W e investigate the management of a merchant wind energy farm co-located with a grid-level storage facility and connected to a market through a transmission line. We formulate this problem as a Markov decision process (MDP) with stochastic wind speed and electricity prices. Consistent with most deregulated electricity markets, our model allows these prices to be negative. As this feature makes it difficult to characterize any optimal policy of our MDP, we show the optimality of a stage-and partial-state-dependent-threshold policy when prices can only be positive. We extend this structure when prices can also be negative to develop heuristic one (H1) that approximately solves a stochastic dynamic program. We then simplify H1 to obtain heuristic two (H2) that relies on a price-dependent-threshold policy and derivative-free deterministic optimization embedded within a Monte Carlo simulation of the random processes of our MDP. We conduct an extensive and data-calibrated numerical study to assess the performance of these heuristics and variants of known ones against the optimal policy, as well as to quantify the effect of negative prices on the value added by and environmental benefit of storage. We find that (i) H1 computes an optimal policy and on average is about 17 times faster to execute than directly obtaining an optimal policy; (ii) H2 has a near optimal policy (with a 2.86% average optimality gap), exhibits a two orders of magnitude average speed advantage over H1, and outperforms the remaining considered heuristics; (iii) storage brings in more value but its environmental benefit falls as negative electricity prices occur more frequently in our model.Note: All experiments are run on a computer with Intel(R) Core(TM) i7-3770K 3.40 GHz CPU and 8 GB RAM.Zhou, Scheller-Wolf, Secomandi, and Smith: Managing Wind-Based Electricity Generation Production and Operations Management 28(4), pp. 970-989,
Electricity cannot yet be stored on a large scale, but technological advances leading to cheaper and more efficient industrial batteries make grid-level storage of electricity surpluses a natural choice. Because electricity prices can be negative, it is unclear how the presence of negative prices might affect the storage policy structure known to be optimal when prices are only nonnegative, or even how important it is to consider negative prices when managing an industrial battery. For fast storage (a storage facility that can both be fully emptied and filled up in one decision period), we show analytically that negative prices can substantially alter the optimal storage policy structure, e.g., all else being equal, it can be optimal to empty an almost empty storage facility and fill up an almost full one. For more typical slow grid-level electricity storage, we numerically establish that ignoring negative prices could result in a considerable loss of value when negative prices occur more than 5% of the time. Negative prices raise another possibility: rather than storing surpluses, a merchant might buy negatively priced electricity surpluses and dispose of them, e.g., using load banks. We find that the value of such a disposal strategy is substantial, e.g., about $118 per kilowatt-year when negative prices occur 10% of the time, but smaller than that of the storage strategy, e.g., about $391 per kilowatt-year using a typical battery. However, devices for disposal are much cheaper than those for storage. Our results thus have ramifications for merchants as well as policy makers. This paper was accepted by Serguei Netessine, operations management.
This paper examines crop planning decision in sustainable agriculture-that is, how to allocate farmland among multiple crops in each growing season when the crops have rotation benefits across growing seasons. We consider a farmer who periodically allocates the farmland between two crops in the presence of revenue uncertainty where revenue is stochastically larger and farming cost is lower when a crop is grown on rotated farmland (where the other crop was grown in the previous season). We characterize the optimal dynamic farmland allocation policy and perform sensitivity analysis to investigate how revenue uncertainty of each crop affects the farmer's optimal allocation decision and profitability. Using a calibration based on a farmer growing corn and soybean in Iowa we show that growing only one crop over the entire planning horizon, as employed in industrial agriculture, leads to a considerable profit loss-that is, making crop planning based on principles of sustainable agriculture has substantial value. We propose a simple heuristic allocation policy which we characterize in closed form. Using our model calibration we show that (i) the proposed policy not only outperforms the commonly suggested heuristic policies in the literature, but also provides a near-optimal performance; (ii) compared to the optimal policy, the proposed policy has a higher allocation of crops to rotated farmland, and thus it is potentially more environmentally friendly.
Coaxial electrospinning is a novel technique for producing core–shell nanofibers that provide a robust structure and deliver hydrophilic bioactive agents.
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