all the switching devices can be turned on at ZVS for MNPC in mode 5C. At low power power level, all the switching devices can be turned on at ZVS for MNPC in mode 5C. At low power level,Q3 Q3and andQ4 Q4are areturned turnedon onatatZVS ZVSwhile whileQ1, Q1,Q2, Q2,Q5, Q5,Q6, Q6,Q7 Q7and andQ8 Q8are areturned turnedoff offatatZCS ZCSfor for level, MNPC when d is smaller than 1. A similar situation can be seen when d is larger than 1. As a result, MNPC when d is smaller than 1. A similar situation can be seen when d is larger than 1. As a result, allthe theswitching switchingdevices devicescan canachieve achievesoft-switching soft-switchingatatboth bothlow lowpower powerlevel leveland andhigh highpower powerlevel levelby by all MNPCand andGMBPC. GMBPC. MNPC 4.4.5.Limitations LimitationsofofBackflow BackflowPower PowerOptimization OptimizationMethods Methods 4.4.5. Unlike the the SPS SPS control, control, both both MNPC MNPCand andGMBPC GMBPCcan canensure ensuresoft-switching soft-switchingoperation operationfor forall all Unlike switching devices with arbitrary d. However, the effective power transmission time of GMBPC switching devices with arbitrary d. However, the effective power transmission time of GMBPC reduces when d approaches 1. This isthat because that the optimization GMBPC doesthe notzero take a reduces lot whena dlot approaches to 1. This to is because the optimization of GMBPCofdoes not take the zero power transmission into consideration. Minimum backflow power is obtained at the cost power transmission into consideration. Minimum backflow power is obtained at the cost of increasingof increasing zero power transmission when to 1. that It indicates that stress the current stress and zero power transmission time when dtime is close to d1.isItclose indicates the current and rms value value of GMBPC become than SPS control d is1.close 1. As athe result, the advantage ofrms GMBPC become larger thanlarger SPS control when d is when close to As atoresult, advantage of full of full soft-switching in GMBPC may be counteracted by increasing current. In spite of this, GMBPC soft-switching in GMBPC may be counteracted by increasing current. In spite of this, GMBPC is still is still effective to improve the performance DAB when d is far effective to improve the performance of DAB of when d is far from 1. from 1. Results 5.5.Results 5.1. 5.1.Implementation ImplementationMethod Methodfor forGMBPC GMBPC The ofof MNPC is presented in [9]. Therefore, only the the implementation of Theimplementation implementationmethod method MNPC is presented in [9]. Therefore, only implementation GMBPC is introduced in this section. Replacing the “d” in (17) and (33) by 1/d, the expressions of D of GMBPC is introduced in this section. Replacing the “d” in (17) and (33) by 1/d, the expressions 1of and D2 can Therefore, an implementation method is developed for GMBPC. As D1 and D2 be caninterchangeable. be interchangeable. Therefore, an implementation method is developed for GMBPC.
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As shown in Figure 7c, D11 and D22 changes monotonically with transmission power k. Therefore, the output of PI controller, i.e., m, can be used to denote D11 or D22 directly. shown in Figure 7c, D1 and D2 changes monotonically with transmission power k. Therefore, the output When d is larger than 1: of PI controller, i.e., m, can be used to denote D1 or D2 directly. d d 1 When d is larger than 1: D11 dm, D22 m, D11, when 0 m 22 (42) dd 1 d dd+1 1 D1 = dm, D2 = m, ϕ = D , when 0 ≤ m ≤ 2 (42) d1 +d1 (d1 1) D D d + d1+ 1 1 1 d 11 22 D11 1 22 22 m, D22 m, , when 22 m 1 (43) d d dd + 11 1d 1 − d + (d + 21) D1 − D2 1 D1 = 1 − 2 + 2 m, D2 = m, ϕ = , when 2 ≤m≤1 (43) 2 d d than 1: d +d+1 When d is smaller When d is smaller than 1: m d d 22 d D11 m, D22 m , d D11, when 0 m 22 d2 + d (44) D1 = m, D2 = ,dϕ = d 1D1 , when 0 ≤ m ≤ (44) d d2d+d1 + 1 d d+1
1 dd+ ((dd + 1)1D d 22 dd2 + d 22 22 11 D 22 D 1 − ) D − 2 D m , D 1 d md , , when m 1 1 2 2 11 = 1 − 22 d + md , ϕ = D1 = m, D , when 2 22 d 22 dd2 +1d + 1 ≤ m ≤ 1
(45) (45)
The control structure method is is illustrated illustrated in in Figure Figure 15. 15. structure for for the the GMBPC GMBPC method
V2ref+
PI
m d
d 1 (42)(43) d 1 (44)(45)
D1 D2 φ
DAB Converter
V2
Figure 15. 15. Control Control structure structure for for the the GMBPC GMBPC method. Figure method.
5.2. Experimental Experimental Results Results 5.2. An experimental prototype is is built built to to verify of the An experimental prototype verify the the effectiveness effectiveness of the proposed proposed control control method method and theoretical analysis. Figure 16 is a photo of experimental prototype. The transformer and theoretical analysis. Figure 16 is a photo of experimental prototype. The transformer turnsturns ratio ratio is 1. Switching frequency kHz. The inductance L isAll 64 switching µH. All switching devices in s is 20 n is 1.nSwitching frequency fss is 20 fkHz. The inductance L is 64 μH. devices in both the both the primary H-bridge and secondary H-bridge are IXFX160N30TMOSFETs (IXYS, Lampertheim, primary H-bridge and secondary H-bridge are IXFX160N30TMOSFETs (IXYS, Lampertheim, Germany). The control control system system is is based based on on the the EP4CE15E22C8N EP4CE15E22C8N FPGA FPGA (Altera, (Altera, San San Jose, Jose, CA, CA, USA). USA). Germany). The The Beaverton, OR, OR, The current current waveforms are recorded by a Tektronix A622current probe (Tektronix, Beaverton, USA). The current waveforms lag behind the voltage waveforms about 2 µs. USA). The current waveforms lag behind the voltage waveforms about 2 μs. MOSFET MOSFET
Secondary Secondary Bridge Bridge
Primary Primary Bridge Bridge complementary complementary Inductance Inductance
FPGA FPGA controller controller
Transformer Transformer
Figure 16. Experimental prototype. Figure 16. Experimental prototype.
Figure 17 illustrates the operating waveforms when V11 = 120 V, V22 = 60 V while Figure 18 Figurethe 17operating illustrateswaveforms the operating waveforms when V = 120 V, V 2 = 60 V while 18 illustrates when V11 = 60 V, V 22 = 120 1V. At low power level, i.e., PFigure oo = 144 W illustrates the operating waveforms when V = 60 V, V = 120 V. At low power level, i.e., P = 144 W o 1 2 and k = 0.1, both MNPC and GMBPC have good effect on the reduction on the current stress and rms value.
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and k = 0.1, both MNPC and GMBPC have good effect on the reduction on the current stress and rms value. Energies 2017, 10, 1403 21 of 28 Energies 2017, 10, 1403
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ab vvab
cd vvcd
ab vvab
ab vvab cd vvcd
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iL HSiL HS
cd vvcd
iiLL ZCS:Q2 ZVS:Q5 ZVS:Q3 ZCS:Q8 ZCS:Q2 ZVS:Q5 ZVS:Q3 ZCS:Q8
(a) (a)
ZCS:Q2 ZCS:Q6 ZVS:Q3 ZCS:Q8 ZCS:Q2 ZCS:Q6 ZVS:Q3 ZCS:Q8
(b) (b) ab vvab vvcd
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ab vvab
cd vvcd
cd vvcd
cd
iiLL
iiLL
(d) (d)
iiLL
(e) (e)
(f) (f)
Figure 17. Operating waveforms under V1 = 120 V, V2 = 60 V, Po = 144 W; (a) SPS; (b) GMBPC; (c)
Figure 17. Operating waveforms under V1 V =1120 V, V =260 V, PV,o =Po144 W;W; (a) (a) SPS; (b)(b) GMBPC; (c)(c) MNPC Figure 17. Operating waveforms under = 120 V,2 V = 60 = 144 SPS; GMBPC; MNPC and Po = 500 W; (d) SPS; (e) GMBPC; (f) MNPC (vab = 50 V/div, vcd = 50 V/div, iL = 10 A/div). MNPC and P o = 500 W; (d) SPS; (e) GMBPC; (f) MNPC (v ab = 50 V/div, v cd = 50 V/div, i L = 10 A/div). and Po = 500 W; (d) SPS; (e) GMBPC; (f) MNPC (vab = 50 V/div, vcd = 50 V/div, iL = 10 A/div). cd vvcd
cd vvcd v ab vab
ab vvab HS HS
iiLL
iiLL
iiLL ZCS:Q2 ZVS:Q5 ZVS:Q3 ZCS:Q8 ZCS:Q2 ZVS:Q5 ZVS:Q3 ZCS:Q8
(a) (a)
ab vvab
(c) (c) cd vvcd
cd vvcd
ab vvab
iiLL (d) (d)
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(b) (b) cd vvcd
iiLL
cd vvcd v ab vab
ab vvab
iiLL (e) (e)
(f) (f)
Figure 18. Operating waveforms under V1 = 60 V, V2 = 120 V, Po = 144 W; (a) SPS; (b) GMBPC; (c) Figure 18. Operating waveforms under V1 = 60 V, V2 = 120 V, Po = 144 W; (a) SPS; (b) GMBPC; (c)
Figure 18. Operating waveforms V 1 = 60(f)V,MNPC V 2 = 120 = 144 W; (b)iLGMBPC; (c) MNPC MNPC and Po = 500 W; (d) SPS;under (e) GMBPC; (vabV, =P 50o V/div, vcd (a) = 50SPS; V/div, = 10 A/div). MNPC and Po = 500 W; (d) SPS; (e) GMBPC; (f) MNPC (vab = 50 V/div, vcd = 50 V/div, iL = 10 A/div). and Po = 500 W; (d) SPS; (e) GMBPC; (f) MNPC (vab = 50 V/div, vcd = 50 V/div, iL = 10 A/div). In Figure 17a–c, the current stress is about 14 A with SPS, 9 A with GMBPC and 8 A with MNPC. In Figure 17a–c, the current stress is about 14 A with SPS, 9 A with GMBPC and 8 A with MNPC. MNPC has the minimum current stress. At high power level, i.e., Po = 500 W and k = 0.35, the MNPC has the minimum current stress. At high power level, i.e., Po = 500 W and k = 0.35, the
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In Figure 17a–c, the current stress is about 14 A with SPS, 9 A with GMBPC and 8 A with MNPC. difference of current current stress and rms rms value value between SPS and optimized methods is smaller smaller than the the MNPC has of the minimum current stress. At high powerSPS level, i.e., Po = 500 W and k = is 0.35, the difference difference stress and between and optimized methods than difference at low power level. At low power level, Q5 to Q8 suffer the hard-switching operation with of current stress rmslevel. valueAt between SPS and smaller than the difference at difference at lowand power low power level,optimized Q5 to Q8 methods suffer theishard-switching operation with SPS control as shown in Figure 17a while Q1 to Q4 suffer the hard-switching operation with SPS low power level. At low power level, Q5 to Q8 suffer the hard-switching operation with SPS control as SPS control as shown in Figure 17a while Q1 to Q4 suffer the hard-switching operation with SPS controlin asFigure shown17a in Figure Figure 18a. As can be seen seen in Figure Figure 17b,c 17b,cand and Figure Figurewith 1b,c,SPS all switching switching devices shown while Q1 toAs Q4can suffer the hard-switching operation control as devices shown control as shown in 18a. be in 1b,c, all in GMBPC and MNPC can achieve soft-switching (ZVS or ZCS), leading to smaller voltage spikes for in 18a. can be seen in Figure 17b,c and (ZVS Figure allleading switching devices in GMBPC in Figure GMBPC andAs MNPC can achieve soft-switching or1b,c, ZCS), to smaller voltage spikesand for and can at switching moments. At At high power level, the the soft-switching cannot still be achieved in MNPC achieve soft-switching (ZVS orpower ZCS), level, leading tosoft-switching smaller voltage spikes forbe vabachieved and vcd at vvabab and vvcdcd at switching moments. high cannot still in SPS control, as shown in Figures 17d and 18d. However, the GMBPC and MNPC operate in mode 5C switching moments. power the However, soft-switching cannot still achieved in SPS control, SPS control, as shownAt inhigh Figures 17dlevel, and 18d. the GMBPC and be MNPC operate in mode 5C at high power level, so ZVS is guaranteed for all the switching devices. Experimental results verify as shown in Figures 17d and 18d. However, the GMBPC and MNPC operate in mode 5C at high at high power level, so ZVS is guaranteed for all the switching devices. Experimental results verify the full fulllevel, soft-switching operation in infor whole load range by by GMBPC and MNPC. MNPC.results Figureverify 19 shows shows the power so ZVS is guaranteed all the switching devices. Experimental the full the soft-switching operation whole load range GMBPC and Figure 19 the operating waveforms under V 1 = 95 V, V 2 = 120 V and P o = 230 W (k = 0.1). Because the voltage soft-switching operation in whole GMBPC 19 shows thethe operating operating waveforms under V1 = load 95 V,range V2 = by 120 V and and Po =MNPC. 230 W Figure (k = 0.1). Because voltage conversion ratio d is close to 1, the current stress in MNPC has little difference from the current stress waveforms under V = 95 V, V = 120 V and P = 230 W (k = 0.1). Because the voltage conversion ratio o conversion ratio d is1 close to 1,2the current stress in MNPC has little difference from the current stress inisSPS SPS control. However, as shown in Figure 19b, the current stress with GMPBC is larger than that din close to 1, the current stress in MNPC has little difference from the current stress in SPS control. control. However, as shown in Figure 19b, the current stress with GMPBC is larger than that with SPS control and MNPC. Based on the theoretical analysis, the current rms value with GMPBC However, as shown inMNPC. Figure 19b, theon current stress with GMPBCthe is larger than with SPSGMPBC control with SPS control and Based the theoretical analysis, current rmsthat value with is also larger than that with SPS control and MNPC in this case. Compared to SPS control, although and MNPC. Based on the theoretical analysis, the current rms value with GMPBC is also larger than is also larger than that with SPS control and MNPC in this case. Compared to SPS control, although the switching loss can be reduced with soft-switching in GMPBC, the conduction loss is increased that with SPS control this case. ComparedintoGMPBC, SPS control, although the switching loss the switching loss canand be MNPC reducedinwith soft-switching the conduction loss is increased with increasing current in this case. Therefore, the efficiency may not be improved by GMBPC when can be reduced with soft-switching in GMPBC, the conduction loss is increased with increasing current with increasing current in this case. Therefore, the efficiency may not be improved by GMBPC when close toTherefore, 1. in this case. the efficiency may not be improved by GMBPC when d is close to 1. ddisis close to 1.
vvcdcd
vvcdcd vvabab
vvabab
iiLL
vvcdcd
vvabab
iiLL
iiLL
(a) (a)
(b) (b)
(c) (c)
Figure 19. 19. Operating waveforms waveforms under VV11 == 95 95 V, V2 = 120 V, V, PPoo == 230 230 W; W; (a) (a) SPS; SPS; (b) (b) GMBPC; GMBPC; (c) (c) Figure Figure 19. Operating Operating waveforms under under V 1 = 95V,V,V2V=2 120 = 120 V, Po = 230 W; (a) SPS; (b) GMBPC; MNPC. MNPC. (c) MNPC.
Figure20a,b 20a,bshow showthe theefficiency efficiencyηηηvaried variedwith withoutput outputpower powerPPPo.o.The Theefficiency efficiencyisisimproved improvedaaalot lot Figure 20a,b show the efficiency varied with output power improved lot Figure o byGMBPC GMBPCand andMNPC MNPCespecially especiallyat atlower lowerpower powerlevel. level.At Atmost mostof ofthe theoperation operationpoints, points,MNPC MNPChas has by GMBPC and MNPC especially at lower power level. the operation points, MNPC has by the highest efficiency than other two control methods. the highest highest efficiency efficiency than than other other two two control controlmethods. methods. the
94 94 92 92
GMBPC GMBPC
90 90 88 88 86 86 84 84 82 82 80 80 00
95 95
MNPC MNPC SPS SPS
90 90 (%) Efficiency (%) Efficiencyηη
(%) Efficiency (%) Efficiencyηη
98 98 96 96
85 85
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80 80 75 75
SPS SPS
70 70 65 65
100 200 200 300 300 400 400 500 500 600 600 700 700 100 Po (W) Po (W)
(a) (a)
60 60 50 100 150 200 250 300 350 400 450 500 550 50 100 150 200 250 P300 350 400 450 500 550 o (W) Po (W)
(b) (b)
Figure20. 20.Efficiency Efficiencyvaried varied with output power o; (a) V1 = 120 V, V2 = 60 V; (b) V1 = 60 V, V2 = 120 V. Figure with output power PoPP;o(a) 60 V, V, V22 ==120 120V. V. Figure 20. Efficiency varied with output power ; (a)VV1 1== 120 120V, V,VV22 == 60 V; V; (b) (b) V V11 == 60
InFigure Figure20a, 20a,the theefficiency efficiencyof ofGMBPC GMBPCisislower lowerthan thanthe theefficiency efficiencyof ofSPS SPScontrol controlat athigher higherpower power In level. In Figure 20b, both GMBPC and MNPC has larger efficiency than SPS control. In general, level. In Figure 20b, both GMBPC and MNPC has larger efficiency than SPS control. In general,
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In Figure 20a, the efficiency of GMBPC is lower than the efficiency of SPS control at higher power level. In Figure 20b, both GMBPC and MNPC has larger efficiency than SPS control. In general, GMBPC and MNPC are two effective methods to improve the performance of DAB especially when d is far from 1. 6. Conclusions This paper proposes three optimized control methods for global minimum backflow power on the primary side, on the secondary side and on both sides, respectively. The comparative analysis results show that GMBPC has better performance than the other two optimized methods. GMBPC can reduce backflow power in both sides at the same time. The concept of maximum non-active power transmission time is proposed in this paper. The effective power transmission time ratio is maximized to improve the performance of DAB. The derived optimized control method, i.e., MNPC, achieves both the maximum effective power transmission time and minimum current stress of DAB at the same time. Comparative analysis shows that effective power transmission time ratio δe in GMBPC decreases when d approaches to 1 while δe in MNPC and SPS increases when d approaches to 1. The conclusion can be drawn that performance of DAB may not be improved by GMBPC when d is close to 1.Finally, a prototype is built to verify the effectiveness of theoretical analysis and the proposed control methods by experimental results. Acknowledgments: The authors appreciate the support of China State Grid Company Research Project, “Basic theory and Simulation of AC&DC seamless hybrid flexible distribution networks” (PD71-17-024) and the support of “Fundamental Research Funds for the Central Universities” (E17JB00160). Author Contributions: All authors made significant contributions to this research. More specifically, Fei Xiong performed the experiments, carried out the theoretical analysis and wrote the paper. Junyong Wu design the methodology and revised the paper. Liangliang Hao provided important comments on the paper’s structure. Zicheng Liu corrected the language and format of the paper. Conflicts of Interest: The authors declare no conflicts of interest.
Parameter List V1 V2 L n φ D1 D2 Ths A k d vab vcd iL Qp Qs Qsum kimax tpz tsz tpez tsez
dc-bus voltage on the primary side. dc-bus voltage on the secondary side. The inductance reflected to the primary side consist of leakage inductance and the additional complementary inductance. Turns ratio. The outer phase shift ratio between the drive signals of Q1 (or Q2) and Q5 (or Q6). The inner phase shift ratio in primary H-bridge between the drive signals of Q1 (or Q2) and Q3 (or Q4). The inner phase shift ratio in secondary H-bridge between the drive signals of Q5 (or Q6) and Q7 (or Q8). Half switching period. The constant coefficient Ths /(2L). Normalized transmission power to reference value AV 1 V 2 . The voltage conversion ratio V 2 /V 1 . The output voltage in primary H-bridge. The output voltage in secondary H-bridge. The transformer current. The backflow power in primary side. The backflow power in secondary side. The sum of backflow power in primary side and secondary side. The maximum transmission power in mode i (i = 1, 2, 3, 4 . . . ). The zero power transmission time in primary side. The zero power transmission time in secondary side. The maximum equivalent zero power transmission time in primary side. The maximum equivalent zero power transmission time in secondary side.
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The maximum nonactive power transmission time in primary side. The maximum nonactive power transmission time in secondary side. The effective power transmission time. The non-active power transmission time ratio (NTR) in primary side. The nonactive power transmission time ratio (NTR) in secondary side. The effective power transmission time ratio (ETR) in primary side. The effective power transmission time ratio (ETR) in secondary side. The effective power transmission time ratio. The output of PI controller.
Appendix A. Derivation Process for Objective 1 at Medium Power Level Objective 1: Elimination of primary backflow power Qp with minimum secondary backflow power Qs : Q p = 0 and min( Qs )
(A1)
The backflow power Qs in mode 5A is: Qs = A[V1 V2 ( D2 + ϕ − 1)2 +
(V1 D1 − V2 D2 )2 ] 4
(A2)
According to the expression of iL (t0 ), the following relationship can be obtained: ϕ=−
1 1 i (t ) D − D + 1 + C, where C = − L 0 2d 1 2 2 2V2 A
(A3)
The optimized control parameters for minimum Qs are derived as: 2(1+C )d2 +(1+2C )d + 2d2 +d2d+1 k c D1 = 2d2 +2d+1 = 0, D2 = 1 − k c ⇒ =0 2 (1+2C )d2 +Cd d k ϕ = 2d2 +2d+1 + 2d2d++ 2d+1 c r 2 2 2 (1−2C )d +(1+2C )d−(2d +2d+1)k where k c = ( d2 + d +1) (
∂Qs ∂D1 ∂Qs ∂D2
(A4)
It can be derived that current conditions for mode 5A, i.e., iL (t0 ) ≥ 0, iL (t1 ) ≥ 0, iL (t2 ) ≥ 0, and iL (t3 ) ≥ 0, are satisfied in (A4) so long as C ≤ 0. Taking derivative of Qs with respect to variable C, we can obtain: dQs ≤ 0, when C ≤ 0 and k ≥ k4max dC
(A5)
Equation (A5) indicates that Qs reaches its minimum value exactly when C = 0, i.e., iL (t0 ) = 0. The optimized control parameters can be solved by substituting C = 0 into (A4), as shown in (20).
Appendix B. Derivation Process for MNPC at High Power Level At high power level, the optimized control strategy will work in mode 5C. Six modes are distinguished in mode 5C with different non-active power transmission time, as shown in Figure A1. The constraint conditions in these modes are listed in Table A1. Table A1. Constraint conditions in Mode 5C.align equation in table. Mode
Constraints
te
Mode 5Ca Mode 5Cb Mode 5Cc Mode 5Cd Mode 5Ce Mode 5Cf
i L (t0 ) + i L (t1 ) ≥ 0, D1 = 1, D2 ≤ 1 i L (t0 ) + i L (t1 ) ≥ 0, D1 < 1, D2 ≤ 1, (1 − D1 + ϕ) Ths ≤ tsna ≤ Ths i L (t0 ) + i L (t1 ) ≥ 0, D1 < 1, D2 ≤ 1, ϕThs ≤ tsna < (1 − D1 + ϕ) Ths i L (t0 ) + i L (t1 ) < 0, D1 ≤ 1, D2 = 1 i L (t0 ) + i L (t1 ) < 0, D1 ≤ 1, D2 < 1, (1 − D1 + ϕ) Ths ≤ t pna ≤ Ths i L (t0 ) + i L (t1 ) < 0, D1 ≤ 1, D2 < 1, ( D2 − D1 + ϕ) Ths ≤ t pna < (1 − D1 + ϕ) Ths
te = Ths − tsna te = Ths − tsna te = ( D1 − ϕ) Ths te = Ths − t pna te = Ths − t pna te = ( D1 − ϕ) Ths
Non-active power transmission time tpna , tsna and effective power transmission time te in these modes are listed in Table A2. Similar to [10,26], a numerical method is used to help to find the optimized operation mode.
Energies 2017, 10, 1403
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Table A2. Nonactive power transmission time in mode 5C. Nonactive Power Transmission Time tpna , tsna and Effective Power Transmission Time te
Mode Mode 5Ca
Li L (t0 ) V2 −V1
t pna = − V12L +V2 i L (t0 ), tsna =
+
L
q
V2 −V1 2V1 2 2 V1 +V2 i L ( t0 ) + V1 +V2 i L ( t1 ) V2 −V1
+ ϕThs , te = Ths − tsna
t pna = − V12L i (t ) + (1 − D1 ) Ths , te = ( D1 − ϕ) Ths r +V2 L 0
Mode 5Cb tsna =
Li L (t3 ) V1 −V2
V1 V1 −V2 (V1 −V2 )V1 2 2 2 V2 i L ( t3 ) − V1 +V2 i L ( t1 ) − (V1 +V2 )V2 i L ( t0 )
−L
+
V1 −V2
+ (1 − D1 + ϕ) Ths ,
t pna = − V12L t0 ) + (1 − D1 ) Ths , te = ( D1 − ϕ) Ths +V2 i L (q tsna = VL2 i L (t0 ) + VL2 V1V+1V2 i L (t0 )2 + V1V+2V2 i L (t1 )2 + ϕThs , q V −V 2V − Li L (t1 )+ L V +2V i L (t1 )2 + V1 +V2 i L (t0 )2 2 2 1 1 t pna = + (1 − D1 + ϕ) Ths , V1 −V2 2L tsna = V1 +V2 i L (t1 ), te = Ths − t pna r V −V V (V −V ) V 2 2 2 L V2 i L (t2 ) + V2 (V1 +V2 ) i L (t1 ) + V1 +V2 i L (t0 ) 2 1 1 2 1 1 − Li L (t2 ) t pna = V1 −V2 + + (1 − D1 + ϕ) Ths , V1 −V2 tsna = V12L i ( t ) + ( 1 − D ) T , t = T e 2 hs hs − t pna +V2 L 1 q V1 V2 2 2 − Li L (t1 )+ L V +V i L (t1 ) + V +V i L (t0 ) 2 2 1 1 + ( D2 − D1 + ϕ) Ths , t pna = V1 tsna = V12L i ( t ) + ( 1 − D 2 ) Ths , te = ( D1 − ϕ ) Ths +V2 L 1
Mode 5Cc
Mode 5Cd
Mode 5Ce
Mode 5Cf
The values of te in mode 5C under different transmission power k are depicted in Figure A2. As shown in Figure A2, A, B and C are the optimized operation points under certain k with maximum te . The numerical optimization results indicate that the maximum te occurs only when D1 = 1 and d > 1 or when D2 = 1 and d < 1. The optimized control derivation Energies 2017, 10, 1403parameters can be derived just in these two operation modes. As a result, the26 of 28 process can be simpler with the help of numerical optimization results. vcd
vcd
vab
vcd
vab
iL
tpez
vab
iL
tpez
te
tpz
te
Ts
t tsez
t23 tsez tsz
tsz
t0 t1t2
t3t4 t5t6
(a)
t7t8
t0 t1t2t3
vab vcd
iL
tpez
t23
t
tsez
t3
t0 t1(t2)
tpz
Ts
te
t4 t5(t6)
t7
t8
t8
(c)
vab vcd tpz
t4 t5t6t7
(b)
vab
tpez
t34 tsez
tsz
t7(t8) t0 t1t2
t3(t4) t5t6
Ts
t tsez
t23 tsez
tpz
te
Ts
t tsez
iL
tpez
vcd
iL
tpez
tpz
Ts
te
t23
Ts
te
t12
t
tsez tsz
iL
t
tsez tsz
t3
t0 t1t2
t4 t5t6
(d)
t7
t0 t1 t2 t3
t8
t4 t5 t6
(e)
t7
t8
(f)
FigureA1. Six operating modes in mode 5C; (a) mode 5Ca; (b) mode 5Cb; (c) mode 5Cc; (d) mode
Figure A1. Six operating modes in mode 5C; (a) mode 5Ca; (b) mode 5Cb; (c) mode 5Cc; (d) mode 5Cd; 5Cd; (e) mode 5Ce; (f) mode 5Cf. (e) mode 5Ce; (f) mode 5Cf.
z
k 0.35
k 0.40
A
B
B
te (us )
te (us )
A
C
k 0.45
z
C
k 0.45
k 0.40 x
y
D2
x
D1
k 0.35
y
D2 D1
t3
t0 t1(t2)
t4 t5(t6)
t7
t8
t3
t0 t1t2
t4 t5t6
(d)
t7
t0 t1 t2 t3
t8
t4 t5 t6
(e)
t7
t8
(f)
FigureA1. Six operating modes in mode 5C; (a) mode 5Ca; (b) mode 5Cb; (c) mode 5Cc; (d) mode Energies 2017, 1403 5Ce; (f) mode 5Cf. 5Cd; (e)10,mode
z
k 0.35
k 0.40
A
B
B
te (us )
te (us )
A
26 of 27
C
k 0.45
z
C
k 0.45
k 0.40 k 0.35
x x
D1
y
y
D2 D1
D2
(a)
(b)
FigureA2. transmission power power k; k; (a) (a) V V1 = = 60, V2 = 120 V; Figure A2. Effective Effective power power transmission transmission time time ttee versus versus transmission 1 60, V 2 = 120 V; (b) V 1 = 120, V2 = 60 V. (b) V 1 = 120, V 2 = 60 V.
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