Branch Contingencies Research Articles

Power system data-driven dispatch using improved scenario generation considering time-series correlations

Reinforcement learning (RL) is recently studied for realizing fast and adaptive power system dispatch under the increasing penetration of renewable energy. RL has the limitation of relying on samples for agent training, and the application in power systems often faces the difficulty of insufficient scenario samples. So, scenario generation is of great importance for the application of RL. However, most of the existing scenario generation methods cannot handle time-series correlation, especially the correlation over long time scales, when generating the scenario. To address this issue, this paper proposes an RL-based dispatch method which can generate power system operational scenarios with time-series correlation for the agent’s training. First, a time-generative adversarial network (GAN)-based scenario generation model is constructed, which generates system operational scenarios with long- and short-time scale time-series correlations. Next, the “N-1” security is ensured by simulating “N-1” branch contingencies in the agent’s training. Finally, the model is trained in parallel in an actual power system environment, and its effectiveness is verified by comparisons against benchmark methods.

Formulating Connectedness in Security-Constrained Optimal Transmission Switching Problems

This paper focuses on the issue of network connectedness (NC) in security-constrained optimal transmission switching problems, which is complicated by branch contingencies and corrective line switching. Two criteria are firstly proposed with the principle of preserving NC as much as possible within reasonable limits. By extending the electrical flow based NC constraints, a proposition is derived to associate different cases of NC with the optimum of a linear program, yielding the mathematical formulation of the NC criteria. By Karush-Kuhn-Tucker conditions, this formulation is further transformed into a tractable version which can be incorporated with existing SCOTS models without affecting the applicability of original solution approaches. Finally, case studies on various networks and SCOTS models demonstrate the efficacy of the proposed approach.

Application of triangle count in branch contingency screening

In this paper, a triangle count-based branch contingency screening scheme is proposed for transmission power systems. Different triangle count algorithms are compared. A parallel triangle count algorithm is implemented in the graph database for speed-up. Then, a modified performance index is proposed. A structure-related constant called Line Outage Severity Factor (LOSF) is defined to avoid redundant computation when updating the screening results under different operating points. Numerical acceleration techniques are also leveraged to update the screening results when system topology changes. Experiments of N − 1 and N − 2 analysis on three testbed systems demonstrate that about 20% of contingency cases can be ruled out with relatively low risk in missing critical contingencies, which reduces the computational burdens for succeeding stages of the contingency analysis.

Valuing consumer participation in security enhancement of microgrids

This study proposes a time-based security (TBS) evaluation mechanism for radial microgrids (MGs) short-term operation. In the proposed framework, system security is modelled using time-based sensitivity analysis in the load points. Occurring branch contingencies in a radial MG creates some islands with oscillating frequencies. The settling time of frequency oscillation, as the successful islanding time, and the island's capability to continue the load supply are considered in TBS assessment. A system frequency response model and the stored energy of storages are used to calculate the two mentioned factors. Depending on the loads' sensitivities to the successful islanding time and the service continuity duration, they are exposed to extreme damage. In the case of branches' sudden outages, it may be impossible to operate the MG without any extreme damage of loads, due to the capacity shortage in the island, dynamic behaviours of the MG and inadequate stored energy of storages. Under these conditions, the load shedding unit participates considering the customer damage function. To evaluate the performance of the proposed security assessment mechanism, the 123-bus distribution test system is precisely analysed.

Graph-theoretic algorithms for cyber-physical vulnerability analysis of power grid with incomplete information

A key focus recently has been in assessing the risk of a coordinated cyber-physical attack and minimizing the impact of a successful attack. Most of the cyber-attackers will have limited system information and conventional power grid N − 1 security analysis cannot be extended to assess the risk. Centrality measures are widely used in the network science and an attacker with incomplete information can use it to identify power system vulnerabilities by defining the system as a complex network but without real-time system measurements. This paper presents a graph theory based centrality indices for vulnerability assessment of the power system due to various bus and branch contingencies using limited system information and provides a preliminary defense mechanism to prevent such an attack. Proposed work answers the fundamental question of possible attack scenarios by balancing risk (limited information with low risk to get caught or high risk attack to access more system information) and impact (identifying contingencies with maximal impact on system operation). Statistical comparisons are made between the graph theory measures compared to the corresponding DC power flow based N − X linear sensitivity measures. A unified N − X centrality based performance index is proposed and validated against the AC power flow based performance index by doing the real-time simulations of an N − 3 attack scenario. Defensive mechanisms using topology-based performance indices are also presented.

A new second-order method for branch contingency analysis and static voltage security

This work presents a method for static contingency analysis. The complex bus voltages after the outage of a transmission line (or a transformer) are estimated from one base case power flow solution and sensitivity relationships. As the steady-state power network equations are expressed in rectangular coordinates, the linearity of the Jacobian and the invariance of the Hessian allow the computation of sensitivity relationships with extra second-order information. This increases considerably the accuracy of the estimates of the power system variables and makes easier to handle the reactive power generation constraints, thus resulting in higher accuracy in the voltage estimation with limited additional computational effort. Numerical results with both test systems of different sizes and a real system illustrate the characteristics of the proposed methodology.

MIP-Based Stochastic Security-Constrained Daily Hydrothermal Generation Scheduling

This paper presents the application of a mixed-integer programming (MIP) approach for solving stochastic security-constrained daily hydrothermal generation scheduling (SCDHGS). Power system uncertainties including generating units and branch contingencies and load uncertainty are explicitly considered in the stochastic programming of SCDHGS. The roulette wheel mechanism and lattice Monte Carlo simulation (LMCS) are first employed for random scenario generation wherein the stochastic SCDHGS procedure is converted into its respective deterministic equivalents (scenarios). Then, the generating units are scheduled through MIP over the set of deterministic scenarios for the purpose of minimizing the cost of supplying energy and ancillary services over the optimization horizon (24 h) while satisfying all the operating and network security constraints. To a more realistic modeling of the DHGS problem, in the proposed MIP formulation, the nonlinear valve loading effect, cost, and emission function are modeled in linear form, and prohibited operating zones (POZs) of thermal units are considered. Furthermore, a dynamic ramp rate of thermal units is used, and for the hydro plants, the multiperformance curve with spillage and time delay between reservoirs is considered. To assess the efficiency and powerful performance of the aforementioned method, a typical case study based on the standard IEEE-118 bus system is investigated, and the results are compared to each other in different test systems.

Large-scale branch contingency analysis through master/slave parallel computing

Contingency analysis (CA) requires fast execution time for real-time power system operations. Because CA problems can naturally be divided into separate subtasks, parallel computing helps to speed up the computation time. This paper proposes a master/slave parallel computing architecture and studies the computation of CA in a large-scale power system through high performance computing, adopting a message passing interface for implementation. In particular, although the execution time of CA varies, there is a tradeoff between having an imbalanced workload and “paying” a synchronization penalty for parallel computing: either factor blocks the progress of scalability. The proposed layered dynamic scheduling method is effective to tackle the challenge of high synchronization cost and workload imbalance and have the potential to further scale for the N − 2 contingency analysis.

A “Random Chemistry” Algorithm for Identifying Collections of Multiple Contingencies That Initiate Cascading Failure

This paper describes a stochastic “Random Chemistry” (RC) algorithm to identify large collections of multiple (n-k) contingencies that initiate large cascading failures in a simulated power system. The method requires only O(log (n)) simulations per contingency identified, which is orders of magnitude faster than random search of this combinatorial space. We applied the method to a model of cascading failure in a power network with n=2896 branches and identify 148243 unique, minimal n-k branch contingencies (2 ≤ k ≤ 5) that cause large cascades, many of which would be missed by using pre-contingency flows, linearized line outage distribution factors, or performance indices as screening factors. Within each n-k collection, the frequency with which individual branches appear follows a power-law (or nearly so) distribution, indicating that a relatively small number of components contribute disproportionately to system vulnerability. The paper discusses various ways that RC generated collections of dangerous contingencies could be used in power systems planning and operations.

Dynamic voltage stability prediction of power systems by a new feature selection technique and probabilistic neural network

With continued increase in the electrical energy demand and tendency towards maximizing economic benefits in power transmission system, especially in the liberalized electricity markets, real-time voltage security analysis has become a growing concern in electric power utilities. However, static analysis methods, such as power flow based methods, have difficulty in evaluating voltage stability and some voltage stability feasible region boundaries may not be correctly analyzed by these methods due to the use of simple models for the system components. On the other hand, dynamic modeling and evaluation of voltage stability are complex, expensive, and time consuming. In this paper, a new feature selection technique combined with a probabilistic neural network (PNN) is proposed for this purpose. A major difference of our paper with the previous research works in the area is that this paper proposes voltage stability prediction, while the previous works usually focus on the voltage stability evaluation. The proposed dynamic voltage stability prediction method is examined on the IEEE 14-bus and New England 39-bus test systems and the effectiveness of the proposed method is demonstrated. Also, the effect of different load models, branch contingencies, and generator contingencies is evaluated. Another advantage of the proposed prediction method is that it can be used for varied topologies and configurations of the power system. Copyright © 2010 John Wiley & Sons, Ltd.

A new method for redundancy analysis of measurements applied to three-phase state estimation

In this paper, a new method based on the properties of the Gram matrix is proposed to verify the redundancy of measurements in three-phase state estimation. The Gram matrix is constructed using rows of the measurement Jacobian matrix as vectors. The method can be used for measurement systems planning or updating of three-phase networks so that the overall system remain observable even under possible branch contingencies and loss of measurements. It is a fast and robust numerical method based on the Gram matrix factorization that is easy to implement. A small numerical example that shows the application of the method is presented.

Application of a New Sensitivity Analysis Framework for Voltage Contingency Ranking

In this paper, a new sensitivity analysis framework for voltage contingency ranking has been presented. The proposed sensitivity analysis is a combination of linear sensitivities and eigenvalue analysis. The sensitivity analysis framework can determine the voltage stability status of the power system due to the occurrence of each contingency. Moreover, stability margin or instability depth of the post-contingency state is determined in the framework. In other words, a severity index is obtained for each voltage contingency and so the contingencies can be ranked. This rank shows bottlenecks of the power system in the priority order, a property that is a key issue for both planners and operators of the power system. The proposed method can also evaluate islanding contingencies as well as the nonislanding ones. Moreover, the method can consider the generator contingencies in addition to the branch contingencies in a unique framework. The proposed method has been tested on the New Zealand test system and Iran's power network. Obtained results, discussed comprehensively, confirm the validity of the developed approach.

Multiple Contingency Selection for Transmission Reliability and Transfer Capability Studies

This paper develops a multiple contingency selection procedure that can identify the single contingencies that cause thermal stress on the same branch or branches and, thereby, produce critical multiple contingences. This multiple contingency selection procedure is required if enumerative transmission reliability is to be successfully applied since all critical single and multiple contingences can be identified without excessive computation or false alarm or misclassification problems. The multiple contingency selection is accomplished by determining a list of contingencies for each branch that have: apparent power flows that exceed {alpha} {times} 100% of the thermal limit and apparent power flow changes that exceed {beta} {times} 100% of the thermal limit. A branch contingency measure is used to rank these single contingencies. Combination of the single contingencies taken from any branch's list of contingencies would produce multiple critical contingences with thermal overloads on that branch assuming superposition holds. The BOUNSM computer program that provides the information for the enumerative transmission reliability program also provides the information required to perform a transfer capability study. A monitored branch measure, which is the sum of the branch contingency measures for a particular branch, would identify the branches, paths, and interfaces that are most insecure for anmore » anticipated transfer and must be specified to run a transfer capability study. The combination of branch's list of contingencies for each of these branches, paths, and interfaces would be the list of contingencies that needs to be specified to perform a transfer capability study.« less

Critical Review of Branch Contingency Selection Methods

A number of different types of branch contingency selection methods has been devised over the last decade, while some have been available for over 30 years. Each method has its strengths and weaknesses and needs to be evaluated for a particular application. This paper critically reviews branch contingency selection methods. All techniques are first discussed in detail. This discussion is followed by an evaluation table containing uniform attributes by which the methods can be compared. A brief description of spafsity techniques and possible future developments closes the paper.

Power System Observability: On-Line Measurement Set Contingency Analysis

Based on the common property of the measurement to branch incidence matrix M and the node to branch incidence matrix A both being totally unimodular matrices, a direct, flexible and fast procedure for on-line measurement and/or network contingency analysis is presented. If the product matrix W = MAt is considered, where W is defined as the measurement to node incidence matrix, it is shown that its Gramian, i.e. G (i) = det (WtW) is nonzero for observable networks and equals zero for nonobservable networks. Therefore. to verify if a network is, or not, algebraically observable, implies evaluating the determinant of a symmetrical and sparse matrix of order (N-1) whose elements are integers. Real or simulated, single or multiple measurement and branch contingencies may be analysed by appropriately modifying the initial matrix W. The computer time is practically not affected by the type of the contingency considered, being strictly a function of N the number of network nodes.

Evaluation of a local DC load flow screening method for branch contingency selection of overloads

The author presents a novel screening method, involving a local DC solution, for branch flow limit violations (overloads) which, when incorporated with a performance index (PI) method, can greatly enhance the selection capabilities for online as well as study purposes. The local DC screening method and PI method are compared to results obtained from a full-system DC load flow assessment of two cases: a 24-bus system and a 584-bus representation of the Mid-Continent Area Power Pool system. The results indicate that, when these two methods are combined, excellent contingency selection capabilities are produced. The philosophy for this implementation and the details needed to implement the local DC screening method are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

AEP Automatic Contingency Selector Branch Outage Impacts on Load Bus Voltage Profile

This paper presents the details of a computationally efficient automatic voltage contingency selection algorithm developed for implementation at the AEP's new system control center in Columbus, Ohio. The methodology is based on the quantification of the real-time system-wide impacts of the transmission branch (line and transformer) outages on the load bus voltage profile via the fast computation of a quadratic system Performance Index (PI) for every branch, and subsequent sorting of the results according to the severity of effects. The algorithm enjoys superior computational complexity compared to the previously published work. An application of the algorithm to the AEP EHV real-time data base is presented as an illustration. The essence of the algorithm is to quickly rank branch contingency events in such a manner that sequential contingency testing could be carried out (with an on-line full AC load flow function, for example), starting with the most severe contingency (in terms of causing abnormal voltage profile) and terminating when the sequence of contingencies no longer poses problems.

Analytical and computational improvements in performance-index ranking algorithms for networks

Performance-index ranking algorithms, relatively recent innovations in network analysis, are distinguished by the fact that they can rank a large set of network parameter and injection change cases very rapidly. To date, their major application has been for automatic contingency selection in power systems. Here, various enhancements to the approach are given and it is shown how general ranking formulas, valid for multiple branch contingencies, can be derived easily. A ranking formula for generator contingencies, hitherto unavailable, is presented. A sparse matrix technique that permits the rapid exact evaluation of the ranking formulas is given. The speed of the performance-index ranking algorithm is estimated for several large network problems, and found to be orders of magnitude higher than that of its direct though more versatile alternative, explicit linearized contingency evaluation.

Fast Linear Contingency Analysis

This paper reports on a linear contingency analysis program that computes linearized real power flow changes resulting from branch outages and generation or load changes. A modern formulation has been adopted based on the relation ΔP = Δθ rather than using current injections and the bus admittance matrix. For maximum speed in processing such a large number of contingencies, the explicit inverse (triangular portion) of H is computed by the back substitution method. Multiple branch contingencies require essentially the same time as would the same number computed individually. Multiple generation or load changes are handled most efficiently by a single repeat solution for Δθ using the sparse factors of H and a sparse ΔP vector. Explicit branch distribution and generation shift factors are computed only for display to the operator.