## A rolling horizon approach for optimal management of microgrids under stochastic uncertainty

This paper proposes a hybrid particle swarm optimization algorithm in a rolling horizon framework to solve the aircraft landing problem (ALP). ALP is an important optimization problem in air traffic control and is well known as NP-hard. The problem consists of allocating the arriving aircrafts to runways at an airport and assigning a landing time to each aircraft. Each aircraft has an optimum target landing time determined based on its most fuel-efficient airspeed and a deviation from it incurs a penalty which is proportional to the amount of deviation.

Since the modeling is a crucial step in solving the ALP, we are concerned in this research with modeling the landing procedure of aircrafts for single and multiple runway system. The model solution for the static case using an exact method is presented. Computational experiments show the benefits of the proposed approach compared to the ATC rule applied to the aircrafts; the First Come First Served (FCFS) discipline. In order to reduce the impact of the randomness and volatility of renewable energy on the economic operation of AC/DC hybrid microgrids, a multi-time-scale rolling optimization strategy is proposed for the grid-connected AC/DC hybrid microgrids. It considers the source-load uncertainty declined with time scale reduction, and the scheduling cooperation problem of different units on different time scales.

In particular, we show that the error goes to zero for any fixed rolling horizon as this Doeblin measure of control over the future decreases. The theory is illustrated through an application to vehicle deployment. This paper investigates the effect of demand side management (DSM) program in distribution network on network losses and loading margin. The composite load model comprising constant impedance, constant current, constant power and induction motor loads is used to model the loads in the network.

To solve this challenging NP-hard problem, this paper develops a unique hybrid solution algorithm that combines a rolling horizon algorithm with an accelerated Benders decomposition algorithm. Extensive computational experiments are performed on benchmark test instances to evaluate the hybrid algorithm’s efficiency and robustness in solving the DFLP problem.

This paper will elaborate on whether such a system is also applicable for flights are faced with en-route delays, the most unpredictable part of arrival management. First the MILP model is extended to optimize the weekly operation schedule to better manage the heat-cold storage systems.

This enables a more accurate analysis of the changes in load flow and network loadability limit after applying a DSM program across all the buses in a distribution network with distributed generation. The analysis shows how shifting different load components (namely constant impedance load or induction motors), and reconnecting them at different times following a DSM action (the so called load payback) affect the network performance. The network used in this paper is a modified IEEE 33 bus distribution network Keywords-Demand side management, distribution network, load margin, network losses, load modelling.

## Energy

decomposition algorithm was developed that combines sample average approximation with an enhanced Progressive Hedging (PH) algorithm to solve this challenging NP-hard problem. Some heuristics such as Rolling Horizon (RH) heuristic, variable xing technique were later applied to further enhance the PH algorithm. Mississippi and Alabama were selected as a testing ground and ArcGIS was employed to visualize and validate the modeling results. The results of the analysis reveal promising insights that could lead to recommendations to help decision makers achieve a more cost-effective environmentally-friendly supply chain network.

Finally, the effect of the energy storage system on the proposed optimization problem is investigated. Under convective weather conditions, aircraft rerouting in terminal airspace is essential to ensure flight safety and reduce air traffic delays.

This work presents a Mixed Integer Linear Programming (MILP) approach based on a combination of a rolling horizon and stochastic programming formulation. The objective of the proposed formulation is the optimal management of the supply and demand of energy and heat in microgrids under uncertainty, in order to minimise the operational cost. Delays in the starting time of energy demands are allowed within a predefined time windows to tackle flexible demand profiles. This approach uses a scenario-based stochastic programming formulation.

These scenarios consider uncertainty in the wind speed forecast, the processing time of the energy tasks and the overall heat demand, to take into account all possible scenarios related to the generation and demand of energy and heat. Nevertheless, embracing all external scenarios associated with wind speed prediction makes their consideration computationally intractable. Hence, the two-stage stochastic MILP formulation is introduced into a rolling horizon approach that periodically updates input information.

The results obtained for a real-world test case are reported and discussed. By far the most common planning procedure found in practice is to approximate the solution to an infinite horizon problem by a series of rolling finite horizon solutions. Although many empirical studies have been done, this so-called rolling horizon procedure has been the subject of few analytic studies.

We provide a cost error bound for a general rolling horizon algorithm when applied to infinite horizon nonhomogeneous Markov decision processes, both in the discounted and average cost cases. We show that a Doeblin coefficient of ergodicity acts much like a discount factor to reduce this error.

- The objective of the proposed formulation is the optimal management of the supply and demand of energy and heat in microgrids under uncertainty, in order to minimise the operational cost.
- This work presents a Mixed Integer Linear Programming (MILP) approach based on a combination of a rolling horizon and stochastic programming formulation.

In this paper, we propose a three-time-scale optimal strategy of the day-ahead, intraday and real-time dispatching stage and a two-level rolling optimal strategy of the intraday and real-time stage, aiming at minimizing the operating cost. We added the power penalty cost in the rolling optimization model to limit the energy state of the energy storage system in the constraint, and improve the power correction and tracking effect of the rolling optimization. A typical-structure AC/DC hybrid microgrid is analyzed in this paper and the simulation results are shown to demonstrate the feasibility and effectiveness of the proposed multi-time-scale rolling optimal dispatch. Recently, there have been frequent fluctuations in the wholesale prices of electricity following the increased penetration of renewable energy sources.

The landing time of each aircraft is constrained within a specified time window and must satisfy minimum separation time requirement with its preceding aircrafts. The objective is to minimize the total penalty cost due to deviation of landing times of aircrafts from the respective target landing times.

Therefore, retailers face price risks caused by differences between wholesale prices and retail rates. As a hedging against price risk, retailers can utilize critical peak pricing (CPP) in a price-based program. This study proposes a novel multi-stage stochastic programming (MSSP) model for a retailer with self-generation photovoltaic facility to optimize both its bidding strategy and the CPP operation, in the face of several uncertainties. Using MSSP, decisions can be determined sequentially with realization of the uncertainties over time.

Furthermore, to ensure a global optimum, a mixed integer non-linear programming is transformed into mixed integer linear programming through three linearization steps. In a numerical simulation, the effectiveness of the proposed MSSP model is compared with that of a mean-value deterministic model based on a rolling horizon method. We also investigate the optimal strategy of a retailer by changing various input parameters and perform a sensitivity analysis to assess the impacts of different uncertain parameters on the retailer’s profit.

This could mean flights need to be delayed and wait in a holding area. A change is noticeable from conventional ad-hoc techniques to trajectory-based strategic and tactical planning and control tools. These solutions take a large number of variables into account and start the process of making an arrival sequence up to 500 nautical miles from the destination airport by the means of speed reduction to meet a set time for a certain waypoint. However, this requires a collaborative approach involved multiple organizations.

## Fuel-constrained preventive maintenance scheduling for an electric power utility

A rolling-horizon algorithm is proposed for optimizing the operating schedule of a given cogeneration energy system while taking into account time-variable loads, tariffs and ambient conditions, as well as yearly fiscal incentives. The presented algorithm is based on the Mixed Integer Linear Programming (MILP) model developed by the authors for optimizing the daily schedule of cogeneration systems and networks of heat and power plants. The energy hub optimization scheduling problem is formulated as a multi-period stochastic problem with the minimum total energy cost as the objective. Compared to 24-hour day-ahead scheduling, rolling horizon optimization is used in the EH scheduling and shows its superiority. In real-time rolling horizon scheduling, the optimization principle ensured that the result is optimized each moment, so it avoids energy waste caused by overbuying energy.

The performance of the proposed algorithm is evaluated on a set of benchmark instances involving upto 500 aircrafts and 5 runways. Computational results reveal that the proposed algorithm is effective in solving the problem in short computational time. The real time Aircraft Landing Problem (ALP) within an Air Traffic Control (ATC) system is typically a large scale problem.

Reading some papers , it seems a common way to reduce the optimization time of a Mixed Integer Linear Programming problem is to use something called Rolling Horizon, which is synonymous to Receding Horizon Control and Model Predictive Control. A higher demand for air traffic and increasing delays in airspace near some of the largest airports in the world provides a challenge for Air Navigation Service Providers. With the Single European Sky Air Traffic Management Research Program, a joint approach was initiated to deal with this problem that mainly occurs in the Terminal Maneuvering Areas. Prior to the approach, an arrival sequence is made that schedules the most optimal order in which flights approach.

Then traffic simulation is conducted to analyze the capacity and delays of the rerouting in the approach path in Shanghai terminal area. Experimental results indicate that this model can increase airspace capacity and operational efficiency of air traffic compared with the traditional air traffic rerouting approaches. This study presents a well-known capacitated dynamic facility location problem (DFLP) that satisfies the customer demand at a minimum cost by determining the time period for opening, closing, or retaining an existing facility in a given location.