Optimal Location of Series FACTS Device using Loss Sensitivity Indices. 3.2 Development of Loss Sensitivity Indices

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1 Chapter 3 Optimal Location of Series FACTS Device using Loss Sensitivity Indices 3.1 Introduction The location and sizing of series FACTS devices constitute a major step in the application of FACTS devices. This chapter presents the development of methodologies based on loss sensitivity indices for determining the optimal location of series FACTS device. Both active and reactive power line losses have been considered in this development of sensitivity indices. The efficacy of these methods have been tested on 5,9,14,30 bus IEEE and 14 Bus part of Indian power network. 3.2 Development of Loss Sensitivity Indices FACTS sizing and allocation constitutes a milestone problem in power system. In this regard, various methods of location of FACTS controllers have given below. Generally, location of FACTS devices in the power system have obtained based on static and / or dynamic performances. There are several methods for finding optimal location of FACTS devices in vertically integrated system as well as unbundled power system. The objective of the series device placement may be reduction in the real power loss of a particular line, reduction in the total system real power loss, reduction in the total system reactive power loss and maximum power transfer in the system. Sensitivity analysis is a widely used terminology to describe the analysis based on the evaluation of the rate of change of one group of variables in a system with respect to another group. There are many different ways to perform the analysis depending on the selected variables and methodologies used to calculate the sensitivities. In this chapter the loss sensitivity indices have been developed based on active & reactive power losses in each line with respect to the control variable of the FACTS device of the power network. PET Research centre, PESCE, Mandya 72

2 Loss sensitivity index is a method based on the sensitivity of total system active and reactive power loss with respect to control variable of the FACTS devices. In this research, a method based on the sensitivity of the total system reactive power loss with respect to the control variable of the TCSC has carried out. Consider TCSC to be placed between the buses i and j, we consider net line series reactance as a control parameter. Loss sensitivity indices with respect to real power is b ij and with respect to reactive power is a ij. This control parameter of TCSC placed between buses i and j can be written as, Q L a ij 3.1 X ij P L b ij 3.2 X ij These factors can computed at a base load flow solution as given below. Consider a line connected between buses i and j and having a net series impedance of Xij and Qi is the net reactive power injected in the bus i. The bus sensitivity index with respect to Xij computed as, Real part P i = 3.3 P i = Imaginary part PET Research centre, PESCE, Mandya 73

3 Where P L =P i + P j, i and j are the buses 1 & 2 (Figure 3.1b) The criteria used in the selection of optimal placement of TCSC is δp L /δx ij and δq L /δx ij should have a positive or a value nearer to the origin called sensitivity index Thyristor Controlled Series Capacitor (TCSC) Modeling FACTS devices can be modeled as power injection model. The injection model describes the FACTS devices as a device that injects a certain amount of active and reactive power to a node, so that the FACTS device is represented as PQ elements. The advantage of power injection model is that it does not destroy the symmetrical characteristic of the admittance matrix and allows efficient and convenient integration of FACTS devices into existing power system analytical tools. During steady state operation, TCSC can be considered as an additional reactance -jx c. The value of x c is adjusted according to control scheme specified. Figure 3.1(a) shows a model of transmission line with one TCSC which is connected between bus-i and bus-j. The line flow change is due to series capacitance which is represented as a line without series capacitance with power injected at the receiving and sending ends of the line as shown in Figure 3.1(b). Z = r + j x i j i j i j Bus - i ib s h -jx c jb s h Bus - j Fig. 3.1(a) TCSC model PET Research centre, PESCE, Mandya 74

4 Z = r + j x i j i j i j Bus - i S ic S j c Bus - j Fig. 3.1(b) Injection model of TCSC The real power injections at bus-i(p ic ) and bus-j(p jc ) are given by [55]: P ic =V 2 i G ij V i Vj[ G ij cosδ ij + B ij sinδ ij ] 3.15 P jc =V 2 j G ij V i Vj[ G ij cosδ ij - B ij sinδ ij ] 3.16 Similarly, the reactive power injections at bus-i (Q ic ) and bus- j (Q jc ) can be expressed as: Q ic = V 2 i B ij V i Vj[ G ij sinδ ij - B ij cosδ ij ] 3.17 Q jc = V 2 j B ij + V i Vj[ G ij sinδ ij + B ij cosδ ij ] 3.18 Where: ΔG ij r 2 ij x r (x c ij x 2 ij r 2 ij c 2x ) x ij ij 2 xc ΔB ij r 2 ij x c x r 2 ij 2 ij r 2 ij x 2 ij x ij x c x x c ij 2 Where G ij and B ij are the change in conductance and change in susceptance of the line i-j. This model of TCSC is used to properly modify the parameters of transmission lines with TCSC for optimal location [100]. Static Series Synchronous Compensator (SSSC) The Static Synchronous Series Compensator (SSSC) is a series connection FACTS controller dependent on VSC and can be considered as advanced kind of controlled series compensation, just as a STATCOM is an advanced SVC. A SSSC own several merits over a TCSC such as (a) elimination of bulky passive components (capacitors and reactors), PET Research centre, PESCE, Mandya 75

5 (b) improved technical characteristics, (c) symmetric capability in both inductive and capacitive operating modes, (d) the connection availability of an energy source on the DC port to exchange active power with the AC grid. A solid-state synchronous voltage source, consisting of a multi-pulse, voltagesourced inverter and a DC capacitor, is shown in series with the transmission line in Figure 3.2. Fig. 3.2 Schematic diagram for the SSSC. In general, the active and reactive power exchange is controlled by the phase displacement of the injected voltage related to the current. For example, when the injected voltage is in phase with the line current, then only active power is exchanged, and if it is in quadrature with the line current then only reactive power is exchanged. The series-connected synchronous voltage source is an extremely powerful tool for power flow control and, it is able to control both the transmission line impedance and angle. Its capability to exchange active power with the grid makes it very effective in enhancing dynamic stability by means of alternately inserting a virtual positive and PET Research centre, PESCE, Mandya 76

6 negative damping resistance in series with the line by the disturbed generators angular deceleration and acceleration. The idea of the solid-state synchronous voltage source for compensation of series reactive depends on the rule that the characteristic of the impedance with the frequency of the practically employed series capacitor, which is different than the filter techniques, has no role in achieving the required line compensation. The goal of the series capacitor is summarized to generate a suitable voltage at the fundamental AC network frequency in series with the line to eliminate the voltage drop produced via the inductive impedance of the line by the fundamental part of the line current. So that the resulting total voltage drop of the compensated line becomes electrically equivalent to that of a shorter line. Therefore, if an AC voltage supply with fundamental frequency, which has a quadrature lagging following to the line current and the magnitude depends on the line current is flowed in series with the line. A series compensation is equal to the one developed by a series capacitor during the fundamental frequency is supplied. The voltage source can be described in mathematical form as follows: Vn = jkxi Vn is the compensating value of the injected voltage, I is the phasor of the line current, X is the impedance of the series reactive line, and k is the series compensation degree. For conventional series compensation, k is defined as X C /X, where X C is the impedance of the series capacitor. For regular capacitive compensation, the output voltage must lag the line current by 90 degrees, in order to directly oppose the inductive voltage drop of the line impedance. However, the output voltage of the inverter will be opposed by a proper control method to direct it to be leading the line current with 90 degrees. Then, the inserted voltage is in phase with the voltage developed by the inductive reactance of line. Therefore, the series compensation owns the equivalent effect as if the reactive impedance was raised. This capability can be invested to increase the effectiveness of power oscillation damping and, with sufficient inverter rating; it can be used for fault PET Research centre, PESCE, Mandya 77

7 current limitation. Series compensation by a synchronous voltage source that can be limited to the fundamental frequency is worthy to that provided with series capacitive compensation in that it cannot produce undesired electrical resonances with the transmission grid, and for this reason, it cannot cause sub-synchronous resonance. However, by appropriate control it can damp sub-synchronous oscillations, which may happen because of present series capacitive compensations by inserting non-fundamental voltage components with proper magnitudes, phase angles and frequencies, in addition to the fundamental component, in series with the line. Due to the stipulated 90-degree phase relationship between the inverter output voltage and the line current, this, via the series insertion transformer, flows through the inverter as the load current, the inverter in the solid-state voltage source theoretically exchanges only reactive power with the AC system. As explained previously, the inverter can internally generate all the reactive power exchanged and thus can be operated from a relatively small. In practice, however, the semiconductor switches of the inverter are not loss-less, and so the energy saved in the DC capacitor would be balanced through the inverter internal losses. The typical deviation from 90 degrees is a fraction of a degree. In this way, the inverter draws a small value of active power from the AC network to balance the internal losses and save the DC capacitor voltage at the required level. That control procedure can also be applied to raise or reduce the DC capacitor voltage by making the inverter voltage lag the line current by an angle smaller or greater than 90 degrees. Thereby, control the magnitude of the AC output voltage of the inverter and the degree of series compensation. 3.3 Simulation using MATLAB/SIMULINK Introduction The objective of this is to bring about the basic tools needed to use the SIMULINK package SIMULINK is an extension to MATLAB which uses a icon-driven interface for the construction of a block diagram representation of a process. A block diagram is simply a graphical representation of a process (which is composed of an input, the system, and an output). PET Research centre, PESCE, Mandya 78

8 Fig.3.3 A very simple block diagram of a process Typically, the MATLAB m-file ode45 is used to solve sets of linear and nonlinear ordinary differential equations. One of the reasons why MATLAB is relatively easy to use is that the ``equation solvers'' are supplied for us, and we access these through a command line interface (CLI). However, SIMULINK uses a graphical user interface (GUI) for solving process simulations. Instead of writing MATLAB code, we simply connect the necessary ``icons'' together to construct the block diagram. The ``icons'' represent possible inputs to the system, parts of the systems, or outputs of the system. SIMULINK allows the user to easily simulate systems of linear and nonlinear ordinary differential equations. A good background in matrix algebra and lumped parameter systems as well as an understanding of MATLAB is required, and we highly recommend that the student thoroughly reads and works through this tutorial. Many of the features of SIMULINK are user-friendly due to the icon-driven interface, yet it is important to spend some time experimenting with SIMULINK and its many features. Dynamic simulation packages (such as MATLAB, SIMULINK, etc.) are being used more and more frequently in the chemical process industries for process simulation and control system design. After completing this tutorial, the student should be able to ``build'' and simulate block diagram representations of dynamic systems Getting Started in Simulink Simulink is an icon-driven state of the art dynamic simulation package that allows the user to specify a block diagram representation of a dynamic process. Assorted sections of the block diagram are represented by icons which are available via various "windows" that the user opens (through double clicking on the icon). The block diagram is composed of icons representing different sections of the process (inputs, state-space models, transfer functions, outputs, etc.) and connections between the icons (which are made by "drawing" a line connecting the icons). Once the block diagram is "built", one has to specify the parameters in the various blocks, for example the gain of a transfer function. Once these parameters are specified, then the user has to set the integration PET Research centre, PESCE, Mandya 79

9 method (of the dynamic equations), step size, start and end times of the integration, etc. in the simulation menu of the block diagram window. In order to use SIMULINK, one must ``start'' a MATLAB session Once MATLAB has started up, type simulink (SMALL LETTERS!) at the MATLAB prompt (>>) followed by a carriage return (press the return key). A SIMULINK window should appear shortly, with the following icons: Sources, Sinks, Discrete, Linear, Nonlinear, Connections, and Extras (this window is shown in Figure 4.2). Next, go to the file menu in this window and choose New in order to begin building the block diagram representation of the system of interest. Fig.3.4 Simulink block library window. NOTE: The results are obtained using SIMULINK/MATLAB in the following section. The results give the bus voltage,power (P and Q) initiated at the dummy buses placed near the actual bus. The power flow is calculated by considering the algebraic sum of the powers at the buses the line is connected to. 3.4 Case studies: The efficacy of algorithms developed based on loss sensitivity indices have been tested on IEEE 5, 14, 30 as well as a part of a practical Indian power network. In order to study the location of TCSC using loss sensitivity active power loss method, the following systems are considered. The factor bij is calculated for each line and the line sensitive to active power loss is highlighted. The TCSC is located in those lines Case 1: IEEE 5 bus system The 5 bus system considered is a IEEE bench mark system consisting of 5 buses, 7 lines, 3 generators. The system data is given in the APPENDIX. The single line diagram is as shown in figure 3.5. PET Research centre, PESCE, Mandya 80

10 BUS 1 BUS BUS BUS 3 BUS Fig.3.5 Single line diagram of IEEE 5 bus system Fig.3.6 Simulink model of 5-Bus System PET Research centre, PESCE, Mandya 81

11 Table 3.1 Line power flow Line No. Line Power P(MW) L L L L LL L ll Table3.2. Line Losses Line Nos P(MW) From T It is seen from the results that the location of FACTS device is in line connected between nodes 2-5, Hence this is chosen as the proper location for locating TCSC. Fig.3.7 Simulink model of 5-Bus System with TCSC PET Research centre, PESCE, Mandya 82

12 Fig.3.8. Simulink phasor model of TCSC Fig.3.9 Simulink internal phasor model of TCSC Specification of TCSC Frequency = 50 Hz Manual alpha (deg) = 78 TCSC capacitance (F) = e-6 TCSC reactance (H) = 0,043 Average firing delay (s) = 4e-3 PET Research centre, PESCE, Mandya 83

13 Simulink Results Table3.3. Line active power flow with TCSC Line No. Line Power P(MW) L L L L LL L ll Table3.4. Line Losses with TCSC Losses b/w Bus P(MW) From T Summary of the Result Comparison of Line Losses with & without TCSC for IEEE-5 bus system is presented below, Table3.5. Comparison of without and with TCSC Line Losses b/w bus 2 and bus 5 WITHOUT TCSC WITH TCSC 0.91 MW 0.86 MW PET Research centre, PESCE, Mandya 84

14 power (MW) Adaptive controller strategies for FACTS controllers in a power system to enhance stability & 2 1 & 3 2 & 3 3 & 4 2 & 4 2 & 5 4 & 5 without TCSC with TCSC Fig.3.10 Graphical Comparison of Line Losses of 5-Bus System Simulink Model With and Without TCSC Result analysis It is seen from the results that the optimal location of FACTS devices based on loss sensitivity indices based on active power is in line connected between nodes 2 and 5. The TCSC is located in the line number 5 connected between buses 2 and 5, the line with highest loss. The results after locating TCSC is tabulated in table no 3.6 and 3.7. As seen from the above mentioned tables it is observed that the loss is 0.91 MW before placing TCSC and it is 0.86 MW after placing the TCSC Case 2: IEEE 30-Bus System In order to study effectiveness of the loss reduction method of locating TCSC a higher order system is considered. A IEEE 30 bus system is considered. A 30 bus system consists of 30 buses, 41 lines, 7 generators. and 20 loads. The detailed bus data, line data, generator data is given in the APPENDIX. The single line diagram is as shown in Fig The SIMULINK model of 30 bus system is as shown in Fig 3.12 without placing TCSC. Fig 3.12 gives the power flow analysis of this system. In this proposed method the TCSC is located in branches which are considered to be sensitive based on losses. That is the losses are calculated based on load flow analysis. The branch having more loss is identified and the lines surrounding it in a concentric way are considered and TCSC is located in each and every branch in this concentric and losses are calculated again. The system considered for proving the credibility of the method is IEEE 30 bus system. PET Research centre, PESCE, Mandya 85

15 29 T G6 T 1 G5 T2 T 3 22 G G4 G2 G3 Fig 3.11 IEEE 30-bus single line diagram PET Research centre, PESCE, Mandya 86

16 Fig 3.12 Simulink model of 30-bus system PET Research centre, PESCE, Mandya 87

17 Simulink Result Fig 3.13 Simulink output of 30-bus system In order to find the line flows in each transmission line, there is necessity of placing 2 additional dummy buses along with the existing buses in each transmission line. This is done only to find the line flows from one bus to another. This will not change the performance of the original power system. The new buses are numbered as L2 to L85. Whereas the original buses are numbered as B1 to B30. PET Research centre, PESCE, Mandya 88

18 Output of IEEE 30 bus system without TCSC Table 3.6 Line Losses Table 3.7Line Losses LINE INDICATOR LINE FLOW P (MW) LINE LOSSES P (MW) From Lines Line Loss P(MW) L2 L L2 L L4 L L4 L L6 L L6 L L8 L L8 L L10 L L10 L L12 L L12 L L14 L L14 L L16 L L16 L L18 L L18 L L20 L L20 L21 0 L22 L L22 L23 0 L24 L L24 L L26 L L26 L L28 L L28 L29 0 L30 L L30 L L32 L L32 L33 0 L34 L L34 L L36 L L36 L L38 L L38 L L40 L L40 L L42 L L42 L43 0 L44 L L44 L L46 L L46 L L48 L L48 L L50 L L50 L51 0 L52 L L52 L L54 L L54 L L56 L L56 L L58 L L58 L L60 L L60 L L62 L L62 L L64 L L64 L L66 L L66 L L68 L L68 L L70 L L70 L L72 L L72 L L74 L L74 L L76 L L76 L L78 L L78 L79 0 L80 L e e L80 L L82 L e e L82 L L84 L e e L84 L To PET Research centre, PESCE, Mandya 89

19 From the above table it is found that the losses are more in line number 31 between buses 22 and 24. TCSC is placed in all the lines surrounding this line and after placing it losses are calculated. It is found that the losses will be minimum when TCSC is placed in line number 35 between buses 25 and 27. Output with TCSC. IEEE 30-bus with TCSC Fig 3.14 Simulink model of 30-bus system with TCSC PET Research centre, PESCE, Mandya 90

20 Results Fig 3.15 Simulink output of 30-bus system with TCSC PET Research centre, PESCE, Mandya 91

21 Table 3.8 Line losses Line Indicator Line Flow P (MW) Line Losses P (MW) L2 L L4 L L6 L L8 L L10 L L12 L L14 L L16 L L18 L L20 L L22 L L24 L L26 L L28 L L30 L L32 L L34 L L36 L L38 L L40 L L42 L L44 L L46 L L48 L L50 L L52 L L54 L L56 L L58 L L60 L L62 L L64 L L66 L L68 L L70 L L72 L ,023 L74 L L76 L L78 L L80 L e e L82 L e e L84 L e e PET Research centre, PESCE, Mandya 92

22 Comparison of Line losses of 30-bus system with & without TCSC without TCSC WithFACTS Fig.3.16 Comparison of Line losses of 30-bus system with & without TCSC It can be found by placing TCSC between the busses 25 and 27 in line no.35 the line losses is reduced from MW to MW, Hence loss is reduced by 2.61% Capacitance1 Capacitance 2 Capacitance 3 0 Line Losses Fig 3.17 Variation of Line Losses for different Capacitance values Capacitance 1=21.977µF Capacitance 2=11.977µF Capacitance 3=6977µF PET Research centre, PESCE, Mandya 93

23 3.4.3 Case 3: IEEE 30 Bus system with SSSC Fig 3.18 Simulink model of 30-bus system with SSSC Fig 3.19 Phasor model of SSSC PET Research centre, PESCE, Mandya 94

24 Simulink Result Fig.3.20 Simulink output of 30-bus system with SSSC PET Research centre, PESCE, Mandya 95

25 BUSES bus2 bus4 bus6 bus8 bus10 bus12 bus14 bus16 bus18 bus20 bus22 bus24 bus26 bus28 bus30 P(MW) Adaptive controller strategies for FACTS controllers in a power system to enhance stability Comparision of Linepower in 30 bus system between TCSC and SSSC Fig.3.21 Comparison of Line power in 30 bus system b/w TCSC and SSSC - SSSC Power Flow -TCSC Power Flow It can be found by placing TCSC and SSSC between the busses 25 and 27 in line no.35 the Line power flow is enhanced from MW to MW, Hence power transmission capability has increased by %. SUMMARY Table 3.9 Comparison of Power transmission capability with and without FACTS device POWER FLOW (MW) LINE WITH FACTS WITHOUT NUMBER WITH WITH FACTS TCSC SSSC e e e e PET Research centre, PESCE, Mandya 96

26 Bus Power (MW) without FACTS device Bus Power (MW) with TCSC Bus Power (MW) with SSSC Fig 3.22 Comparison of Power transmission capability with and without FACTS device This section aims at locating the TCSC and SSSC and comparing the performance of the two series FACTS devices. TCSC and SSSC is modeled using MATLAB/SIMULINK and results obtained are encouraging. Power system is the most complicated man made system. The problem associated with it also is very complicated. The power system of today needs to be made more flexible in terms of its transmission capability. The erection of new lines is cumbersome and is not economically feasible. The alternate method would be to enhance the transmission capability of the existing transmission lines. This can be achieved by using FACTS device. As seen from the results of I) Implementation of TCSC in a IEEE 30-bus system : The loss reduction is around 2.61% which is considerable value II) Implementation of SSSC in a IEEE 30-bus system : The power transmission capability has increased by % which is considerable value for an actual system. PET Research centre, PESCE, Mandya 97

27 3.4.4 Case 4: 14 Bus Actual System. 10 Kanlyampetta KM P = Q = 1 Basthipura 14 HN Pura 7 Kadakola KM Q = 2 Thubinakere 3 KR pet 13 CR patna 39.6 KM 58.2 KM 46.8 KM 27.4 KM 27.4 KM 76 KM P = Q = P = Q = 5 Hootgally P = 4 Kushalnagar 6 Vajmangala 11 Tk.halli 12 Kanaka pura 19.7 KM 56.6 KM P = P = Q = P = Q = Q = 8 Ch Nagar 44.8 KM 40 KM P = Q = P = Q = 45 KM P = Q = P = Q = 33.7 KM 9 Madhunalli P = Q = Fig 3.23 Real 220KV Bastipura System. PET Research centre, PESCE, Mandya 98

28 Table 3.10 Abbreviations Bus no. Bus Name Abbreviations 1 slack Bastipura 2 tbk Thubinakere 3 krp KR pet 4 ksh Kushalnagar 5 htg Hootagally 6 vaj Vajmangala 7 kad Kadkola 8 Ch CH nagar 9 Tnp Madhunalli 10 kzk Kanlyampetta 11 tkh TK Halli 12 Knk Kanakapura 13 Crp CH patna 14 G-pura HN pura Fig 3.24 Simulink model of 14-bus actual system without TCSC PET Research centre, PESCE, Mandya 99

29 Fig 3.25 Simulink model of 14-bus actual system with TCSC PET Research centre, PESCE, Mandya 100

30 Simulink Result Table 3.11 Transmission line losses without TCSC Table 3.12 Transmission line losses With TCSC Line losses Line losses Total losses Total losses Result Analysis Comparison of Line Losses with & without TCSC for 14-bus actual system is presented below, Table 3.13 Comparison of Line loss without and with TCSC Line Losses b/w bus 6 and bus 11 WITHOUT TCSC WITH TCSC 0.03MW 0.01MW PET Research centre, PESCE, Mandya 101

31 1,14 3,13 5,6 6,11 1 1,2 1,4 1,4 1,5 1,5 1,7 1,7 5,7 10,7 8,9 8,9 7,8 11,9 11,9 7,8 Adaptive controller strategies for FACTS controllers in a power system to enhance stability without TCSC with TCSC x-axis -Lines Y-axis- losses Fig 3.26Graphical Comparison of Line Losses of 14-Bus System Simulink Model With and Without TCSC It is observed that line flows are reduced in the maximum congested lines. However, no significant effect is observed in the minimum congested line. The above method if applied for all the lines, involves a lot of computation. 3.5 Location based on reactive power loss sensitivity method Case 1: IEEE 9 bus system Fig.3.27 Single line diagram of IEEE 9 bus system PET Research centre, PESCE, Mandya 102

32 COMPONENTS OF IEEE 9 BUS SYSTEM Generators-3 nos Load-3 nos Bus-9 nos Transformer-3 nos Table 3.14 Sensitivity Method performance index Bus no From Bus To Bus r ij x ij B/2 vi vj dij (rij)2 (xij)2 (vi)2 (vj)2 cos(dij) aij Table 3.15 Before placement of TCSC Bus no Voltage (v) Impedance (z) Real Power (p) Reactive Power (q) j j j j j j Table 3.16 After placement of TCSC in line 3 Bus no Voltage (V) Impedance (Z) Real Power (P) Reactive Power (Q) j j j j j j j j j PET Research centre, PESCE, Mandya 103

33 Table 3.17 After placement of TCSC in Line 7 Bus no Voltage (V) Impedance (Z) Real Power (P) Reactive Power(Q) j j j j j j j j j Table 3.18 After placement of TCSC in line 8 Bus no Voltage (V) Impedance (Z) Real Power (P) Reactive Power(Q) j j j j j j j j j PET Research centre, PESCE, Mandya 104

34 3.5.2 Case 2: IEEE 14 bus System Location of TCSC Found by the Loss Sensitivity reactive power indices TABLE 3.19 Reactive Power Loss Sensitivity Index for each Line Branch Line a ij The most positive lines are highlighted. It can be observed from the above table that TCSC can be placed either in line 9-10 or 7-8 which are most sensitive lines. PET Research centre, PESCE, Mandya 105

35 Table 3.20 Result for Optimal Location of TCSC Line Xold Xeff= Line losses Xtcsc Power in Xoldadded MW Mvar MW Xtcsc Power in Mvar PET Research centre, PESCE, Mandya 106

36 3.5.3 Case 3: 14 Bus Actual System Bus no From Bus To Bus Table 3.21 Sensitivity method rij xij vi vj dij cos(dij) aij Table 3.22 After placing TCSC in line 1-2 Table 3.23 After placing TCSC in line 7-10 BUS NO VOLTAGE (V) BUS NO VOLTAGE (V) PET Research centre, PESCE, Mandya 107

37 3.6 Locating TCSC by changing the degree of compensation (K) Table 3.24 Before Placement of TCSC in line 1-4 Line Aij Line flow Line losses Total power losses MVA MW MVAR MW MVAR MW MVAR Table 3.25 After Placement of TCSC in line 1-4 Line K Aij Line flow Line losses Total power losses MVA MW MVAR MW MVAR MW MVAR Table 3.26 Before Placement of TCSC in line 6-11 Line Aij Line flow Line losses Total power losses MVA MW MVAR MW MVAR MW MVAR PET Research centre, PESCE, Mandya 108

38 Table 3.27 After Placement of TCSC in line 6-11 Line K Aij Line flow Line losses Total power losses MVA MW MVAR MW MVAR MW MVAR Table 3.28 Before Placement of TCSC in line 7-10 Line Aij Line flow Line losses MVA Total power losses MW MVAR MW MVAR MW MVAR Table 3.29 After Placement of TCSC in line 7-10 Line K Aij Line flow Line losses Total power losses MVA MW MVAR MW MVAR MW MVAR Table 3.30 Before Placement of TCSC in line 8-9 Line Aij Line flow Line losses MVA Total power losses MW MVAR MW MVAR MW MVAR PET Research centre, PESCE, Mandya 109

39 Table 3.31 After Placement of TCSC in line 8-9 Line K Aij Line flow Line losses Total power losses MVA MW MVAR MW MVAR MW MVAR Conclusion This chapter presents the development of hybrid method using both active and reactive power loss sensitivity factors to decide on the optimal location of FACTS controllers in transmission line for given loading conditions and for given network. The methods developed have been simulated using MATLAB/SIULINK and the results obtained are promising. The systems considered include IEEE 5 bus, 9 Bus, 14 Bus, 30 Bus and 14 bus actual system. The results are found to be in the right direction. In these methods even though the location of FACTS devices is identified the optimal degree of compensation necessary has to be determined by conducting repeated load flow studies by varying the degree of compensation. This limitation can be overcome by application of AI techniques which is discussed in the next chapter. The cost analysis has also been carried out in this chapter. PET Research centre, PESCE, Mandya 110