Accurate and Computationally Efficient Modeling of Flyback Transformer Parasitics and their Influence on Converter Losses D. Leuenberger, J. Biela Laboratory for High Power Electronic Systems - ETH Zurich Physikstrasse 3, Zurich, Switzerland [email protected] Abstract Emerging renewable energy applications, such as PV micro inverters, demand for high step-up isolated DC-DC converters with high reliability and low cost, at high efficiency. Thanks to its low part-count the flyback converter is an optimal candidate for such applications. To achieve high efficiency over a wide load range, a decent transformer design must be performed, considering also the effects of the transformer parasitics. Therefore this work analyzes the influence of the transformer parasitic capacitances and leakage inductance in such a way, that it presents a complete tool to consider the transformer parasitics in the flyback-converter design process. A loss-analysis is performed for all three operation modes of the flyback-converter and methods for modeling the parasitic elements are discussed. To model the frequency dependence of the leakage inductance a new method is proposed. The applied models are explained in-depth and verified with measurements on prototype transformers. 1 Introduction Flyback converters feature an isolated DC-DC conversion at lowest possible part count and are one of the very basic, standard power electronic circuits. Despite that fact, the flyback converter is still subject of various recent research publications aiming to improve the performance of the flyback converter in various ways, such as ad- vanced soft switching techniques [1], online efficiency optimized control or additional clamping circuits [2]. This continuing interest in the flyback converter is caused by emerging renewable energy applications, such as PV micro inverters, which demand for isolated high step-up converters with high reliability and low cost at high efficiency. Though PV converters must feature high efficiency over a wide load range. At low load, different loss components become dominant and the operation mode of the flyback converter might need to be changed, e.g. from bound- ary (BCM) to discontinuous conduction mode (DCM). Choosing an optimal transformer design, which optimizes the efficiency over the whole load range, becomes the main challenge. A detailed analysis of the different loss components of the converter, including the transformer, is necessary to perform this task. Core losses, winding losses and losses caused by the transformer leakage inductance are usually considered for the converter design [3],[4]. However, also the parasitic transformer capacitance causes losses, which are often omitted. When minimizing the leakage inductance by means of interleaving of layers or lower layer distances, the parasitic capacitance increases. Hence there exists a tradeoff between leakage inductance and parasitic capaci- tance, also shown in [5] for the example of a high-voltage flyback-transformer. In order to find the optimal winding arrangement of the transformer it is therefore necessary to include the influence of the parasitic capacitances in the design process. Besides the work in [5], there exist various publications that deal with modeling the parasitic capacitances of transformers in general. Effects of parasitic capacitances in flyback converters are only discussed in [6] and [7], which derive the adapted operation mode, but do not consider the influence on losses. This work aims to analyze the influence of both transformer parasitics in such a way, that it presents a complete tool to consider the transformer parasitics in the flyback-converter design process. This includes not only the loss- analysis, but also the more involving part of modelling the transformer parasitics. Figure 1: a) GaN/SiC high step-up flyback-converter prototype for PV micro-inverter, b) Two-port transformer, general para- sitics equivalent circuit, [8] Starting from the general equivalent circuit for a two winding transformer, the general equivalent circuit for a fly- back transformer is derived step by step in section 2. This allows then to investigate the influence on the operation modes and to derive formulas for the losses caused by the parasitic elements. Section 3 deals with fast and accurate methods to model the parasitic elements, suitable also for model based optimization. A new method is proposed, to more accurately consider the frequency dependence of the leakage inductance. Finally, the derived tools are applied for a model-based optimization of a DC-DC flyback-converter in section 4. 2 Non-ideal Flyback Transformer The parasitic elements of any two port transformer can be split into an electrostatic and a magnetic part. The electrostatic behaviour of the transformer can be described by the equivalent circuit proposed in [8] and [9], con- sisting of six equivalent capacitances, the 6C-model. The magnetic part consists of the transformer magnetizing inductance Lmag and the leakage inductances between the primary and the secondary winding, referred to as the T-equivalent circuit [10]. The complete general equivalent circuit is shown in fig.1b). 2.1 General Flyback Transformer Equivalent Circuit The general transformer equivalent circuit in fig.1b) can be simplified for flyback-operation, by taking into account the specific operating conditions of the converter. • Equivalent Parasitic Capacitance: In flyback converter operation, the transformer is subject to a bipolar voltage pulse Vpulse on the primary winding. Furthermore in most applications there is a constant isolation voltage Viso between the negative rail of the primary and the secondary, see fig.2a). C4 C6 Ipulse 1:n 1:n C1 C 2 Ceq,p Vpulse Vp nVp Vp nVp C5 C3 Viso + - a) Iiso b) Figure 2: a) Electrostatic model of flyback converter operation, b) general input-equivalent circuit Under this operating condition, the total electrostatic energy stored in the transformer can be expressed from the 6C-model by 1 2 2 2 2 1 2 Wtra f o = Vp [C1 +C2n +C4(N − 1) +C5n +C6] + Viso[C3 +C4 +C5 +C6]+ 2 2 (1) 1 V V [C (n − 1) +C n −C ]: 2 p iso 4 5 6 The first part of this equation contains the energy, that the source Vpulse must deliver to charge the primary input to Vp, if Viso = const. Its structure allows for derivation of the energy equivalent capacitor 2 2 2 Ceq;p = C1 +C2n +C4(n − 1) +C5n +C6 (2) The second part in (1) contains the energy delivered by the source Viso, to charge C3;C4;C5;C6 to Viso, under the condition that Vp = 0V. The last part of (1) is the additional energy delivered by Viso, when Vp 6= 0V. It is caused by the charging currents of C4,C5 and C6 flowing through Viso. The equivalent capacitance Ceq;p fully describes the dynamic behaviour as well as the capacitive energy seen from the flyback transformer primary and secondary input. There is a high frequency current Iiso flowing through the source Viso, though this current does not cause losses in the voltage-source Vpulse. The losses caused by Iiso can only be determined on a system-level context. For the flyback converter analysis, the terms in (1) containing Viso are therefore not relevant and the electrostatic model can be simplified to a one capacitor model as shown in fig. 2b). • L-Type Magnetic Model: The flyback converter operates the transformer as a coupled inductor. Figure 3a) shows the equivalent magnetic circuit under these operating conditions. At turn-off of switch Sin, the current commutates from the input to the output-side. However due to Ls;1 and Ls;2 the current can not commutate immediately. A resonance takes places through the loop Comloop marked in fig. 3a), which leads to an overshoot of the blocking voltage at switch Sin. Changing the model to the simpler L-equivalent circuit, ( fig. 3b), does not influence this resonance, as the inductance Ls is still within the same loop. The difference in the two models is the current through Lmag. The T-equivalent reproduces a distortion in iL;mag caused by the resonance. The L-equivalent can not account for the magnetizing current distortion. For low leakage inductance, Ls Lmag, this distortion has a negligible influence on converter operation and transformer losses. As a flyback- transformer must fulfill this requirement for performance reasons anyway, the L-equivalent can usually be applied to model the magnetic behavior. L L Lσ,w1 σ,w2 ideal: σ ideal: 1:k 1:k’ ComLoop + Ceq,p Vin - Lmag Vout Lmag a) Sin Dout b) Figure 3: a) Schematic of T-equivalent magnetic circuit in flyback operation b) General equivalent transformer circuit for 0 flyback converter operation, with k ' n for Ls Lmag. Finally, the general flyback transformer equivalent circuit is derived from the simplified electrostatic and magnetic model. The equivalent circuit referred to the primary side is shown in fig.3b). The equivalent capacitance Ceq;p is in parallel to Lmag, to correctly reproduce the resonance taking place between Ls and Ceq;p. 2.2 Flyback Converter Operation under Non-ideal Conditions and Losses caused by the Parasitics The parasitic elements of the flyback transformer influence the operation of the converter and cause additional losses, depending on the operation mode. In the following subsections, the operation of the non-ideal flyback converter is analyzed for the different operation modes and analytical formulas are derived to calculate the losses caused by the parasitic elements. Figure 4: Flyback Operation in BCM with valley switching: Vin = 20V, Vout = 20V, n = 2, Lmag = 20µH, P = 40W 2.2.1 Boundary Conduction Mode (BCM) Figure 4 shows simulated current and voltage waveforms of a DC-DC flyback converter operating in BCM. Its switching period is split into four intervals. The first interval, [t0;t1], and the third interval [t2;t3] correspond to the operation-intervals of an ideal flyback converter.