Computational analysis of cascading failures in power networks

Climate change is one of the most pressing issues of our time and mitigating it requires a reduction of CO2 emissions. A big step towards achieving this goal is increasing the share of renewable energy sources, as the energy sector currently contributes 35% to all greenhouse gas emissions. However, integrating these renewable energy sources challenges the current power system in two major ways. Firstly, renewable generation consists of more spatially distributed and smaller power plants than conventional generation by nuclear or coal plants, questioning the established hierarchical structures and demanding a new grid design. Restructuring becomes necessary because wind and solar plants have to be placed at favorable sites, e.g., close to coasts in the case of wind. Secondly, renewables do not provide a deterministic and controllable power output but introduce power fluctuations that have to be controlled adequately. Many solutions to these challenges are build on the concept of smart grids, which require an extensive information technology (IT) infrastructure communicating between consumers and generators to coordinate efficient actions. However, an intertwined power and IT system raises great privacy and security concerns. Is it possible to forgo a large IT infrastructure in future power grids and instead operate them purely based on local information? How would such a decentrally organized system work? What is the impact of fluctuation on short time scales on the dynamical stability? Which grid topologies are robust against random failures or targeted attacks? This thesis aims to establish a framework of such a self-organized dynamics of a power grid, analyzing its benefits and limitations with respect to fluctuations and discrete events. Instead of a centrally monitored and controlled smart grid, we propose the concept of Decentral Smart Grid Control, translating local power grid frequency information into actions to stabilize the grid. This is not limited to power generators but applies equally to consumers, naturally introducing a demand response. We analyze the dynamical stability properties of this framework using linear stability methods as well as applying numerical simulations to determine the size of the basin of attraction. To do so, we investigate general stability effects and sample network motifs to find that this self-organized grid dynamics is stable for large parameter regimes. However, when the actors of the power grid react to a frequency signal, this reaction has to be sufficiently fast since reaction delays are shown to destabilize the grid. We derive expressions for a maximum delay, which always desynchronizes the system based on a rebound effect, and for destabilizing delays based on resonance effects. These resonance instabilities are cured when the frequency signal is averaged over a few seconds (low-pass filter). Overall, we propose an alternative smart grid model without any IT infrastructure and analyze its stable operating space. Furthermore, we analyze the impact of fluctuations on the power grid. First, we determine the escape time of the grid, i.e., the time until the grid desynchronizes when subject to stochastic perturbations. We simulate these events and derive an analytical expression using Kramer's method, obtaining the scaling of the escape time as a function of the grid inertia, transmitted power, damping etc. Thereby, we identify weak links in networks, which have to be enhanced to guarantee a stable operation. Second, we collect power grid frequency measurements from different regions across the world and evaluate their statistical properties. Distributions are found to be heavy-tailed so that large disturbances are more common than predicted by Gaussian statistics. We model the grid dynamics using a stochastic differential equation to derive the scaling of the fluctuations based on power grid parameters, identifying effective damping as essential in reducing fluctuation risks. This damping may be provided by increased demand control as proposed by Decentral Smart Grid Control. Finally, we investigate discrete events, in particular the failure of a single transmission line, as a complementary form of disturbances. An initial failure of a transmission line leads to additional load on other lines, potentially overloading them and thereby causing secondary outages. Hence, a cascade of failures is induced that propagated through the network, resulting in a large-scale blackout. We investigate these cascades in a combined dynamical and event-driven framework, which includes transient dynamics, in contrast to the often used steady state analysis that only solves static flows in the grid while neglecting any dynamics. Concluding, we identify critical lines, prone to cause cascades when failing, and observe a nearly constant speed of the propagation of the cascade in an appropriate metric. Overall, we investigate the self-organized dynamics of power grids, demonstrating its benefits and limitations. We provide tools to improve current grid operation and outline a smart grid solution that is not reliant on IT. Thereby, we support establishing a 100% renewable energy system.

Power networks can be modeled as networked structures with nodes representing the bus bars (connected to generator, loads and transformers) and links representing the transmission lines. In this manuscript we study cascaded failures in power networks. As network structures we consider IEEE 118 bus network and a random spatial model network with similar properties to IEEE 118 bus network. A maximum flow based model is used to find the central edges. We study cascaded failures triggered by both random and targeted attacks to the edges. In the targeted attack the edge with the maximum centrality value is disconnected from the network. A number of metrics including the size of the largest connected component, the number of failed edges, the average maximum flow and the global efficiency are studied as a function of capacity parameter (edge critical load is proportional to its capacity parameter and nominal centrality value). For each case we identify the critical capacity parameter by which the network shows resilient behavior against failures. The experiments show that one should further protect the network for a targeted attack as compared to a random failure.

It is an extra heavy burden to maintain the distribution network model since of its frequent changing and large scale. In reality, the network model may involve significant parameter errors, which makes the model not applicable. This paper presents a robust data-driven approach to linearize the three-phase power flow. A three-phase linear power flow (LPF) model for active distribution networks (ADNs) is proposed. To address the issues of measurement outliers and data collinearity, the support vector regression (SVR) algorithm is applied to the linearization regression to obtain the proposed three-phase LPF model. The training process is offline and the obtained LPF model can be used to calculate the power flow online. Numerical tests demonstrate that the proposed approach can achieve satisfactory calculation accuracy with high computational efficiency, even under data collinearity and measurement outliers. Since the proposed LPF has very high accuracy, this model can be incorporated into distribution networks optimization problems.

Performance and reliability of electrical power grids under cascading failures

As the coupling and integration of multi-energy flow in the integrated energy system (IES) deepen increasingly, the cascading failure will develop across different energy systems more easily and widely through the energy hub (EH). And it brings great challenges to the security and reliability of IES. The defects of the present cascading failure model of IES have been summarized, and a novel search strategy of fault chains in IES combined heating and power network was proposed in this paper. First, the initial risk assessment index of each energy branch is proposed to form the initial fault sets. Then, combined heat and power control (CHPC) strategies are introduced to deal with the branch overload conditions during the cascading failure. What is more, in order to reduce the workload and overcome the limitation of present methods, we analyzed the relevance of the branches to be predicted by using the kernel fuzzy C-means (KFCM) clustering algorithm and select the branches with the highest value of relevance as the subsequent failure. Based on the predicted fault chain, vulnerability analysis is presented to locate critical component and find out the correlation between cascading outages. The comprehensive evaluation index is also established to effectively evaluate the impact severity of cascading failure. Finally, the case studies are carried out on the combined heating and power systems to demonstrate the effectiveness of the proposed method.

A realistic and practicable modeling of unbalanced distribution networks (DNs) is the missing link in most studies undertaken in these networks, e.g., optimal power flow (OPF), energy markets, etc. To address the issue, this letter proposes an unbalanced linear three-phase four-wire power flow (PF) model based on current injection equations at nodes. Also, the ZIP representation is considered for loads. The model can be easily generalized for unbalanced three-wire networks with minor changes and assumptions. Hence, the scope of the proposed method can be extended to cover both low-voltage and medium-voltage DNs. The performance of the proposed model is verified through simulations on two IEEE test feeders.

The massive power flow transferring triggers the node overload cascade, which further activates the protection system hidden failures. In this study, we propose a cascading failure model based on complex network theory by combining the node overload failures and hidden failures of transmission lines in blackouts together. The model concerns the electrical characteristics, which has not been involved in the existed cascading failure model when modelling node loads. The cascading failure simulations on the 500 kV Center China power grid and the IEEE‐300‐bus test system demonstrate that the proposed cascading failure model with node load built on electrical characteristics can bring better network invulnerability than the model with that constructed on pure structure topology. Meanwhile, the proposed model can better exhibit the negative aspects of hidden failures in the blackouts. The deliberate attacks based on high‐risk nodes can decrease the invulnerability of power grids more seriously compared with those based on high‐degree and high‐load nodes. The results provide a new way to analyse the power grid cascading failure mechanism based on the complex network theory.

When the power grid is disturbed to a certain degree, it may be extremely deteriorated. At this time, corresponding control measures need to be taken to eliminate or reduce the risks. For an unsafe normal state, the system can be restored to a safe state through preventive control. This paper proposes a risk-based power grid operational control strategy by using the optimal power flow method to solve the problem of power grid operational control based on risk parameters with the goal of minimizing the power grid operating risks. Under the condition of satisfying steady-state operational constraints, by adjusting the control measures that can be used in the system, such as active power generation, the safe operational state of the system with the least operational risk is realized. To avoid the poor effectiveness of alternating current power flow of large power grid, linearized power flow model is employed. Simulation results using an IEEE 118-node system and East China Power Grid system. The proposed operational control strategy can achieve the effect of eliminating or reducing operating risks, which provide effective decision-making for the dispatch operators to deal with risks.

Electric power has become an essential part of daily life: we plug our electronic devices in, switch our lights on, and expect to have power. As the availability of power is usually taken for granted in modern societies, we mostly feel annoyed at its absence and perceive the importance of power during outages which have severe effects on the public order. Blackouts have had disastrous consequences for many countries and they continue to occur frequently. Such examples demonstrate the necessity for careful analysis and planning of power grids, to ultimately increase the reliability of power grids. The power grids have evolved due to economic, environmental and human-caused factors. In addition to the contingency analysis, nowadays, the operation and planning of power grids are facing many other challenges (such as demand growth, targeted attacks, cascading failures, and renewable energy integration). Thus, many questions arise, including: which buses (nodes) to connect with a new line (link)? What are the impacts of malicious attacks on power grids? How may an initial failure result in a cascade of failures? How to prepare for the integration of renewable energy? Answering such questions requires developing new concepts and tools for analysing and planning of power grids. Power grids are one of the largest and the most complex man-made systems on earth. The complex nature of power grids and its underlying structure make it possible to analyse power grids relying on network science. The applications of network science on power grids have shown the promising potential to capture the interdependencies between components and to understand the collective emergent behaviour of complex power grids. This thesis is motivated by the increasing need of reliable power grids and the merits of network science on the investigation of power grids. In this context, relying on network science, we model and analyse the power grid and its near-future challenges in terms of line removals/additions, malicious attacks, cascading failures, and renewable integration.

A distributed random algorithm for controlling electrical power flow after a failure in (or attack on) a power transmission grid is proposed. The aim is to minimize load shedding and to avoid a cascaded failure in the network. The DC power flow model is used to simulate the power flow in the network. The algorithm is based only on the information about the closest neighbours of each node. A mathematically rigorous proof of convergence with probability 1 of the proposed algorithm is provided.

Summary form only given. The most severe failures in power grids are often characterized as cascading failures where an initial event triggers consequent failures all along the grid often leading to blackouts. Upon identifying a failure and its cascade potential, timely control actions should be performed by the grid operators to mitigate the effect of the cascade. These actions have to be delivered to one or more control devices, creating a dependency between the power grid and its control network. This paper examines the dependency of the operation of the power grid on the control network. Different from literature studies on failure control, our dependency model captures the impact of networking parameters. We formulate an algorithmic model that describes the impact of this dependency on cascade control. Based on this model, we propose an efficient cascade control algorithm using load shedding with consideration of delays in the communication network for power grids. Finally, we evaluate the impact of the power-communication network dependency with uncontrolled grids, ideal/simple control grids and our proposed control scheme. The results demonstrate that the proposed algorithm can significantly reduce the failure of power lines while sustaining larger power demand for users.

On 18 August 2005, one of the biggest power outages in world history occurred in Java-Bali power grids system in Indonesia which impacts on almost 100 billion people for about 3 hours. A failure in the 500 kV transmission line between Saguling-Cibinong has caused the transmission line to break down resulting in the power grid network to dissolve into two separate networks, which in the end led to cascading failure along the whole grid. Power grid topology plays an important role in determining system behavior when one or more connections failed and impacting the whole network. In the worst case, cascading failure might take place which disturbs the whole networks. The objectives of the paper are to understand how a cascading failure incident takes place in power grids and find the correlation between key parameters using complex network theory to improve power grids robustness. The paper concentrate on an edge-based attack model as it has a resemblance with the Java-Bali power outages incident in 2005. The result indicates characteristics of small-world network from Java-Bali power grid, with different tunable parameters and load ratios, have an impact on network cascading failure likelihood.

In this paper, we propose a measurement-based approach to the real-time economic dispatch (ED). The realtime ED is a widely used market scheduling problem seeking to economically balance electricity system supply and demand and provide locational marginal prices (LMPs) while respecting system reliability requirements. The ED is a convex optimization problem with a linear or quadratic objective, typically the minimization of generator costs or the maximization of social surplus. The constraints capture power balance and network flow capacity limits and are formulated using a linearized power flow model. Our approach utilizes power system sensitivities estimated from phasor measurement unit (PMU) measurements to reformulate the model-based power flow and network flow constraints. The resulting measurement-based real-time ED overcomes the vulnerabilities of the model-based real-time ED. The dispatch instructions and LMPs calculated with our measurement-based real-time ED accurately, and adaptively, reflect real-time system conditions. We illustrate the strengths of the proposed approach via several case studies.

In this paper, a novel analytical model is proposed to predict the average transmission-capacity loss and load loss during a cascading failure as a function of time and their steady state values. Cascading failures in the power grid are described using a Markov-chain approach, in which the state transition probabilities depend on the number and capacities of the failed lines. The transition matrix is characterized parametrically using Monte Carlo simulations of cascading failures in the power grid. The severity of cascading failure is estimated using two metrics: the expected number of transmission-line failures and the amount of load shedding/load loss (inferred from the average transmission capacity loss) in the steady state. These two metrics provide critical information regarding the severity of a cascading failure in a power grid (in terms of both the distribution of blackout sizes and the amounts of load shedding). One of the benefits of this model is that it enables the understanding of the effect of initial failures and of the operating parameters of the power grid on cascading failures.

Power grids are closely related to people's daily life, and cascading failure plays a vital role in their reliability, which has attracted intensive research interests in the past few years. Numerous researches concerning cascading failure in dynamic power grids, still, most of them focus on the prediction of cascading failure and recovery after failure while Time-of-Arrival (TOA) of cascading failure is rarely concerned. The TOA -based prediction of cascading failure often needs to consider the entire cascading process of the target network during the entire cascading failure process, which brings great loss in network reliability and computational overhead. In light of this, we propose a prediction model of cascading failure based on TOA to implement the prediction of cascading failure in dynamic power grids. We successfully perform our model on two artificial synthetic networks and one real-world network by comparing against four widely used prediction models. We further analyze the non-negligible superiority of our scheme overall benchmarks. As far as we know, we are the first to introduce the conception of TOA for cascading failure prediction in the dynamic power grids.