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It has become an important task for many voltage stability studies to find avoltage stability index. The voltage stability indices provide reliable informationabout proximity of voltage instability in a power system. In this paper, the Lindicator has been proposed, which aims to detect the weakest load buses in theelectrical power networks. The L indicator has been checked by its application tothe (WSCC 9bus and IEEE 14bus) test systems. Finally, the proposed indicatorhas been applied to the Iraqi power grid (400 kV) considering differentcontingencies, such as lines outage, generated power reduction and loadingincrease. The short computation time of this indicator and its efficient detection ofthe weakest load buses in the Iraqi power grid, allow the operators to apply it in onlinevoltage stability monitoring based on measurements.
أن أيجاد دليل لأستقرارية الفولتية في العديد من الدراسات المتعلقة في أستقرارية الفولتية قدأصبح من المهام الضرورية. أن هذه الدلائل تعطي معلومات وثيقة عن مدى اقتراب نظام القدرةوالذي يهدف إلى ،(L indicator) من عدم أستقرارية الفولتية. في هذا البحث، تم اقتراح الدليلL ) الكشف عن قضبان الأحمال الضعيفة في شبكات القدرة الكهربائية. لقد تم التحقق من الدليلأخيراً، تم .(IEEE 14bus) و (WSCC 9bus) بتطبيقه على منظومتي الاختبار (indicatorتطبيق الدليل المقترح على شبكة القدرة العراقية فائقة الفولتية ( 400 كيلو فولت) مع أخذ بعضالحالات الطارئة بنظر الاعتبار كخروج خط نقل من الخدمة وحدوث نقص في توليد القدرة وزيادة الأحمال. أن زمن الحساب القصير لهذا الدليل وكفاءته في تشخيص العقد الضعيفة لشبكةالقدرة الكهربائية العراقية تتيح للمشغلين بتطبيقه لمراقبة أستقرارية الفولتية آنيا ً إعتماداً علىالقياسات.PDF created
Due to raise in demand, the transmission system becomes more exhausted, which in turn, forces the system to be more susceptible to voltage instability. The aim of this research is to study the enhancement in voltage stability margin by installation the SVC which is represented as Static of VAR Compensator or STATCOM that is represented as Static of Synchronous Compensator. Voltage stabilization dilemma considers an essential issue in the electric networks which may lead to a voltage collapse in electric power networks. Lindex has been used to predict and identify points of breakdown voltages in the power system with sufficient accuracy. L index has been employed due to its accuracy and effectiveness in the computing voltage collapse points for different load buses with sufficient precision at a short circuit and also at various loads situations. Voltage stability index has been tested on the 9wscc test system and 14IEEE test system .Then it has been applied to the Iraqi national grid 400 kV. A shunt facts(SVC or STATCOM) devices are installed individually at the weak bus bar based on Voltage Stability Index(L indicator) detection, The simulation results are first obtained for an uncompensated system, and the voltage profiles are studied. The results so obtained are compared with the results obtained after compensating the system with SVC and STATCOM to show the voltage stability margin enhancement. The outcomes acquired after simulation demonstrate the performances of shunt fact devices (SVC and STATCOM) when connected to a system Subjected to 3phase short circuit fault at different locations. All the simulation results have been carried out using MATLAB version 7.10 and Power System Analysis Toolbox (PSAT) package.
voltage stability  voltage collapse  voltage stability indices  L indicator  MATLAB and Power System Analysis Toolbox  PSAT.
Series compensation is frequently found on long transmission lines used to improve voltage stability. Due to the long transmission lines, voltage begins to decay as the line moves further from the source. Series compensation devices placed strategically on the line to increase the voltage profile of the line to levels near 1.0 p.u.. This paper presents a novel optimum location and optimum percentage compensation value of a series capacitor as a compensation method to enhance the voltage stability and loss reduction. The proposed method is applied to a 11bus power system.The load flow analysis using NewtonRaphson approach for the 11bus test system was designed and tested using MATLAB 7 programming language.
غالبا ما يتم استخدام التعزيز المربوط على التوالي عبر استخدام المتسعة في خطوط النقل وذلك لتحسين الفولتية. بسب المسافات الطويلة لخطوط النقل, فأن الفولتية تبدأ بالأنخفاض كلما ابتعدنا عن المصدر. ولأجل هذا يتم استخدام متسعات موزعة وفق حسابات لتحافض على الفولتية بمستوى 1 للوحدة الثابتة (p.u.). تم في هذا البحث استخدام الية مثلى لوضع او استخدام المتسعة لتحسين الفولتية ولتقليل الخسائر. حيث تم تطبيق الطريقة على منظومة أفتراضية عالمية ذات 11 عقدة (IEEE11BUS).تم استخدام طريقة الجريان نيوتن رافسون على هذه المنظومة وأستخدمت اللغة البرمجية .MATLAB 7
voltage stability  loss reduction  series capacitor  load flow
Abstract:The current paper aimed to present a computer simulation method to know the power system state which may be in case of voltage collapse, voltage instability or voltage stability by using eigenvalue analysis as well as identifying the weaken nodes in that power system using eigenvector analysis which is used to find the participation factor. The high participation factor values lead to the weaken nodes in the power system that required to treatment by installing shunt capacitors in those locations to improve the power system performance and reduce the losses power. The simulation results obtained by tested the proposed method on 30bus, 30 lines distribution system and the satisfied results are obtained. The simulation results showed the efficiency and flexibility of proposed algorithm. Proposed algorithm has been implemented using MATLAB language version (7.5).
المستخلصيهدف البحث الحالي الى تقديم طريقة محاكاة حاسوبية لمعرفة حالة منظومة القدرة والتي يمكن ان تكون في حالة أنهيار الفولتية أو في حالة أستقرار أوعدم أستقرار الفولتية بأستخدام تحليل (eigenvalue ) بالأضافة الى تحديد النقاط الأضعف في المنظومة والتي بحاجة الى معالجة بأستخدام تحليل (eigenvector ) الذي يستخدم لأيجاد معامل الأشتراك. قيم معامل الأشتراك العليا تشير الى النقاط الأضعف في المنظومة والتي يتطلب معالجتها بتنصيب متسعات التوازي في تلك العقد لتحسين أداء المنظومة وتقليل الخسائر فيها.وللحصول على نتائج عملية المحاكاة تم اختبار الطريقة المقترحة على منظومة توزيع قدرة كهربائية مؤلفة من (30) عمومي توصيل و (30 ) خط نقل وتم استحصال النتائج التي بينت كفاءة ومرونة الطريقة المقترحة. طريقت المحاكاة المقترحة بنيت بأستخدام برامجيات MATLAB7.5.
Abstract: This paper discusses the transient voltage stability of a synchronous generator at its bus in a power system with a detailed transient modeling for the generator after being subjected to a three phase fault, and designing a TakagiSugeno first order fuzzy logic controller with center of area defuzzification algorithm as a fuzzy logic controller based exciter to stabilize the terminal voltage and to damp its oscillations so as to keep the generator under balanced working conditions. The proposed exciter can be easily modified by changing the steady state field voltage value to be applied to any other synchronous generator. This paper also used the integral of square error as an indicator of the terminal voltage stability and monitored all of the generator variables specially the rotor angle to see whether the generator will maintain synchronism or not after the occurrence of the fault.
Voltage stability  Fuzzy controller  Exciter  Integral of square error.
AbstractThis paper presents an Optimal Power Flow (OPF) formulation that is based on multiobjective optimization methodology, which can minimize both of operating costs and losses and it would at same time result in maximizing the distance to voltage collapse. A “Maximum Distance to Voltage Collapse” algorithm, which incorporates constraints on the current operating condition, is firstly presented, while OPF formulations which incorporate voltage stability criteria is secondly presented. The algorithm built on MatlabSimulink is tested on an IEEE 6bus test system using a standard power flow model, where the effect of maximum loading point limits is demonstrated.
المستلخصيقدم هذا البحث صيغة لحل سريان الحمل بطريقة مثلى واعتمادا على أساسيات مهمة بحيث تكون كلفة التشغيل وخسائر النظام اقل ما يمكن وفي نفس الوقت يكون النظام بعيد عن انهيار الفولتية أي بأعلى استقرارية لها. أولاً تم استخدام خوارزمية حساب استقرارية الفولتية في ظروف التشغيل الحالية وبعيداً عن انهيار الفولتية. ثانياً استخدم خوارزمية لحل سريان الحمل بطريقة مثلى مع أعلى استقرارية للفولتية. استخدم برنامج MatlabSimulink لهذا التحليل مع التطبيق على نموذج نظام ذو ستة عقد مع الأخذ بنظر الاعتبار تأثير أقصى حمل.
13 1 2005Regional Referred Scientific JournalPublishedby the College of EngineeringMosul UniversityVolume 13 Number2 1 2005Abbas Fadheel DawoodFor Enquires write to Editor In Chief.ALRAFIDAIN ENGINEERINGCollege of Engineering / Mosul University/ MosulIRAQhttp://rafidain.5u.comEmail: rafiengg2004@yahoo.comThe views expressed in the issue are those of the authorsand do not reflect the views of the Editorial Board or thePolicy of the College of Engineering.Secretary:Professor Dr. Sabah Mohammed JamelDr. Sami Abdul MawjoudDr. Abdullah Y. TayibDr. Ahmed Khorsheed AlSulaifanieAlRafidain Engineering Vol. 13 No. 1 2005ENGLISH SECTIONCONTENTSNo. Title Page No.1. Vibrational characteristics of Rotating ShaftContaining a Transverse CrackByMohammed Jamel, S. , Al â Sarraf, Z.S. and ALRawi,M.N . . . . . . . . . . . 12. The Memorization Behaviors of different MIOSStructuresByMohamad , W.F. and Ali, L.S. . . . . . . . . . . . . . 173. Bifurcation and Voltage Collapse in the Electricalpower SystemsByAl Sammak, A.N.B. . . . . . . . 254. Performance of Outdoor MIMO System and Effectof Antenna SeparationByAbosh, A.M. â¦â¦..425. Characteristics of Flow Over Normal and ObliqueWeirs with semicircular CrestsByNoori, B.M.A and Chilmeran, T.A.H. â¦â¦â¦496. Coefficient of Discharge of Chimney Weir UnderFree and Submerged Flow ConditionsByHayawi, H.A.M., Yahya, A.A.g and Hayawi,G.A.M. 62Al_Rafidain engineering Vol.13 No.1 20051VIBRATIONAL CHARACTERISTICS OF A ROTATINGSHAFT CONTAINING A TRANSVERSE CRACKDr. SABAH MOHAMMED JAMELPROFESSORZIAD SHAKEEB ALSARRAF MOHAMMED NAJEEB ALRAWIASSISTANT LEACTURE ASSISTANT LEACTUREMechanical Engineering Department, College of Engineering, Mosul UniversityABSTRACT:The influence of a transverse crack upon the dynamic behavior of a rotatingshaft is studied. Introduction of such a crack results in lower transverse naturalfrequencies due to the added local flexibility. The strain energy release function isrelated to the compliance of the cracked shaft that is to the local flexibility due tointroduction of crack. This function is related to the stress intensity factor, which fortransverse of a shaft with a crack has a known expression. As a result, the localflexibility of the shaft due to the presence of the crack has been computed. This result,can be further utilized to yield the dynamic response of a shaft with complex geometry.Starting from the equation of motion for the shaft under bending to derive theexpression of calculating the natural frequency of the shaft.Two cases of fixing the shaft are suggested in this study to investigate andanalyze the vibration characteristics of the shaft with and without cracks. Thefundamental natural frequency showed strong dependence on the crack depth, Thisdependence is smaller as the order of the frequency increase. Experimental results are inclose agreement with those practical from the theoretical analysis. Finally, the resultsshowed that the change in dynamic response due to the crack is high enough to allowthe detection of the crack and estimation of its magnitude.Ø§ÙØµÙØ§Øª Ø§ÙØ§ÙØªØ²Ø§Ø²ÙØ© ÙÙØ¹Ù ÙØ¯ Ø§ÙØ¯ÙØ§Ø± Ø§ÙÙ ØªØ¶Ù Ù Ø´ÙÙØ§ Ù Ø³ØªØ¹Ø±Ø¶ÙØ§Ø£.Ø¯. ØµØ¨Ø§Ø Ù ØÙ Ø¯ Ø¬Ù ÙÙ Ù ÙØ§ Ø¹ÙÙØ§ÙØ³ÙØ¯ Ø²ÙØ§Ø¯ Ø´ÙÙØ¨ Ø¹Ø¨Ø¯ Ø§ÙØ¨Ø§ÙÙ Ø§ÙØµØ±Ø§Ù Ø§ÙØ³ÙØ¯ Ù ØÙ Ø¯ ÙØ¬ÙØ¨ Ø¹Ø¨Ø¯ Ø§ÙÙÙ Ø§ÙØ±Ø§ÙÙÙ Ø¯Ø±Ø³ Ù Ø³Ø§Ø¹Ø¯ Ù Ø¯Ø±Ø³ Ù Ø³Ø§Ø¹Ø¯ÙÙ ÙØ°Ø§ Ø§ÙØ¨ØØ« ØªÙ Ø¯Ø±Ø§Ø³Ø© ØªØ£Ø«ÙØ± Ø§ÙØ´Ù Ø§ÙØ¹Ø±Ø¶Ù Ø¹ÙÙ Ø§ÙØ³ÙÙÙ Ø§ÙØ¯Ø§ÙÙÙ ÙÙÙ ÙÙØ¹Ù ÙØ¯ Ø§ÙØ¯ÙØ§Ø±. Ø§Ø¨ØªØ¯Ø§Ø¡ÙØ§ Ù Ù Ù Ø¹Ø±ÙØ©Ø§Ù ÙØ¬ÙØ¯ Ø§ÙØ´Ù ÙÙ Ø§ÙØ¹Ù ÙØ¯ ÙÙÙÙ Ù Ù ÙÙÙ Ø© Ø§ÙØªØ±Ø¯Ø¯Ø§Øª Ø§ÙØ·Ø¨ÙØ¹ÙØ© Ø§ÙØ¹Ø±Ø¶ÙØ© Ù Ù Ø®ÙØ§Ù ÙØ¬ÙØ¯ Ø§ÙÙ Ø±ÙÙØ© Ø§ÙÙ ÙÙØ¹ÙØ© Ø§ÙÙ ØªÙÙÙØ©Ø¨Ù ÙØ·ÙØ© Ø§ÙØ´Ù . ÙÙ Ø§ Ø§Ù Ø¯Ø§ÙØ© Ø·Ø§ÙØ© Ø§ÙØ§ÙÙØ¹Ø§Ù Ø§ÙÙ ØªØØ±Ø±Ø© ÙØ§ÙÙ ØªØ¹ÙÙØ© Ø¨Ù ÙØ·ÙØ© Ø§ÙØ´Ù Ù Ù Ø®ÙØ§Ù Ù Ø·Ø§ÙØ¹Ø© Ø§ÙØ´Ù ÙÙØ¹Ù ÙØ¯Ø§ÙØ¯ÙØ§Ø± Ø®ÙØ§Ù ÙØ¬ÙØ¯ Ø§ÙÙ Ø±ÙÙØ© Ø§ÙÙ ÙÙØ¹ÙØ© Ø ÙØ¥Ù ÙØ°Ù Ø§ÙØ¯Ø§ÙØ© Ù Ø±ØªØ¨Ø·Ø© Ø¨Ù Ø¹Ø§Ù Ù Ø´Ø¯Ø© Ø§ÙØ§Ø¬ÙØ§Ø¯ ÙØªØ¹Ø¨ÙØ± ÙÙØ¬ÙØ¯ Ø§ÙØ´Ù Ø§ÙØ¹Ø±Ø¶Ù. ÙØ°Ø§ ÙÙØ¯ ØªÙ ØØ³Ø§Ø¨ Ø§ÙÙ Ø±ÙÙØ© Ø§ÙÙ ÙÙØ¹ÙØ© ÙÙØ¹Ù ÙØ¯ Ø®ÙØ§Ù Ù ÙØ·ÙØ© Ø§ÙØ´Ù . ØÙØ« Ø§Ù Ø§ÙÙØªØ§Ø¦Ø¬ Ø§ÙØªÙ ØªÙ Ø§ÙØØµÙÙ Ø¹ÙÙÙØ§ ÙÙ ÙÙØ§ÙØ§Ø³ØªÙØ§Ø¯Ø© Ù ÙÙØ§ ÙÙ ØªØØ¯ÙØ¯ Ø§ÙØ§Ø³ØªØ¬Ø§Ø¨Ø© Ø§ÙØ¯Ø§ÙÙÙ ÙÙÙØ© ÙÙØ¹Ù ÙØ¯ Ø°Ø§Øª Ø§ÙØªØ±ÙÙØ¨ Ø§ÙÙ Ø¹ÙØ¯ .Ø§Ø¨ØªØ¯Ø§Ø¡ÙØ§ Ù Ù Ù Ø¹Ø§Ø¯ÙØ© Ø§ÙØØ±ÙØ© ÙÙØ¹Ù ÙØ¯ Ø§ÙÙ ØªØ¹Ø±Ø¶ ÙÙØ§ÙØÙØ§Ø¡ ÙÙØ¯ ØªÙ ØªØÙÙÙ ÙØØ³Ø§Ø¨ Ù Ø¹Ø§Ø¯ÙØ© Ø§ÙØªØ±Ø¯Ø¯ Ø§ÙØ·Ø¨ÙØ¹ÙÙØ¸Ø±ÙÙ ØªØ«Ø¨ÙØª Ø§ÙØ¹Ù ÙØ¯ . ÙÙØ¯ Ø§Ø¹ØªÙ Ø¯Øª Ø§ÙØ¯Ø±Ø§Ø³Ø© Ù Ù Ø®ÙØ§Ù Ø§Ø®Ø° ØØ§ÙØªÙÙ ÙØªØ«Ø¨ÙØª Ø§ÙØ¹Ù ÙØ¯ ÙÙ Ù Ø«Ù Ø¯Ø±Ø§Ø³Ø© ÙØªØÙÙÙB & K ) Ø§ÙØµÙØ§Øª Ø§ÙØ§ÙØªØ²Ø§Ø²ÙØ© ÙÙØ¹Ù ÙØ¯ ÙÙ ØØ§ÙØ© ÙØ¬ÙØ¯ ÙØ¹Ø¯Ù ÙØ¬ÙØ¯ Ø´Ù ÙØ°ÙÙ Ø¨Ø§Ø³ØªØ®Ø¯Ø§Ù Ø¬ÙØ§Ø² Ù ØÙÙ Ø§ÙØ§ÙØªØ²Ø§Ø²Ø§ØªÙØªØÙÙÙ Ø§ÙÙ ÙØ¬Ø§Øª Ø§ÙØ§ÙØªØ²Ø§Ø²ÙØ© ØÙØ« Ø¨ÙÙØª Ø§ÙÙØªØ§Ø¦Ø¬ Ø£Ù Ø§ÙØªØ±Ø¯Ø¯ Ø§ÙØ·Ø¨ÙØ¹Ù Ø§ÙØ§Ø³Ø§Ø³Ù ÙØ¹ØªÙ Ø¯ Ø¨Ø´ÙÙ ÙØ¨ÙØ± (Type 2515Ø¹ÙÙ Ø¹Ù Ù Ø§ÙØ´Ù ÙÙØ°Ø§ Ø§ÙØ§Ø¹ØªÙ Ø§Ø¯ ÙÙÙ ÙÙÙ Ø§ Ø²Ø§Ø¯Øª ÙÙÙ Ø© Ø§ÙØ£Ø³ ÙÙØªØ±Ø¯Ø¯ ÙÙØ³Ù .Ø¨ÙÙØª Ø§ÙÙØªØ§Ø¦Ø¬ Ø£Ø®ÙØ±ÙØ§ Ø£Ù Ø§ÙØªØºÙØ± ÙÙ Ø§ÙØ§Ø³ØªØ¬Ø§Ø¨Ø© Ø§ÙØ¯Ø§ÙÙÙ ÙÙÙØ© Ø®ÙØ§Ù ÙØ¬ÙØ¯ Ø§ÙØ´Ù ÙØ¹Ø¯ ÙØ§ÙÙÙØ§ ÙÙ Ø§ÙÙØ´Ù ÙØªÙØ¯ÙØ±ÙÙÙ Ø© Ø§ÙØ´Ù .Submitted 20 th Feb. 2004 Accepted 4th Jan 2005Al_Rafidain engineering Vol.13 No.1 20052NOMENCLATURE:A Crosssection area of the shaft (m2)a Crack depth (mm)C Local flexibility (Compliance) (m/N)C1, C2, C3, C4 ConstantCw Wave velocity (m/sec)D Diameter of the shaft (mm)E Young modulus of elasticity (N/m2)I Second moment of area (m4)KIII Stress intensity factorL Length of the shaft (m)M Bending moment (N.m)P(x) Uniform load (N)R Radius of the shaft (mm)r Distance to the crackT Torque (N.m)V Shear force (N)Î½ Poissonâs ratioX Displacement (mm)Y Deflection (mm)Greekn Î² Frequency factorÏ Density (kg/m3)Ï Frequency with crack (HZ)o Ï Frequency without crack (HZ)n Ï Natural Frequency (HZ)1. INTRODUCTIONSince the midseventies the dynamic behavior of cracked shaft has beeninvestigated increasingly because damages in turbines, generators, pumps, and othermachines occurred quite often. This caused costly shutdowns of entire plants and wassometimes followed by the total loss of the machine. Fracture of a shaft which meanscrack are originated at points of stress concentration either inherent in design orintroduced during fabricate on or operation.Cracks defined as micro or macro interrupt the continuums are in principleunavoidable. Also the initiation occurs during the vibration especially when the shaft isunbalance or misalign [1].Singularity in elastic structure can introduce their dynamic behavior. Jones andOâDonnnell [2] showed that axisymmetric solids have considerable local flexibility attheir junctures. Cracks are associated with local flexibilities that can introduceconsiderable local flexibilities, which influence considerably the dynamic response ofAl_Rafidain engineering Vol.13 No.1 20053the structure. Such analyses have been reported for turbine vanes [3], welded plates [4]and for framed structures [5]. It was shown experimentally that changes in naturalfrequencies due to cracks can be safely detected in certain machines and structures andtheir magnitude can be estimated. Cracks often appear in a variety of machinery.2. LOCAL FLEXIBILITYSih and Loeber [6,7] studied the somewhat similar problem of transverse wavescattering about a pennyshaped crack. They studied the scattering of a given wave dueto the pennyshaped crack by way of the field equation solved by a finite Hankeltransform. Although the same procedure could be used for problem at hand, and theenergy method was utilized, based on the wealth of data existing for the strain energyrelease function. Also by using the vibration analyzer devise to calculate the frequencyof the shaft then to make a relation between the change in frequency with thecompliance.A transverse crack of depth (a) is considered on a shaft of radius (R). The shafthas local flexibility due to crack; itâs depending on the direction of the applied forces.We considered just only bending deformation, and the axial force which give couplingwith transverse motion of the cracked shaft will not considered here, also shear stressare not considered. Therefor the shaft is bent by a pure bending moment.The strain energy in the shaft due to a torque T is2T 2C U = (1)where C is the local flexibility (compliance) of the shaft due to crack.2( )121 2a R aT CAG Uâ ââ=ââ=Ï (2)Hertzberg [8] suggested that by measuring the flexibility of a test specimen or acomponent model, with various crack depth (a), the value of the gradientaCââ as functionof (a) could be determined, leading to the determination of the strain energy releasefunction. Miller [9] demonstrated that the energy release rate G could be related to thestress intensity factor K as2Î¼2III G = K (3)Where Î¼ is the shear modulus and the mode III stress intensity factor III K is defined bythe relationAl_Rafidain engineering Vol.13 No.1 2005402sin2( ) terms of order rrKIII + + â¥â¦â¤â¢â£= â¡Î¸ÏÏ (4)Giving the shear stresses in the vicinity of the crack at distance (R) from its tip.Equation (2) and (3) yield2( ) 22R aTKdadC = III Ï âÎ¼ (5)Integrating= â« âaIII R a daTC K0222(Ï )Î¼ (6)An expression is needed for the stress intensity factor III K for the problem athand. For a shaft with a crack Bueckner [10] has outlined a method for thedetermination of K as a function of the crack depth. Benthem and Koiter [11] haveapproximated the stress intensity factor K for a solid cylinder with a crack through thefollowing expression: â¥â¦â¤â¢â£= â¡ + 2 + 2 + 3 + 4 + 20.208 521128351658321 18K 3 Î» Î» Î» Î» Î» Î» (7)where Î» = (R  a) /R, Fig. 1.Fig 1. Geometry of a shaft with a transverse crackThe dimensionless stress intensity factor K is defined by the relationR ra R aR aK T2( ) 1( )2 1/ 23 â¥â¦â¤â¢â£â¡ ââ=ÏÏ (8)Therefore, comparison with equation (4) yields2RaAl_Rafidain engineering Vol.13 No.1 20055KRa R aR aK T III1/ 23( )( )2â¥â¦â¤â¢â£â¡ ââ=Ï (9)The flexibility ( C ) in dimensionless form becomesâ« ââ=aK a daR aRRR aRaRR C0233 5( )( )1 2( )4Ï Î¼ Ï(10)The integral has the value3. EQUATION OF MOTIONIn order to find the special function of the natural frequency of the shaft itshould be calculate the equation of motion that representing the analysis of the shaftunder the shear and bending effects, then to find the deflection of the shaft. A horizontalshaft is used with a length (L), and a uniform distributed load P (x) on the whole shaft.This accomplished by take a segment from the shaft in order to study the force effect.Fig. 2.Fig 2. Effect of Forces on the rotating shaftWe assume that the bending moment of the shaft is M (x,t) and the shear force isV (x,t), then the segment have a displacement (x) from the left end and have a length(dx). By taking the summation of the forces in the vertical direction equal to zero.V + Pdx â (V + dV ) = 0 (11)0.0017(1 / ) 0.008(1 / ) 0.0920.0086(1 / ) 0.0044(1 / ) 0.0025(1 / )0.035(1 / ) 0.01(1 / ) 0.029(1 / )7 93 4 64 2+ â + â â+ â + â + â= â â + â + â +a R a Ra R a R a RC a R a R a RM(x,t) M(x,t) +dM(x,t)/dxV(x,t) V(x,t) +dV(x,t)/dxP(x,t)dxxy(x,t)Al_Rafidain engineering Vol.13 No.1 20056And the summation of the moments applied on the shaft equal to zero.M â (M + dM) +Vdx = 0 (12)From the equation (11) and (12), we get22 ( , ) ( , )xP x t M x tââ= (13)From the strength of materials [12], the following relation ship is derivedbetween the elastic curve (curvature) and bending moment, and also bending stiffness(EI) of the shaft as below.EIMR1 =(14)After applying the equation above we get the function of fourth order as,44 ( , ) ( , )xP x t EI y x tââ= (15)Depending on the Newtonâs second law the equation (15) written as22 ( , ) ( , ) ( )tP x t A x dx y x tââ= Ï (16)where Ï = density of the shaft metalApplying Equation (16) and (15) in equation (13), get2244 ( , ) ( ) ( , ) ( , ) ( )tP x t A x dx y x txEI x y x tââ= âââÏ (17)For the case of the free vibration, P (x,t)=0. Then equation (17) may be written as( , ) ( , ) 022442 =ââ+ââty x txC y x t w (18)AC EI w Ï= (19)where w C =Wave velocityAl_Rafidain engineering Vol.13 No.1 20057Initial conditionsSince, equation (18) involves a second order derivative to time and a fourth orderderivative with respect to (x), two initial conditions and four boundary conditions areneeded for finding a solution. This is accomplished by using the separation of variablestechnique.Let a function y (x,t) be the product of two separate functions, one with respectto (x) and the another with respect to (t).y(x,t) (x).g (t) n n =Ï (20)now,( ) . ( )2222xtg ttynn Ïââ=ââ(21)( ) . ( )4444g txxxynnââ=ââ Ï(22)Substitution in equation (18), to get. ( ) 0( ). ( )( )22442 =ââ+ââxtg t g txC x nnnnw ÏÏ(23)22242 4 ( )( )( ) 1( ) nnnnnwtg tx g txxC ÏÏÏ= âââ=ââ(24)( ) 0( ) 444â =ââxxxn nn Î² ÏÏ(25)where , 224wnn CÏÎ² =then the general solution becomey(x,t) C cosÎ²x C sinÎ²x C coshÎ²x C sinhÎ²x 1 2 3 4 = + + + (26)where C1, C2, C3, C4 constants, and the natural frequency is given by:Al_Rafidain engineering Vol.13 No.1 2005842ALEIn nL ÏÏ = Î² (27)4. THEORETICAL AND EXPERIMENTAL INVESTIGATIONThe research contributes a study on a model of two cases of fixing end conditionof rotating shaft to analysis the vibration behavior and effect on the dynamiccharacteristics with and without a crack, and also to find the change of local flexibility(compliance).The First Case:(Fixed simply supported shaft)The shaft is fixed to the left end and the other end is simply supported Fig. 3.The shaft used in this study, had a diameter (D=8 mm), and a length is (L=0.6m),density ( Ï =7800 Kg/m3), the Young modulus (E=207*109 N/m2), second moment ofarea (I=Ï*D4/64 m4), and Frequency factor ( nL1 Î² =3.926602)[3].Fig 3. Model of the first state of fixing the shaftFirst the value of the natural frequency of the shaft from equation (27) wascalculated, In case of no crack. Then the calculation repeated experimentally to find thenatural frequency of the rotating shaft, by means of vibration analyzer (B & K Type2515) to investigate the vibration characteristics of shaft.Second, it is used equation (10) to find the local flexibility of the shaft andchange this property by increasing the depth of crack, and effect this on the vibrationresponse of the shaft. Then in order to find the values of frequency due to cracktheoretically, we can put the values get from equation (10) in the relation between thelocal flexibility (C) and change in natural frequency with and without a crack [13].L R2 R1M W(N/m)xAl_Rafidain engineering Vol.13 No.1 20059â¥ â¥ â¥ â¥ â¥â¦â¤â¢ â¢ â¢ â¢ â¢â£â¡ââ ââ ââ âââ= 1 12oDC LÏÏExperimental model Fig. 4 is accomplished where a D.C Motor throughcoupling connects the shaft to the left is made for this purpose, and pinned to the rightend by use bracket. The speed of shaft must be controlled by using voltage variabletransformer (shown below) how give the range between (0250) volts. The calculationof frequency was taken using a portable vibration analyzer (B & K Type 2515) toinvestigate the vibration spectrum of rotating shaft with and without crack. Thevibration signal was received from the accelerometer that put contact to the near pointof the rotating shaft (the accelerometer was fixed on the bearing of shaft). Thentransform to the vibration analyzer to analysis by using (F.F.T.) relation, and the outputshown by the digital monitor screen of the vibration device.Fig 4.Experimental model of the shaftThe experimental result is plotted in Fig. 5.Vs the theoretical function. In theexperiment, shafts were firstly examined by calculating the natural frequency andinvestigate the vibration dynamic behavior. After that the crack was made by means ofsawcut which is supported transversely to the center of the shaft, also the depth ofcrack in this study is taken between (a/D = 0  0.75).Al_Rafidain engineering Vol.13 No.1 200510Fig 5.Frequency drop vs crack depth ratioDue to figure above the measured value of the frequency change Ï /Ï o againstthe relative crack depth is done, here Ï is the transverse natural frequency with thecrack and o Ï the same frequency without the crack. There will be some deferencebetween the theoretical and experimental results of change of natural frequency withcrack depth ratio.So this is normally because due to experimental part there is some parametereffect to the frequency like the effect of rotation speed of the shaft, the accuracy ofcrack depth. Also in case of low lubrication of the shaft and bearings then the frictionoccurred and causes change in frequency values, in spite of the fixing of accelerometerto the near point of the rotating shaft. All these points will causes some differencebetween the theoretical and experimental results, but on the other side the experimentalresults are in close agreement with the theoretical.The Second Case:(Fixed simply supported shaft with a concentrated load at the center)The shaft is fixed to the left end and the other end is simply supported to theright but with concentrated load (rotor disk) at the center Fig. 6. The shaft was used inthis study, with diameter (D=8 mm), and a length is (L=0.6,0.5,0.4m), density ( Ï =7800Kg/m3), the Young modulus (E=207*109 N/m2). The disk have a mass (m=0.139 Kg)and the density of disk ( Ï =2770 Kg/m3), the second moment of area (I=Ï*D4/64 m4),Frequency factor ( nL1 Î² =3.926602).0.0 0.2 0.4 0.6 0.8 1.0(a/ D)0.900.920.940.960.981.001.02(Ï/ÏÎ¿)D=8 mmL=600 mmPresent Work (Theoritical)Present Work (Experimental)(TheoreticalAl_Rafidain engineering Vol.13 No.1 200511Fig 6. Model of the second state of fixing the shaftAs in the first case, we calculate the value of the natural frequency of the shaft incase of no crack and no concentrated load; this is accomplished by using equationsmentioned before. Then we repeat it after fixing the disk in the middle of shaft length,then make a crack near the disk position and calculate the change of frequency due tovariable crack depth Fig. 7. Using three lengths of shaft (0.6,0.5,0.4m) does this and themass of disk is (0.139 Kg).Second we calculate experimentally the value of the natural frequency of theshaft and change this value in case of no crack, no load (disk) and with disk and crackfor three length of shaft as in Fig. 8.The theoretical and experimental results of figures(7,8) below show a good close in values, and there will be some difference because dueto experimental part of the effect of rotation speed of the shaft, and the accuracy ofcrack depth. Also the fixed of the accelerometer to the near point of the rotating shaft.All will exhibit some change in values in comparison with theoretical results.Fig 7.Effect the crack and the load (disk)On the change of frequency (Theoretical)L/2 R R 2 1MW(N/m)xL/2W1350 400 450 500 550 600 650Length (mm)406080100120140160180Frequency (Hz)Theoriticalm1=0.139 KgPerfect ShaftWith a DiskWith a Disk & CrackTheoreticalAl_Rafidain engineering Vol.13 No.1 200512Fig 8. Effect the crack and the load (disk)On the change of frequency (Experimental)5. THE COMPLIANCE (LOCAL FLEXIBILITY)To find the local flexibility of the rotating shaft theoretically, we used equation(10) to find the local flexibility of the shaft and note this change of property byincreasing the depth of crack and effect this on the vibration response of the shaft.In this work it suggest the range of crack depth between (00.75 a/D) then putthese values in equation (10) was derived before, in order to find the change offlexibility due to increasing crack. In experiment we used the relation between the localflexibility (C) and change in natural frequency with and without a crack [13]. Fig. 9.Fig 9. Theoretical against Experimental results forThe dimensionless crack depth against local flexibility350 400 450 500 550 600 650Length (mm)406080100120140160180Frequency (Hz)Experimentalm1=0.139 KgPerfect ShaftWith a DiskWith a Disk & Crack1E3 1E2 1E1 1E+0 1E+1 1E+2 1E+3Local Flexibility (C)0.00.10.20.30.40.50.60.70.80.91.01.11.2(a / D)Theoritical WorkExperimental WorkTheoreticalW kAl_Rafidain engineering Vol.13 No.1 200513From the results of change of frequency and equation (10) the cracked shaftlocal flexibility (compliance) was computed and entered in figure above, as a functionof the crack depth. At small crack depths (a/D) there is a considerable discrepancybetween theoretical and experimental results which was to be expected due to thedifficulty in accurate measurement of small frequency differences which appear forcracks with (a/D) in the range (00.4).The dimensionless Local flexibility functions, equation (10) are plotted In Fig.10. As in figure below,Fig 10. Dimensionless Flexibility of the Cracked ShaftIn Bending, and In TensionThey observed the difference between the values of flexibility that calculatedfrom the equation (10) theoretically and compare it by the values contributed byDimarogonas [13] who study the compliance of the stationary cracked shaft with opencrack.The results showed the variable in points were gets from analytical solutionbecause in this study the shaft was under bending only and other property was neglected.So these assumptions will leads to some difference between the two studies, but theyhave the same behavior in changing the local flexibility due to the crack depth ratio.6. DISCUSSIONThe natural frequency of a rotating shaft found to be considerably influenced bythe presence of a transverse crack. The quantitative evaluation of this effect based onthe derivation of an equation of motion to derive the formula of calculating the naturalfrequency of the rotating shaft. Also it is depending on the strain energy function to getthe integral relation between the local flexibility and the stress intensity factor.By the present method, it is notice from the curves mentioned above that thenatural frequency of the rotating shaft will be decreased by increasing the depth of crack1E3 1E2 1E1 1E+0 1E+1 1E+2 1E+3Local Flexibility (C)0.00.10.20.30.40.50.60.70.80.91.01.11.2(a / D)Theoritical Work Bending)Dimarogonas (Tension)Theoretical Work (Bending)Al_Rafidain engineering Vol.13 No.1 200514refer to the changing of the vibration spectrum of the shaft Fig (11). Also increasing thecrack depth rapidly decreases the values of frequencies. This is done by using a portablevibration analyzer (B & K Type 2515) with magnetic acceleration which support to thenear point of rotating shaftIt is noticed that the vibration characteristic of the rotating shaft changes due tothe crack depth, which causes reduction in natural frequencies. Also this lower offrequency will increase by increasing the crack depth so itâs used the ratio of the crackto the diameter of the shaft in the range (00.75).The effect of adding the mass on the shaft (rotor disk) causes to decrease thevalues of natural frequencies, And by increasing the crack depth on the shaft which leadto lowered in natural frequencies due to supporting the disk. As mentioned above.The crack on the rotating shaft will change in some property like the localflexibility. So the local flexibility of a shaft in bending due to the crack is evaluatedfrom the theoretical and experimental results relating to the derivation of the strainenergy release function to the crack depth, contributed by some authors.These methods can have many practical applications because there is a wealth ofanalytical results for strain energy release function. For present work itâs noticed thatlocal flexibility increased by increasing the crack depth and this observed by calculatingthe theoretical values of local flexibility from the equation derived above. And for theexperimental results the calculate the values of natural frequencies of the rotating shaftwith and without crack then used the expression which depend on finding the flexibilityfrom the change of frequencies to get the local flexibility.It is noticed that through the crack detectability. Cracks of smaller than 0.2relative crack depth can be identified only in a quite environment by a skilled observer.For such depths above 0.2 the identification is very easy.For industrial application this level of crack detectability is rather adequate formost application. Moreover, careful measurement and good knowledge of the uncrackedshaft behavior might render the method applicable even for relative crack depths of theorder of 0.1.Finally, this work will represent a technique for nondestructive testing methodsdepending on, use the vibration analysis and the spectrum of vibration and monitoring iton a screen. So it can used also for identification of the location and the magnitude ofthe crack on a rotating shaft, without direct inspection, even at running conditions. Itallows also for continuous monitoring in shaft in service, especially for machine whichhas welded rotors and frequent inspections are impractical.Al_Rafidain engineering Vol.13 No.1 2005157.REFERENCES[1] Donald, J. and Wulpi, âFailures of Shaftsâ, Metallurgical Consultant, 2000.[2] Jones, D. P. and OâDonnel, W.J. âLocal flexibility for axisymmetric juncturesâ.Trans ASME J. Engng Ind. 15 (1971).[3] Rao, S.S., âMechanical Vibrationâ, 3rd edition, 1995.[4] Chondros, T. G. and Dimarogonas, A. D. âIdentification of cracks in welded jointsof complex structuresâ, J. Sound and Vibration 69, pp. 531538. 1980.[5] Chondros, T. G. and Dimarogonas, A. D. âIdentification of cracks in circular plateswelded at the contourâ, ASME J. paper No.79DET106. Design Engng Tech,Conf., St. Louis, and U.S.A. (Sept. 1980).[6] Sih, G. C. and Loeber, J. E. âVibration of an Elastic Solid Containing a PennyShaped Crackâ. J. Acoust. Soc. Am.44, pp. 12371245 (1968).[7] Loeber, J. F. and Sih, G. C. âwave Scattering about a PennyShaped Crack on aBimaterial Interface, in Dynamic Crack Propagationâ. (Ed. G. Sih), pp. 513528,Nordhoff, Leyden (1973).[8] Richard. W. Hertzberg. âDeformation and Fracture Mechanics of EngineeringMaterialsâ. 4th edition. John Wiley & Sons, Inc. (1996).[9] Miller, K. J., âAn Introduction to Fracture Mechanicsâ, Mechanical and Thermalbehavior of Metallic Materials, pp. 97131, (1982).[10] Bueckner, H. F. âField Singularities and related integral representationsâ. InMethods of Analysis and Solution of Crack Problems, (Ed. G. Sih), pp. 239.Noordhoff, Leyden. (1973).[11] Benthem, J. P. and Koiter, W. T. âAsymptotic approximations to crack problemsâ.ibid, pp. 174198. (1981).[12] Morrow, H. W., âStatic and Strength of Materialsâ, 3rd edition, Prentice Hall,(1998).[13] Dimarogonas, A., and Massouros, G., âTorsional Vibration of a Shaft with aCircumferential Crackâ, Engineering Fracture Mechanics, Vol. 15, No.34, pp.439444, (1981).Al_Rafidain engineering Vol.13 No.1 200516200250300350400450500mplitude (nm/s)0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)050100150200250300350400450500Amplitude (nm/s) (x/L)=0.5(2a/D)=0.19Freq.=87.4 Hz(x/L)=0.5(2a/D)=0.476Freq.=69.6 Hz0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)050100150200250300350400450500Amplitude (nm/s)Without CrackFreq.=91.2 Hz0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)050100150200250300350400450500Amplitude (nm/s)0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)050100150200250300350400450500Amplitude (nm/s)(x/L)=0.5(2a/D)=0.19Freq.=87.4 Hz(x/L)=0.5(2a/D)=0.476Freq.=69.6 Hz0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)050100150200250300350400450500Amplitude (nm/s)0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)050100150200250300350400450500Amplitude (nm/s)(x/L)=0.1(2a/D)=0.19Freq.=90 Hz(x/L)=0.1(2a/D)=0.476Freq.=88.2 Hz0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)050100150200250300350400450500Amplitude (nm/s)0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)050100150200250300350400450500Amplitude (nm/s)(x/L)=0.3(2a/D)=0.19Freq.=90 Hz(x/L)=0.32a/D)=0.476Freq.=82.4 HzWithoutCrack(a/D)=0With Crack(a/D)=0.190.2With Crack(a/D)=0.3Freq.=86.73With Crack(a/D)=0.5Freq.=84.6With Crack(a/D)=0.7Freq.=82.32With Crack(a/D)=0.75Freq.=72.6Fig 11. Experimental measurement of spectrumvibrationfor several crack depth of shaftAl_Rafidain engineering Vol.13 No.1 200517THE MEMORIZATION BEHAVIORS OF DIFFERENTMIOS STRUCTURESW. F. MOHAMAD L. S. ALIELECTRICAL ENGINEERING DEPARTMENTCOLLEGE OF ENGINEERINGUNIVERSITY OF MOSULABSTRACT: In this chapter the various kinds of charge storage cells are discussedas a result of examining many samples with different structures. The CV, IV and RVmeasurements of the structures confirm the memorization capability of MIOS devices.The examined structures reveal three kinds of memory actions. The first one is thecharge storage capability which can be shown through (CV) curve shifting as the devicewas exposed to certain stress for a certain time. The second is the electronic switchingthat is demonstrated by the fact that the switching between ON and OFF states andback to original state can only be obtained by inverting the polarity of the applied biasvoltage. The third kind of memorization action is that the device can be switched into avariety of stable intermediate resistance states. The new resistance state is determinedby the height of the programming pulse applied to the device. This memory action isnoticed from RV characteristic and known as a nonvolatile analogue memory behavior.Ù Ø®ØªÙÙØ© MIOS Ø³ÙÙÙÙØ§Øª Ø§ÙØ®Ø²Ù ÙØ§ÙØ°Ø§ÙØ±Ø© ÙÙ ØªØ±Ø§ÙÙØ¨Ø¯. ÙÙØ§Ø¹ ÙØ±Ù Ø§Ù Ù ØÙ Ø¯ Ø¯. ÙÙÙ Ø§Ù Ø³ÙØ± Ø¹ÙÙÙÙ ÙØ°Ø§ Ø§ÙØ¨ØØ« ØªÙ Øª Ø¯Ø±Ø§Ø³Ø© Ù Ø®ØªÙÙ Ø£ÙÙØ§Ø¹ Ø®ÙØ§ÙØ§ Ø§ÙØ®Ø²Ù ÙØ°ÙÙ Ø¨Ø¹Ø¯ ÙØØµ ÙÙ Ø§Ø°Ø¬ Ø°Ø§Øª ØªØ±Ø§ÙÙØ¨ Ù Ø®ØªÙÙØ©. ÙØªØ§Ø¦Ø¬Ø£Ø¸ÙØ±Øª Ø§ÙØªØ±Ø§ÙÙØ¨ Ø§ÙÙ ÙØÙØµØ© .(MIOS) ØªØ¯Ø¹Ù Ø§Ù ÙØ§ÙÙØ© Ø§ÙØ®Ø²Ù ÙÙ ÙØ¨Ø§Ø¦Ø· Ø§Ù (RV) ÙØ§Ù (CV) ÙØ§Ù (IV) ÙÙØ§Ø³Ø§Øª Ø§ÙØ«ÙØ§Ø«Ø© Ø£ÙÙØ§Ø¹ Ù Ù Ø¹Ù ÙÙØ§Øª Ø§ÙØ®Ø²Ù ÙØ§ÙØ°Ø§ÙØ±Ø©Ø Ø§ÙÙÙØ¹ Ø§ÙØ£ÙÙ ÙÙ Ø§Ù ÙØ§ÙÙØ© Ø®Ø²Ù Ø§ÙØ´ØÙØ§Øª ÙÙ Ø§ÙØªØ±ÙÙØ¨Ø© ÙØ§ÙØªÙ ÙÙ ÙÙ Ù ÙØ§ØØ¸ØªÙØ§Ø¨Ø¹Ø¯ ØªØ¹Ø±ÙØ¶ Ø§ÙÙØ¨ÙØ·Ø© Ø§ÙÙ Ø§Ø¬ÙØ§Ø¯ ÙÙØ±Ø¨Ø§Ø¦Ù ÙØ²Ù Ù Ù Ø¹ÙÙ. ÙØ§ÙÙÙØ¹ Ø§ÙØ«Ø§ÙÙ ÙÙ Ø§Ø¸ÙØ§Ø±Ù Ø¹Ù Ù (CV) Ù Ù Ø®ÙØ§Ù Ø²ØÙ Ù ÙØÙÙ Ø§ÙÙÙ Ù Ø«Ù Ø§ÙØ±Ø¬ÙØ¹ Ø§ÙÙ (ON) ÙØ§Ù (OFF) Ù ÙØªØ§Ø Ø§ÙÙØªØ±ÙÙÙ ÙØ§ÙØ°Ù ÙÙ ÙÙ Ù ÙØ§ØØ¸ØªÙ Ù Ù Ø®ÙØ§Ù ØªØÙÙ Ø§ÙÙ ÙØªØ§Ø Ø¨ÙÙ ØØ§ÙØªÙ Ø§ÙØ§ÙØØ§ÙØ© Ø§ÙØ£ØµÙÙØ© ÙØ°ÙÙ Ø¨Ø¹Ø¯ ÙÙØ¨ Ø§ÙÙØ·Ø¨ÙØ© ÙÙÙÙÙØªÙØ© Ø§ÙÙ Ø³ÙØ·Ø©. ÙØ§ÙÙÙØ¹ Ø§ÙØ«Ø§ÙØ« ÙÙØ®Ø²Ù ÙØ§ÙØ°Ø§ÙØ±Ø© ÙÙ Ø§Ù ÙØ§ÙÙØ© Ø§Ø³ØªØ®Ø¯Ø§Ù Ø§ÙÙØ¨ÙØ·Ø©ØÙØ« ÙÙ ÙÙ (OFF) Ù (ON) ÙÙ ÙØªØ§Ø Ø§ÙÙØªØ±ÙÙÙ ÙÙ ÙÙ ØªØÙÙÙÙ Ø¨ÙÙ ØØ§ÙØ§Øª Ù ÙØ§ÙÙ ÙØ© Ù Ø®ØªÙÙØ© ÙÙ Ø³ØªÙØ±Ø© ØªØªÙØ³Ø· ØØ§ÙØªÙ Ø§ÙØªØØ¯ÙØ¯ Ø§ÙÙ ÙØ§ÙÙ Ø© ÙÙØØ§ÙØ© Ø§ÙØ¬Ø¯ÙØ¯Ø© Ù Ù Ø§Ø±ØªÙØ§Ø¹ ÙØ¨Ø¶Ø© Ø§ÙØ¨Ø±Ù Ø¬Ø© Ø§ÙÙ Ø³ÙØ·Ø©. ÙÙØ¯ ÙÙØØ¸Øª Ø¹Ù ÙÙØ© Ø§ÙØ®Ø²Ù ÙØ°Ù Ù Ù Ø®ÙØ§Ù Ø¯Ø±Ø§Ø³Ø©ÙÙØ°Ù ØªØ¹Ø±Ù Ø¨Ø³ÙÙÙÙØ© Ø§ÙØ°Ø§ÙØ±Ø© Ø§ÙØªÙØ§Ø¸Ø±ÙØ© Ø§ÙØºÙØ± Ù ØªØ·Ø§ÙØ±Ø©. .(RV) Ø®ØµØ§Ø¦Øµ Ø§ÙSubmitted 23 rd March. 2004 Accepted 2nd Dec 2004Al_Rafidain engineering Vol.13 No.1 2005181 INTRODUCTIONEssentially the memory devices are structures whose resistance and capacitance varywith magnitude and polarity of applied voltages [1]. The storage devices may be volatile ornonvolatile. They can be used as an analogue or digital memories. The MOS structure is animportant type of the memory devices. Recently the shunt capacitance and shunt conductanceof such structures have been studied and investigated thoroughly [2,3]. The retention andendurance of charges in the nonvolatile memories depend on the oxide layer of the device.The oxide layer is the most important part in the MOS structure. This layer limits the type ofthe storage device. It is known that the leakage current is responsible for enhanced charge lossin flash EEPROM memory. The leakage current is a tunneling process via neutral traps. Theleakage current induced by FowlerNordheim (FN) stress in MOS capacitors increasesdrastically when the oxide thickness decreases [2,3]. The MOS device is essential structure inflash EEPROM memory. It is more important to study the factors and parameters whichinfluence switching and retention of memorization in MIOS structures.2 MIOS DEVICE FABRICATIONThe MIOS devices used in the present investigation were fabricated as follows:After the wet chemical treatment of the silicon wafers have been carried out, thermaloxides were grown thermally at 800 oC in dry oxygen for time intervals 15 mins, 25 mins and35 mins that yield silicon dioxide of thicknesses 7.75 nm, 15.5 nm and 21.7 nm respectively.The oxide thickness tox was calculated from CV measurement realized at 100 KHz. We areaware that this method gives a rough estimation of the oxide thickness, but for this work wedo not need a precise measurement of oxide thickness.The wet chemical treatment wasrepeated for cleaning only the back sides of all silicon wafers after thermal silicon dioxide(SiO2)th growth. Then aluminum was thermally vacuum evaporated on the back side of allwafers as a back contact with thickness of 200 nm. Postmetallization annealing was carriedout under vacuum for 60 mins at 400 oC, for making a good ohmic contact between siliconand aluminum as a back contact.Then thermal vacuum evaporated (SiO)d film of 100 nmthickness was deposited with a rate of 0.2 nm/sec on a part of the thermal grown silicondioxide (SiO2)th using a suitable mask to form (SiO)d 100 nm second insulator layer.For othersamples the second insulator layer was fabricated by thermal vacuum evaporated (SiO2)dfilms of 100 nm thickness with deposition rate of 0.2 nm/sec on the thermal grown silicondioxide (SiO2)th to form (SiO2)d 100 nm.For each kind of the MIOS devices, two types of gatecontacts were fabricated. For some devices a strip of NiCr of 40 nm was deposited with a rateof 0.2 nm/sec on the second insulator layer using a suitable metallic mask with an aperture of2 mm width and 20 mm length.In the last step, for all devices, aluminum gate contacts of 200Al_Rafidain engineering Vol.13 No.1 200519nm thick were thermally vacuum deposited through the metallic mask with ( 1 and 2 mm)diameter holes.3 MIOS CHARGE STORAGE CAPABILITYFor the MIOS (Al/(SiO2)d100 nm/(SiO2)th7.75 nm/pSi) structure the high frequency (1MHz) capacitance voltage (CV) curves were measured before and after stress voltage toevaluate the effect of the stress on the capacitors as shown in Figs.(1) and (2). From the highfrequency CV curves, the characteristics of the flatband voltage shifts were obtained. Thedistribution of the generate dinterfacestatesdensities were calculated. Before stressing, oxidecharges are found to be 1.63 Ã 1011 charge / cm2.After the stress of â 10 V for 1000 sec, the CVcurve indicates the presence of the positive charge in the dioxide. The change in oxidecharges are calculated after the stress and are found to be equal to ÎVFB Ã Cacc, i.e. (2.6 Ã 1011charge/cm2).That occurred because of tunneling of holes from ptype silicon substrate into thegate structure [4]. Comparing the two CV characteristics for strip gate and dot gate samples,it is clear that the shift window in the dot gate sample approaches 2.5 V while in the strip gatesample is about 2 V.This is attributed to the more recombination of electron injected frommetal gate with stored positive charges, and the more tunneling back of holes near Si/SiO2interface into Si substrate in the strip gate sample after removing a stress voltage because oflarger area and larger defects. Hence, the density of remained store charges will be less [5].4 MIOS DIGITAL PROGRAMMABLE RESISTOR MEMORYSwitching action of the two kinds of devices has been studied after exposing them to astress voltage of 10 V for 1000 sec. The experimental IV curves for each device in âOFFâand âONâ states are illustrated in Figs.(3) and (4). It is clear from both figures that thesedevices exhibit memory switching [6]. Both the ONstate and the OFFstate characteristicsextrapolate through the IV origin. The onstate is thus retained once the bias is removed,giving a nonvolatile, memory switching. By applying a negative bias the device can beswitched from conducting ONstate back to the OFFstate. From the two characteristicsshown, the behavior of each device differs from the other. The switching voltage from theOFFstate (line AB) to ONstate (line CAD) for the device of SiO deposited insulator isbetween (56) V, while that for SiO2 deposited insulator is between (78) V. In the reversedirection the switching voltage from the ONstate (line CAD) to the OFFstate (line EA) forthe device of SiO deposited insulator is between â 3V and â 4V, while that for SiO2deposited insulator is between â 6V and â 7 V.The two devices are of the same thermal tunnel silicon dioxide of7.75 nm thickness. The difference in the switching voltages is attributed to the seconddeposited insulator difference, because both deposited insulators (SiO and SiO2) have thesame thickness (100 nm). The forming effect in SiO deposited layer happens at a voltage lessthan that of SiO2 deposited layer, i.e. the insulation reliability of SiO is less than that of SiO2Al_Rafidain engineering Vol.13 No.1 200520[7]. Although the programming mechanism of this memory device is not yet understood fully[1], it is thought that the current in a formed device is carried by a filament which is less than1 Î¼m in diameter. Formation of a filament may be associated with a diffusion of the top metalinto the insulator layer, resulting in a dispersion of metallic atoms in the insulating (SiO andSiO2) matrix [8].7 6 5 4 3 2 1 00.30.40.50.60.70.80.91Gate voltage (v)C/CaccBefore stressAfter stress of10 v 1000 secCacc=31 nF/cm2Area=3.14Ã 102 cm2Deposited SiO2TH=100 nmFig.(55) MIOS CV characteristics for thermalSiO2 TH=7.75 nm with dot gate7 6 5 4 3 2 1 0 10.40.50.60.70.80.91Gate voltage (v)C/CaccBefore stressAfter stress of10 v 1000 secCacc=31 nF/cm2Area=0.4 cm2Deposited SiO2 TH=100 nmFig.(54) MIOS CV characteristics for thermalSiO2 TH=7.75 nm with strip gate(1)(2)Al_Rafidain engineering Vol.13 No.1 20052110 5 0 5 1060004000200002000400060008000Gate voltage (v)Gate current (Î¼A)ON stateOFF stateAfter stress of 10 v 1000 secDeposited SiO2 TH=100 nmFig.(56) MIOS IV characteristics for thermalSiO2 TH=7.75 nm with dot gate4 2 0 2 4 64000300020001000010002000Gate voltage (v)Gate current (Î¼A)Deposited SiO TH=100 nmAfter stress of 10 v 1000 secON stateOFF stateFig.(57) MIOS IV characteristics for thermalSiO2 TH=7.75 nm with dot gateA BCEDA BCDE(3)(4)Al_Rafidain engineering Vol.13 No.1 2005225 MIOS ANALOGUE PROGRAMABLE RESISTOR MEMORYNonvolatile memory switching has been observed inAl/(SiO2)d 100 nm/(SiO2)th 21.7 nm/(pSi) (MIOS) structure. Evidence for filamentaryconduction is found for devices that are in their low impedance state. The switchingphenomenon requires the existence of two impedance states which are stable at zero appliedbias. The device tested showed memory switching and their initial state was one of highresistance. Fig.(5) shows analogue switching characteristic of Al/(SiO2)d 100 nm/(SiO2)th 21.7nm/(nSi) (MIOS) device.After the device was exposed to stress voltage of 40 V for 1000 sec., the devicedisplayed a nonvolatile, analogue memory behavior. The resistance state is determined by theheight of the programming pulse applied to the device. The range of programming voltagesthat can be applied is referred to as the programming window. The operation of the deviceinvolves the following processes [1]:1. Forming: This is an only one time process in which a stress of 40 V for 1000 sec isapplied across the device electrodes. This creates a vertical deep conducting channel ofsubmicron width, which can be programmed to a value in the range 500 Î© to 600 KÎ©.2. Writing: To decrease the device resistance, positive âwriteâ pulses are applied.3. Erasing: To increase the device resistance, negative âeraseâ pulses are applied.4. The device resistance can be âreadâ using a voltage of less than 0.2 V without causingreprogramming.0.5 1 1.5 2 2.5 3 3.50100200300400500600700Pulse height (v)Bulk resistance of the structure (KÎ© )+ve writing pulsesve erasing pulsesDeposited SiO2 TH=100 nmAfter stress voltage +40 v1000 secFig.(522) MIOS bulk resistance versus applied pulseheight for thermal SiO2 TH=21.7 nm with dot gate(5)Al_Rafidain engineering Vol.13 No.1 200523The programming pulses (write or erase), which range between 1 V and 3 V, are typically 500nsec width. In Fig.(5) the device resistance is seen to increase from 500 Î© toward 600 KÎ©depending on the heightof the erase negative pulse. The magnitude of write positive pulse is used to set the finalresistance of the device. The programming window is 2 V.It is thought [9] that the current in a formed device is carried by a filament, which isless than 1 Î¼m in diameter. Formation of a filament may be associated with a diffusion of thetop metal into the amorphous SiO2 layers, resulting in a dispersion of metallic atoms in theinsulatingSiO2 matrix [10]. At SiSiO2 interface, when the device is in the high resistance state, it ischaracterized by a large device voltage and low device current. In this state the semiconductorunder the tunnel oxide is deep depleted since any minority charge at SiSiO2 interface iseffectively drained away by the tunneloxide. At switching point the device becomes unstabledue to the initiation of a regenerative feedback mechanism [3], which collapses the width ofthe deepdepletion region to its stronginversion value.6 CONCLUSIONSThe examined devices manifest three kinds of memorization phenomena. The first one is thecharge storage capability which can be noticed through CV curve displacement when stressingthe device. The second is the digital memory switching which is demonstrated by the fact that theswitching between ON and OFF states and back can only be obtained by inverting the polarity ofapplied bias voltage. The third kind of memorization noticed in this work is that a device can beswitched into a variety of stable intermediate resistance states. The new resistance states could bedetermined by the height of the programming applied pulses. This phenomenon is known as theanalogue memorization.7 REFERENCES[1] A. F. Murray and L. W. Buchan, âA users guide to nonvolatile onchip analogue memoryâ,Electronics & Communication Engineering Journal PP. 5363, April, 1998.[2] P. L. Swart and C. K. Cmpbell, âEffect of losses and parasitic ona voltagecontrolled tunable distributed RC notch filterâ IEEE J. SolidState Circuits,Vol. SC8, No. 1, PP. 3536, 1973.[3] J. G. Simmons, L. Faraone, U. K. Mishra, and F. L. Hsueh, âDetermination of theswitching criterion for metal/tunnel oxide/n/ p+ silicon switching devicesâ, IEEEElectron Device Letters, Vol. EDL2, No. 5, PP. 109112, 1981.Al_Rafidain engineering Vol.13 No.1 200524[4] A. Meinertzhgen, C. Petit, M. Jourdain, and F. Mondon, âAnode hole injection and stressinduced leakage current decay in metaloxidesemiconductor capacitorsâ, SolidStateElectronics Vol. 44, PP. 623630, 2000.[5] T. Y. Huang and W. W. grannemann, âNonvolatile memory properties of metal / SrTiO3 /SiO2 / Si structuresâ, Thin Solid Films, 87, PP. 159165, 1982.[6] J. M. Shannon and S. P. Lau, âMemory switching in amorphous siliconrich siliconcarbideâ, Electronics Letters Vol. 35, No. 22, PP. 19761977, 1999.[7] H. F. Wolf âSemiconductorsâ Copy right 1971, by John Wiley & Sons, Inc.[8] G. Dearnaley, D. V. Morgan, and A. M. Stoneham, âA model for filament growth andswitching in amorphous oxide filmsâ, J. NonCrystalline Solids 4, PP. 593612, 1970.[9] H. Kroger and H. A. Ricahrd Wegener, âMemory switching inpolycrystalline silicon filmsâ, Thin Solid Films, 66, PP. 171176,1980.[10] D. V. Morgan, A. E. Guile and Y. Bektore, âSwitching times and arc cathode emittingsite lifetimes for aluminum oxide filmsâ, Thin Solid Films, 66, PP. L 35L 38, 1980.Al_Rafidain engineering Vol.13 No.1 200525Bifurcation and Voltage C ollapse in theElectrical Power SystemsMr. Ahmed N. B. Alsammak, M.Sc.Electrical Engineering DepartmentUniversity of MosulMosul â IraqAbstract:Voltage stability is indeed a dynamic problem. Dynamic analysis isimportant for a better understanding of voltage instability process. In this workan analysis of voltage stability from bifurcation and voltage collapse point ofview based on a center manifold voltage collapse model. A static and dynamicload models were used to explain voltage collapse. The basic equations of asimple power system and load used to demonstrate voltage collapse dynamicsand bifurcation theory. These equations are also developed in a manner, which issuitable for the MatlabSimulink application. As a result detection of voltagecollapse before it reach the critical collapse point was obtained as original point.Keywords: Power System Stability, Voltage Stability, Voltage Collapse,Bifurcation, Reactive Power Compensation and MatlabSimulink.Ø§ÙØªØ´Ø¹ÙØ¨ ÙØ§ÙÙÙØ§Ø± Ø§ÙÙÙÙØªÙØ© ÙØ£ÙØ¸Ù Ø© Ø§ÙÙØ¯Ø±Ø© Ø§ÙÙÙØ±Ø¨Ø§Ø¦ÙØ©Ø£ØÙ Ø¯ ÙØµØ± Ø¨ÙØ¬Øª Ø§ÙØ³Ù Ø§ÙÙØ³Ù Ø§ÙÙÙØ¯Ø³Ø© Ø§ÙÙÙØ±Ø¨Ø§Ø¦ÙØ©Ø¬Ø§Ù Ø¹Ø© Ø§ÙÙ ÙØµÙØ§ÙÙ ÙØ®Øµ:Ø§Ø³ØªÙØ±Ø§Ø±ÙØ© Ø§ÙÙÙÙØªÙØ© ÙÙ Ø¨Ø§ÙØªØ£ÙÙØ¯ Ù Ø³Ø£ÙØ© Ø¯ÙÙØ§Ù ÙÙÙØ© ÙØ°Ø§ ÙØ§ÙØªØÙÙÙ Ø§ÙØ¯ÙÙØ§Ù ÙÙÙ Ù ÙÙ Ø¬Ø¯ÙØ§ ÙÙÙÙ Ø¹Ù ÙÙØ§Øª Ø¹Ø¯Ù Ø§Ø³ØªÙØ±Ø§Ø±ÙØ© Ø§ÙÙÙÙØªÙØ© ÙÙ ÙØ°Ø§ Ø§ÙØ¨ØØ« ØªÙ ØªØÙÙÙ Ø§Ø³ØªÙØ±Ø§Ø±ÙØ© Ø§ÙÙÙÙØªÙØ© Ø¨Ø§ÙØªØ±ÙÙØ² Ø¹ÙÙÙÙØ·Ø© Ø§ÙÙÙØ§Ø± Ø§ÙÙÙÙØªÙØ© ÙØ§ÙØªØ´Ø¹ÙØ¨ ÙÙØ°ÙÙ Ø¹ÙÙ ÙÙØ¹ Ø£Ù Ø³Ø¨Ø¨ ÙØ°Ø§ Ø§ÙØ§ÙÙÙØ§Ø± ÙÙØ¶Ø ÙØ°ÙÙ ØªØ£Ø«ÙØ±Ø§Ø³ØªØ®Ø¯Ø§Ù Ø§ÙØ£ØÙ Ø§Ù Ø§ÙØ«Ø§Ø¨ØªØ© ÙØ§ÙÙ ØªØØ±ÙØ© ÙØ§ÙÙ ØªÙ Ø«Ù Ø¨Ø§ÙÙ ØØ±ÙØ§Øª Ø§ÙØØ«ÙØ©. Ø§ÙÙ Ø¹Ø§Ø¯ÙØ§Øª Ø§ÙØ£Ø³Ø§Ø³ÙØ© ÙÙÙ ÙØ°Ø¬ÙØ¸Ø§Ù Ø§ÙÙØ¯Ø±Ø© ÙØ§ÙØ£ØÙ Ø§Ù (Ø§ÙÙ Ø³ØªØ®Ø¯Ù Ø© ÙØªÙØ¶Ø Ø£Ù Ø´Ø±Ø Ø§ÙÙÙØ§Ø± Ø§ÙÙÙÙØªÙØ© ÙØ§ÙØªØ´Ø¹ÙØ¨) ØªÙ Øª Ù Ø¹Ø§Ù ÙØªÙØ§Ø¨Ø·Ø±ÙÙØ© Ø¨ØÙØ« ØªÙÙÙ Ù ÙØ§Ø³Ø¨Ø© ÙÙ ØªØÙÙÙØ§Øª Ø¨Ø±ÙØ§Ù Ø¬ Ø§ÙÙ Ø§ØªÙØ§Ø¨. ÙØ´Ù Ø§ÙÙÙØ§Ø± Ø§ÙÙÙÙØªÙØ© ÙØ¨Ù ØØ¯ÙØ«ÙØ§ÙÙ ÙÙØ·Ø© Ø§ØµÙÙØ© ÙÙ ÙØ°Ø§ Ø§ÙØ¨ØØ«.Submitted 23 rd Feb. 2004 Accepted 2nd Dec 2004Al_Rafidain engineering Vol.13 No.1 200526List of symbols:V = Amplitude terminal load voltage (p.u.).Î´ = Internal terminal load voltage angle in degree.Em = Amplitude of generator internal voltage (p.u.).Î´m = Internal generator voltage angle in degree.Eo = infinity bus or slack bus voltage (p.u.).C = compensated load capacitor in p.u.Yo = Amplitude of equivalent impedance for the transformerand transmission line in p.u.Ym = Amplitude of equivalent impedance for the generator, transformerand transmission line in p.u.M =Generator moment of inertia p.u.dm = damping coefficientPm = Mechanical power.P&Q = Real and reactive power load demand respectively.Kpw, Kpv,Kqw,Kqv and Kqv2 = Constant parameters for the real and reactive load power.Ï = Speed and equal toÎ´& .1. Introduction:The continuing interconnections of bulk power systems, brought about byeconomic and environmental pressures, have led to an increasingly complexsystem that must operate ever closer to limits of stability. This operatingenvironment has contributed to the growing importance of the problemsassociated with the dynamic stability assessment of power systems. To a largeextent, this is also due to the fact that most of the major power systembreakdowns are caused by problems relating to the system dynamic responses. Itis believed that new types of instability emerge as the system approaches thelimits of stability.One type of system instability, which occurs when the system is heavilyloaded, is voltage collapse. This event is characterized by a slow variation in thesystem operating point, due to increase in loads, in such a way that voltagemagnitudes gradually decrease until a sharp, accelerated change occurs.Voltage collapse in electric power systems has recently receivedsignificant attention in the literature (see, e.g., [1] for a synopsis), this has beenattributed to increases in demand which result in operation of an electric powersystem near its stability limits. A number of physical mechanisms have beenidentified as possibly leading to voltage collapse. From a mathematicalperspective, voltage collapse has been viewed as arising from a bifurcation of thepower system governing equations as a parameter is varied through some criticalvalue. In several papers [915], voltage collapse is viewed as an instabilitywhich coincides with the disappearance of the steady state operating point as aAl_Rafidain engineering Vol.13 No.1 200527system parameter, such as a reactive power demand is quasistatically varied. Inthe language of bifurcation theory, these papers link voltage collapse to a fold orsaddle node bifurcation of the nominal equilibrium point.Dobson and Chiang [2] presented a mechanism for voltage collapse, whichpostulates that this phenomenon occurs at a saddle node bifurcation ofequilibrium points. They employed the Center Manifold Theorem to understandthe ensuing dynamics, In the same paper., they introduced a simplex examplepower system containing a generator, an infinite bus and a nonlinear load (asshown in Fig.(1)). The saddle node bifurcation mechanism for voltage collapsepostulated in Ref.[2] was investigated for this example in [3] and in [4].All essential distinction exists between the mathematical formulation ofvoltage collapse problems and transient stability problems. In studying transientstability [5,6], one often interested in whether or not a given power system canmaintain synchronism (stability) after being subjected to a physical disturbanceof moderate or large proportions. The faulted power system in such a case hasbeen perturbed in a severe way from steadystate, and one studies the possibilityof the postfault system returning to steadystate (regaining synchronism). In thevoltage collapse scenario, however, the disturbance may be viewed as a slowchange in a system parameter, such as a power demand. Thus, the disturbancedoes not necessarily perturb the system away from steadystate. The steadystatevaries continuously with the changing system parameter until it disappears at asaddle node bifurcation point. It is therefore not surprising that saddle nodebifurcation is being studied as a possible route to voltage collapse [7].In this paper a suitable model is set up to analyze the power system in [2].This model is then used with the some cases such as change in load and in thereactive load power as well as using constant and dynamic load, as inductionmotor.The basic equations of the power system and load are also developed in amanner, which is suitable for the MatlabSimulink application [8] and notdepended on ready programs (compact program package) such as Auto [16]. Thecomputer results show that voltage collapse may be studied before bifurcationwith a static model and after bifurcation with a dynamic model so the goal of thiswork is to show the richness of the qualitative behaviors, which may occur nearvoltage collapse, and to illustrate their effect on system trajectories.2. SaddleNode Bifurcations &Voltage CollapseA saddlenode bifurcation is the disappearance of a system equilibrium asparameters change slowly. The saddlenode bifurcation of mot interest to powersystem engineers occurs when a stable equilibrium at which the power systemoperates disappears [1]. The consequence of this loss of the operatingequilibrium is that the system state changes dynamically. In particular, thedynamics can be such that the system voltages fall in a voltage collapse. Since asaddlenode bifurcation can cause a voltage collapse there for it is useful to studysaddlenode bifurcations of power system models in order to avoid thesecollapses, such as using PID controller to control saddlenode bifurcations [17].Al_Rafidain engineering Vol.13 No.1 2005283. Reactive Power and Voltage Collapse:Voltage collapse typically occurs in power systems which are heavilyloaded, faulted and/or have reactive power shortages. Voltage collapse is systeminstability that it involves many power system components and their variables atonce. Indeed, voltage collapse often involves an entire power system, although itusually has a relatively larger involvement in one particular area of the powersystem [1].Although many other variables are typically involved, some physicalinsight into the nature of voltage collapse may be gained by examining theproduction, transmission and consumption of reactive power. Voltage collapse isassociated with the reactive power demands of loads not being met because oflimitations in the production and transmission of reactive power. Limitations arethe productions of reactive power include generator and SVC reactive powerlimits and the reduced reactive power produced by capacitors at low voltages.The primary limitations on the transmission of reactive power are the highreactive power loss on heavily loaded lines and line outages. Reactive powerdemands of loads increases with the increasing of load, motor stalling, orchanges in load composition such as an increased proportion of compressor load.4. The ModelThis section summarizes an example from [4] to illustrate how voltagecollapse model applies to the power system model shown in Fig.(1). Onegenerator is a slack bus and the other generator has constant voltage magnitudeE, and angle dynamics given by the swing equation:Mâ Î´&&m=âdmâ Ï +Pm+Emâ Vâ Ymâ sinÎ´( âÎ´mâÎ¸m)+Em2 â Ymâ sinÎ¸(m) â¦..(4.1)where M, dm, and Pm, are the generator moment of inertia, damping coefficientand mechanical power respectively.The load model includes a dynamic induction motor based on a model ofWalve [13] with a constant PQ load in parallel. The induction motor modelspecifies the real and reactive power demands P and Q of the motor in terms ofload voltage V and frequency Î´& . The combined model for the motor and the PQload [2] is:P Po P1 K K (V T V) pw pV= + + â Î´& + + â & â¦..(4.2)22 Q Qo Q1 K K V K V qw qV qV = + + â Î´&+ â + â â¦..(4.3)where Po, Qo are the constant real and reactive powers of the motor and P1, Q1represent the PQ load.From eq.(4.3):Kqwâ Kqv â V â Kqv2â V 2 +Q âQo âQ1Î´& = â¦..(4.4)Substituted eq. (4.4) in eq.(4.2) we get:T KqwKpvV KpwKqv V KpwKqv KqwKpv V Kpw Qo Q Q Kqw Po P Pâ â â â + â â â â + â + â â â + â= 2 ( ) ( 1 ) ( 1 ) 2& ..(4.5)Al_Rafidain engineering Vol.13 No.1 200529thus,Î´&m =Ïm â¦..(4.6)From eq.(4.1)&(4.6) we get:Mm dm Ïm Pm Em V Ym sin(Î´ Î´m Î¸m) Em2 Ym sin(Î¸m)Ïâ â + + â â â â â + â â & = â¦..(4.7)In eq.(4.3) Q1 is chosen as the system parameter so that increasing Q1corresponds to increasing the load reactive power demand. The load alsoincludes a capacitor C as part of its constant impedance representation in order tomaintain the voltage magnitude at a normal and reasonable value. It isconvenient to derive the Thevenin equivalent circuit with the capacitor. Theadjusted values are:1 2 cos( )'22oYoCYoCEo Eoâ Î¸â + â= â¦..(4.8)' 1 2 cos( ) 22oYoCYoYo Yo C â Î¸â = â + â â¦..(4.9)â â â ââ ââ â â ââââ â â = + â1 cos( )sin( )' tan 1oYoCoYoCo oÎ¸Î¸Î¸ Î¸ â¦..(4.10)The real and reactive powers supplied to the load by the network are:P(Î´ ,V) = âEo'â Yo'â Vâ sin(Î´ +Î¸o')âEmâ Vâ Ymâ sinÎ´( âÎ´m+Î¸m)+V2 â (Yo'â sinÎ¸( o')+Ymâ sinÎ¸(m)) â¦..(4.11)Q(Î´ ,V) = Eo'â Yo'â Vâ cosÎ´( +Î¸o')+Emâ Vâ Ymâ cosÎ´( âÎ´m+Î¸m)âV2 â (Yo'â cosÎ¸( o')+Ymâ cosÎ¸(m)) â¦..(4.12)In order to compute bifurcation value Q1 and the associated bifurcationequilibrium point, the following approximate formulas [15] are used as shown inappendix (A) equation (A3). The bifurcation value is:Qo + Q1 â (â Kqv + Eo'â Yo'+Emâ Ym)â V + (Kqv2 + Yo'+Ym)â V 2 = 0â¦..(4.13)and the voltage magnitude at the bifurcation equilibrium point is:( )( ) QoKqv Yo YmQ Kqv Eo Yo Em Ym ââ + +â + â + â =4 2 '' ' 2*1 â¦..(4.14)Formulas (4.13) and (4.14) are derived from the approximate static model givenin Ref.[15]:( )(Kqv Yo Ym)V Kqv Eo Yo Em Ymâ + +â + â + â =4 2 '* ' ' â¦..(4.15)The last three equations show the relationship between the bifurcation point andcertain load, transmission network and generator parameters.Al_Rafidain engineering Vol.13 No.1 2005305. BifurcationsConsider the modified power system model described by Ref.[2] which isgiven by (4.1), (4.2)&(4.3) in the general form:x& = F(x,Î» ) â¦..(5.1)where x is the state vector and Î» is a timevarying parameter vector. Specifically,in the power system model described in section (4), x = (Î´,Ï,V) and Î» denotesthe parameter vector that includes real and reactive power demands at each loadbus. The parameters in (5.1) are subject to variation and, as a result, changes mayoccur in the qualitative structure of the solutions of the static equation associatedwith (5.1), i.e., solutions of F(x,Î»)=0 for certain values of Î». For example, achange in the number of solutions for x may occur as the parameters vary. As aresult, the dynamic behavior of (5.1) may be altered.Bifurcation theory [1] is concerned with branching of the static solutions of(5.1) and, in particular, it is interested in how solutions x(Î») branch as Î» varies.These changes, when they occur, are called Bifurcations and the parametervalues at which a bifurcation happens are called bifurcation values.It is important in our following analysis of voltage collapse to distinguishtwo different periods: the period before bifurcation and the period afterbifurcation. Power systems are normally operated near a stable equilibriumpoint. As system parameters change slowly, the stable equilibrium point changesposition but remains a stable equilibrium point. This situation may be modeledwith the static model F(x, Î»)=0 by regarding F(x, Î»)=0 as specifying the positionof the stable equilibrium point x as a function of Î». (Here it would be moreprecise to call F(x, Î»)=0 a quasistatic model since Î» varies and causescorresponding variations in (x). This model may also be called parametric loadflow model. Exceptionally, variation in Î» will cause the stable equilibrium pointto bifurcate. The stable equilibrium point of (5.1) may then disappear or becomeunstable depending on the way in which the parameter is varied and the specificstructure of the system.After the bifurcation, the system state will evolve according to thedynamics of (5.1). (Some types of bifurcation result in the persistence of thestable equilibrium point even after the bifurcation and the static model apply justas before the bifurcation. However, we do not expect this sort of bifurcation tobe typical in power systems.) To summarize, analysis of a typical bifurcation of aEoâ 0 C Emâ Î´mVâ Î´Fig.(1) Power System Model.ââ ââââ â â â2ÏÎ¸o Yo ââ ââââ â â â2ÏYm Î¸m~ Load ~Al_Rafidain engineering Vol.13 No.1 200531stable equilibrium point in a power system with slowly moving parameters hastwo parts:(1) Before the bifurcation when the (quasi) static model applies.(2) After the bifurcation when the dynamical model (5.1) applies.The current research on voltage collapse uses the static model and only considersthe system before the bifurcation.6. Simulation ProcedureIn this work, the voltage stability procedure used to perform the simulationby the proposed model would be presented by a simple block diagram as shownin Fig.(2). The simulation have been made with the use of the stepbystepsolution with using ode15s, ordinary differential equations which used to solvestiff problem with good accuracy. The used program is Matlab 6.0 [8] to whichfast and accuracy results could be obtained. The differential equations from 4.1to 4.7 are arrangement in such away by using the following figure to the results.Fig.(2) Simulink model for the sample system.Al_Rafidain engineering Vol.13 No.1 2005327. Results and DiscussionA model of the sample system shown in Fig.(1) and foregoing equationsare used to illustrate the process of voltage collapse. For the bifurcationsanalysis, Fig.(3) shows the bifurcation diagram, which is appears the relatesbetween voltage magnitude V and reactive power demand Q1. This figureinvestigates a generic mechanism leading to disappearance of stable equilibriumpoints and the consequent system dynamics for oneparameter dynamicalsystems. To simplify the discussion, note first that in Fig.(3) which shows therelation between six bifurcationâs depicted. For Q1<10.95,a stable equilibriumpoint exists. (Upper left in Fig.(3)). As Q1 is increased, an unstable (âsubcriticalâ)Hopf bifurcation is encountered at point Q1=10.95. As Q1 is increasedfurther the stationary point regains stability at Q1=Q1*=11.42 through a stable(âsupercriticalâ) Hopf bifurcation.Fig.(4) shows an example of a typical voltage collapse, for the fourth ordermodels, phenomenon after a saddle node bifurcation. The initial conditions usedto generate the simulations are: Î´m=0.35,Ï =0.001,Î´ =0.14,andV =0.9. Note theoscillatory nature of solution due to varying in Q1, where Q1=11.25+0.005t Theprevious example, Fig.(4), demonstrated the center manifold model for theStable equilibriumUnstable equilibriumSaddlenode bifurcation.Saddlenode for periodic orbits bifurcation.Perioddoubling bifurcation.Hopf bifurcation.Stable periodic orbit.Unstable periodic orbit.Fig.(3) Bifurcation diagram.Al_Rafidain engineering Vol.13 No.1 200533dynamics of voltage collapse after a sad
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Voltage instability problems in power system is animportant issue that should be taken into consideration duringthe planning and operation stages of modern power systemnetworks. The system operators always need to know when andwhere the voltage stability problem can occur in order to applysuitable action to avoid unexpected results. In this paper, a studyhas been conducted to identify the weakest bus in the powersystem based on multivariable control, modal analysis, andSingular Value Decomposition (SVD) techniques for both staticand dynamic voltage stability analysis. A typical IEEE 3machine, 9bus test power system is used to validate thesetechniques, for which the test results are presented anddiscussed
Voltage stability  multivariable control  modal analysis  singular value decomposition  power system dynamics
This paper presents a study of static synchronous compensator (STATCOM). One of the Flexible AC Transmission System (FACTS) devices, it can significantly improve power systems stability. Consisting of voltage sourced converters connected to an energy storage device on one side and to the power system on the other, it specifically can provide reactive support to buses.This work presents a simple algorithm for identifying weak buses to determine the best location for STATCOM. Singularity of the power flow Jacobian matrix as an indicator of steadystate stability has used, the sign of the determinant of the load flow Jacobian was used to determine the system stability, by computing eigenvalues, eigenvectors , minimum singular value of loadflow Jacobian Matrix and sensitivity analysis between power flow and bus voltage changes. Load flow analysis of the Iraqi grid 400 KV network has been carried out using Newton Rephson Method with and without STATCOM. The result of Load flow analysis show improvement in bus voltage with the use of STATCOM in the system.
في هذا البحث تم دراسة ثابت المعوض المتزامن (STATCOM). واحد من أجهزة نظام نقل التيار المتردد المرنة ،حيث يمكن أن يحسن إلى حد كبير استقرار أنظمة الطاقة. يتكون من محولات مصادر الجهد متصلة إلى جهاز تخزين الطاقة على جانب واحد ونظام الطاقة من جهة أخرى، فإنه على وجه التحديد يمكن أن توفر دعم لل bus بالقدرة التفاعلية.في هذا العمل تم الاعتماد على خوارزمية بسيطة لتحديد buses الضعيفة لتحديد أفضل موقع لSTATCOM، استخدمت singularity لمصفوفة جاكوبين لتدفق الطاقة كمؤشر على استقرارية النظام ،حيث تم اعتماد أشارة المحدد لمصفوفة جاكوبين لتدفق الحمل لتحديد استقرار النظام، من خلال حساب القيم الذاتية (eigenvalue)، المتجهات الذاتية (eigenvectors) ، وminimum singular value لمصفوفة جاكوبين لسريان الحمل وتحليل الاستجابة بين تدفق الطاقة وتغيرات مجمع الجهد.تم تحليل سريان الحمل للشبكة العراقية ٤٠٠ كف باستخدام طريقة نيوتن رافسن مع وبدون STATCOM. ونتائج التحليل أظهرت تحسنا في مجمع الجهد ((bus voltage بأستخدام STATCOM في النظام.
Fact  Statcom  Load flow  Voltage Stability.  Fact  Statcom  سريان الحمل  استقرارية الفولتية
The operation and structure of distribution system are changing with the integration of Distributed Generation (DG) units, where these units may have effect on power losses, stability, voltage profile, power quality and other quantities. Therefore the optimum location, size and number of DG units are necessary to avoid the negative impacts on electric power system. In this work, the Particle Swarm Optimization (PSO) technique is used to find the optimal number and locations of DG in order to minimize the active power losses. The thermal limit of transmission lines and transformers was studied to detect the lines or transformers which exceed the limit in order to process it. The voltage stability of distribution network has been investigated, using L index method.
ان عمل وتركيب نظام التوزيع يتغير مع اضافة وحدات التوليد الموزع (DG )، حيث انها تؤثر على خسائر القدرة ، الاستقرارية ، الفولطية ، جودة الطاقة وكميات اخرى، لذلك فان اختيار الموقع الامثل والحجم وعدد وحدات التوليد الموزع (DG ) ضروري لتجنب التأثيرات السلبية على نظام الطاقة الكهربائية. في هذا البحث استخدمت تقنية (PSO ) لإيجاد العدد والموقع الامثلان لوحدات التوليد الموزع (DG ) لتقليل خسائر القدرة الفعالة. بعد ذلك تم دراسة الحد الحراري لخطوط نقل الطاقة الكهربائية والمحولات لتحديد الخطوط والمحولات التي تجاوزت الحد ومعالجتها. كذلك تم دراسة استقرارية الفولطية لشبكة التوزيع باستخدام طريقة ( L INDEX).
Distributed generation  DG  Thermal limit  Voltage stability  Particle Swarm Optimization  PSO.
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