Mardavij Roozbehani

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—The paper proposes a framework for modeling and analysis of the dynamics of supply, demand, and clearing prices in power systems with real-time retail pricing and information asymmetry. Characterized by passing on the real-time wholesale electricity prices to the end consumers, real-time pricing creates a closed-loop feedback system between the physical(More)
We study the problem of approximating the joint spectral radius (JSR) of a finite set of matrices. Our approach is based on the analysis of the underlying switched linear system via inequalities imposed between multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class(More)
In previous works, the authors introduced a framework for software analysis, which is based on optimization of Lyapunov invari-ants. These invariants prove critical software properties such as absence of overflow and termination in finite time. In this paper, graph models of software are introduced and the software analysis framework is further developed(More)
— The paper proposes a mathematical model for describing the dynamic evolution of supply, demand, and market clearing prices under real-time pricing mechanisms that pass on–either directly or a (static) function of–the real-time wholesale electricity market prices to the end consumers. The effects that such mechanisms could pose on the stability and(More)
—This paper is concerned with optimal utilization of storage, characterization of the economic value of storage in the presence of ramp-rate constraints and stochastically-varying electricity prices, and characterization of the price elasticity of demand induced by optimal utilization of storage. The ramp constraints limit the charging and discharging rate(More)
Modeling and analysis techniques are presented for real-time, safety-critical software. Software analysis is the task of verifying whether the computer code will execute safely, free of run-time errors. The critical properties that prove safe execution include bounded-ness of variables and termination of the program in a finite number of steps. In this(More)
  • M Roozbehani, M Rinehart, M A Dahleh, S K Mitter, D Obradovic, H Mangesius
  • 2011
—In this paper, we propose a new real-time retail pricing model characterized by ex-post adjustments to exanté price, and investigate the stability and efficiency properties of the ensuing closed loop system. Under this pricing mechanism, electricity is priced at the exanté price (calculated based on predicted demand) up to the amount consumed at the(More)
—This paper presents a mathematical model of consumer behavior in response to stochastically-varying electricity prices, and a characterization of price elasticity of consumption induced by optimally shifting flexible demands within a fixed time window. The approach is based on deriving the optimal load-shifting policy through a finite horizon stochastic(More)