Altı fazlı enerji iletim sistemlerinde seri kompansator lokalizasyonunun tayini

Abstract

Gün geçtikçe büyüyen elektrik enerjisinin gelecekteki gereksinimini karşılamak için mevcut üç +0211 enerji iletimi yerine aynı sistemin güç iletim yeteneğini artıran çok-fazlı enerji iletimi bir seçenek olarak görülmektedir. Bu aşamada, çok fazlı sistemler arasında çifte devre uc fazlı hattın güç iletim yeteneğini M 7S.S daha -fazla artıran alti fazlı enerji iletimi en ümit verici olanıdır. Altı-fazlı enerji İletimi gerçekleşirse, en can alıcı sorun bu tip sistemlerin planlamasıdır. Planlamanın en önemli unsuru ise sistemin koruma dizaynıdır. Bu dizayn ise arıza analizini gerektirir. Bu tez çalışmasında altı-fazlı enerji iletim sisteki altı.ayrı iletim devre modelinde ele alınarak seri kompanzasyon etkilerinin incelenmesinde çalışılmıştır. Hesaplamalarda altı faz sisteme Özgü olan arıza tiplerinin analizi bilgisayar ile her modelin baralarında yapılarak' karşılaştırma yapılmıştır.

Increased demand for electrical power, increased cost and restrictions on rights of way, and higher transmission efficiency requirements are some o-f the major reasons -for building high-voltage lines. Continued uprating o-f transmission line voltages seems to have reached the point of saturation. High voltage lines, however, present strong electric -fields at the ground sur-face with possible biological ef-fects, visual pollution, audible noice and increasing difficult problems in acquiring new rights o-f way, etc. A pressing need, there-fore, appears to exist for better transmission alternatives. Multiphase transmissions in the place of a conventional three-phase has been found to utilize rights of way in an efficient manner and offers a very appealing and unique solution to the problem of the increased demand for electric energy. At present, six- phase transmissions is -considered to be the most promising among the multiphase systems for possible realization in the near future. The existing double- circuit three-phase lines may be converted to six-phase lines quite easily with only a change in the secondary connection of the transformes feedin the double-circuit lines to obtain six-phase operation. If these were to become a reality, careful planning of such transmission system is crucial, The most important aspect of the planning is the design of a protective scheme for six-phase systems. Suchs a design requires detailed fault analysis of these systems. vi A -few balanced -faults occur on a real power transmissions system and their fault analysis ie easy. On the other hand, line-to-ground faults, which is unsyrometrical in nature, are more likely to occur and their analysis requires an important tool, namely, thE theory of symmetrical components. Though Fortescue postulated that a symmetrical component theory could be developed for any n-phase system. Accoring to Fortescue 'e Theorem, six ur.Dalanced (voltage or current) phasors of a six-phase system can be resolved into six balanced systems of phasors. The balanced sets of components are : i) First -(or positive ) sequence components, ii) Second-sequence components, iii) Third-sequence components, iv) Fourth-sequence compnents, v) Fifth- (or negative ) sequence components end vi) Sixth- (or zero ) sequence components. Each of the ith sequence components (i-0,1,2,3,4,5! consist of six phasors equal in magnitude and displaced from each other by i (60) in phase. Let the six phases of the original system be a, b, c, d, e, f with phase sequence 'abcdef. The six sets of sequence components for an unbalanced phase voltages V, a V,. V, V, V and V are depicted in Figure 1. One b c d e f can observe easily that the first - (orpositive) sequence components have the original phase sequence. The other sets of components shown in the Figure 1 are self- explanatory. vii V al 'bl Pozitive-Sequence Components V V c2' f2 V V a2* d2 vb2« ve2 Second-Sequence Components Va3' Vc3 V V V vb3' vd3 Third-Sequence Components e3 a4l ve4 c4 ' f 4 Vb4' Ve4 Fourth-Sequence Components rc5 'd5' Negative-Sequence Components Zero-Sequence Components Figure 1 - Six balanced sets of symmetrical components of six unbalanced? phasors. The original unbalance phsors can be expressed in terms of their symmetrical components by the fd lowing equation. V = V + V +V + V + V + V a al aS a3 a4 a5 aO V = v +v +v + v + v +v b bl b£ b3 b4 b5 bO V = V + V + V + V +V +V c cl c2 c3 c4 c5 cO V =v +V +V +V + V +V d di de d3 d4 d5 dO V = V + V +V +V +V +V e el e2 e3 e4 e5 eO V == V +V + V + V + V + V f fi fS f3 f4 f5 fO Knowing the sequence component sets, the unbalanced voltage phasors can synthesized graphically cr analytically using uquation (1). i Let the six-phase operator be b=e /3=u.5+j O.Eofa This operator b is related to the three-phase operator a by : b = -a Figure E shows the phasor diagram of the various powers of operator b. Equation (2) summerises sone of the functions of operator b and its relation to operators a and j. 2 *. i Figure E. Phasor diagram of the various powers of operator b. ix 2 5 * b - 0.5 + j 0.866 = -a <= (b"> b = -0.5 + j 0.E66 = a = (b ) o bM= -1 + j 0.0 4 e b s -0.5 - j 0.B66 b a 5 b = 0.5 - j 0.866 « -a S 3 4 5 1+b + b + b + b + b =0 o 1 + bw= 0 sı e l+b+b = l + a + a = 0 ' b + b"+ b"= 0 Referring to Figure 1, the following relationships between the sequence components of b phase and a phase (reference) could be easily verified. Similar relationship could be written for other phases. 5 V = b V bl al 4 V = b V bE aE V = bWV b3 a3 E V = b V b4 a4 V = b V b5 a5 V - b V bO aO Now, equation (i) can be written -using these various relationships as î f 11111 5 4 3 2 1 b b b b b S 3 4 S b b b b b (4) or V » E T 3 V p 6 £ (5) where T <= six-phase symmetrical component transformation matrix. Equation <4) or (5) relatess the unbalanced set of voltage phasors to their sequence components. The inverse relationship is : -1 - V*[T] V e 6 p (6) It should be stressed at this point that equation (5) and (&) are very often used -for unsymmetrical fault analysis. It should be observed that both ET 3 and its inverse are symmetric matrices. That ib, T -1 T -1 ET 3 « ET 3 and ET 3 = ET 3 e e 6 e Equations similar to (5) and (6) can easily be written -for line currents. That is ; (7) ET 3 = ET 3 T p ?> s ET 3 « ET 3 T 5 6 p (3) XI The neutral current 1=1 +1 +1 +1 +I+I n a b c d e f will be non-zero zero if the current phasors are balanced and is also equal to 61 / aO To determine the effects of condansators in series on a six-phase transmission system, 380 kV three-phase double circuit Keban - Bolbasi is converted to 3BÛ kV six-phase line. The total magnitude of the condansatar in series is distributed to the different places of the line. Then the fault currents of all buses are calculated to compare each other.