Local Water Storage Control for the Developing World

Most cities in India do not have water distribution networks that provide water throughout the entire day. As a result, it is common for homes and apartment buildings to utilize water storage systems that are filled during a small window of time in the day when the water distribution network is active. However, these water storage systems do not have disinfection capabilities, and so long durations of storage (i.e., as few as four days) of the same water leads to substantial increases in the amount of bacteria and viruses in that water. This paper considers the stochastic control problem of deciding how much water to store each day in the system, as well as deciding when to completely empty the water system, in order to tradeoff: the financial costs of the water, the health costs implicit in long durations of storing the same water, the potential for a shortfall in the quantity of stored versus demanded water, and water wastage from emptying the system. To solve this problem, we develop a new Binary Dynamic Search (BiDS) algorithm that is able to use binary search in one dimension to compute the value function of stochastic optimal control problems with controlled resets to a single state and with constraints on the maximum time span in between resets of the system

Calibrated Stochastic Dynamic Models for Resource Management

In this paper we develop a positive calibrated approach to stochastic dynamic programming. Risk aversion, discount rate, and intertemporal substitution preferences of the decision-maker are calibrated by a procedure that minimizes the mean squared error from data on past decisions. We apply this framework to managing stochastic water supplies from Oroville Reservoir, located in Northern California. The calibrated positive SDP closely reproduces the historical storage and releases from the dam and shows sensitivity of optimal decisions to a decision-maker's risk aversion and intertemporal preferences. The calibrated model has average prediction errors that are substantially lower than those from the model with an expected net present value objective.Resource /Energy Economics and Policy,

On the Economic Value and Price-Responsiveness of Ramp-Constrained Storage

The primary concerns of this paper are twofold: to understand the economic value of storage in the presence of ramp constraints and exogenous electricity prices, and to understand the implications of the associated optimal storage management policy on qualitative and quantitative characteristics of storage response to real-time prices. We present an analytic characterization of the optimal policy, along with the associated finite-horizon time-averaged value of storage. We also derive an analytical upperbound on the infinite-horizon time-averaged value of storage. This bound is valid for any achievable realization of prices when the support of the distribution is fixed, and highlights the dependence of the value of storage on ramp constraints and storage capacity. While the value of storage is a non-decreasing function of price volatility, due to the finite ramp rate, the value of storage saturates quickly as the capacity increases, regardless of volatility. To study the implications of the optimal policy, we first present computational experiments that suggest that optimal utilization of storage can, in expectation, induce a considerable amount of price elasticity near the average price, but little or no elasticity far from it. We then present a computational framework for understanding the behavior of storage as a function of price and the amount of stored energy, and for characterization of the buy/sell phase transition region in the price-state plane. Finally, we study the impact of market-based operation of storage on the required reserves, and show that the reserves may need to be expanded to accommodate market-based storage

A Three-Step Methodology to Improve Domestic Energy Efficiency

Increasing energy prices and the greenhouse effect lead to more awareness of energy efficiency of electricity supply. During the last years, a lot of technologies have been developed to improve this efficiency. Next to large scale technologies such as windturbine parks, domestic technologies are developed. These domestic technologies can be divided in 1) Distributed Generation (DG), 2) Energy Storage and 3) Demand Side Load Management. Control algorithms optimizing a combination of these techniques can raise the energy reduction potential of the individual techniques. In this paper an overview of current research is given and a general concept is deducted. Based on this concept, a three-step optimization methodology is proposed using 1) offline local prediction, 2) offline global planning and 3) online local scheduling. The paper ends with results of simulations and field tests showing that the methodology is promising.\u