Single Loop, Zero Reactive Power in Dual-Active

1

Single Loop, Zero Reactive Power in Dual-Active-Bridge Converters J. R. Rodríguez, Member,V. Venegas R, Member, IEEE, Edgar L. Moreno-Goytia, Member IEEE, F. H. Villa Vargas, Member, IEEE, Edgar D. Castañeda S., Member,  Abstract — This paper mathematically models and analyses various control methods for Dual-Active-Bridge (DAB) converters focusing in: its performance to reduce the reactive power to zero while keeping the load current without discontinuities for any range of operation; minimizing the number of PI feedback loops to a single one; the reduction of IRMS and ripple voltage; reduction of losses, altogether compared to the conventional SPSC method. After comparations a novel control scheme using a single PI feedback-loop for abating reactive power is proposed. The simulation, mathematical model of the converter and the experimental results obtained from the laboratory-scale version of the DAB controller shows the performance of the proposal and its relative advantages. Index Terms—single-loop control, DC–DC converter, dual active bridge (DAB), phase-shift control, Bidirectional converter. I. INTRODUCTION

Modernization of the transmission and distribution grids require from the new systems based on power electronic converter to have characteristics such as high efficiency, high power density, and bidirectional power flow to fit into the distributed generation and smartgrids concepts. Due to its characteristics, the dual active bridge (DBA) converter fullfil well, with the forementioned requirement for DC-DC conversion and can be a key enabling technology in the implementation of the smart grid concept. The DBA have also opportunity in next generation of DC power grids, as detailed in. For instance, combined with VSC technologies novel electronic power transformers structures can be thoroughly implemented [2] [3]. In this applications, power exchanges between the grid and ultracapacitors [4], stack of batteries and energy storage systems, electrical vehicles [5][6], fuel cells or other DC grids at different voltage levels, all of these by controlling the power flux bidirectionality as required in a smart grids and distributed generation contexts. In general, the DBA is a two-port topology, each port based on an H-bridge structure, linked through a high-frequency transformer as shown in Fig. 1.

J. R. Rodríguez V. Venegas R, Edgar L. Moreno-Goytia, F. H. Villa Vargas, Edgar D. Castañeda S, are with the programa de Graduados e Investigación en Ingeniería Eléctrica from the Instituto Tecnológico de Morelia, Tecnológico 1500, Lomas de Santiaguito, C.P.58120. Tel.4433171870. Morelia, México. E-mail [email protected], [email protected], [email protected].

Q

P I DC1

VDC 1

I DC 2

L

H Bridge

VS

VP

1:

H Bridge

IC

IOUT RL

VDC 2

C

High Frequency

m1

Transforme r

m2

Fig. 1 General Topology of the DAB converter.

For the operation of this transformer, the potential difference at its winddings at VL produces a current flux Iλ through stray inductance Lλ of high frequency transformer. The polarity and flux direction depends on the phase relationship between modulations m1 and m2 of the H-bridges which phase shift is controlled by D2 and the pulse width “μ” of D1, being μ =1 -D1. In this way, at the transformer terminals there are two-level square voltage waveforms with 50% of duty cycle for D1=0, or a three-level one with 0 < D2 < 1[1]. For bidirectional DAB converters, the primary and secondary voltages applied to the transformer are both squarewave ac. Their interaction is through the leakage inductance of the transformer. Therefore, the phase of the primary current is not always the same as the primary voltage. A greater current proportion of Iλ is delivered to the load in one switching period and consumed by the RC load, defined as active current (IλA) while the other portion is sent back to the primary voltage source. This is defined as reactive current (IλQ) in isolated bidirectional dc–dc converters. A widely use technique for the power flux control in DAB converters is the Single-Phase-Shift-Control (SPSC) [7]. This scheme has a single control for the phase shift control between modulations m1 and m2. However, despite its relative simplicity, the implementation of this technique implies an inherent fraction of reactive power, produced at any active power range. Such fraction of power restricts the power capacity of the converter. The reduction of the reactive current to zero has various advantages: i) The RMS and Peack currents of Iλ (IλRMS and IλP) are reduced; ii) the current stress on the switches is reduced, and iii) the capacitor value is reduced due a reduction of the ripple voltage. These advantages have motivated appearance of different techniques in the literature based on phase shift and pulse width control as a way to achieved high efficiency and high power density at lower cost and a simpler implementation of the control scheme.

2 On these directions, the Dual Phase Shift Control (DPSC) technique [8] is a proposal using two PI feedback-loops to achieve a double phase shift, outer-phase (D2) e inner-phase (D1). These phase shifts can have a wide range of values for different power levels. However, as is detailed in [8], the implementation of two PI feedback-loops fully synchronized have various complexities, although a DAB converter with zero reactive power can be achieved in a small range of active power values using D2=0.5. On the other hand, taking into account the work in [9], the authors present experimental results for various values of independent surfaces for D2 = 1/3; ¼; y ½, using a semi-closed control loop (only one control variable is used). However, the bidirectional current flux characteristic is lost, when the independent surfaces on the phase shift (D2 = constant) is applied, because the direction of the current flow depends upon the phase changes [10], in addition to this technique generates discontinuities in an operating range. A number of control strategies, which are based on variations in the phase shift, maintaining μ constant, are analyzed in [9]. These techniques are able to eliminate the reactive power in a certain range of operation and the bidirectional characteristic is maintained. On the other hand, the application of μ constant leads to discontinuities in the current wave shape of the transformer. In the pursue of maintaining the continuity of the current Iλ, different methods, as the trapezoidal and the triangular, have been applied , but these methods also require two PI feedback loops. In reference [10], a single feedback-loop control for a DAB converter with current monitoring is presented. Although this proposal performs well the bidirectional power flow between the source and a super capacitor, it cannot reduce the reactive power to zero. The latter reduces the power density capacity of the converter and increases the ripple voltage which implies higher implementation complexity. Other studies compare different control methods and presents small signal models as well as detailed steady-state analysis and loss calculations [11]. From these comparisons, an algorithm which selects the most suitable control method for a given operation condition, is tailored considering the power and voltage of the converter. Such algorithm has a good performance but the dynamic changes between different control methods can cause unwanted transients in the converter and also the software resources requirements difficult its implementation. In the way to contribute in the improvement of DAB converters, this paper introduces an easy-to-implement control technique using a single feedback PI variable, which fully comply with the characteristics stated in [1] such as decreased peak current (IλP), to reduce reactive current to zero (IλQ=0), to increase power capability, increase converter efficiency and minimize the output capacitance and stress in all switches. The feedback PI variable controls the duty cycle for the three levels of the converter and the shift angle between m1 y m2. The theorical analysis and simulation results for IλR, IλP, IλRMS, IλA, and IλQ, are compared with those obtained from techniques SPSC, and independent surfaces for “μ” and “D2”.

P DC1

VDC 1

I CD 1 VP

I DC 2

VS '

I

 

PDC_OUT

P DC2

VL  

Average H  Bridge

VS

 

S1

S3

S2

Ideal Transformer

IC

VDC 2 S4

IOUT RL

C

H  Bridge

Figure 2. Equivalent Circuit of the DAB converters

II. AVERAGED MODEL Figure 2 shows an equivalent circuit of the DAB converter for a lossless system. The transformation (α) ratio is equal to the voltage ratio: (1) VDC1   VCD2

Vs '   Vs

(2)

VP and Vs are the voltages at the AC terminals of the converter; VDC2 is the CD voltage at the capacitor terminals, which depends on IC=IDC_2-IOUT. Considering a three levels PWM scheme, the commutation functions S1 and S2 are defined in Table I. TABLE I COMMUTATION FUNCTIONS FOR H-BRIDGE PWM CONTROL

S1  S 2

S3  S 4

VPWM

IdC

1 1 0 0

0 1 0 1

VDC 0 0 -VDC

IL 0 0 -IL

From Table I, it can be established (2) and (3):

VP  (S1  S3 )VDC1  m1  VDC _1

(2)

VS  (S1  S3 )VDC _ 2  m2  VDC _ 2

(3)

The IλP current flowing in the circuit formed by mesh VP, VS’ and the inductance Lλ in Fig. 2 is given by: I L 

x

 0

VL  d  I  0 L

(5)

Where Iλ0 is initial condition of Iλ and Vλ is defined as: VL  VP  Vs '

(6)

The currents at the CD terminals of the H-bridge can be defined as: I DC _ 1  m1  I L

(7)

I DC _ 2  m2  I L

(8)

In order to keep the input/output power ratio:

VDC1  I DC1  VDC 2  I DC 2

(9)

In this way, a circuit based on dependent sources is obtained by using the transformer mutual inductance and the equivalent values of the voltages at terminals as shown in Fig 2.

3

D2 2VCD

 4VCD

VL

I

I A IP

I DC 1 x

IQ



D2

D2

Vs '

VP

I R a) μ = π (cte)

t

2VCD

t

2VCD

t 2

D2 = π/3

VP

Vs '

 VL

I

I DC1  I R

IP

x

t

2VCD

t

2VCD

t

 VL

I

IP

t

t I A

I DC 1

t

IR

x

2

 b) μ= π/3

Vs '

VP

2



D2= π/2(cte)

c) μ= π/2(cte)

D2= π/3

Figure 3. Waveforms of different values of “μ” and “D2”

III. ANALYSIS OF SYSTEMS WITH A SINGLE FEEDBACK-LOOP. For purpose of analysis, IDC1 is divided in three parts: IλQ is the reactive or return current, IλR is the current for the charging period and IλA is the stable peak current, where IDC1= IλQ+ IλR+ IλA as show on Fig. 3 A. Mode 1.- Single Phase Shift carrier As can be seen in Fig.3 a), in the first modulation method (SPSC), for μ = π D2 = π/3, a reactive current, proportional to the phase shift (D2), is always present. A considerable portion of the current is contributing to the reactive power, in this case IλR = -IλQ. The large current at low power output operations results in lower system efficiency and large electrical stress on the semiconductor switches. B. Mode 2.- Independent surface for “D2” In the second method, an independent surface is taken for D2. Show the wave forms for μ=π/3 D2=π/2, as can be notice in Fig. 3 b), the system does not have reactive power in a determined operating range. However, the current wave Iλ shows discontinuities and the method is not able to handle bidirectional flow when the phase shift is constant.

VP

2VCD

VS´

t

 I

2VCD

t

VL

I AR I P

I DC _1

I P

I DC_ 2

D2

1 x1

IA

t

Carry_ 2

Carry_1

 D1

x3

t

x2

1

t 0

 t 1 t 2 2

Figure. 4. Proposed Method for IAQ=0

C. Mode 3.- Independent surface for “D1” For the third method in Fig.3 c), the independent surface is for μ= π/2 D2= π/3, It can be noticed that Iλ flows bidirectional but it have discontinuities. From the results obtained for the different methods, it can be determined that for converters for which the voltage ratio is equal to the transformer ratio, it is necessary to achieve bidirectional flow, continuity of Iλ, and the reduction of the reactive power to zero. D. Mode 4.- Proposed Control Method The proposed method in this paper are: i) VL should never be zero during the zero crossing point of Iλ; ii) The energy discharged from Iλ to VDC2 must be the same stored energy during the charge period for VDC1, meaning this that the inductance must be subjected to the voltage value of VDC1 or VDC2 but never to its potential difference. In order to achieved such characteristics, this research work proposes the modulation scheme shown in Fig. 4 which shows that the voltage VLλ comprises the algebraic sum of the instantaneous voltage Vp and Vs', where it never increases in magnitude, only the duty cycle.

For the power flux from VDC1 to VDC2 in the time 0