Analysis of different aspects by flexible AC transmission system (FACTS) and distributed-FACTS (D-FACTS) devices on IEEE 14, 30 and 57 bus system

A electric power system have numerous components utilized in generation, transmission and distribution systems; due to its complex structure a major issue of stability, frequency maintain, power instability in tie-lines and cascading failures exists. To deal with these problems, power electronics based devices: flexible AC transmission system (FACTS) and distributed-FACTS (D-FACTS) devices are placed on optimal location. This paper represents load flow methods: Newton-Raphson method, GaussSeidel method, Fast-Decoupled method, FACTS devices (static synchronous series compensation, unified power flow controller) and D-FACTS devices, used for calculating different line parameter for IEEE 14, 30 and 57 bus system. These methods have varying qualities: convergence, accuracy, reliability, stability etc. The simulation outcomes show comparative analysis of active power, reactive power under steady state condition through different IEEE bus system. Keyword Flexible AC transmission system (FACTS), distributed flexible AC transmission system (DFACTS), static synchronous series compensation (SSSC), unified power flow controller (UPFC)

 Create a bus admittance matrix Y-bus for the power system,  A primary approximation for the voltages (both magnitude and phase angle) at IEEE bus systems,  Substitute it in the power flow equation and determine the deviations,  Update the estimated voltages based on N-R, G-S and F-D method,  Implement the FACTS and D-FACTS devices on IEEE 14,30 and 57 bus systems. The FACTS and D-FACTS devices are used to provide controllability and stability. The elementary equation for power-flow analysis is derived from the nodal analysis equations for the power system [9].
where Y ij is the admittance of line between i th and j th bus. Apparent power injected at bus 'i' is given by, here P i and Q i are true and imaginary power at i th bus, δ j voltage angle of i th bus, θ ij angle of Y ij element of Y bus. Above equation is known as the load flow equation to update voltage magnitudes and angle with growth rate r [10]:

III. EXPLANATION OF APPLIED METHODOLOGIES
Load flow analysis is iterative and time taking approaches. To solve this analysis, linear equations are required. Different methods are available to solve these iterations:

A. Gauss-Seidel (G-S) Method
It is an iterative method and has a set of values of the unknown quantities. The process to solve all the identified and real quantities diminishes a pre-specified value to occur. In the G-S load flow, the initial voltage of i th bus is given by [11][12][13][14]. Knowing the real and reactive power injected at any bus as: The updated voltage at bus after iteration is: where V i (acc) is acceleration factor and k is acceleration factor constant. The value of  has to be below 2.0 for the convergence to occur.

B. Newton-Raphson (N-R) Method
N-R load flow is solved for non-linear equation at each iteration, a jacobian matrix solves for the modification in the bus system [15]. 1 2

C. Fast-Decoupled (F-D) Method
A significant and beneficial property of power system is that the transformation in active power is primarily governed by the changes in the voltage angle, but not voltage magnitude. Due to the changes, in the imaginary power are primarily influenced by the changes in voltage magnitudes, but not in the voltage angles [16,17].
FACTS are power electronics based devices which are used for enhancing system utilization and power transfer capacity in addition to stability, security & reliability of interconnected power system. Use of high speed power electronics controllers give chances for increasing efficiency and greater control that flows in the recommended transmission system [18][19][20][21]. Table 1 elaborates the different qualities of FACTS devices, used in this paper.

E. Distributed flexible AC transmission system (D-FACTS)
D-FACTS device provides purely reactive/capacitive compensation. The concept of distributed series impedance can be realized for variable line impedance. Control active power flow is used for illustrating the feasibility of D-FACTS, it can be configured to operate autonomous during certain conditions to communicate wireless, allowing them to receive commands for impedance injection changes [22,23].
D-FACTS devices are power flow controller devices which are light-weight, small in size. A D-FACTS device changes the effective line impedance by producing a voltage drop across the line current [24].

IV. SIMULATION MODEL, RESULT AND DISCUSSION
The finest position for reactive power compensation static voltage stability margin is the feeblest bus of the system. The feeblest bus of the system could be found using tangent vector study. The feeblest bus is defined as the adjacent to experiencing a voltage collapse.
The simulation result are shown in various parts: Part (i) shows simulation results of IEEE 14 bus compression graph with voltage, current, true and reactive power with FACTS and D-FACTS devices; Part (ii) presents voltage, current and power vs. bus number graph for 30 bus system and Part (iii) presents different graphs by using FACTS, D-FACTS device on 57 bus system.
It can be clearly observed through graphs that FACTS and D-FACTS devices remarkably improve the performance of bus system.
(i). 14 Bus system  As shown by graphs, required number of iteration gets reduced by applying in various FACTS, SSSC, UPFC and D-FACTS devices, and the following objectives are achieved: upgraded voltage across various bus systems, amplified power transfer capability. After D-FACTS devices are installed in certain fixed locations, their control objectives can easily be changed to target other lines flows. Thus, D-FACTS device can provide versatile control for power systems, which could be a competent research field in future.