J. P. Zhan

Fast

This letter presents a new method, the fast λ-iteration (FλI) method, to solve the economic dispatch (ED) problem considering the prohibited operating zones (POZs) and ramp rate limits of generation units. Necessary conditions for the optimal solution of the ED problem are presented and proved. The efficiency of the method has been verified on a 15-unit system and a Korea 140-unit system.

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Economic dispatch with valve-point effect (EDVPE) considered is presented as a more accurate model of the real problem compared to the conventional economic dispatch model. It is basically a non-convex, non-differentiable, and multi-modal optimization model with many local minima. Part I of the paper focuses on the local minimum analysis of the EDVPE. The analysis indicates that a local minimum consists of the singular points, the small convex regions, and the output of a slack unit that is dispatched to balance the load demand. Two types of local minima are identified and the second type could be ignored. To verify the rationality of the analyses, a traverse search has been performed to solve the EDVPE with and without considering the transmission loss on different test systems. All the simulation results support the analysis given in the paper. To effectively solve the EDVPE on a large-scale power system, based on the analysis presented in this paper, a new method, dimensional steepest decline method, is proposed in Part II of the paper.

-Iteration Method for Economic Dispatch With Prohibited Operating Zones

Economic dispatch (ED) considering valve-point effect, multiple fuel options, prohibited operating zones of generation units is a more accurate model compared to a conventional ED model. It is non-smooth and thus evolutionary algorithms (EAs) are so far the only feasible approaches for the model. In Part II of the paper, a new method, the dimensional steepest decline method (DSD), is proposed for the ED with non-smooth objectives. The DSD is based on the local minimum analysis of the ED problem presented in Part I of the paper. The fuel costs decline rate between each two adjacent singular points is utilized to find the optimal solutions in a serial sequence. The computational complexity of the DSD is analyzed. The DSD has been applied to solve different types of ED problems on different test systems, including large-scale systems. The simulation results show that DSD can obtain more accurate solutions and consume much less time and its advantage is more obvious on large-scale systems, in comparison with the state-of-art EAs.

Economic Dispatch With Non-Smooth Objectives—Part I: Local Minimum Analysis

This paper presents a new technique called morphology singular entropy (MSE), based on which a phase selector for transmission lines is developed. MSE combines mathematical morphology, singular value decomposition (SVD), and entropy theory, making it insensitive to noise and easy to extract the features of the fault-induced transients. Voltage signals are used as inputs of the proposed MSE-based phase selector. Each signal is processed by a multiscale morphological filter first, and a matrix consisting of the outputs of the filter is formed. By decomposing the matrix using SVD, the singular values are obtained, and then the entropy in association with this signal can be calculated. Afterwards, in order to improve the sensitivity and reliability of the phase selection, four classification indices derived from the entropies are defined. The phase selection is performed by comparing these four indices to a preset threshold. Simulation data generated using PSCAD/EMTDC and real-life data have been employed to verify the performance of the proposed method.

Economic Dispatch With Non-Smooth Objectives—Part II: Dimensional Steepest Decline Method

This paper presents a new model for the integrated maintenance scheduling (IMS) of generators and transmission lines, which is formulated as a high dimensional, mix-integer and highly constrained optimization problem. The advantage of the new model is that the number of integer variables is greatly reduced in comparison with that in the traditional IMS model in a large scale power system. Besides, a fast group search optimizer (FGSO) algorithm is developed to solve the new IMS model, whose objective is to minimize the total costs of maintenance and power production. The effectiveness of the new model and the FGSO has been evaluated on the IEEE reliability test system. Simulation results show that the new model is successfully solved by FGSO and particle swarm optimizer (PSO). FGSO consumes much less time to find a near optimal solution and has better convergence performance in comparison with GSO and PSO.

Morphology Singular Entropy-Based Phase Selector Using Short Data Window for Transmission Lines

For the generation maintenance scheduling (GMS) problem, a producer hopes to maximize its profit while ISO is to guarantee the system reliability. Thus, the GMS is a multi-objective optimization problem. In the GMS, there are large numbers of both continuous and integer variables, which complicates the resolving of the GMS. This paper proposes a new GMS model, which is suitable to be solved by the non-dominated sorting genetic algorithm-II (NSGA-II). In the GMS model, the maintenance status of a generator is encoded into an integer variable and both the online status and the start-up status are represented by the generation variables. The GMS model on the IEEE reliability test system is solved by NSGA-II with a set of Pareto-optimal solutions obtained. The simulation results show that the GMS can be efficiently solved by NSGA-II. The simulation results also show that one producers profit conflicts with another ones, and that the reliability objective is independent of the other objectives.

Integrated maintenance scheduling of generators and transmission lines based on fast group searching optimizer

Dissolved gas analysis (DGA) has proved to be one of the most useful techniques to detect the incipient faults of power transformers. This paper presents a novel method named multi-kernel support vector classifier (MKSVC), to analyze the DGA for fault diagnosis of transformers. Different from the conventional support vector machine (SVM), MKSVC uses a combined kernel formed through a linear combination of several basis kernels. In MKSVC, each basis kernel extracts a specific type of information from the training data, providing a partial description of the data. Given many partial descriptions of the data, a convex optimization is obtained by a linear combination. Thus, the learning problem can be solved by iteratively computing this optimization problem. The MKSVC method is evaluated using 318 fault data in comparison with several commonly used methods. The diagnostic results show that the diagnostic accuracy of MKSVC prevail those of the commonly used methods.