Line Outage Distribution Factors Research Articles

Sensitivity Analysis and Distribution Factor Calculation under Power Network Branch Power Flow Exceedance

As the scale of power systems continue to expand and their structure becomes increasingly complex, it is likely that branch power flow exceedance may occur during the operation of power systems, posing threats to the safe and stable operation of entire systems. This paper addresses the issue of branch flow exceedance in power networks. To enhance the operational efficiency and optimize the adjustment effects, this paper proposes a method for eliminating branch power flow exceedance by improving the particle swarm optimization (PSO) algorithm through the introduction of sensitivity and distribution factors. Firstly, it introduces the basic theory and calculation methods of sensitivity analysis, focusing on deriving the calculation principles of power flow sensitivity and voltage sensitivity, used to predict the responses of power flow at each branch in the power network to power or voltage changes. Subsequently, the paper provides a detailed derivation of the calculation principles for the line outage distribution factor (LODF), which effectively assesses the changes in branch power flow in the power network under specific conditions. Finally, a method for eliminating branch power flow exceedance based on a combination of sensitivity analysis and PSO algorithm is proposed. Through case analysis, it is demonstrated how to use the sensitivity and distribution factor to predict and control the power flow exceedance issues in power systems, verifying the efficiency and practicality of the proposed method for eliminating branch power flow exceedance. The study shows that this method can rapidly and accurately predict and address branch power flow exceedance in power system, thereby enhancing the operational safety of the power system.

Fast Simultaneous Feasibility Test for Security Constrained Unit Commitment

We present a novel fast security analysis method to perform a simultaneous feasibility test (SFT) for security constrained unit commitment (SCUC). Given an SCUC solution, SFT computes base and contingent line flows, overloads, and sensitivities for formulating the violated constraints in the SCUC solver. We use the Sherman-Morrison-Woodbury (SMW) formula to handle topology changes across hours and contingencies. We first developed this SMW-based SFT for contingencies relative to a static network as a generalization of line outage distribution factors (LODFs) achieving the speed of LODFs and modeling complex contingencies as in commercial SFTs. Speedup of the SMW method over commercial methods comes from moving computation from the solve phase to a startup phase. We now extend the SMW technique to network changes across hours and contingencies, permitting deployment on a single compute node due to speedup of the startup phase. The fast SMW-based SFT can be used in a callback, improving over the traditional SCUC-SFT iteration due to a stronger guarantee of satisfying security constraints and to overall speedup since the SCUC solver is invoked only once. The memory required by the SMW-based SFT is large but manageable, and we formulate a technique to decrease this by 80% when implemented.

Polynomial Line Outage Distribution Factors for Estimating Expected Congestion and Security

Polynomial Line Outage Distribution Factors for Estimating Expected Congestion and Security

Development of Static Model for a Current Based UPFC

The power system loads are dispersed across the network and generators are concentrated in a few key locations. In between generation and loads, there exist transmission systems. FACTS devices have applications to regulate voltage magnitude and angle, and impedance of the system. In FACTS devices, UPFC is one of its kind. Generally, line outages are occurred due to the faults on the transmission lines. One of the sensitive measures to understand the line outages is Line Outage Distribution Factor (LODF). In this paper, a suitable location is identified for UPFC to place where the line outage distribution factor is quite high in the system through line outage distribution factor.

Key Transmission Section Search Based on Graph Theory and PMU Data for Vulnerable Line Identification in Power System

Failure of vulnerable lines in the power system often results in tidal shifts, and triggering chain failures and their corresponding transmission sections are concentrated manifestations of the weak links in the power system. It is very important to identify the vulnerable lines and search the transmission section to prevent the chain faults as well as to analyze the stability of the power system. Aiming at the problems of inaccurate search of vulnerable lines, difficulties adapting to the complex and changing power system as well as wrong selection and omission of transmission section search in the existing references, this paper proposes an algorithm for searching vulnerable lines and their key transmission sections based on the graph theory and PMU (phasor measurement unit) data. First, the method combines with the graph theory and PMU data to construct the grid topology map. Second, the comprehensive indicators for screening vulnerable lines are proposed by fully considering the network topology and line capacity, which combines with power exchange efficiency and energy fluctuation probability. Third, the distance matrix in the Floyd algorithm is transformed into a unit group that can store more elements, which reduces the traversal times of the algorithm and improves computational efficiency. The fast localization of transmission cross sections associated with vulnerable lines is realized. Finally, the critical transmission cross sections are screened according to the line outage distribution factor and line safety margin. The IEEE 39-bus system is selected for simulation experiments, and the simulation results show that the key transmission section search method proposed in this paper can better adapt to the variable power grid and is faster and more accurate than the other common method.

Critical Nodes Identification for Power Grid Based on Electrical Topology and Power Flow Distribution

The continuous development of the power industry has driven the increasing scale and complexity of power grids. There are critical nodes within these grids, the failure of which can easily lead to serious power system accidents. In order to effectively identify the critical nodes in a power grid, a critical nodes identification algorithm considering electrical topology and power flow distribution (ETPD-CNIA) is proposed. First, a node interaction model based on the line outage distribution factors is presented. Then, the model is introduced into the PageRank algorithm to calculate the node importance based on the electrical network topology. Finally, considering the node importance based on both the electrical network topology and the actual power flow distribution by an adaptive coefficient, the critical nodes are identified effectively. Simulations on the IEEE 39-bus system and the IEEE 118-bus system show that, compared with existing algorithms, the proposed ETPD-CNIA is more effective and accurate in identifying critical nodes in the power grid.

Determination of key transmission section and strong correlation section based on matrix aggregation algorithm

With the increasing complexity of high-proportion new energy connected to power systems, the volatility and uncertainty of the power system increase, resulting in the changing operation status of the system. The original general sections may become key transmission sections. According to the power flow characteristics of power systems, this paper proposes an improved matrix aggregation algorithm to determine the initial transmission sections. On this basis, this paper defines an improved comprehensive index based on line outage distribution factor and line load rate. According to the principle of emphasis on detection in the actual power system operation, weight coefficients are considered for the two parameters to determine the key transmission sections. Finally, the correlation between multiple transmission sections is analyzed by quantifying the impact of the trip off line on the power flow transfer of other lines, and the strong correlation section is obtained. Case studies of the IEEE 39 bus system show the validity and effectiveness of the proposed method in this paper.

Optimal Configuration of Battery Energy Storage for AC/DC Hybrid System Based on Improved Power Flow Exceeding Risk Index

After the fault disturbance (DC bi-polar blocking) in the AC/DC hybrid system, when the battery energy storage system (BESS) near the fault location is used to eliminate the power transfer, some sensitive and vulnerable transmission lines still have the problem of power flow exceeding the limit value. Therefore, an optimal configuration of BESS for AC/DC hybrid systems based on power flow exceeding risk index is proposed, which is used to eliminate the impact of power transfer on transmission lines. Firstly, considering the line outage distribution factor, the power flow exceeding risk index is established, which is used to judge the sensitive and vulnerable transmission lines on the shortest path power flow after the fault in the AC/DC hybrid system. The shortest path power flow is found by using the Dijkstra algorithm; the transmission lines nodes of the shortest path power flow are selected as candidate nodes for BESS configuration. Secondly, considering the safe and stable operation capability of the transmission lines, a multi-objective optimal mathematical model of BESS configuration for the AC/DC hybrid system is established, which minimizes the annual investment cost of BESS and maximizes the sum of the power flow exceeding risk index. Finally, the CEPRI36V7 power grid model in Power System Analysis Software Package (PSASP) is used for simulation analysis to verify the effectiveness of the proposed method.

Line outage distribution factors of a linearized AC model with reactive power and voltage magnitude for resilience-constrained economic dispatch

Research on preventive generation dispatch schemes for resilient power system operation is often based on the DC power flow model, ignoring the influence of reactive power and voltage magnitude. This paper presents an in-depth study of a linearized AC power flow (LAC) model with reactive power and voltage magnitude to derive sensitivity factors, including shift factors and line outage distribution factors, for pre-contingency and post-contingency power flow calculations for N-k contingencies. Based on the derived sensitivity factors, a resilience-constrained economic dispatch (LAC-RCED) strategy is developed, which considers the security constraints of N-1 contingency for all lines and N-2 contingency for the affected lines, as well as optimization objectives to improve the power flow distribution in the transmission system. To deal with the computational difficulties associated with the N-k contingency constraints, an iterative contingency filtering algorithm based on the derived line outage distribution factor is proposed for contingency screening and creating security constraints for violated contingency scenarios. In the case study, the accuracy of the power flow solution obtained from the derived sensitivity factors is investigated by comparison with the AC model. The proposed LAC-RCED model and the iterative contingency filtering algorithm are tested on the IEEE 30-bus and 118-bus systems. • Derive the LODFs of N-k contingencies for a linearized AC power flow model. • Develop a resilience-constrained economic dispatch strategy by the derived LODFs. • Propose an iterative contingency filtering process to handle the security constraint.

Faster identification of redundant security constraints in SCUC

One of the main reasons why it has long been difficult to solve the security-constrained unit commitment (SCUC) problem is that there are a large number of security constraints in SCUC such as transmission constraints in the base case and N-1 criterion constraints, and adding all of them to the model will make the solution of the problem very challenging. Related research shows that most of these security constraints are redundant for solving SCUC, so identifying and eliminating most of the redundant security constraints in the model will greatly improve the speed of solving SCUC. In this paper, a fast and efficient algorithm is proposed for identifying redundant security constraints in SCUC. The proposed algorithm introduces parameters in the basic transmission constraints to additionally limit the transmission capacity. In the N-1 constraints based on Line Outage Distribution Factor (LODF), more redundant constraints are identified and removed in the model by comparing the upper limit of transmission line capacity with the maximum transmission power flow that may occur in the line when the system is running. More importantly, the proposed algorithm does not need to solve additional auxiliary optimization problems or iteratively solve multiple models, and only needs to identify a large number of redundant security constraints through a quick calculation and logical judgment in the early stage of model establishment. It has been tested on the IEEE 30-bus system and the IEEE 118-bus system. The numerical experimental results show that the algorithm can identify 98.52% and 99.3% of redundant security constraints, and the computational speed is 1.63 times and 17.85 times of the full model, respectively. Compared with other methods in the literature, it has more advantages in computational efficiency.

Battery energy storage train routing and security constrained unit commitment under solar uncertainty

The location of solar parks far from load areas may lead to transmission congestion and thus solar curtailment for secure system operation. Battery energy storage (BES) Train as mobile storage can transmit solar energy from site to load centers using a transport network while relieving lines from congestion. Therefore, stochastic security-constrained unit commitment (SCUC) with BES Train is modeled in this paper under solar uncertainty and N-1 critical line contingency. Time-space network models transportation constraints of BES Train routing problem. To reduce the computational burden, this paper proposes modeling of line outage distribution factor (LODF) for DC power flow that reduces the nonzero coefficients of post-contingency network constraints. The benders decomposition technique simplifies stochastic optimization for the mixed-integer linear programming (MILP) problem. BES Train integrated modified IEEE reliability test and 118-bus system is investigated as a case study. Simulations evaluate the effect of BES Train, solar uncertainty and critical line contingency state with LODF on operation costs, BES Train scheduling, solar curtailment, congestion and computational time. The proposed model shows that BES Train is an economical option for large solar integration to reduce transmission congestion and curtail solar power effectively.

Large-Scale Preventive Security-Constrained Unit Commitment Considering N-k Line Outages and Transmission Losses

This paper presents a new formulation for the preventive security-constrained unit commitment problem modeling <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> line outages and transmission losses. The pre- and post-contingency transmission constraints, representing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> line outages, are explicitly included by using generalized generation distribution factors. To account for security, a contingency selection procedure based on line outage distribution factors finds a list of worst-case contingencies. Transmission losses are incorporated using piecewise linear expressions. The proposed model is formulated as an instance of mixed-integer linear programming. The effectiveness of the proposed approach is illustrated with the IEEE 57-bus system and the 1,354-bus portion of the European transmission system. As empirically evidenced, the explicit consideration of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N-k</i> line outages and transmission losses leads to different decisions in the generation scheduling and dispatch, ensuring secure power system operation.

Generalized Contingency Analysis Based on Graph Theory and Line Outage Distribution Factor

Identifying the multiple critical components in power systems whose absence together has severe impact on system performance is a crucial problem for power systems known as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(N-x)$</tex-math></inline-formula> contingency analysis. However, the inherent combinatorial feature of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N-x$</tex-math></inline-formula> contingency analysis problem incurs by the increase of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(N-x)$</tex-math></inline-formula> term, making the problem intractable for even relatively small test systems. We present a new framework for identifying the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N-x$</tex-math></inline-formula> contingencies that captures both topology and physics of the network. Graph theory provides many ways to measure power grid graphs, i.e., buses as nodes and lines as edges, allowing researchers to characterize system structure and optimize algorithms. This article proposes a scalable approach based on the group betweenness centrality concept that measures the impact of multiple components in the electric power grid as well as line outage distribution factors that find the lines whose loss has the highest impact on the power flow in the network. The proposed approach is a quick and efficient solution for identifying the most critical lines in power networks. The proposed approach is validated using various test cases, and results show that the proposed approach is able to quickly identify multiple contingencies that result in violations.

Security Constrained Unit Commitment Based on Modified Line Outage Distribution Factors

The N-1 criterion is universally taken as the security constrains in the security-constrained unit commitment (SCUC) problem. The line outage distribution factors (LODF) is widely used in the N-1 continency for its state independence and computational efficiency. However, the LODF based model fails to consider reactive power and voltage magnitude. This paper closes this gap by deriving modified line outage distribution factors (MLODF) based on a linear power flow model. The proposed model, though state-independent, provides high-quality approximation of voltage magnitudes. Then, we apply this model to formulate the SCUC problem and propose an iterative solution process based on MLODF post-contingency filter to set up the contingency constraints. The simulation results of the benchmark test systems verify the accuracy of proposed MLODF. The six-bus and IEEE 118-bus systems show that the MLODF based model can provide a more accurate and secure generation schedule comparing with the traditional LODF based model while ensuring the AC feasibility for most N-1 continency.

Cascading Failure Mitigation Via Transmission Switching

After decades of research, cascading blackouts remain one of the unresolved challenges in the bulk power system operations. A new perspective for measuring the susceptibility of the system to cascading failures is clearly needed. The newly developed concept of system stress metrics may be able to provide new insights into this problem. The method measures stress as susceptibility to cascading failures by analyzing the network structure and electrical properties. This paper investigates the effectiveness of transmission switching in reducing the risk of cascading failures, measured in system stress metrics. Based on line-outage distribution factors, an algorithm is developed to identify and test the switching candidates quickly. A case study analyzing different stress metrics on the IEEE 118-bus test system is presented. The results show that transmission switching identified by our proposed algorithm could be used in preventive as well as corrective mechanisms to reduce the system's susceptibility to cascading failures. Contrary to the conventional operation wisdom that switching lines out of service jeopardizes reliability, our results suggest the opposite; system operators can often use transmission switching, when the system is under stress, as a tool to reduce the risk of cascading failures.

Decentralized approach for security enhancement of wind‐integrated energy systems coordinated with energy storages

Wind speed fluctuations in wind-integrated energy systems render the need for the fast and proper response of the conventional thermal generating units. This is while ramping constraints of these units as the backbone of the traditional power generation cycle depreciate their response, which poses a serious security challenge. This article is aimed at enhancing the security of multiarea wind-integrated energy systems by the coordinated deployment of energy storage systems (ESSs). To realize a practical model, a probabilistic reformulation of decentralized security-constrained optimal power flow by taking into account the thermal units' ramping constraints is developed, which tackles the uncertainties of wind speed fluctuations through a proper provision of ramping requirements by ESSs. Moreover, the optimality condition decomposition algorithm is used to solve security-constrained optimal power flow at each area of the energy system in a decentralized manner. Furthermore, to reduce the computational burden, a contingency filtering approach is employed that filters the uncritical conditions during the solution process. Different scenarios of transmission line and generator outages are explored by linear outage factors, including the line outage distribution factor and the power transfer distribution factor. In the established model, the value of loss of load and the value of wind curtailment factors are employed to reflect the economic impact of load shedding and wind energy curtailment. For supplying the lost power in generation outages, the participation factor of the connected sources is modified, which considers the remained generation capacity of sources. To assess the efficiency of the proposed model, the New England 39-bus testbed is put under extensive investigation. The results are discussed in depth.

Augmented Power Dispatch for Resilient Operation through Controllable Series Compensation and N-1-1 Contingency Assessment

Research on enhancing power system resilience against extreme events is attracting significant attention and becoming a top global agenda. In this paper, a preventive augmented power dispatch model is proposed to provide a resilient operation. In the proposed model, a new N-1-1 security criterion is proposed to select disruptive N-1-1 contingency cases that might trigger cascading blackouts, and an iterative contingency assessment process based on the line outage distribution factor is proposed to deal with security constraints. In terms of optimization objectives, two objectives related to power flow on the transmission line are considered to reduce the possibility of overload outages. Controllable series compensation devices are also considered in the model to improve the power flow distribution. Case studies conducted on the modified IEEE 30-bus, 118-bus and Polish 2382-bus systems show that the power flow solution of the proposed power dispatch model can avoid some branches from undertaking excessively heavy loads, especially lines forecasted to be affected by extreme events. The results of blackout simulations through a hidden failure cascading outage simulation model show that the average power losses of the proposed model are reduced by around 40% in some cases as compared to the classical economic dispatch model.

Universal Statistics of Redistribution Factors and Large Scale Cascades in Power Grids

Cascades of failures are among the biggest threats to supply networks such as power grids: An initially failing element may trigger the failure of other elements, thereby eventually causing the entire network to collapse. Here, we analyse the statistics of Line Outage Distribution Factors (LODFs), which describe the rerouting of electric power flows after a line failure. In particular, we demonstrate that absolute LODFs are approximately log-normally distributed throughout network topologies. We then illustrate that this log-normal distribution of redistribution factors results in a heavy tailed distribution of outage sizes in a simplified, stochastic cascade model over a certain range of parameters. This cascade model extends previous stochastic cascade models by adding more realistic redistribution mechanisms as well as including more realistic initial trigger events. Our results demonstrate that the statistics of redistribution factors is a fundamental trait throughout different networks and presents a possible explanation for the vast occurrence of heavy tailed distributions in real-world reanalyses of power outage sizes.

Novel AC Distribution Factor for Efficient Outage Analysis

We propose novel line outage distribution factors under AC power flow (AC-LODF) for providing very efficient approximate post-outage power flow solution. The AC-LODF is derived by using holomorphic embedding (HE) approach, and the approximate post-outage power flow solution is obtained with Pade approximation (PA). Tests on IEEE 14-bus system, and Polish 2383-bus system verify that the proposed AC-LODF is effective on most outages, and can significantly speed up outage analysis.

A novel sensitivity analysis for optimal design of superconductive fault current limiter in microgrids

Several studies concluded that installing superconductive fault current limiters (SFCLs) at generators’ sides in microgrid systems (MGSs), at the secondary side of each transformer in the system, at each load or at the location with most fault occurrences improve both the reliability and the stability of the system. However, increasing the number of SFCLs in the system leads to an increase in the cost. This paper intents to find the optimal locations and size of SFCLs to improve the stability and the reliability of the studied MGS during a faulty condition by protecting transformers in the system from tripping. The number of SFCLs should be less than the number of transformers which leads to less cost of the initial installations. In order to achieve this goal, this paper presents a novel sensitivity analysis inside a multi-objective optimization method to find the best solution for the optimal location and size of the SFCLs. A line outage distribution factor sensitivity analysis method is utilized to investigate the effect of line outage on the entire system. Also, the effects of each location in the system have been taken into consideration in this study. The results in this paper prove the robustness of the proposed approach which enhances the stability and reliability of the power network while minimizing the required impedance and number of SFCLs.