Enerji iletim sistemlerinde açma-kapama olaylarının analizleri için hat parametrelerinin EMTP yardımıyla hesabı
Calculation of line parameters for the analyses of power system switching transient using EMTP
- Tez No: 46448
- Danışmanlar: DOÇ.DR. ADNAN KAYPMAZ
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Enerji iletim sistemleri, Energy transmission systems
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Enerji iletim sistemlerinde birçok problemin analiz edilebilmesi için iletim hatlarına ait parametre değerlerinin tam olarak tespit edilmesi gereklidir. Fakat sistemde toprak dönüşlü kısımların bulunmasından dolayı hat parametreleri frekansa oldukça bağlıdır ve meydana gelen matematiksel ifadelerin çözümleri oldukça karmaşık bir hal almaktadır. Bu çalışmada özellikle geçici olayların analizlerinde büyük önem taşıyan bu parametre hesapları için geliştirilen teoriler incelenmiş, hat yapısı ve geometrisinin parametreler üzerindeki etkileri seçilen bir örnek hat için araştırılmıştır. Bu amaçla l.T.Ü. bünyesinde bulunan Elektromagnetic Transients Program (EMTP)'den yararlanılmıştır. Geçici olay analizlerinde hat parametrelerinin doğru hesaplanmaları kadar önemli olan diğer bir konu da uygun hat modellerinin seçimidir. Bugün için bilgisayarların olmadığı dönemlerden kalan, Transient Şebeke Analizörleri (TNA) ile yapılan sabit parametreli çözümler geçici olaylar için son derece yetersiz kalmaktadır. Günümüzde elektrik şebekelerinin büyüklüğü nedeni ile bu tip analizörlerin kullanımları pratik olarak imkansız hale gelmiştir. Bilgisayar teknolojisindeki hızlı gelişme sayesinde bugün için en karmaşık şebeke yapılarında bile bu tür geçici olay analizleri rahatlıkla yapılabilmektedir. Tezde bilgisayarlar için geliştirilen çeşitli hat modellerinin sürekli ve geçici hal frekans cevapları, örnek bir şebeke üzerinde EMTP yardımıyle incelenerek elde edilen sonuçlar grafik halinde verilmiştir. Elde edilen bu sonuçlardan modeller arasında meydana gelen farkların, özellikle geçici olay analizleri esnasında meydana geldiği ve bunun sebebinin geçici olay sırasında meydana gelen yüksek frekanslı bileşenlerin model tarafından söndürülebilmesiyle ilgili olduğu şeklinde ifade edilmektedir. Bu bakımdan analizler sonucu dağılmış parametreli ve frekansa bağlı hat modellerinin geçici olaylarda daha doğru sonuçlar verdiği anlaşılmaktadır. Ayrıca sıfır bileşen empedansının önemli olmadığı geçici olay analizleri için, frekans bağımlı hat modelleri gibi çok hassas modellerin kullanılmasının, bu tür modellerin bellek gereksinimindeki ve hesap zamanındaki artışlar yüzünden, gereksiz olduğu sonucuna varılmıştır. yi
Özet (Çeviri)
SUMMARY CALCULATION OF LINE PARAMETERS FOR THE ANALYSES OF POWER SYSTEM SWITCHING TRANSIENT USING EMTP A knowledge of parameters of multi conductor transmission lines is necessary in analysing a number of problems in power-transmission systems. The parameters may be generally divided into two groups, namely those as powei frequency, which are required in to study load flow, system stability and fault levels and those at higher frequencies, which are neded for studying the effects of restriking voltages, switching over voltages, radio interference and the propagation characteristics of power-line carrier signals. Calculating of these parameters with simplified formulas are enough for short circuit and load flow studies, but for the flowing types of applications, estimation of line parameters in detailed is needed: - Steady-state problem at power frequency with complicated coupling effects. An example is calculation of included voltages and currents in a de-energized three-phase line. - Steady-state problems at higher frequencies. Examples are analysis of harmonics, or the analysis of power line carrier communication, on untransposed lines. - Transients' problems. Typical examples are switching and lightning surge studies. The parameters R, L, C of overhead transmission lines are distributed along the line, and can, in general, not be treated as lumped elements. Some of them are also functions of frequency. For this reason, giving mathematical expressions for line parameters is a bit difficult. In 1926, Carson solved the equation for the self and mutual impedance's of a conductor in the presence of a semi-infinite homogeneous earth. In his solution for magnetic field, results were expressed in terms of convergent infinite series. Carson's formula, which is the basis of solution methods for line parameters, is normally accurate enough for power system studies for homogeneous earth. This formula is based on flowing simplified assumptions: - Conductors are perfectly horizontal above ground, and are long enough so that three-dimensional effects can be neglected. The sag is taken in to account indirectly by using an average height above ground. XII- The aerial space is homogeneous without loss, with permeability \Xq and permittivity s0. - The earth is homogeneous with uniform resistivity p, permeability Hq and permittivity s0, and is bounded by a flat plane with infinite extent, to which the conductors are parallel. The earth behaves as a conductor, 1/p»<as0 displacement currents may be neglected. - The spacing between conductors is at least one order of magnitude larger than the radius of the conductors, so that proximity effects (current distribution within one conductor influenced by current in an adjacent conductor) can be ignored. As just mention that Carson assumed the homogeneous earth with no displacement currents. The earth, however, is not homogeneous and ite resistivity varies along the depth of the earth layer. The assumption of a homogeneous earth may cause some difference in theoretical results from actual field test results. In chapter 2, these are pointed out. Forming of the series impedance matrix of transmission lines another important subject. Because of the electromagnetic effects, this matrix contains self and mutual impedance between conductors and earth layer. Calculation of this matrix is difficult unless the earth is homogeneous. The equations that were developed for homogeneous earth by Carson are: 2k = Zw = ARk + j(ca^lnŞ-+AXik) 2* dik Zii = (R-int ernal + ARb) + j(® § In ^ + Xi-int emai + A Xü) where: Ho = permeability of free space (H/km) Rj.jntemai ~ A.C resistance of conductor i in Q/unit length, h j = avarage height above ground of conductor i, Djk = distance between conductor i and image of conductor k (m), dik = distance between conductors i and k (m), rj = radius of conductor i,(m) xi-ınternal = internal reactance of conductor i, AR, AX = Carson's correction terms for earth return effects The correction terms of AX and AR in these equations are for the earth return effect, and are functions of the angle between the images and conductor, and of parameter r where: r = 47tV5.10"4-Dj- yıııwith D - 2h in (m) for self impedance, = D in (m) for mutual impedance, p = earth resistivity One of the terms of series impedance matrix is internal impedance that is beiong to the conductor. The internal impedance of solid round wires can be calculated with well-known skin effect formulas. The internal reactance can be calculated for certain types of conductors, as part of the internal impedance Rinternal+JXjnternal- Since Xinternal is only small part of the total reactance for non magnetic conductors, its accurate determination is somewhat academic. However, Rinternal has more practical interest than Xinternal. The calculation of Rinternal and Xinternal for the stranded conductors is complicated by irregular surface profile of the conductor due to stranding. Stranded conductors can usually approximate as solid conductors and at pov/er frequency. Rinternal is equal to the d.c. resistance per unit length of the conductor. However, if skin effect is significant, manufacturer's power frequency value is used. The internal inductance, hence the Xinternal is calculated in the standard way by the concept of geometric mean radius. When high frequencies are considered, the current is confined to the surface of outer layer of the strands, owing to the skin effect. By assuming that the depth of penetration is very small, the current density at surface of conductor is proportional to the magnetic field intensity at the surface. There is also another approximation of the steel-reinforced aluminum cables (ACSR). In this approximation, it can be approximated as tubular conductors when the influence of the steel core is negligible, which is more likely to be the case with an even number of layers of aluminum strands, since the magnetization of steel core caused by one layer spiraled in one direction is more or less canceled by the next layer spiraled in opposite direction. Hence, EMTP uses this approximation of an ACSR as a tubular conductor, and so in chapter 2, line parameters were calculated using it. If the magnetic material of steel core is of influence, then calculations probably become unreliable, and current depended, measured values should be used instead. Besides series impedance matrix, to provide shunt-suseptance parameters, shunt admitance matrix should be formed. Its elements are easy to compute from geometry of the tower configürasyon and from the conductor radii if the flowing asurnptions will be made: - The air is lossles and the earth uniformly at zero potential. - The radii are at least an order of magnutude smaller than the distances among the conductors. Both assumptions are reasonable for overhead lines. The general form of tiiis matrix is [Y]a(!G]+ja>[C]. G shunt conductance is usually ignored, because their influence is negligible on overhead lines, except at very low frequencies approaching d.c, where the line behavior is determined by R and G, with a>L and ©C becoming negligibly small. With this approach, xivshunt admittance matrix become real, symmetric and frequency independent. However, at high frequencies like 1 MHz, zero potential level becomes to shift below to ground surface. For this reason capacitance matrices at this frequency level are not frequency independent any more, and the correction terms should be added to them. Nowadays, utilizing computer program techniques make the calculation of the parameters' matrices easier. However, for increasing of efficiency of computers, some solution methods should be used. For example, matrices are made smaller order by reducing the number of elements. This process can be made eliminating the ground wires or replacing bundled sub-conductors with equivalent single conductor. Normally, ground wires are continuous and grounded at every tower, which are typically 250 to 350 m apart. In that case it is permissible for frequencies up to 250 kHz to assume that the ground wire potential is continuously zero. This allows a reduction in the order of series impedance and shunts admittance matrices. Moreover, for a reduction in the order of matrices, bundled conductors can be replaced with single equivalent conductors. On high voltage power lines, bundle conductors, which are usually symmetric, are often used. Two methods can be used for calculating the line parameters of bundle conductors, which are namely matrix reduction and equivalent phase conductors. With first method, the parameters originally calculated with each sub-conductor being represented as an individual conductor. Since the voltages are equal for the sub conductors within a bundle, this voltage equality is then used to reduce the order of matrices to the number of equivalent phase conductors. With second method, the concept of geometric mean distance is used to replace the bundle of sub conductors by a single equivalent conductor. In chapter 2, line parameters were calculated using these methods, and then the differences between them were found to remain below 0.1% level over 0.01 Hz-107 Hz frequency band width. While it is well known that ground wires have an influence on zero sequence parameters, it is less well known that they can influence positive sequence parameters, too. Of practical importance is the increase in the positive sequence resistance Rd if the line has ground wires which are grounded at every tower. Since the mutual impedances from three phase conductors to the ground wire are never exactly equal, and so there is always a small longitudinal voltage induced in the ground wire. This induced voltage produces a circulating current which flows through the ground wire, towers and ground. To avoid these circulating currents which produce the losses some utility companies use segmented ground wires in an arrangement which has the form of T: the ground wire is grounded in the middle and insulated at the adjacent towers to the left and right. In chapter 2, it is shown that using segmented ground wires causes some degreases in positive sequence resistance about 4% at 50 Hz and increases in zero sequence reactance and resistance about between 13-30% and 37-62% respectively over 0.01 Hz-107 Hz frequency band width according to the continious ground wires for a sample line. xvMany lines in power systems are untransposed and have the number of M phases. However, many transposed lines are not balanced, because each section of transposition barrel may no longer be short compared with the wave length of the highest frequencies occurring in particular study, in which case each section must be represented as an untransposed line. The solutions of M-phase transmission line equations become simpler if the M coupled equations can be transformed to M de coupled equations. These de coupled equations can then be solved as if single phase equations. For balanced lines this transformation is achieved with symmetrical components or Clark's Components easily but untransposed lines, the matrices can be transformed the diagonalized matrices with eigenvalue/eigenvector theory. The transformation matrices are normally complex and frequency dependent. With a frequency dependent transformation matrix, modes are only defined at the frequency at which the transformation matrix was calculated. Then the concept of converting a polyphase line into de coupled single phase lines can not be used over the entire frequency range. The solution methods for transients are much simpler if the modal composition is the same for all frequencies, in other words, if the transformation matrices are constant with real coefficients. Fortunately, this is indeed possible for transmission lines. Electromagnetic transients in power systems may be produced by switching actions, faults, or lightning strikes. For many years digital computer methods have been used studying transmission line transients. Many of the techniques employed are based on the use of traveling waves, with assumption of lossless or distortionless propagation characteristics. The general purpose transients program (Electromagnetic Transients Program or EMTP) developed at Bonneville Power Administration (BPA), which is based on Bergeron's method of characteristics, was also at first restoicted to lossless, distortionless, or combination with lumped line resistance. Historically, the first line models in the EMTP were cascade connection of 71-circuits, partly to proof that computers could match switching surge study results obtained on Transient Network Analizer's (TNA) at that time. The need for traveling wave solutions first arose in connection with rattier simple lightiiing arrester studies, where lossless single-phase line models seem to be adequate. In chapter 3, briefly discusses the solution method used in the EMTP for such lines. This method was already known in 1920's and 1930's and strongly advocated by Bergeron; it is therefore often called Bergeron's metiiod. It soon became apparent that traveling wave solutions were much faster and better suited for computers than cascaded 7i-circuits. To make the fraveling wave solutions useful for switching surge studies, two changes were neded from the simple single-phase lossless line: First, losses had to be included, which could be done with reasonable accuracy by simply lumping R in three places. Secondly, the method had to be extended to M- phase lines, which was achieved by transforming phase quantities to modal quantities. Originally, this was limited to balanced lines with built-in XVItransformation matrices, then extended to double-circuit lines, and finally generalized to untransposed lines. While traveling wave solutions with constant distributed L, C and constant lumped R produced reasonably accurate answers in many cases, there were also cases where the frequency dependence, especially of the zero sequence impedance, could not be ignored. Choosing constant line parameters at tie dominant resonance frequency sometimes improved the results. Eventually, frequency-depended line models were developed by Budner, by Meyer and Dommel, who based on work of Snelson, by Semlyen and by Ametani. A careful re-evaluation of frequency-dependence by J. Marti led to fairly reliable solution method. In chapter 3, J.Marti's method will therefore be discussed in detail. XVII
Benzer Tezler
- EMPT ile enerji iletim sistemlerinde açma-kapama olayları analizleri
Switching phenomena analyses of power transmission systems with EMTP
TANER DENİZ
Yüksek Lisans
Türkçe
1995
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiDOÇ.DR. ADNAN KAYPMAZ
- Generatör ve transfarmatör bloğundan oluşan sistemin yüksek frekans davranışı
Başlık çevirisi yok
YAŞAR CİNAKLI
Yüksek Lisans
Türkçe
1994
Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrolİstanbul Teknik ÜniversitesiPROF.DR. M. KEMAL SARIOĞLU
- Transformatör sargılarında oluşan hızlı değişimli geçici olayların incelenmesi ve enerji iletim sistemlerinin modellenmesinde yeni bir yaklaşım
Investigation of high speed transients on transformer windings and a new approach in modelling of energy transmission systems
A.OĞUZ SOYSAL
Doktora
Türkçe
1985
Elektrik ve Elektronik Mühendisliğiİstanbul Teknik ÜniversitesiPROF. DR. M. KEMAL SARIOĞLU
- Büyük güçlü devre kesicilerin yapı ve problemleri
Başlık çevirisi yok
LEVENT YILDIRIM
Yüksek Lisans
Türkçe
1988
Elektrik ve Elektronik MühendisliğiMarmara ÜniversitesiElektrik-Elektronik Ana Bilim Dalı
DOÇ. DR. NESRİN TARKAN
- Enerji sistemlerinde bilgisayar destekli röle koordinasyonu
Computer aided relay coordination in the power systems
ADNAN KAKİLLİ
Doktora
Türkçe
1999
Eğitim ve ÖğretimMarmara ÜniversitesiElektrik Eğitimi Ana Bilim Dalı
PROF.DR. İRFAN GÜNEY