Optimal Operation Of Energy Storage Research Articles

A moment and sum-of-squares extension of dual dynamic programming with application to nonlinear energy storage problems

We present a finite-horizon optimization algorithm that extends the established concept of Dual Dynamic Programming (DDP) in two ways. First, in contrast to the linear costs, dynamics, and constraints of standard DDP, we consider problems in which all of these can be polynomial functions. Second, we allow the state trajectory to be described by probability distributions rather than point values, and return approximate value functions fitted to these. The algorithm is in part an adaptation of sum-of-squares techniques used in the approximate dynamic programming literature. It alternates between a forward simulation through the horizon, in which the moments of the state distribution are propagated through a succession of single-stage problems, and a backward recursion, in which a new polynomial function is derived for each stage using the moments of the state as fixed data. The value function approximation returned for a given stage is the point-wise maximum of all polynomials derived for that stage. This contrasts with the piecewise affine functions derived in conventional DDP. We prove key convergence properties of the new algorithm, and validate it in simulation on two case studies related to the optimal operation of energy storage devices with nonlinear characteristics. The first is a small borehole storage problem, for which multiple value function approximations can be compared. The second is a larger problem, for which conventional discretized dynamic programming is intractable.

Optimal Storage Operation Under Demand Charge

We study the optimal operation of energy storage operated by a consumer who owns intermittent renewable generation and faces (possibly random) fluctuating electricity prices and demand charge. We formulate the optimal storage operation problem as a finite horizon dynamic program, with an objective of minimizing the expected total cost (the sum of energy cost and demand charge). The incorporation of demand charge faces the consumer with more complicated trade-offs on storage operation, e.g., discharging the storage when the energy price is relatively low may not save energy cost, but could help to save the demand charge if the net demand is high. We establish an important threshold structure for an optimal storage operation policy, which enables us to implement the optimal policy in realistic settings with random electricity prices. Numerical results demonstrate that the characterized optimal threshold policy significantly outperforms the policy that is shown to be optimal without demand charge in the literature, even at a low-demand charge rate 6$/kW.

Optimal Operation of Energy Storage with Random Renewable Generation and AC/DC Loads

We study the optimal operation of energy storage owned by a consumer who has intermittent renewable generation and faces time-varying (random) electricity prices and different types of ac/dc loads. We formulate the optimal storage operation problem as a finite-horizon dynamic program, with an objective of minimizing the expected energy cost. The incorporation of different types of ac/dc energy sources and appliances complicates the sequential decision making problem on storage operation. We provide a complete characterization on an optimal threshold policy, and implement the characterized optimal policy in realistic settings with random renewable generation and electricity prices. Numerical results demonstrate that the optimal dynamic programming (DP) solution saves 5%–12% of the total cost resulting from conventional DP solutions (that ignore the difference in ac/dc conversion efficiencies). Further, the value of storage (the consumer’s net benefit obtained by optimally operating the storage) increases with renewable generation. For example, as the (average) solar generation increases from 40% to 100% of the average (total) demand, the value of a 32 kWh (80 kWh) storage increases from 2.0% to 5.4% (7.2% to 14.9%, respectively) of the maximum energy cost.

Optimal operation of energy storage in buildings: Use of the hot water system

We consider the optimal operation of energy storage in buildings with focus on the optimization of an electric water heating system. The optimization objective is to minimize the energy costs of heating the water, with the requirement that we should satisfy the uncertain demand at any time. The main complications in this problem are the time varying nature of the electricity price and the unpredictability of the future water demand. In this paper we use the water heating system as an example for formulating a general framework which could easily be applied to similar problems with energy storage capacity. Feasibility and optimality are discussed and the main points are illustrated in the simulation case studies.

Optimal operation of energy storage devices with RESs to improve efficiency of distribution grids; technical and economical assessment

Abstract Electricity distribution grids are a crucial part of power systems as they are providing customers with the power demanded. This importance, absorbs a huge funding to be invested in this section. To reduce distribution grid losses, a wide variety of approaches are being deployed including optimal distribution substation placement and network reconfiguration. Introduction of higher storage capacities has made it possible to use them in power grids while it is highly appreciated to generate energy in a distributed manner and store it near customers due to environmental considerations. In this research, the idea of adding energy storage devices to the grid is investigated and its effect is studied on the efficiency of distribution grids. The objective function introduced in this paper calculates electricity grid losses while considering limitations of using energy storage devices. Dynamic programming is used to solve the problem on CIGRE low voltage grid as a standard benchmark. Several experiments show efficiency of the proposed method. In achieving results, simultaneous use of photovoltaic and energy storage devices is considered. Finally, the most economical solution is proposed after an economic evaluation of the solutions.

Mean-Conditional Value-at-Risk Optimal Energy Storage Operation in the Presence of Transaction Costs

This paper addresses the formulation and solution of an optimal energy storage management problem under risk consideration and transaction costs of trading energy with the power grid. The price evolves as a stochastic process, capable of correctly explaining the seasonality effects as well as the tail fatness and spikiness in its distribution. Transaction costs capture the price impact of the storage operation on the electricity spot price. A risk analysis of an optimal risk neutral deterministic policy as well as the simple myopic policy indicates that the realized operational cost may notably differ from the expected cost by a considerable probability. This difference suggests that we need to consider risk. Using the downside risk measure of conditional value-at-risk, an optimal risk averse conversion and transmission strategy, among the grid, the renewable power generation source, and an energy storage is proposed to fully satisfy the electricity demand and minimize the expected operational cost as well as the risk. Our numerical study using data from NYISO demonstrates the impacts of risk consideration and the transaction cost parameters on the optimal strategy structure, its expected cost, and its risk.