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This study aims to introduce a methodology for optimal allocation of spinning reserves taking into account load, wind and solar generation by application of the univariate and bivariate parametric models, conventional intra and inter-zonal spinning reserve capacity as well as demand response through utilization of capacity outage probability tables and the equivalent assisting unit approach.

The method uses a novel approach to model wind power generation using the bivariate Farlie–Gumbel–Morgenstern probability density function (PDF). The study also uses the Bayesian network (BN) algorithm to perform the adjustment of spinning reserve allocation, based on the actual unit commitment of the previous hours.

The results show that the utilization of bivariate wind prediction model along with reserve allocation adjustment algorithm improve reliability of the power grid by 2.66% and reduce the total system operating costs by 1.12%.

The method uses a novel approach to model wind power generation using the bivariate Farlie–Gumbel–Morgenstern PDF. The study also uses the BN algorithm to perform the adjustment of spinning reserve allocation, based on the actual unit commitment of the previous hours.

Analytic and computational techniques for evaluating reliability functions and data are described. Estimation and goodness‐of‐fit tests using graphical methods and interactive procedures are presented, based on several alternative distributions.

The use of power sectionalizers in electric power distribution networks as disconnecting devices for optimum network configuration is indispensable. Major reasons to use sectionalizers, here manual sectionalizers, is their lower installation and operating prices compared to other types of disconnecting devices and that most of conventional realistic electric power distribution systems are still using manual sectionalizers due to their ease of procurement. However, in case of failure for these switches, power supply interruptions are unavoidable unless optimum solutions are used for configuration (and possibly reconfiguration) of sectionalizers. Thus, in this research, binary exchange market algorithm (BEMA) as a novel evolutionary metaheuristic is used to meet the maximized customer satisfaction by optimized configuration of sectionalizers within electric power distribution networks in the presence of distributed generations (DGs). To solve the problem, BEMA is used on sectionalizing switch placement problem, which has only two open and close (0/1) states. A novel multi-objective optimization problem has been formulated as a function of two aspects, namely, improved reliability index (for customer benefit) and minimized sectionalizing switch costs (for utility benefits). Simulations are carried out in three different case studies to validate the effectiveness of the BEMA both in theory and practice: Standard IEEE 33-bus test system, practical feeder-8 of MeshkinShahr Town’s electric power distribution network in northwest of Iran; and Roy Billinton test system Bus 4 (RBTS-Bus 4). The obtained results are compared with those of the previously validated ant colony optimization (ACO) technique in RBTS-Bus 4.

The optimum configuration of sectionalizers in the presence of DGs has been formulated as a multi-objective function consisting of two conflicting objectives. First objective is to improve the power distribution network reliability indices. Second objective is to fulfill the first objective with a minimized sectionalizing switch cost. The latter is probably obtained by reducing the number of installed sectionalizers. The obtained results by BEMA have been compared with those of ACO technique.

In this paper, optimal configuration of sectionalizers has been performed based on a multiobjective function by binary exchange market algorithm. By simulations carried out on two standards and one practical test systems, the proposed algorithm effectiveness was confirmed and the obtained results were compared to ACO algorithm. Changing weighting factors shows that better satisfaction can be obtained when difference between the weighting factors is relatively greater. In other words, the reliability membership function is more than switch cost membership, and thus, if the values of two weighting factors are close enough, the satisfaction level reduces. The number of installed sectionalizing switches by BEMA and ACO techniques in different scenarios were performed.

Proposal of a novel multi-objective function for finding optimal location of sectionalizers in the presence of DGs with binary exchange market algorithm whose merit over the other heuristics is to consider all the problem specifications only in one multi-objective function. Despite previously reported works that have used various high-priced protective devices for achieving the enhanced reliability this research only utilizes inexpensive manual sectionalizers with the least possible cost in the presence of DGs. Two standard test cases IEEE 33-bus test system and RBTS-Bus 4 and one realistic test case feeder-8 of MeshkinShahr Town power distribution network in northwest of Iran are used to demonstrate the effectiveness of the proposed technique in theory and real-world applications. Thus, utilities may take the advantage of the proposed method for configuration of sectionalizers in their own local power distribution systems throughout the country.

The purpose of this paper is to show the effect of randomness of wind speed on the capacity value estimation of wind power. Three methods that incorporate hourly wind speed have been evaluated.

Wind speed is simulated using autoregressive moving average method and is included in the calculation of reliability index as a negative load on an hourly basis. The reliability index is calculated before and after the addition of wind capacity. Increment of load or alteration of conventional capacity will lead to capacity estimation.

Among the aforementioned three methods, the former two exclude the availability rate and give the exact value for wind capacity addition. The third method is based on the availability rate and provides a little higher capacity value, indicating a clear correlation between availability and capacity value.

The methods that exclude the availability rate show consistent results. By including the availability rate, the third method predicts the inverse relation between the availability rate and the capacity value.

Reliability is a major quality characteristic which has grown in importance as products/systems have become ever more sophisticated. Neglecting it could spell great losses in terms of patronage, revenue, and even lives. The purpose of this paper is to present a multi‐criteria optimisation model and methodology for the Pareto optimal assignment of reliability to the components of a series‐parallel system in order to maximise its reliability.

The subsystems' reliabilities are maximised independently but simultaneously in order to maximise the overall system reliability, while a penalty function modelling cost of reliability improvement is minimised. The resultant continuous and nonlinear optimisation problem is scalarised by a convex combination of the criteria and the MATLAB Optimisation Toolbox is used to generate the solutions.

The results for an illustrative example problem extracted from the literature show that: higher reliabilities could be assigned to the components, in order to achieve or exceed target system reliability; cost increased sharply with slight improvements in the component reliabilities, and the model was stable under the weighting scheme used.

The novelty of this work is in: the multi‐criteria optimisation view taken of the design problem; the focus on the subsystems' reliabilities and cost as the criteria to be optimised; the use of the two aforementioned qualities for the purpose of Pareto assignment of component reliabilities in a system's design; and the use of the model and methodology in the context of series‐parallel systems.

The purpose of this paper is to derive a closed-form expression for the steady-state availability of a cold standby repairable k-out-of-n system. This makes the availability calculation much easier and accurate.

Assuming exponential distributions for system failure and repair, the Markov method is employed to derive the formula.

The proposed formula establishes an easier and faster venue and provides accurate steady-state availability.

The formula is valid for the case when the probability density function of the component failure and the repair is exponential.

The Markov method has never been used in the literature to derive the steady-state availability of a cold standby repairable k-out-of-n: G system.

In the paper, the problem of uncertain data in reliability analysis of complex systems is examined. The analysis is addressed to system reliability assessment with imprecise knowledge of component reliabilities, an item becoming more and more important for systems affected by considerable technological change. Starting from component uncertain data, a new method for the whole system reliability uncertainty description, based upon a Bayesian approach and not depending on the reliability model of each component, is proposed. The reliability value of each component is considered as a random variable described by a Negative Log‐Gamma distribution. The proposed methodology makes it possible to compute the features of system reliability uncertainty (i.e. reliability distribution, confidence intervals, etc.) as functions of component uncertain data, thus characterizing the propagation of uncertainty from the components to the system. Numerical applications, related to a test system, are presented to show the validity of the method and its “robustness”, i.e. it is shown that it yields satisfactory results also when component reliabilities are not Negative Log‐Gamma but Beta distributed.

Long-term reliability analysis of generation capacity based on the forecasted load demand helps to identify the optimal generation expansion plan of the system. This paper analyzes the generation adequacy of Mexico’s National Interconnected Power System (MNIPS) using loss of load expectation (LOLE) and loss of energy expectation (LOEE) indices.

These indices are calculated through an analytical (recursive) method and are then compared with values recommended by the North American Electric Reliability Council (NERC). Weekly indices are computed to analyze the load curtailment options that may occur in some periods.

Forecasted values, including load and generation capacity considering maintenance schedules, additions of new generating units and permanently shut down units in accordance with the long-term expanding-system plan have been considered. The load forecast uncertainty is also included.

This is original work.

System reliability optimisation in today’s world is critical to ensuring customer satisfaction, businesses competitiveness, secure and uninterrupted delivery of services and safety of operations. Among many systems configurations, complex systems are the most difficult to model for reliability optimisation. The purpose of this paper is to assess the performance of a novel optimisation methodology of the authors, developed to address the difficulties in the context of a gas carrying system (GCS) exhibiting dual failure modes and high initial reliability.

The minimum cut sets involving components of the system were obtained using the fault tree approach, and their reliability constituted into criteria which were maximised and the associated cost of improving their reliabilities minimised. Pareto optimal generic components and system reliabilities were subsequently obtained.

The results indicate that the optimisation methodology could improve the system’s reliability even from an initially high one, granted that the feasibility factor for improving a component’s reliability was very high. The results obtained, in spite of the size (41 objective functions and 18 decision variables), the complexity (dual failure modes) and the high initial reliability values provide confidence in the optimisation model and methodology and demonstrate their applicability to systems exhibiting multiple failure modes.

The GCS was assumed either failed or operational, its parameters precisely determined, and non-repairable. The components failure rates were exponentially distributed and failure modes independent. A single weight vector representing expression of preference in which components reliabilities were weighted higher than cost was used due to the stability of the optimisation model to weight variations.

The high initial reliability values imply that reliability improvement interventions may not be a critical requirement for the GCS. The high levels could be sustained through planned and systematic inspection and maintenance activities. Even so, purely from an analytical stand point, the results nevertheless show that there was some room for reliability improvement however marginal that is. The improvement may be secured by: use of components with comparable levels of reliability to those achieved; use of redundancy techniques to achieve the desired levels of improvement in reliability; or redesigning of the components.

The novelty of this work is in the use of a reliability optimisation model and methodology that focuses on a system’s minimum cut sets as criteria to be optimised in order to optimise the system’s reliability, and the specific application to a complex system exhibiting dual failure modes and high component reliabilities.