Abstract
We consider a farm of Kite Power Systems (KPS) in the field of Airborne Wind Energy (AWE), in which each kite is connected to an electric ground generator by a tether. In particular, we address the problem of selecting the best layout of such farm in a given land area such that the total electrical power generated is maximized. The kites, typically, fly at high altitudes, sweep a greater area than that of traditional wind turbines, and move within a conic shaped volume with vertex on the ground station. Therefore, constraints concerning kite collision avoidance and terrain boundaries must be considered. The efficient use of a given land area by a set of KPS depends on the location of each unit, on its tether length and on the elevation angle. In this work, we formulate the KPS farm layout optimization problem. Considering a specific KPS and wind characteristics of the given location, we study the power curve as a function of the tether length and elevation angle. Combining these results with an area with specified length and width, we develop and implement a heuristic optimization procedure to devise the layout of a KPS farm that maximizes wind power generation. (C) 2019 Published by Elsevier Ltd.

Abstract
An Airborne Wind Energy System (AWES) is a concept to convert wind energy into electricity, which comprises a tethered aircraft connected to a ground station. These systems are capable of harvesting high altitude winds, which are more frequent and more consistent. Among AWES, there are Pumping Kite Generators (PKG) that involve a rigid or flexible kite connected to a motor/generator placed on the ground through a light-weight tether. Such PKG produces electrical power in a cyclical two-phased motion with a traction phase and a retraction phase. During the traction phase, the aim is to maximize power production. This goal is achieved by controlling the kite such that it performs an almost crosswind motion, keeping a low elevation angle in order to maximize the tether tension. During the retraction phase, the tether tension force is minimized by steering the kite while the tether is reeled-in. Such strategy assures that the cyclical two-phased motion has a positive electrical balance at the end of the overall cycle. In a first stage, we solve an optimal control problem to compute the optimal plan for the kite trajectory during the traction phase, maximizing power production. Such trajectory is then used to define a time-independent geometrical path, which in turn is used as the reference path for the path-following control procedure that is developed in a second stage, and for which results are also presented. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
In this work, we study a mathematical model for a smart irrigation system, formulated as an optimal control problem and discretized and transcribed into a nonlinear programming problem using a fine mesh. In order to solve the resulting optimization problem, one needs to use Optimization solvers. Hence, we implemented the proposed mathematical model in AMPL and solved it using the IPOPT solver on the NEOS server (https://neos-server.org/neos/index.html). We also tested the model creating several scenarios. The numerical results shows that the mathematical model produces qualitatively good responses. Moreover the execution times are made in few seconds. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
We consider the problem of planning the aggregate energy consumption for a set of thermostatically controlled loads for demand response, accounting price forecast trajectory, and thermal comfort constraints. We address this as a continuous-time optimal control problem, and analytically characterize the structure of its solution in the general case. In the special case when the price forecast is monotone and the loads have equal dynamics, we show that it is possible to determine the solution in an explicit form. Taking this fact into account, we handle the non-monotone price case by considering several subproblems, each corresponding to a time subinterval where the price function is monotone, and then allocating to each subinterval a fraction of the total energy budget. This way, for each time subinterval, the problem reduces to a simple convex optimization problem with a scalar decision variable, for which a descent direction is also known. The price forecasts for the day-ahead energy market typically have no more than four monotone segments, so the resulting optimization problem can be solved efficiently with modest computational resources. © 2017 IEEE.

Abstract
We consider the problem of determining the optimal aggregate power consumption of a population of thermostatically controlled loads such as air conditioners. This is motivated by the need to synthesize the demand response for a load serving entity (LSE) catering a population of such customers. We show how the LSE can opportunistically design the aggregate reference consumption to minimize its energy procurement cost, given day-ahead price, load forecast, and ambient temperature forecast, while respecting each individual load's comfort range constraints. The resulting synthesis problem is intractable when posed as a direct optimization problem after Euler discretization of the dynamics, since it results in a mixed-integer linear programming problem with number of variables typically of the order of millions. In contrast, in this paper, we show that the problem is amenable to continuous-time optimal control techniques. Numerical simulations elucidate how the LSE can use the optimal aggregate power consumption trajectory thus computed, for the purpose of demand response.

Abstract
We address the problem of generating electrical power through Airborne Wind Energy Systems, using a kite connected to a generator on the ground. We propose a controller to steer the kite to follow a pre-defined eight-shaped path based on a nonlinear guidance logic. The controller has an easy implementable explicit form, has asymptotic stability guarantees and a large domain of attraction. We report simulations of a complete production cycle, including a production phase and a recovery phase. Also, we provide a Lyapunov stability analysis. © 2019 American Automatic Control Council.