Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization

We give an overview of a complex systems approach to large blackouts of electric power transmission systems caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics and dynamics of series of blackouts with approximate global models. Blackout data from several countries suggest that the frequency of large blackouts is governed by a power law. The power law makes the risk of large blackouts consequential and is consistent with the power system being a complex system designed and operated near a critical point. Power system overall loading or stress relative to operating limits is a key factor affecting the risk of cascading failure. Power system blackout models and abstract models of cascading failure show critical points with power law behavior as load is increased. To explain why the power system is operated near these critical points and inspired by concepts from self-organized criticality, we suggest that power system operating margins evolve slowly to near a critical point and confirm this idea using a power system model. The slow evolution of the power system is driven by a steady increase in electric loading, economic pressures to maximize the use of the grid, and the engineering responses to blackouts that upgrade the system. Mitigation of blackout risk should account for dynamical effects in complex self-organized critical systems. For example, some methods of suppressing small blackouts could ultimately increase the risk of large blackouts.     

Analysis of cascading failure in electric grid based on power flow entropy

Large-scale blackouts are an intrinsic drawback of electric power transmission grids. Here we propose a concept of power flow entropy to quantify the overall heterogeneity of load distribution and then investigate the relationship between the power flow entropy and cascading failure. Simulation results, from the small-world 300-node test system and the IEEE 300-bus system, show that the power flow entropy has close relations with the cascading failure in terms of both the dynamic propagation course and the static blackout size. Particularly, at the early stage of failure spreading the potential large blackout can be identified according to the power flow entropy. The power flow entropy can serve as an index not only for long-term planning, but also for short-term operational defense to large-scale blackouts.     

Complex dynamics of blackouts in power transmission systems

In order to study the complex global dynamics of a series of blackouts in power transmission systems a dynamical model of such a system has been developed. This model includes a simple representation of the dynamical evolution by incorporating the growth of power demand, the engineering response to system failures, and the upgrade of generator capacity. Two types of blackouts have been identified, each having different dynamical properties. One type of blackout involves the loss of load due to transmission lines reaching their load limits but no line outages. The second type of blackout is associated with multiple line outages. The dominance of one type of blackout over the other depends on operational conditions and the proximity of the system to one of its two critical points. The model displays characteristics such as a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America.     

An LCOR model for suppressing cascading failure in weighted complex networks

Based on the relationship between capacity and load, cascading failure on weighted complex networks is investigated, and a load-capacity optimal relationship (LCOR) model is proposed in this paper. Compared with three other kinds of load-capacity linear or non-linear relationship models in model networks as well as a number of real-world weighted networks including the railway network, the airports network and the metro network, the LCOR model is shown to have the best robustness against cascading failure with less cost. Furthermore, theoretical analysis and computational method of its cost threshold are provided to validate the effectiveness of the LCOR model. The results show that the LCOR model is effective for designing real-world networks with high robustness and less cost against cascading failure.     

Magnetic and electric phase transitions in the Hubbard model

Within the Hubbard model, two boson Green’s functions that describe the propagation of collective excitations of the electronic system—magnons (states with a single electron spin flip) and doublons (states with two electrons at one site of the crystal lattice)—are calculated for a Coulomb interaction of arbitrary strength and for an arbitrary electron concentration by applying a decoupling procedure to the double-time X-operator Green’s functions. It is found that the magnon and doublon Green’s functions are similar in structure and there is a close analogy between them. Instability of the paramagnetic phase with respect to spin ordering is investigated using the magnon Green’s function, and instability of the metallic phase to charge ordering is analyzed with the help of the doublon Green’s function. Criteria for the paramagnet-ferromagnet and metal-insulator phase transitions are found.     

An exactly soluble model with tricritical points for structural-phase transitions

We present and study a lattice-dynamical model whose static and dynamic properties can be described exactly for all dimensionsd≧3 (d an integer) and which, in addition, exhibits tricritical points. For certain model parameters, the tricritical behaviour is found to be identical to that of the spherical model. By changing the model parameters continuously however, the transition suddenly becomes of first order at a tricritical point (TCP). The order parameter and the susceptibility are given explicitly ford≧3. The tricritical exponents are Gaussian. The critical dynamics is also discussed.     

Analysis of cascading failure in complex power networks under the load local preferential redistribution rule

In recent years several global blackouts have drawn a lot of attention to security problems in electric power transmission systems. Here we analyze the cascading failure in complex power networks based on the local preferential redistribution rule of the broken node’s load, where the weight of a node is correlated with its link degree k$k$ as k^β$k^{\beta }$. It is found that there exists a threshold α^∗${\alpha }^{\ast }$ such that cascading failure is induced and enhanced when the value of tolerance parameter is smaller than the threshold. It is also found that the larger β$\beta$ is the more robust the power network is.     

Charge-changing transitions in an extended Lipkin-type model

Charge-changing transitions are considered in an extended Lipkin-Meshkov-Glick (LMG) model taking into account explicitly the proton and neutron degrees of freedom. The proton and neutron Hamiltonians are taken to be of the LMG form and, in addition, a residual proton-neutron interaction is included. Model charge-changing operators and their action on eigenfunctions of the model Hamiltonian are defined. Transition amplitudes of these operators are calculated using exact eigenfunctions and then the RPA approximation. The best agreement between the two kinds of calculation is obtained when the correlated RPA ground state, instead of the uncorrelated HF ground state, is employed and when the proton-neutron residual interaction, besides the proton-proton and neutron-neutron residual interactions, is taken into account in the model Hamiltonian. Received: 4 May 1998     

Critical temperature for shape transitions in excited nuclei

The behavior of shell effects with temperature is studied within the framework of the finite-temperature Hartree-Fock-Bogoliubov theory with the Gogny force. Thermal shape fluctuations in the quadrupole degree of freedom are taken into account in the frame of the Landau theory. Numerical results for the superfluid-to-normal and deformed-to-spherical phase transitions are presented for the nucleus ¹⁶⁴Er. We find that the critical temperature for the deformed-spherical shape transition is much lowered when the thermal shape fluctuations are considered.Received: 31 October 2002, Published online: 17 February 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 21.10.Ky Electromagnetic moments - 21.10.Ma Level density     

Interband transitions in a spherical quantum layer in the presence of an electric field: Spherical rotator model

The interband transitions in a spherical GaAs quantum layer in the presence of an arbitrarily directed electric field are studied theoretically within the framework of the rigid spherical rotator model. The problem is solved under the assumption that the external field is a perturbation. Within the framework of the dipole approximation an expression for the interband absorption coefficient is obtained, and the absorption threshold frequency is determined. The corresponding selection rules are derived. A comparison with the case of quantum transitions in a spherical quantum layer in the presence of a radial electric field is performed.     

Low-Lying electric dipole transitions in tin isotopic chain within the RPA model

A nuclear structuremodel based on a finite rank approximation of Skyrme interaction is applied to calculate the distribution of dipole strength in tin isotopes. The model is based on the quasiparticle random phase approximation. The results obtained with the three types of parametrizations of the Skyrme forces (SLy4, SkM*, and SIII) are compared. The low-lying part of dipole strength distribution reveals the existence of a group of slightly collective states, and the corresponding E1 transition strength increases with the enlargement of neutron excess. The group is associated with the pygmy resonance. The text was submitted by the authors in English.     

Probabilities of radiative dipole transitions of parahelium in an electric field

Quadratic Stark corrections to the wave functions, matrix elements, and probabilities of transitions between the singlet states ¹ S ₀ and ¹ P ₁ of helium atoms are calculated. The coefficients of the polynomials that depend on the effective principal quantum number of the upper level v _f and that approximate the numerical values of the polarizabilities, the quadratic corrections to the wave functions, and the probabilities of transitions to highly excited Rydberg states with large v _f are determined. The results of calculations testify that the probabilities of all σ transitions n _i ¹ S ₀ → n _f ¹ P ₁ and π transitions to the states with n _f > n _i /2 are decreased with increasing electric field strength, except for the transition 2¹ S ₀ → 2¹ P ₁, whose probability increases both for σ and for π transitions.     

CSNS/RCS脉冲电源均匀传输线障碍点分析

通过研究均匀传输线特征阻抗失配原理,发现传输电缆特征阻抗失配会导致负载终端励磁电流幅值发生畸变。对电源主电路关键参数进行分析,发现均匀传输线匹配阻抗失配会造成磁铁处励磁电流幅值变小,上升时间变短。建立均匀传输线障碍点等效模型,推导出脉冲电源传输线障碍点处反射系数,对串联电阻和并联电阻障碍点深入分析,发现传输线特征阻抗失配,会导致匹配负载处有功功率减小。最后通过高压电缆被击穿故障使其得以验证。     

Simultaneous backward data transmission and power harvesting in an ultrasonic transcutaneous energy transfer link employing acoustically dependent electric impedance modulation

The advancement and miniaturization of body implanted medical devices pose several challenges to Ultrasonic Transcutaneous Energy Transfer (UTET), such as the need to reduce the size of the piezoelectric resonator, and the need to maximize the UTET link power-transfer efficiency. Accordingly, the same piezoelectric resonator that is used for energy harvesting at the body implant, may also be used for ultrasonic backward data transfer, for instance, through impedance modulation.     

Superradiant transitions between high-lying levels of Sr in an external electric field

Superradiant transitions were observed between high lying levels in Sr. The transitions react very sensitively to an external electric field. Superradiant cascades or one transition in a superradiant branching can be suppressed. The square root of the high of a superradiant pulse decreases with the second power of the electric field strength. This behaviour can be explained by calculations.Dedicated to Prof. Dr. Herbert Welling on the occasion of his 60th birthday     

Critical disorder and phase transitions in random diode arrays

Random diode arrays represent a new class of nonlinear disordered systems related to the physics of thin-film semiconductor structures and some others. When a disorder strength grows through a certain critical value, they undergo a phase transition from almost uniform to strongly nonuniform random electric potential. A piecewise continuous topography of random potential is predicted.     

调制偏振光及空间正交方位信息传递系统物理模型

受到调制的偏振光可作为方位信息的载体在空间传递,从而实现方位角度信息的传递和精密测量,这是偏振光的一个新的应用领域,在航空航天、地质测量、生物医药、军事等领域具有广泛的应用前景.文章首先介绍了调制偏振光的物理意义和空间正交方位信息传递系统的应用领域,然后介绍了利用调制偏振光进行空间正交方位信息传递系统的物理模型,并分析了一个具体实现方案.