Determining Optimal SVC Location for Voltage Stability Using Multi-Criteria Decision Making Based Solution: Analytic Hierarchy Process (AHP) Approach

Due to latest blackouts in the world, voltage instability and voltage collapse have become the main issues studied in electrical power systems. For this purpose, various Flexible AC Transmission Systems (FACTS) devices have been utilized for many years, increasing voltage stability while at the same time improving system performance, reliability, supply quality and providing environmental benefits. These devices location for enhancing voltage stability is a significant problem for actual power networks. When determining the best location of the controller, an optimal solution should be found to increase the loading margin and also reduce voltage deviation and power losses. In the literature, the weight coefficients of the criteria were chosen equally or approximate values were obtained by trial and error method and Multi-Criteria Decision Making (MCDM) techniques have never been used in finding the optimal location of FACTS devices. This article presents a novel technique for optimal location of Static Var Compensator (SVC) devices in power systems using MCDM. The simulation was conducted on Power System Analysis Toolbox (PSAT) in MATLAB. In the proposed approach, IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems were used and the optimal location was found out with Analytic Hierarchy Process (AHP), an MCDM technique. The consistency of the results has been checked and the reliability has been increased, and the results of the application are promising. In addition, the optimal location of the SVC for different contingencies was found, and the effects of the overloaded lines and Phase-Shifting Transformer (PST) on the network were analyzed.


I. INTRODUCTION
Voltage stability has a major place in terms of power systems stability. Voltage instability is mainly caused by sagging in reactive power in the grid. Even though this problem is mainly experienced in an area of critical importance, the instability affects the whole power grid [1].
The Power Electronics Technology has offered the opportunity to develop FACTS devices for stable power system operations. Number of power-electronic controllers have been developed and referred to as FACTS in the last two The associate editor coordinating the review of this manuscript and approving it for publication was Zhiyi Li .
decades. FACTS controllers are intensely used for voltage control. In addition, they are installed in the electrical grid for the purpose of minimizing losses, controlling load flow, improving of transient stability and harmonic mitigation [2]. Shunt capacitors are generally used for reactive power compensation, but they are also installed to reduce power loss and enhance voltage profile of interconnected grid. SVC, due to its low cost and excellent results on power system improvements, is widely used shunt FACTS controller. The loading margin and power transmission capability can be increased by using shunt capacitor, SVC and STATCOM. Nevertheless, with regard to decreasing losses and enhancing the voltage profile, SVC and STATCOM perform better. On the other hand, SVC and STATCOM are more costly than a basic shunt capacitor.
It is difficult and unnecessary to install shunt controllers on all buses because of financial reasons. The identification of the best placement for compensation devices includes calculating the network's stability conditions. However, owing to nonlinearity of the load flow equations, the problem is highly complicated and extensive research must be undertaken to solve it [3].
Multi-objective approaches have become common in latest years for optimum allocation of FACTS controllers. Learning and intelligent optimization methods are used to calculate FACTS devices' optimal placement and capacity. Generally, heuristic algorithms that give the closest solution in a short time are used instead of the mathematical model that gives the most accurate solution. Fitness function centered on several goals is maximized in these methods. Nevertheless, it is not certain that these methods provide the minimum level of satisfaction for the objectives. Selecting suitable weights to show relative importance of different objectives poses another challenge. In the literature, the weight coefficients of the criteria were chosen equally or approximate values were obtained by trial and error method. In previous studies, MCDM methods have never been used to determine these weights in finding the optimal location of various FACTS devices. In some of these articles, criteria weights were considered equal [4]- [21]. In some other articles, criteria weights determined by the decision maker were used [22]- [31]. In some publications, weights were used both equally and at the values determined by the decision maker and in different combinations according to different scenarios [32]- [36]. In all these studies, decision makers determined criteria weights according to their own importance levels, but did not control their consistency. To put it more clearly, authors determined random weights in the selection process, and did not base this on a scientific basis. Therefore, it is clear that there is a significant deficiency in the reliability of the results. This study mainly aims to fill this gap in the literature.
In view of the above, this article addresses the most suitable placement of SVC as a constrained multi-objective optimization problem. For this purpose, the multi-objective optimization problem is converted into a single objective function using the MCDM technique. In this proposed method, considering the operation and load constraints, three objectives are achieved simultaneously while the SVC controller is in the optimal location: increasing the range to loading margin, reducing the bus voltage deviation and minimizing the power losses. The obtained results have shown the efficiency of the suggested method.

A. FACTS CONTROLLERS
The traditional concepts and practices of energy systems have altered during latest years. Better use of the existing energy systems by installing FACTS devices is essential to boost capacities [28].
The philosophy behind the FACTS devices is to use power electronics to control power flow in a grid, enabling complete loading of the transmission line. Power electronic controlled devices such as SVCs; have been used for many years in electrical power systems. N. Hingorani, however, introduced the FACTS concept as a philosophy of total network control [37], [38].
The FACTS controller devices can be categorized as series controllers, shunt controllers, combined series-shunt controllers and combined series-series controllers. Depending on the compensation level, the series compensator is the best choice to increase the power transfer capacity. The shunt compensator is the best option to increase the stability margin. In fact, for a given operating point, if a transient fault occurs, all compensators considerably increase the stability margin. However, this is mainly true for shunt compensation [38]. Conventional compensation is commonly done with reactive power capacitors connected in parallel to the system. Conventional compensation systems may be sufficient for slow load changes and steady state operation. However, under rapidly changing load conditions, the response time may increase and there may be a delay in providing reactive power. In addition, since the contactors switch without considering the grid voltage and the voltage on the compensator, high transient currents may occur on the capacitors. FACTS devices are used because conventional compensation methods have such disadvantages and cause several power quality problems. This study focused on voltage stability. Therefore, shunt FACTS device-SVC is selected for application. SVC was preferred because it is cheaper than STATCOM and Unified Power Flow Controller (UPFC) in terms of total cost [39]. Also, the literature was reviewed and it was determined that SVC is the most widely used FACTS device due to its low cost and positive effect on system performance [40].

B. MODELLING OF SVC
SVC is most commonly described as a shunt-connected static reactive power generator or absorber, consisting of a capacitor and a thyristor-controlled reactor [41]. Fig. 1-a shows the SVC's main structure for one phase. Fig. 1-b presents equivalent circuit of SVC. In practice, a SVC is regarded a variable reactance with the limited ranges of firing angle. The reactive power and current injected into the bus k are calculated with Eq. (1) and (2).
where I SVC and Q SVC are the injected/absorbed reactive current and reactive power of SVC respectively. B SVC is the susceptance of the SVC and V k is the voltage of the bus at which SVC is connected [42] III. MULTI-CRITERIA DECISION MAKING MCDM can be described as problems where multiple criteria are optimized, ranked and the best alternative is chosen.  Nowadays, the difficult and complex decision processes need to be supported by decision making tools that will enable the decision maker to make more efficient, fast and accurate decisions as well as individual skills and experiences.
In the literature there are numerous MCDM methods (e.g. Analytic Hierarchy Process (AHP), Analytic Network Process, MOORA, ELECTRE, VIKOR, PROMETHEE, TOPSIS, ORESTE, ARAS, COPRAS etc.). These methods can be applied to selection, sorting and ranking problems. When choosing the MCDM method to be used, factors such as interdependence of criteria, relations between criteria, computability and simplicity should be taken into account. For example, Analytical Network Process or some fuzzy MCDM methods are used in problems where computation time is important. The aim of this study is to accurately determine the most suitable location and to increase the reliability of the results. AHP is the most preferred method of MCDM as it provides significant convenience to users in terms of computability and comprehensibility. Therefore, in this paper AHP method have been implemented to determine weights of criteria.

A. AHP
AHP is the MCDM method that T. L. Saaty developed in the 1970s. AHP method aims to compare alternatives in pair-wise for criteria and criteria weights, also systematically evaluates several data or elements simultaneously. This technique determines the comparative importance and meaning of each element in the hierarchy. These numerical values represent the weights or priorities [43]. The first stage is the creation of a hierarchical model. In the concepts section, this problem is clarified in more detail. In the second step, pair-wise comparison matrices are constructed. According to expert guidance, matrices are constructed to show the comparative importance of each variable, for all levels in a hierarchical system using values varying from 1 to 9 with ranges of 2 to show equally important, moderately important, strongly important, very strongly important and extremely important, respectively. In the case when five levels are insufficient, 2, 4, 6 and 8 are used as the adjacent medians [44].
After calculating pair-wise comparisons, eigenvalue λ max is used to determine the consistency index CI. Decision consistency can then be checked by calculating the consistency ratio CR for the appropriate matrix size. If the CR value is below 0.1, the decision matrix is acceptable. For other cases, judgement matrix is inconsistent. In these cases, decisions should be revised and enhanced in order to achieve a consistent matrix [45]. As shown in Fig. 2, the AHP technique can be expressed in series of steps [44].

B. MULTI-CRITERIA DECISION MAKING CONCEPTS
In decision analysis, each alternative should evaluate according to the pre-defined criteria by the decision maker. In this study, N A alternatives and N O criteria show the number of different load buses and the objectives respectively. In the AHP method, hierarchy is formed at least three levels: global goal (first level), individual objectives (second level) and alternatives (third level) [46]. The solution structure of AHP is hierarchically presented in Fig. 3.
After determining the global goal at the first level, objective and pair-comparison matrices should be defined. The N O objectives found in the second level are either weighed using the same weight (all weights w (j) equal 1/N O ), or a different definition of weight, as per the preference of the decision maker. Each of the N A options at the third level are evaluated at the second level with regard to the N O objectives [46]. B objective matrix, symbolizes the connections between the objectives and alternatives, and b ij is performance value of ith alternative with respect to jth objective.
At the third level, N O pair-comparison matrices, symbolized as D (j) , are formed. The elements of this matrix show the decision maker's personal preferences. These elements are quantitative assessments made for one objective at once. Quantification is performed with a ratio of nine levels ( Table 1) defined in terms of the scale of the Saaty [47]. The D (j) matrix is created with the reciprocal of each element in its symmetrical position. The principal diagonal elements are all equal to 1 [46]. In the AHP method, the matrix D (j) must be consistent, meaning the following multiplying condition must be satisfied by the entries in the matrix [48]: The comparison between the alternatives, however, cannot allow a perfect verify the consistency with the discrete and amplitude-limited Saaty's scales. To this end, AHP method can be used for values below CR consistency ratio predefined by matrix size and CR value can be determined as follows: where • The consistency index CI (j) is calculated based on the maximum eigenvalue λ (j) max as: • The reference consistency index RI is shown in Table 2, and its value is determined by considering the N A . The index CI (j) is compared with RI and the matrix D (j) is regarded as consistent if CI (j) < 0.1. It must be noted that only the scale of Saaty and definition of multiplicative consistency based upon Eq. (4) can confirm the condition in the ratio of CR (j) [46].

IV. PROPOSED METHODOLOGY A. CONTINUATION POWER FLOW METHOD
In this study, Continuation Power Flow (CPF) was used to determine the system's peak loadability limit. The CPF technique calculates the value called the maximum loadability margin λ max , corresponding to the point of voltage collapse in the nose curve. In power systems, CPF method is widely used for load flow problems. Unlike other power flow techniques, in CPF, the entire nose curve is obtained even after the voltage collapse point (critical point). The CPF method uses the predictor-corrector technique to obtain the PV or λV nose curve, as shown in Fig. 4 [49], [50]. The critical point in the PV curve shows the maximum loadability of the system. At normal initial load conditions, λ can be increased to estimate an approximate solution by a tangent predictor. The correction step for a conventional load flow determines the complete solution [51].

B. OBJECTIVE FUNCTION
Generally, a multi-objective optimization problem requires simultaneously optimized a series of objectives which is linked with equality and inequality constraints [52]. Identified objectives in this article are explained below.
• Loading Margin The improvement of voltage stability is accomplished with commonly used voltage collapse proximity index, called Voltage Stability Margin (VSM) or Load Margin maximization. This value is the largest load change that can be sustained by the power system at reference operating point in a bus or group of buses. In our problem, the goal is to determine minimum value of the sum of objective functions. Thus, the maximization of VSM can be presented as inverse of maximum loadability: where λ critical indicates the loading factor value at the critical point. This value corresponds to the λ max value in the CPF method [53].
• Voltage Deviation Inacceptable service quality can be caused by overly low voltages, causing voltage instability problems. The FACTS controllers should be connected to optimal placements to improve the voltage profile of the system and to prevent voltage collapse. Therefore, minimizing the bus voltage deviation has been identified as the second aim [54]. This objective function can be calculated as shown in Eq. (8): where V m is the voltage magnitude at bus m, V mref is the nominal voltage of bus m and N is the number of buses. In this study, acceptable bus voltage range is selected in the range 0.90 −1.10 p.u.
• Active power losses From a financial perspective, active power losses (P loss ) should also be minimized [53]. P loss can be represented as follows: where, g m is the conductance of transmission line, V i is the voltage of bus i, V j is the voltage of bus j, δ i is the voltage angle of bus i, δ j is the voltage angle of bus j. The objective function can be formulated as shown in Eq. (10) by considering the equality and inequality constraints.  The functions f 1 , f 2 and f 3 are defined above.
Subject to: where, ω 1 , ω 2 and ω 3 are weighting factors of VSM objective function, voltage deviation objective function and active power losses objective function respectively. While determining the weighting factors of multi-objective optimization, the priorities of the decision maker are taken into consideration. For this reason, voltage stability has been determined as the main problem in the case study presented here. VSM exerts the greatest influence on the voltage stability, while voltage deviation and active power losses have less influence on the voltage stability. The pair-wise comparison matrix showing the criterion importance is given in Table 3. The coefficients (weights) ω 1 , ω 2 and ω 3 are calculated by AHP method to 0.724, 0.193 and 0.083 respectively.

V. SIMULATION RESULTS AND DISCUSSION
In order to improve voltage stability, the simulation method includes determining the optimal bus location for SVC. Optimal SVC location is determined by placing compensator at  various buses in test systems and running CPF. To this end, PSAT software in MATLAB is used [55]. In MCDM based programming, the optimal place is determined.
• IEEE 14-bus The proposed method is tested on IEEE 14-bus system. Fig. 5 shows the IEEE 14-bus network. There are five synchronous machines in this system, generators at bus 1 and 2, and synchronous capacitors for reactive power support at bus 3, 6 and 8. Test system consists of 20 transmission lines and 14 buses with 11 loads. Total active and reactive loads in the system are 259 MW and 77.4 MVAr respectively. Since the reactive power limits of the generator are taken into account, the objective function F is calculated at a loading factor near to the critical point. Fig. 6 demonstrates SVC's optimal location for three objectives.
Criteria values in the decision matrix were converted to proportional values in order not to dominate to each other. Table 4 shows the calculation results of the proposed approach and also emphasizes that the best place for SVC is bus 9 in this test system. Table 4 obviously demonstrates the importance of the MCDM technique used in this study in combining identified objectives and sustaining the minimum level of satisfaction for the objective function. It can be observed from Table 4 that bus 12 provides minimum power losses but, loading margin is not acceptable. Similarly, bus 14 gives the best value in voltage deviation and desirable value in loading margin but, active power loss is very high. The comparison outcomes for loading factor and voltage profile without SVC and with SVC connected at bus 9 are shown in Figs. 7, 8 and 9 respectively to reflect the effectiveness of the proposed method. After running CPF, a loading margin of 4.03 was found in the system. It means that when the loading reaches 4.03 times system's base load, the voltage collapse occurs. Fig. 7 demonstrates the system's PV curves without SVC and with SVC at bus 9. For the SVC connected at bus 9, system loading margin increases from 4.03 to 4.17.
After running the CPF, bus voltage values found are shown in Fig. 8. The generally accepted technique is that optimal location for the SVC is the weakest bus (bus 5). Fig. 9 shows the comparison of bus voltage values in case SVC is installed  in bus 5 and bus 9. It is clearly seen that bus 5 is a worse location in terms of voltage profile.
Furthermore, the loadability limit, which indicates the power transmission capacity of the components in the network, increases from 2.88 to 3.37 for the SVC connected to Bus 9. Fig. 9 shows the voltage profile of the system where the loading factor is equal to 3.37. From Fig. 9, it can be seen that even when the system is overloaded, the SVC connected to bus 9 improves the voltage profile.
In power system operation, it is possible to determine the overloaded lines and transmission limits in the network under the operating conditions determined by the load flow analysis. In addition, the reliability of the system is also tested with the contingency analysis made to observe the VOLUME 9, 2021  effect of a transmission line or generator outage in the system. Contingency analysis is the study of the effects on line power flows and bus voltages of the remaining system in case outage of any element (N-1 criterion). Thus, the measures to be taken in such a case are tried to be determined in advance [56]- [58].
In this study, contingency analysis was performed by outage of the transmission lines one by one in the IEEE 14-bus test system. The new objective function values and optimal SVC locations for each case are summarized in Table 5.
In the normal operating state, the values in the first three rows were close to each other and bus 9 was found to be the optimal placement. As can be seen from Table 5, the most suitable location in half of the contingency situations is the bus 14. Bus 9 for outage of five different lines and bus 10 for outage of two different lines is the optimal SVC location.  Considering the contingencies, it would be more accurate to place the SVC on the bus 14. It is also noteworthy that the bus 4 and bus 11, which previously had high objective function values, were found to be the most suitable location for the three different line outage cases.
The Phase-Shifting Transformer (PST) is a special type of transformer used to control the power flow on the transmission line. Thanks to the special winding in its construction, the output voltage has a different phase angle from the input voltage. This can also be expressed as supplying a voltage with a different phase angle to the power system. The main function of PST is to control the power flowing on the transmission line by changing the phase angle [59], [60]. The phase angle in the PST must be chosen carefully as overloading the transformer will worsen the primary side voltage and destroy the equipment [61].
In this study, the effects of PST on the test system were examined and the results were compared with SVC. For this purpose, the most loaded transformer in the network (between bus 5 and bus 6) was changed with PST and phase angle range was determined between −45 • to +45 • . Loading factor,  power losses and bus voltage values obtained according to different angles are given in Table 6.
As it is clearly seen in the table, when the PST angle value is changed, the loadability of the system decreased, and the power losses first increased and then started to decrease. Compared to the case of SVC at bus 9, it is seen that the power losses are lower at all phase angle values. However, SVC gave better results in load factor and busbar voltage values. In the base load voltage profile of the system given in Fig. 10, the application results of SVC and PST were compared. Considering the criterion weights, it would be more accurate to install SVC in the system in terms of voltage stability. PST can be used in applications that aim to reduce power losses.    • IEEE 30-bus The proposed method has also been tested on the IEEE 30 bus system. Fig. 11 shows the IEEE 30-bus network. There are six synchronous machines in this system, generators at bus 1 and 2, and synchronous capacitors for reactive power support at bus 5, 8, 11 and 13. Test system consists of 41 transmission lines and 30 buses with 21 loads. Total active and reactive loads in the system are 283.4 MW and 126.2 MVAr respectively.
Since the reactive power limits of the generator are taken into account, the objective function F is calculated at a loading factor near to the critical point. Fig. 12 demonstrates SVC's optimal location for three objectives.
Criteria values in the decision matrix were converted to proportional values in order not to dominate to each other. Table 7 shows the calculation results of the proposed  approach and also emphasizes that the best place for SVC is bus 24 in this test system. Table 7 obviously demonstrates the importance of the MCDM technique used in this study in combining identified objectives and sustaining the minimum level of satisfaction for the objective function. It can be observed from Table 7 that bus 3 provides minimum power losses but, loading margin is not acceptable. Similarly, bus 19 gives the best value in voltage deviation and desirable value in active power loss but, loading margin is very high. The comparison outcomes for loading factor and voltage profile without SVC and with SVC connected at bus 24 are shown in Figs. 13, 14 and 15 respectively to reflect the effectiveness of the proposed method. After running CPF, a loading margin of 2.96 was found in the system. It means that when the loading reaches 2.96 times system's base load, the voltage collapse occurs. Fig. 13 demonstrates the system's PV curves without SVC and with SVC at bus 24. For the SVC connected at bus 24, system loading margin increases from 2.96 to 3.31.
After running the CPF, bus voltage values found are shown in Fig. 14. The generally accepted technique is that optimal location for the SVC is the weakest bus (bus 30). Fig. 15 shows the comparison of bus voltage values in case SVC is installed in bus 24 and bus 30. It is clearly seen that bus 30 is a worse location in terms of voltage profile.
Furthermore, the loadability limit, which indicates the power transmission capacity of the components in the network, increases from 1.79 to 2.26 for the SVC connected to bus 14. Fig. 15 shows the system's voltage profile at a loading factor of λ = 2.26. From Fig. 15, it can be seen that even when the system is overloaded, the SVC connected to bus 24 improves the voltage profile.
There are various factors that can cause contingency in power systems such as generator outage, line outage and overloads and these cause extreme situations such as voltage collapse, overloads in other branches, sudden system voltage rise or drop [62]. Contingencies occur in the power systems when the MVA rating of the transmission line exceeds certain limit values and several types of corrective actions are required to solve such problems [63]. IEEE 14-bus and 30 bus test systems don't have line limits. Line and transformer limits have been proposed by the authors in several articles [64]- [66]. In this study, the line limits suggested in [65] were used and congestion was created in the lines for the simulation purposes. To this end, line overloads were created by considering line outages. The percentage values of the overloaded lines before and after SVC placement are given in Table 8.
In the IEEE 30-bus system, there are no overloaded lines in 27 cases for 41 contingency scenarios. Although there are 33 overloaded lines in the other 14 cases, the power flowing to only 11 lines has decreased below the limit values with the installation of SVC on the proper buses. However, it is noteworthy that the SVC placed at the bus 6 solves the overloading problem in the line between the bus 6 and bus 8 in almost all cases. As seen at Table 8, in the case of contingency, SVC at the buses does not improve the condition of the overloaded lines. As a matter of fact, shunt compensators absorb or inject current from the line like a current source, so they are mostly used to control the voltage around the connection point. In accordance with this purpose, FACTS devices such as UPFC and TCSC (Thyristor Controlled Series Compensator) can be used to control the power flow in the network and solve the overloading problem in the lines.
• IEEE 118-bus In order to demonstrate the effectiveness of the proposed method, it is finally tested on the IEEE 118-bus system. Fig. 16 shows the IEEE 118-bus network. There are nineteen generators and thirty-five synchronous capacitors in this system. Test system consists of 177 transmission lines and 118 buses with 91 loads. Total active and reactive loads in the system are 3668 MW and 1438 MVAr respectively. VOLUME 9, 2021 In IEEE 14-bus and 30 bus test systems, the rated values of SVC were taken between −100 MVAr and +100 MVAr. IEEE 118-bus test system is a larger network model; therefore, the SVC is rated as −300/+300 MVAr in order to see the effect of compensation more clearly. Since the reactive power limits of the generator are taken into account, the objective function F is calculated at a loading factor near to the critical point. Fig. 17 demonstrates SVC's optimal location for three objectives.
Criteria values in the decision matrix were converted to proportional values in order not to dominate to each other. Table 9 shows the calculation results of the proposed approach and also emphasizes that the best place for SVC is bus 44 in this test system. Table 9 obviously demonstrates the importance of the MCDM technique used in this study in combining identified objectives and sustaining the minimum level of satisfaction for the objective function. It can be observed from Table 9 that bus 44 gives the best value in voltage deviation and second best in loading margin, but in the worst location in terms of active power losses. Similarly, bus 38 has the best value in loading margin, and interestingly, it has the worst value in voltage deviation. After running CPF, a loading margin of 3.19 was found in the system. It means that when the loading reaches 3.19 times system's base load, the voltage collapse occurs. Fig. 18 demonstrates the system's PV curves without SVC and with SVC at bus 38 and bus 44. For the SVC connected at bus 44, system loading margin increases from 3.19 to 3.21.
After running the CPF, bus voltage values found are shown in Fig. 19. It is noteworthy that, unlike other IEEE test systems, the optimal location for SVC is the weakest bus (bus 44). Fig. 20 shows the comparison of bus voltage values in case SVC is installed in bus 44 and bus 38.
Furthermore, the loadability limit, which indicates the power transmission capacity of the components in the network, increases from 2.38 to 3.08 for the SVC connected to bus 44. Fig. 20 shows the voltage profile of the system where the loading factor is equal to 3.08. From Fig. 20, it can be seen that even when the system is overloaded, the SVC connected to bus 44 improves the voltage profile. It is clearly seen that bus 38 with the best loading margin gives similar results in terms of voltage profile as the case without SVC.

VI. CONCLUSION
A MCDM method was proposed in this paper using AHP technique to improve voltage stability. On the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems, this method's efficiency has been indicated. The method attempted to optimize allocation of the FACTS controller according to three goals: increasing the loading margin, reducing voltage deviation and reducing active power losses. By using objective function ranking, optimal SVC location has presented among the weakest buses. It has been identified that SVC can be placed optimally in bus 9 for the IEEE 14-bus system, bus 24 for the IEEE 30-bus system and bus 44 for the IEEE 118-bus system. By applying this approach to actual systems, power system operators can be provided with useful information for voltage stability and its improvement. The results presented by this approach are promising and promoting for possible applications. This method can be also useful in larger power systems for various FACTS placement strategies. Different contingencies were analyzed in the IEEE 14-bus test system and bus 14 was found to be the most appropriate location in half of the line outages. It has also been shown that SVC on buses does not improve the condition of overloaded lines in case of contingencies. In addition, the effects of PST on the test system were examined and the results were compared with SVC. It has been seen that SVC gives better results in loading margin and bus voltage values.
The present research focused on only three objectives. Future studies might include other objectives such as cost minimization in generator units, FACTS installation cost reduction, etc. Additionally, different FACTS devices such as STATCOM may be used or the number of controllers may be increased in future applications.