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Vijay Gupta

Publications and source records attributed to Vijay Gupta.

106 records · Page 6Linked to original sources
arXiv2016

Minimizing Risk of Load Shedding and Renewable Energy Curtailment in a Microgrid with Energy Storage

We consider a microgrid with random load realization, stochastic renewable energy production, and an energy storage unit. The grid controller provides the total net load trajectory that the microgrid should present to the main grid and the microgrid must impose load shedding and renewable energy curtailment if necessary to meet that net load trajectory. The microgrid controller seeks to operate the local energy storage unit to minimize the risk of load shedding, and renewable energy curtailment over a finite time horizon. We formulate the problem of optimizing the operation of the storage unit as a finite stage dynamic programming problem. We prove that the multi-stage objective function of the energy storage is strictly convex in the state of charge of the battery at each stage. The uniqueness of the optimal decision is proven under some additional assumptions. The optimal strategy is then obtained. The effectiveness of the energy storage in decreasing load shedding and RE curtailment is illustrated in simulations.

math.OC↗
arXiv2016

Pricing Energy in the Presence of Renewables

At present, electricity markets largely ignore the fact that renewable power producers impose significant externalities on non-renewable energy producers. This is because consumers are generally guaranteed electricity within certain load parameters. The intermittent nature of production by renewable energy producers implies that they rely on non-renewable producers so that the aggregate power delivered meets the promised quality of service. This implicit insurance provided by the non-renewable power sector to consumers is not currently priced and leads to an often ignored, hidden monetary transfer from non-renewable producers to renewable producers. As the fraction of energy supplied by renewable resources increases, these externalities also increase. In this paper, we quantify these externalities by developing the market clearing price of energy in the presence of renewable energy. We consider a day-ahead electricity market where renewable and non-renewable generators bid by proposing their asking price per unit of energy to an independent system operator (ISO). The ISO's problem is a multi-stage stochastic optimization problem to dispatch energy from each generator to minimize the cost of purchased energy on behalf of the consumers. We incorporate the notion of load variance using the Conditional Value-at-Risk (CVAR) measure in the day-ahead electricity market to ensure that the generators are able to meet the load within a desired confidence level. We analytically derive the market clearing price of energy as a function of CVAR. It is shown that a higher penetration level of the renewable energies may increase the market clearing price of energy.

math.OC↗
arXiv2016

Incentivizing Truth-Telling in MPC-based Load Frequency Control

We present a mechanism for socially efficient implementation of model predictive control (MPC) algorithms for load frequency control (LFC) in the presence of self-interested power generators. Specifically, we consider a situation in which the system operator seeks to implement an MPC-based LFC for aggregated social cost minimization, but necessary information such as individual generators' cost functions is privately owned. Without appropriate monetary compensation mechanisms that incentivize truth-telling, self-interested market participants may be inclined to misreport their private parameters in an effort to maximize their own profits, which may result in a loss of social welfare. The main challenge in our framework arises from the fact that every participant's strategy at any time affects the future state of other participants; the consequences of such dynamic coupling has not been fully addressed in the literature on online mechanism design. We propose a class of real-time monetary compensation schemes that incentivize market participants to report their private parameters truthfully at every time step, which enables the system operator to implement MPC-based LFC in a socially optimal manner.

math.OC↗
arXiv2016

Approximation by (p,q)-Baskakov-Beta operators

In the present paper, we consider $(p,q)$-analogue of the Baskakov-Beta operators and using it, we estimate some direct results on approximation. Also, we represent the convergence of these operators graphically using MATLAB.

math.CA↗
arXiv2016

(p,q)-Beta Functions and Applications in Approximation

In the present paper, we consider (p,q)-analogue of the Beta operators and using it, we propose the integral modification of the generalized Bernstein polynomials. We estimate some direct results on local and global approximation. Also, we illustrate some graphs for the convergence of (p,q)-Bernstein-Durrmeyer operators for different values of the parameters p and q using Mathematica package.

math.CA↗
arXiv2015

Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.

math.OC↗
arXiv2015

Distributed Charging Control of Electric Vehicles Using Online Learning

We propose an algorithm for distributed charging control of electric vehicles (EVs) using online learning and online convex optimization. Many distributed charging control algorithms in the literature implicitly assume fast two-way communication between a distribution company and EV customers. This assumption is impractical at present and raises privacy and security concerns. Our algorithm does not use this assumption; however, at the expense of slower convergence to the optimal solution. The proposed algorithm requires one-way communication, which is implemented through the distribution company publishing the pricing profiles of the previous days. We provide convergence results of the algorithm and illustrate the results through numerical examples.

math.OC↗
arXiv2015

Approximation by Complex Baskakov-Szasz-Durrmeyer Operators in Compact Disks

In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in the open disk of radius R. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on the positive real axis.

math.CA↗
arXiv2015

A Switched Dynamical System Framework for Analysis of Massively Parallel Asynchronous Numerical Algorithms

In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across processing elements (PEs) after each iteration, which results in significant idle time. Thus, there is a trend towards relaxing the synchronization and adopting an asynchronous model of computation to reduce idle time. However, it is not clear what is the effect of this relaxation on the stability and accuracy of the numerical algorithm. In this paper we present a new framework to analyze such algorithms. We treat the computation in each PE as a dynamical system and model the asynchrony as stochastic switching. The overall system is then analyzed as a switched dynamical system. However, modeling of massively parallel numerical algorithms as switched dynamical systems results in a very large number of modes, which makes current analysis tools available for such systems computationally intractable. We develop new techniques that circumvent this scalability issue. The framework is presented on a one-dimensional heat equation as a case study and the proposed analysis framework is verified by solving the partial differential equation (PDE) in a $\mathtt{nVIDIA\: Tesla^{\scriptsize{TM}}}$ GPU machine, with asynchronous communication between cores.

eess.SY↗
arXiv2015

On the trade-off between control performance and communication cost in event-triggered control

We consider a stochastic system where the communication between the controller and the actuator is triggered by a threshold-based rule. The communication is performed across an unreliable link that stochastically erases transmitted packets. To decrease the communication burden, and as a partial protection against dropped packets, the controller sends a sequence of control commands to the actuator in each packet. These commands are stored in a buffer and applied sequentially until the next control packet arrives. In this context, we study dead-beat control laws and compute the expected linear-quadratic loss of the closed-loop system for any given event-threshold. Furthermore, we provide analytical expressions that quantify the trade-off between the communication cost and the control performance of event-triggered control systems. Numerical examples demonstrate the effectiveness of the proposed framework.

eess.SY↗
arXiv2014

Moment Estimations of new Szász-Mirakyan-Durrmeyer operators

In [10] Jain introduced the modified form of the Szász-Mirakjan operator, based on certain parameter $0\leβ<1$. Several modifications of the operators are available in the literature. Here we consider actual Durrmeyer variant of the operators due to [10]. It is observed here that the Durrmeyer variant has the nice properties and one need not to take any restriction on $β$ in order to get convergence. We establish moments using the Tricomi's confluent hypergeometric function and Stirling numbers of first kind, also estimate some direct results

math.CA↗
arXiv2014

Anytime Control using Input Sequences with Markovian Processor Availability

We study an anytime control algorithm for situations where the processing resources available for control are time-varying in an a priori unknown fashion. Thus, at times, processing resources are insufficient to calculate control inputs. To address this issue, the algorithm calculates sequences of tentative future control inputs whenever possible, which are then buffered for possible future use. We assume that the processor availability is correlated so that the number of control inputs calculated at any time step is described by a Markov chain. Using a Lyapunov function based approach we derive sufficient conditions for stochastic stability of the closed loop.

math.OC↗
arXiv2013

Stochastic Stability of Event-triggered Anytime Control

We investigate control of a non-linear process when communication and processing capabilities are limited. The sensor communicates with a controller node through an erasure channel which introduces i.i.d. packet dropouts. Processor availability for control is random and, at times, insufficient to calculate plant inputs. To make efficient use of communication and processing resources, the sensor only transmits when the plant state lies outside a bounded target set. Control calculations are triggered by the received data. If a plant state measurement is successfully received and while the processor is available for control, the algorithm recursively calculates a sequence of tentative plant inputs, which are stored in a buffer for potential future use. This safeguards for time-steps when the processor is unavailable for control. We derive sufficient conditions on system parameters for stochastic stability of the closed loop and illustrate performance gains through numerical studies.

math.OC↗
arXiv2013

Sequence-based Anytime Control

We present two related anytime algorithms for control of nonlinear systems when the processing resources available are time-varying. The basic idea is to calculate tentative control input sequences for as many time steps into the future as allowed by the available processing resources at every time step. This serves to compensate for the time steps when the processor is not available to perform any control calculations. Using a stochastic Lyapunov function based approach, we analyze the stability of the resulting closed loop system for the cases when the processor availability can be modeled as an independent and identically distributed sequence and via an underlying Markov chain. Numerical simulations indicate that the increase in performance due to the proposed algorithms can be significant.

math.OC↗
arXiv2010

Convergence Speed of the Consensus Algorithm with Interference and Sparse Long-Range Connectivity

We analyze the effect of interference on the convergence rate of average consensus algorithms, which iteratively compute the measurement average by message passing among nodes. It is usually assumed that these algorithms converge faster with a greater exchange of information (i.e., by increased network connectivity) in every iteration. However, when interference is taken into account, it is no longer clear if the rate of convergence increases with network connectivity. We study this problem for randomly-placed consensus-seeking nodes connected through an interference-limited network. We investigate the following questions: (a) How does the rate of convergence vary with increasing communication range of each node? and (b) How does this result change when each node is allowed to communicate with a few selected far-off nodes? When nodes schedule their transmissions to avoid interference, we show that the convergence speed scales with $r^{2-d}$, where $r$ is the communication range and $d$ is the number of dimensions. This scaling is the result of two competing effects when increasing $r$: Increased schedule length for interference-free transmission vs. the speed gain due to improved connectivity. Hence, although one-dimensional networks can converge faster from a greater communication range despite increased interference, the two effects exactly offset one another in two-dimensions. In higher dimensions, increasing the communication range can actually degrade the rate of convergence. Our results thus underline the importance of factoring in the effect of interference in the design of distributed estimation algorithms.

cs.IT↗