Data-driven optimization of bus schedules under uncertainties

Plusieurs sous-problèmes d’optimisation se posent lors de la planification des transports publics. Le problème d’itinéraires de véhicule (PIV) est l’un d’entre eux et consiste à minimiser les coûts opérationnels tout en assignant exactement un autobus par trajet planifié de sorte que le nombre d’autobus entreposé par dépôt ne dépasse pas la capacité maximale disponible. Bien que les transports publics soient sujets à plusieurs sources d’incertitude (à la fois endogènes et exogènes) pouvant engendrer des variations des temps de trajet et de la consommation d’énergie, le PIV et ses variantes sont la plupart du temps résolus de façon déterministe pour des raisons de résolubilité. Toutefois, cette hypothèse peut compromettre le respect de l’horaire établi lorsque les temps des trajets considérés sont fixes (c.-à-d. déterministes) et peut produire des solutions impliquant des politiques de gestion des batteries inadéquates lorsque la consommation d’énergie est aussi considérée comme fixe. Dans cette thèse, nous proposons une méthodologie pour mesurer la fiabilité (ou le respect de l’horaire établi) d’un service de transport public ainsi que des modèles mathématiques stochastiques et orientés données et des algorithmes de branch-and-price pour deux variantes de ce problème, à savoir le problème d’itinéraires de véhicule avec dépôts multiples (PIVDM) et le problème d’itinéraires de véhicule électrique (PIV-E). Afin d’évaluer la fiabilité, c.-à-d. la tolérance aux délais, de certains itinéraires de véhicule, nous prédisons d’abord la distribution des temps de trajet des autobus. Pour ce faire, nous comparons plusieurs modèles probabilistes selon leur capacité à prédire correctement la fonction de densité des temps de trajet des autobus sur le long terme. Ensuite, nous estimons à l'aide d'une simulation de Monte-Carlo la fiabilité des horaires d’autobus en générant des temps de trajet aléatoires à chaque itération. Nous intégrons alors le modèle probabiliste le plus approprié, celui qui est capable de prédire avec précision à la fois la véritable fonction de densité conditionnelle des temps de trajet et les retards secondaires espérés, dans nos modèles d'optimisation basés sur les données. Deuxièmement, nous introduisons un modèle pour PIVDM fiable avec des temps de trajet stochastiques. Ce problème d’optimisation bi-objectif vise à minimiser les coûts opérationnels et les pénalités associées aux retards. Un algorithme heuristique basé sur la génération de colonnes avec des sous-problèmes stochastiques est proposé pour résoudre ce problème. Cet algorithme calcule de manière dynamique les retards secondaires espérés à mesure que de nouvelles colonnes sont générées. Troisièmement, nous proposons un nouveau programme stochastique à deux étapes avec recours pour le PIVDM électrique avec des temps de trajet et des consommations d’énergie stochastiques. La politique de recours est conçue pour rétablir la faisabilité énergétique lorsque les itinéraires de véhicule produits a priori se révèlent non réalisables. Toutefois, cette flexibilité vient au prix de potentiels retards induits. Une adaptation d’un algorithme de branch-and-price est développé pour évaluer la pertinence de cette approche pour deux types d'autobus électriques à batterie disponibles sur le marché. Enfin, nous présentons un premier modèle stochastique pour le PIV-E avec dégradation de la batterie. Le modèle sous contrainte en probabilité proposé tient compte de l’incertitude de la consommation d’énergie, permettant ainsi un contrôle efficace de la dégradation de la batterie grâce au contrôle effectif de l’état de charge (EdC) moyen et l’écart de EdC. Ce modèle, combiné à l’algorithme de branch-and-price, sert d’outil pour balancer les coûts opérationnels et la dégradation de la batterie.The vehicle scheduling problem (VSP) is one of the sub-problems of public transport planning. It aims to minimize operational costs while assigning exactly one bus per timetabled trip and respecting the capacity of each depot. Even thought public transport planning is subject to various endogenous and exogenous causes of uncertainty, notably affecting travel time and energy consumption, the VSP and its variants are usually solved deterministically to address tractability issues. However, considering deterministic travel time in the VSP can compromise schedule adherence, whereas considering deterministic energy consumption in the electric VSP (E-VSP) may result in solutions with inadequate battery management. In this thesis, we propose a methodology for measuring the reliability (or schedule adherence) of public transport, along with stochastic and data-driven mathematical models and branch-and-price algorithms for two variations of this problem, namely the multi-depot vehicle scheduling problem (MDVSP) and the E-VSP. To assess the reliability of vehicle schedules in terms of their tolerance to delays, we first predict the distribution of bus travel times. We compare numerous probabilistic models for the long-term prediction of bus travel time density. Using a Monte Carlo simulation, we then estimate the reliability of bus schedules by generating random travel times at each iteration. Subsequently, we integrate the most suitable probabilistic model, capable of accurately predicting both the true conditional density function of the travel time and the expected secondary delays, into the data-driven optimization models. Second, we introduce a model for the reliable MDVSP with stochastic travel time minimizing both the operational costs and penalties associated with delays. To effectively tackle this problem, we propose a heuristic column generation-based algorithm, which incorporates stochastic pricing problems. This algorithm dynamically computes the expected secondary delays as new columns are generated. Third, we propose a new two-stage stochastic program with recourse for the electric MDVSP with stochastic travel time and energy consumption. The recourse policy aims to restore energy feasibility when a priori vehicle schedules are unfeasible, which may lead to delays. An adapted algorithm based on column generation is developed to assess the relevance of this approach for two types of commercially available battery electric buses. Finally, we present the first stochastic model for the E-VSP with battery degradation. The proposed chance-constraint model incorporates energy consumption uncertainty, allowing for effective control of battery degradation by regulating the average state-of-charge (SOC) and SoC deviation in each discharging and charging cycle. This model, in combination with a tailored branch-and-price algorithm, serves as a tool to strike a balance between operational costs and battery degradation

Smart electric vehicle charging strategy in direct current microgrid

This thesis proposes novel electric vehicle (EV) charging strategies in DC microgrid (DCMG) for integrating network loads, EV charging/discharging and dispatchable generators (DGs) using droop control within DCMG. A novel two-stage optimization framework is deployed, which optimizes power flow in the network using droop control within DCMG and solves charging tasks with a modified Djistra algorithm. Charging tasks here are modeled as the shortest path problem considering system losses and battery degradation from the distribution system operator (DSO) and electric vehicles aggregator (EVA) respectively. Furthermore, a probabilistic distribution model is proposed to investigate the EV stochastic behaviours for a charging station including time-of-arrival (TOA), time-of-departure(TOD) and energy-to-be-charged (ETC) as well as the coupling characteristic between these parameters. Markov Chain Monte Carlo (MCMC) method is employed to establish a multi-dimension probability distribution for those load profiles and further tests show the scheme is suitable for decentralized computing of its low burn-in request, fast convergent and good parallel acceleration performance. Following this, a three-stage stochastic EV charging strategy is designed to plug the probabilistic distribution model into the optimization framework, which becomes the first stage of the framework. Subsequently, an optimal power flow (OPF) model in the DCMG is deployed where the previous deterministic model is deployed in the second stage which stage one and stage two are combined as a chance-constrained problem in stage three and solved as a random walk problem. Finally, this thesis investigates the value of EV integration in the DCMG. The results obtained show that with smart control of EV charging/discharging, not only EV charging requests can be satisfied, but also network performance like peak valley difference can be improved by ancillary services. Meanwhile, both system loss and battery degradation from DSO and EVA can be minimized.Open Acces

Energy sustainable paradigms and methods for future mobile networks: A survey

In this survey, we discuss the role of energy in the design of future mobile networks and, in particular, we advocate and elaborate on the use of energy harvesting (EH) hardware as a means to decrease the environmental footprint of 5G technology. To take full advantage of the harvested (renewable) energy, while still meeting the quality of service required by dense 5G deployments, suitable management techniques are here reviewed, highlighting the open issues that are still to be solved to provide eco-friendly and cost-effective mobile architectures. Several solutions have recently been proposed to tackle capacity, coverage and efficiency problems, including: C-RAN, Software Defined Networking (SDN) and fog computing, among others. However, these are not explicitly tailored to increase the energy efficiency of networks featuring renewable energy sources, and have the following limitations: (i) their energy savings are in many cases still insufficient and (ii) they do not consider network elements possessing energy harvesting capabilities. In this paper, we systematically review existing energy sustainable paradigms and methods to address points (i) and (ii), discussing how these can be exploited to obtain highly efficient, energy self-sufficient and high capacity networks. Several open issues have emerged from our review, ranging from the need for accurate energy, transmission and consumption models, to the lack of accurate data traffic profiles, to the use of power transfer, energy cooperation and energy trading techniques. These challenges are here discussed along with some research directions to follow for achieving sustainable 5G systems.Comment: Accepted by Elsevier Computer Communications, 21 pages, 9 figure

Energy Generation Scheduling in Microgrids Involving Temporal-Correlated Renewable Energy

In this paper, a cost minimization problem is formulated to intelligently schedule energy generations for microgrids equipped with unstable renewable sources and energy storages. In such systems, the uncertain renewable energy will impose unprecedented scheduling challenges. To cope with the fluctuate nature of the renewable energy, an uncertainty model based on renewable energies’ moment statistics is developed. Specifically, we obtain the mean vector and second-order moment matrix according to predictions and field measurements and then define uncertainty set to confine the renewable energy generation. The uncertainty model allows the renewable energy generation distributions to fluctuate within the uncertainty set. We develop chance constraint approximations and robust optimization approaches based on a Chebyshev inequality framework to firstly transform and then solve the scheduling problem. Numerical results based on real-world data traces evaluate the performance bounds of the proposed scheduling scheme. It is shown that the temporal correlation information of the renewable energy within a proper time span can effectively reduce the conservativeness of the solution. Moreover, detailed studies on the impacts of different factors on the proposed scheme provide some interesting insights which shall be useful for the policy making for the future microgrids

Integration of Energy Storage into a Future Energy System with a High Penetration of Distributed Photovoltaic Generation

Energy storage units (ESU) are increasingly used in electrical distribution systems because they can perform many functions compared with traditional equipment. These include peak shaving, voltage regulation, frequency regulation, provision of spinning reserve, and aiding integration of renewable generation by mitigating the effects of intermittency. As is the case with other equipment on electric distribution systems, it is necessary to follow appropriate methodologies in order to ensure that ESU are installed in a cost-effective manner and their benefits are realized. However, the necessary methodologies for integration of ESU have not kept pace with developments in both ESU and distribution systems. This work develops methodologies to integrate ESU into distribution systems by selecting the necessary storage technologies, energy capacities, power ratings, converter topologies, control strategies, and design lifetimes of ESU. In doing so, the impact of new technologies and issues such as volt-VAR optimization (VVO), intermittency of photovoltaic (PV) inverters, and the smart PV inverter proposed by EPRI are considered. The salient contributions of this dissertation follow. A unified methodology is developed for storage technology selection, storage capacity selection, and scheduling of an ESU used for energy arbitrage. The methodology is applied to make technology recommendations and to reveal that there exists a cost-optimal design lifetime for such an ESU. A methodology is developed for capacity selection of an ESU providing both energy arbitrage and ancillary services under a stochastic pricing structure. The ESU designed is evaluated using ridge regression for price forecasting; Ridge regression applied to overcome numerical stability and overfitting issues associated with the large number of highly correlated predictors. Heuristics are developed to speed convergence of simulated annealing for placement of distributed ESU. Scaling and clustering methods are also applied to reduce computation time for placement of ESU (or any other shunt-connected device) on a distribution system. A probabilistic model for cloud-induced photovoltaic (PV) intermittency of a single PV installation is developed and applied to the design of ESU

Optimization and Communication in UAV Networks

UAVs are becoming a reality and attract increasing attention. They can be remotely controlled or completely autonomous and be used alone or as a fleet and in a large set of applications. They are constrained by hardware since they cannot be too heavy and rely on batteries. Their use still raises a large set of exciting new challenges in terms of trajectory optimization and positioning when they are used alone or in cooperation, and communication when they evolve in swarm, to name but a few examples. This book presents some new original contributions regarding UAV or UAV swarm optimization and communication aspects

Methodologies for the analysis of value from delay-tolerant inter-satellite networking

In a world that is becoming increasingly connected, both in the sense of people and devices, it is of no surprise that users of the data enabled by satellites are exploring the potential brought about from a more connected Earth orbit environment. Lower data latency, higher revisit rates and higher volumes of information are the order of the day, and inter-connectivity is one of the ways in which this could be achieved. Within this dissertation, three main topics are investigated and built upon. First, the process of routing data through intermittently connected delay-tolerant networks is examined and a new routing protocol introduced, called Spae. The consideration of downstream resource limitations forms the heart of this novel approach which is shown to provide improvements in data routing that closely match that of a theoretically optimal scheme. Next, the value of inter-satellite networking is derived in such a way that removes the difficult task of costing the enabling inter-satellite link technology. Instead, value is defined as the price one should be willing to pay for the technology while retaining a mission value greater than its non-networking counterpart. This is achieved through the use of multi-attribute utility theory, trade-space analysis and system modelling, and demonstrated in two case studies. Finally, the effects of uncertainty in the form of sub-system failure are considered. Inter-satellite networking is shown to increase a system's resilience to failure through introduction of additional, partially failed states, made possible by data relay. The lifetime value of a system is then captured using a semi-analytical approach exploiting Markov chains, validated with a numerical Monte Carlo simulation approach. It is evident that while inter-satellite networking may offer more value in general, it does not necessarily result in a decrease in the loss of utility over the lifetime.In a world that is becoming increasingly connected, both in the sense of people and devices, it is of no surprise that users of the data enabled by satellites are exploring the potential brought about from a more connected Earth orbit environment. Lower data latency, higher revisit rates and higher volumes of information are the order of the day, and inter-connectivity is one of the ways in which this could be achieved. Within this dissertation, three main topics are investigated and built upon. First, the process of routing data through intermittently connected delay-tolerant networks is examined and a new routing protocol introduced, called Spae. The consideration of downstream resource limitations forms the heart of this novel approach which is shown to provide improvements in data routing that closely match that of a theoretically optimal scheme. Next, the value of inter-satellite networking is derived in such a way that removes the difficult task of costing the enabling inter-satellite link technology. Instead, value is defined as the price one should be willing to pay for the technology while retaining a mission value greater than its non-networking counterpart. This is achieved through the use of multi-attribute utility theory, trade-space analysis and system modelling, and demonstrated in two case studies. Finally, the effects of uncertainty in the form of sub-system failure are considered. Inter-satellite networking is shown to increase a system's resilience to failure through introduction of additional, partially failed states, made possible by data relay. The lifetime value of a system is then captured using a semi-analytical approach exploiting Markov chains, validated with a numerical Monte Carlo simulation approach. It is evident that while inter-satellite networking may offer more value in general, it does not necessarily result in a decrease in the loss of utility over the lifetime

optimizing the operation of energy storage using a non linear lithium ion battery degradation model

Abstract Given their technological and market maturity, lithium-ion batteries are increasingly being considered and used in grid applications to provide a host of services such as frequency regulation, peak shaving, etc. Charging and discharging these batteries causes degradation in their performance. Lack of data on degradation processes combined with requirement of fast computation have led to over-simplified models of battery degradation. In this work, the recent experimental evidence that demonstrates that degradation in lithium-ion batteries is non-linearly dependent on the operating conditions is incorporated. Experimental aging data of a commercial battery have been used to develop a scheduling model applicable to the time constraints of a market model. A decomposition technique that enables the developed model to give near-optimal results for longer time horizons is also proposed