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附錄1:外文翻譯
超級電容器電動葫蘆再生制動策略
摘要:全球范圍內(nèi)對環(huán)境問題的關注越來越多,使得動力設備的節(jié)能成為重中之重。為提高電動葫蘆的能量效率和行駛范圍,設計并討論了再生制動系統(tǒng)。該系統(tǒng)采用獨特的超級電容器方式進行能量儲存系統(tǒng)。雙向新娘DC / DC轉(zhuǎn)換器調(diào)節(jié)流過超級電容器的電流流動有兩種模式:升壓和降壓,取決于流向。為了在超級電容器上提供恒定的輸入和輸出電流,該系統(tǒng)使用雙比例積分(PI)控制策略來調(diào)節(jié)PWM到DC / DC轉(zhuǎn)換器的占空比。還研究了永磁同步電機(PWSM)驅(qū)動系統(tǒng)。采用空間矢量脈寬調(diào)制(SVPWM)技術,以及雙閉環(huán)矢量控制模型,詳細分析了PMSM特性。該再生制動系統(tǒng)的總體模型和控制策略最終在MATLAB和Simulink環(huán)境下構建和模擬。建立了一個測試平臺來獲得實驗結果。結果分析表明,該系統(tǒng)可以恢復一半以上的重力勢能。仿真和實驗結果證明了超級電容接口電路和PMSM的SVPWM策略的雙PI控制策略的有效性。
1引言*
隨著氣候變化和能源危機的問題在全世界越來越受到重視,工業(yè)化國家加大了減少化石燃料使用的努力。這一努力中最重要的步驟之一是將汽車和建筑車輛的電源從熱機轉(zhuǎn)變?yōu)榭勺兯俣入姍C。變速電機驅(qū)動系統(tǒng)不僅具有更高的效率,還可以利用風力發(fā)電和太陽能等可再生能源產(chǎn)生的電力。變速馬達驅(qū)動器具有自己的技術問題,但驅(qū)動中的快速加速和減速作為應用經(jīng)常要求,將電源置于短暫但電壓波動較大的地方。簡易解決方案是在變頻器直流母線上增加制動電阻,但會導致相當大的浪費。一個更為常見和復雜的解決方案是整合一個
能量儲存系統(tǒng)(ESS)進入系統(tǒng)以吸收能量,同時制動并在需要時重新生成。能量儲存系統(tǒng)[1-8]已經(jīng)在電動車(EV),混合動力電動汽車(HEV)和插電式混合動力汽車中應用。
傳統(tǒng)上,電氣ESS擁有廣泛的技術,并具有各種形式,例如電化學系統(tǒng)(例如電池,流通池),動能儲存(例如飛輪)和潛在能量存儲(例如抽水電,壓縮空氣)[9]。超級電容器的開發(fā)[10-12]為下一代純電動車提供了吸引人的選擇。最近的研究成果提出了在再生制動系統(tǒng)中使用超級電容器的方法。 WEI和Wang [13]提出了三種典型配置的性能分析和比較,以闡明不同拓撲的優(yōu)缺點。徐和謝[14]將其研究納入EV / HEV ESS系列電容器的電壓均衡方法。一個新的電池/
由CAO和EMADI [15]為EV,HEV和插電式HEV提出了超級電容器混合能量存儲系統(tǒng)(HESS),使用更小的DC / DC轉(zhuǎn)換器來維持超級電容器的電壓。 YAN和PATTERSON [16]提出了一種新穎的電源管理方案,以實現(xiàn)電動車輛的高性能和降低成本,實現(xiàn)短車隊應用。采用鋅 - 溴電池為普通驅(qū)動提供連續(xù)功率,同時使用超級電容器在加速期間提供峰值功率需求,并在減速期間存儲再生制動能量。 EV電動機在恒定轉(zhuǎn)矩模式下以低于基本速度的速度運行,并且在恒定功率模式下以超過基本速度的速度運行,以實現(xiàn)高效率和低成本。 AHMED和CHEMIELEWSKI [17]已經(jīng)建立了一個模型,旨在模擬燃料電池車輛中預期的負載,包括直流電機,DC / DC轉(zhuǎn)換器和用于峰值剃刮和再生制動的可充電電池。該模型還包括車輛的運動學,因此可以連接到標準化的驅(qū)動循環(huán)場景。 LU和CORZINE [18]引入了一套新的方法,將超級電容器組直接集成到用于大型車輛推進的級聯(lián)多電平逆變器中。這個想法是用超級電容器替代常規(guī)直流鏈路電容器,以便結合儲能單元和電機驅(qū)動器。這些研究已經(jīng)證明使用超級電容器作為混合動力車輛中的電池的可行補充存儲裝置來延長電池壽命。超級電容器被認為是輔助電源,其可以在啟動期間輔助燃料電池和燃料電池動力車輛的快速功率瞬變。
目前,沒有關于應用于起重設備的基于超級電容器的ESS的文獻研究。在這項研究中,將采用一種僅用于電動葫蘆的超級電容式儲能系統(tǒng),與傳統(tǒng)的汽車再生制動系統(tǒng)的超級電容器/電池混合動力方式不同。超級電容式儲能系統(tǒng)可以大大簡化電路結構,擴大控制總線。
首先將分別討論永磁同步電機(PMSM)和DC / DC轉(zhuǎn)換器的控制方案。然后基于DSP的控制系統(tǒng)是基于控制策略和數(shù)字信號處理技術開發(fā)的。隨后研究了整體系統(tǒng)結構和控制策略。本實驗開發(fā)并構建了再生制動系統(tǒng)的實施方案。最后,比較了仿真結果和實驗結果,分析了整個能量回收系統(tǒng)的效率。
2超級電容器儲能系統(tǒng)
2.1 DC / DC轉(zhuǎn)換器的控制策略
具有充電率高,效率高,功率密度高,循環(huán)壽命長,無維護[19]優(yōu)點的電動葫蘆作為電動葫蘆的儲能。超級電容器作為儲能單元通過DC / DC轉(zhuǎn)換器集成到逆變器直流鏈路中。根據(jù)輸入輸出條件,DC / DC轉(zhuǎn)換器可以作為升壓或降壓轉(zhuǎn)換器工作。
圖。 1顯示了DC / DC轉(zhuǎn)換器升壓運行的PSIM仿真模型。升壓操作用于驅(qū)動PMSM和放電超級電容器。
IGBT2在受控的占空比下接通和關斷,以將所需的能量從超級電容器傳遞到DC鏈路。當IGBT2導通時,從超級電容器中取出能量并存儲在電感器L1中。 IGBT2關斷時,能量超級電容器具有充電率高,
高效率,高功率密度,長循環(huán)壽命,無需維護[19],作為電動葫蘆的儲能。超級電容器作為儲能單元通過DC / DC轉(zhuǎn)換器集成到逆變器直流鏈路中。該
DC / DC轉(zhuǎn)換器可以根據(jù)輸入輸出條件作為升壓或降壓轉(zhuǎn)換器工作。圖。 1顯示了DC / DC轉(zhuǎn)換器升壓運行的PSIM仿真模型。升壓操作用于驅(qū)動PMSM和放電超級電容器。 IGBT2以受控的工作周期接通和關斷,以將所需的能量從超級電容器傳送到DC鏈路。當IGBT2接通時,從超級電容器中取出能量并存儲在該電容器中
電感L1。當IGBT2關斷時,L1中的電能通過D1傳輸?shù)街绷髂妇€。當放電超級電容器時,轉(zhuǎn)換器用作剛性電壓源到電動機控制器。升壓轉(zhuǎn)換器自動調(diào)節(jié)電壓,然后獲得穩(wěn)定的輸出電壓。確保超級電容器工作在安全,可靠和高效的條件下,采用雙PI閉環(huán)。
如圖所示。如圖2所示,DC / DC轉(zhuǎn)換器的工作原理是用于在再生制動期間對超級電容器充電。在降壓操作期間,轉(zhuǎn)換器將能量從直流鏈路傳輸?shù)匠夒娙萜?。該操作通過對IGBT1的受控操作來實現(xiàn)。當IGBT1接通時,能量從鏈路總線傳遞到超級電容器,電感L1存儲部分能量。當IGBT1關斷時,存儲在電感L1中的剩余能量通過D2轉(zhuǎn)移到超級電容器中。雙PI閉環(huán)控制策略用于調(diào)節(jié)IGBT的PWM占空比。由于電感線圈,續(xù)流二極管和濾波電容器的影響,直流/直流轉(zhuǎn)換器電流隨著IGBT周期性導通和關斷而成為脈動電流,但輸出電流保持連續(xù)平穩(wěn)。如果負載是電阻性的,輸出直流電壓也保持連續(xù)平穩(wěn)。 DC / DC轉(zhuǎn)換器保持逆變器直流母線的恒定電壓,而超級電容器電壓具有寬的變化范圍。
2.2 DC / DC轉(zhuǎn)換器的仿真和實驗結果
為了評估再生制動能量系統(tǒng)控制原理的有效性和可用性,分別在降壓和升壓運行條件下建立了DC / DC轉(zhuǎn)換器的系統(tǒng)PSIM仿真模型。升壓和降壓轉(zhuǎn)換器的仿真結果如圖1所示。圖3(a), 3(b)。結果表明,當前25 A時,超級電容器的電壓逐步上升或下降8 V。
電動機空載實驗在超級電容器的循環(huán)壽命期間進行。圖。圖4(a)?圖圖4(b)顯示了實驗結果,包括電機速度,電容器電流,直流母線電壓和超級電容器
電壓。數(shù)據(jù)顯示,在一個循環(huán)中,放電時間約為170秒,充電時間約為45秒。超級電容放電時,直流母線電壓約為570V,充電時為540V。超級電容器的最大電壓為300V,最小電壓為200V。如圖3(a)所示,超級電容器的放電電流比較平滑,因為電機是電阻的。
3矢量控制的PMSM
3.1 PMSM的數(shù)學建模
永磁同步電機(PMSM)由于功率密度高,效率高,轉(zhuǎn)矩慣量大,運行可靠等特點而得到廣泛應用。該PMSM工作在發(fā)電機或電機模式。操作模式由定子和轉(zhuǎn)子產(chǎn)生的磁場的旋轉(zhuǎn)速率偏差決定(電機模式為正,發(fā)電機模式為負)。本文討論的PMSM具有以下假設:核心飽和度和機器繞組漏電感被忽略;氣隙中的磁勢假定為正弦分布;磁場中的高次諧波可以忽略不計。根據(jù)坐標變換原理,數(shù)學PMSM的模型可以通過旋轉(zhuǎn)參考系(d-q參考系)中的這些方程表示:
3.2 SVPWM原理
空間矢量脈寬調(diào)制(SVPWM)技術廣泛應用于逆變器[20-21]。當定子通量空間矢量由三相正弦電壓提供時,定子磁通空間矢量以恒定的速度旋轉(zhuǎn)。同時,通量矢量的運動形成一個環(huán)形空間旋轉(zhuǎn)場。電壓矢量也是如此。當磁通矢量在空間中旋轉(zhuǎn)一段時間時,電壓矢量也沿著磁通圓的切線旋轉(zhuǎn)一段時間。因此,其軌跡與通量圓相符。 SVPWM是一種使用八個空間電壓矢量產(chǎn)生接近定子的磁通圓的技術電機的磁通圓??臻g矢量脈寬調(diào)制技術用于通過電壓源逆變器用計算出的定子電壓空間矢量激勵電機。本文采用空間矢量脈寬調(diào)制的兩個閉環(huán)矢量控制模型。圖。圖5給出了所提出的控制方案的框圖。
4系統(tǒng)結構
4.1能源管理戰(zhàn)略
電動葫蘆經(jīng)常用于施工。 如圖所示。 6,具有再生能量系統(tǒng)的電動葫蘆主要由超級電容器,DC / DC轉(zhuǎn)換器,編碼器,三相逆變器,PMSM,微處理器DSP,檢測系統(tǒng)和硬件保護組成。
編碼器檢測PMSM速度和方向。霍爾傳感器檢測超級電容器和直流母線的電壓,電流和溫度。微處理器DSP不僅調(diào)整降壓和升壓操作之間的DC / DC轉(zhuǎn)換器,還可以根據(jù)傳感器信號控制電機速度和方向。如果溫度或電流為自動,保護系統(tǒng)將自動切斷電路
電源管理策略如下:當負載下降時,電機作為發(fā)電機工作。在此過程中,如果超級電容器電壓小于300 V,則DC / DC轉(zhuǎn)換器將工作在降壓運行,并對超級電容器充電,直到超級電容器電壓高達300 V.然后超級電容器將被切斷,電阻制動將被采納。然而,在起重負載過程中,如果超級電容器電壓高于200 V,則DC / DC轉(zhuǎn)換器將在升壓操作中工作,并對超級電容器進行放電。但如果
超級電容器電壓小于200 V,電機將通過AC 380 V電源供電,以取代超級電容器作為能源。為了實現(xiàn)安全,可靠和高效的運行,超級電容器以各種恒定電流在20A下進行充放電,電壓范圍為200-300V。雙向DC / DC轉(zhuǎn)換器的工作模式取決于內(nèi)部超級電容器的能量和PMSM的工作站。
4.2再生制動系統(tǒng)仿真
為了評估這種再生制動系統(tǒng)的可行性,基于MATLAB / Simulink進行仿真,如圖7
電機電路采用直接轉(zhuǎn)矩控制(DTC)感應電機驅(qū)動,在調(diào)速時具有空間矢量脈寬調(diào)制。感應電動機是
由PWM電壓源逆變器饋電。速度控制回路使用PI控制器為DTC塊產(chǎn)生磁通和轉(zhuǎn)矩參考。 DTC塊計算
電機扭矩和通量估計并將其與各自的參考值進行比較。然后由獨立的PI調(diào)節(jié)器控制轉(zhuǎn)矩和通量,計算參考電壓矢量。然后通過空間矢量調(diào)制方法控制電壓源逆變器,以便輸出所需的參考電壓。
電氣系統(tǒng)還包含一個DC / DC轉(zhuǎn)換器。這里,DC / DC轉(zhuǎn)換器將超級電容器適配到直流母線。根據(jù)超級電容器內(nèi)部能量和PMSM工作狀態(tài),DC / DC轉(zhuǎn)換器可以作為升壓或降壓轉(zhuǎn)換器工作。
在t = 0時刻,電機轉(zhuǎn)速設定為1500轉(zhuǎn)/分鐘。然后,在t = 20s時,電動機施加-1 500 r / min的負參考速度斜坡。相應地,首先提起負載并且超級電容器放電。然后降低負載,并對超級電容器充電。超級電容器信號(電壓和電流),直流鏈路信號(電壓)和電機信號的仿真結果如圖1所示。 8, 9。
如圖。圖8(a)?圖如圖8(c)所示,當負載上升時,超級電容器的電壓從250V下降到200V。然后電壓保持恒定直到PMSM反向。
隨后,在負載下降的過程中,超級電容器電流約為10A,電壓開始上升,在t = 40s時達到244V。但是,如果降額時超高電壓電壓低于200 V時起升負載或高于300 V,則超級電容器將從直流母線斷開。
圖11顯示了實驗結果,包括電機轉(zhuǎn)速,直流母線電壓,瞬時電流和超級電容器在10A充放電電流下的實際電壓。如圖。如圖11所示,電機在前20秒內(nèi)以1500轉(zhuǎn)/分鐘運行,然后改變方向,速度升至1500轉(zhuǎn)/分鐘。當超級電容器充電時,逆變器直流母線的電壓為600V,超級電容放電時為570V負載越低,超級電容器的電壓從200V升高到232V,充電電流約為10 A.負載上升時,超級電容放電電流為-10A。
超級電容器的電位能方程如下:
載荷的重力勢能為G E = mgh,總機械效率為mh= 0.8。根據(jù)實驗結果,從機械能到電勢能的能量轉(zhuǎn)換效率為eh= 0.83。能量回收率為h= 0.65。圖。圖12示出了超級電容器的5A放電電流的實驗結果。從機械能到電位能的能量轉(zhuǎn)換效率為0.72。能量回收率為0.58。比較圖12,如圖11所示,回收能在10 A時比5 A.
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附錄2:外文原文
Regenerative Braking Strategy for Motor Hoist by Ultracapacitor
Abstract:Rising concern in environmental issues on global scale has made energy saving in powered equipment a very importantsubject. In order to improve the energy efficiency and driving range of a motor hoist, regenerative braking system is designed anddiscussed. The system takes a unique ultracapacitor-only approach to energy.storage system. The bi-directional bride DC/DC converterwhich regulates current flow to and from the ultracapacitor operates in two modes: boost and buck, depending on the direction of theflow. In order to provide constant input and output current at the ultracapacitor, this system uses a double proportional-integral (PI)control strategy in regulating the duty cycle of PWM to the DC/DC converter. The permanent magnet synchronous motor (PWSM)drive system is also studied. The space vector pulse width modulation (SVPWM) technique, along with a two-closed-loop vector controlmodel, is adopted after detailed analysis of PMSM characteristics. The overall model and control strategy for this regenerative brakingsystem is ultimately built and simulated under the MATLAB and Simulink environment. A test platform is built to obtain experimentalresults. Analysis of the results reveals that more than half of the gravitational potential energy can be recovered by this system.Simulation and experimentation results testify the validity of the double PI control strategy for interface circuit of ultracapacitor andSVPWM strategy for PMSM.
1 Introduction*
As issues of climate change and energy crisis aregathering more and more attention worldwide,industrialized nations have increased effort to reduce fossilfuel usage. One of the most significant steps in this effort isto change the power source of automobiles andconstruction vehicles from heat engines to variable speedmotors. Not only is the variable speed motor drive systemgenerally more efficient, it can also utilize electric powergenerated from renewable sources such as wind and solar.Variable speed motor drive does have technical problem ofits own, however: quick acceleration and deceleration inthe drive, as the application often requires, put the powersource under transient but large voltage fluctuations. Thecheap and easy solution is to add a braking resistor to theinverter DC link, but it leads to considerable waste. A morecommon and sophisticated solution is to incorporate an
energy storage system (ESS) into the system to absorb theenergy while braking andregenerate it when needed.Energy storage system[1–8] has seen applications inelectricvehicles (EV), hybrid electric vehicles (HEV) and plug-inhybrid electric vehicles.
Traditionally electrical ESS embraces a broad range oftechnologies and comes in a variety of forms, such aselectrochemical systems (e.g. batteries, flow cells), kineticenergy storage (e.g. flywheel) and potential energy storage(e.g. pumped hydroelectric, compressed air)[9].The development of ultracapacitor[10–12] has provided anattractive alternative for the next-generation pure-electricvehicles. Recent research results have proposed manmethods to use ultracapacitors in the regenerative brakingsystem. WEI and WANG[13] presented the performanceanalysis andcomparison of three kinds of typicalconfigurations to clarify the advantages and disadvantagesof different topologies. XU and XIE[14] devoted theirresearch into the voltage-equalization method for seriesultracapacitors in EV/HEV ESS. A new battery/
ultracapacitor hybrid energy storage system (HESS), usinga much smaller DC/DC converter to maintain the voltageof the ultracapacitor, was proposed by CAO and EMADI[15]for EV, HEV and plug-in HEV. YAN and PATTERSON[16]presented a novel power management scheme to achievehigh performance and cost reduction in an electric vehiclefor short profile fleet application. Zinc-bromine batteriesare employed to provide the continuous power for normaldriving while ultracapacitors are employed to provide forpeak power demand during acceleration and to stor regenerative braking energy during deceleration. The EV motor operates in constant torque mode at a speed belowthe base speed and in constant power mode at a speed over the base speed for high efficiency and low cost. AHMED and CHEMIELEWSKI[17] have built a model aimed at mimicking the load expected in a fuel cell vehicle, including a DC motor, DC/DC converters and a rechargeable battery for peak-shaving and regenerative braking. This model also includes the kinematics of the vehicle, and thus can be connected to standardized drive cycle scenarios. LU and CORZINE[18] introduced a new set of methods to directly integrate ultracapacitor banks into cascaded multilevel inverters that are used for large vehicle propulsion. The idea is to replace the regular DC link capacitors with ultracapacitors in order to combine the energy storage unit and motor drive. These researches have all demonstrated the using ultracapacitor as a viable supplementary storage device to batteries in hybrid vehicles to extend the battery life. Ultracapacitor has been considered as an auxiliary power source which can assist the fuel cell during startup and fast power transients of fuel-cell powered vehicles.
Currently there has been no documented research on ultracapacitor-based ESS applied to hoisting equipment. In this research, an ultracapacitor-only energy storage system for motor hoist will be adopted, which differs from the traditional vehicle regenerative braking system’s ultracapacitor/battery hybrid approach. The ultracapacitoronly energy storage system can simplify the circuit structure and expand the control bus greatly.
First, the control schemes for permanent magnet synchronous motor (PMSM) and DC/DC converter will be separately discussed. Then a DSP-based control system is developed based on the control strategy and digital signal processing technique. The overall system structure and control strategy are subsequently studied. An implementation scheme of the regenerative braking system has been developed and built for this experiment. At last, the simulation results and experimental results are compared and the efficiency of the entire energy recovery system is analyzed.
2 Ultracapacitor Energy Storage System
2.1 Control strategy of DC/DC converter
Ultracapacitor with the advantages of high charge rate, high efficiency, high power density, long cycle life, no maintenance[19], is preferred as the energy storage for motor hoist. The ultracapacitor as energy storage unit is integrated into inverter DC link through a DC/DC converter. The DC/DC converter can work as a boost or buck converter depending on input-output conditions.
Fig. 1 shows PSIM simulation model of the boost operation of the DC/DC converter. The boost operation isused for driving PMSM and discharging the ultracapacitor.
The IGBT2 is switched on and off at a controlled dutycycle, to transfer the required amount of energy from the ultracapacitor to the DC link. When IGBT2 is switched ON, energy is taken from the ultracapacitor and stored in the inductor L1. When IGBT2 is switched OFF, the energy Ultracapacitor with the advantages of high charge rate,
high efficiency, high power density, long cycle life, no maintenance[19], is preferred as the energy storage for motor hoist. The ultracapacitor as energy storage unit is integrated into inverter DC link through a DC/DC converter. The
DC/DC converter can work as a boost or buck converter depending on input-output conditions. Fig. 1 shows PSIM simulation model of the boost operation of the DC/DC converter. The boost operation is used for driving PMSM and discharging the ultracapacitor. The IGBT2 is switched on and off at a controlled duty cycle, to transfer the required amount of energy from the ultracapacitor to the DC link. When IGBT2 is switched ON, energy is taken from the ultracapacitor and stored in the
inductor L1. When IGBT2 is switched OFF, the energystored in L1 is transferred into DC link through D1. When discharges ultracapacitors, the converter is used as a stiff
voltage source to electric motor controller. The boost converter adjusts voltage automatically and then get asteady output voltage. To ensure that the ultracapacitor
works in a safe, reliable and high efficient condition,double PI closed-loop is adopted.
As shown in Fig. 2, the DC/DC converter works as abuck converter, which used for charging the ultracapacitor during regenerative braking. During the buck operation, the converter transfers energy from the DC link to the ultracapacitor. That operation is accomplished by a controlled operation on IGBT1. When IGBT1 is switched on, the energy goes from the link bus to the ultracapacitor, and inductor L1 stores part of this energy. When IGBT1 is switched OFF, the remaining energy stored in inductor L1is transferred into the ultracapacitor through D2. Double PI closed-loop control strategy is used for regulating the duty cycle of PWM of the IGBTs. The DC/DC converter currentbecomes pulsating current as IGBTs periodically turning on and off, however, the output current keeps continuous and smooth, owing to the effect of inductance coil, freewheeling diode and filter capacitor. If the load is resistive, the output DC voltage also keeps continuous and smooth. The DC/DC converter maintains constant voltage of the inverter DC link, whereas the ultracapacitor voltage has wide variation ranges.
2.2 Simulation and experiment results of the DC/DC converter
To evaluate the effectiveness and availability of the control principle of the regenerative braking energy system, the system PSIM simulation models of DC/DC converter are established under buck and boost operation condition respectively. The boost and buck converter simulation results are shown in Fig. 3(a) and Fig. 3(b) respectively. The results show that the voltage of ultra-capacitor step up or down 8 V per second at current 25 A.
The motor no-load experiment is carried out during a cycle-life of the ultracapacitor. Fig. 4(a)–Fig. 4(b) shows the experiment results, including the velocity of motor, theultracapacitor current, DC link voltage and ultracapacitor
voltage. The data shows that in a cycle, the discharging time is about 170 s and the charging time is about 45 s. The DC link voltage is about 570 V while ultracapacitor is discharged, and is 540 V when charged. The maximum voltage of the ultracapacitor is 300 V and the minimum voltage is 200 V. Compared with Fig. 3(a), the discharging current of the ultracapacitor is more smooth, because the motor is resistive.
3 Vector-Control for PMSM
3.1 Mathematical modeling of PMSM
Permanent magnet synchronous motor (PMSM) has been widely used due to its high power density, efficiency, high large torque-to-inertia ratio and reliable operation. The
PMSM operates in either generator or motor mode. The operation mode is dictated by the rotating rate deviation of the magnetic field generated by the stator and rotor(positive for motor mode, negative for generator mode).
The PMSM discussed in this paper has these assumptions: the core saturation and machine winding leakage inductance are ignored; the magnetic potential in the air gap is assumed to be in sine distribution; the higher harmonic wave in magnetic field is negligible. According to the coordinate tr
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