A Stochastic Resource-Sharing Network for Electric Vehicle Charging

We consider a distribution grid used to charge electric vehicles such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We focus on resource-sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of EVs. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. We illustrate our findings with a case study using the SCE 47-bus network and several special cases that allow for explicit computations.Comment: 13 pages, 8 figure

A stochastic resource-sharing network for electric vehicle charging

We consider a distribution grid used to charge electric vehicles subject to voltage stability and various other constraints. We model this as a class of resource

Asymptotic analysis of Emden–Fowler type equation with an application to power flow models

Emden–Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden–Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model. Thus, we place Emden–Fowler type equations in the context of electrical engineering. We derive properties of the continuous solution of this specific Emden–Fowler type equation and study the asymptotic behavior of its discrete analog. We conclude that the discrete analog has the same asymptotic behavior as the classical continuous Emden–Fowler type equation that we consider.</p

Asymptotic analysis of Emden–Fowler type equation with an application to power flow models

Emden–Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden–Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model. Thus, we place Emden–Fowler type equations in the context of electrical engineering. We derive properties of the continuous solution of this specific Emden–Fowler type equation and study the asymptotic behavior of its discrete analog. We conclude that the discrete analog has the same asymptotic behavior as the classical continuous Emden–Fowler type equation that we consider

A stochastic resource-sharing network for electric vehicle charging

We consider a distribution grid used to charge electric vehicles subject to voltage stability and various other constraints. We model this as a class of resource-sharing networks known as bandwidth-sharing networks in the communication network literature. Such networks have proved themselves to be an effective flow-level model of data traffic in wired and wireless networks. We focus on resource sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system, subject to voltage stability constraints, by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of cars. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. For the class of weighted proportional fairness control, we show additional appealing properties under the linearized Distflow model, such as fairness, and a product form property of the stochastic model

A stochastic resource-sharing network for electric vehicle charging

We consider a distribution grid used to charge electric vehicles subject to voltage stability and various other constraints. We model this as a class of resource-sharing networks known as bandwidth-sharing networks in the communication network literature. Such networks have proved themselves to be an effective flow-level model of data traffic in wired and wireless networks. We focus on resource sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system, subject to voltage stability constraints, by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of cars. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. For the class of weighted proportional fairness control, we show additional appealing properties under the linearized Distflow model, such as fairness, and a product form property of the stochastic model