Large Number Of Contingencies Research Articles

Interpretable data‐driven contingency classification for real‐time corrective security‐constrained economic dispatch

AbstractHigh penetrations of renewable energy are crucial for low‐carbon power systems. However, the higher volatility of renewable power generation pushes real‐time operations closer to equipment limits. It is thus important to utilize flexibilities in the system through corrective security‐constrained economic dispatch (SCED) that allows generators to take corrective adjustments after contingencies. The corrective SCED problem, containing a large number of contingencies, and corresponding post‐contingency decisions and constraints, is very large in scale and difficult to solve using purely model‐based methods within the strict time limits of real‐time markets. To accelerate the solution process, this paper develops a novel interpretable data‐driven contingency classification method. Historical data and their potentially useful patterns are utilized in interpretable data‐driven decision tree classifiers. To directly consider continuous features, such as net load values, and to consider imbalanced datasets without much additional complexity, Improved Strong Optimal Classification Trees (ISOCTs) are developed with new branching threshold constraints and category weights in the objective function. ISOCTs are then embedded into a hybrid model‐based and data‐driven framework to guarantee the accuracy of the real‐time active contingency set and the resulting security of dispatch decisions. Numerical testing results demonstrate the classification accuracy, computational efficiency, and interpretability of the proposed approach.

Bus-bar splitting for enhancing voltage stability under contingencies

As one of the network topology optimization ways, bus-bar splitting has been applied for various purposes. In this paper, the performance of bus-bar splitting on a look-ahead (i.e., short-term, say 30 min) power system (i.e., pre-splitting base case) with contingencies is evaluated. The proposed problem aims to find an ‘optimal’ bus-bar splitting scheme that can maximize the load margin of a look-ahead base case and ensure the load margin of each contingency case with a desirable level. Due to the complexity and nonlinear nature of the proposed problem, it is very difficult to be solved with the available solvers, and a large number of contingencies (including N−1 and N−k contingencies) and bus-bar splitting schemes need to be examined. A four-stage methodology is presented for online computing efficiency. Moreover, the group properties of contingencies are explored and illustrated in this paper, which is utilized to reduce the number of nonlinear constraints from a large number of contingencies and relieve the computational burden. The other advantage of the proposed methodology is that it can derive multiple effective solutions from which the operators can choose one. The effectiveness of the proposed methodology is demonstrated on the IEEE 118-bus and 1648-bus power systems with promising results.

Multilabel learning for the online transient stability assessment of electric power systems

Dynamic security assessment of a large power system operating over a wide range of conditions requires an intensive computation for evaluating the system's transient stability against a large number of contingencies. In this study, we investigate the application of multilabel learning for improving training and prediction time, along with the prediction accuracy, of neural networks for online transient stability assessment of power systems. We introduce a new multilabel learning method, which uses a contingency clustering step to learn similar contingencies together in the same multilabel multilayer perceptron. Experimental results on two different power systems demonstrate improved accuracy, as well as significant reduction in both training and testing time.

Expected security constrained reactive power planning

The adequate reactive power resources are expected to maintain system integrity under both normal and post contingency operations. Nowadays, the power systems are leading to high-risk operating points, hence, the number of probable contingencies, which should be considered in security constrained reactive power planning (SCRPP), has widely increased. However, considering a large number of contingencies in SCRPP is not practically possible. This study presents an index named expected violation index to consider numerous contingencies in SCRPP. At first, a multi-objective algorithm for the proposed expected SCRPP approach is presented. This novel algorithm uses the probability of each contingency to invest on them more efficiently. Next, it presents a method for selecting candidate buses to install reactive power resources. Then, the effectiveness of the proposed method is analysed using a multi-objective particle swarm optimisation algorithm on IEEE 30-bus test system. Finally, a reliability-based quantitative method is presented for selecting among final Pareto optimal solution. Using the proposed method, the system designers are capable to consider a large number of contingencies in their SCRPPs, to invest more purposefully in reactive power equipment, and to select their most appropriate option among different feasible choices in the optimal Pareto solution.

Flexible sequential designs for multi-arm clinical trials.

Adaptive designs that are based on group-sequential approaches have the benefit of being efficient as stopping boundaries can be found that lead to good operating characteristics with test decisions based solely on sufficient statistics. The drawback of these so called 'pre-planned adaptive' designs is that unexpected design changes are not possible without impacting the error rates. 'Flexible adaptive designs' on the other hand can cope with a large number of contingencies at the cost of reduced efficiency. In this work, we focus on two different approaches for multi-arm multi-stage trials, which are based on group-sequential ideas, and discuss how these 'pre-planned adaptive designs' can be modified to allow for flexibility. We then show how the added flexibility can be used for treatment selection and sample size reassessment and evaluate the impact on the error rates in a simulation study. The results show that an impressive overall procedure can be found by combining a well chosen pre-planned design with an application of the conditional error principle to allow flexible treatment selection.

A Generic Approach for Solving Nonlinear-Discrete Security-Constrained Optimal Power Flow Problems in Large-Scale Systems

This paper proves the practicality of an iterative algorithm for solving realistic large-scale security-constrained optimal power flow (SCOPF) problems. This algorithm is based on the combination of a contingency filtering scheme, used to identify the binding contingencies at the optimum, and a network compression method, used to reduce the complexity of the post-contingency models included in the SCOPF formulation. We show that by combining these two complementary ideas, it is possible to solve in a reasonable time SCOPF problems on large power system models with a large number of contingencies. Unlike most results reported for large-scale SCOPF problems, our algorithm uses a nonlinear AC network model in both pre-contingency and post-contingency states, optimizes both active/reactive powers flows jointly, and treats the discrete variables. The proposed algorithm is implemented with state-of-the-art solvers and applied to two systems: a national grid with 2563 buses and 1297 contingencies, and a model of the European transmission network with 9241 buses and 12000 contingencies.

Some Efficient Optimization Methods for Solving the Security-Constrained Optimal Power Flow Problem

The security-constrained optimal power flow problem considers both the normal state and contingency constraints, and it is formulated as a large-scale nonconvex optimization problem. We propose a global optimization algorithm based on Lagrangian duality to solve the nonconvex problem to optimality. As usual, the global approach is often time-consuming, thus, for practical uses when dealing with a large number of contingencies, we investigate two decomposition algorithms based on Benders cut and the alternating direction method of multipliers. These decomposition schemes often generate solutions with a smaller objective function values than those generated by the conventional approach and very close to the globally optimal points.

Treatment selection in multi-arm, multi-stage clinical trials

Adaptive designs that are based on group-sequential approaches have the benefit of being efficient as stopping boundaries can be found that lead to good operating characteristics with test decisions based solely on sufficient statistics. The drawback of these so called “pre-planned adaptive” designs is that unexpected design changes are not possible without impacting the error rates. “Flexible adaptive designs”, and in particular designs based on p-value combination, on the other hand can cope with a large number of contingencies at the cost of reduced efficiency. In this presentation we focus on so called multi-arm multi-stage trials which compare several active treatments against control at a series of interim analysis. We will discuss how these “pre-planned adaptive designs” can be modified to allow for flexibility. We then show how the added flexibility can be used for treatment selection and evaluate the impact on power in a simulation study. The results show that a combination of a well chosen pre-planned design and an application of the conditional error principle to allow flexible treatment selection results in an impressive overall procedure.

Uncertainty consideration in power system well-being assessment using fuzzy set approach

With increased energy demand, less new transmission, and open access, the power system is experiencing a much greater level of power transfer. These new requirements push the system to its limits for maximum economic benefit, while maintaining sufficient security margins that require network analysis. A practical interconnected system can collapse due to a number of different limits being exceeded such as thermal and operating reserve. Usually probabilistic methods are used in the conventional reliability assessment. The large amount of uncertainty is implicit in the estimate of system reliability because of insufficient failure data and variation in environmental conditions. In practice, limits are imposed by the operators on power system parameters, like line flows and bus voltages are crisps when dealing the deterministic technique, but in real, these limits are no longer of a crisp nature and are considered as soft constraints. The reliability parameters such as failure and repair rates used in the probabilistic models basically come from historical operation records, and leads to considerable data uncertainty. In this paper an approach to assess the health of the bulk power system by incorporating the fuzzy sets is suggested. To deal with the issue of large number of contingencies, a fuzzy logic based ranking of outages is also illustrated. This paper provides an approach to extend the conventional probabilistic reliability analysis by including fuzzy set for the assessment of wellbeing of a composite power system in the adequacy domain.

Fast computation of post-contingency system margins for voltage stability assessments of large-scale power systems

A technique to compute the post-contingency system margins for voltage stability assessment is presented. The voltage collapse point of the system base case is first computed using a traditional PV curve method. When a contingency is applied to this fully stressed base case, loads must be shed in order to maintain voltage stability. The key idea of the proposed method is to determine the right amount of load shedding that leaves the post-contingency system at its nose point. The system margin is equal to the base case margin minus the load shedding amount. The amount of load to shed is computed by a modified power flow method, where the amount of loading shedding is parameterised by an additional unknown variable. The technique has been tested on a large-scale power system with 1725 buses. The results show that the proposed approach is very efficient for voltage stability assessment when a large number of contingencies are involved.

A parallel asynchronous decomposition for on-line contingency planning

Traditional formulations of security-constrained-optimal-power-flows represent contingencies by hard constraints. The disadvantages are four-fold. First, the conflicts among contingencies must be arbitrated apriori, before their effects are known. Second, the feasible region shrinks with an increase in the number of contingencies. Third, computational time increases with the number of contingencies. Fourth, hard constraints provide poor models of fuzzy quantities such as equipment ratings and operating guidelines. This paper develops a modeling framework without these disadvantages. Specifically, it allows for soft constraints and always has feasible solutions. The effects of conflicts among contingencies are displayed so system operators can arbitrate them in an informed manner. Moreover, each contingency can be handled asynchronously and in parallel. In other words, the computational time, for handling an arbitrarily large number of contingencies, remains the same as for performing an optimal power flow without any contingencies (provided that a computer is dedicated to each contingency).

Two applications of parallel processing in power system computation

This paper discusses performance improvements achieved in two power system software modules through the use of parallel processing techniques. The first software module, EVARISTE outputs a voltage stability indicator for various power system situations. This module was designed for extended real-time use and is therefore required to give guaranteed response times. The second module, MEXICO, assesses power system reliability and operating costs by simulating a large number of contingencies for generation and transmission equipment. This module, used for power system planning purposes, uses a Monte-Carlo method to build the various power system states, and makes heavy demands on CPU time for running simulations. Like many power system computation packages, both software modules are well-suited to coarse-grain parallel processing. The first module was parallelized on a machine capable of integrating up to thirty-two processors. The distributed-memory machine and the second on a shared-memory machine. In this paper, the authors start by a description of the n process used in these two cases, then go on to give details on the performance levels achieved, discussing aspects of programming, parameter selection (number of situations processed, number of processors), and machine characteristics (limitations due to interprocessor communications network, for instance).

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.