Ram Rajagopal

Bringing Wind Energy to Market

Wind energy is a rapidly growing source of renewable energy generation. However, the current extra-market approach to its assimilation into the electric grid will not scale at deep penetration levels. In this paper, we investigate how an independent wind power producer might optimally offer its variable power into a competitive electricity market for energy. Starting with a stochastic model for wind power production and a model for a perfectly competitive two-settlement market, we derive explicit formulae for optimal contract offerings and the corresponding optimal expected profit. As wind is an inherently variable source of energy, we explore the sensitivity of optimal expected profit to uncertainty in the underlying wind process. We also examine the role of forecast information and recourse markets in this setting. We quantify the role of reserves in increasing reliability of offered contracts and obtain analytical expressions for marginal profits resulting from investments in improved forecasting and local auxiliary generation. The formulae make explicit the relationship between price signals and the value of such firming strategies.

Household Energy Consumption Segmentation Using Hourly Data

The increasing US deployment of residential advanced metering infrastructure (AMI) has made hourly energy consumption data widely available. Using CA smart meter data, we investigate a household electricity segmentation methodology that uses an encoding system with a pre-processed load shape dictionary. Structured approaches using features derived from the encoded data drive five sample program and policy relevant energy lifestyle segmentation strategies. We also ensure that the methodologies developed scale to large data sets.

The role of co-located storage for wind power producers in conventional electricity markets

In this paper we study the problem of optimizing contract offerings for an independent wind power producer (WPP) participating in conventional day-ahead forward electricity markets for energy. As wind power is an inherently variable source of energy and is difficult to predict, we explore the extent to which co-located energy storage can be used to improve expected profit and mitigate the the financial risk associated with shorting on the offered contracts. Using a simple stochastic model for wind power production and a model for the electricity market, we show that the problem of determining optimal contract offerings for a WPP with co-located energy storage can be solved using convex programming.

Network-Based Consensus Averaging With General Noisy Channels

This paper focuses on the consensus averaging problem on graphs under general imperfect communications. We study a particular class of distributed consensus algorithms based on damped updates, and using the ordinary differential equation method, we prove that the updates converge almost surely to the consensus average for various models of perturbation of data exchanged between nodes. The convergence is not asymptotic in the size of the network. Our analysis applies to various types of stochastic disturbances to the updates, including errors in update calculations, dithered quantization and imperfect data exchange among nodes. Under a suitable stability condition, we prove that the error between estimated and true averages is asymptotically Gaussian, and we show how the asymptotic covariance is specified by the graph Laplacian. For additive perturbations, we show how the scaling of the asymptotic MSE is controlled by the spectral gap of the Laplacian.

Detection and Statistics of Wind Power Ramps

Ramps events are a significant source of uncertainty in wind power generation. Developing statistical models from historical data for wind power ramps is important for designing intelligent distribution and market mechanisms for a future electric grid. This requires robust detection schemes for identifying wind ramps in data. In this paper, we propose an optimal detection technique for identifying wind ramps for large time series. The technique relies on defining a family of scoring functions associated with any rule for defining ramps on an interval of the time series. A dynamic programming recursion is then used to find all such ramp events. Identified wind ramps are used to propose a new stochastic framework to characterize wind ramps. Extensive statistical analysis is performed based on this framework, characterizing ramping duration and rates as well as other key features needed for evaluating the impact of wind ramps in the operation of the power system. In particular, evaluation of new ancillary services and wind ramp forecasting can benefit from the proposed approach.

Distributed Online Simultaneous Fault Detection for Multiple Sensors

Monitoring its health by detecting its failed sensors is essential to the reliable functioning of any sensor network. This paper presents a distributed, online, sequential algorithm for detecting multiple faults in a sensor network. The algorithm works by detecting change points in the correlation statistics of neighboring sensors, requiring only neighbors to exchange information. The algorithm provides guarantees on detection delay and false alarm probability. This appears to be the first work to offer such guarantees for a multiple sensor network. Based on the performance guarantees, we compute a tradeoff between sensor node density, detection delay and energy consumption. We also address synchronization, finite storage and data quantization. We validate our approach with some example applications.

Simultaneous Optimization of Sensor Placements and Balanced Schedules

We consider the problem of monitoring spatial phenomena, such as road speeds on a highway, using wireless sensors with limited battery life. A central question is to decide where to locate these sensors to best predict the phenomenon at the unsensed locations. However, given the power constraints, we also need to determine when to activate these sensors in order to maximize the performance while satisfying lifetime requirements. Traditionally, these two problems of sensor placement and scheduling have been considered separately; one first decides where to place the sensors, and then when to activate them.

Real-Time Measurement of Link Vehicle Count and Travel Time in a Road Network

A system is described that measures the vehicle count and travel time in the links of a road network. The measurements require matching vehicle signatures recorded by a wireless magnetic sensor network. The matching algorithm is based on a statistical model of the signatures. The model itself is estimated from the data. The approach is first discussed for a single-lane road and extended to multiple-lane roads. The algorithm yields a correct matching rate of 75% for a false matching rate of 5% and reliably estimates the number of vehicles on each link and its travel-time distribution. The system is tested on a 0.9-mi-long segment of San Pablo Avenue, Albany, CA.

RSSI-Fingerprinting-Based Mobile Phone Localization With Route Constraints

Accurate positioning of a moving vehicle along a route enables various applications, such as travel-time estimation, in transportation. Global Positioning System (GPS)-based localization algorithms suffer from low availability and high energy consumption. A received signal strength indicator (RSSI) measured in the course of the normal operation of Global System for Mobile Communications (GSM)-based mobile phones, on the other hand, consumes minimal energy in addition to the standard cell-phone operation with high availability but very low accuracy. In this paper, we incorporate the fact that the motion of vehicles satisfies route constraints to improve the accuracy of the RSSI-based localization by using a hidden Markov model (HMM), where the states are segments on the road, and the observation at each state is the RSSI vector containing the detected power levels of the pilot signals sent by the associated and neighboring cellular base stations. In contrast to prior HMM-based models, we train the HMM based on the statistics of the average drivers behavior on the road and the probabilistic distribution of the RSSI vectors observed in each road segment. We demonstrate that this training considerably improves the accuracy of the localization and provides localization performance robust over different road segment lengths by using extensive cellular data collected in Istanbul, Turkey; Berkeley, CA, USA; and New Delhi, India.

Optimal electric energy storage operation

Estimating the arbitrage value of storage is an important problem in power systems planning. Various studies have reported different values based numerical solutions of variations of a basic model. In this paper, we instead rely on a closed form solution for storage control. The closed form highlights the right type of forecasting that is required and allows large horizon problems to be solved. We study various scenarios and provide a simple methodology for evaluating the arbitrage value of storage.