Direct Current Power Flow Model Research Articles

To Prevent or Promote Grid Expansion? Analyzing the Future Role of Power Transmission in the European Energy System

Future energy supply systems must become more flexible than they are today to accommodate the significant contributions expected from intermittent renewable power sources. Although numerous studies on planning flexibility options have emerged over the last few years, the uncertainties related to model-based studies have left the literature lacking a proper understanding of the investment strategy needed to ensure robust power grid expansion. To address this issue, we focus herein on two important aspects of these uncertainties: the first is the relevance of various social preferences for the use of certain technologies, and the second is how the available approaches affect the flexibility options for power transmission in energy system models. To address these uncertainties, we analyze a host of scenarios. We use an energy system optimization model to plan the transition of Europe’s energy system. In addition to interacting with the heating and transport sectors, the model integrates power flows in three different ways: as a transport model, as a direct current power flow model, and as a linearized alternating current power flow model based on profiles of power transfer distribution factors. The results show that deploying transmission systems contribute significantly to system adequacy. If investments in new power transmission infrastructure are restricted—for example, because of social opposition—additional power generation and storage technologies are an alternative option to reach the necessary level of adequacy at 2% greater system costs. The share of power transmission in total system costs remains widely stable around 1.5%, even if cost assumptions or the approaches for modeling power flows are varied. Thus, the results indicate the importance of promoting investments in infrastructure projects that support pan-European power transmission. However, a wide range of possibilities exists to put this strategy into practice.

Robustness analysis of power system dynamic process and repair strategy

The growing importance of power systems in the development of modern society has increasingly drawn attention to the various dangers to which these systems are exposed. This paper proposes a dynamic response process analysis framework of power systems with the aim of exploring the response of the system when it encounters a fault and the repair process after the disaster. The analysis framework establishes three models to analyze power system structure and functional robustness: a purely topological model, an artificial flow model, and a direct current power flow model. We present different analysis metrics under different models, simulate three fault scenarios, and conduct an evaluation and analysis. According to the analysis results and considering the robust analysis conclusion and the concept of graph theory, we have formulated four repair strategies and made a simulated comparison of the repair processes. Taking IEEE39 and IEEE300 as examples, the effectiveness of the analysis framework is verified, the repair effect is verified, and the optimal repair strategy is determined.

Power network robustness analysis based on electrical engineering and complex network theory

The growing importance of power systems in the development of modern society has increasingly focused the attention on the various dangers to which these systems are exposed. This paper proposes a robust analysis framework based on complex network theory with the aim of exploring the robustness of the power system from a methodological perspective. The analysis framework establishes three models: a purely topological model, an artificial flow model, and a direct current power flow model to analyze the power system structure and functional robustness. We present different analysis metrics under different models, simulate three fault scenarios, and conduct an evaluation and analysis. The validity of the evaluation analysis was further verified by adopting IEEE300 and two randomly generated 1000-node network models that meet the characteristics of small world and scale, respectively, for detailed robustness analysis. The results show that the proposed method can effectively analyze a power system from the perspectives of pure topology, artificial flow, and direct current power flow. The case analysis based on the IEEE300 network and systems with different network characteristics proves that the framework is effective for the evaluation of power systems with different characteristics.

A study of cascading failures in real and synthetic power grid topologies

AbstractUsing the direct current power flow model, we study cascading failures and their spatial and temporal properties in the U.S. Western Interconnection (USWI) power grid. We show that yield (the fraction of demand satisfied after the cascade) has a bimodal distribution typical of a first-order transition. The single line failure leads either to an insignificant power loss or to a cascade which causes a major blackout with yield less than 0.8. The former occurs with high probability if line tolerance α (the ratio of the maximal load a line can carry to its initial load) is greater than 2, while a major blackout occurs with high probability in a broad range of 1 < α < 2. We also show that major blackouts begin with a latent period (with duration proportional to α) during which few lines overload and yield remains high. The existence of the latent period suggests that intervention during early stages of a cascade can significantly reduce the risk of a major blackout. Finally, we introduce the preferential Degree And Distance Attachment model to generate random networks with similar degree, resistance, and flow distributions to the USWI. Moreover, we show that the Degree And Distance Attachment model behaves similarly to the USWI against failures.

Adequacy and security analysis of interdependent electric and gas networks

In this article, adequacy and security assessments on the coupled operations of the electric and gas networks are performed. Extreme operating conditions and fault of components are considered as events that can impact the interdependent systems. The electric and gas networks are represented by an event-based direct current power flow model and by a transient one-dimensional mass flow model, respectively. Furthermore, the automations and safety strategies enforced by transmission system operators are represented within an original modelling approach. A quantitative analysis is performed with reference to the simplified energy infrastructures of Great Britain. Results highlight the contingencies which can jeopardize security and identify the components that are prone to fail and induce large gas pressure instabilities and loss of supply, and the locations in the gas grid that are susceptible to pressure violation. Moreover, a simulated 30% increase of the peak gas demand in 2015 is a limit for safe operations of the gas network, but the coupled systems are robust enough to avoid the spread of a cascading failure across networks. These results allow preventing critical operating conditions induced by the interaction between networks and can guide safety-based decisions on system reinforcements and the development of mitigating actions.

A Mathematical Framework to Optimize Critical Infrastructure Resilience against Intentional Attacks

AbstractThis article establishes a tri‐level decision‐making model supporting critical infrastructure (CI) resilience optimization against intentional attacks. A novel decomposition algorithm is proposed to exactly identify the best pre‐event defense strategy (protecting vulnerable components and building new lines), the worst‐case attack scenario, and the optimal postevent repair sequence of damaged components. As different types of CIs have different flow models, this article mainly considers the direct current power flow model and the maximal flow model for illustrative purposes. The proposed framework is illustrated by a simple but representative case system with nine nodes, and main results include: (1) the marginal value of extra defense investment under low defense budget is more considerable for mitigating system resilience loss, especially under large intentional attacks; (2) no defense strategy is always the best under different attack budgets; (3) increasing amount of repair resources can dramatically enhance CI resilience, but makes the pre‐event defense strategy less effective; (4) the use of maximal flow model can provide a lower bound estimation of the resilience loss from the power flow model; (5) the optimum defense strategy and the worst‐case attack identified by minimizing CI resilience loss largely differ from those by minimizing CI vulnerability, where the latter does not consider the recovery actions. Finally, the algorithm complexity is analyzed by comparing with the enumeration method and by testing two larger electric power systems.

Nonlinear Medium-Term Hydro-Thermal Scheduling With Transmission Constraints

In this paper, a nonlinear model for medium-term hydro-thermal scheduling problems with transmission constraints is presented. A nonlinear formulation of hydro power production functions of discharge and storage is used for proper representation of head variation in cascaded reservoirs. Transmission networks are formulated as a direct-current power flow model with support to load attainment over multiple levels representing peak and off-peak hours, enabling varying degrees of both network topology and load balance nodes representation over time stages. Sparse matrix structures that arise from the mathematical formulation allow fast decoupled computation of search directions in a primal-dual interior-point framework. Computational tests with very large case studies are presented. Analysis of numerical algorithm convergence is provided along with insightful optimal solution interpretative commentary.

Comparisons of complex network based models and direct current power flow model to analyze power grid vulnerability under intentional attacks

Many scholars have applied complex network based models to investigate power grid vulnerability, but how effective are these models to capture the real performance is an interesting topic. This paper selects two typical complex network based models, including a purely topological model (PTM) and a betweenness based model (BBM), as well as a direct current power flow model (DCPFM), to simulate the topology-based and flow-based vulnerability of power grid under degree, betweenness, maximum traffic and importance based intentional attacks. The relationships of vulnerability results from different models are analyzed and discussed for model comparisons. Taking IEEE 300 power grid with line capacity set proportional to tolerant parameter tp as example, the results show that there exists a critical node attack intensity AI=0.147, above which the three models produce almost identical topology-based vulnerability results under each attack strategy at any tp⩾1, while producing identical flow-based vulnerability results from PTM and DCPFM occurs at AI>0.147, and AI>0.73 for BBM and DCPFM, which indicates that the PTM can better approach the DCPFM for flow-based vulnerability analysis under intentional attacks. Similar results are also found for intentional edge attacks and other power grids.

Comparisons of purely topological model, betweenness based model and direct current power flow model to analyze power grid vulnerability

This paper selects three frequently used power grid models, including a purely topological model (PTM), a betweennness based model (BBM), and a direct current power flow model (DCPFM), to describe three different dynamical processes on a power grid under both single and multiple component failures. Each of the dynamical processes is then characterized by both a topology-based and a flow-based vulnerability metrics to compare the three models with each other from the vulnerability perspective. Taking as an example, the IEEE 300 power grid with line capacity set proportional to a tolerance parameter tp, the results show non-linear phenomenon: under single node failures, there exists a critical value of tp = 1.36, above which the three models all produce identical topology-based vulnerability results and more than 85% nodes have identical flow-based vulnerability from any two models; under multiple node failures that each node fails with an identical failure probability fp, there exists a critical fp = 0.56, above which the three models produce almost identical topology-based vulnerability results at any tp ≥ 1, but producing identical flow-based vulnerability results only occurs at fp = . In addition, the topology-based vulnerability results can provide a good approximation for the flow-based vulnerability under large fp, and the priority of PTM and BBM to better approach the DCPFM for vulnerability analysis mainly depends on the value of fp. Similar results are also found for other failure types, other system operation parameters, and other power grids.