Editors' Introduction: Uncertain Reserve

Demand response (DR) can provide reserves in power systems but a fundamental challenge is that the amount of capacity available from DR is time-varying and uncertain. We propose a stochastic optimal power flow (OPF) formulation that handles uncertain energy from wind and uncertain reserves provided by DR. To handle the uncertainty, we formulate chance constraints and use a scenario based methodology to solve the stochastic OPF problem. This technique allows us to provide a-priori guarantees regarding the probability of constraint satisfaction. Additionally, we devise a strategy for the reserves, provided either by the generators or the loads, that could be deployed in real time operation. To evaluate the effectiveness of our methodology, we carry out a simulation based analysis on the IEEE 30-bus network. Our case studies show that optimizing over the reserves provided by DR, even though they are uncertain, results in lower total cost compared to the case where only generation side reserves are taken into account. We also carry out a Monte Carlo analysis to empirically estimate the probability of constraint satisfaction and demonstrate that it is within the theoretical limits.

Whenever any type of ore deposit is developed, it comes with significant risks, such as uncertain reserves, harsh climate conditions, and other uncontrollable factors. To manage these risks effectively, companies need to quickly adapt to changing conditions. This paper presents a method for evaluating risks using a simulation model. The main objective is to identify factors of operational risk and determine the project parameters that have the greatest impact on the probability of a risk event. The method includes the classification of operational risks based on the way they arise; the creation of a risk decomposition matrix dividing risks by production tasks; and the construction of a mathematical model using the identified risk factors. The method was tested by developing a simulation model of an underground mine conveyor network in Anylogic (8.9.2) software. A simulation experiment showed that conveyor shutdowns could result in an 11.23% reduction in annual revenue. Based on the results, recommendations were made on how these risks can be reduced and on the need to implement a transport system to increase resilience.

Real Options, Sequential Bargaining Game and Network Effects in Natural Gas Production

This paper develops a multi-period chance constrained optimal power flow model to schedule generation and reserves from both generators and aggregations of controllable electric loads. In contrast to generator-based reserve capacities, load-based reserve capacities are less certain because they depend on load usage patterns and ambient conditions. This paper is divided in two parts. In part I, we develop a reserve scheduling framework managing uncertain power from wind and uncertain reserves provided by controllable loads, and solve the problem using a probabilistically robust optimization method that may require large numbers of uncertainty scenarios but provides a priori guarantees on the probability of constraint satisfaction, assuming no knowledge of the uncertainty distributions. The solution of this problem offers us a policy-based strategy for real-time reserve deployment. We derive simple rules, based on the cost parameters of the resources, to determine when load-based reserves will be preferable. In part II, we reformulate the problem assuming the uncertainty follows multivariate normal distributions and re-solve the problem, comparing the results against the randomized technique. To evaluate the performance of the methods, we conduct simulations using the IEEE 30-bus network.

Optimizing residential heating and energy storage flexibility for frequency reserves

The problem of finding agents’ rational strategies in bargaining with incomplete information is well known to be challenging. The literature provides a collection of results for very narrow uncertainty settings, but no generally applicable algorithm. This lack has led researchers to develop heuristic approaches in an attempt to find outcomes that, even if not being of equilibrium, are mutually satisfactory. In the present paper, we focus on the principal bargaining protocol (i.e., the alternating-offers protocol) where there is uncertainty regarding one agent’s reserve price. We provide an algorithm based on the combination of game theoretic analysis and search techniques which finds pure strategy sequential equilibria when they exist. Our approach is sound, complete and, in principle, can be applied to other uncertainty settings, e.g., uncertain discount factors, and uncertain weights of negotiation issues in multi-issue negotiation. We experimentally evaluate our algorithm with a number of case studies showing that the average computational time is less than 30 s and at least one pure strategy equilibrium exists in almost all (about 99.7 %) the bilateral bargaining scenarios we have looked at in the paper.

Reliability of corrosion-damaged steel structures using interval probability theory