N. C. Sahoo

Solving shortest path problem using particle swarm optimization

This paper presents the investigations on the application of particle swarm optimization (PSO) to solve shortest path (SP) routing problems. A modified priority-based encoding incorporating a heuristic operator for reducing the possibility of loop-formation in the path construction process is proposed for particle representation in PSO. Simulation experiments have been carried out on different network topologies for networks consisting of 15-70 nodes. It is noted that the proposed PSO-based approach can find the optimal path with good success rates and also can find closer sub-optimal paths with high certainty for all the tested networks. It is observed that the performance of the proposed algorithm surpasses those of recently reported genetic algorithm based approaches for this problem.

Multi-objective particle swarm optimization based on fuzzy-Pareto-dominance for possibilistic planning of electrical distribution systems incorporating distributed generation

This paper presents a multi-objective planning approach for electrical distribution systems under uncertainty in load demand incorporating distributed generation (DG). Both radial and meshed systems are considered. The overall influence of load demand uncertainty on planned networks is investigated in detail. Uncertainty in load demand is possibilistically modeled using a fuzzy triangular number. The two objectives in system planning are: (i) minimization of total installation and operational costs, and (ii) minimization of the risk factor. The risk factor is a function of the contingency load-loss index (CLLI), which measures load loss under contingencies, and the degree of network constraints violations. CLLI minimization improves network reliability. The network variables optimized are: (i) the network structure type (radial or meshed), (ii) the number of feeders and their routes, and (iii) the number and location of sectionalizing switches. The optimization tool is a multi-objective particle swarm optimization (MOPSO) variant that uses heuristic selection and assignment of leaders or guides for efficient identification of non-dominated solutions. The optimal number, location, and size of the DG units are determined in another planning stage. Performance comparisons between the planning approaches with possibilistic and deterministic load models highlight the relative merits and demerits. The advantages of networks obtained using the proposed planning approach in the context of DG integration are described. The proposed planning approach is validated using three typical distribution systems.

Multi-objective planning of electrical distribution systems incorporating sectionalizing switches and tie-lines using particle swarm optimization

Abstract A multi-objective planning approach for electrical distribution systems using particle swarm optimization is presented in this paper. In this planning, the number of feeders and their routes, number and locations of sectionalizing switches, and number and locations of tie-lines of a distribution system are optimized. The multiple objectives to determine optimal values for these planning variables are: (i) minimization of total installation and operational cost and (ii) maximization of network reliability. The planning optimization is performed in two steps. In the first step, the distribution network structure, i.e., number of feeders, their routes, and number and locations of sectionalizing switches are determined. In the second step, the optimum number and locations of tie-lines are determined. Both the objectives are minimized simultaneously to obtain a set of non-dominated solutions in the first step of optimization. The solution strategy used for the first step optimization is the Strength Pareto Evolutionary Algorithm-2 (SPEA2) based multi-objective particle swarm optimization (SPEA2–MOPSO). In the second step, the solutions/networks obtained from the previous step are further optimized by placement of tie-lines. SPEA2-based binary MOPSO (SPEA2–BMOPSO) is used in the second step of optimization. The proposed planning algorithm is tested and evaluated on different practical distribution systems.

Mono- and multi-objective planning of electrical distribution networks using particle swarm optimization

This paper presents a comprehensive study on mono- and multi-objective approaches for electrical distribution network design using particle swarm optimization (PSO). Specifically, two distribution network design problems, i.e., static and expansion planning, are solved using PSO. The network planning involves optimization of both network topology and branch conductor sizes. Both the planning problems are used to illustrate mono- and multi-objective optimization of distribution networks. Firstly, three PSO variants, i.e., PSO with inertia weight (PSO-IW), PSO with constriction factor (PSO-CF), and comprehensive learning PSO, are evaluated on a mono-objective (minimization of total cost of installation and energy loss) static planning problem. A novel encoding/decoding technique is devised to represent the network as a particle in PSO. Also, a heuristics based branch conductor size selection algorithm has been developed and used. Statistical tests performed to compare the performances of the three PSO variants reveal that the PSO-CF exhibits relatively better performance. Subsequently, the PSO-CF is applied for mono-objective expansion planning and multi-objective static and expansion planning problems. In the multi-objective planning with two conflicting objectives (total cost of installation and energy loss, and total non-delivered energy), the Pareto-optimality principle based tradeoff is done using the strength Pareto evolutionary algorithm-2. The efficiency of PSO for distribution system planning problem, in general, is demonstrated through different examples.

Multivariable nonlinear control of STATCOM for synchronous generator stabilization

A static synchronous compensator (STATCOM) is a typical flexible ac transmission system device playing a vital role as a stability aid for small and large transient disturbances in an interconnected power system. This article deals with design and evaluation of a feedback linearizing nonlinear controller for STATCOM installed in a single-machine infinite-bus power system. In addition to the coordinated control of ac and dc bus voltages, the proposed controller also provides good damping to the electromechanical oscillation of the synchronous generator under transient disturbances. The efficiency of the control strategy is evaluated by computer simulation studies. The comparative study of these results with the conventional cascade control structure establishes the elegance of the proposed control scheme.

Experimental Investigations on Computer-Based Methods for Determination of Static Electromagnetic Characteristics of Switched Reluctance Motors

Because of the doubly salient structure of the switched reluctance motor (SRM) and its intentional operation in deep magnetic saturation for higher power density, its static electromagnetic characteristics are highly nonlinear functions of rotor position and phase current. This makes the accurate experimental measurement/determination of these characteristics a difficult task. This paper presents a comprehensive discussion and analysis on the different (most practiced) computer-based methods for the determination of these characteristics for a typical SRM. A digital signal processor (DSP)-based completely automated SRM drive system has been used for these studies. For all the offline computations, user-friendly MATLAB/Simulink-based models have been developed. The experimental methods, computational models, measurement results, and appropriate postmortem discussions for the determination of static flux linkage, inductance, and electromagnetic torque characteristics for an 8/6 four-phase SRM are reported.

Simple heuristics-based selection of guides for multi-objective PSO with an application to electrical distribution system planning

In multi-objective particle swarm optimization (MOPSO), a proper selection of local guides significantly influences detection of non-dominated solutions in the objective/solution space and, hence, the convergence characteristics towards the Pareto-optimal set. This paper presents an algorithm based on simple heuristics for selection of local guides in MOPSO, named as HSG-MOPSO (Heuristics-based-Selection-of-Guides in MOPSO). In the HSG-MOPSO, the set of potential guides (in a PSO iteration) consists of the non-dominated solutions (which are normally stored in an elite archive) and some specifically chosen dominated solutions. Thus, there are two types of local guides in the HSG-MOPSO, i.e., non-dominated and dominated guides; they are named so as to signify whether the chosen guide is a non-dominated or a dominated solution. In any iteration, a guide, from the set of available guides, is suitably selected for each population member. Some specified proportion of the current population members follow their respective nearest non-dominated guides and the rest follow their respective nearest dominated guides. The proposed HSG-MOPSO is firstly evaluated on a number of multi-objective benchmark problems along with investigations on the controlling parameters of the guide selection algorithm. The performance of the proposed method is compared with those of two well-known guide selection methods for evolutionary multi-objective optimization, namely the Sigma method and the Strength Pareto Evolutionary Algorithm-2 (SPEA2) implemented in PSO framework. Finally, the HSG-MOPSO is evaluated on a more involved real world problem, i.e., multi-objective planning of electrical distribution system. Simulation results are reported and analyzed to illustrate the viability of the proposed guide selection method for MOPSO.

Efficient Computation of Shortest Paths in Networks Using Particle Swarm Optimization and Noising Metaheuristics

This paper presents a novel hybrid algorithm based on particle swarm optimization (PSO) and noising metaheuristics for solving the single-source shortest-path problem (SPP) commonly encountered in graph theory. This hybrid search process combines PSO for iteratively finding a population of better solutions and noising method for diversifying the search scheme to solve this problem. A new encoding/decoding scheme based on heuristics has been devised for representing the SPP parameters as a particle in PSO. Noising-method-based metaheuristics (noisy local search) have been incorporated in order to enhance the overall search efficiency. In particular, an iteration of the proposed hybrid algorithm consists of a standard PSO iteration and few trials of noising scheme applied to each better/improved particle for local search, where the neighborhood of each such particle is noisily explored with an elementary transformation of the particle so as to escape possible local minima and to diversify the search. Simulation results on several networks with random topologies are used to illustrate the efficiency of the proposed hybrid algorithm for shortest-path computation. The proposed algorithm can be used as a platform for solving other NP-hard SPPs.

Fuzzy-Pareto-dominance driven possibilistic model based planning of electrical distribution systems using multi-objective particle swarm optimization

This paper presents a fuzzy-Pareto dominance driven possibilistic model based planning of electrical distribution systems using multi-objective particle swarm optimization (MOPSO). This multi-objective planning model captures the possibilistic variations of the system loads using a fuzzy triangular number. The MOPSO based on the Pareto-optimality principle is used to obtain a set of non-dominated solutions representing different network structures under uncertainties in load demands and these non-dominated solutions are stored in an elite archive of limited size. Normally, choosing the candidate non-dominated solutions to be retained in the elite archive while maintaining the quality of the Pareto-approximation front as well as maintaining the diversity of solutions on this front is very much computationally demanding. In this paper, the principles of fuzzy Pareto-dominance are used to find out and rank the non-dominated solutions on the Pareto-approximation front. This ranking in turn is used to maintain the elite archive of limited size by discarding the lower ranked solutions. The two planning objectives are: (i) minimization of total installation and operational cost and (ii) minimization of risk factor. The risk factor is defined as a function of an index called contingency-load-loss index (CLLI), which captures the effect of load loss under contingencies, and the degree of network constraint violations. The minimization of the CLLI improves network reliability. The network variables that are optimized are: (i) number of feeders and their routes, and (ii) number and locations of sectionalizing switches. An MOPSO (developed by the authors), based on a novel technique for the selection and assignment of leaders/guides for efficient search of non-dominated solutions, is used as the optimization tool. The proposed planning approach is validated on a typical 100-node distribution system. Performance comparisons between the planning approaches with the possibilistic and deterministic load models are provided highlighting the relative merits and demerits. It is also verified that the proposed solution ranking scheme based on the fuzzy-Pareto dominance is very much better from both quality and computational burden point of view in comparison with the other well-known archive truncation techniques based on clustering and solution density measurement etc.

Particle Swarm Optimization Combined with Local Search and Velocity Re-Initialization for Shortest Path Computation in Networks

This paper presents the application of particle swarm optimization (PSO) based search algorithm for solving the single source shortest path problem (SPP) commonly encountered in graph theory. A new particle encoding/decoding scheme has been devised for representing the SPP parameters as a particle. In order to enhance the search capability of PSO, a selective local search mechanism and periodic velocity re-initialization of particles have been incorporated. Simulation results on several networks with random topologies are used to illustrate the efficiency of the proposed hybrid PSO algorithm for computation of shortest paths in networks