No Arabic abstract
With the rapid growth in renewable energy and battery storage technologies, there exists significant opportunity to improve energy efficiency and reduce costs through optimization. However, optimization algorithms must take into account the underlying dynamics and uncertainties of the various interconnected subsystems in order to fully realize this potential. To this end, we formulate and solve an energy management optimization problem as a Markov Decision Process (MDP) consisting of battery storage dynamics, a stochastic demand model, a stochastic solar generation model, and an electricity pricing scheme. The stochastic model for predicting solar generation is constructed based on weather forecast data from the National Oceanic and Atmospheric Administration. A near-optimal policy design is proposed via stochastic dynamic programming. Simulation results are presented in the context of storage and solar-integrated residential and commercial building environments. Results indicate that the near-optimal policy significantly reduces the operating costs compared to several heuristic alternatives. The proposed framework facilitates the design and evaluation of energy management policies with configurable demand-supply-storage parameters in the presence of weather-induced uncertainties.
Increasing wind turbines (WT) penetration and low carbon demand can potentially lead to two different flow peaks, generation and load, within distribution networks. This will not only constrain WT penetration but also pose serious threats to network reliability. This paper proposes energy storage (ES) to reduce system congestion cost caused by the two peaks by sending cost-reflective economic signals to affect ES operation in responding to network conditions. Firstly, a new charging and discharging (C/D) strategy based on Binary Search Method is designed for ES, which responds to system congestion cost over time. Then, a novel pricing method, based on Location Marginal Pricing, is designed for ES. The pricing model is derived by evaluating ES impact on the network power flows and congestion from the loss and congestion components in Location Marginal Pricing. The impact is then converted into an hourly economic signal to reflect ES operation. The proposed ES C/D strategy and pricing methods are validated on a real local Grid Supply Point area. Results show that the proposed Location Marginal Pricing-based pricing is efficient to capture the feature of ES and provide signals for affecting its operation. This work can further increase network flexibility and the capability of networks to accommodate increasing WT penetration.
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost functional, in general, the value function is not differentiable in the domain. Then, we characterize the value function as a viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation. Based on the result, we derive a necessary and sufficient condition for the $L^0$ optimality, which immediately gives the optimal feedback map. Especially for control-affine systems, we consider the relationship with $L^1$ optimal control problem and show an equivalence theorem.
We study the canonical quantity-based network revenue management (NRM) problem where the decision-maker must irrevocably accept or reject each arriving customer request with the goal of maximizing the total revenue given limited resources. The exact solution to the problem by dynamic programming is computationally intractable due to the well-known curse of dimensionality. Existing works in the literature make use of the solution to the deterministic linear program (DLP) to design asymptotically optimal algorithms. Those algorithms rely on repeatedly solving DLPs to achieve near-optimal regret bounds. It is, however, time-consuming to repeatedly compute the DLP solutions in real time, especially in large-scale problems that may involve hundreds of millions of demand units. In this paper, we propose innovative algorithms for the NRM problem that are easy to implement and do not require solving any DLPs. Our algorithm achieves a regret bound of $O(log k)$, where $k$ is the system size. To the best of our knowledge, this is the first NRM algorithm that (i) has an $o(sqrt{k})$ asymptotic regret bound, and (ii) does not require solving any DLPs.
This paper proposes a new algorithm -- the underline{S}ingle-timescale Dounderline{u}ble-momentum underline{St}ochastic underline{A}pproxunderline{i}matiounderline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel optimization problems. We focus on bilevel problems where the lower level subproblem is strongly-convex and the upper level objective function is smooth. Unlike prior works which rely on emph{two-timescale} or emph{double loop} techniques, we design a stochastic momentum-assisted gradient estimator for both the upper and lower level updates. The latter allows us to control the error in the stochastic gradient updates due to inaccurate solution to both subproblems. If the upper objective function is smooth but possibly non-convex, we show that {aname}~requires $mathcal{O}(epsilon^{-3/2})$ iterations (each using ${cal O}(1)$ samples) to find an $epsilon$-stationary solution. The $epsilon$-stationary solution is defined as the point whose squared norm of the gradient of the outer function is less than or equal to $epsilon$. The total number of stochastic gradient samples required for the upper and lower level objective functions matches the best-known complexity for single-level stochastic gradient algorithms. We also analyze the case when the upper level objective function is strongly-convex.
This work considers energy management in a grid-connected microgrid which consists of multiple conventional generators (CGs), renewable generators (RGs) and energy storage systems (ESSs). A two-stage optimization approach is presented to schedule the power generation, aimed at minimizing the long-term average operating cost subject to operational and service constraints. The first stage of optimization determines hourly unit commitment of the CGs via a day-ahead scheduling, and the second stage performs economic dispatch of the CGs, ESSs and energy trading via an hour-ahead scheduling. The combined solution meets the need of handling large uncertainties in the load demand and renewable generation, and provides an efficient solution under limited computational resource which meets both short-term and long-term quality-of-service requirements. The performance of the proposed strategy is evaluated by simulations based on real load demand and renewable generation data.