Non-monotonic increase of robustness with capacity tolerance in power grids

The robustness of different scale power grids is analyzed based on complex network theory in terms of electrical betweenness and weighted efficiency. The robustness of a power grid does not always increase monotonically with the capacity. This property is different from the results obtained in previous studies, which have indicated that the robustness increases monotonically with capacity. To understand the non-monotonic phenomenon, the cascading failure is divided into several sub-stages, and we analyze the number of overloaded nodes and the average remaining load in each sub-stage. The results indicate that the increasing capacity is barely able to reduce the number of overloaded nodes at the beginning of malfunction, which may lead to more nodes being removed subsequently, including certain nodes with many connections or large load. More loads remain in the power grid such that certain nodes cannot take the load. This eventually causes overloading of more nodes and a decline in the robustness of the power grid. The conclusion may be useful for power grid planners seeking to design grids with cost-effective capacity.     

利用节点效率评估复杂网络功能鲁棒性

为了克服现有复杂网络鲁棒性研究模型只考虑节点失效的局部影响性和网络拓扑鲁棒性的缺陷, 提出了一种利用节点效率来评估复杂网络功能鲁棒性的方法. 该方法综合考虑节点失效的全局影响性, 利用网络中节点的效率来定义各节点的负载、极限负载和失效模型, 通过打击后网络中最终失效节点的比例来衡量网络的功能鲁棒性, 并给出了其评估优化算法. 实验分析表明该方法对考虑节点负载的复杂网络功能鲁棒性的评定可行有效, 对于大型复杂网络可以获得理想的计算能力.     

An electrical betweenness approach for vulnerability assessment of power grids considering the capacity of generators and load

Most existing research on the vulnerability of power grids based on complex networks ignores the electrical characteristics and the capacity of generators and load. In this paper, the electrical betweenness is defined by considering the maximal demand of load and the capacity of generators in power grids. The loss of load, which reflects the ability of power grids to provide sufficient power to customers, is introduced to measure the vulnerability together with the size of the largest cluster. The simulation results of the IEEE-118 bus system and the Central China Power Grid show that the cumulative distributions of node electrical betweenness follow a power-law and that the nodes with high electrical betweenness play critical roles in both topological structure and power transmission of power grids. The results prove that the model proposed in this paper is effective for analyzing the vulnerability of power grids.     

Power oscillation suppression by robust SMES in power system with large wind power penetration

The large penetration of wind farm into interconnected power systems may cause the severe problem of tie-line power oscillations. To suppress power oscillations, the superconducting magnetic energy storage (SMES) which is able to control active and reactive powers simultaneously, can be applied. On the other hand, several generating and loading conditions, variation of system parameters, etc., cause uncertainties in the system. The SMES controller designed without considering system uncertainties may fail to suppress power oscillations. To enhance the robustness of SMES controller against system uncertainties, this paper proposes a robust control design of SMES by taking system uncertainties into account. The inverse additive perturbation is applied to represent the unstructured system uncertainties and included in power system modeling. The configuration of active and reactive power controllers is the first-order lead–lag compensator with single input feedback. To tune the controller parameters, the optimization problem is formulated based on the enhancement of robust stability margin. The particle swarm optimization is used to solve the problem and achieve the controller parameters. Simulation studies in the six-area interconnected power system with wind farms confirm the robustness of the proposed SMES under various operating conditions.     

Optimal intentional islanding to enhance the robustness of power grid networks

Intentional islanding of a power system can be an emergency response for isolating failures that might propagate and lead to major disturbances. Some of the islanding techniques suggested previously do not consider the power flow model; others are designed to minimize load shedding only within the islands. Often these techniques are computationally expensive. We aim to find approaches to partition power grids into islands to minimize the load shedding not only in the region where the failures start, but also in the topological complement of the region. We propose a new constraint programming formulation for optimal islanding in power grid networks. This technique works efficiently for small networks but becomes expensive as size increases. To address the scalability problem, we propose two grid partitioning methods based on modularity, properly modified to take into account the power flow model. They are modifications of the Fast Greedy algorithm and the Bloom algorithm, and are polynomial in running time. We tested these methods on the available IEEE test systems. The Bloom type method is faster than the Fast Greedy type, and can potentially provide results in networks with thousands of nodes. Our methods provide solutions which retain at least 40–50% of the system load. Overall, our methods efficiently balance load shedding and scalability.     

基于复杂网络的电网结构健壮性及Braess悖论现象研究

应用复杂网络理论,建立电力系统的改进导纳模型,结合电网拓扑特性和电气特性对电网的级联故障进行研究.通过随机移除传输线引发电网级联故障,研究网络的节点数、平均度、发电站数量以及发电站的分布状况对系统健壮性的影响,并对小世界电网级联故障过程中的布雷斯(Braess)悖论现象进行分析.研究表明:网络的健壮性与其拓扑结构密切相...     

Dynamical robustness analysis of weighted complex networks

Robustness of weighted complex networks is analyzed from nonlinear dynamical point of view and with focus on different roles of high-degree and low-degree nodes. We find that the phenomenon for the low-degree nodes being the key nodes in the heterogeneous networks only appears in weakly weighted networks and for weak coupling. For all other parameters, the heterogeneous networks are always highly vulnerable to the failure of high-degree nodes; this point is the same as in the structural robustness analysis. We also find that with random inactivation, heterogeneous networks are always more robust than the corresponding homogeneous networks with the same average degree except for one special parameter. Thus our findings give an integrated picture for the dynamical robustness analysis on complex networks.     

Matching of an extended high-current Z-discharge to a pulsed power system

Conditions for matching an extended high-current Z-discharge to a pulsed power system are numerically investigated. The power system consists of a pulsed voltage generator and a long transmission line. Experiments are aimed at generating a highly ionized dense plasma as an active medium for an extreme ultraviolet laser on hydrogen-like ions of nitrogen (λ = 13.4 nm). Emphasis is on the distribution of the energy transmitted from a storage ring to a load among its components and on the reduction of the energy that remains in the electrical circuit by the end of the pump pulse and will inevitably dissipate in the discharge tube. The solution of this problem will make it possible to diminish the load on the walls of the discharge chamber and extend its service life. It is shown that energy deposition into the load is effective when the timeaveraged sum of the ohmic and dynamic components of the discharge resistance is roughly equal to the wave impedance of the transmission line. In this case, the wave reflected from the load carries away a minimal energy, which allows for optimization of the energy deposited into the load. The input and output energy balances for different matching conditions are calculated with an eye to designing an efficient short-wavelength extreme ultraviolet laser with a long service life of the discharge tube.     

Controlling chaos in power system based on finite-time stability theory

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.     

静止无功补偿器和发射器在电弧炉动态无功补偿系统中的应用

发展高效绿色电炉冶炼技术是淘汰落后产能、钢铁产业调整升级的重要举措。电弧炉作为核心生产设备,防止其生产运行中无功冲击造成的电压跌落至关重要。而目前单一的有源、无源补偿方式无法同时满足电弧炉负荷日益增长的大容量且快速响应的无功补偿需求。研究了静止无功补偿器(SVC)和静止无功发射器(SVG)相结合的混联补偿方式,分析了SVC在分相不平衡大容量补偿及SVG在无功快速响应方面中的特性,并针对某钢厂电弧炉工作运行情况,计算其无功需求,充分利用其原有的SVC装置,设计混联SVG方案来抵消剩余无功缺口,使用PSCAD/EMTDC进行了联合应用仿真,证实其理论有效性。     

Hierarchical distributed stabilization of power networks

Large fluctuation of electric power due to high penetration of renewable energy sources such as photovoltaic and wind power generation increases the risk to make the whole power network system unstable. The conventional frequency control called load frequency control is based on PID (proportional-integral-derivative) control or more advanced centralized and decentralized/distributed control. If we could more effectively use information on the state of the other neighbor generators, we can expect to make the whole system more robust against the large frequency fluctuation. This paper proposes a fundamental framework towards the design of hierarchical distributed stabilizing controllers for a network of power generators and loads. This novel type of distributed controller, composed of a global controller and a set of local controllers, takes into account the effect of the interaction among the generators and loads to improve robustness for the variation of locally stabilizing controllers.     

Extremal harmonic active control of power for a monocylinder hybrid powertrain

This article presents a real-life application for the extremal harmonic active control of power [1] applied on a hybrid engine setup. The active control was adapted for a hybrid powertrain constituted of a one-cylinder diesel engine coupled with a permanent magnet synchronous machine. The problem was formulated in the harmonic domain and the control objective was to extremalize energetic criterions. Three criterions were considered: minimizing the speed ripple of the engine, maximizing the mechanical reactive power (mechanical impedance adaptation) and maximizing the active electric power for energy harvesting. The results show that, for the first and second orders of the ripple, speed oscillations can be completely cancelled and reactive power and active power can be optimized on-line. The implicit extremal controller converged rapidly, remaining stable even when the mean engine speed changed abruptly. These results confirm the robustness and the applicability of the extremal harmonic active control for industrial applications.     

Long-range response to transmission line disturbances in DC electricity grids

We consider a DC electricity grid composed of transmission lines connecting power generators and consumers at its nodes. The DC grid is described by nonlinear equations derived from Kirchhoff's law. For an initial distribution of consumed and generated power, and given transmission line conductances, we determine the geographical distribution of voltages at the nodes. Adjusting the generated power for the Joule heating losses, we then calculate the electrical power flow through the transmission lines. Next, we study the response of the grid to an additional transmission line between two sites of the grid and calculate the resulting change in the power flow distribution. This change is found to decay slowly in space, with a power of the distance from the additional line. We find the geographical distribution of the power transmission, when a link is added. With a finite probability the maximal load in the grid becomes larger when a transmission line is added, a phenomenon that is known as Braess’ paradox. We find that this phenomenon is more pronounced in a DC grid described by the nonlinear equations derived from Kirchhoff's law than in a linearised flow model studied previously in Ref. [1]. We observe furthermore that the increase in the load of the transmission lines due to an added line is of the same order of magnitude as Joule heating. Interestingly, for a fixed system size the load of the lines increases with the degree of disorder in the geographical distribution of consumers and producers.     

Development and comparison of spectral methods for passive acoustic anomaly detection in nuclear power plants

We have developed spectral signal processing methods for passive acoustic anomaly detection in nuclear power plants. Furthermore, we compared the developed and existing methods by applying them to stationary sounds recorded in a controlled environment. Our new methods show significant improvement, in particular concerning robustness against false alarms. The results also demonstrate that clear detection of a given sound at a given signal-to-noise ratio is highly dependent on the distribution of characteristic frequency content in the spectrum in relation to the background noise and the spectral uncertainty. Since the frequency monitoring principle used here is quite rigid, we stress the need for research on more flexible methods, also taking into account differences between experiments and real reactor systems.     

Compact pulsed power generator using an inductive energy storagesystem with two-staged opening switches

The pulsed power generator, named ASO-I, is extremely compact and light in comparison with a conventional pulsed power generator, which consists of a Marx bank and a water pulse forming line. The ASO-I has a two-staged opening switch, consisting of fuses in water and a plasma erosion opening switch, and can be operated hundreds of times a day at an output power of 230 kV and 35 kA. The parallel fuses are effective for power multiplication, and small differences in length of the parallel fuses do not influence the output power. The risetime of current through the short-circuit load decreases with the increase of the gap length of the spark gap, which is placed between the fuses and the load. The plasma erosion opening switch can be operated as a second opening switch, and the risetime of the current through the short-circuit load decreases from 250 to 10 ns. The maximum resistance of the plasma erosion opening switch is 3.5 Ω with an open-circuit load     

Self-organized criticality in a computer network model

We study the collective behavior of computer network nodes by using a cellular automaton model. The results show that when the load of network is constant, the throughputs and buffer contents of nodes are power-law distributed in both space and time. Also the feature of 1/f noise appears in the power spectrum of the change of the number of nodes that bear a fixed part of the system load. It can be seen as yet another example of self-organized criticality. Power-law decay in the distribution of buffer contents implies that heavy network congestion occurs with small probability. The temporal power-law distribution for throughput might be a reasonable explanation for the observed self-similarity in computer network traffic.     

Robust SMES controller design for stabilization of inter-area oscillation considering coil size and system uncertainties

It is well known that the superconducting magnetic energy storage (SMES) is able to quickly exchange active and reactive power with the power system. The SMES is expected to be the smart storage device for power system stabilization. Although the stabilizing effect of SMES is significant, the SMES is quite costly. Particularly, the superconducting magnetic coil size which is the essence of the SMES, must be carefully selected. On the other hand, various generation and load changes, unpredictable network structure, etc., cause system uncertainties. The power controller of SMES which is designed without considering such uncertainties, may not tolerate and loses stabilizing effect. To overcome these problems, this paper proposes the new design of robust SMES controller taking coil size and system uncertainties into account. The structure of the active and reactive power controllers is the 1st-order lead-lag compensator. No need for the exact mathematical representation, system uncertainties are modeled by the inverse input multiplicative perturbation. Without the difficulty of the trade-off of damping performance and robustness, the optimization problem of control parameters is formulated. The particle swarm optimization is used for solving the optimal parameters at each coil size automatically. Based on the normalized integral square error index and the consideration of coil current constraint, the robust SMES with the smallest coil size which still provides the satisfactory stabilizing effect, can be achieved. Simulation studies in the two-area four-machine interconnected power system show the superior robustness of the proposed robust SMES with the smallest coil size under various operating conditions over the non-robust SMES with large coil size.     

Effect of Eliminating Edges on Robustness of Scale-Free Networks under Intentional Attack

We study the robustness of complex networks under edge elimination. We propose three different edge elimination strategies and investigate their effects on the robustness of scale-free networks under intentional attack. We show that deleting a proper fraction of edges connecting hub nodes and hub nodes can enhance the robustness of scale-free networks under intentional attack.     

Social power and opinion formation in complex networks

In this paper we investigate the effects of social power on the evolution of opinions in model networks as well as in a number of real social networks. A continuous opinion formation model is considered and the analysis is performed through numerical simulation. Social power is given to a proportion of agents selected either randomly or based on their degrees. As artificial network structures, we consider scale-free networks constructed through preferential attachment and Watts–Strogatz networks. Numerical simulations show that scale-free networks with degree-based social power on the hub nodes have an optimal case where the largest number of the nodes reaches a consensus. However, given power to a random selection of nodes could not improve consensus properties. Introducing social power in Watts–Strogatz networks could not significantly change the consensus profile.     

Mitigation strategies on scale-free networks against cascading failures

According to the dynamic characteristics of the cascading propagation, we introduce a mitigation mechanism and propose four mitigation methods on four types of nodes. By the normalized average avalanche size and a new measure, we demonstrate the efficiencies of the mitigation strategies on enhancing the robustness of scale-free networks against cascading failures and give the order of the effectiveness of the mitigation strategies. Surprisingly, we find that only adopting once mitigation mechanism on a small part of the overload nodes can dramatically improve the robustness of scale-free networks. In addition, we also show by numerical simulations that the optimal mitigation method strongly depends on the total capacities of all nodes in a network and the distribution of the load in the cascading model. Therefore, according to the protection strength for scale-free networks, by the distribution of the load and the protection price of networks, we can reasonably select how many nodes and which mitigation method to efficiently protect scale-free networks at the lower price. These findings may be very useful for avoiding various cascading-failure-induced disasters in the real world and for leading to insights into the mitigation of cascading failures.