Author:
Henri Huillet, Chief Executive Officer at GAIA Converter
Date
01/01/2024
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Figure 1: The resonant circuit in an LLC converter
Meeting the stringent EMI requirements imposed by MEA applications can be challenging. In this article, Henri Huillet, Chief Executive Officer at GAIA Converter examines how three-phase, LLC DC-DC converters can offer an effective solution. Drawing upon a recent time domain analysis conducted by GAIA Converter and Universidad Politecnica de Madrid, this article compares two LLC converter configurations: single-phase and three-phase, illustrating how the latter provides additional benefits which make it ideal for MEA applications.
‘More Electric Aircraft’ or MEA defines the ongoing trend towards replacing hydraulically powered actuators, pumps and other equipment in aircraft with electrically powered alternatives. By utilizing electrically powered equipment that is more efficient, has smaller footprint and is more reliable, engine fuel can be saved and emissions minimized while operating and maintenance costs are reduced. To achieve these results, the power conversion stages between the different voltage rails must be as low-loss and light-weight as possible. A typical main aircraft bus is nominally 270VDC and this is down-converted to 28VDC, with isolation, then again to other load voltages. In this article we will look at a choice of two design topologies that might be used for the first stage of power conversion.
Conventional LLC converters: pros and cons
In many applications, ‘LLC’ converters have become a popular conversion topology. These resonant-type converters with low dynamic losses display low EMI signature and often can use just a single magnetic element with a resonant inductor Lr formed from leakage inductance of the transformer. Regulation is achieved by varying switching frequency and drives to the switches are simple pulse trains at 50% duty cycle. Control is complex however and digital signal processors are often used, but an end-product can have high performance and high power density.
As ever, no one topology is perfect in all conditions. MEA applications have a requirement to limit variation of switching frequency to +/-15% of nominal from minimum to maximum load and across the ‘normal’ input voltage range of 235VDC to 285VDC. The limits are relaxed only in abnormal input conditions down to 220VDC and up to 320VDC. While a ‘standard’ LLC converter can be designed for these ranges, some of the benefits are lost, particularly in the magnetics. This is because for a small frequency variation, the resonant inductor Lr needs to be a similar inductance to the transformer magnetizing inductance Lm. Consequently, integrating Lr into the transformer as intentional leakage inductance becomes impractical and inefficient. Lr must therefore be a separate discrete component. Additionally, the LLC topology has relatively high input and output ripple currents, which add to component stresses and mandate relatively large capacitors.
The benefits of using three-phase LLC converters
There is a little-used alternative to the simple LLC converter – a three-phase version. Although it has a higher component count, a three-phase LLC converter promises to be more efficient and smaller overall. Because total area of silicon is less, the transformer is smaller and input and output ripple currents are greatly reduced, implying smaller capacitors and lower losses.
Conventional vs. three-phase LLC converters
In the three-phase LLC circuit, the transformer primary is in a ‘Y’ configuration to separate out the three magnetizing inductances Lm,A, B and C and corresponding uncoupled ‘resonant’ inductors Lr,A, B and C. The three output windings are in a delta configuration, to utilize the windings efficiently, resulting in lower ripple current in the windings by a factor of √3 compared with the single-phase LLC. The winding complexity of the transformer is higher than that of the single-phase LLC, but overall size is around 40% smaller and losses a significant 65% lower.
The reduction in size is offset to an extent by requiring three resonant inductors rather than one, although total losses in them are about the same. Six primary switches and six secondary synchronous rectifiers are required with the three-phase LLC compared with two and two respectively for the single-phase LLC. However, lower total dissipation is spread over multiple devices in the three-phase LLC meaning total semiconductor footprint can be smaller and individual junction temperatures lower for enhanced reliability. In any case, the switch count may not be so different between the topologies, as, in the single-phase LLC, devices might typically need to be paralleled anyway because of the higher operating current.
Comparative time domain analysis of LLC converters
There has been little written in the literature about the three-phase LLC topology, so GAIA Converter in conjunction with researchers at the Universidad Politecnica de Madrid set out to generate a methodology that would lead to equations for the voltage-gain curves. These are essential to the design process and indicate expected variation in frequency, required across all conditions. LLC converter analysis is recognized as complex and the approach usually taken is similar to other topologies, where the frequency or ‘s’ domain response of the power train is evaluated, indicating ‘poles’ and ‘zeroes’ in the response and graphed as a ‘Bode’ plot. To simplify the analysis, a so-called ‘First Harmonic Approximation’ (FHA) is made, which ignores contributions to output power from second and higher order harmonics of the transformer currents. This method however does not give a fully accurate picture of performance, particularly when predicting gain above and below resonance.
Instead, GAIA Converter and Universidad Politecnica de Madrid opted for a ‘time domain analysis’. This method is complex and requires significant computation but is the most accurate. Waveforms are split into discrete time intervals, values for applied circuit voltages identified and resistive, capacitive and inductive network values evaluated, which include what may be non-linear effects such as output capacitance of switches.
The circuit of a series resonant converter can be represented as Figure 1, the differential equation that defines its time domain characteristic is Equation 1 and this solves for inductor current as in Equation 2. Constants c and c′ are found from evaluating boundary conditions, which depend on the particular resonant topology and operating conditions.
For the three-phase LLC converter, a set of five equations are identified for the five conditions in Equation set 3 and the ten constants derived from boundary conditions in Equation set 4
From the equations, voltage gain of the resonant tank can be evaluated as it varies with frequency.
The researchers compared time domain analysis results with those from the FHA method and also from a Plecs® simulation for the circuit. The results are given in Figure 2, showing complete agreement between Plecs® and the time domain analysis method, with the FHA method deviating by about 5% maximum below resonance and by about 3% maximum above resonance.
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Figure 2: Comparison analysis of three-phase LLC resonant tank gain, Time domain, FHA and Plecs® simulation
Designing a SWaP-optimized LLC converter for MEA
As an exercise, the research team compared results from an existing single-phase LLC design already optimized for size weight and power (SWaP) and a simulation of a three-phase version, both providing 1kW (600W minimum) from an input of 235VDC to 285VDC and with an output of 28VDC. Switching frequency variation limit was +/-15% maximum, minimum efficiency was 96% and allowed converter height 13mm.
The single-phase LLC used a matrix transformer and separate resonant inductor while the three-phase LLC used a gapped planar transformer and three separate resonant inductors. These all used TP5E material and were custom-designed using low-loss winding techniques such as litz wire and planar copper layers optimized for low skin and proximity losses. For both converters, GaN HEMT cells were used as primary switches and silicon MOSFETs as secondary switches.
The most notable results, shown in Table 1, were an overall 15% reduction in losses and a 20% improvement in power density when using the three-phase LLC. Additionally, for the same output capacitance, the three-phase LLC achieved about 100x reduction in ripple voltage.
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Table 1: Losses and footprint compared – single and three-phase LLC converters
Conclusion
The research project undertaken by GAIA Converter and Universidad Politecnica de Madrid demonstrates that a time domain analysis of the three-phase LLC converter provides accurate results. When the analysis technique is used to design a real-world converter for MEA applications, the three-phase LLC topology achieves significant and valuable gains in efficiency and power density compared with the single-phase LLC approach.
