SISO Control Strategy of Resonant Dual Active Bridge with a Tuned CLC Network

This paper proposed a linear state-space model for a resonant dual active bridge with a tuned capacitor-inductor-capacitor network which is applied to an energy storage system. The proposed model is used for predicting the behavior of the proposed system and estimated the state variables under large signal variation. Using the proposed model, a decoupled control strategy was designed which realizes the high frequency link currents control and also improves the efficiency of the converter. By applying the steady-state relationship between state variables and the system inputs, the controller was simplified to a single proportional integral (PI) controller instead of from three PI controllers, which was implemented on a low cost digital signal processor and verified experimentally.


Introduction
Recently, dual active bridges (DABs) have received an increasing attention due to their bidirectional power transmission and galvanic isolation capabilities, which can provide a high power density and accommodate a wide range of voltages by operating in both buck and boost modes. Early DAB converters were controlled using single-phase-shift (SPS) control to allow for bidirectional power transfer at variable power levels, which can easily achieve soft switching when the magnitudes of the two ac voltages are matched by the transformer ratio. However, when the converter is operated outside of the proper voltage range, the zero-voltage switching (ZVS) can hardly be achieved and the peak current will increase which then lead to an increase of switching and conduction losses [1]. In order to reduce the switch current stresses and the attendant switching and conduction losses, many other complicated control strategies have been proposed [2] [3] which have shown an improved soft switching range and lower conduction losses, however, these methods usually require more complicated control systems and still have a large reactive current at rated power.
In order to improve the soft switching range, a number of quasi-resonant type DAB topologies, consisting of series resonant networks, have been investigated [4] [5]. The most common resonant dual active bridge (RDAB) topology is the series RDAB (SRDAB) [6] - [8], which has received an increasing attention due to it low requirement of resonant network components and its inherent dc blocking capability. However, it needs a wide switching frequency range to modulate the power transfer, which make the design of controller and filter being more complicated.
Regardless of control and resonant schemes employed, the existing DABs typically requires a more complex control system, particularly when they operate with wide load and supply voltage variations. In this paper, based on linear state-space model and mathematical analysis, a simplified decoupled control strategy for a capacitor-inductance-capacitor (CLC) tuned resonant DAB is proposed and implemented with a single PI controller which achieves the control of both the primary and secondary ac current amplitudes while ensuring soft switching of the switches at a wide voltage range. An experimental prototype is designed and operated in various conditions to investigate the performance of the control scheme. The structure of capacitor-inductor-capacitor (CLC) RDAB is shown in Fig. 1. Two additional capacitors C1 and C2 is added to the primary side and secondary side of transformer Tx, respectively, which then act as an integral part of resonant network with Tx 's leakage and mutual inductance L1 and L2. The two full-bridge converters are controlled using a Three Phase Shift (TPS) modulation scheme as demonstrated in Fig.2. The switches of each leg are controlled to have a duty cycle of 50% and the output of the first leg is phase shifted from the output of the second leg by α1 for the primary bridge and α2 for the second bridge. The output of the secondary full-bridge v2 is phase shifted from the output of the primary full-bridge v1, to lead v1 by ɸ. The outputs of the full-bridge converter have been simplified into voltage source vB1 and vB2, which are represented by the Fourier series in (1) and (2).

Basic operation of the RDAB
, … The magnitude of the power transferred has been quantified in a previous paper by the author [9], which was shown that majority of the power was transferred at the fundamental frequency of the tuned resonant network. The tuned network presents a high impedance to harmonics generated by the converters. Consequently, the effects of these harmonics on the power transfer will be insignificant and therefore ignoring harmonics, the magnitude of the power can be simplified to (3):  In order to simplify the mathematical analysis, the converter works at fundamental frequency is simplified as shown in Fig.3 (a), where the voltage across C1 and L1 behaves as a capacitor (C1_net) voltage. Then the fundamental circuit at switching frequency is illustrated in Fig.3 (b) while circuit resistance have a relatively insignificant effect on the current and will, therefore, be ignored and their losses can be allowed for late, then the relationships between original circuit and the equivalent circuit are shown as follows:

Mathematical analysis of RDAB
The resonant network consisted with C1_net, C2_net and L2 is tuned to the fundamental of the switching frequency fs as follow: Substituting (7) to (4) to (6), the following relationship among T-equivalent circuit (shown in Fig. 4(a)) was found:  To recognize the relationship between bridge currents, i1 and i2, and voltages, v1 and v2, a deltaequivalent circuit of resonant network is illustrated in Fig. 4(b), where the independences are calculated as follows: According to KVL and KCL of delta network and the inductances relationship (9), at the switching frequency and steady-state, the bridge current can be calculated as shown in (10) and (11), which shows that i1 is decoupled with v1 and i2 is decoupled with v2 (as shown in Fig. 4c).
To investigate the effects that the modulation variables have on the current, (1) and (2) have been substituted into (10) and (11), the magnitudes of the high frequency link current i1 and i2 are abstained as (12) and (13), where it can be found that the magnitudes of currents i1 and i2 are controlled by the phase shift α2 and α1respectively. The relationships between the voltages and currents in (10) and (11) are illustrated in Fig. 4(c), where i2 is fixed to lead v1 by 90° and v2 is fixed to lead i1 by 90°. As it can be seen that when ɸ is fixed at 90° or -90° (depending on the power flow direction), the currents of the bridges (i1 and i2) will align to the voltages (v1 and v2), which then results in unity power factor (UPF) at the ac terminals of both fullbridge converters. The relationship among pulse width, voltage and current is illustrated in Fig. 5, where α1 controls the pulse width of v1 and therefore the magnitude of the fundamental component of v1, α2 controls the pulse width of v2, while ɸ controls the phase difference between v1 and v2. According to the relationships between currents and voltages shown in Fig. 4(c), the voltage midpoint corresponds to the current starting point, it can be expressed as ɸ also controls the phase difference between i1 and v1, as well as the phase different between i2 and v2, which is illustrated in Fig 5. In UPF applications, ɸ is fixed at 90° or -90°, the power transfer is modulated using α1 and α2, the freedom of the system is simplified to two degrees. As shown in Fig. 6(a), in the maximum power transmission, the converter is zero-current switching or near ZCS, however, at the magnitude of power transfer is modulated down using α1 and α2, some of the switches start hard switching as can be seen in Fig. 6(b). This leads to an increase of the switching loss in high frequency link and a decrease of the power transmission efficiency of the system. From the analysis of Fig. 5, when the relationship among the three freedoms of the system can be implemented as (14), a wide power range of soft-switching can be achieved as shown in Fig. 6(c).

Control scheme design of RDAB
The purpose of the RDAB control is to control the amplitudes of the currents in the resonant tank, i1 and i2, by α1 and α2, while ensuring soft switching of the switches by modulating ɸ. In order to simplify the control algorithm, the d-q decoupling control is introduced, and the d-axis is oriented in the direction of v1, the relationship between the steady-state voltage and the phase angle in the d-q frame is derived as follows: Since v1q is zero due to the selection of v1d as the reference frame (as shown in Fig.4 (c)), v1d is the only input that affects i2 and the current i2 lead v1 by 90, the following assumptions can be made: By submitting (14) to (15) -(22), the relationships between primary side and secondary side can be found as follows: As it can be seen, v2q and v2d can be calculated by v1, i1d and i1q can be calculated by i2q, and the amplitude of i2q or i2 depends on v1, the system transmission power can be adjusted by controlling the amplitude of α1, whereby the degree of freedom of the system is reduced to 1. At the same time, the maximum soft switch control will be achieved. According to the above analysis, the input and output relationship of the AC system is directly related, the single-in-single-out (SISO) modulation algorithm is proposed, as shown in Fig. 7. α1 and α2 are varied to control the magnitudes of the currents i1 and i2, while ɸ will be varied along with the change to improve the soft switching range of the converter. As mentioned before, the input of the AC system is directly related to the output, therefore, only the amplitude of i2q which is the same as the amplitude of i2 is needed for the control. This measurement can be easily realized through the use of an inexpensive current transformer (CT). Additionally, only one PI controller is implemented, the inputs for the other loops are derived from (23) -(26), which make the RDAB being more flexible for complicated applications like hybrid DC-AC microgrid which is enabled by energy storage systems.

Experimental results
An experimental prototype of CLC tuned RDAB was designed to investigate the performance of the control strategy and the mathematical analysis (as shown in Fig. 8). In Fig. 10, the voltage and current waveforms of the primary and secondary H bridges with varying phase shifts are illustrated. From Fig.10, all the switches in the primary and secondary full bridges realize the soft switching. The power throughput and efficiency of the prototype RDAB under various modulation levels are shown in Fig. 9.
The maximum efficiency of the system is observed at rated power and is approximately 96%. Furthermore, the system efficiency is maintained well above 82% even at lower modulation factors, which suggest a significant improvement in performance in comparison to conventional DAB converters.

Conclusion
In this paper, a mathematical analysis has been presented to accurately predict the performance of the proposed SISO control strategy. Experimental results of a prototype RDAB, operated under various conditions, have been presented to demonstrate the improved performance of the converter. Results indicate that the proposed SISO control strategy for resonant DAB topology has a good closed-loop dynamic response and steady-state performance, while indicates a potential to further increase the operating efficiency by employing a purpose-designed transformer, which will be smaller than that of a conventional DBA converter on account of the lower operating currents.