Abstract: In this article we quantify the effect of uncertainty of climate and environmental policies on transmission and generation investments, as well as on CO2 emissions in Chile. We use a two-stage stochastic planning model with recourse or corrective investment options to find optimal portfolios of infrastructure both under perfect information and uncertainty. Under a series of assumptions, this model is equivalent to the equilibrium of a much more complicated bi-level market model, where a transmission planner chooses investments first and generation firms invest afterwards. We find that optimal investment strategies present important differences depending on the policy scenario. By changing our assumption of how agents will react to this uncertainty we compute bounds on the cost that this uncertainty imposes on the system, which we estimate ranges between 3.2% and 5.7% of the minimum expected system cost of $57.6B depending on whether agents will consider or not uncertainty when choosing investments. We also find that, if agents choose investments using a stochastic planning model, uncertain climate policies can result in nearly 18% more CO2 emissions than the equilibrium levels observed under perfect information. Our results highlight the importance of credible and stable long-term regulations for investors in the electric power industry if the goal is to achieve climate and environmental targets in the most cost-effective manner and to minimize the risk of asset stranding. (C) 2018 Elsevier B.V. All rights reserved.

Abstract: We propose a novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems that have to consider a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen's inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improves upon the standard Benders' algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen's inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. However, the decomposition phase is required to attain optimality gaps. Use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

Abstract: Benders decomposition is one of the most applied methods to solve two-stage stochastic problems (TSSP) with a large number of scenarios. The main idea behind the Benders decomposition is to solve a large problem by replacing the values of the second stage subproblems with individual variables and progressively forcing those variables to reach the optimal value of the subproblems, dynamically inserting additional valid constraints, known as Benders cuts. Most traditional implementations add a cut for each scenario (multicut) or a single cut that includes all scenarios. In this paper, we present a novel Benders adaptive-cuts method, where the Benders cuts are aggregated according to a partition of the scenarios, which is dynamically refined using the linear program-dual information of the subproblems. This scenario aggregation/disaggregation is based on the Generalized Adaptive Partitioning Method (GAPM), which has been successfully applied to TSSPs. We formalize this hybridization of Benders decomposition and the GAPM by providing sufficient conditions under which an optimal solution of the deterministic equivalent can be obtained in a finite number of iterations. Our new method can be interpreted as a compromise between the Benders single-cuts and multicuts methods, drawing on the advantages of both sides, by rendering the initial iterations faster (as for the single-cuts Benders) and ensuring the overall faster convergence (as for the multicuts Benders). Computational experiments on three TSSPs [the Stochastic Electricity Planning, Stochastic Multi Commodity Flow, and conditional value-at-risk (CVaR) Facility Location] validate these statements, showing that the new method outperforms the other implementations of Benders methods, as well as other standard methods for solving TSSPs, in particular when the number of scenarios is very large. Moreover, our study demonstrates that the method is not only effective for the risk-neutral decision makers, but also that it can be used in combination with the risk-averse CVaR objective.