Electrical and Electronic Engineering - Research Publications
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ItemLong-Term Stochastic Planning in Electricity Markets Under Carbon Cap Constraint: A Bayesian Game Approach(IEEE, 2016-01-01)Carbon price in an electricity market provides incentives for carbon emission abatement and renewable generation technologies. Policies constraining or penalizing carbon emissions can significantly impact the capacity planning decisions of both fossil-fueled and renewable generators. Uncertainties due to intermittency of various renewable generators can also affect the carbon emission policies. This paper proposes a Cournot-based long-term capacity expansion model taking into account carbon cap constraint for a partly concentrated electricity market dealing with stochastic renewables using a Bayesian game. The stochastic game is formulated as a centralized convex optimization problem and solved to obtain a Bayes-Nash Equilibrium (Bayes-NE) point. The stochastic nature of a generic electricity market is illustrated with a set of scenarios for wind availability, in which three generation firms (coal, gas, and wind) decide on their generation and long-term capacity investment strategies. Carbon price is derived as the dual variable of the carbon cap constraint. Embedding the carbon cap constraint in the game indicates more investment on renewable generators and less on fossil-fueled power plants. However, the higher level of intermittency from renewable generation leads to a higher carbon price to meet the cap constraint. This paves the way towards storage technologies and diversification of distributed generation as means to encounter intermittency in renewable generation.
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ItemConvergence Analysis of Quantized Primal-dual Algorithm in Quadratic Network Utility Maximization Problems(IEEE, 2015)This paper examines the effect of quantized communications on the convergence behavior of the primal-dual algorithm in quadratic network utility maximization problems with linear equality constraints. In our set-up, it is assumed that the primal variables are updated by individual agents, whereas the dual variables are updated by a central entity, called system, which has access to the parameters quantifying the system-wide constraints. The notion of differential entropy power is used to establish a universal lower bound on the rate of exponential mean square convergence of the primal-dual algorithm under quantized message passing between agents and the system. The lower bound is controlled by the average aggregate data rate under the quantization, the curvature of the utility functions of agents, the number of agents and the number of constraints. An adaptive quantization scheme is proposed under which the primal-dual algorithm converges to the optimal solution despite quantized communications between agents and the system. Finally, the rate of exponential convergence of the primal-dual algorithm under the proposed quantization scheme is numerically studied.
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ItemLower Bounds on the Best-Case Complexity of Solving a Class of Non-cooperative Games(Elsevier, 2016)This paper studies the complexity of solving the class G of all N-player non-cooperative games with continuous action spaces that admit at least one Nash equilibrium (NE). We consider a distributed Nash seeking setting where agents communicate with a set of system nodes (SNs), over noisy communication channels, to obtain the required information for updating their actions. The complexity of solving games in the class G is defined as the minimum number of iterations required to find a NE of any game in G with ε accuracy. Using information-theoretic inequalities, we derive a lower bound on the complexity of solving the game class G that depends on the Kolmogorov 2ε-capacity of the constraint set and the total capacity of the communication channels. We also derive a lower bound on the complexity of solving games in G which depends on the volume and surface area of the constraint set.