Yunjian Xu

Demand Response With Capacity Constrained Supply Function Bidding

We study the problem faced by an operator who aims to allocate a certain amount of load adjustment (either load reduction or increment) to multiple consumers so as to minimize the aggregate consumer disutility. We propose and analyze a simple uniform-price market mechanism where every consumer submits a single bid to choose a supply function from a group of parameterized ones. These parameterized supply functions are designed to ensure that every consumers load adjustment is within an exogenous capacity limit that is determined by the current power system operating condition. We show that the proposed mechanism yields bounded efficiency loss at a Nash equilibrium. In particular, the proposed mechanism is shown to achieve approximate social optimality at a Nash equilibrium, if the total capacity limit excluding the consumer with the largest one is much larger than the total amount of load to be adjusted. We complement our analysis through numerical case studies.

On the operation and value of storage in consumer demand response

We study the optimal operation and economic value of energy storage operated by a consumer who faces (possibly random) fluctuating electricity prices and seeks to reduce its energy costs. The value of storage is defined as the consumers net benefit obtained by optimally operating the storage. We formulate the operation problem as a dynamic program. Under the assumption that consumer utility (received from electricity consumption) is additively separable over time, we establish a threshold structure of the optimal operation policy for a consumer who faces random electricity prices and stochastic demand. For a more general setting that incorporates the inter-temporal substitution effect in consumer demand, if the consumer always faces the same (realized) purchasing and selling price, then it is optimal for her to use the storage only for arbitrage, and therefore the VoS does not depend on the consumers demand.

On incentive compatibility of deadline differentiated pricing for deferrable demand

A large fraction of the total electric load is comprised of end-use devices whose demand is inherently deferrable in time. While this latent flexibility in demand can be leveraged to absorb variability in supply from renewable generation, the challenge lies in designing incentives to induce the desired response in demand. In the following, we study a novel forward market, where consumers consent to deferred service of pre-specified loads in exchange for a reduced per-unit price for energy. The longer a customer is willing to defer, the larger the reduction in price. The proposed deadline-differentiated forward contract provides a guarantee on the aggregate quantity to be delivered by a consumer-specified deadline. Under the earliest-deadline-first (EDF) scheduling policy, which is shown to be optimal for the supplier, we explicitly characterize differentiated prices yielding an efficient competitive equilibrium between supply and demand. We also show that such prices are incentive compatible (IC) in that every consumer would like to reveal her true deadline type to the supplier, provided that the other consumers are truth-telling.

The Economics of the Cloud

This article proposes a model to study the interaction of price competition and congestion in the cloud computing marketplace. Specifically, we propose a three-tier market model that captures a marketplace with users purchasing services from Software-as-a-Service (SaaS) providers, which in turn purchase computing resources from either Provider-as-a-Service (PaaS) or Infrastructure-as-a-Service (IaaS) providers. Within each level, we define and characterize market equilibria. Further, we use these characterizations to understand the relative profitability of SaaSs and PaaSs/IaaSs and to understand the impact of price competition on the user experienced performance, that is, the “price of anarchy” of the cloud marketplace. Our results highlight that both of these depend fundamentally on the degree to which congestion results from shared or dedicated resources in the cloud.

A Unifying Market Power Measure for Deregulated Transmission-Constrained Electricity Markets

Market power assessment is a prime concern when designing a deregulated electricity market. In this paper, we propose a new functional market power measure, termed transmission constrained network flow (TCNF), that unifies three large classes of transmission constrained structural market power indices in the literature: residual supply based, network flow based, and minimal generation based. Furthermore, it is suitable for demand-response and renewable integration and hence more amenable to identifying market power in the future smart grid. The measure is defined abstractly, and allows incorporation of power flow equations in multiple ways; we investigate the current market operations using a DC approximation and further explore the possibility of including detailed AC power flow models through semidefinite relaxation, and interior-point algorithms from Matpower. Finally, we provide extensive simulations on IEEE benchmark systems and highlight the complex interaction of engineering constraints with market power assessment.

Cooperation of Storage Operation in a Power Network With Renewable Generation

In this paper, we seek to properly schedule the operation of multiple storage devices so as to minimize the expected total cost (of conventional generation) in a power network with intermittent renewable generation. Since the power network constraints make it intractable to compute optimal storage operation policies through dynamic programming-based approaches, we propose a Lyapunov optimization-based online algorithm (LOPN), which makes decisions based only on the current state of the system (i.e., the current demand and renewable generation). The proposed algorithm is computationally simple and achieves asymptotic optimality (as the capacity of energy storage grows large). To improve the performance of the LOPN algorithm for the case with limited storage capacity, we propose a threshold-based energy storage management (TESM) algorithm that utilizes the forecast information (on demand and renewable generation) over the next a few time slots to make storage operation decisions. Numerical experiments are conducted on IEEE 6- and 9-bus test systems to validate the asymptotic optimality of LOPN, and compare the performance of LOPN and TESM. Numerical results show that TESM significantly outperforms LOPN when the storage capacity is relatively small.

Meeting Inelastic Demand in Systems With Storage and Renewable Sources

We consider a system where inelastic demand for electric power is met from three sources: 1) the grid; 2) in-house renewables such as solar panels; and 3) an in-house energy storage device. In our setting, energy demand, renewable power supply, and cost for grid power are all time-varying and stochastic. Furthermore, there are limits and inefficiency associated with charging and discharging the energy storage device. We formulate the storage operation problem as a dynamic program with parameters estimated from real-world demand, supply, and cost data. As the dynamic program is computationally intensive for large-scale problems, we explore algorithms based on approximate dynamic programming (ADP) and apply them to a test data set. Using the real-world test data, we numerically compare the performance of two ADP-based algorithms against Lyapunov optimization-based algorithms that require no statistical knowledge. Our results ascertain the value of storage and the value of installing a renewable source.

The economics of the cloud: price competition and congestion

This letter provides an overview of our recent work studying the impacts of price competition and congestion in the cloud marketplace. Specifically, we discuss a three-tier market model that studies a vertical marketplace where users purchase services from Software-as-a-Service (SaaS) providers, which in turn purchase computing resources from either Provider-as-a-Service (PaaS) or Infrastructure-as-a-Service (IaaS) providers.Jonatha Anselmi Basque Center for Applied Mathematics Danilo Ardagna Dip. di Elettronica e Informazione, Politecnico di Milano John C.S. Lui Computer Science & Engineering, Chinese University of Hong Kong Adam Wierman Computing and Mathematical Sciences, California Inst. of Technology Yunjian Xu Computing and Mathematical Sciences, California Inst. of Technology Zichao Yang Computer Science & Engineering, Chinese University of Hong Kong

Deadline Differentiated Pricing of Deferrable Electric Loads

A large fraction of total electricity demand is comprised of end-use devices whose demand for energy is inherently deferrable in time. Of interest is the potential to use this latent flexibility in demand to absorb variability in power supplied from intermittent renewable generation. A fundamental challenge lies in the design of incentives that induce the desired response in demand. With an eye to electric vehicle charging, we propose a novel forward market for deadline-differentiated electric power service, where consumers consent to deferred service of prespecified loads in exchange for a reduced price for energy. The longer a consumer is willing to defer, the lower the price for energy. The proposed forward contract provides a guarantee on the aggregate quantity of energy to be delivered by a consumer-specified deadline. Under the earliest-deadline-first (EDF) scheduling policy, which is shown to be optimal for the supplier, we explicitly characterize a non-discriminatory, deadline-differentiated pricing scheme that yields an efficient competitive equilibrium between the supplier and consumers. We further show that this efficient pricing scheme, in combination with EDF scheduling, is incentive compatible in that every consumer would like to reveal her true deadline to the supplier, regardless of the actions taken by other consumers.

On the value of storage at consumer locations

We study the economic value of energy storage operated by a consumer who faces fluctuating electricity prices and seeks to reduce its energy costs. The value of storage is defined as the consumers net benefit obtained by optimally operating the storage. We formulate the operation problem as a dynamic program. For a general setting with random electricity prices and stochastic demand, we show that by solving a sequence of (deterministic) convex optimization problems one can obtain an optimal operation policy as well as the value of storage. For an important special case where the consumer is faced with deterministic time-variant prices and (deterministic) inelastic demand, we propose a simple greedy algorithm that simultaneously computes the optimal operation policy and the economic value of a finite-capacity electric storage. We employ the proposed algorithm to numerically explore the value of storage under different pricing mechanisms.