Search results for: multiple power flow solutions

Authors: P. Acharjee, S. K. Goswami

Abstract:

Particle Swarm Optimization (PSO) with elite PSO parameters has been developed for power flow analysis under practical constrained situations. Multiple solutions of the power flow problem are useful in voltage stability assessment of power system. A method of determination of multiple power flow solutions is presented using a hybrid of Particle Swarm Optimization (PSO) and local search technique. The unique and innovative learning factors of the PSO algorithm are formulated depending upon the node power mismatch values to be highly adaptive with the power flow problems. The local search is applied on the pbest solution obtained by the PSO algorithm in each iteration. The proposed algorithm performs reliably and provides multiple solutions when applied on standard and illconditioned systems. The test results show that the performances of the proposed algorithm under critical conditions are better than the conventional methods.

Keywords: critical conditions, ill-conditioned systems, localsearch technique, multiple power flow solutions, particle swarmoptimization.

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Authors: Mashitah Mohd Hussain, Salleh Serwan, Zuhaina Hj Zakaria

Abstract:

This paper presents a method to estimate load profile in a multiple power flow solutions for every minutes in 24 hours per day. A method to calculate multiple solutions of non linear profile is introduced. The Power System Simulation/Engineering (PSS®E) and python has been used to solve the load power flow. The result of this power flow solutions has been used to estimate the load profiles for each load at buses using Independent Component Analysis (ICA) without any knowledge of parameter and network topology of the systems. The proposed algorithm is tested with IEEE 69 test bus system represents for distribution part and the method of ICA has been programmed in MATLAB R2012b version. Simulation results and errors of estimations are discussed in this paper.

Keywords: Electrical Distribution System, Power Flow Solution, Distribution Network, Independent Component Analysis, Newton Raphson, Power System Simulation for Engineering.

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Authors: A.V.Naresh Babu, S.Sivanagaraju, Ch.Padmanabharaju, T.Ramana

Abstract:

The interline power flow controller (IPFC) is one of the latest generation flexible AC transmission systems (FACTS) controller used to control power flows of multiple transmission lines. This paper presents a mathematical model of IPFC, termed as power injection model (PIM). This model is incorporated in Newton- Raphson (NR) power flow algorithm to study the power flow control in transmission lines in which IPFC is placed. A program in MATLAB has been written in order to extend conventional NR algorithm based on this model. Numerical results are carried out on a standard 2 machine 5 bus system. The results without and with IPFC are compared in terms of voltages, active and reactive power flows to demonstrate the performance of the IPFC model.

Keywords: flexible AC transmission systems (FACTS), interline power flow controller (IPFC), power injection model (PIM), power flow control.

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Authors: A. Alsaadi, B. Gholami

Abstract:

An effective approach for unbalanced three-phase distribution power flow solutions is proposed in this paper. The special topological characteristics of distribution networks have been fully utilized to make the direct solution possible. Two matrices–the bus-injection to branch-current matrix and the branch-current to busvoltage matrix– and a simple matrix multiplication are used to obtain power flow solutions. Due to the distinctive solution techniques of the proposed method, the time-consuming LU decomposition and forward/backward substitution of the Jacobian matrix or admittance matrix required in the traditional power flow methods are no longer necessary. Therefore, the proposed method is robust and time-efficient. Test results demonstrate the validity of the proposed method. The proposed method shows great potential to be used in distribution automation applications.

Keywords: Distribution power flow, distribution automation system, radial network, unbalanced networks.

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Authors: M. A. At-Tasneem, N. T. Rao, T. M. Y. S. Tuan Ya, M. S. Idris, M. Ammar

Abstract:

River flow over micro hydro power (MHP) turbines of multiple arrays arrangement is simulated with computational fluid dynamics (CFD) software to obtain the flow characteristics. In this paper, CFD software is used to simulate the water flow over MHP turbines as they are placed in a river. Multiple arrays arrangement of MHP turbines lead to generate large amount of power. In this study, a river model is created and simulated in CFD software to obtain the water flow characteristic. The process then continued by simulating different types of arrays arrangement in the river model. A MHP turbine model consists of a turbine outer body and static propeller blade in it. Five types of arrangements are used which are parallel, series, triangular, square and rhombus with different spacing sizes. The velocity profiles on each MHP turbines are identified at the mouth of each turbine bodies. This study is required to obtain the arrangement with increasing spacing sizes that can produce highest power density through the water flow variation.

Keywords: Micro hydro power, CFD, arrays arrangement, spacing sizes, velocity profile, power.

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Authors: Mohammad Najafi, Ali Jamshidi

Abstract:

We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.

Keywords: Hirota bilinear method, potential Kadomtsev-Petviashvili equation, multiple soliton solutions, multiple singular soliton solutions.

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Authors: Djilani Kobibi Youcef Islam, Hadjeri Samir, Djehaf Mohamed Abdeldjalil

Abstract:

The Flexible AC Transmission System (FACTS) technology is a new advanced solution that increases the reliability and provides more flexibility, controllability, and stability of a power system. The Unified Power Flow Controller (UPFC), as the most versatile FACTS device for regulating power flow, is able to control respectively transmission line real power, reactive power, and node voltage. The main purpose of this paper is to analyze the effect of the UPFC on the load flow, the power losses, and the voltage stability using NEPLAN software modules, Newton-Raphson load flow is used for the power flow analysis and the modal analysis is used for the study of the voltage stability. The simulation was carried out on the IEEE 14-bus test system.

Keywords: FACTS, load flow, modal analysis, UPFC, voltage stability.

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Authors: Saeed Hosseini, Ali Reza Tahavvor

Abstract:

Sound processing is one the subjects that newly attracts a lot of researchers. It is efficient and usually less expensive than other methods. In this paper the flow generated sound is used to estimate the flow speed of free flows. Many sound samples are gathered. After analyzing the data, a parameter named wave power is chosen. For all samples the wave power is calculated and averaged for each flow speed. A curve is fitted to the averaged data and a correlation between the wave power and flow speed is found. Test data are used to validate the method and errors for all test data were under 10 percent. The speed of the flow can be estimated by calculating the wave power of the flow generated sound and using the proposed correlation.

Keywords: Flow generated sound, sound processing, speed, wave power.

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Authors: A. Moussouni, L. Mouzai, M. Bouhadef

Abstract:

The purpose of this investigation is to relate the rain power and the overland flow power to soil erodibility to assess the effects of both parameters on soil erosion using variable rainfall intensity on remoulded agricultural soil. Six rainfall intensities were used to simulate the natural rainfall and are as follows: 12.4mm/h, 20.3mm/h, 28.6mm/h, 52mm/h, 73.5mm/h and 103mm/h. The results have shown that the relationship between overland flow power and rain power is best represented by a linear function (R2=0.99). As regards the relationships between soil erodibility factor and rain and overland flow powers, the evolution of both parameters with the erodibility factor follow a polynomial function with high coefficient of determination. From their coefficients of determination (R2=0.95) for rain power and (R2=0.96) for overland flow power, we can conclude that the flow has more power to detach particles than rain. This could be explained by the fact that the presence of particles, already detached by rain and transported by the flow, give the flow more weight and then contribute to the detachment of particles by collision.

Keywords: Laboratory experiments, soil erosion, flow power, erodibility, rainfall intensity.

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Authors: Eduardo N. Velloso, Fernando M. N. Dantas, Luciano S. Barros

Abstract:

A common complaint from power system analysis students lies in the overly complex tools they need to learn and use just to simulate very basic systems or just to check the answers to power system calculations. The most basic power system studies are power-flow solutions and short-circuit calculations. This paper presents a simple tool with an intuitive interface to perform both these studies and assess its performance in comparison with existent commercial solutions. With this in mind, Elegant is a pure Python software tool for learning power system analysis developed for undergraduate and graduate students. It solves the power-flow problem by iterative numerical methods and calculates bolted short-circuit fault currents by modeling the network in the domain of symmetrical components. Elegant can be used with a user-friendly Graphical User Interface (GUI) and automatically generates human-readable reports of the simulation results. The tool is exemplified using a typical Brazilian regional system with 18 buses. This study performs a comparative experiment with 1 undergraduate and 4 graduate students who attempted the same problem using both Elegant and a commercial tool. It was found that Elegant significantly reduces the time and labor involved in basic power system simulations while still providing some insights into real power system designs.

Keywords: Free- and open-source software, power-flow, power system analysis, Python, short-circuit.

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Authors: Aniruddha Bhattacharya, Pranab Kumar Chattopadhyay

Abstract:

Optimal reactive power flow is an optimization problem with one or more objective of minimizing the active power losses for fixed generation schedule. The control variables are generator bus voltages, transformer tap settings and reactive power output of the compensating devices placed on different bus bars. Biogeography- Based Optimization (BBO) technique has been applied to solve different kinds of optimal reactive power flow problems subject to operational constraints like power balance constraint, line flow and bus voltages limits etc. BBO searches for the global optimum mainly through two steps: Migration and Mutation. In the present work, BBO has been applied to solve the optimal reactive power flow problems on IEEE 30-bus and standard IEEE 57-bus power systems for minimization of active power loss. The superiority of the proposed method has been demonstrated. Considering the quality of the solution obtained, the proposed method seems to be a promising one for solving these problems.

Keywords: Active Power Loss, Biogeography-Based Optimization, Migration, Mutation, Optimal Reactive Power Flow.

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Authors: Manisha Dubey, Gaurav Gupta, Anoop Arya

Abstract:

The demand for power supply increases day by day in developing countries like India henceforth demand of reactive power support in the form of ancillary services provider also has been increased. The multi-line and multi-type Flexible alternating current transmission system (FACTS) controllers are playing a vital role to regulate power flow through the transmission line. Unified power flow controller and interline power flow controller can be utilized to control reactive power flow through the transmission line. In a restructured power system, the demand of such controller is being popular due to their inherent capability. The transmission pricing by using reactive power cost allocation through modified matrix methodology has been proposed. The FACTS technologies have quite costly assembly, so it is very useful to apportion the expenses throughout the restructured electricity industry. Therefore, in this work, after embedding the FACTS devices into load flow, the impact on the costs allocated to users in fraction to the transmission framework utilization has been analyzed. From the obtained results, it is clear that the total cost recovery is enhanced towards the Reactive Power flow through the different transmission line for 5 bus test system. The fair pricing policy towards reactive power can be achieved by the proposed method incorporating FACTS controller towards cost recovery of the transmission network.

Keywords: Inter line power flow controller, Transmission Pricing, Unified power flow controller, cost allocation.

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Authors: R. Abdul Wahab, R. Mohd Fuad Tengku Aziz, N. Othman, S. Saleh, N. Razali, M. Al Baqir Zinal Abidin, M. Hanif Md Nasir

Abstract:

This paper will discuss how we optimize our physical verification flow in our IC Design Department having various rule decks from multiple foundries. Our ultimate goal is to achieve faster time to tape-out and avoid schedule delay. Currently the physical verification runtimes and memory usage have drastically increased with the increasing number of design rules, design complexity, and the size of the chips to be verified. To manage design violations, we use a number of solutions to reduce the amount of violations needed to be checked by physical verification engineers. The most important functions in physical verifications are DRC (design rule check), LVS (layout vs. schematic), and XRC (extraction). Since we have a multiple number of foundries for our design tape-outs, we need a flow that improve the overall turnaround time and ease of use of the physical verification process. The demand for fast turnaround time is even more critical since the physical design is the last stage before sending the layout to the foundries.

Keywords: Physical verification, DRC, LVS, XRC, flow, foundry, runset.

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Authors: Eiichi Sasaki, Shin-ichi Takehiro, Michio Yamada

Abstract:

We study bifurcation structure of the zonal jet flow the streamfunction of which is expressed by a single spherical harmonics on a rotating sphere. In the non-rotating case, we find that a steady traveling wave solution arises from the zonal jet flow through Hopf bifurcation. As the Reynolds number increases, several traveling solutions arise only through the pitchfork bifurcations and at high Reynolds number the bifurcating solutions become Hopf unstable. In the rotating case, on the other hand, under the stabilizing effect of rotation, as the absolute value of rotation rate increases, the number of the bifurcating solutions arising from the zonal jet flow decreases monotonically. We also carry out time integration to study unsteady solutions at high Reynolds number and find that in the non-rotating case the unsteady solutions are chaotic, while not in the rotating cases calculated. This result reflects the general tendency that the rotation stabilizes nonlinear solutions of Navier-Stokes equations.

Keywords: rotating sphere, two-dimensional flow, bifurcationstructure

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Authors: Naimi Abdelhamid, Othmane Abdelkhalek

Abstract:

With the current rise in the demand of electrical energy, present-day power systems which are large and complex, will continue to grow in both size and complexity. Flexible AC Transmission System (FACTS) controllers provide new facilities, both in steady state power flow control and dynamic stability control. Thyristor Controlled Series Capacitor (TCSC) is one of FACTS equipment, which is used for power flow control of active power in electric power system and for increase of capacities of transmission lines. In this paper, a Backstepping Power Flow Controller (BPFC) for TCSC in multimachine power system is developed and tested. The simulation results show that the TCSC proposed controller is capable of controlling the transmitted active power and improving the transient stability when compared with conventional PI Power Flow Controller (PIPFC).

Keywords: FACTS, Thyristor Controlled Series Capacitor (TCSC), Backstepping, BPFC, PIPFC.

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Authors: Samina Elyas Mubeen, R. K. Nema, Gayatri Agnihotri

Abstract:

In this paper the performance of unified power flow controller is investigated in controlling the flow of po wer over the transmission line. Voltage sources model is utilized to study the behaviour of the UPFC in regulating the active, reactive power and voltage profile. This model is incorporated in Newton Raphson algorithm for load flow studies. Simultaneous method is employed in which equations of UPFC and the power balance equations of network are combined in to one set of non-linear algebraic equations. It is solved according to the Newton raphson algorithm. Case studies are carried on standard 5 bus network. Simulation is done in Matlab. The result of network with and without using UPFC are compared in terms of active and reactive power flows in the line and active and reactive power flows at the bus to analyze the performance of UPFC.

Keywords: Newton-Raphson algorithm, Load flow, Unified power flow controller, Voltage source model.

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Authors: M. Salehi, A. A. Motie Birjandi, F. Namdari

Abstract:

Weak damping of low frequency oscillations is a frequent phenomenon in electrical power systems. These frequencies can be damped by power system stabilizers. Unified power flow controller (UPFC), as one of the most important FACTS devices, can be applied to increase the damping of power system oscillations and the more effect of this controller on increasing the damping of oscillations depends on its proper placement in power systems. In this paper, a technique based on controllability is proposed to select proper location of UPFC and the best input control signal in order to enhance damping of power oscillations. The effectiveness of the proposed technique is demonstrated in IEEE 9 bus power system.

Keywords: Unified power flow controller (UPFC), controllability, small signal analysis, eigenvalues.

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Authors: Jayendra Krishna, Laxmi Srivastava

Abstract:

Power flow (PF) study, which is performed to determine the power system static states (voltage magnitudes and voltage angles) at each bus to find the steady state operating condition of a system, is very important and is the most frequently carried out study by power utilities for power system planning, operation and control. In this paper, a counterpropagation neural network (CPNN) is proposed to solve power flow problem under different loading/contingency conditions for computing bus voltage magnitudes and angles of the power system. The counterpropagation network uses a different mapping strategy namely counterpropagation and provides a practical approach for implementing a pattern mapping task, since learning is fast in this network. The composition of the input variables for the proposed neural network has been selected to emulate the solution process of a conventional power flow program. The effectiveness of the proposed CPNN based approach for solving power flow is demonstrated by computation of bus voltage magnitudes and voltage angles for different loading conditions and single line-outage contingencies in IEEE 14-bus system.

Keywords: Admittance matrix, counterpropagation neural network, line outage contingency, power flow

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

A method has been developed for preparing load models for power flow and stability. The load modeling (LOADMOD) computer software transforms data on load class mix, composition, and characteristics into the from required for commonly–used power flow and transient stability simulation programs. Typical default data have been developed for load composition and characteristics. This paper defines LOADMOD software and describes the dynamic and static load modeling techniques used in this software and results of initial testing for BAKHTAR power system.

Keywords: Load Modelling, Static, Power Flow.

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Authors: Mostafa Alinezhad, Mehrdad Ahmadi Kamarposhti

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According to the increasing utilization in power system, the transmission lines and power plants often operate in stability boundary and system probably lose its stable condition by over loading or occurring disturbance. According to the reasons that are mentioned, the prediction and recognition of voltage instability in power system has particular importance and it makes the network security stronger.This paper, by considering of power system contingencies based on the effects of them on Mega Watt Margin (MWM) and maximum loading point is focused in order to analyse the static voltage stability using continuation power flow method. The study has been carried out on IEEE 14-Bus Test System using Matlab and Psat softwares and results are presented.

Keywords: Contingency, Continuation Power Flow, Static Voltage Stability, Voltage Collapse.

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Authors: Irina Eglite, Andrei A. Kolyshkin

Abstract:

The effect of small non-parallelism of the base flow on the stability of slightly curved mixing layers is analyzed in the present paper. Assuming that the instability wavelength is much smaller than the length scale of the variation of the base flow we derive an amplitude evolution equation using the method of multiple scales. The proposed asymptotic model provides connection between parallel flow approximations and takes into account slow longitudinal variation of the base flow.

Keywords: shallow water, parallel flow assumption, weaklynonlinear analysis, method of multiple scales

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Authors: Vai Kuong Sin, Chon Kit Chio

Abstract:

In this paper, the two-dimensional reversed stagnationpoint flow is solved by means of an anlytic approach. There are similarity solutions in case the similarity equation and the boundary condition are modified. Finite analytic method are applied to obtain the similarity velocity function.

Keywords: reversed stagnation-point flow, similarity solutions, asymptotic solution

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Authors: Mohamed Ali

Abstract:

The boundary layer flow and heat transfer on a stretched surface moving with prescribed skin friction is studied for permeable surface. The surface temperature is assumed to vary inversely with the vertical direction x for n = -1. The skin friction at the surface scales as (x-1/2) at m = 0. The constants m and n are the indices of the power law velocity and temperature exponent respectively. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as the buoyancy parameter λ and the suction/injection parameter fw for air (Pr = 0.72) are studied. The choice of n and m ensures that the used similarity solutions are x independent. The results show that, assisting flow (λ > 0) enhancing the heat transfer coefficient along the surface for any constant value of fw. Furthermore, injection increases the heat transfer coefficient but suction reduces it at constant λ.

Keywords: Stretching surface, Boundary layers, Prescribed skin friction, Suction or injection, similarity solutions, buoyancy effects.

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Authors: Udomsak Thongkrajay, Padej Pao-La-Or, Thanatchai Kulworawanichpong

Abstract:

Installation of power compensation equipment in some cases places additional buses into the system. Therefore, a total number of power flow equations and voltage unknowns increase due to additional locations of installed devices. In this circumstance, power flow calculation is more complicated. It may result in a computational convergence problem. This paper presents a power flow calculation by using Newton-Raphson iterative method together with the proposed load transfer technique. This concept is to eliminate additional buses by transferring installed loads at the new buses to existing two adjacent buses. Thus, the total number of power flow equations is not changed. The overall computational speed is expectedly shorter than that of solving the problem without applying the load transfer technique. A 15-bus test system is employed for test to evaluate the effectiveness of the proposed load transfer technique. As a result, the total number of iteration required and execution time is significantly reduced.

Keywords: Load transfer technique, Newton-Raphson power flow, ill-condition

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Authors: Lütfü Saribulut, Mehmet Tümay, İlyas Eker

Abstract:

FACTS devices are used to control the power flow, to increase the transmission capacity and to optimize the stability of the power system. One of the most widely used FACTS devices is Unified Power Flow Controller (UPFC). The controller used in the control mechanism has a significantly effects on controlling of the power flow and enhancing the system stability of UPFC. According to this, the capability of UPFC is observed by using different control mechanisms based on P, PI, PID and fuzzy logic controllers (FLC) in this study. FLC was developed by taking consideration of Takagi- Sugeno inference system in the decision process and Sugeno-s weighted average method in the defuzzification process. Case studies with different operating conditions are applied to prove the ability of UPFC on controlling the power flow and the effectiveness of controllers on the performance of UPFC. PSCAD/EMTDC program is used to create the FLC and to simulate UPFC model.

Keywords: FACTS, Fuzzy Logic Controller, UPFC.

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Authors: M. R. AlRashidi, M. F. AlHajri, M. E. El-Hawary

Abstract:

An enhanced particle swarm optimization algorithm (PSO) is presented in this work to solve the non-convex OPF problem that has both discrete and continuous optimization variables. The objective functions considered are the conventional quadratic function and the augmented quadratic function. The latter model presents non-differentiable and non-convex regions that challenge most gradient-based optimization algorithms. The optimization variables to be optimized are the generator real power outputs and voltage magnitudes, discrete transformer tap settings, and discrete reactive power injections due to capacitor banks. The set of equality constraints taken into account are the power flow equations while the inequality ones are the limits of the real and reactive power of the generators, voltage magnitude at each bus, transformer tap settings, and capacitor banks reactive power injections. The proposed algorithm combines PSO with Newton-Raphson algorithm to minimize the fuel cost function. The IEEE 30-bus system with six generating units is used to test the proposed algorithm. Several cases were investigated to test and validate the consistency of detecting optimal or near optimal solution for each objective. Results are compared to solutions obtained using sequential quadratic programming and Genetic Algorithms.

Keywords: Particle Swarm Optimization, Optimal Power Flow, Economic Dispatch.

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Authors: Umar Alhaji Mukhtar, Abubakar Mohammed El-jummah

Abstract:

This research involved the utilization of fluid flow energy to predict power output using Lead Zirconate Titanate (PZT) piezoelectric stacks. The aim of this work is to extract energy from a controlled level of pressure fluctuation in single-phase flow which forms a part of the energy harvesting technology that powers flow meters. A device- Perspex box was developed and fixed to 50.8 mm rig to induce pressure fluctuation in the flow. An experimental test was carried out using the single-phase water flow in the developed rig in order to measure the power output generation from the piezoelectric stacks. 16 sets of experimental tests were conducted to ensure the maximum output result. The acquired signal of the pressure fluctuation was used to simulate the expected electrical output from the piezoelectric material. The results showed a maximum output voltage of 12 V with an instantaneous output power of 1 µW generated, when the pressure amplitude is 2.6 kPa at a frequency of 2.4 Hz.

Keywords: Energy harvesting, experimental test, perspex rig, pressure fluctuation.

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Authors: Puneet Chawla, Balwinder Singh

Abstract:

Recently, increased attention has been devoted to the voltage instability phenomenon in power systems. Many techniques have been proposed in the literature for evaluating and predicting voltage stability using steady state analysis methods. In this paper P-V and Q-V curves have been generated for a 57 bus Patiala Rajpura circle of India. The power-flow program is developed in MATLAB using Newton Raphson method. Using Q-V curves the weakest bus of the power system and the maximum reactive power change permissible on that bus is calculated. STATCOMs are placed on the weakest bus to improve the voltage and hence voltage stability and also the power transmission capability of the line.

Keywords: Voltage stability, Reactive power, power flow, weakest bus, STATCOM.

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Authors: P. S. Bhowmik, D. V. Rajan, S. P. Bose

Abstract:

The load flow study in a power system constitutes a study of paramount importance. The study reveals the electrical performance and power flows (real and reactive) for specified condition when the system is operating under steady state. This paper gives an overview of different techniques used for load flow study under different specified conditions.

Keywords: Load Flow Studies, Y-matrix and Z-matrix iteration, Newton-Raphson method, Fast Decoupled method, Fuzzy logic, Artificial Neural Network.

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Authors: A. S. Telang, P. P. Bedekar

Abstract:

Flexible AC transmission system controllers play an important role in controlling the line power flow and in improving voltage profiles of the power system network. They can be used to increase the reliability and efficiency of transmission and distribution system. The modeling of these FACTS controllers in power flow calculations have become a challenging research problem. This paper presents a simple and systematic approach for a steady state power flow calculations of power system with STATCOM (Static Synchronous Compensator). It shows how systematically STATCOM can be implemented in conventional power flow calculations. The main contribution of this paper is to investigate this approach for two special conditions i.e. consideration of load increase pattern incorporating load change (active, reactive and both active and reactive) at all load buses simultaneously and the line contingencies under such load change. Such investigation proves to be relevant for determination of strategy for the optimal placement of STATCOM to enhance the voltage stability. The performance has been evaluated on many standard IEEE test systems. The results for standard IEEE-30 bus test system are presented here.

Keywords: Load flow analysis, Newton-Raphson (N-R) power flow, Flexible AC transmission system, FACTS, Static synchronous compensator, STATCOM, voltage profile.

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