OBC#
Battery charger design#
A complete and complex analysis of the design and modeling is given in [Deng et al., 2014] where an LLC resonant converter for EV battery charging is studied. The worst-case operating point is identified and used for the design with the aim to globally ensure ZVS. FHA is used in above-resonance region, while for the below-resonance region a specific mode analysis is used. Big challenges are coming from the charging profile that is nonlinear in V–I.
There are several works in the literature addressing the modeling and control of resonant converters. For the battery charging application, the mostly considered topology is the LLC. We can find two main branches in the literature: one concerning the resonant converters them-self, without a particular application; and one that considers the battery charger problem where the load now is time-varying depending on the charging profile, which is usually nonlinear. Moreover, al lot of works have they focus on the circuit/components design and few tackles the control problem comprehensively.
Some survey on these topics.#
A pretty complete overview on resonant converter is given in [Salem et al., 2018]. Several topologies are discussed and it can be a good source of references. Section 4 is dedicated to series resonant convert with: the different operating modes, problems related to the control, possible control solutions (Section 5).
[Safayatullah et al., 2022] is a pretty broad survey on Power converters topologies and control methods for EV fast charging. LLC is the first discussed in section V-A (control in VIII-A). There is also the DAB (Dual Active Bridge) in section V-B/C (control in VIII-B) and multilevel converters. This could be another source of references.
Resonant converter focus:#
Looking into the literature, we have modeling oriented papers and control oriented papers. In modeling, the most used technique is First Harmonic Approximation (FHA), which most of the time is good since the waveforms are sinusoidal, but it happens in the limiting (e.g. lower power) that this assumption fails and then the modeling technique should change. A good paper on these different modeling approaches is [Deng et al., 2014] where, looking at the battery charging application, they do a wide study on the different operating conditions.
To overcome some of this problem the adopted solutions are of two kind: 1) change the control of the full-/half- bridge configuration; 2) change the topology of the circuit.
Control of resonant converter#
Regarding the controls technique we have:
Fixed-frequency: this kind of control law keep the frequency constant and change other parameters of the input. From [Burdio et al., 2001], we can identify:
phase-shift or clamped mode (similar to our three-level solution [Zaupa et al., 2023]);
asymmetrical duty-cycle;
asymmetrical clamped-mode.
Variable-frequency: these techniques offer good soft-switching properties, the downside is that performance is usually affected by the wide range of frequency requested. From [Youssef and Jain, 2004], we can highlight:
variable frequency (for example through a VCO) is one of the most common technique since it offers an easy implementation but the frequency range is very wide;
self-sustained oscillation like in [Bonache-Samaniego et al., 2020, Zaupa et al., 2023] in which the converter sets its operating point at the resonant frequency without needing to know it;
self-sustained phase-shift proposed in [Youssef et al., 2006] in which, together with the self-oscillating behavior, also the phase-modulation technique is used in order to reduce the frequency range.
Usually, the biggest counterpart of these techniques is the big range of frequencies in which the converter has to operate, which from one side complicates the control implementation and on the other side it makes hard to optimize the magnetics of the circuit. Therefore, one research axe has been devoted to find control techniques that allows reducing the frequency range.
Frequency modulation#
Many works in the literature use this kind of control since it is to implement. Usually, a PI controller and a Voltage Controlled Oscillator are sufficient. Few recent works that use this technique, which are cited in this report, are: [Qin et al., 2022, Cittanti et al., 2022, Saadati et al., 2022]
In [Cittanti et al., 2022] two loops are used for the control (outer for the voltage and inner for the current). Full analysis of the 7th order model is done with reduction to 3rd order. The aim of one closed-loop is to keep the performance constant when the operating point is changing. The application is EV fast charging. The implemented control is LUT-based feed-forward with adaptive gain (through a lookup-table).
A bit out of track wrt other works, [Saadati et al., 2022] proposes a novel analog controller design procedure for LLC resonant converter for battery charging. They tackle both the design of the converter and the design of the controller. About the controller, they build a model based on FHA that is then linearized from which a least-square procedure is used to obtain the unknown parameters of the controller.
Frequency and phase-shift modulation#
Next, I try to focus more on the solutions that involve frequency and phase shift modulation (amplitude modulation). Contributions in this direction are more limited and I think that there could be some margin for our work “\(\theta+\varphi\)”.
Youssef 2006:#
This mixed solution was initially (wrt what I’ve found) presented in [Youssef et al., 2006]. The focus is only on resonant converters and the techniques combines self-sustained oscillation with phase shift modulation. The objective is to reduce the frequency range while maintaining ZVS. Also the design procedure is discussed. The controller is composed of two loops: the inner one adjusts the phase shift to ensure ZVS, and the outer one adjusts the output voltage. The controller is implemented analogically, i.e. without a micro-controller. For the analysis “Generalized sampling data modeling” is used.
Bojarski 2014:#
More recent works [Bojarski et al., 2014, Bojarski et al., 2015, Bojarski et al., 2016] propose a so called “phase-frequency control” for the wireless battery charging case (the topology is similar to OBC). Essentially, the control try to keep the frequency nearer to the resonant one while maintaining ZVS, the output is regulated by changing the phase-shift. In [Bojarski et al., 2015] the number of levels it’s not clear and it uses a topology with 12 switches. [Bojarski et al., 2016] presents a 25 kW prototype, it shows that the control is implemented in an FPGA and it provides the scheme.
More recently, works dealing with multilevel resonant converters are the following.
In [Peter and Mathew, 2021], a three-level single stage LLC converter is proposed. The control scheme is dual: frequency modulation is used to regulate the output voltage and PWM is used to control the dc-bus voltage.
In [Alatai et al., 2022] they use a 5-levels converter (2 full-bridge). Reading it fast is not clear how the control law is implemented and it seems more that they are doing constant voltage control.
Topology changes#
In [Liu et al., 2017] a three-phase with 3-levels converter is presented. To have the three levels (\(V_{in}/2\)) a half-bridge topology is used.
In [Ta et al., 2020], a new slightly different topology is proposed, it keeps LLC properties allowing different modulation schemes:
Full-Bridge Converter with Frequency Modulation (FBFM);
Dual-Phase Half-Bridge LLC (D-LCC);
Single-Phase half-bridge LLC.
Essentially, by having a full-bridge configuration for the switches and a transformer with a central point, it is possible to activate the switches so that the topology is different. An interesting point for the design is that the magnetizing inductance can be kept low, so that it can be integrated in the transformer. ZVS is guaranteed in all modes.
In [Li et al., 2020], a bidirectional LLC charger is proposed. The topology is similar to a dual-active-bridge since the rectification is active. This paper is frequently cited for OBC with LLC. It mainly contains the design procedure.
[Qin et al., 2022] proposes a higher order resonant tank that induces better properties. Essentially they are adding degrees of freedom to the design by using, at the place of the capacitor, a block given by two capacitors and an inductor. Classical frequency modulation control is adopted.
In [Li et al., 2023], a slightly different topology is presented. The resonant tank is on the secondary side of the transformer and the resonant elements connection is made in a different way. The resonant tank has a T shape. Battery is modeled as a resistance (its value is determined by the charging curve). The converter behaves either as a LCL or a LC, depending on the charging mode, CC and CV respectively.
In [Wu et al., 2023] different topologies for HF AC-DC converters are discussed. They include DAB (page 7) and resonant LLC (page 8). There is also a 3-levels (5-levels if we consider all positive and negative) with half-bridge topology.
Reference example for the prototype - OBC LLC#
We consider the On Board Charger (OCB) case equipped with a LLC converter as a reference for the design. An example can be found in the following ON Semiconductor design: OBC–TND6318/D (this work has as reference [Deng et al., 2014]). At this link, there are other designs at different power ratings
TND6318 – 10 kW – 80-140 kHz
TND6320 – 6.6 kW – 39-690 kHz
TND6327 – 33 kW – 39-690 kHz
Specifications for OBC–TND6318/D:
Input voltage \(\beta\) \(700\pm{35}{V}\)
Output voltage \(200/{450}{V}\)
Output current \(0/{40}{A}\)
Maximum output power \({10}{kW}\)
Maximum switching frequency 400 kHz
Switching frequency range [80-140 kHz] is higher than our target. The converter is composed of the following two stages: AC–DC and DC–DC (ensures galvanic isolation).