Optimal Placement and Sizing of Thyristor-controlled- series-capacitor using Gravitational Search Algorithm

This paper represents the Gravitational Search Algorithm (GSA) that can be used to determine the optimal location and rating of Thyristor controlled Series Capacitor (TCSC). TCSC is equipment used to regulate and improve power flow in power system. The method used in this study was GSA. TCSC were the implemented on 500kV Java-Bali Power System. Loadflow results before optimization using Newton Rapshon method showed that active power loss was 297.607MW. While loadflow results after optimization using GSA with 5-TCSC obtained were 287.926MW of active power loss, with 10-TCSC, it was obtained 281.143MW of active power loss. In addition, using 15-TCSC, active power loss obtained was 279.405MW. GSA methods can be used to minimize power losses and transmission lines as well as to improve value of voltage in the range of 0.95+ 1.05pu compared with loadflow results before optimization.The more TCSC is used, then value of active power losses small.


Introduction
To obtain the stability of the power system, reactive power compensation arrangements and power systems voltage that can maintain the network parameters to remain at a predetermined limit are required. Changes in network topology and load conditions often lead to changes in voltage in the power system today. Search on the problem of reactive power must consider the active power losses in transmission lines and power system voltage profile. Reactive power flow can be adjusted by changing the transformer tap position, increasing the capability of generating reactive power generation. In addition, reactive power compensation arrangements can also be done by adding the FACTS (flexible AC transmission system) devices on the power systems line [1], [2].
FACTS devices are ones that can either manage and improve the power flow or increase the stability of the power system. They can also set the parameters and variables defined in the transmission line such as line impedance, terminal voltages, and voltage angle with a quick and effective way. They have the ability to make a power system operate in a more flexible, safe, and economical ways. The pattern of power generation leading to the imposition of too heavy line will result in higher line losses and undermine security and stability of power systems. In such condition, FACTS devices can be used to enhance the ability of the system, by means of controlling power flow on transmission lines [3][4][5].
Artificial intelligence methods developed in this study is the method of gravitational search algorithm (GSA). This GSA method was first introduced by Rashedi in 2009 [18]. It is a method of metaheuristic inspired by Newton's laws of gravity and mass motion. Metaheuristic is a method to find a solution that combines the interaction between local search procedures and higher strategies to create process which is capable to get out of local optima points and perform searching in the solution space to find a global solution [19]. Several studies held by experts used this GSA method, such as on the location of the SVC [20], economic dispatch (ED) on the power system [21], the voltage settings on 500kV Java-Bali Power System [22], and optimization of reactive power dispatch [23].
At the end of this study, GSA methods can be used efficiently to solve various optimization problems in the process of determining the optimal location and rating of FACTS devices in power systems and can assist the engineer in an effort to improve the voltage deviation or to increase the voltage profile and to minimize power loss in power system transmission lines.

The Proposed Method / Algorithm 2.1. Thyristor Controlled Series Capasitor (TCSC)
TCSC is the first series of a FACTS device type being developed. The main unit of this type of FACTS device is the thyristor controlled reactor (TCR). TCR is a static var controller that uses power electronics so that they can perform rapid control of reactive power. The main part of itis an inductor in series with the bipolar thyristor switch. By adjusting the angle of the thyristor firing, variation of inductive reactance is obtained which causes a rapid reactive power exchange between the TCR and the system. To overcome the system requiring a capacitive reactive power, usually a bank of capacitors is connected in parallel with the TCR.
Reactance compensation of transmission line can be done by controlling the TCSC reactance, so the power flowing through the transmission line can be improved. A series of a compensation method, traditionally, uses a capacitor or mechanics switching which tends to be slow. Controls by using thyristor enable rapid network impedance settings, based on the needs of the desired compensation. TCSC can serve as capacitive or inductive compensation respectively by modifying the transmission line reactance. In this simulation, the eq X equivalent of the TCSC is the function of thyristor firing angle of transmission line adjusted to TCSC. Figure 1 shows that the maximum and minimum value of the thyristor firing angle are 0⁰and 90⁰. The maximum compensation limit of TCSC ( max In order to prevent excessive compensation, the compensation degree of TCSC allowed is in the range of 20% inductive and 70% capacitive, so it applies: The rated value of the TCSC is a function of the transmission line reactance where TCSC is located: where line X isthe reactance of the transmission line and TCSC r is the coefficient representing the TCSC compensation level.

Initialization
If one assumes that there is a system with N (dimension of the search space) mass, the mass of the ith position is explained as follows. At first, the position of the mass is fixed randomly.
( ) where d i x = Position of the ith mass in dth dimension.

Fitness Evaluation of the All Agents
For all agents, the best and worst fitness which is calculated at each epoch is described as follows.
where ) (t fit j is Fitness on the jth agent at t time, best(t) and worst(t) is fitness of all agents of the best (minimum) and worst (maximum).

Calculate the Gravitational Constant
The gravitational constant (G (t)) at t time is calculated as follows: where 0 G isinitial value of the gravitational constant is chosen at random, α is constanta, t is current epoch, and T is total iterations of number.

Update Gravity And Enertia Masses
The gravity and inertia masses are updated as follows wherefiti (t) = fitness on the ith agent at t time.
where ) (t Mg i is mass of ith agent at t time.

Calculate the Total Force
The total force acting on ith agent where j rand is Random number between the intervals [0, 1] and Kbestis the set of initial K agent with the best fitness value and the largest mass.
Forces acting on ith massa ( ) at a certain t time is described by the theory of gravity as follows: where Rij(t) is Euclidian distance between ith agents and jth agents and ε is a small constant.

Calculate Acceleration and Speed
The acceleration ( ) of ith agent at t time in dth dimension is calculated through the law of gravity and the laws of motion as follows.
where i rand israndom number between the intervals [0.1]

Position Update Agent
The next position of ith agent in dth ( )

Repetition
The steps from (b) to (g) are repeated until the iterations reach the criterion. At the end of the iteration, the algorithm returns the value associated with the position of the agent on a particular dimension. This value is the global solution of optimization problems as well.
Procedures for implementing the GSA method to the problem of voltage control are shown below: Initializing a population with random positions.

Research Method
The method used to regulate power compensation rekatif using FACTS device was the GSA. It is able to find several possible solutions simultaneously and it does not require prior knowledge or the specific nature of the objective function. In addition, GSA is expected to produce the best solution to find optimal solutions in complex problems. It was started with the random generation of initial population and then selected and mutated to obtain the best population found.

Encoding
The purpose of this encoding was to find the optimal location on TCSC in terms of equations and inequalities. Therefore, the configuration of TCSC is encoded by three parameters: location, type and value ( rf ). Every individual is represented by a number of n FACTS on the string, where the n FACTS is the number of the device that needs to be analyzed in the power system, as shown in Figure 3.
The first value of each string is in accordance with the location information. The value is the transmission line number where TCSC is. Each string has different value locations. In other words, it must be ensured that in one transmission line, there is only one TCSC. The second value is the type of TCSC. The stated value is the 1 value for TCSC and the 0 value for the condition without TCSC. In particular, if there is no TCSC needed on the transmission line, a

Population
The initial population is generated from the following parameters:  First, as shown in Figure 4, a bunch of the resultng string TCSC n was made. For each string, the first value is selected randomly from the Location n possible locations. The second value, a type of TCSC, was obtained by taking a number randomly among selected equipments. In particular, after optimization, if no FACTS device is required for this transmission line, the second value would be set to zero. The third value of each string, containing the value of the TCSC equipment, was chosen at random between -1 and +1. The above operation was repeated as Ind n times to obtain the whole initial population. Calculation of the whole population is shown in Figure 4.

Fitness Calculation
After encoding, each individual in the population was evaluated using the objective function. Since it related to optimization problem with the TCSC, the objective function of this problem was used as fitness function. Fitness function is the quality calculation used to compare different solution. For this purpose, the TCSC was placed on the transmission line to notice the power flow and voltage constraints. Objective function was used as the limit of TCSC placement to prevent undervoltage or overvoltage on each bus and it was able to reduce the power loss on transmission lines.
Objective function for optimizing the placement of TCSC was to minimize the power loss on transmission lines. Objective function for optimal configuration of TCSC are: where nb is Number of buses, G P and G Q is active and reactive power from generators, D P where nc , ng and nt is number of switchable reactive power sources, generators and transformers.
To evaluate the optimization objective function on the placement of TCSC, the best and worst fitness is calculated at each iteration as follows: where ) (t fit j is fitness in the j th agent at t time, ( ) t best and ( ) t worst is the best fitness of all agents (the minimum) and worst (the maximum) fitness of all agents.

d. Calculation of the Gravitational Constant
To update the G gravitational constant in accordance with population fitness of the best agents (minimum) and worst (maximum) using equation (10).

e. The Calculation of Inertia and Gravitational Mass
To calculate the value of inertial mass (M) for each agent, equations (11) and (12). Repetition In this step, the steps from c to h are repeated until the iterations reach the criterion. At the end of the iteration, the algorithm returns the value associated with the position of the agent on a particular dimension. This value is the global solution of optimization problems as well.The GSA algorithm, used to determine the optimal placement of TCSC locations and ratings, are shown in Figure 5.

Data of 500kV Java-Bali Power System
500 kV Java-Bali Power System is an interconnection system that delivers the power to customers in various areas in Java and Bali. Power is supplied from the electric power produced from various sources hydroelectric power (found in plants and SagulingCirata), steam power plant (located on the Suralaya, TanjungJati, and Paiton power plants) and steam gas power plants (consisted of Grati, Muaratawar and Gresik power plant). The single line diagram of power system can be seen in Figure 6.This study used MVA base of 1000 MVA and kV base of 500 kV as the base of 500 kV Java-Bali Power System.

Discussion 4.2.1. Results of Load Flow before Using TCSC Optimation
To know the initial conditions of 500 Java-Bali Power System before optimization using TCSC, the load flow analysis was performed using the Newton Rapson method. The results are shown in Figures 7 and 8.  In Figure 7, it shows that the variation voltage of 500kV Java-Bali Power System is in the range of 0874 to 1.020 pupu. The highest voltage occurs at bus 1 (Suralaya), namely 1.020 pu and the lowest voltage is found on the bus 20 (Pedan).

Load Flow Results after Optimization using the TCSC
Parameters used were GSA methods to determine optimal placement of TCSC locations and ratings on Java-Bali power system shown in Table 1. The results of the convergence curve after optimization using 5 TCSC is shown in Figures 9 and 10 Figure 9. Convergence after optimization using 5 TCSC Figure 10. Location and Rating using 5 TCSC Figure 9 shows that the convergence characteristics after optimization using 5 TCSC is capable of producing the active power losses in transmission lines over the minimum, when compared with the results for load flow before optimization TCSC 287.926 MW and 2355.027 MVAR. In Figure 10, it shows that the greatest location and rating 5 TCSC on transmission system line of 500 kV Java-Bali Power System are at 1-24 lines of pu -0.6302 and the smallest rating capacity occurs in 20-21 lines of -0.1146 pu. The results of the convergence curve after optimization using 10 TCSC is shown in Figures 11 and 12. Figure 11 shows that the convergence characteristics after optimization using 10 TCSC is capable of producing the active power losses in transmission lines over the minimum, when compared with the results of optimization using load flow before TCSC of 281.143 MW and 2023.241 MVAR.
In Figure 12, it shows that the location and the rating of 10 TCSC on transmission lines of 500 kV Java-Bali Power System was greatest at 18-19 with -0.6746 and the smallest rating occurs in 21-22 lines of -0.0477 pu. The results of the convergence curve after optimization using 15 TCSC is shown in Figures 13 and 14.  Figure 13 shows that the convergence characteristics after optimization using 15 TCSC is capable of producing the active power losses in transmission lines over the minimum, when compared with the results of optimization using load flow before TCSC 2082.203 MW and 279.405MVAR.
In Figure 14, it shows that the location and the rating system 15 TCSC on transmission lines of 500 kV Java-Bali Power System was greatest at 1-2 at 0.1885 pu and the capacity of the smallest rating occurs in 11-12 lines of -0.0447 pu.
To keep the voltage at each bus in a span of 0.95 ± 1.05 pu, and the power flowing in each line is smaller than the maximum power, it is necessary to compensate by using TCSC on Java Bali transmission line optimization with the results shown in Figures 15 and 16. Figure 15 shows the voltage variation of 500 kVJava -Bali power system after optimization using 5 TCSC, 10 TCSC and 15 TCSC. It is in the range of 0.95+1.05 pu. The highest voltage occurs at bus 1(Suralaya) of 1.020 pu and the lowest voltage is found on the bus 25 (Ngimbang) of 0.952 pu.
In Figure 16, it shows that the total loss of active and reactive power occuring in 500 kV Java Bali power systems after optimization using 5 TCSC, 10 TCSC and 15 TCSC is

Conclusion
In this paper, the proposed GSA method was used to determine the location and rating of TCSC. Test results using the 500 kVJava-Bali Power System showed that the optimal placement location of TCSC rating using this GSA method could reduce the active power and reactive power losses on the line of 500 kV Java-Bali system as well as improve the value of the voltage to stay in standard limit of 0.95 ±1.05 pu. Then, load flow results after optimization using theTCSC with the GSA methods were compared by using load flow results before optimization using TCSC. The simulation results at 150 kV power generations Java-Bali showed that the GSA method was used to determine the optimal location and rating of TCSC.