Saptarshi Bhattacharya

Price-driven charging of Plug-in Electric Vehicles: Nash equilibrium, social optimality and best-response convergence

As the number of charging Plugged-in Electric Vehicles (PEVs) increase, it is crucial to control the charging of PEVs in order to minimize energy generation and transmission costs, and ensure grid stability. In this work, we analyze the equilibrium properties of a natural price-driven charging control game in the distribution grid, between the utility (that sets the time-dependent energy usage price) and selfish PEVs (that choose their own charging schedules to minimize individual cost). We demonstrate through analysis and simulations that individual best-response strategies converge to socially optimal charging profiles (also equilibrium solutions) under fairly weak assumptions on the (asynchronous) charging profile update processes. We also discuss how the framework can be extended to consider the topology of the distribution tree and associated transmission line capacity constraints.

Extended Second Price Auctions With Elastic Supply for PEV Charging in the Smart Grid

In this paper, we explore the question of efficient allocation of energy, while buying the same from generation companies, to plug-in electric vehicles (PEVs) by aggregator (electricity utility or load serving entities) through auction mechanisms. Recognizing the practical limitations of the Vickrey–Clarke–Groves mechanism, which would be natural to apply in this context, we investigate two practical mechanisms that can be viewed as extensions of second price auction mechanisms and have limited message (bid) complexity. In the first mechanism, the elastic-supply multi-level second price, each PEV agent submits a number of price bids, one for each of a given set of energy levels (energy quantities). In the second mechanism, the elastic-supply progressive second price, the PEV agents submit a 2-D bid indicating the price as well as the desired energy quantity. Taking into account differences across PEV-owners in terms of their willingness-to-pay values and charging time constraints, we analyze the social optimality and incentive compatibility properties of the two auction mechanisms. We also complement our theoretical findings with numerical simulations.

Extended second price auctions for Plug-in Electric Vehicle (PEV) charging in smart distribution grids

Large scale deployment of Plug-in Electric Vehicles (PEVs) in the smart grid environment necessitates the use of appropriate charging control algorithms that handle the additional PEV based load effectively. While ensuring grid stability, these PEV charging control algorithms must ensure that the available energy is delivered to where it is needed the most. In this paper, we explore the question of efficient allocation of energy (charging rates and schedules) to PEVs by the aggregator (electricity utility) through an auction mechanism. Recognizing the practical limitations of the Vickrey-Clark-Groves (VCG) mechanism which would be natural to apply in this context, we investigate two practical mechanisms that can be viewed as extensions of second price auction mechanisms, and have limited message (bid) complexity. In the first mechanism, the multi-level second price (MSP), each PEV agent submits a number of price bids, one for each of a given set of energy levels (energy quantities). In the second mechanism, the progressive second price (PSP), the PEV agents submit a two-dimensional bid indicating the price as well as the desired energy quantity. Taking into account differences across PEV-owners in terms of their willingness-to-pay values and charging time constraints, we analyze the social optimality and incentive compatibility properties of the two auction mechanisms.

Thermally-fair demand response for district heating and cooling (DHC) networks

District heating and cooling networks (DHCs) are complex thermal grids wherein a centrally heated/cooled fluid is circulated through a network of pipes and heat exchangers to meet the heating/cooling needs of residential and commercial buildings. Several factors can hinder efficiencies and impartial distribution of energy among customers in these networks. These include varying levels of building insulation, distance of individual buildings from the central energy source, and thermal losses in network pipes. Moreover, shortage of energy at the central energy source and extreme weather conditions can exacerbate these issues, leading to differing levels of thermal comfort and customer disgruntlement in the long run. In this paper, we propose and study a demand response scheme that attempts to ensure thermal fairness among end-use energy consumers in modern thermal grids. We develop optimization formulations based on thermodynamic models of DHCs, which determine optimal heat inflow/thermostat settings for individual buildings in order to achieve targeted thermal fairness across the network. Our experimental results using physics based models for DHC networks show that it is possible to achieve targeted thermal fairness based social welfare objectives in the DHC network by controlling network parameters such as mass flow rates of water to the consumer premises and the supply water temperature.

Optimal precooling of thermostatic loads under time-varying electricity prices

In this work, we consider the problem of optimal precooling of thermostatic loads by a load serving entity (LSE) under time varying electricity prices. Specifically, we propose a low complexity dynamic programming based algorithm for controlling the switching of HVAC units such that the cost of cooling is minimized while ensuring that the resultant temperatures do not violate the comfort constraints of consumers. Specifically, our algorithm makes use of two facts: (i) the price of electricity vary discretely in time and (ii) the cost-optimal state trajectory under fixed electricity price and ambient temperature, with given initial and final states, can be characterized explicitly in closed-form. We validate our algorithm with a set of numerical simulation studies using real market prices of electricity from the New York electricity market.

Fairness based Demand Response in DHC networks using real time parameter identification

Modern day District Heating and Cooling (DHC) networks are complex interconnections of heat energy sources and heat energy consumers wherein the available energy from the sources is networked to the consumers for meeting their space heating (or cooling) requirements. Often, the energy sources are renewables and thermal run-off from industrial processes which are intermittent. Under extremely exigent conditions (such as very low ambient temperatures), these DHC networks may potentially suffer from energy supply inadequacy. Subsequently, selfish uncoordinated control of heat energy inflow at distributed consumer premises can lead to unfair allocation of the already inadequate energy to different consumers, potentially leading to consumer disgruntlement. Factors such as thermal losses in the network, varying levels of building insulation and different building heat capacities only exacerbate these issues. In this paper, we propose a policy for implementing Demand Response (DR) in DHC networks with an objective of optimizing different fairness based objectives. Specifically, our proposed algorithm estimates dynamically evolving building thermal parameters from continuously recorded temperature sensor measurements from different points in the network. It then uses this knowledge to suggest suitable control of network parameters such as mass flow rate of fluid to the buildings in order to realize the network level thermal fairness based objectives.

DReAM: Demand Response Architecture for Multi-level District Heating and Cooling Networks

In this paper, we exploit the inherent hierarchy of heat exchangers in District Heating and Cooling (DHC) networks and propose DReAM, a novel Demand Response (DR) architecture for Multi-level DHC networks. DReAM serves to economize system operation while still respecting comfort requirements of individual consumers. Contrary to many present day DR schemes that work on a consumer level granularity DReAM works at a level of hierarchy above buildings, i.e. substations that supply heat to a group of buildings. This improves the overall DR scalability and reduce the computational complexity. In the first step of the proposed approach, mathematical models of individual substations and their downstream networks are abstracted into appropriately constructed low-complexity structural forms. In the second step, this abstracted information is employed by the utility to perform DR optimization that determines the optimal heat inflow to individual substations rather than buildings, in order to achieve the targeted objectives across the network. We validate the proposed DReAM framework through experimental results under different scenarios on a test network.

Adaptive thermostat control in residential buildings through uniform clearing price mechanism

Demand response (DR) is potentially an effective tool in the smart grid that allows shifting electric load demand to less congested time slots. These peak-load shaving measures serve to alleviate grid congestion, minimize cost of electricity generation and help in reducing the electricity bills of retail customers. This work considers a demand response approach whereby the local electricity utility (aggregator or load serving entity) takes control of the thermostat of the buildings of participating customers and retains the right to regulate the temperature upto a user-defined amount when the grid is approaching overload conditions. A customers participating in this program declare its user discomfort index, which is a measure of the amount of money the customer expects in return from the utility for temporarily relinquishing its thermostat control. Based on these declared values and the thermal characteristics of the buildings (assumed to be known/estimated by utilities), the utility implements a selection algorithm to choose the least expensive buildings and controls their temperature in return for monetary compensation (or credits). We compare and study the properties of this DR mechanism under two different payment rules associated with: (a) the pay-as-you-bid mechanism, and (b) the uniform clearing price mechanism. Under a test scenario, we demonstrate that such mechanisms are able to bring down overall demand while ensuring the utility does not lose any money. It also ensures that participating customers get a discount on their monthly electricity bills while at the same time resulting in substantial peak-load shaving.

Hedging strategies for risk reduction through weather derivatives in renewable energy markets

Weather elements such as temperature and solar radiation play a crucial role in renewable power production as well as in power consumption. In this research, we address risk management issues of a power producer for its weather, price and production risk exposures. We investigate the extent of natural hedge embedded in the dependence of power production using renewable energy sources and power consumption on weather risk elements. We further develop a framework to construct explicit cross hedges for the risk management objectives of a renewable power producer using weather derivatives: a relatively new class of financial instruments for weather risk management.