Extensions of the Dynamic Programming Framework: Battery Scheduling, Demand Charges, and Renewable Integration

@article{Jones2021ExtensionsOT,
  title={Extensions of the Dynamic Programming Framework: Battery Scheduling, Demand Charges, and Renewable Integration},
  author={Morgan Jones and Matthew M. Peet},
  journal={IEEE Transactions on Automatic Control},
  year={2021},
  volume={66},
  pages={1602-1617}
}
  • Morgan Jones, M. Peet
  • Published 29 November 2018
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
We consider a general class of dynamic programming (DP) problems with nonseparable objective functions. We show that for any problem in this class, there exists an augmented-state DP problem that satisfies the principle of optimality and the solutions to which yield solutions to the original problem. Furthermore, we identify a subclass of DP problems with naturally forward separable objective functions for which this state-augmentation scheme is tractable. We extend this framework to stochastic… Expand
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References

SHOWING 1-10 OF 52 REFERENCES
Solving dynamic programming with supremum terms in the objective and application to optimal battery scheduling for electricity consumers subject to demand charges
  • Morgan Jones, M. Peet
  • Economics, Mathematics
  • 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
  • 2017
TLDR
This paper proposes a general class of optimization problems with forward separable objectives and shows that for any problem in this class, there exists an augmented-state dynamic programming problem which satisfies the principle of optimality and the solutions to which yield solutions to the originalforward separable problem. Expand
Multi-objective dynamic programming for constrained optimization of non-separable objective functions with application in energy storage
  • R. Kamyar, M. Peet
  • Engineering, Computer Science
  • 2016 IEEE 55th Conference on Decision and Control (CDC)
  • 2016
TLDR
Numerical case studies show that optimal energy storage using Tesla's Powerwall battery can reduce the monthly electricity bill by up to 52% relative to the case where no energy storage is used. Expand
Extension of dynamic programming to nonseparable dynamic optimization problems
Abstract The use of dynamic programming is extended to a general nonseparable class where multiobjective optimization is used as a separation strategy. The original nonseparable dynamic optimizationExpand
General approaches for determining the savings potential of optimal control for cooling in commercial buildings having both energy and demand charges
TLDR
A simpler and more practical short-term optimization approach with a demand-limiting heuristic is proposed and evaluated in comparison to the benchmarking optimization results for this case study and achieves most of the potential savings. Expand
Shrinking-horizon dynamic programming
We describe a heuristic control policy for a general finite-horizon stochastic control problem, which can be used when the current process disturbance is not conditionally independent of the previousExpand
Optimal thermostat programming and optimal electricity rates for customers with demand charges
  • R. Kamyar, M. Peet
  • Computer Science, Mathematics
  • 2015 American Control Conference (ACC)
  • 2015
TLDR
It is shown that thermal storage and optimal thermostat programming can reduce electricity bills using current utility prices from utilities Arizona Public Service (APS) and Salt River Project (SRP). Expand
Optimal battery energy storage system (BESS) charge scheduling with dynamic programming
A dynamic programming algorithm for the optimal charge/discharge scheduling of BESS energy storage is presented. It ensures the minimisation of the electricity bill for a given battery capacity,Expand
Experiments with dynamic programming algorithms for nonseparable problems
Abstract In this paper we report on numerical experiments with dynamic programming algorithms designed for solving problems with nonseparable objective functions of the C-programming type. TheExpand
Dynamic consistency for stochastic optimal control problems
TLDR
It is shown that a significant class of dynamic optimization problems are dynamically consistent, provided that an adequate state variable is chosen in Markov Decision Processes, and this notion is linked with the concept of “state variable” in MDP. Expand
More Risk-Sensitive Markov Decision Processes
TLDR
It turns out that under suitable recurrence conditions on the MDP for convex power utility, the minimal average cost does not depend on the parameter of the utility function and is equal to the risk-neutral average cost, in contrast to the classical risk-sensitive criterion with exponential utility. Expand
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