Michael Coulon, Javad Khazaei, W. B. Powell, “SMART-SREC: A stochastic model of the New Jersey solar renewable energy certificate market,” Journal of Environmental Economics and Management, Vol. 73, pp. 13-31, 2015.
New Jersey uses targets to encourage the use of solar energy by setting up a market for solar renewable energy certificates. This paper develops a dynamic programming model of these markets and calibrates the model against historical data for New Jersey.
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D. Jiang, W. B. Powell, “Optimal Hour-ahead Bidding in the Real-Time Electricity Market with Battery Storage Using Approximate Dynamic Programming” Informs J. on Computing, Vol. 27, No. 3, pp. 525-543 (2015).
The hour-ahead bidding problem requires setting a low (buy) and high (sell) bid that determines how a battery is managed one hour in the future, which means that the post-decision state has to include both the bids we just determined, along with other variables such as energy in storage, prices and exogenous energy sources. The dynamic program features a value function that is monotone in all the state variables, which is exploited in the design of an optimal algorithm.
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M. Coulon, W. B. Powell, R. Sircar, “A Model for Hedging Load and Price Risk in the Texas Electricity Market,” Energy Economics, Vol. 40, pp. 976-988, 2013.
We develop a joint model of prices and loads for the Texas electricity market. The model captures the relationship between prices and loads, as well as a variety of seasonal factors.
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Hugo Simao, H. B. Jeong, B. Defourny, W. B. Powell, A. Boulanger, A. Gagneja, L. Wu, R. Anderson, “A Robust Solution for the Load Curtailment Problem,” IEEE Transactions on the Smart Grid, Vol. 4, No. 4, pp. 2209-2019 (2013).
We develop a load curtailment system for New York City using approximate dynamic programming so that we can issue advance notifications to building operators to reduce their demands on the grid before failures have actually happened. The paper compares a cost function approximation (CFA) to a policy based on a value function approximation (VFA).
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J. Enders, W. B. Powell and D. Egan,”Two-Stage Stochastic Program for the Allocation of High-Voltage Transformer Spares in the Electric Grid”, Handbook of Wind Power Systems I, (Sorokin, A.; Rebennack, S.; Pardalos, P.M.; Iliadis, N.A.; Pereira, M.V.F. (Eds.)), Springer, New York, pp. 435-466, 2012.
PJM faced the problem of allocating spare high-voltage transformers in locations that make it possible to respond quickly to failures. This is an integer, two-stage stochastic optimization problem. We solve the problem by approximating the second stage using piecewise linear value functions.
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Jae Ho Kim, W. B. Powell, “Optimal Energy Commitments with Storage and Intermittent Supply,” Operations Research, Vol. 59, No. 6, pp. 1347-1360 (2011).
We develop a simple, analytic policy that determines how much energy we can commit to delivering from a wind farm in a day-ahead (or hour-ahead) market, in the presence of a finite capacity storage device with energy conversion losses. Our policy is derived assuming that wind is uniformally distributed betwee known bounds, but experiments with actual wind show that the approximation is quite robust. The policy is sensitive to the variability of the wind forecast, the capacity of the storage device and the conversion losses. We then use the policy to estimate the value of storage.
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Kim, Jae Ho, Powell, Warren B., An hour-ahead prediction model for heavy-tailed spot prices, Energy Economics (2011), doi:10.1016/j.eneco.2011.06.007
We propose an hour-ahead prediction model for electricity prices that captures the heavy-tailed behavior that we observe in the hourly spot market in the Ercot (Texas) and the PJM West hub grids. We present a model according to which we separate the price process into a thin-tailed trailing-median process and a heavy-tailed residual process whose probability distribution can be approximated by a Cauchy distribution. We show empirical evidence that supports our model.
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Powell, W. B., George, A., A. Lamont and J. Stewart, “SMART: A Stochastic Multiscale Model for the Analysis of Energy Resources, Technology and Policy,” Informs Journal on Computing, Vol. 24, No. 4, pp. 665-682 (2012).
We address the problem of modeling energy resource allocation, including dispatch, storage and the long-term investments in new technologies, capturing different sources of uncertainty such as energy from wind, demands, prices and rainfall. We also wish to model long-term investment decisions in the presence of uncertainty. Accurately modeling the value of all investments such as wind and solar requires handling fine-grained temporal variability and uncertainty in wind and solar in the presence of storage. We propose a modeling and algorithmic strategy based on the framework of approximate dynamic programming (ADP) that can model these problems at hourly time increments over an entire year, or over several decades. We demonstrate the methodology using both spatially aggregate and disaggregate representations of energy supply and demand. This paper describes initial proof of concept experiments for an ADP-based model, called SMART, by describing the modeling and algorithmic strategy, and providing comparisons against a deterministic benchmark as well as initial experiments on stochastic datasets.
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Anderson, B. R. N., Boulanger, A., Powell, W. B., & Scott, W. Adaptive Stochastic Control for the Smart Grid. Proceedings of the IEEE, 99(6), 1098-1115, 2011.
This paper explores a number of stochastic control challenges that arise in smart grid applications, and introduces algorithmic strategies under the general umbrella of approximation dynamic programming.
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Powell, W. B., George, A., A. Lamont and J. Stewart, “SMART: A Stochastic Multiscale Model for the Analysis of Energy Resources, Technology and Policy,” Informs Journal on Computing, Vol. 24, No. 4, pp. 665-682 (2012).
We address the problem of modeling energy resource allocation, including dispatch, storage and the long-term investments in new technologies, capturing different sources of uncertainty such as energy from wind, demands, prices and rainfall. We also wish to model long-term investment decisions in the presence of uncertainty. Accurately modeling the value of all investments such as wind and solar requires handling fine-grained temporal variability and uncertainty in wind and solar in the presence of storage. We propose a modeling and algorithmic strategy based on the framework of approximate dynamic programming (ADP) that can model these problems at hourly time increments over an entire year, or over several decades. We demonstrate the methodology using both spatially aggregate and disaggregate representations of energy supply and demand. This paper describes initial proof of concept experiments for an ADP-based model, called SMART, by describing the modeling and algorithmic strategy, and providing comparisons against a deterministic benchmark as well as initial experiments on stochastic datasets.
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J. Nascimento, W. B. Powell, “An Optimal Approximate Dynamic Programming Algorithm for the Energy Dispatch Problem with Grid- Level Storage,”
This paper proves convergence of the approximate dynamic programming algorithm used within the SMART model for optimizing the use of hydroelectric storage for a fine-grained (hourly) energy dispatch model. The ADP algorithm uses a piecewise linear functional approximation, and does not require any explicit exploration. This is useful in an energy setting because the value function is discretized into thousands of segments.
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L. Hannah, W. B. Powell, and J. Stewart, “One-Stage R&D Portfolio Optimization with an Application to Solid Oxide Fuel Cells,” Energy Systems Journal, Vol. 1, No. 1, 2010.
We propose and test an algorithm for large R&D portfolio optimization problems, which are tested in the context of solid oxide fuel cells. The logic handles large portfolios, such as finding the best 30 proposals out of 100 (or the best 100 proposals out of 300). The algorithm is a heuristic, but is compared to two competing algorithms (one of which is provably convergent). We show that our new algorithm, based on the priniciple of stochastic gradient optimization, reliably produces lower cost designs than the competing algorithms.
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J. Enders, W. B. Powell, D. Egan, “A Dynamic Model for the Failure Replacement of Aging High-Voltage Transformers,” Energy Systems Journal, Vol. 1, No. 1, pp. 31-59 (2010) (c) Springer
This paper introduces a model that supports these efforts by optimizing the acquisition and the deployment of high-voltage transformers dynamically over time. We formulate the problem as a Markov Decision Process which cannot be solved for realistic problem instances. Instead we solve the problem using approximate dynamic programming using three different value function approximations, which are compared against an optimal solution for a simplified version of the problem. The methods include a separable, piecewise linear value function, a piecewise linear, two-dimensional approximation, and a piecewise linear function based on an aggregated inventory that is shown to produce solutions within a few percent with very fast convergence. The application of the best performing algorithm to a realistic problem instance gives insights into transformer management issues of practical interest.
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Enders, J., W. B. Powell and D. Egan “Robust Policies for the Transformer Acquisition and Allocation Problem,”
This paper compares a replacement policy derived using approximate dynamic programming to a replacement policy proposed by a major regional transmission organization based on classical failure analysis. The analysis shows that approximate dynamic programming produces a policy that offers lower cost as well as lower risk.
Ryzhov, I., W. B. Powell, “A Monte-Carlo Knowledge Gradient Method for Learning Abatement Potential of Emissions Reduction Technologies,” Winter Simulation Conference, 2009. M. D. Rossetti, R. R. Hill, B. Johansson, A. Dunkin, and R. G. Ingalls, eds, 2009, pp. 1492-1502.