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Title: | Bir Elektrikli Ulaşım Sisteminin Modellenmesi Ve Simülasyonu |

Other Titles: | modelling And Simulation Of An Electrically Driven Transport System |

Authors: | Bir, Atilla Kurtulan, Salman 22030 Kontrol ve Otomasyon Mühendisliği Control and Automation Engineering |

Keywords: | Benzetim Bilgisayar destekli tasarım Elektrikli ulaşım sistemleri Ulaşım sistemleri Simulation Computer aided design Electric transport systems Transportation systems |

Issue Date: | 1992 |

Publisher: | Fen Bilimleri Enstitüsü Institute of Science and Technology |

Abstract: | Bu çalışmada, elektrikli ulaşım sistemlerinin analiz ve tasarımında kullanılmak üzere bir simülasyon programı geliştirilmiş, serbest uyarmalı doğru akım motor tahrikli İstanbul LRT sistemine uygulanmıştır. Bu programda, sisteme ilişkin bütün fiziksel kısıtlamalar göz önünde bulundurulmuş ve deneysel verilerden de yararlanarak sistemi tam olarak simüle eden bir bilgisayar programı elde edilmiştir. Simülasyon programın da, ulaşım sistemindeki katener, yol profili, seyir direnci, tahrik motorları ve kontrol sistemini oluşturan kısımlar birbirinden bağımsız olarak ele alınmış ve modüler yapıda programlanmıştır. Bu programın gerçeklenmesinde, sisteme ilişkin fark denklemleri modelinden yararlanılmıştır. Sistemin lineer ve lineer olamayan kısımları ayrı ayrı ele alınmış,- lineer kısımlara ilişkin fark denklemleri z-tanım bölgesi transfer fonksiyonlarından türetilmiştir. Lineer olmayan kısımlara ilişkin fark denklemlerinin türetilmesinde, bu kısımlara ilişkin deneysel bağıntılardan yararlanılmıştır. Tahrik motoru olarak kullanılan serbest uyarmalı doğru akım motorunun manyetik akısı için, bu motora ilişkin mıknatıslanma eğrisinden alınan değerlerden hareketle, endüvi reaksiyonu etkisi de göz önünde bulundurularak, en küçük kareler yöntemiyle, manyetik akıya ilişkin bir fonksiyon türetilmiş ve fark denklemi biçiminde düzenlenmiştir. Sistemin fark denklemleri modeli kullanılarak, bilgisayarda programlanması kolay, hiç bir nümerik analiz yöntemi gerektirmeyen, daha doğru sonuç veren ve bütün örnekleme zamanları için kararlı bir yöntem geliştirilmiştir. Bir elektrikli ulaşım aracının belirli bir yolu belirli bir zamanda minimum enerjiyle kat etmesi için gerekli koşullar, faydalı frenlemenin yapıldığı ve yapılamadığı iki ayrı durum için, Kuhn-Tucker koşulları kullanılarak bulunmuş ve bu çözümlerin gerçeklenebilirliliği tartışılmıştır. Simülasyon programı, İstanbul LRT sisteminde, Ulubatlı-Sağmalcılar arasındaki bölgeye uygulanmış ve çeşitli çalışma durumlarına ilişkin simülasyon sonuçları verilmiş ve irdelenmiştir. Computer-aided system design tools are playing increasingly important roles in design and implementation of complex drive systems. These tools are becoming simple, economical to use, and more user- friendly day by day. A newly developed system, however it is complex, can be conveniently designed and simulated on a computer to verify the feasibility of the design parameters. The simulation approach is often time-saving, economical and possesses less risk of damage then the trial-and-error method design. However, it should be noted that the performance of a simulated system can be only as good as its model description, and therefore, working on the simulated system should be considered as a preliminary study of the system. In recent years, computer simulation techniques have been applied to the railway systems. Those applications include railway engineering scheme, operation management and driver training. In this study, a new simulation technique has been developed for traction drive systems and applied to istanbul LRT (light rail transit) system which is driven by separately-excited D.C motors, z-transforms of the model is used directly in this new simulation technique. This technique makes the simulation method stable for all finite sampling period of T. Moreover, this method gives more accurate results and programming becomes much simpler. The difference equations used in the simulation program are derived for linear and non- linear parts of the system, z-transform methods are used in deriving the difference equation for the linear parts of the system equation. For this purpose, a suitable sample and hold device is inserted to the transfer function of the system in s domain then the z-domain equivalents are found. -vi- The difference equations are derived from the equations defined in z-transfer domain. It has been assumed that the parameters related to nonlinear and time varying parts are constant during one sampling period of T. These parameters are then used in the difference equation related to linear parts. This study is divided into the following chapters Chapter It Introduction Chapter 2 1 System description (Rail transit systems) Chapter 3i Modelling of the system Chapter 4i Deriving the difference equation of the system Chapter Si Block and flow diagram of the simulation program Chapter 6 1 Energy optimization Chapter 7i Simulation results In the first chapter, studies concerning the simulation of the rail transit systems are summarized and a review of the existing simulation methods are given. A description of istanbul rail transit systems which we have simulated is presented in chapter 2. In chapter 3, various parts of overall LRT system are taken one by one, and dynamical or static equations, for each part are written in order to obtain the mathematical model of the system. In deriving a dynamical equation for a direct current motor one encounters a non linear relation between magnetic flux and field current. Similarly, there is non-linear relation between armature current and the changes in the field flux due to armature reaction. For these cases, analytical functions have been derived by using least square approximation method with experimental data. Finally, the following equation which is valid in the operating region has been derived for the motor magnetic flux. (jr,raM. -x<)-r.jJ -vli- where If is the field current and Ia is the armature current. Parameters Ç, p, r, Ö are calculated by using Eureka package program. At the end of this chapter, modeling of D.C. traction substations and overhead catenary system have been done by using a circuit model. In this modelling, each train is represented by a current source and substations are represented by an equivalent circuit which consists of a voltage source and resistor in series. In chapter 4, z-transform method has been directly applied for the linear system blocks. There exist actually three blocks for simulating linear parts of a system? namely, integration block, first-order system block and second-order system block. The following difference equation has been obtained by using a polygonal sample-and-hold device for the integration block: y(k) =4F lx(k) +x(k~l) ] +y(Jfc-l) The difference equation derived for the first-order system by using a zero-order sample-and-hold device is given below y(k)=K. (l-e-r'T).x(k-l) +e~Tfx. y(ic-l) where x(k) is input y(k) is output, T is the sampling period, K is the gain, t is the time constant of the system. Finally, the difference equation related to the last block, which is second-order system, has been derived in this chapter. It can be quite easily seen that this are very complicated equations. The difference equations for non-linear parts which are derived are as follows: The magnetic flux function: *(*)-«. {l-e-*-Ie{k))-T.ll (k) The traction (rolling and aerodynamic) resistance (Davis' formula is used) TRR (k) -k0+kx. v(Jc) +k2. v2 (Jc) where kg, k^, k2 are coefficients for train resistance -viii- which depend on the class of track, car suspension system parameters and wheel type? and v is the speed. The grade resistance is given as TRS(k) =m. g. sin (a (k) ) »m. g.tan{tt (Jc) ) =m. g. JlUÛ- where m is total mass of the vehicle, g is acceleration of gravity and h is slope given in thousand percent. Curve resistance (Mützner's formula is used) TRClk)=m.g. %-g-*,*1 where CI, C2, C3 are experimental coefficients and R is curve radius. In chapter 5, block and flow diagrams of simulation programs are given. The simulation program consists of four main modules which are total traction resistance module, driving motors module, filters module and power substation module. In chapter 6, the energy optimization topic has been covered related to rail transit systems. The necessary optimal conditions are derived for the energy consumption of a transit vehicle, travelling between given two stations having a distance of S, in a given fixed time t. It has been assumed that the transit vehicle travels with a constant acceleration and deceleration for energy optimization. Since the system equations are multidimensional and constraints appear to be in inequality type, solutions can only be found out using Kuhn-Tucker conditions given below Vf {x*) +Wh{x*) +jiVgrU*) =0 \ig(x*) =0, |i i0 where f is performance index or cost function, gj (j=l,2,..,n) < 0 are inequality constrains, hj ( j-1,2,..,m) =? 0 are equality constrains. -ix- Energy consumption which has been taken as cost function has been derived for two different states: Energy used without regeneration is derived as E=axvx +«2 vf +«3 vl +a4 vx tx +a5 v? tx +a6 v? tx where Vj is maximum speed, t^ is acceleration time and a1,tt2,...,o6 are coefficients which are given as ax=kQt2, tt2=±m+kxt2, a3=fc2t2 *4=- f, a5=-|ici ' a6=-|^2 Energy used with regeneration is derived as where t2 is start, t3 is end of deceleration time. At the first situation, equality and inequality constraints are as follows h=Sx-vxt2+±vxtx=0 g= tx> » 0 where Sj is total track length. The optimal solution has been found out to bei At the second situation, equality and inequality constraints are given ass ii=21Sr+v1(t1-t2-t3)=0 g2=t2-txZQ gr3 = t3-t2*0 where S is total track length. -x- Then the optimal solution has been found out to be as follows: tj_=0, t2 = t3/ Vi - - Theoretically, both in acceleration and deceleration modes, energy consumption becomes minimum if the acceleration or deceleration is infinity. This can be seen from the solution of the Kuhn-Tucker equation. However, infinite acceleration or deceleration can not be achieved physically. Therefore, one has to apply a maximum acceleration or deceleration which is constrained by comfort, slip and power system. In chapter 7, simulation programs have been applied to Istanbul LRT system and results have been represented as graphs of current, voltage and power of substations (rectifiers) and current, voltage and speed of trains. Six various situations have been examined. The cases are: 1) Running four trains each of which consists of three articulated-cars with track-paralleling at the same instant and two substations in service 2) Running four trains each of which consists of three articulated-cars with track-paralleling at the same instant and one substations in service 3) Running single-train consisting of three articulated- cars and one substation in service. 4) Running single-train consisting of three articulated- cars and one car is out of service. 5) Running single-train consisting of four articulated- cars and one substation in service. 6) Running single-train consisting of four articulated- cars, one substation in service and its voltage reduced to 700 V. -xi- In all situations which have been simulated, it has been assumed that auxiliary load (electric heating system, lighting) has been in service. Finally, simulation results have also been evaluated and discussed in this chapter. This program has the features of working as well the train performance simulator as the electric network simulator. For this reason, the program can be used in designing control algorithms for the drive motors of the train and it can also be used in generating control algorithms in energy optimization. |

Description: | Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1992 Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1992 |

URI: | http://hdl.handle.net/11527/16489 |

Appears in Collections: | Kontrol ve Otomasyon Mühendisliği Lisansüstü Programı - Doktora |

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