Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Energy resource scheduling in a real distribution network managed by several virtual power players

Smart Grids (SGs) appeared as the new paradigm for power system management and operation, being designed to integrate large amounts of distributed energy resources. This new paradigm requires a more efficient Energy Resource Management (ERM) and, simultaneously, makes this a more complex problem, due to the intensive use of distributed energy resources (DER), such as distributed generation, active consumers with demand response contracts, and storage units. This paper presents a methodology to address the energy resource scheduling, considering an intensive use of distributed generation and demand response contracts. A case study of a 30 kV real distribution network, including a substation with 6 feeders and 937 buses, is used to demonstrate the effectiveness of the proposed methodology. This network is managed by six virtual power players (VPP) with capability to manage the DER and the distribution network.

Mixed integer non linear programming and artificial neural network based approach to ancillary services dispatch in competitive electricity markets

Ancillary services represent a good business opportunity that must be considered by market players. This paper presents a new methodology for ancillary services market dispatch. The method considers the bids submitted to the market and includes a market clearing mechanism based on deterministic optimization. An Artificial Neural Network is used for day-ahead prediction of Regulation Down, regulation-up, Spin Reserve and Non-Spin Reserve requirements. Two test cases based on California Independent System Operator data concerning dispatch of Regulation Down, Regulation Up, Spin Reserve and Non-Spin Reserve services are included in this paper to illustrate the application of the proposed method: (1) dispatch considering simple bids; (2) dispatch considering complex bids.

Modeling of the lung impedance using a fractional order ladder network with constant phase elements

The self similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. The fractal geometry is typically characterized by a recurrent structure. This study investigates the identification of a model for the respiratory tree by means of its electrical equivalent based on intrinsic morphology. Measurements were obtained from seven volunteers, in terms of their respiratory impedance by means of its complex representation for frequencies below 5 Hz. A parametric modeling is then applied to the complex valued data points. Since at low-frequency range the inertance is negligible, each airway branch is modeled by using gamma cell resistance and capacitance, the latter having a fractional-order constant phase element (CPE), which is identified from measurements. In addition, the complex impedance is also approximated by means of a model consisting of a lumped series resistance and a lumped fractional-order capacitance. The results reveal that both models characterize the data well, whereas the averaged CPE values are supraunitary and subunitary for the ladder network and the lumped model, respectively.

Complex order biped rhythms

Animal locomotion is a complex process, involving the central pattern generators (neural networks, located in the spinal cord, that produce rhythmic patterns), the brainstem command systems, the steering and posture control systems and the top layer structures that decide which motor primitive is activated at a given time. Pinto and Golubitsky studied an integer CPG model for legs rhythms in bipeds. It is a four-coupled identical oscillators' network with dihedral symmetry. This paper considers a new complex order central pattern generator (CPG) model for locomotion in bipeds. A complex derivative Dα±jβ, with α, β ∈ ℜ+, j = √-1, is a generalization of the concept of an integer derivative, where α = 1, β = 0. Parameter regions where periodic solutions, identified with legs' rhythms in bipeds, occur, are analyzed. Also observed is the variation of the amplitude and period of periodic solutions with the complex order derivative.

Metalearner based on Dynamic Neural Network for Strategic Bidding in electricity Markets

The restructuring of electricity markets, conducted to increase the competition in this sector, and decrease the electricity prices, brought with it an enormous increase in the complexity of the considered mechanisms. The electricity market became a complex and unpredictable environment, involving a large number of different entities, playing in a dynamic scene to obtain the best advantages and profits. Software tools became, therefore, essential to provide simulation and decision support capabilities, in order to potentiate the involved players’ actions. This paper presents the development of a metalearner, applied to the decision support of electricity markets’ negotiation entities. The proposed metalearner executes a dynamic artificial neural network to create its own output, taking advantage on several learning algorithms implemented in ALBidS, an adaptive learning system that provides decision support to electricity markets’ players. The proposed metalearner considers different weights for each strategy, depending on its individual quality of performance. The results of the proposed method are studied and analyzed in scenarios based on real electricity markets’ data, using MASCEM - a multi-agent electricity market simulator that simulates market players’ operation in the market.

Distributed Sensing of Fluid Dynamic Phenomena with the XDense Sensor Grid Network

IEEE International Conference on Cyber Physical Systems, Networks and Applications (CPSNA'15), Hong Kong, China.