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Constriction Factor Based Particle Swarm Optimization for Solving Reactive Power Optimization Problem
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Optimum power flow is a useful tool for planning and operating the electrical system and maintains the economy and safety of the modern electrical system. Teaching, Learning-based Algorithm is one of the new Metaheuristic algorithms which can influence both teachers and students by expediting the interaction among them in sharing the necessary knowledge. The proposed TLBO is designed here to solve the problem of an optimum power flow with STATCOM FACTS device. The optimal location of STATCOM FACTS device on the weak bus is obtained by Analytical Hierarchy Process (AHP) method. The main objective of this study is to reduce fuel cost of generation, reduce active and reactive power loss, improve voltage deviation and enhance voltage stability index within the given control variable constraints. The proposed TLBO algorithm with STATCOM device is evaluated on the standard IEEE-57 bus system. From the simulation result, it shows that the Teaching Learning-based algorithm gives the optimal solution as compared to the recent algorithm mentioned in the literature with some IEEE-57 bus test system.
The losses in electrical power systems are a great problem. Multiple methods have been utilized to decrease power losses in transmission lines. The proper adjusting of reactive power resources is one way to minimize the losses in any power system. Reactive Power Optimization (RPO) problem is a nonlinear and complex optimization problem and contains equality and inequality constraints. The RPO is highly essential in the operation and control of power systems. Therefore, the study concentrates on the Optimal Load Flow calculation in solving RPO problems. The Simple Particle Swarm Optimization (PSO) often falls into the local optima solution. To prevent this limitation and speed up the convergence for the Simple PSO algorithm, this study employed an improved hybrid algorithm based on Chaotic theory with PSO, called Chaotic PSO (CPSO) algorithm. Undeniably, this merging of chaotic theory in PSO algorithm can be an efficient method to slip very easily from local optima compared to Simple PSO algorithm due to remarkable behavior and high ability of the chaos. In this study, the CPSO algorithm was utilized as an optimization tool for solving the RPO problem; the main objective in this study is to decrease the power loss and enhance the voltage profile in the power system. The presented algorithm was tested on IEEE Node-14 system. The simulation implications for this system reveal that the CPSO algorithm provides the best results. It had a high ability to minimize transmission line losses and improve the system's voltage profile compared to the Simple PSO and other approaches in the literature.
The aim of this paper is to introduce a new technique to control the voltage and reactive power in power systems based on Artificial Neural Network (ANN). Feed-forward ANN with Back Propagation training algorithm is used and the training data is obtained by solving several abnormal conditions using Linear Programming (LP). Considering generator voltages, reactive power sources and transformer taps as control variables, and load bus voltages and generator reactive powers as dependent variables. The relations are derived according to sensitivity relations based on Newton-Raphson load flow equations. The system losses are chosen as objective function so that the approach minimizes system losses and enhances voltage profile. This technique is tested by computer simulation on IEEE 6-bus and 14 bus power systems and satisfactory results are obtained.
Power-system-security enhancement deals with the task of taking remedial action against possible network overloads in the system following the occurrence of contingencies. Line overload can be removed by means of generation redispatching and by adjustment of phase-shifting transformers. The paper presents a genetic-algorithm (GA) based OPF algorithm for identifying the optimal values of generator active-power output and the angle of the phase-shifting transformer. The locations of phase shifters are selected based on sensitivity analysis. To overcome the shortcomings associated with the representation of real and integer variables using the binary string in the GA population, the control variables are represented in their natural form. Also, crossover and mutation operators which can deal directly with integers and floating-point numbers are used. Simulation results on IEEE 30-bus and IEEE 118-bus test systems are presented and compared with the results of other approaches.
By integrating a genetic algorithm (GA) with a nonlinear interior point method (IPM), a novel hybrid method for the optimal reactive power flow (ORPF) problem is proposed in this paper. The proposed method can be mainly divided into two parts. The first part is to solve the ORPF with the IPM by relaxing the discrete variables. The second part is to decompose the original ORPF into two sub-problems: continuous optimization and discrete optimization. The GA is used to solve the discrete optimization with the continuous variables being fixed, whereas the IPM solves the continuous optimization with the discrete variables being constant. The optimal solution can be obtained by solving the two sub-problems alternately. A dynamic adjustment strategy is also proposed to make the GA and the IPM to complement each other and to enhance the efficiency of the hybrid proposed method. Numerical simulations on the IEEE 30-bus, IEEE 118-bus and Chongqing 161-bus test systems illustrate that the proposed hybrid method is efficient for the ORPF problem
This paper presents a novel hybrid algorithm combining Firefly Algorithm (FA) and Nelder Mead (NM) simplex method for solving power system Optimal Reactive Power Dispatch (ORPD) problems. The ORPD is a very important aspect of power system operation and is a highly nonlinear, non-convex optimization problem, consisting of both continuous and discrete control variables. Like many other general purpose optimization methods, the original FA often traps into local optima and in order to overcome the shortcoming, in this paper, an efficient local search method called NM simplex subroutine is introduced in the internal architecture of the original FA algorithm. The proposed Hybrid Firefly Algorithm (HFA) avoids premature convergence of original FA by exploration with FA and exploitation with NM simplex. The proposed method is applied to determine optimal settings of generator voltages, tap positions of tap changing transformers and VAR output of shunt capacitors to optimize two different objective functions; such as minimization of real power loss and voltage deviations. The program is developed in Matlab and the proposed hybrid algorithm is examined on two standard IEEE test systems for solving the ORPD problems. For validation purpose, the results obtained with the proposed approach are compared with those obtained by other methods. It is observed that the proposed method has better convergence characteristics and robustness compared to the original version of FA and other existing methods. It is revealed that the proposed hybrid method is able to provide better solutions.
The reactive power dispatch (RPD) problem is a very critical optimization problem of power system which minimizes the real power loss of the transmission system. While solving the said problem, generator bus voltages and transformer tap settings are kept within a stable operating limit. In connection with the RPD problem, solving reactive power is compensated by incorporating shunt capacitors. The particle swarm optimization (PSO) technique is a swarm intelligence based fast working optimization method which is chosen in this paper as an optimization tool. Additionally, the constriction factor is included with the conventional PSO technique to accelerate the convergence property of the applied optimization tool. In this paper, the RPD problem is solved in the case of the two higher bus systems, i.e., the IEEE 57-bus system and the IEEE 118-bus system. Furthermore, the result of the present paper is compared with a few optimization technique based results to substantiate the effectiveness of the proposed study.
This paper presents a harmony search algorithm for optimal reactive power dispatch (ORPD) problem. Optimal reactive power dispatch is a mixed integer, nonlinear optimization problem which includes both continuous and discrete control variables. The proposed algorithm is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and the amount of reactive compensation devices to optimize a certain object. The objects are power transmission loss, voltage stability and voltage profile which are optimized separately. In the presented method, the inequality constraints are handled by penalty coefficients. The study is implemented on IEEE 30 and 57-bus systems and the results are compared with other evolutionary programs such as simple genetic algorithm (SGA) and particle swarm optimization (PSO) which have been used in the last decade and also other algorithms that have been developed in the recent years.
The authors present a consistent treatment of the optimal reactive
power dispatch problem taking into account the uncertainty associated
with load values. Linguistic declarations of loads are translated into
possibility distribution functions via fuzzy sets. The problem is
decomposed into four subproblems via Dantzig-Wolfe decomposition for
reducing the problem dimensions. Voltage constraints within each
subproblem are modeled via fuzzy sets to bias the final solution toward
the static security region. A numerical example is presented to
demonstrate the applicability of the method
This paper presents a decoupled approach for optimal active and reactive power dispatch for the economic operation of an electric utility. The proposed iterative scheme reported in this paper decomposes the optimal load flow problem into a P-subproblem and a Q-subproblem, where the control variables are the active and reactive power outputs of generators. At each iteration the subproblems are solved by quadratic programming using the flexible tolerance optimization method (FTOM). In this approach, constraints are linearized by using sensitivity analysis and the perturbation technique, in order to obtain a wider near-feasible region for this quadratic programming method. This approach has a good computation speed. The results of two test systems and three cases are presented and compared with the results of other methods.
In this paper, self-adaptive real coded genetic algorithm (SARGA) is used as one of the techniques to solve optimal reactive power dispatch (ORPD) problem. The self-adaptation in real coded genetic algorithm (RGA) is introduced by applying the simulated binary crossover (SBX) operator. The binary tournament selection and polynomial mutation are also introduced in real coded genetic algorithm. The problem formulation involves continuous (generator voltages), discrete (transformer tap ratios) and binary (var sources) decision variables. The stochastic based SARGA approach can handle all types of decision variables and produce near optimal solutions. The IEEE 14- and 30-bus systems were used as test systems to demonstrate the applicability and efficiency of the proposed method. The performance of the proposed method is compared with evolutionary programming (EP) and previous approaches reported in the literature. The results show that SARGA solves the ORPD problem efficiently.
A new operations research model of optimal load flow solved by nonlinear programming methods (the generalized reduced gradient algorithm) is presented. As compared to existing optimal power flow models, this model incorporates network performance variables such as scheduled bus voltages as well as topological and elemental constraints.In addition, the development, sensitivity, optimality and efficiency of the model are explored. Several example problems are implemented and solved. Detailed discussions about the ability of the model to work under a wide variety of network contingencies such as loss of generation or load, loss of a line, and network faults are presented. The model is also briefly examined for its use in the study of network voltage regulation.
eberhart @ engr.iupui.edu A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described, 1
This paper is concerned with application of genetic algorithms (GAs) to optimal reactive power dispatch and voltage control of power systems. A decomposed coding structure is proposed in the genetic search approach to code a large number of variables involved in the large-scale systems. Simulation results, compared with that obtained using a conventional gradient-based optimisation method, are presented to show the potential of applications of the proposed methodology in power system economical operations.
The classical optimal power flow problem with a nonseparable objective function can be solved by an explicit Newton approach. Efficient, robust solutions can be obtained for problems of any practical size or kind. Solution effort is approximately proportional to network size, and is relatively independent of the number of controls or binding inequalities. The key idea is a direct simultaneous solution for all of the unknowns in the Lagrangian function on each iteration. Each iteration minimizes a quadratic approximation of the Lagrangian. For any given set of binding constraints the process converges to the Kuhn-Tucker conditions in a few iterations. The challenge in algorithm development is to efficiently identify the binding inequalities.
The optimal power flow (OPF) problem is formulated based upon the decoupling principle well recognized in bulk power transmission loadflow. This principle is exploited by decomposing the OPF formulation into a P-Problem (P- theta real power model) and a Q-Problem (Q-V reactive power model), which simplifies the formulation, improves computation time and permits a certain flexibility in the types of calculations desired (i. e. , P-Problem, Q-Problem or both). The P-Problem is defined as the minimization of hourly production costs by controlling generator real power outputs and tap settings on phase-shifting transformers. Results of three test systems (5 bus, 30 bus and 962 bus systems) are presented. The method has been programmed in a full production version and will accomodate a problem size of up to 1500 buses/2500 lines.
A mathematical formulation of the optimal reactive power control (optimal VAR control) problem and results from tests of the algorithm are presented in this paper. The model minimizes the real power losses in the system. The constraints include the reactive power limits of the generators, limits on the load bus voltages, and the operating limits of the control variables, i.e., the transformer tap positions, generator terminal voltages and switchable reactive power sources. Real power economic dispatch is accomplished by standard techniques.
Characteristics of linear programming (LP) and nonlinear
programming (NLP)-based optimal power flows (OPFs) are discussed, which
allocate (auctions) reactive power support among competing generators in
a deregulated environment. LP-based AC OPF algorithms are frequently
used in practice to optimise the operation and reinforcement of power
systems owing to their reliability. The alternative methods are
NLP-based OPF algorithms, which have developed rapidly in this past
decade motivated by the performance of interior-point algorithms. While
LP algorithms offer reliable performance, the latter offer computation
speed and accuracy for achieving the solution. An LP-based direct
reactive OPF and a NLP-based direct reactive OPF using an interior-point
algorithm, which concurrently solve load flow and optimisation problems,
are developed and analysed. The issue of performance arises from the
difficulties associated with the convergence of a direct LP OPF and the
need for a technique to enforce the convergence of such an OPF. As the
LP OPF may not converge spontaneously to the optimal point, questions
arise as to whether such approaches are appropriate for facilitating the
provision of VAr support in a competitive environment. Although the
overall reactive requirement calculated by the OPF may be reasonably
accurate, a generator's individual commitment may vary considerably. In
contrast, the NLP OPF shows different characteristics: it converges
spontaneously and the solutions are accurate. A comparison between those
two streams of algorithms is presented. Extensive case studies are
carried out over the IEEE-118 bus system to illustrate the impact of
different starting points on the solutions for both LP and NLP
algorithms
The reactive power/voltage control in a distribution substation is
investigated. The purpose is to properly dispatch the shunt capacitors
and onload tap changers at the distribution substation based on the
forecast hourly loads of a main transformer and its primary bus voltage
such that the reactive power flows through the main transformer, and the
transformer secondary bus voltage deviations from the desired values can
be minimised. Practical constraints on secondary bus voltage limits and
the maximum allowable number of switching operations in a day for the
onload tap changers are taken into account. An approach based on dynamic
programming is presented to reach the desired dispatching schedule. To
demonstrate the usefulness of the proposed approach, reactive
power/voltage control in a distribution substation within the service
area of Taipei City District Office of Taiwan Power Company is
performed. It is found that a proper dispatching schedule for the shunt
capacitors and onload tap changers can be reached by the proposed method
The present paper will discuss the efficient, practical and definitive algorithm for dealing with constrained load flow problems. Algorithms based on mathematical programming and algorithms based on the load flow calculation methods have been studied since earlier days. However, on account of numerous control variables to be determined and of inadequate calculating efficiency, the guarantee of unfailing solution is yet to be achieved. In the calculating procedure herein described the extents of adjustments are not determined simultaneously for all the control variables ; the control variables considered likely to produce greater adjusting effect are selected one by one and are adjusted successively. This adjustment method, as a consequence, is useful not only for on-line power system operation but also as simulator software for training system operators.
Since conventional optimal power flow (OPF) algorithms are limited
and too slow for operational planning, power system operation and
planning engineers have been seeking efficient OPF algorithms for three
decades. The interior point method is one of the most efficient
algorithms. In this paper, an improved quadratic interior point (IQIP)
method is used to solve comprehensive OPF problems with a variety of
objective functions, including economic dispatch, VAr planning and loss
minimization. The IQIP method features a general starting point (rather
than selected good point as in the general interior point method) and
fast convergence. Consequently, the OPF package described in this paper
offers huge improvements in speed, accuracy and convergence in solving
multi-objective and multi-constraint optimization problems. It will be a
very useful tool for the power industry
This paper presents a new approach to optimal reactive power
planning based on a genetic algorithm. Many outstanding methods to this
problem have been proposed in the past. However, most these approaches
have the common defect of being caught to a local minimum solution. The
integer problem which yields integer value solutions for discrete
controllers/banks still remain as a difficult one. The genetic algorithm
is a kind of search algorithm based on the mechanics of natural
selection and genetics. This algorithm can search for a global solution
using multiple paths and treat integer problems naturally. The proposed
method was applied to practical 51-bus and 224-bus systems to show its
feasibility and capabilities. Although this method is not as fast as
sophisticated traditional methods, the concept is quite promising and
useful in the coming computer age
An implementation of an interior point method to the optimal
reactive dispatch problem is described. The interior point method used
is based on the primal-dual algorithm and the numerical results in large
scale networks (1832 and 3467 bus systems) have shown that this
technique can be very effective to some optimal power flow applications
The author's consider a new formulation of optimal power flow
(OPF) that makes it eminently suitable for accurate incremental
modeling. G. Zoutendijk's method of feasible directions (1960) for
solving the nonlinear programming problems is adapted for the solution
of the OPF. Hydraulic modeling of systems with a considerable share of
hydraulic generation is considered. The method is very efficient as it
is designed to exploit the special structure of the problem
Capacitor Placement Using Fuzzy And Particle Swarm Optimization Method For Maximum Annual Savings
- Damdar