Switching On and Off the Full Capacity of an M/M/Infinity Queue & Dynamic Pricing and Power Generation Risk Management in Smart Grids
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Part 1. We study a problem of optimal switching on and off the M/M/Infinity queue with holding, running and switching costs. We show that an optimal policy either always runs the system, or is defined by two thresholds M and N such that the system is switched on upon an arrival epoch if the system size accumulates to N and is switches off upon a departure epoch if the system size decreases to M.Part 2. We design an optimal incentive mechanism offered to energy customers at multiple network levels, such as distribution and feeder networks, with the aim of determining the lowest cost aggregate energy demand reduction. Our model minimizes a utility's total cost for this mode of virtual demand generation, i.e., demand reduction, to achieve improvements in both its total systemic costs and load reduction over existing mechanisms. Our scheme assumes that the utility can predict with rebates by observing and learning from their past behavior. Within a single period formulation, we further propose a heuristic policy that segments the customers according to their likelihood of reducing load. Within a muti-period formulation, we observe that customers who are more willing to reduce their aggregate demand over the entire horizon, rather than simply shifting their load to off-peak periods, tend to receive higher incentives, and vice versa. We further consider integrating the demand response and renewable resources into traditional thermal power generation management. A single-period optimal dispatching problem is considered for a network of energy utilities connected via multiple transmission lines, where we seek to find the lowest operational-cost dispatching of various energy sources to satisfy demand. Our model includes traditional thermal resources and renewable energy resources , together with corresponding power transmission constraints, as available generation capabilities within the grid. A key novel addition is the consideration of demand reduction as a virtual generation source that can be dispatched quickly to hedge against the risk of unforeseen shortfall in supply. Demand reduction isdispatched in response to incentive signals sent to consumers. The control options of our optimization model consist of the dispatching order and dispatching amount of the thermal generators together with the rebate signals sent to end-users at each node of the network under a simple demand response policy. Numerical experiments based on our analysis of representative data are presented to illustrate the effectiveness of demand response as a hedging option.