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小型風力發(fā)電機總體結(jié)構的設計 開題報告 班級（學號）：機0405-19 姓名：崔亮 指導老師： 許寶杰 一、綜述 1.課題研究的目的和意義 能源是發(fā)展國民經(jīng)濟和提高人民生活的重要物質(zhì)基礎，是經(jīng)濟發(fā)展的“火車頭”，能源已成為制約國民經(jīng)濟發(fā)展的重要因素。社會經(jīng)濟發(fā)展推動能源需求的持續(xù)增長，要求不斷開發(fā)新的能源。雖然，人類的技術進步旨在提高能源的利用效率、減少能源的消耗，但現(xiàn)今的能源生產(chǎn)量依然滿足不了人類發(fā)展的需求。由于對能源的渴求，人們無節(jié)制地開采石油、煤炭、天然氣等這些埋在地層深處的維系人類生存的“能源食糧”，不僅嚴重地污染了我們的生存空間，惡化了自然環(huán)境，而且?guī)砹烁膳碌膼汗茉纯萁?。傳統(tǒng)化石能源資源的減少，引發(fā)的石油危機和石油總體價格的攀升，已在向世人警示能源安全問題,引起對能源安全的廣泛擔憂?，F(xiàn)實告誡人們，要生存就必須尋求開發(fā)新能源。[1] 我國地域遼闊，廣大邊遠山區(qū)、沿海島嶼和少數(shù)民族地區(qū)地廣人稀、交通不便，利用大電網(wǎng)的延伸解決供電問題非常困難，而這些地區(qū)風力資源往往又比較豐富。充分利用這些地區(qū)的風力資源來解決無電、缺電問題，對改善當?shù)厝嗣竦纳钏?，發(fā)展地方經(jīng)濟具有深遠的意義。小型風力發(fā)電系統(tǒng)具有機組投資小，使用靈活，非常適用于解決居住相對分散、風力資源較好的無電地區(qū)居民的基本生活用電及部分小型生產(chǎn)用電問題。[2]小型風力發(fā)電技術作為農(nóng)村能源的組成部分，它的進一步推廣應用，將會推動農(nóng)村能源的發(fā)展，對于改善用能結(jié)構，特別是邊遠山區(qū)等的生產(chǎn)、生活用能，推動生態(tài)和環(huán)境建設諸領域的發(fā)展將發(fā)揮積極作用，具有廣闊的市場前景。[3] 風能具有隨機性和不確定性，風力發(fā)電系統(tǒng)是一個復雜系統(tǒng)。簡化小型風力發(fā)電系統(tǒng)的結(jié)構、降低成本、提高可靠性及實現(xiàn)系統(tǒng)優(yōu)化運行，具有重要的理論意義和實際應用價值。 2.課題的研究現(xiàn)狀及已有成果 風能的利用有著悠久的歷史。近年來,資源的短缺和環(huán)境的日趨惡化使世界各國開始重視開發(fā)和利用可再生、且無污染的風能資源。自80年代以來,風能利用的主要趨勢是風力發(fā)電。風力發(fā)電最初出現(xiàn)在邊遠地區(qū),應用的方式主要有:1)單獨使用小型風力發(fā)電機供家庭住宅使用;2)風力發(fā)電機與其它電源聯(lián)用可為海上導航設備和遠距離通信設備供電;3)并入地方孤立小電網(wǎng)為鄉(xiāng)村供電。[4] 風電場是由多臺并網(wǎng)型風力發(fā)電機組,并按一定規(guī)律排列組成的風力發(fā)電機群。每臺風力發(fā)電機組一般包括風力機、異步發(fā)電機和中間的傳動連接機構:輪轂、齒輪箱、連軸器。通常機端還有并聯(lián)電容器,提供異步發(fā)電機運行時所需的無功功率,以提高發(fā)電場的功率因數(shù)。[5] 1 風力機現(xiàn)代風力機從基本結(jié)構上分為兩類,即水平軸風機(HAWT)和立軸風機(VAWT),如圖1所示，這兩類風機都是利用空氣動力升力原理來獲取風能的。目前水平軸風機較多采用。水平軸風機輪轂上有三個或兩個風翼,也稱葉片。葉片用強化聚酯玻璃纖維、膠合板、鋁或鋼制造。[6] 風力機通過葉片捕獲風能,將風能轉(zhuǎn)換為作用在輪轂上的機械轉(zhuǎn)矩。風力機的特性通常用風能利用系數(shù)CP—尖速比λ曲線來表示,如圖2所示。不同漿距角β時,風能利用系數(shù)CP對應的尖速比λ不同。這里尖速比λ=ωmR/V,R為葉片半徑(m),ωm是風機的機械轉(zhuǎn)速(r/s),V是作用于風輪機的迎面風速(m/s)。對于同一CP,風輪機可能有兩個運行點,它們分別對應于風輪機的高風速運行區(qū)和低風速運行區(qū)。當風速變化時風輪機的運行點將要發(fā)生變化。 對一臺實際的風力機,其捕獲風能轉(zhuǎn)變?yōu)闄C械輸出功率Pm的表達式為 Pm= 0.5ρACPV3 式中 ρ——空氣密度,kg/m3 A——掃掠面積,m2 風力機的整體設計和相應的運行控制策略應盡可能追求CP最大,從而增加其輸出功率。然而實際應用中輸出功率的提高卻受到兩方面的限制:一方面是電氣回路中元器件的功率限制;另一方面是機械傳動系統(tǒng)元件存在轉(zhuǎn)速上限。因此風機存在三個典型運行狀態(tài):保證恒定CP,控制風力機轉(zhuǎn)速(維持λ不變)直到轉(zhuǎn)速達到極限;風力機以恒定速度運行,通過調(diào)節(jié)風力機可使CP具有較大數(shù)值,直到最大輸出功率;當風速過大,輸出功率達到極限時風力機按恒定功率控制,使輸出功率限制在額定值附近。[7] 2 風力機的功率調(diào)節(jié) 功率調(diào)節(jié)是風輪機的關鍵技術之一,目前投入運行的機組主要有兩類功率調(diào)節(jié)方式:一類是定漿距失速控制;另一類是變漿距控制。 1)漿距失速控制 風力機的功率調(diào)節(jié)完全依靠葉片的氣動特性,稱為定漿距風力發(fā)電機組。這種機組的輸出功率隨風速的變化而變化,從CP的關系看,難以保證在額定風速之前CP最大,特別是在低風速段。這種機組通常設計有兩個不同功率,不同極對數(shù)的異步發(fā)動機。大功率高轉(zhuǎn)速的發(fā)動機工作于高風速區(qū),小功率低轉(zhuǎn)速的發(fā)動機工作于低風速區(qū),由此來調(diào)整λ,追求最佳CP。當風速超過額定風速時,通過葉片的失速或偏航控制降低CP,從而維持功率恒定。實際上難以做到功率恒定,通常有些下降,如圖3所示。 2)變漿距控制 為了盡可能提高風力機風能轉(zhuǎn)換效率和保證風力機輸出功率平穩(wěn),風力機將進行漿距調(diào)整。在定漿距基礎上加裝漿距調(diào)節(jié)環(huán)節(jié),稱為變漿距風力機組。變漿距風力發(fā)電機組的功率調(diào)節(jié)不完全依靠葉片的氣動特性,它要依靠與葉片相匹配的葉片攻角改變來進行調(diào)節(jié)。在額定風速以下時攻角處于零度附近,此時,葉片角度受控制環(huán)節(jié)精度的影響,變化范圍很小,可看作等同于定漿距風機。在額定風速以上時,變漿距機構發(fā)揮作用,調(diào)整葉片攻角,保證發(fā)動機的輸出功率在允許范圍以內(nèi)。變漿距風力機的起動風速較定漿距風力機低,停機時傳動機械的沖擊應力相對緩和。風機正常工作時,主要采用功率控制。[9] 3 發(fā)電機 目前風力發(fā)電所采用的發(fā)電機主要有兩種:同步發(fā)電機和異步發(fā)電機。而采用最多的是籠型異步發(fā)電機?；\型異步發(fā)電機既可以孤立運行,也可以聯(lián)網(wǎng)運行。由于它的低耗、高可靠性、無需勵磁裝置和電刷、結(jié)構簡單尺寸小、堅固耐用、基本上無需維修,它已成為風力及其它發(fā)電系統(tǒng)的最理想設備。 異步發(fā)電機作為并網(wǎng)型發(fā)電設備的方案可分為兩類:恒速恒頻發(fā)電系統(tǒng)和變速恒頻發(fā)電系統(tǒng)。 1)恒速恒頻發(fā)電系統(tǒng) 恒速運行的風力機轉(zhuǎn)速不變,而風速經(jīng)常變化,因此葉尖比λ不可能經(jīng)常保持在最佳值(即使采用變漿距葉片),CP值往往與最大值相差很大,使風力機常常運行于低效狀態(tài)。恒速恒頻發(fā)電系統(tǒng)中,多采用籠型異步電機作為并網(wǎng)運行的發(fā)電機,在并網(wǎng)后其輸出功率在輸出功率P(或轉(zhuǎn)矩)與轉(zhuǎn)速n/ns曲線的穩(wěn)定區(qū)內(nèi)運行,如圖4所示。異步發(fā)電機的轉(zhuǎn)子速度高于同步轉(zhuǎn)速。當風力機傳給發(fā)電機的機械功率隨風速而增加時,發(fā)電機的輸出功率及其反轉(zhuǎn)矩也相應增大,運行點發(fā)生改變。當轉(zhuǎn)子速度高于同步轉(zhuǎn)速3%~5%時達到最大值,若超過這個轉(zhuǎn)速,異步發(fā)電機進入不穩(wěn)定區(qū),產(chǎn)生的反轉(zhuǎn)矩減小,導致轉(zhuǎn)速迅速升高,引起飛車,這是十分危險的。 異步發(fā)電機并網(wǎng)運行時,一方面向電網(wǎng)輸出有功功率,另一方面又必須從電網(wǎng)吸收落后的無功功率。異步發(fā)電機向電網(wǎng)輸出的電流大小及功率因數(shù),取決于轉(zhuǎn)差率及電機的參數(shù)。轉(zhuǎn)差率與異步發(fā)電機負荷的大小有關,電機的參數(shù)無法改變。[8] 風力發(fā)電機多采用機端并聯(lián)電容器以提高功率因數(shù),如圖5所示。運行中當發(fā)電機和并聯(lián)電容器與電網(wǎng)突然斷開時,電容器的過勵和異步發(fā)電機轉(zhuǎn)速上升可能引起有害的自勵現(xiàn)象。自勵產(chǎn)生的過電壓可能危及發(fā)電機和電容器的絕緣,必須予以重視。一方面應從最不利的過速情況來選擇電容器的電容量,另一方面在保護線路上要采取措施。 2)變速恒頻發(fā)電系統(tǒng) 雖然目前風力發(fā)電系統(tǒng)采用最多的異步發(fā)電機都屬于恒速恒頻發(fā)電系統(tǒng),但變速恒頻發(fā)電系統(tǒng)可以使風力機在很大風速范圍內(nèi)按最佳效率運行的重要優(yōu)點越來越引起人們的重視。從風力機的運行原理可知,這就要求風力機的轉(zhuǎn)速正比于風速保護并保持一個恒定的最佳葉尖比λ,從而使風力機的風能利用系數(shù)CP保持最大值不變,風力發(fā)電機組輸出最大的功率。例如目前已投入應用的一項變速技術是通過調(diào)節(jié)發(fā)電機轉(zhuǎn)子電流的大小和相位來追求CP最優(yōu)和輸出。[10] 二、研究內(nèi)容 小型風力發(fā)電機系統(tǒng)是一個典型的機電一體化系統(tǒng)。小型風力發(fā)電系統(tǒng)效率很高，但它不是只由一個發(fā)電機頭組成的，而是一個有一定科技含量的小系統(tǒng)：風力發(fā)電機＋充電器＋數(shù)字逆變器。風力發(fā)電機由機頭、轉(zhuǎn)體、尾翼、葉片組成。每一部分都很重要，各部分功能為：葉片用來接受風力并通過機頭轉(zhuǎn)為電能；尾翼使葉片始終對著來風的方向從而獲得最大的風能；轉(zhuǎn)體能使機頭靈活地轉(zhuǎn)動以實現(xiàn)尾翼調(diào)整方向的功能；機頭的轉(zhuǎn)子是永磁體，定子繞組切割磁力線產(chǎn)生電能。風機工作穩(wěn)定是一個非常重要的問題，通過回顧過去成功的小型風力發(fā)電機組的設計，就可以發(fā)現(xiàn)它們的共同特點是簡單，只有簡單才可能做到活動部件少，應力連續(xù)而無突變，才能使小型風力發(fā)電機工作穩(wěn)定。所以本課題是設計一款結(jié)構簡單、使用方便、成本低、易維修、使用壽命長的小型風力發(fā)電機。其研究內(nèi)容具體如下： (1) 小型風力發(fā)電機整體方案設計； (2) 進行小型風力發(fā)電機的機械裝配圖設計； (3) 對裝置的運動過程進行仿真計算分析； (4) 根據(jù)功能要求進行修改，進一步的優(yōu)化； (5) 恒速控制系統(tǒng)方案設計； (6) 試制原理模型裝置。 三、實現(xiàn)方法及其預期目標 本課題研制的是小型風力發(fā)電機總體結(jié)構設計，總體要求是結(jié)構簡單、使用方便、易維修、使用壽命長。在滿足功能要求的前提下，盡可能使發(fā)電機外型美觀、可靠性強、制造簡單、價格低廉。 目標：1.完成小型風力發(fā)電機組總體結(jié)構的設計方案并試進行模型驗證。 2.完成小型風力發(fā)電機恒速控制的系統(tǒng)設計方案。 該小型風力發(fā)電機的主體部分包括風輪、發(fā)電機、調(diào)向機構、調(diào)速機構和停車機構、塔架、蓄電池。具體如下： 1)風輪 用2～3個葉片組成,它把風能轉(zhuǎn)化為機械能。 2)發(fā)電機 采用永磁式交流發(fā)電機,風輪驅(qū)動發(fā)電機產(chǎn)生交流電,經(jīng)過整流后變成直流電儲存在蓄電池中?？刂破骱湍孀兤? 3)調(diào)向機構、調(diào)速機構和停車機構 為了從風中獲取能量,風輪旋轉(zhuǎn)面應垂直于風向,在小型風力機中,這一功能靠風力機的尾翼作為調(diào)向機構來實現(xiàn)。同時隨著風速的增加,要對風輪的轉(zhuǎn)速有所限制,這是因為既要防止過快的轉(zhuǎn)速對風輪和風力機的其他部件造成損壞。 在風速較大時,特別是蓄電池已經(jīng)充滿的情況下,應人工控制風力機停機。小型風力機中設計有手動剎車機構,在實踐中可采用側(cè)偏停機方式,即在尾翼上固定一軟繩,當需要停機時,拉動尾翼,使風輪側(cè)向于風向,從而達到停機的目的。 4)塔架 由塔管和3～4根拉索組成。 5)蓄電池 采用汽車用鉛酸電瓶,也可用近年來國內(nèi)開發(fā)出的適用于風能太陽能應用的專用鉛酸蓄電池。 6)控制器和逆變器 控制器的功能是控制和顯示風力機對蓄電池的充電,使其不至于過充放,以保證正常使用和整個系統(tǒng)的可靠工作。逆變器是把直流電(12 V、24 V、36 V、48 V)變成220 V交流電的裝置。 四、對進度的具體安排 1．第1-3周 調(diào)研，查閱資料，學習相關理論，研究總體方案。 2．第 4 周 撰寫并提交調(diào)研報告和開題報告； 3．第5-7周 確定總體方案，完成相關計算； 4．第8-11周 完成結(jié)構設計圖； 5．第12-15周 完成恒速控制系統(tǒng)方法的設計； 6．第16-17周 撰寫并提交畢業(yè)論文、審閱、評審并修改畢業(yè)論文； 7．第 18 周 完成畢業(yè)答辯。 五、參考文獻 1、　陳通漠. 世界風電20 年及發(fā)展趨向. 風力發(fā)電, 1999(3) . 2、　周篁. 馬勝紅1 世界風力發(fā)電簡況. 風力發(fā)電, 1999(4) . 3、 陳宗器.風力發(fā)電綜述與我國的開發(fā)設想.電機與控制學報.1997. (1) 4、　周小謙. 中國電力工業(yè)發(fā)展的前景. 中國電力, 1999,32(10) . 5、 符亞杰.淺談小型風力發(fā)電系統(tǒng).風力發(fā)電.2007.(8) 6、　肖勁松. 風力機組控制理論研究的現(xiàn)狀與展望. 風力發(fā)電, 2000(2) . 7、 牛山泉.三野正洋著.小型風車手冊.汪淑貞譯. 1987.34一36 8、 中國農(nóng)業(yè)機械化科學院主編.中國風力機圖冊[M].1983.234一240 9、 章瑋. 無刷雙饋電機電動狀態(tài)下的能量分析. 電機及控制學報, 2000(2) . 10、 潘文霞. 風力發(fā)電機的發(fā)展現(xiàn)狀.中小型電機. 2001,28(4) 指導老師： 年 月 日 督導老師： 年 月 日 領導小組審查意見： 審查人簽字： 年 月 日 Self-Excitation and Harmonics in Wind Power Generation E. Muljadi ， C. P. Butterfield National Renewable Energy Laboratory, Golden, Colorado 80401 H. Romanowitz Oak Creek Energy Systems Inc.,Mojave, California 93501 R. Yinger Southern California Edison,Rosemead, California 91770 Traditional wind turbines are commonly equipped with induction generators because they are inexpensive, rugged, and require very little maintenance. Unfortunately, induction generators require reactive power from the grid to operate，capacitor compensation is often used. Because the level of required reactive power varies with the output power, the capacitor compensation must be adjusted as the output power varies. The interactions among the wind turbine, the power network, and the capacitor compensation are important aspects of wind generation that may result in self-excitation and higher harmonic content in the output current. This paper examines the factors that control these phenomena and gives some guidelines on how they can be controlled or eliminated. 1．Introduction Many of today’s operating wind turbines have fixed speed induction generators that are very reliable, rugged, and low cost. During normal operation, an induction machine requires reactive power from the grid at all times. The most commonly used reactive power compensation is capacitor compensation. It is static, low cost. Different sizes of capacitors are generally needed for different levels of generation. Although reactive power compensation can be beneficial to the overall operation of wind turbines, we should be sure the compensation is the proper size and provides proper control. Two important aspects of capacitor compensation, self-excitation and harmonics ,are the subjects of this paper. 2．Power System Network Description A diagram representing this system is shown in Fig(1). The power system components analyzed include the following: ? An infinite bus and a long line connecting the wind turbine to the substation ? A transformer at the pad mount ? Capacitors connected in the low voltage side of the transformer ? An induction generator For the self-excitation, we focus on the turbine and the capacitor compensation only the right half of Fig. For harmonic analysis, we consider the entire network shown in Fig. 3. Self-Excitation 3.1 The Nature of Self-Excitation in an Induction Generator. Self-excitation is a result of the interactions among the induction generator, capacitor compensation, electrical load, and magnetic saturation. This section investigates the self-excitation process in an off-grid induction generator, knowing the limits and the boundaries of self-excitation operation will help us to either utilize or to avoid self-excitation. Fixed capacitors are the most commonly used method of reactive power compensation in a fixed-speed wind turbine. An induction generator alone cannot generate its own reactive power; it requires reactive power from the grid to operate normally, and the grid dictates the voltage and frequency of the induction generator. One potential problem arising from self-excitation is the safety aspect. Because the generator is still generating voltage, it may compromise the safety of the personnel inspecting or repairing the line or generator. Another potential problem is that the generator’s operating voltage and frequency may vary. Thus, if sensitive equipment is connected to the generator during self-excitation, that equipment may be damaged by over/under voltage and over/ under frequency operation. In spite of the disadvantages of operating the induction generator in self-excitation, some people use this mode for dynamic braking to help control the rotor speed during an emergency such as a grid loss condition. With the proper choice of capacitance and resistor load, self-excitation can be used to maintain the wind turbine at a safe operating speed during grid loss and mechanical brake malfunctions。 3.2 Steady-State Representation. The steady-state analysis is important to understand the conditions required to sustain or to diminish self-excitation. As explained above, self-excitation can be a good thing or a bad thing, depending on how we encounter the situation. Figure 2 shows an equivalent circuit of a capacitor compensated induction generator. As mentioned above, self-excitation operation requires that the balance of both real and reactive power must be maintained. Equation （1）gives the total admittance of the system shown in Fig(2): ++=0 （1） where = effective admittance representing the stator winding, the capacitor, and the load seen by node M = effective admittance representing the magnetizing branch as seen by node M,referred to the stator side = effective admittance representing the rotor winding as seen by node M, referred to the stator side Equation 1 can be expanded into the equations for imaginary and real parts as shown in Eqs.2and3: （2） Fig. 2 Per phase equivalent circuit of an induction generator under self-excitation mode Fig.3 A typical magnetization characteristic = stator winding resistance = stator winding leakage inductance = rotor winding resistance = rotor winding leakage inductance = stator winding resistance S = operating slip = operating frequency = load resistance connected to the terminals C = capacitor compensation =阻抗 One important aspect of self-excitation is the magnetizing characteristic of the induction generator. Figure 3 shows the relationship between the flux linkage and the magnetizing inductance for a typical generator; an increase in the flux linkage beyond a certain level reduces the effective magnetizing inductance . This graph can be derived from the experimentally determined no-load characteristic of the induction generator. The voltage at the terminals of the induction generator presented in Fig . （5） shows the impact of changes in the capacitance and load resistance. As shown in Fig. （5）, the load resistance does not affect the terminal voltage, especially at the higher rpm （higher frequency）, but the capacitance has a significant impact on the voltage profile at the generator terminals. A larger capacitance yields less voltage variation with rotor speed, while a smaller capacitance yields m ore voltage variation with rotor speed. As shown in Fig. 6, for a given capacitance, changing the effective value of the load resistance can modulate the torque-speed characteristic. These concepts of self-excitation can be exploited to provide dynamic braking for a wind turbine as mentioned above to prevent the turbine from running away when it loses its connection to the grid; one simply needs to choose the correct values for capacitance （a high value） and load resistance to match the turbine power output. Appropriate operation over a range of wind speeds can be achieved by incorporating a variable resistance and adjusting it depending on wind speed. 3.3 Dynamic Behavior. This section examines the transient behavior in self-excitation operation. We choose a value of 3.8 mF capacitance and a load resistance of 1.0 for this simulation. The constant driving torque is set to be 4500 Nm. Note that the wind turbine aerodynamic characteristic and the turbine control system are not included in this simulation because we are more interested in the self-excitation process itself. Thus, we focus on the electrical side of the equations. Figure 7 shows time series of the rotor speed and the electrical output power. In this case, the induction generator starts from rest. The speed increases until it reaches its rated speed. It is initially connected to the grid and at t=3.1 seconds （s）, the grid is disconnected and the induction generator enters self-excitation mode. At t=6.375 s, the generator is reconnected to the grid, terminating the self-excitation. The rotor speed increases slightly during self-excitation, but, eventually, the generator torque matches the driving torque （4500 Nm）, and the rotor speed is stabilized. When the generator is reconnected to the grid without synchronization, there is a sudden brief transient in the torque as the generator resynchronizes with the grid. Once this occurs, the rotor speed settles at the same speed as before the grid disconnection. Figure 8 (a) plots per phase stator voltage. It shows that the stator voltage is originally the same as the voltage of the grid to which it is connected. During the self-excitation mode 3.1 s0,Q>0. (c) Phasor diagram for P>0,Q <0. From Fig. 10, we can say that the circuit will resonate at different frequencies as the capacitor C is varied. Two harmonic components must exist to generate harmonics currents in the systems—a harmonic source (due to magnetic saturation as shown in Fig. 3) and a circuit that will resonate at certain levels of capacitance compensation. 4.3 Dynamic Simulation. Now consider how the harmonic sources are generated in the transformer. Most utility-size wind turbines are equipped with a pad-mount step-up transformer that connects them to the utility. When the transformer is saturated, the nonlinear characteristic of the magnetic circuit generates a nonsinusoidal current. Figure 11(a) shows the per-phase equivalent circuit of a transformer. The iron core loss of a transformer is usually represented as an equivalent resistance,, in parallel with the magnetizing reactance . In this study, the core loss is small enough to be neglected (i.e., the value of = represents an open circuit; thus, the equivalent resistance is not drawn in the equivalent circuit). The magnetizing flux linkage is proportional to the ratio of the voltage and the frequency: where = the magnetizing voltage = flux linkage = the base frequency = 磁化的電壓 The flux linkage of the transformer can be found from Eq.(7). The relationship between the flux linkage and the magnetizing inductance due to the magnetizing current is nonlinear. When the magnetizing current is low, the flux (and flux linkage) varies linearly with the magnetizing current, but eventually saturation is reached and the nonlinear characteristic starts; further increases in magnetizing current will produce smaller increases in the flux linkage. In the saturation region, the resulting output current will be nonsinusoidal , as shown in Fig. 12, due to the nonlinearity of the magnetizing inductance. Fig. 12 The output voltage and current of a transformer under light load condition There are two types of operation that can cause saturation. The first one occurs when the transformer operates at a higher voltage level. One example of this operation is when the transformer is lightly loaded. As a result, the magnetizing branch is exposed to a high voltage , producing a large magnetizing current in the magnetizing branch. The second type of operation that can result in high saturation is when the transformer is operated with a leading power factor (supplying reactive power to the grid Vs). The voltage across the magnetizing reactance (referred to the primary side) can be expressed as where =+ j= line impedance connecting the transformer to the voltage source VS = + j = primary winding impedance of the transformer == = resistance of the primary and secondary winding of the transformer == = leakage reactance of the primary and secondary winding of the transformer = voltage at the infinite bus = current flowing in the primary winding = reactance of the line = line resistance As an illustration, we can use the phasor diagrams shown in Figs. 11(b) and 11(c). For the case of simplicity in the phasor diagram illustrations, we can simplify the equivalent circuit shown in Fig. 11(a) as an ideal transformer with only its leakage reactance represented. In Fig. 11(a), the real power P and reactive power Q are considered to be flowing from the right to the left (positive values flow from the turbine to the grid). When P >0, Q<0 (the turbine generates real power but absorbs reactive power), then < , and we have normal operation. On the other hand, when P>0, Q>0 (the turbine generates both real and reactive power), then < and we may experience saturation. 22