Alternatif Akım-doğru Akım Sisteminde Ayrık Yöntem Kullanımı İle İlgili Optimal Güç Dağılımı Hesabı İçin Yeni Bir Yaklaşım

Abstract

Sunulan bu çalışma ile ilk defa negatif gr adi eni yön¬ tem yardımıyla alternatif akım-doğru akım optimal güç akı¬ şı gerçekleştirilmiş ve yine ilk olarak bir ayrık alterna¬ tif akım - doğru akım güç akışı yaklaşımı optimizasyon he¬ saplamalarında kullanılabilir duruma getirilmiştir. Ayrık yöntemden bu amaca uygun olarak faydalanabilmek icin»algo¬ ritmasında bazı değişikliklerin yapılması gerekmektedir. Bu çalışmada yapılan değişikliklerin, ayrık yöntemi üstün kılan genel yapıya zarar vermediği,' yakınsama iterasyon sayısı ile hızında olumsuz yönde bir değişmeye yol açmadı¬ ğı gösterilmiştir. Önerilen yaklaşım içinde, çoğu çalışmadan farklı ola¬ rak, alternatif akım sistemi içinde yer alan kademe ayar¬ lı transformatörlerin kademe ayar değerleri bara admitans matrisine sokulmadan güç akışı hesaplamalarında kullanıl¬ mıştır. Böylece kademe ayarının her yeni değerleri için bara admitans matrisi tekrar hesaplanmamaktadır. Ayrıca bu yaklaşım optimizasyon hesaplamalarında da kolaylıklar sağlamaktadır. Doğru akım sistemi değişkenlerinden çeviri¬ ci aktif güçleri, çevirici transformatörleri kademe ayar değerleri ve referans çevirici çıkışı doğru gerilim değe¬ ri kontrol değişkenleri olarak; çeviriciye doğru akan al¬ ternatif akım faz açıları, referans çevirici dışındaki di¬ ğer çevirici çıkış doğru gerilim değerleri, çevirici çı¬ kışı doğru akım değerleri ve tetikleme açıları ise durum değişkenleri olarak kabul edilmiştir. Böylece ayrık yön¬ tem yaklaşımı genel hatları ile korunmuştur. Ayrıca, kade¬ me ayar değeri ve referans çevirici çıkışı doğru gerilim değerinin kontrol değişkenleri olarak seçilmesi ile de,al¬ goritma içinde yapılan hesaplamalar optimizasyon sürecine taşınmış, böylece güç akışı hesaplama süresi azaltılmıştır. Hesaplamalar, hem P-aktif hem de Q-reaktif optimal güç akışını aynı algoritma içinde gerçekleştirebilecek bir yaklaşım üzerine bina edilmiştir. Böyle bir yaklaşım ise, kontrol değişkenlerinin optimizasyon türüne göre ayrıma tabi tutulmasını gerektirmiştir. Kontrol değişkenlerinin optimizasyon türü ile ilgisi gözetilerek, çevirici aktif güçleri P,geri kalanlar ise Q optimizasyonu kontrol değiş¬ keni olarak alınmıştır. Ayrık yaklaşıma ait tüm eşitlik¬ ler, optimizasyon hesaplamalarına yeni bir Lagrange sabi¬ ti yardımı ile taşınmıştır. Çalışma sonunda, yukarıda ge¬ nel hatları ile açıklanan alternatif akım-doğru akım opti¬ mal güç akışı yaklaşımı örnek bir sistem üzerinde test edilmiştir.

Electric utilities, and many of the manufacturing industries they ser ve, are on the threshold of revolution- ar y change brought about by high-power electronics. Över the last two decades the increasingly dense integration of low-voltage low-current circuits on small silicon chips has transformed of f içe equipment and communication netv/orks. During t h© next two decades the development of semiconductor devices f ör high-voltage high-current appli- cations will bring about an equally fundamental transfor- mation in majör industrial equipment. and u-tility net.works. This power electronics revolution has already begun. Power electronics is now being used t o make A.C-DC convert,- ers för high voltage DC transmission, static VAR compensators, uninterruptible power supplies t,o protect- sensitive equipment, and drives för adjustable-speed mo¬ tor s. in the near future, power semiconductor devices are expected to make the electricity generated by photovolta- ic and wind f acil i ti es which ar e mor e easily compatible with utility transmission networks. Över the longer term, these devices may even replace mechanical switches on dis- tributive power lines. The true impact of power electron¬ ics on electric power systems is yet to be realized. We are sure that you appreciate that, by and large, the AÇ power system of today is a mechanically controlled system and as a result there is no high-speed control. Al- so because of mechanical control, it can not be initiated frequently since mechanical devices tend to wear out very quickly compared t o s tat i c electronic devices. Power semi- conductor devices in HVDC and other power applications are switched every cycle with negligible loss of life. Power flow through an a. c line is a function of the phase angle, the line end voltages, and impedance. There is no high speed control över these parameters. Phase an¬ gle control is rarely utilized and, when it is used, the control is by means of slow mechanical phase shifters. Tap changers, reactors, and capacitors are generally mechanically switched and as a result they are also "slow" methods för controlling the power system. Of course there is no control över the l i ne impedance. Somehow, we arrive at the required steady-state power flow while maintaining voltages within the saf e tolerable limits through the use of generalden scheduling and the occasional changing of transformer tap changers, and the switching of shunt re- actors and capacitors. On top of that, the AÇ system has the curse of reactive pover, which loads up the lines and causes problems in voltage control. Consequences of this lack of precise control are the problems with stabiliy, power flowing through other than the intended lines, high- er losses, high ör low voltages, cascade tripping, ete. Now let us look at HVDC transmission. The phase an- gle does not play a role on the DC side, voltage is con¬ trol l ed at high speed by the converters and the inductan- ce and capacitance of the l ine are not a liability. True, the li ne resistance is not controlled but this is not ne- cessary because the voltage is controlled. Thus the free- dom from uncontrolled parameters and the high speed con¬ trol of voltages gives us a transmission system through which the desired power can be controlled in either direc- tion with considerable freedom from the AA frequency, the ÂC voltage, and the AÇ system impedance. We can say in l O, £O, ör even 3O years, anticipate to be the trend in power system design based on the use of power semiconductors devices . Pover semiconductor devices, inci uding the thyristor and its variations with and without turn-off capability, con- tinue to make majör strides. We can assume that a single device rated up to 2O kV and a few thousand amperes, with high di/dt and dv/dt capability and l över losses and cost will become a reality. Already silicon-bonded packaging which will cut the device cost by a. third has been shown to be a realistic goal. Furthermore, the combined technol- ogy of integrated circuits and MOS controlled thyristors , in connection with AÇ system analysis. The principal reason son för the significant increase in the application of HVDC transmission is that HVDC provides a high degree of flexibility in the pover system. As mentioned before, po- wer flow can be controlled in either direction with con- sider able freedom from the system frequency, AÇ voltage and system impedance. Hovever, the problem with the AÇ transmission system is that it has no high speed control of the the phase angle, the impedance, ör the voltage. But advances in pover semiconductors applications might xii change this. HVDC, fast controllable phase-shifters, series comp- ensation and static var compensators ali play a signific- ant role in FACTS. Since 1952, when the first modern high voltage di- rect current transmission system began öperating, lots of HVDC system ha ve been built successfully öper at ed. These ar e mostly t wo-t er mi nal systems f ör transmitting bul k po- wer betveen two points. Because these systems have been so successful, there is much interest in building HVDC systems with more than two termi nals. These are known as mul ti t er mi nal systems. Power control in an HVDC system is obtained by cont- rolling the voltages at the inverter and rectifier. The voltage control can be accomplished by using transformer taps to VAR the AÇ voltage ör by varying the ignition an- gle of the rectifier ör inverter. The current in an HVDC system is function of the difference betveen the DC volt¬ ages at the rectifier side and the inverter side. Thus the DC current can be controlled by varying either volt¬ age. The rectifier is normally used for current control, and the inverter establishes the DC system voltage. in modern HVDC systems, the valves are thyristor modüles con- sisting of seri es/parallel arrays of thyristors to meet system voltage and current requirements. The thyristors are controlled by the AÇ voltage and gate firing pulses. For a thyristor to turn on, it needs a positive forvard anode to cathode voltage and a firing pulse at its gate. The conduction time of the thyristor determines the DC voltage and this conduction interval is controlled by the ignition angle. The ignition angle can vary f r om O-9O degrees for a rectifier and from 9O-18O degrees for an inverter, but for various operating reasons they are not normally öperated at the extremes of these ranges. HVDC transmission system has the folloving advanta- g&s över AÇ transmission. 1- l ine losses are lower because there is no reacti- ve pover flow, 2- power flow is much mor e controllable, 3- stability of connected AÇ system is increased, 4- smaller conductors and transmission coridors are required, 5- short circuit currents are limited, xiii 6- thermal costruction can be stages to coincide with load growth, 7- no additional reactive power is required för voltage supported effect's ör stability, 8- connection is asynchronous, so AÇ systems at dif- ferent frequencies ör systems with stability problems can be connected, 9- HVDC systems can continue to operate w±th öne out of service. The disadvantages of HVDC system ar e: 1- cost of converters is high at the preseni, time, 2- converters require reactive power, 3- converters generate harmoni es, therefore they re- quire filters, 4- converters have low överioad çapability, lack of HVDC circuit breaker hampers mul ti terminal ör netvork öperation. The Gauss method för the solution of simultaneous equation was the first numerical method used to sol ve the complex AÇ load flow equations. This method was supersed- ed by the Gauss-Siedel metod.the Nevton and the decoupled Newton load flow method. Each development improved the convergence pröperties and shortened the time required to obtain a solution. it is envisioned that multi termi nal HVDC system will initially be incorporated into the AÇ system solely as bul k power transmission facilities, in which such the num- ber of DC terminals will be a small fraçtion of the total number of buses in the power system. in view of this fact, there is a case för solving AC-DC load flow problem with minimal sacrifice in efficiency of the techniques already used för the AÇ problems. The AC-DC load flow can be ob- tained by solving the combined system equations simultane- ously för. by a sequential process iterating back and förth between the AÇ and DC netvork equations. in the simultaneous solution method the DC load flow equations are directly incörporated into the Nevton AÇ load flow equations. The combined set of equations are then solved simultaneously in every iteration of Newton load flow algorithm. On.the other hand, in the sequential solution method, the direct current terminals are treated as loads ör power sources on the AÇ system and iteration betveen AC-DC load flow algorithm are made to match bound- ary conditions between two systems. This method has the xi v advantage that, there is no need to replace or restructure any existing AC load flow program that may be providing satisfactory performance. For a DC link with two terminals, the Newton formula tion requires 13 residual equations and the corresponding Jacobien expansion to account for all variables involved, equations for just the DC converters and the network are fairly simple, however they are complicated by the variety of controls and constraints on some variables. The DC met hod used in this thesis presents a Gauss method of soluti on for the DC system equations which avoids the elaborate representations used in the Newton formulation. The DC load flow algorithm developed utilizes the Gauss iterative procedure. The algorithm has been proved to possess excellent convergence properties for this par ticular application. A typical example of a four terminal system converges to a solution in two or three iterations. Given a set of reasonable scheduled powers and AC bus vol tages, the algorithm converges on the best possible solu tion. Best in the sense that it minimizes the mean squar ed error of the scheduled currents and also satisfies con straints which are imposed on the converter voltages, valve currents, firing angles, and transformer taps. The ability of the algorithm to arrive either at the required solution which satisfied the set of scheduled powers or that of providing a compromise solution when set of scheduled powers could not be met within the oper ational and equipment constraints set, is a valuable fea ture in application where a compromise solution is better better than none. This characteristic makes the algorithm suitable for on-line applications. The real and reactive powers of the converters can be regarded as P and Q loads on the AC system. Neglecting the transformer, the P and Q flows at the primary AC bus will be the same as the real and reactive powers calcula ted for the converter. But for a three winding transform er with tap changer on the primary side, an iterative so lution on the transformer equations will be required to determine the P and Q flows at the primary AC bus. Using the sequential approach, the DC load flow algorithm can be combined with any existing AC load flow algorithm. Since the AC system voltages can be initially approximated closer than the reactive power requirements of converters, to start off, a DC load flow is performed prior to the AC load flow. With updated values of the P and Q flows, the AC load flow routine computes a new set of AC bus voltages which is than used in the next load flow. Iteration xv between AC and DC load flow algorithm is performed until the maximum change in P and Q of the converters between successive iterations fall below prescribed tolerances. Experience with this sequential schema has been good. In this thesis, some of the parameters which are used in monopolar or bipolar mult i terminal direct current systems have been chosen as control (super basic) variables and other ones as dependent (basi c ) variables. Any of ter minals of AC-DC systems have been chosen as slack termi nal. Dependent variables of DC system in this thesis are DC terminal current »I, DC terminal voltaqe V, (except d v av for slack terminal >, triggering angle ex. or y. anc; power factor angle