We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously differentiable exact penalty function. This reformulation is based on replacing the Lagrange multipliers in the augmented Lagrangian of the original problem by Lagrange multiplier functions. The expressions of these Lagrange multiplier functions, which depend upon the gradients of the objective function and the constraints, can make the unconstrained penalty function non-convex in general even if the original problem is convex. We establish sufficient conditions on the objective function and the constraints of the original problem under which the unconstrained penalty function is convex. This enables us to use Nesterov's accelerated gradient method for unconstrained convex optimization and achieve a guaranteed rate of convergence which is better than the state-of-the-art first-order algorithms for constrained convex optimization. Simulations illustrate our results.
This paper presents one of the first real-life demonstrations of coordinated and distributed resource control for secondary frequency response in a power distribution grid. A series of tests involved up to 69 heterogeneous active distributed energy resources consisting of air handling units, unidirectional and bidirectional electric vehicle charging stations, a battery energy storage system, and 107 passive distributed energy resources consisting of building loads and solar photovoltaic systems. The distributed control setup consists of a set of Raspberry Pi endpoints exchanging messages via an ethernet switch. Actuation commands for the distributed energy resources are obtained by solving a power allocation problem at every regulation instant using distributed ratio-consensus, primal-dual, and Newton-like algorithms. The problem formulation minimizes the sum of distributed energy resource costs while tracking the aggregate setpoint provided by the system operator. We demonstrate accurate and fast real-time distributed computation of the optimization solution and effective tracking of the regulation signal over 40minute time horizons. An economic benefit analysis confirms eligibility to participate in an ancillary services market and demonstrates up to $49k of potential annual revenue for the selected population of distributed energy resources.
A photovoltaic cell produces electrical energy directly from visible light. However, their efficiency is fairly low. So, the solar cell costs expensive as compared to other energy resources products. Various factors affect solar cell efficiency. This paper presents the most important factors that affecting efficiency of solar cells. These effects are cell temperature, MPPT (maximum power point tracking) and energy conversion efficiency. The changing of these factors improves solar cell efficiency for more reliable applications. There is a large energy demand due to industrial development and population growth especially in India. The main challenge in replacing conventional energy sources with newer and more environmentally friendly alternatives, such as solar and wind energy, is how to capture the maximum energy and deliver the maximum power at a minimum cost for a given load. The output power of photovoltaic cells or solar panels has nonlinear characteristics and these are also affected by temperature, light intensity and load.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.