A Consensus-ADMM Approach for Strategic Generation Investment in Electricity Markets
2018 IEEE Conference on Decision and Control (CDC)
This paper addresses a multi-stage generation investment problem for a strategic (price-maker) power producer in electricity markets. This problem is exposed to different sources of uncertainty, including short-term operational (e.g., rivals' offering strategies) and long-term macro (e.g., demand growth) uncertainties. This problem is formulated as a stochastic bilevel optimization problem, which eventually recasts as a large-scale stochastic mixed-integer linear programming (MILP) problem with
... (MILP) problem with limited computational tractability. To cope with computational issues, we propose a consensus version of alternating direction method of multipliers (ADMM), which decomposes the original problem by both short-and long-term scenarios. Although the convergence of ADMM to the global solution cannot be generally guaranteed for MILP problems, we introduce two bounds on the optimal solution, allowing for the evaluation of the solution quality over iterations. Our numerical findings show that there is a trade-off between computational time and solution quality. NOTATION The main notation is listed below while other symbols are defined throughout the paper as needed. A subscript t/γ/h/k in the notation refers to the corresponding values in the t th time stage/ γ th long-term scenario/ h th operating condition/ k th market scenario. Superscript/subscript (·) stands for the existing (E/e) and candidate (C/c) generation units, respectively. In addition, superscripts Conv and WP stand for conventional and wind power units, respectively. A. Sets and Indices c ∈ C Set of candidate generation units. d ∈ D Set of demands. e ∈ E Set of existing generation units. h ∈ H Set of wind-load operating conditions. (k, k ) ∈ K Set of short-term market scenarios. r ∈ R Set of rival generation units. (t, τ ) ∈ T Set of time stages in the planning horizon. (γ, γ ) ∈ G Set of long-term scenarios. B. Parameters a t Amortization rate [%]. b D tkd Utility of demand d [$/MWh].