胡瀟瀟，吳琨（同濟(jì)大學(xué)電子與信息工程學(xué)院，上海 201804）

一種兩級式變換器的最優(yōu)工作點(diǎn)分析

胡瀟瀟，吳琨
（同濟(jì)大學(xué)電子與信息工程學(xué)院，上海 201804）

本文詳細(xì)分析了一種兩級式變換器的優(yōu)化設(shè)計(jì)，針對諧振變換器級聯(lián)Buck電路的結(jié)構(gòu)，根據(jù)開關(guān)損耗和導(dǎo)通損耗，量化了變壓器的匝比與效率之間的關(guān)系，理論計(jì)算出了該變換器的最優(yōu)工作點(diǎn)。該兩級式變換器適用于48V母線電壓輸入的VRM，解決了傳統(tǒng)單級式變換器在此應(yīng)用上出現(xiàn)的占空比失控和效率低等問題。此外，本文搭建了一臺48V輸入、5V/8A輸出的原理樣機(jī)驗(yàn)證了理論分析的正確性。

兩級式變換器；最優(yōu)工作點(diǎn)；開關(guān)損耗；導(dǎo)通損耗

本文引用格式：胡瀟瀟，吳琨.一種兩級式變換器的最優(yōu)工作點(diǎn)分析［J］.新型工業(yè)化，2016，6（7）：22-27.

0　引言

隨著超大規(guī)模集成電路的飛速發(fā)展，計(jì)算機(jī)以及通訊設(shè)備對供電電源提出了越來越高的要求。Intel公司對VRM（Voltage Regulator Module）的輸出電壓、電流的需求［1］如下：輸出電壓越來越低（＜1V），輸出電流越來越大（＞150A）。與此同時(shí)，要求輸出電壓在動態(tài)變化時(shí)電壓波動量小（＜2％oV）［1］。VRM向著低電壓、大電流、高可靠性、高效率的方向發(fā)展［2-3］。

輸入直流母線上的損耗會隨負(fù)載功率的提高而相應(yīng)增加。為減小直流母線上的損耗，VRM的輸入電壓由原先的5V提高到12V，以及未來將達(dá)到48V［4-6］。這使得輸入電壓與輸出電壓相差十分懸殊，不利于變換器的設(shè)計(jì)。文獻(xiàn)［7］提出了采用電感帶抽頭的Buck變換器以擴(kuò)展占空比，并結(jié)合多相交錯并聯(lián)技術(shù)，優(yōu)化了VRM的設(shè)計(jì)。然而，帶中間抽頭的Buck變換器對占空比的擴(kuò)展畢竟是有限的，當(dāng)輸入電壓為24V以上時(shí)，其不再適用。文獻(xiàn)［8］提出的磁集成推挽正激變換器可以通過調(diào)整變壓器的匝比來實(shí)現(xiàn)占空比的擴(kuò)展，倍流整流方式可以提高變換器的效率，磁集成技術(shù)則提高了功率密度。

當(dāng)母線電壓達(dá)到48V時(shí)，一般采用兩級式結(jié)構(gòu)代替?zhèn)鹘y(tǒng)的單級結(jié)構(gòu)。由于諧振電路轉(zhuǎn)換效率高、易于設(shè)計(jì)EMI并且便于實(shí)現(xiàn)軟開關(guān)［9］等優(yōu)點(diǎn)，常被用于兩級式變換器的前級。具體地，可令諧振變換器的開關(guān)頻率固定，通過控制后級來調(diào)節(jié)輸出。

本文詳細(xì)分析了一種兩級式變換器的開關(guān)損耗和導(dǎo)通損耗，量化了變壓器的匝比與效率之間的關(guān)系，理論計(jì)算出了該變換器的最優(yōu)工作點(diǎn)。此外，本文搭建了一臺48V輸入、5V/8A輸出的原理樣機(jī)驗(yàn)證了理論分析的正確性。

1　兩級式變換器的結(jié)構(gòu)

兩級式變換器由1個隔離型變換器級聯(lián)1個Buck變換器［10］構(gòu)成。隔離型變換器實(shí)現(xiàn)大幅降壓功能，Buck變換器用于調(diào)節(jié)輸出電壓。

本文選擇有源鉗位正激諧振電路作為兩級式變換器中的隔離變換器。即采用的兩級式變換器的結(jié)構(gòu)為“有源鉗位正激諧振+Buck”（如圖1）。

圖1　兩級式變換器Fig.1　Two-stage converter

有源鉗位正激諧振電路是基于有源鉗位正激電路上的諧振。有源鉗位正激拓?fù)浣Y(jié)構(gòu)［11］與傳統(tǒng)的單端正激變換器的拓?fù)浣Y(jié)構(gòu)基本相同，但通過增加輔助開關(guān)管和儲能電容，就能解決變壓器磁飽和的問題。在此優(yōu)勢的基礎(chǔ)上，通過增加輸入大電感、諧振電容，去除副邊濾波電感和續(xù)流二極管，形成有源鉗位正激諧振電路。利用諧振電路自身的結(jié)構(gòu)特點(diǎn)［9］，較容易實(shí)現(xiàn)軟開關(guān)，已廣泛應(yīng)用于高效率和高功率密度的場合。然而，對諧振變換器而言，開關(guān)頻率在諧振頻率附近時(shí)工作狀態(tài)最佳。調(diào)節(jié)開關(guān)頻率會降低效率，同時(shí)開關(guān)頻率的大范圍變化會使得EMI和磁元件的設(shè)計(jì)難度加大。為解決上述問題，目前較多采用的方案是兩級串聯(lián)結(jié)構(gòu)［12］。保持有源鉗位正激諧振變換器的開關(guān)頻率恒定，通過調(diào)節(jié)Buck電路的占空比來調(diào)節(jié)輸出

2　變壓器匝比n對兩級式變換器效率的影響分析

如圖1所示，Cr為諧振電容。T為有源鉗位正激諧振電路的變壓器，其勵磁電感值為Lm，N1、N2為變壓器T的原副邊繞組，Lr為諧振電感與變壓器T原邊漏感之和。將開關(guān)管Q1、Q2和Q5的占空比設(shè)定為0.5，且開關(guān)頻率恒定。開關(guān)管Q3和Q4占空比可調(diào)，且Q3和Q4的占空比互補(bǔ)。

為簡化電路分析，下文的描述主要針對穩(wěn)態(tài)工作的情況，并建立在如下假設(shè)之上：

1）輸入電感足夠大，可認(rèn)為輸入是一個電流源。

2）輸出電容足夠大，可認(rèn)為輸出電壓恒為Vo。

3）變壓器T的原副邊匝比n=N1/N2。

有源鉗位正激諧振電路的輸出電壓V1由變壓器T的匝比n決定，輸出電壓V1的大小又影響著Buck電路的占空比D2，從而影響兩級式變換器的效率。

由于有源鉗位正激諧振的輸出電壓V1與匝比n之間無法用具體公式表達(dá)，但其之間有一一對應(yīng)的關(guān)系。通過改變變壓器匝比n，借助中間電壓V1從而量化出各開關(guān)管的開關(guān)損耗和導(dǎo)通損耗之和與Buck電路的占空比D2的數(shù)量關(guān)系，從而分析出該兩級式變換器的最佳工作點(diǎn)，使得該變換器效率最高。

（1）開關(guān)損耗

因?yàn)橛性淬Q位正激諧振電路的開關(guān)管都是零電流開通和關(guān)斷，所以開關(guān)損耗為0。開關(guān)損耗主要體現(xiàn)在Buck電路上。

由于Buck電路采用同步整流技術(shù)，開關(guān)損耗主要在主開關(guān)管Q3上。其計(jì)算公式為：

其中V1為Buck的輸入電壓，也是有源鉗位正激諧振電路的輸出電壓，f為開關(guān)頻率，LIΔ為電感紋波電流，ton2_r、toff2_f為Buck開關(guān)管Q3的導(dǎo)通上升時(shí)間和關(guān)斷下降時(shí)間，Io是Buck的輸出電流?？山普J(rèn)為ton2_r=toff2_f=t。上式（1）可簡化成：

（2）導(dǎo)通損耗

有源鉗位正激諧振電路各開關(guān)管的導(dǎo)通損耗之和為：

式中）（1 rmsQI、）（2 rmsQI、）（5 rmsQI為一個周期內(nèi)流過Q1、Q2、Q5的電流有效值，1QR、2QR、5QR為開關(guān)管Q1、Q2、Q5的導(dǎo)通電阻。

Buck電路各開關(guān)管的導(dǎo)通損耗之和為：

式中IQ3（rms）、IQ4（rms）為一個周期內(nèi)流過Q3、Q4的電流有效值，RQ3、RQ4為開關(guān)管Q3、Q4的導(dǎo)通電阻。

根據(jù)Buck電路的工作原理，可得：

式中D2為Buck電路的占空比。Io是Buck的輸出電流。

又因?yàn)檫x用的開關(guān)管Q3、Q4型號相同，所以RQ3=RQ4。

上式（5）可簡化成：所以開關(guān)管的總導(dǎo)通損耗：

綜上，兩級式變換器的開關(guān)損耗和導(dǎo)通損耗之和為：

針對本實(shí)驗(yàn)參數(shù)t=100ns，f=300k，R=0.625ohm，

上式（8）可簡化為：

上式（9）即為該兩級式變換器的開關(guān)損耗和導(dǎo)通損耗之和與Buck電路的占空比D2、輸出電流Io之間的數(shù)量關(guān)系。

即當(dāng)Buck的占空比為0.5時(shí)所對應(yīng)的匝比是使得兩級式變換器效率最高的?？紤]到死區(qū)時(shí)間以及其他損耗的影響，Buck的占應(yīng)比控制在0.4到0.45之間。

3　實(shí)驗(yàn)結(jié)果

采用“有源鉗位正激諧振+Buck”方案，結(jié)合PCB表面貼元件技術(shù)，控制諧振電感Lr不變，通過改變變壓器T原邊匝比（副邊匝比保持不變），從而改變Buck電路的占空比D2，搭建了輸入48V，輸出5V/8A的樣機(jī)，電路的具體參數(shù)如表1所示：

表1　變換器參數(shù)Tab.1　Parameters of the converter

實(shí)驗(yàn)測得開關(guān)管Q2的柵源極電壓波形2gV，諧振電流i的波形，第一級輸出電壓V1波形以及開關(guān)管Q3的柵源極電壓波形3gV。測試了不同變壓器T匝比下的實(shí)驗(yàn)波形，如下圖（3）、（4）、（5）所示。最佳工作點(diǎn)的實(shí)驗(yàn)波形（圖4）與理論分析計(jì)算的D2占空比波形相符。

為驗(yàn)證分析的正確性，分別測試了9：3；10：3；11：3；12：3；13：3；14：3；15：3這7種變壓器匝比的（副邊匝數(shù)保持不變，恒為3匝）兩級式變換器的效率，并繪制了效率曲線，如圖6所示。

圖3　匝比10∶3實(shí)驗(yàn)波形Fig.3　Waveforms of 10∶3

圖4　匝比12∶3實(shí)驗(yàn)波形Fig.4　Waveforms of 12∶3

圖5　匝比15∶3實(shí)驗(yàn)波形Fig.5　Waveforms of 15∶3

圖6　測試的效率曲線Fig.6　Measured efficiency curves

從效率曲線圖可以看出，當(dāng)變壓器T的匝比為12：3時(shí)兩級式變換器的效率最高，接近88％，此時(shí)對應(yīng)的Q3的占空比D2約為0.4，與理論分析相一致。

4　結(jié)論

本文詳細(xì)分析了“有源鉗位正激諧振+Buck”兩級式變換器的開關(guān)損耗和導(dǎo)通損耗，量化了變壓器的匝比與效率之間的關(guān)系。實(shí)驗(yàn)結(jié)果驗(yàn)證了計(jì)算所得變換器最優(yōu)工作點(diǎn)的正確性。該變換器適用于48V母線電壓輸入的VRM，具有以下優(yōu)點(diǎn)：①控制簡單可靠，易于實(shí)現(xiàn)；②高效率；③工作穩(wěn)定。

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本文引用格式：WEI Xu-guang.The Interlayer Stress Analysis of Polyethylene-steel Composite Pipes［J］.新型工業(yè)化，2016，6（7）：28-33.

DOI：10.19335/j.cnki.2095-6649.2016.07.005

Abstract：Polyethylene-steel Composite Pipes is widely used in conveying corrosive media occasions，but the pipe may lose effectiveness in the process of transporting hot and cold media，so the research of stress distribution and variation in polyethylene-steel composite pipes is very necessary.This article frst assume that a thin adhesive layer is in between the polyethylene and steel，the adhesive layer along the axial shear stress is the major cause of the polyethylene layer and the steel pipe off sticky.Secondly，we use a method of fnite element to computer simulation by ANSYS，and verify initial assumptions.Finally，based on simulation data，we analyse the adhesive layer stress distribution and the variation with different parameters to change.Through the above research，preliminarily summarize the variation and distribution of interlaminar stress，and provide technical support for future design and process improvement of polyethylenesteel pipe.

Keywords：Laminated Polyethylene-steel Composite Pipes；Interlaminar Stress；Finite elements；ANSYS

Citation：WEI Xu-guang.The Interlayer Stress Analysis of Polyethylene-steel Composite Pipes［J］.The Journal of New Industrialization，2016，6（7）：28-33.

1　Introduction

Due to the outstanding corrosion-resistance character of the polyethylene-steel composite pipes（PSCP），it had been widely used into corrosive fluid transporting and different chemical industry fields.However，during past long term of practical applications it turns out that the constantly separation of polyethylene layer and steel layer causing pipe jam had limited the further application and became the main cause of all failure of polyethylene-steel composite pipes［1］.There is a very thin glue layer between the polyethylene layer and the steel layer，which under circulate thermal working conditions we assume would be a powerful axle tangential stressed，which be considered as the main cause of the constantly separation of polyethylene layer and steel layer.Unfortunately，we don't pay attention to this phenomenon at home and abroad，but also the lack of relevant technical information，so the research of polyethylene-steel composite pipes interlaminar stress distribution and variation is very necessary.This paper first assumption that the polyethylene-steel composite pipes has a thin adhesive layer between the thermal expansion and contraction and the role of stress，the adhesive layer by a larger，along the axial shear stress is the major cause of the PE layer and the steel pipe off sticky.Secondly，we use a method of finite element［2］to computer simulation by ANSYS［3］and obtain the reference of some typical operating conditions simulated data for the future engineering applications，verified initially assumptions.Finally，based on simulation data，we analyse the adhesive layer stress distribution and the variation with different parameters to change.

2　Problem description and model

2.1Physical descripiton of problem

The structure of polyethylene-steel composite pipes［4］is shown in Figure 1.the outer layer is steel while the inner layer is polyethylene material solidified from hot air spraying，the relevant physical and

geometrical parameters is listed in Table 1.

Tab.1　The physical and geometrical parameters of PSCP

Fig 1.Thephysical model of polyethylene-steel composite pipe

2.2Mathematical description and model

Three directions of stress distribution should be taken into consideration during the analysis of stress components between polyethylene layers and steel layers such as：σx，σy，σzand τy，τxyz，τxz.The following formula was derived based on the relationship between the stress and variation of orthogonal isotropic material at the main direction：

According to plane coordinate conversion，it can be transferred into：

Where，σ1，σ2，σ3，σx，σy，σzrepresent axial stress；1，ε1，ε2，ε3，εx，εy，εzrepresent relevant axial stress strain；τ12，τ23，τ13，τxy，τyz，τxzrepresent tangential stress；γ12，γ23，γ13，γxy，γyz，γxzrepresent relevant tangential stress stain.

3　Experiment and data analysis

3.1Experimental scheme

In this paper，we make a thermal expansion model to model and postprocess and use common working condition that DN=60mm，L=3m as example：

1）Modeling with soild45 finite element

2）Inputting material data is shown in Table 1

3）The outcome of modeling procedure is shown in Figure 2 and Figure 3

Mostly，classic procedure of computer simulation progress are as follows：

1）With reference to the existing grid method［5-6］，we impose symmetry constraints in caliber .Only a quarter of entire pipe is modeled to reduce workload of computer simulations and work intensitythe.The symmetrical and axial displacements is applied at two symmetrical section and center of pipe respectively according to current means of meshing and modeling.

Fig.2　Tangential stress distribution between layers

Fig.3　Axial stress distribution between layers

2）Inputting reference temperature：25°C，the working temperature of this single simulation is 30℃.

3）Computer calculating and data recording

3.2Raw data record and process

3.2.1Raw thermal expansion data of PSCP

The maximum axial stress and tangential stress calculated by the following relevant parameters：the reference temperature is 25°C and the working temperature are 30°C，35°C，40°C，45°C，50°C，55°C，60°C，65°C；the length of pipe are 2m，3m，4m，5m，6m，7m，8m，9m，10m respectively；the diameter of pipe are 20mm，40mm，60mm，80mm，100mm respectively.

Considering that there are three variables，in order to facilitate the calculation and display of results，we take DN as the group variable，the temperature and the length of pipe as within-group variation.Because of the limited paper space，only a list of maximum radial force and normal stress，of which the length L=1，2，3...10mm and DN=20，40 mm .The details are as follows：

Tab.2　Raw data of the maximum tangential stress at DN=20mm

Tab.3　Raw data of the maximum axial stress at DN=20mm

Tab.4　Raw data of the maximum tangential stress at DN=40mm

Tab.5　Raw data of the maximum axial stress at DN=40mm

3.2.2Raw intial stress raw data of manufacturing PSCP

The simulation working condition in this section is that pipe diameter：DN=80mm，pipe length：L=2m，manuf- acturing temperature：300°C［7］，cooling temperature：20°C，the outcome data is as follows（which is dominated by practical computer performance used in this paper that no longer lengthscould be simulated otherwise the program would report error and exit）：

As shown in Figure 4 and Figure 5，from simulation results，we can find that the maximum stress concentrate on the surface of steel layer and the tangential stress is greater than the axial stress along the simulations.

Tab.6　Raw data of the initial maximum tangential stress at DN=80mm

Tab.7　Raw data of the initial maximum axial stress at DN=100mm

Fig.4　The distribution of maximum initial tangential stress

Fig.5　The distribution of maximum initial axial stress

3.3Data analysis

3.3.1Regular pattern of Srz ＆ Sr changing with pipe Length

Fig.6　The maximum tangential stress with the change of diameter

Fig.7　The maximum axial stress with the change of diameter

3.3.2 Regular pattern of Srz ＆ Sr changing with pipe diameter

3.3.3Regular pattern of Srz ＆ Sr changing with working temperature

Fig.8　The maximum tangential stress with the change of length

Fig.9　The maximum axial stress with the change of length

Fig.10　The maximum tangential stress with the change of temperature

3.3.4Stress distributions along the diameter of PSCP pipe

Common simulation parameters：DN=80mm，L=6m，reference temperature T1=25°C，reference temperature T2=60℃

3.3.5Initial Stress distributions along with the diameter of PSCP pipe

3.4Major conclutions

1）The interlayer stress variation regularity with the pipe

length：As shown in Fig 6 and Fig 7，both tangential and axial stress distribution is only related to temperature variation，which is not related to diameter variation according to mass mount of data analyses.

2）Regular pattern of interlayer stress along with diameter variation according to Fig 8 and Fig 9：

（1）Both the tangential and axial stress increase with the increasing of pipe diameter.

（2）Both the absolute value of the maximum tangential and axial stress decrease with the increasing of pipe diameter.

（3）The maximum tangential stress Srz increase with the increasing of the absolute value of pipe diameter.

Fig.12　The maximum tangential stress distribution along with pipe diameter

Fig.13　The maximum axial stress distribution alongwith pipe diameter

Fig.14　The initial tangential stress distributionalong pipe diameter

Fig.15　The initial axial stress distribution alongpipe diameter

3）Both the tangential and axial stress is linear relative to the temperature variation according to Fig 10，F(xiàn)ig 11within the given temperature region（30℃-65℃）.

4）The relationship between the maximum tangential stress and axial stress：the maximum axial stress usually is greater than the maximum tangential stress which is usually within the difference belowan order of magnitude when the temperature difference is little，however，the difference between them increase with the increase of temperature difference，especially when the temperature difference is very big，the maximum axial stress is far greater than the relevant tangential stress.

5）The tangential stress distribution along with the classic common used diameter of pipe：the tangential stress decrease with the pipe diameter.

6）The axial stress distribution along with the classic common used diameter of pipe：the maximum axial stress appeared at the contact layer of Polyethylene layer and steel layer according to Fig 13.

7）The distribution of initial stress under classic working condition：Manufacturing temperature：300℃，cooling temperature：20℃

（1）Distribution of initial tangential stress：the initial stress increase with the diameter from inner layer with the maximum value of 709Mpa.

（2）Distribution of initial axial stress：the maximum initial stress value of 472Mpa appeared at the contact layer between polyethylene layer and steel layer.

4　Summary and Outlook

This paper simulated stress distribution between those two layers via computer simulation under different groups of classic boundary conditions，trying to point out some regular pattern of polyethylene layer and steel layer with boundary condition changing.As the result of above research，we astonished find out that the stress between layers had not be taken into consideration by current pipe manufacturing technology，which would rise with the temperature difference rising and would became extremely dangerous to polyethylene-steel composite pipes when the temperature different gets very much from the original boundary conditions.We believe this paper testified the hypothesis proposed before and would provide some helpful reference value to the further improvement of polyethylene-steel composite pipes designing and manufacturing technology.But the conclusions of this paper based only on computer simulation than practical thermal-stress circulation experiment data，for which these conclusions can only be taken as technological references than actual experiment conclusions.In addition，The PE plastic layer was considered as static layer with static parameters such as elastic modulus，Poisson ratio and thermal coefficient of expansion，however，as everyone knows that the solidification of plastic material is dynamic and very complicated whose material parameters could not possibly be static and the same as normality，so the conclusions about initial stress distribution is only ideally simulated rather than the practical application situation.The actual distribution of initial stress need further study.

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An Optimal Operating Point Analysis of Two-stage Converter

HU Xiao-xiao，WU Kun
（College of Electrical and Information Engineering，Tongji University，Shanghai 201804，China）

This paper analyses the optimal design of a two-stage converter in detail，aims at resonant converter cascading Buck circuit，bases on the switching loss and conduction loss，quantifes the relationship between the transformer turns ratio and the effciency，and calculates the optimal operating point of the converter.The two-stage converter is suitable for 48V input bus voltage VRM，and solves the problems such as uncontrolled duty ratio and low effciency often come up against in traditional single converter.In addition，a prototype with 48V input and 5V/8A output is built to verify the analysis.

Two-stage converter；Optimal operating point；Switching loss；Conduction loss

The Interlayer Stress Analysis of Polyethylene-steel Composite Pipes

WEI Xu-guang
（Northeastern University Engineering ＆ Research Institute Co.，Ltd，GuiYang 550000）

10.19335/j.cnki.2095-6649.2016.07.004

HU Xiao-xiao，WU Kun.An Optimal Operating Point Analysis of Two-stage Converter［J］.The Journal of New Industrialization，2016，6（7）：22-27.

胡瀟瀟（1991-），女，碩士研究生，主要研究方向?yàn)閮杉壥阶儞Q器的效率優(yōu)化；吳琨（1992-），男，碩士研究生，主要研究方向?yàn)樽儞Q器拓?fù)浜涂刂撇呗浴?/p>