Honeywell 80363214-100

三相电路中，由于其三相电源u[u_a,u_b,u_c]^T及三相负载电流i[i_a,i_b,i_c]^T都是三维函数，三相电源之间、三相负载之间互相影响，从而使得功率现象与单相电路有了很大的不同。
      在传统功率理论(对称正弦)中，三相瞬时有功功率之和为常数，且无功功率只在相间流动。在畸变和不对称的情况下，有功功率是否还满足这一性质，三相电路中无功电流的流动是否只局限于三相之间，是否存在三相电源与三相负载间的无功流动，这是值得探讨的理论问题。
    为便于探讨，本文首先从对称正弦三相电路开始分析。
2  对称正弦三相电路中功率现象解释
    如图１所示的对称正弦三相电路，其电源为对称正弦电压源，负载为对称线性负载。其中

依据传统功率理论，有

    负载R+jX中的X不论如何变化，三相瞬时无功功率之和都为零。也就是，在任一瞬时，各相负载有的在利用电磁场蓄能，有的将前一段时间的电磁场蓄能释放出来，各相的电磁场蓄能功率之和为零，任一相的电磁场蓄能功率都由其他两相提供而不是由电源提供，无功功率只在相间流动，不存在电源与负载间流动的无功功率。
    由于是对称正弦电路，如果把三相电源作为一个整体，则其输出的总功率不随时间变化。同样，三相负载作为一个整体，其吸收的总功率也不随时间变化。设三相电源为同步发电机，这一点可以由发电机气隙中存在同步旋转的正弦磁动势，带动发电机的原动机输出恒定转矩得出。
    对称正弦电路的特点：
   （1）无功功率只在相间流动，不存在电源与负载间流动的无功功率；
   （2）任一瞬时，三相电源输出的总功率总是等于各相有功功率之和；
   （3）任一瞬时，三相电源输出的总功率(各相有功功率之和)为恒值。
3  非正弦及不对称三相电路中功率现象解释
       对于非正弦及不对称三相电路，由于电压、电流不再是简单的正弦函数且三相电路之间互有影响，而使得三相电路的功率现象变得十分复杂。三相电路的三相瞬时有功功率之和能否保持为不变的常数，三相电路(尤其是三相三线电路)中是否只存在相间流动的无功功率等，均为无统一结论的问题。
       本文作者认为：三相瞬时有功功率之和为常数且无功功率只在相间流动，这只是对称正弦电路中电源电压、负载电流波形为对称正弦的一个特点（也是优点）。但三相瞬时有功功率之和为常数并不应该（在很多情况下也不可能）成为非正弦及不对称三相电路中有功电流的确定原则。例如，在三相电压任意畸变且不对称的情况下，可以设三相电压在t₀时刻同时过零点，即

    在这种情况下，无论有功电流i_pa(t)，i_pb(t)，i_pc(t)如何定义，三相瞬时有功功率之和在t₀时刻都为零，即

    假设负载为线性电阻，由于负载消耗了功率，不可能说电源在任意时刻发出的有功功率都为零。因此，不论如何定义有功电流，电源发出的三相瞬时有功功率之和都是波动的。实际上，三相瞬时有功功率之和存在波动，这是电源电压畸变且不对称所必须付出的代价。
       本文作者还认为：由于电源电压、负载电流不再是简单的对称正弦波，非正弦及不对称三相电路中的无功功率也不仅仅在相间流动，而有可能存在三相电源与三相负载间的无功流动，如图2所示 ^[1]。图中，三相电源为对称正弦电压源，负载为不对称线性电容负载。

    上式为一周期量^[1](周期为电源周期的1/2)，并不恒等于零。这说明，三相电路中不仅存在相间无功流动，而且有可能存在电源与负载间的无功流动。
4  三相电路中无功功率的分类
4.1  无功功率的分类
      在通用瞬时功率理论体系^[2,3]中三相三线制电路有功电流、无功电流为

4.2   相间流动的无功功率q₁
       对三相电路在空间上(三相间)按照某一目标对其功率分布进行优化, 优化的结果将满足：任意时刻的三相无功功率瞬时值之和为零。由于是在空间上进行优化，故可将这部分无功功率定义为相间流动的无功功率。
   （1）三相四线制电路中相间流动的无功功率定义
       以**小能量传输损失(电流**小做功能力损失)为目标函数，可得三相四线制电路相间流动的无功电流i_qa1、i_qb1、i_qc1的求解模型为

定义相间流动的无功功率

   （2）三相三线制电路中相间流动的无功功率定义
    对于三相三线制电路，在目标函数式(2)、约束条件式(3)之外，还应增加约束条件

    相间流动的无功功率定义与三相四线制电路相同。
       由约束条件式(5)可以看出，本文所定义的相间流动的无功功率其三相各个分量之和总是为零。这正是相间流动的无功功率的本质特征。
4.3  电源与负载间流动的无功功率
       三相电路总无功电流(无功功率)与相间流动的无功电流(无功功率)之差，即为电源与负载间流动的无功电流i_q2(无功功率q₂)．即

5  性质
       对于三相四线制电路，有





6  结论
    （1）本文指出：“无功只在相间流动且三相瞬时有功功率之和为常数”仅是三相电路在电源电压、负载电流为对称正弦波时的特例，这当然是一个很大的优点，但却不应该(在很多情况下也不可能)成为非正弦及不对称三相电路中有功电流、无功电流的确定原则。在非正弦及不对称电路中，无功不仅会在相间流动而且可能在作为一个整体的三相电源与作为一个整体的三相负载间流动；
    （2）本文运用**小能量传输损失(或称**小作功能力损失)的原则进一步在通用瞬时有功功率的基础上确定了三相电路中三相电源与三相负载间流动的无功功率及三相电路间流动的无功功率。进一步完善了通用瞬时功率体系。在这一体系中，三相电源与三相负载间流动的无功电流、三相电路间流动的无功电流、有功电流之间存在两两正交的关系。
    （3）在电力电子装置广泛应用的今天，对无功功率、谐波的分析、治理、管理、收费等的研究是一个热门课题^[4~7]。本文的工作与文[1]、[3]的研究对这一课题的研究具有一定的理论指导意义。现代工业的发展对电能质量的要求越来越高，如何为电力用户提供安全可靠的“绿色”电源是目前电源研究领域的热点。UPS作为一种不间断供电电源，是关键设备得以正常运行的保证。为适应发展的要求，近年来也在不断地进行完善和改进。先后出现了后备式、在线式、三端口在线互动式及双变流器串-并联补偿式等几种结构类型的UPS。其中由Kamran^[1]和Silva^[2]提出的双变流器串－并联补偿式UPS^[1~4]，既可以补偿非线性负载中的无功电流及谐波电流，同时还可以补偿电源电压的谐波及基波偏差，较传统双变换在线式UPS而言，输入功率因数高，输出能力强，具有综合的电能质量调节能力，是一种值得推广应用的新型UPS。目前国外UPS厂家只有某公司拥有此项专利技术，在市场上已经推出Silcon DP300E系列大功率UPS，国内则刚刚处在研究的初始阶段^[5]，还有许多研究工作需要进行。

    由上述分析可知，在非线性负载、电源电压高于或低于额定值v_R且含有谐波电压时，这种UPS通过串、并联补偿变流器的共同作用，可使负载电压u_L补偿到与电源电压同相的额定正弦电压u_R，避免了网侧谐波电压对负载的影响；同时电源仅输入基波有功电流i_s，功率因数近乎为1，克服了传统双变换在线式UPS因输入整流部分所带来的输入功率因数较低的缺点。通常电源基波电压偏离额定值小于±15%，因此变流器Ⅰ仅补偿Du≤±15%的额定电压，其容量仅为系统容量的20%左右。正常时市电与双变流器共同对负载供电，两变流器的**功率强度只有负载功率的20%，相对始终在100%负载功率下工作的传统双变换在线式UPS而言，不仅整机效率高，功率器件损耗小，寿命长，可靠性高，而且有足够的功率裕量去应付特殊的负载（冲击负载、瞬间过载等），因此输出能力得到很大的增强，相同容量的造价也降低了。一旦市电停电，变流器Ⅱ从蓄电池获取电能继续不间断的对负载供电；当电网正常后，重新恢复市电与双变流器共同对负载供电，在正确的控制策略作用下，可以实现输出电压无间隙、无突变。
3  双变流器串-并联补偿式UPS控制策略
3.1  串联变流器受控为基波正弦电流源
    在图1所示UPS中，采用双变流器串-并联补偿后应实现：市电输入电流i_s是与v_s1同相的正弦有功电流，电源供电的功率因数为1；同时使得负载电压v_L为基波正弦电压，且v_L=v_R（额定值）并与v_s1同相。
    串联变流器Ⅰ作为基波正弦电流源运行，向交流电网注入电压△v=△v₁+△v_k，△v_k与电源谐波电压v_sk大小相等、方向相反，△v₁=△vs₁-v_R。同时串联变流器向电网串联注入基波正弦电流i_s，i_s与v_s1同相，使交流电源电流中无谐波电流，无功电流，供电功率因数为1，其控制框图如图2所示。


的电流控制指令，经dq/ABC变换后获得三相指令电流再经滞环电流比较后获得串联变流器的PWM开关控制信号，使电源电流i_s跟踪I_S^*，则可实现作为正弦电流源的串联变流器对电源电流的控制功能和对电源谐波电压的补偿（隔离）功能。由于系统在运行期间始终并接蓄电池工作，维持了直流端电压的基本恒定，且忽略电池充电功率和系统中电感、电容、开关器件的功率损耗，因此在此控制框图中没有添加直流端电压控制环节。

3.2  并联变流器受控为基波正弦电压源
   并联变流器Ⅱ作为基波正弦电压源运行，输出与v_s1同相的额定值正弦波电压v_R，同时经L₂、C₂后输出补偿电流为

    则由图1可得到三相静止ABC系统电流平衡方程为


节器输出、补偿电流前馈及电容电流交叉解耦电流之和，经电流滞环控制作用，使并联变流器输出电流i₂包含负载所需要的无功电流i_2q和谐波电流i_2h及恰如其分的有功电流i_2d。

     根据以上控制策略，由于串联变流器受控为基波正弦电流源，电源电流i_s为与电源基波电压同相的正弦有功电流，从而使得非线性负载中的无功和谐波电流经并联变流器得到补偿。同时并联变流器受控为基波正弦电压源，使负载输入电压v_L为与电源基波电压v_s1同相的正弦波额定电压v_R，从而使得电源电压中的谐波与基波偏差经串联变流器得到补偿（或隔离）。
4  系统特性仿真结果
    基于上述控制策略，在MATLAB SIMUlink环境下建立了系统的连续域仿真模型， 并对其工作特性进行了仿真。图1中交流电源电压v_s的基波v_s1在其额定值v_R（线电压380V/相电压220V）的±15%范围变化。v_s中的5次谐波电压v₅、7次谐波电压v₇各为基波电压值的5％。负载为三相相控桥整流装置，R=19.7W，L=50mH，相控角a=30º，直流负载功率10kW。直流端接蓄电池E_b=600V，其内阻R_b=0.1W，直流电容C=4700mF。串联变压器变比N=4，滤波电感L₁=1mH， L₂=0.5mH，滤波电容C₂=150mF。
    采用图2、3所示控制系统和控制策略，图4、5分别示出在电源基波电压v_S1=1.15v_R和v_s1=0.85v_R两种工况下，电源电压v_s、A相负载电流i_LA、A相串联变流器电网侧补偿电压△v_A(v_CA/N )、A相并联变流器补偿电流i_3A、负载电压v_L、电源电流i_s及直流电压V_dc的示波图。图6则给出了上述两种工况下，电网掉电和电网恢复供电切换动作时的A相输出电压及输入电流动态变化波形。

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Thermo Scientific Dionex Viper Capillaries SST Flex Cap IDxL 0.13x65mm 6040.2307

Spectra-Physics 265 Lab Exciter System Power Supply Unit PSU for 164 Laser

Sapphire Scivex 625-2017 Precision Dispense Pump Stepper Motor w/ E5 Encoder

Dionex ICS3000-CD Cell Card FAB 061816-09 Ion Chromatography System Plug-In

Thermo Scientific Dionex CRD-200 4mm RFIC Carbonate Removal Device 062983 Lab #2

HP Agilent 5890 GC 19243-60650 EPC Septa 1cc/min 100PSI Inlet Purge Regulator

Becton Dickinson 03-20030-02 SSC/FL2 FL1/FL3 PCB FACScan Fluorescence Cytometer

Thermo Dionex 6082.0500 2.5μL PEEK Semi-Micro Flow Cell UltiMate 3000 DAD MWD

Rheodyne Idex 9650E-026 10-Port Injection Valve Fluidic Platform Assembly

Thermo Electron 70111-61091 Rod Driver Amplifier Board PCB PCA Assembly Module

HP Agilent 19243-60500 Column Inlet Septum Nut Assembly For 5890 Chromatograph

Molecular Devices SpectraMAX 190 Absorbance Microplate Reader Spectrophotomet?er

Zygo Mark IV-XP Laser Interferometer 50W Power Supply Unit 6189-0100-01 w/ Cable

Norgren Kloehn 20451 3-Way Non-Distributin?g Aluminum Ceramic Rotary Valve Lab

Dionex ICS3000 CPU Board Replacement PCB PCA FAB 061812-12 Assy 061813 DC Lab

Tecan Cavro XLP 737212-A Sample Syringe Column Pump for Dionex AS/AS50 w/Head

HP/Agilent 18594-60040 BCD/Remote Board for 5890/7673B Autosampler Controller

QualiTau M26 MIRA TDDB Analyzer Test Chamber Oven Sys

Thermo Scientific Dionex TurboFlow HTLC Cyclone 0.5x50mm Column CH-953288Q

LN2 Liquid Nitrogen Vent Controller Switch Plug-In Module Status Indicator

Eratron PPS-82015P Digital Display Controller Panel PS8200 Plasma Power Supply

Jasco HT-16M Video Trench Depth Measuring Microscope

Systec 9000-1130 ZHCR Constant Run Vacuum Pump w/Controller PCB & L-Bracket Assy

Rheodyne 9650E 10-Port Injection Valve Fluidic Platform w/C7733-9012K Motor

Baxter S8223-1 S/P Vortex Mixer Shaker Analog Variable Speed Touch 500-3000RPM

Saia UBD53N06RAZ60 Rotary Stepper Motor for Dionex AD25 Absorbance Detector O.B.

Saia UBD53N06RA Rotary Stepper Motor for Dionex AD25 Absorbance Detector O.B.

Rheodyne Idex 9750E-025 2-Position 6-Port Fluid Platform Automated Valve Assy #2

Thermo BetaBasic-18 71505-052130 502.1mm 5μm Particle Lab HPLC Column

GE Amersham Pharmacia Biotech Hypercassette RPN 11650 1012in Autoradiography

Mitutoyo FS100 Finescope Lab Microscope Stand FS110 NO TRINOCULAR HEAD

Dionex AS-DV Autosampler Replacement RX PCB Board ASSY 069315 FAB 069314-02

NEW VWR AccuPower 500 10-500VDC 5-500mA Digital Electrophoresis Power Supply Lab

Rheodyne MHP-9900-601-1 Idex 10-Port Switching/Injec?tor HPLC Fluid Valve TitanHP

Heraeus DS-270-J 185-400nm 1.0mm Aperture T10 Deuterium Lamp Bulb DS270J

Reichert 10/0.25∞/0.17 Plan Achro Microscope Objective Laboratory 1732 10

Revco ULT 2186 A-0-F Ultra Low Temperature Laboratory Freezer 115V 15.2A

Keithley 866 -55-150°C Digital LCD Thermometer 2252Ω Thermistor w/YSI 402 Probe

Tekmar 14-5330-090 Cryofocusing Interface Logic Board PCB for 3000/3100/6000

Ametek Dycor Thermox M100 MDE Lab Quadrupole RGA Residual Gas Analyzer Unit

Newport AD-100 Ultra High Resolution Motorized Linear Actuator 13mm Travel

Toyo Sokki Tedea Huntleigh 1004 15080-FBS 0.6kg Capacity Single Point Load Cell

MacConnell Research MP4800 Automated Plasmid Mini-Prep DNA Purification System

Anko MityFlex 907-101-60172-1 115V Lab Fluid Transfer Peristaltic Pump

NEW Labomed 1.5x Auxiliary Objective for CZM6 Trinocular Microscope 4123025

VWR Sheldon 1225PC Digital Laboratory Water Bath 9020912 120V 6.0A 0-100°C

Lot 12 Thermo Scientific Dionex OnGuard II RP 2.5cc Filter Cartridge 057084

NEW Watlow St. Louis FireRod Lab Cartridge Heater 240V 1000W GZA43-J12H14

Alpha Innotech AITM-26 MultiImage Light Cabinet AlphaImager Gel Imaging System

Terra Universal 1570-29 Adjustable Vibration Free Lab Work Station Table White

Tencor Instruments 10-00020 Alpha-Step Profilometer Surface Profiler Laboratory

Savant VP-190 Two/Dual-Stage Rotary Vane Mechanical Vacuum Pump 1/2HP 5.8CFM

Thermo Scientific Dionex ICS-3000 RCH-1 Reaction Coil Heater Assembly 061747

Andros M1026-60150 Small Vacuum/Pressure Pump w/Portescap Motor 22V2R-28-216E

Thermo Scientific Dionex CarboPac PA-100G 2x50mm BioLC Guard Column 057183 Lab

Perkin Elmer L225-0137 Laboratory Benchtop Microplate Plate Reader 12V 0.6A 1.8°

Spectral Energy GM 252 Motorized Lamp Power Supply Assembly Laboratory

Torsion Balance Apothecary Calibration Weight Set +Wooden Box 100G-1000G

NEW Marchi Associates TC MI-K SDSM-1417 Thermocouple Sensor 6” Probe 16” Wire

Metrohm 732 IC Detector Ion Chromatography Conductivity Detector Lab 1.732.0010

VWR 810 7"x7" Glass Top 60-1600RPM Digital Magnetic Stirrer Mixer Lab 11301-010

American Optical 40/.66 Plan EPI Microscope Objective Laboratory AO 2567 S 40

NEW Labomed 2.0 Auxiliary Objective for CZM6 Trinocular Microscope 4123027

HP Agilent ZORBAX GF-250 9.4mmIDx250mm 4um HPLC Gel Filtration Filter Column Bio

Thermo Scientific Dionex ICS 3000 Pump Motor Assembly Chromatography NO HEADS

CRS FRIDGE Refrigerated Lab 120-Microplate Carousel w/SAC Single Axis Controller

Dionex IonPac CS17 RFIC 2x250mm Cation-Exchange Analytical Column Chromatography

AO American Optical EpiStar 2571 Illuminated Laboratory Microscope Base Unit

K&E/Brunson 71-5175 Long Extension Module for Cup Mount Adapter Keuffel-Esser

Lot 5 BD Falcon 250ml 75cm2 Canted Neck Tissue Cell Culture Flask Plug Seal Cap

MDA Scientific 710000 Continuous Toxic Gas Analyzer Monitor Detector Ser-7100 #1

Haber 15K-1 EMP Hi Voltage Electromolecula?r Propulsion System Analyzer Tester

Teledyne Tekmar 14-5235-090 Communications Interface PCB Electronic Board

Anelva/Eito Denshi AD-75 Junction V1 DT-DV DC Power Regulator 9004-21881B-03

Met One R4700.3MRAD.HRD Remote Particle Counter 0.3-0.5 Micron 2080880-2

Cole-Parmer 150mm Correlated Flowmeter N112-02 Magnified Pressure Gauge Valve

Beckman Coulter J6-HC High-Capacity 6KRPM Analog Centrifuge NO ROTOR 208V Lab

Alcatel 5150 CP High Vacuum Turbo Molecular Pump Assembly +W2S107-AA01-40 Fan

Millipore Waters Lab HPLC Pump Fluid Unit Multisolvent Delivery System

Follet FZR FZR4-ADA Undercounter Lab Medical Restaurant Freezer 2-Shelves 3.5cu

Rheodyne Idex MHP 9907-000 2-Position 6-Port Switching Injection Valve Titan HP

Lot 7 Dionex 8-Position Vial Holder 10mL for AS-AP Autosampler ICS 069877 Lab

Perkin-Elmer 9600 GeneAmp PCR System DNA Thermal Cycler Lab Analyzer Gene Amp

Rheodyne Idex 9750E-025 2-Position 6-Port Fluidic Platform Automated Valve Assy

Kinetic Systems V241-ZA41 96-Channel High-Level Scanning Multiplexer Module

Rheodyne Idex TR042604A 6-Port Switching/Injec?tor HPLC Fluid Valve Lab Assy

Rheodyne 7410 3-Position 4-Port 2-Loop Disc Micro-Scale Sample Injector Valve

HP Agilent 5890 GC 19362-60565 Mass Flow Controller+1924?3-60650 Purge Regulator

Bio-Rad PhD Autoimmune IFA EIA Testing Workstation Gray Box Controller Module #1

Thermo Scientific Dionex ProPac WAX-10 4x250mm Analytical Column HPLC 054999 Lab

Applied Biosystems/MDS SCIEX API-150EX Mass Spectrometer Single Quadruple LC/MS

National Instruments NI 181045-02 VXI-MXI C-Size Interface Module w/INTX

Zymark TWISTER-H Microplate Robot Handler w/2x Stackers Lab Robotic Handling

Applied Biosystems SOLiD EZ Bead Amplifier Amp Component Lab Emulsion PCR ABI #1

Varian 4-Channel Argon Station Shutter Controller for 3000/3190 Sputter System

Reichert EpiStar Illuminated Lab Microscope w/ AO MicroStar Trinocular Head

Perkin-Elmer Optima 3000 Spectrometer+N0?69-0166 Peristaltic Pump+AS-90 Sampler

Brailsford TD-4SBD2 DC Brushless Single-Head 4-5LPM Diaphragm Air Pump 12-18V

Isco 16 Column Module Lab CombiFlash Separation System SQ 1600 Chromatography

Thermo Scientific ES800 75μm x 15cm PepMap RSLC C18 3μm EASY-Spray HPLC Column

Thermo Scientific Accucore aQ HPLC Column 502.1mm 2.6μm 50? 17326-052130

Thermo Scientific ES801 50um x 15cm PepMap RSLC C18 2um EASY-Spray HPLC Column

Thermo Scientific Dionex ICS 3000 Pump Motor Assembly Chromatography NO HEADS #2

HP/Agilent 44470A 10-Channel Relay Multiplexer Module for 3488A Switch/Control

PMS Airnet 201 0.1CFM Lab Air Monitoring Defect-Causing Particle Sensor #2

Rheodyne Idex MHP 9907-000 2-Position 6-Port Injection Valve w/Mounting Assembly

Bausch & Lomb Industrial 25X 0.31 N.A. Lab Microscope Optical Objective

MDA Scientific 710000 Continuous Toxic Gas Analyzer Monitor Detector Ser-7100 #2

Swagelok Biopharm SS316L-SFF1 Eccentric Reducer 2" to 3/4" ASME-BPE ECC Fitting