Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.Comment: 20 page

DC fault protection strategy considering DC network partition

This paper investigates DC network partition and alternative DC fault protection strategy for Multi-terminal HVDC (MTDC) system. Fast acting DC Circuit Breakers (DCCBs) or fault blocking DC-DC converters can be configured at strategic locations to allow the entire MTDC system to be operated interconnected but partitioned into islanded DC network zones following faults. In case of any DC fault event, the DCCBs or DC-DC converters at the strategic cable connections that link the different DC network partitions are opened or blocked such that the faulty DC network zone is quickly isolated from the remaining of the MTDC system. Thus, the healthy DC network zone can remain operational or recover quickly to restore power transmission. Each DC zone can be protected using AC circuit breakers and DC switches for cost reduction. The validity of the proposed protection strategy is confirmed using MATLAB/SIMULINK simulation

Protection of large partitioned MTDC networks using DC-DC converters and circuit breakers

This paper proposes a DC fault protection strategy for large multi-terminal HVDC (MTDC) network where MMC based DC-DC converter is configured at strategic locations to allow the large MTDC network to be operated interconnected but partitioned into islanded DC network zones following faults. Each DC network zone is protected using either AC circuit breakers coordinated with DC switches or slow mechanical type DC circuit breakers to minimize the capital cost. In case of a DC fault event, DC-DC converters which have inherent DC fault isolation capability provide ‘firewall’ between the faulty and healthy zones such that the faulty DC network zone can be quickly isolated from the remaining of the MTDC network to allow the healthy DC network zones to remain operational. The validity of the proposed protection arrangement is confirmed using MATLAB/SIMULINK simulations

On superintegrable monopole systems

Superintegrable systems with monopole interactions in flat and curved spaces have attracted much attention. For example, models in spaces with a Taub-NUT metric are well-known to admit the Kepler-type symmetries and provide non-trivial generalizations of the usual Kepler problems. In this paper, we overview new families of superintegrable Kepler, MIC-harmonic oscillator and deformed Kepler systems interacting with Yang-Coulomb monopoles in the flat and curved Taub-NUT spaces. We present their higher-order, algebraically independent integrals of motion via the direct and constructive approaches which prove the superintegrability of the models. The integrals form symmetry polynomial algebras of the systems with structure constants involving Casimir operators of certain Lie algebras. Such algebraic approaches provide a deeper understanding to the degeneracies of the energy spectra and connection between wave functions and differential equations and geometry.Comment: 12 page

Automatic Inference of Cross-modal Connection Topologies for X-CNNs

This paper introduces a way to learn cross-modal convolutional neural network (X-CNN) architectures from a base convolutional network (CNN) and the training data to reduce the design cost and enable applying cross-modal networks in sparse data environments. Two approaches for building X-CNNs are presented. The base approach learns the topology in a data-driven manner, by using measurements performed on the base CNN and supplied data. The iterative approach performs further optimisation of the topology through a combined learning procedure, simultaneously learning the topology and training the network. The approaches were evaluated agains examples of hand-designed X-CNNs and their base variants, showing superior performance and, in some cases, gaining an additional 9% of accuracy. From further considerations, we conclude that the presented methodology takes less time than any manual approach would, whilst also significantly reducing the design complexity. The application of the methods is fully automated and implemented in Xsertion library.Comment: 10 pages, 3 figures, 2 tables, to appear in ISNN 201

Protection and post-fault recovery of large HVDC networks using partitioning and fast acting DC breakers at strategic locations

DC fault protection arrangements for a large multi-terminal HVDC network are proposed where fast-acting DC circuit breakers are only used at strategic locations with the large DC network to be operated interconnected but partitioned into islanded DC zones in case of any DC fault events in one of the DC zones. Each DC network zone can be protected using low cost, slow protection devices such as AC circuit breakers coordinated with DC switches or slow mechanical type DC circuit breakers. This ensures the maximum ‘loss-of-infeed’ for any AC networks connected to the large HVDC system is kept within acceptable limits with reduced investment in protection cost as expensive fast acting DC circuit breakers are kept to a minimum. A post-fault recovery method of the faulty section is proposed including the reconnection with the healthy part of the network to ensure reliable and smooth restoration of the large multi-terminal HVDC network. A detailed pre-fault and post-fault power flow analysis is also conducted in a multi-terminal DC network with DC voltage droop control. The proposed protection arrangements and post-fault recovery method are validated by simulation of a two-zone, six-terminal DC network with respective radial and meshed configurations