##
Enerji iletiminde seri kompanzatörlerin gerilim kararlılığına etkileri

Enerji iletiminde seri kompanzatörlerin gerilim kararlılığına etkileri

##### Dosyalar

##### Tarih

1996

##### Yazarlar

Serimazın, M. Ziyaeddin

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

Institute of Science and Technology

Institute of Science and Technology

##### Özet

Bu çalışmada, seri kompanzatörlerin gerilim kararlılığına etkilerini araştırmaya yönelik incelemeler yapılmıştır, öncelikle enerji iletim hatları hakkında detaylı bilgiler verilmiştir. İletim hatları tanımlanırken, kısa hatlar, orta uzunluktaki hatlar ve uzun hatlar olarak üç grupta toplanmıştır. İletim hatlarının hangi kategoriye gireceğine yönelik kriterler verilmiştir. Kısa enerji iletim hatları için basit bir modellemeyle, hattın tamm bağıntıları yazılmıştır. Ota uzunluktaki iletim hatları için enerji iletim hattının % ve T-eşdeğer devre modelleri verilmiştir ve buna bağlı kalınarak hatan devre denklemleri çıkarılmıştır. Uzun enerji iletim hatlarında dağılmış parametreler dikkate ammış, ve hatun karakteristik büyüklüklerini içeren hiperbolik bağıntılar mcelenrniştir. Daha sonra iletim hatlarının seri veya paralel bağlı olamalan durumunda, eşdeğer ABCD katsayılarının iradeleri verilmiştir. Enerji iletim hattının ilettiği güçlerin bağıntıları ve bunlara ilişkin diyagramlar ele alınmıştır. Çalışma için örnek olarak alınan Keban-Kayseri-Gölbaşı ham. taratılmış ve devre modeli elde edilmiştir. Bu modele göre enerji iletim hatanın seri kompanzatörlerinin aynı değerde olduğu dengeli durum ve farklı değerde olduğu dengesiz durum için Vg-Pr eğrileri ve Ps-Vs eğrileri, hattın ABCD parametreleri ve bunlara ilişkin güç bağıntıları kullanılarak doğrudan yöntemle çazürniştir. Daha sonraki bölümlerde enerji iletim hattının üç modeli için farklı bir yöntemle, analitik olarak, Ps-Vs eğrileri çizdirilmiş ve kararlılık incelemelerinde önemli yer tutan kritik güç Pscrit, limit güç Pslim, işletme gerilim düşümü AVop, ve gerilim indikatörü Kv-yk, güç indikatörü Kp-yk ve kararlılık indikatörü Ks-yk 'nın güç faktörü cos (j> "ye göre değişimleri grafik olarak çizilmiştir. Bu çalışmalar devre için seçilen üç model için tekrarlanmış ve en uygun işletme koşullan açısından Buradaki amaç, dengeli işletme koşullarında aynı değerde olan seri kompanzatörlerin bir arıza sonunda değerlerini değiştirip dengesizlik oluşturmaları durumunda, hatan davranışı hakkında bilgi edinebilmektir. Bu amaca yönelik olarak, son aşamada hatan farklı dengesiz durumları ve farklı devre modelleri için Ps-Vs eğrileri çizilmiş ve dengesiz durumda hattın davranışı incelenmiştir.

In this study, the effects of series compensators on voltage stability are examined. Firstly, energy transmission lines are determined generally, and their characteristic quantities are declaired. As a criteria of the length of energy tranmission lines, they can be considered as short lines for a length less than SO km's, as medium-length lines for a length between 80 km's and 240 km's. Even though in some special cases integrated parameters can be vised for lengths less man 320 km's like medium-length lines, for energy tranmission lines longer than 240 km's distributed parameters are taken into consideration most commonly. In this section energy tranmission lines are also considered in three groups as short transmission lines, middle long transmission lines and long energy transmission lines. For the short transmission lines simple circuit equivalents and relations are given as well as the equivalent circuit and the phasor diagrams of them. Middle long transmissions lines are considered with their % and T equivalents giving their models with ABCD parameters. For the Tc-equivalent circuit, the shunt admittances are devided in two and connected to each end of the line. For the T-equivalent circuit, the series impedances of the energy tranmission lines are devided in two and connected to each end of the line similarly. For the long transmission lines, distributed line parameters are studied and hyperbolic relations between quantities are given. These hyperbolic relations between quantities of the end of the line are derived from the differential equations of the second order as shown in 2.5. In the same section, the characteristic quantities like characteristic impedance Zc and propagation factor of the line are determined as well as Surge Impedance Loading - SIL. The ABCD parameters of the energy tranmission line are expressed by means of characteristic quantities of the line as shown in 2. 10. Equivalent circuits for series and parallel circuits are given and the terms for equivalent ABCD patameters are discussed. Hie equivalent parameters of the serially and parallel connected lines are expressed by means of ABCD parameters of each connected line. The complex power Pr + j Qr is derived and expressed by means of the transmission angles a, p and 5. The components of the complex power Pr and Qr are also studied in the same sections. According to the above examinations power diagrams of energy tranmission line and expression of the maximum transmission power are taken into consideration. In the following section of the study, the sample energy transmission line Keban-Kayseri-Golbasi is introduced and its parameters are given in a circuit diagram as per unit quantities. After that the six circuit models of energy tranmission lines, which are most commonly used in studies of stability, are introduced. The first three of them are used in later sections. The definitions of parameters of energy tranmission lines are also studied. One of the most important facts of voltage stability are the P-V diagrams of the energy tranmission line. In this study two different methods are considered to derived the P-V diagrams of the energy tranmission line. First, the so called analytical method is given introducing also the critical values of energy tranmission line like Sait, Vcrit and Petit In the same section a sample P-V diagram is also introduced. Later the meaning of the P-V diagrams is described taking the effects of the line's characteristics on the voltage stability nto consideration. When the transmitted power factor cos $ changes from lugging values to leading values, that means from the capacitive values to the inductive ones, the stability area of the P-V diagrams becomes larger and the critical transmitted power increases. The same critical power value becomes lower with increasing line length. Against this the critical voltage value increases with increasing line length. The effect of the loss factor of the energy tranmission line on the P-V diagram is that the critical value and the stability area increase with decreasing loss factor. Further more the effect of the sending end voltage is shown in the same section. X! When the sending end voltage increases, the critical voltage and power values also increase. If the energy is transmitted through two parallel lines in state of one line, the critical power value increases while the critical voltage value stays nearly constant. When on the receiving end shunt capacitors exist, the critical power and voltage values increase while they are getting lower when the received reactive power increases. In the same section the effects of shunt compansation, serial and shunt compansation together and shunt compansation alone are also considered giving also the according P-V diagrams and the modelling of the sample transmission line is made by considering the line, which has two parallel arms, as series %- circuits. For observing the P-V diagrams of the sample line, the line is modelled first taking its x-circuit model into consideration. Therefore anry one parallel arm of the energy tranmission line is calculated as one circuit. Golbasi-Kayseri it-circuit and Kayseri -Keban ^-circuit are calculated seperatery and from these ABCD parameters the complete model of the line is derived In the first step the Ps-Vs diagrams are drawn for the balanced statement of the line, that means the serial compansators on each phase are equal. Additionally the Vs-Pr diagrams are also drawn for the same statement And in the next step the same work is done for the unbalanced statement of the sample energy transmission line. In the both situations Vs-Pr trends and Vs-Ps trends have been drawn by means of ABCD parameters of the line and related power equations with the direct method. This direct method consists of calculations with the voltage and current values of the line ends and the related ABCD parameters of the energy tranmission line. In the further section the P-V diagrams of the energy tranmission line are derived by means of the analytical method using the complex components of current, voltage, active and reactive power. According to complex manipulations an equation of fourth order is obtained and the geometrical locations of the solutions from this fourth order equation give us the P-V diagram directly. XH By these calculations the first three circuit modes of the sample energy tranmission line is taken into consideration and the complex ABCD parameters are calculated separately for each mode. Further more some new definitions like Kv-yk, Kp-yk and Ks-yk are given as well as the special values like VKm, Vop, PKm and Pop. The trends, how these special values change against transmitted power factor cos are given in related diagrams. These studies have been repeated for three models of the sample energy transmission line and have been compared with each other according to the most appropriate operation. The intention of these calculations is to examine the behaviour of the line after a failure of the compensators creating an unbalanced situation which are normally operating balanced. In the last section the P-V diagrams for both balanced and unbalanced statements of the sample energy tranmission line are drawn by using the so called analytical method for various circuit models and the response of the line in unbalanced situation has been examined. When the receiving end voltage increases, the Pscrit value of the energy tranmission line, which defines the stability border, also increases; that means according to the stability the line can transmit higher powers with more security. For a certain circuit mode when the receiving end busbar is assumed as an infinite busbar, different voltages for every phase are obtained for the unbalanced statement of the serial compensators. This fact is in accordance with definitions for unbalanced statements. For the decreasing values of the serial compansators the Pscrit critical power value also decrease; in addition for the idle operating the amplitude of the sending end voltage Vs decreases too. xm When the transmission power factor cos «j> is considered as a parameter, for its values changing from -7c/2 to +%/2 the Pscrit critical power values of the energy transmission line also increase. A comparison between the different circuit modes shows that Mode 1 leaves the stability area earlier than the others and passes the critical values earlier. Mode 2 and Mode 3 are more convinient from this point of view. For the changing values of the transmission power factor cos<{> from -tc/2 to +x/2 the limit sending end power values Pslim also increase. The circuit modes Mode 2 and Mode 3 have cos (jhPslim trends with greater slopes than Mode 1 has. That means, Mode 2 and Mode 3 have larger capacity to be loaded than Mode 1. When the sending end power values Ps are assumed as a parameter, for a certain cos AVop increases for higher values of Ps. With other words, for üıe lower transmission power values more suitable operating statements can be obtained. It can be said that Mode 2 and Mode 3 operate with lower voltage drops than Model. When the sending end power values Ps is considered as parameters, cos § - Kv-yk trends can be drawn and for decreasing values of Ps, the values of the indicator Kv-yk increase. In addition to this the diagrams for Mode 1, Mode 2 and Mode 3 are rearîy similar and they have a decreasing slope. The Kp-yk indicator values decrease for the values of tranmission power factor cos $ chancing from -nil to +7t/2. However this increasing is faster by Mode 1 than Mode 2 and Mode 3. That means Kp-yk indicators for Mode 2 and Mode 3 keep their high values for higher cos . The behaviours of Mode 2 and Mode 3 are also similar by the unbalanced statement. If the reactance of the serial eompansator in the unbalanced phase is higher than the other ones, the critical power value in the Ps-Vs diagrams of the balanced phases is greater than the one in the unbalanced phase. In that situation the unbalanced phase limits the balanced phases and the total power transmitted through the energy transmission line is also limited. For some special values of the capacitor reactance in the unbalanced phase, the balanced phases are forced to operate m the unstable areas. One can say that Mode 1 is less convinient to operate in the either balanced or unbalanced statements than the circuit modes Mode 2 and Mode 3. The circuit mode Mode 1 goes easily to the unstable area and in the most of the operations its limit values are very closed to the critical values.

In this study, the effects of series compensators on voltage stability are examined. Firstly, energy transmission lines are determined generally, and their characteristic quantities are declaired. As a criteria of the length of energy tranmission lines, they can be considered as short lines for a length less than SO km's, as medium-length lines for a length between 80 km's and 240 km's. Even though in some special cases integrated parameters can be vised for lengths less man 320 km's like medium-length lines, for energy tranmission lines longer than 240 km's distributed parameters are taken into consideration most commonly. In this section energy tranmission lines are also considered in three groups as short transmission lines, middle long transmission lines and long energy transmission lines. For the short transmission lines simple circuit equivalents and relations are given as well as the equivalent circuit and the phasor diagrams of them. Middle long transmissions lines are considered with their % and T equivalents giving their models with ABCD parameters. For the Tc-equivalent circuit, the shunt admittances are devided in two and connected to each end of the line. For the T-equivalent circuit, the series impedances of the energy tranmission lines are devided in two and connected to each end of the line similarly. For the long transmission lines, distributed line parameters are studied and hyperbolic relations between quantities are given. These hyperbolic relations between quantities of the end of the line are derived from the differential equations of the second order as shown in 2.5. In the same section, the characteristic quantities like characteristic impedance Zc and propagation factor of the line are determined as well as Surge Impedance Loading - SIL. The ABCD parameters of the energy tranmission line are expressed by means of characteristic quantities of the line as shown in 2. 10. Equivalent circuits for series and parallel circuits are given and the terms for equivalent ABCD patameters are discussed. Hie equivalent parameters of the serially and parallel connected lines are expressed by means of ABCD parameters of each connected line. The complex power Pr + j Qr is derived and expressed by means of the transmission angles a, p and 5. The components of the complex power Pr and Qr are also studied in the same sections. According to the above examinations power diagrams of energy tranmission line and expression of the maximum transmission power are taken into consideration. In the following section of the study, the sample energy transmission line Keban-Kayseri-Golbasi is introduced and its parameters are given in a circuit diagram as per unit quantities. After that the six circuit models of energy tranmission lines, which are most commonly used in studies of stability, are introduced. The first three of them are used in later sections. The definitions of parameters of energy tranmission lines are also studied. One of the most important facts of voltage stability are the P-V diagrams of the energy tranmission line. In this study two different methods are considered to derived the P-V diagrams of the energy tranmission line. First, the so called analytical method is given introducing also the critical values of energy tranmission line like Sait, Vcrit and Petit In the same section a sample P-V diagram is also introduced. Later the meaning of the P-V diagrams is described taking the effects of the line's characteristics on the voltage stability nto consideration. When the transmitted power factor cos $ changes from lugging values to leading values, that means from the capacitive values to the inductive ones, the stability area of the P-V diagrams becomes larger and the critical transmitted power increases. The same critical power value becomes lower with increasing line length. Against this the critical voltage value increases with increasing line length. The effect of the loss factor of the energy tranmission line on the P-V diagram is that the critical value and the stability area increase with decreasing loss factor. Further more the effect of the sending end voltage is shown in the same section. X! When the sending end voltage increases, the critical voltage and power values also increase. If the energy is transmitted through two parallel lines in state of one line, the critical power value increases while the critical voltage value stays nearly constant. When on the receiving end shunt capacitors exist, the critical power and voltage values increase while they are getting lower when the received reactive power increases. In the same section the effects of shunt compansation, serial and shunt compansation together and shunt compansation alone are also considered giving also the according P-V diagrams and the modelling of the sample transmission line is made by considering the line, which has two parallel arms, as series %- circuits. For observing the P-V diagrams of the sample line, the line is modelled first taking its x-circuit model into consideration. Therefore anry one parallel arm of the energy tranmission line is calculated as one circuit. Golbasi-Kayseri it-circuit and Kayseri -Keban ^-circuit are calculated seperatery and from these ABCD parameters the complete model of the line is derived In the first step the Ps-Vs diagrams are drawn for the balanced statement of the line, that means the serial compansators on each phase are equal. Additionally the Vs-Pr diagrams are also drawn for the same statement And in the next step the same work is done for the unbalanced statement of the sample energy transmission line. In the both situations Vs-Pr trends and Vs-Ps trends have been drawn by means of ABCD parameters of the line and related power equations with the direct method. This direct method consists of calculations with the voltage and current values of the line ends and the related ABCD parameters of the energy tranmission line. In the further section the P-V diagrams of the energy tranmission line are derived by means of the analytical method using the complex components of current, voltage, active and reactive power. According to complex manipulations an equation of fourth order is obtained and the geometrical locations of the solutions from this fourth order equation give us the P-V diagram directly. XH By these calculations the first three circuit modes of the sample energy tranmission line is taken into consideration and the complex ABCD parameters are calculated separately for each mode. Further more some new definitions like Kv-yk, Kp-yk and Ks-yk are given as well as the special values like VKm, Vop, PKm and Pop. The trends, how these special values change against transmitted power factor cos are given in related diagrams. These studies have been repeated for three models of the sample energy transmission line and have been compared with each other according to the most appropriate operation. The intention of these calculations is to examine the behaviour of the line after a failure of the compensators creating an unbalanced situation which are normally operating balanced. In the last section the P-V diagrams for both balanced and unbalanced statements of the sample energy tranmission line are drawn by using the so called analytical method for various circuit models and the response of the line in unbalanced situation has been examined. When the receiving end voltage increases, the Pscrit value of the energy tranmission line, which defines the stability border, also increases; that means according to the stability the line can transmit higher powers with more security. For a certain circuit mode when the receiving end busbar is assumed as an infinite busbar, different voltages for every phase are obtained for the unbalanced statement of the serial compensators. This fact is in accordance with definitions for unbalanced statements. For the decreasing values of the serial compansators the Pscrit critical power value also decrease; in addition for the idle operating the amplitude of the sending end voltage Vs decreases too. xm When the transmission power factor cos «j> is considered as a parameter, for its values changing from -7c/2 to +%/2 the Pscrit critical power values of the energy transmission line also increase. A comparison between the different circuit modes shows that Mode 1 leaves the stability area earlier than the others and passes the critical values earlier. Mode 2 and Mode 3 are more convinient from this point of view. For the changing values of the transmission power factor cos<{> from -tc/2 to +x/2 the limit sending end power values Pslim also increase. The circuit modes Mode 2 and Mode 3 have cos (jhPslim trends with greater slopes than Mode 1 has. That means, Mode 2 and Mode 3 have larger capacity to be loaded than Mode 1. When the sending end power values Ps are assumed as a parameter, for a certain cos AVop increases for higher values of Ps. With other words, for üıe lower transmission power values more suitable operating statements can be obtained. It can be said that Mode 2 and Mode 3 operate with lower voltage drops than Model. When the sending end power values Ps is considered as parameters, cos § - Kv-yk trends can be drawn and for decreasing values of Ps, the values of the indicator Kv-yk increase. In addition to this the diagrams for Mode 1, Mode 2 and Mode 3 are rearîy similar and they have a decreasing slope. The Kp-yk indicator values decrease for the values of tranmission power factor cos $ chancing from -nil to +7t/2. However this increasing is faster by Mode 1 than Mode 2 and Mode 3. That means Kp-yk indicators for Mode 2 and Mode 3 keep their high values for higher cos . The behaviours of Mode 2 and Mode 3 are also similar by the unbalanced statement. If the reactance of the serial eompansator in the unbalanced phase is higher than the other ones, the critical power value in the Ps-Vs diagrams of the balanced phases is greater than the one in the unbalanced phase. In that situation the unbalanced phase limits the balanced phases and the total power transmitted through the energy transmission line is also limited. For some special values of the capacitor reactance in the unbalanced phase, the balanced phases are forced to operate m the unstable areas. One can say that Mode 1 is less convinient to operate in the either balanced or unbalanced statements than the circuit modes Mode 2 and Mode 3. The circuit mode Mode 1 goes easily to the unstable area and in the most of the operations its limit values are very closed to the critical values.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996

Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1996

Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1996

##### Anahtar kelimeler

Enerji iletim sistemleri,
Gerilim,
Kompansatör,
Energy transmission systems,
Voltage,
Compensator