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The economic dispatch has the objective of generation allocation to the power generators in such a manner that the total fuel cost is minimized while all operating constraints are satisfied. Conventional optimization methods assume generator cost curves to be continuous and monotonically increasing, but modern generators have a variety of nonlinearities in their cost curves making this assumption inaccurate, and the resulting approximate dispatches cause a lot of revenue loss. Evolutionary methods like particle swarm optimization perform better for such problems as no convexity assumptions are imposed, but these methods converge to sub-optimum solutions prematurely, particularly for multimodal problems. To handle the problem of premature convergence, this paper proposes to apply a novel self-organizing hierarchical particle swarm optimization (SOH_PSO) for the nonconvex economic dispatch (NCED). The performance further improves when time-varying acceleration coefficients are included. The results show that the proposed approach outperforms previous methods for NCED. Index Terms--Nonconvex economic dispatch (NCED), premature convergence, prohibited operating zones (POZ), ramp rate limits, self-organizing hierarchical particle swarm optimization (SOH_PSO), time-varying acceleration coefficients (TVAC), valve point loading effect.

Increased loading and contingencies often lead to situations where the optimal power flow solution no longer remains within the secure region. In such situations there is a need of determining control actions to be taken quickly, as otherwise the system may become unstable. Hence it is important to quantify the degree of insecurity of the power system both in planning as well as at operational stages. The distance in parameter space between an insecure operating point and the closest point on feasible (secure) hyper-surface has been used as a measure of degree of insecurity. A method based on two-phase optimization neural network has been presented to compute the degree of insecurity and the voltages and angles at all the buses of the system corresponding to the closest secure point. Inclusion of security limits on power system variables assures a solution representing a secure system. When compared with conventional non-linear optimization techniques, the proposed neural network is superior, as it can be easily implemented using digital hardware and is highly suitable for real time implementation in energy management system. The proposed method has been tested on IEEE 30-bus test system and a practical 75-bus Indian system. The results achieved are compared with results from a conventional method. Insecurity arising due to increase in load and contingencies has been considered in this work. Keywords: Two-phase neural network; Degree of insecurity; Non-linear optimization; Constrained minimization; Closest secure point; Euclidean norm

A fuzzy neural network comprising of a screening module and ranking module is proposed for online voltage contingency screening and ranking. A four-stage multioutput parallel self-organizing hierarchical neural network (PSHNN) has been presented in this paper to serve as the ranking module to rank the screened critical contingencies online based on a static fuzzy performance index formulated by combining voltage violations and voltage stability margin. Compared to the deterministic crisp ranking, the proposed approach provides a more informative and flexible ranking and is very effective in handling contingencies lying on the boundary between two severity classes. Angular distance-based clustering has been employed to reduce the dimension of the fuzzy PSHNN. The potential of the fuzzy PSHNN to provide insight into the ranking process, without having to go through the complicated task of rule framing is demonstrated on IEEE 30-bus system and a practical 75-bus Indian system. Index Terms--Angular distance-based clustering, contingency ranking, fuzzy neural network, fuzzy overall performance index, linguistic categories, membership values, parallel self-organizing hierarchical neural network, ranking module, screening module.