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)
The paper proposes a mechanism for real-time retail pricing of electricity in smart power grids, with price stability as the primary concern. In previous articles, the authors argued that relaying the real-time wholesale market prices to the end consumers creates a closed loop feedback system which could be unstable or lack robustness, leading to extreme(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 realtime wholesale electricity market prices to the end consumers. The effects that such mechanisms could pose on the stability and efficiency(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)
We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we(More)
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)
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)