Distributed Load Control in Multiphase Radial Networks

The current power grid is on the cusp of modernization due to the emergence of distributed generation and controllable loads, as well as renewable energy. On one hand, distributed and renewable generation is volatile and difficult to dispatch. On the other hand, controllable loads provide significant potential for compensating for the uncertainties. In a future grid where there are thousands or millions of controllable loads and a large portion of the generation comes from volatile sources like wind and solar, distributed control that shifts or reduces the power consumption of electric loads in a reliable and economic way would be highly valuable.

Load control needs to be conducted with network awareness. Otherwise, voltage violations and overloading of circuit devices are likely. To model these effects, network power flows and voltages have to be considered explicitly. However, the physical laws that determine power flows and voltages are nonlinear. Furthermore, while distributed generation and controllable loads are mostly located in distribution networks that are multiphase and radial, most of the power flow studies focus on single-phase networks.

This thesis focuses on distributed load control in multiphase radial distribution networks. In particular, we first study distributed load control without considering network constraints, and then consider network-aware distributed load control.

Distributed implementation of load control is the main challenge if network constraints can be ignored. In this case, we first ignore the uncertainties in renewable generation and load arrivals, and propose a distributed load control algorithm, Algorithm 1, that optimally schedules the deferrable loads to shape the net electricity demand. Deferrable loads refer to loads whose total energy consumption is fixed, but energy usage can be shifted over time in response to network conditions. Algorithm 1 is a distributed gradient decent algorithm, and empirically converges to optimal deferrable load schedules within 15 iterations.

We then extend Algorithm 1 to a real-time setup where deferrable loads arrive over time, and only imprecise predictions about future renewable generation and load are available at the time of decision making. The real-time algorithm Algorithm 2 is based on model-predictive control: Algorithm 2 uses updated predictions on renewable generation as the true values, and computes a pseudo load to simulate future deferrable load. The pseudo load consumes 0 power at the current time step, and its total energy consumption equals the expectation of future deferrable load total energy request.

Network constraints, e.g., transformer loading constraints and voltage regulation constraints, bring significant challenge to the load control problem since power flows and voltages are governed by nonlinear physical laws. Remarkably, distribution networks are usually multiphase and radial. Two approaches are explored to overcome this challenge: one based on convex relaxation and the other that seeks a locally optimal load schedule.

To explore the convex relaxation approach, a novel but equivalent power flow model, the branch flow model, is developed, and a semidefinite programming relaxation, called BFM-SDP, is obtained using the branch flow model. BFM-SDP is mathematically equivalent to a standard convex relaxation proposed in the literature, but numerically is much more stable. Empirical studies show that BFM-SDP is numerically exact for the IEEE 13-, 34-, 37-, 123-bus networks and a real-world 2065-bus network, while the standard convex relaxation is numerically exact for only two of these networks.

Theoretical guarantees on the exactness of convex relaxations are provided for two types of networks: single-phase radial alternative-current (AC) networks, and single-phase mesh direct-current (DC) networks. In particular, for single-phase radial AC networks, we prove that a second-order cone program (SOCP) relaxation is exact if voltage upper bounds are not binding; we also modify the optimal load control problem so that its SOCP relaxation is always exact. For single-phase mesh DC networks, we prove that an SOCP relaxation is exact if 1) voltage upper bounds are not binding, or 2) voltage upper bounds are uniform and power injection lower bounds are strictly negative; we also modify the optimal load control problem so that its SOCP relaxation is always exact.

To seek a locally optimal load schedule, a distributed gradient-decent algorithm, Algorithm 9, is proposed. The suboptimality gap of the algorithm is rigorously characterized and close to 0 for practical networks. Furthermore, unlike the convex relaxation approach, Algorithm 9 ensures a feasible solution. The gradients used in Algorithm 9 are estimated based on a linear approximation of the power flow, which is derived with the following assumptions: 1) line losses are negligible; and 2) voltages are reasonably balanced. Both assumptions are satisfied in practical distribution networks. Empirical results show that Algorithm 9 obtains 70+ times speed up over the convex relaxation approach, at the cost of a suboptimality within numerical precision.

Une heuristique à grand voisinage pour un problème de confection de tournée pour un seul véhicule avec cueillettes et livraisons et contrainte de chargement

Dans ce mémoire, nous présentons un nouveau type de problème de confection de tour- née pour un seul véhicule avec cueillettes et livraisons et contrainte de chargement. Cette variante est motivée par des problèmes similaires rapportés dans la littérature. Le véhi- cule en question contient plusieurs piles où des colis de hauteurs différentes sont empilés durant leur transport. La hauteur totale des items contenus dans chacune des piles ne peut dépasser une certaine hauteur maximale. Aucun déplacement n’est permis lors de la li- vraison d’un colis, ce qui signifie que le colis doit être sur le dessus d’une pile au moment d’être livré. De plus, tout colis i ramassé avant un colis j et contenu dans la même pile doit être livré après j. Une heuristique à grand voisinage, basé sur des travaux récents dans le domaine, est proposée comme méthode de résolution. Des résultats numériques sont rapportés pour plusieurs instances classiques ainsi que pour de nouvelles instances.

Problèmes de tournées de véhicules avec contraintes de chargement

Cette thèse s’intéresse aux problèmes de tournées de véhicules où l’on retrouve des contraintes de chargement ayant un impact sur les séquences de livraisons permises. Plus particulièrement, les items placés dans l’espace de chargement d’un véhicule doivent être directement accessibles lors de leur livraison sans qu’il soit nécessaire de déplacer d’autres items. Ces problèmes sont rencontrés dans plusieurs entreprises de transport qui livrent de gros objets (meubles, électroménagers). Le premier article de cette thèse porte sur une méthode exacte pour un problème de confection d’une seule tournée où un véhicule, dont l’aire de chargement est divisée en un certain nombre de piles, doit effectuer des cueillettes et des livraisons respectant une contrainte de type dernier entré, premier sorti. Lors d’une collecte, les items recueillis doivent nécessairement être déposés sur le dessus de l’une des piles. Par ailleurs, lors d’une livraison, les items doivent nécessairement se trouver sur le dessus de l’une des piles. Une méthode de séparation et évaluation avec plans sécants est proposée pour résoudre ce problème. Le second article présente une méthode de résolution exacte, également de type séparation et évaluation avec plans sécants, pour un problème de tournées de véhicules avec chargement d’items rectangulaires en deux dimensions. L’aire de chargement des véhicules correspond aussi à un espace rectangulaire avec une orientation, puisque les items doivent être chargés et déchargés par l’un des côtés. Une contrainte impose que les items d’un client soient directement accessibles au moment de leur livraison. Le dernier article aborde une problème de tournées de véhicules avec chargement d’items rectangulaires, mais où les dimensions de certains items ne sont pas connus avec certitude lors de la planification des tournées. Il est toutefois possible d’associer une distribution de probabilités discrète sur les dimensions possibles de ces items. Le problème est résolu de manière exacte avec la méthode L-Shape en nombres entiers.

Smart coordination of energy storage units (ESUs) for voltage and loading management in distribution networks

This paper proposes a distributed control approach to coordinate multiple energy storage units (ESUs) to avoid violation of voltage and thermal constraints, which are some of the main power quality challenges for future distribution networks. ESUs usually are connected to a network through voltage source converters. In this paper, both ESU converters active and reactive power are used to deal with the above mentioned power quality issues. ESUs' reactive power is proposed to be used for voltage support, while the active power is to be utilized in managing network loading. Two typical distribution networks are used to apply the proposed method, and the simulated results are illustrated in this paper to show the effectiveness of this approach.

Loading Artificial Magnetic Conductor and Artificial Magnetic Conductor Absorber with Negative Impedance Convertor Elements

The general properties of a frequency selective surface loaded with negative impedance converter (NIC)-based active loads are discussed from a theoretical perspective.The stability problem associated with NIC circuits embedded in artificial magnetic conductor (AMC) and AMC absorber applications is studied using pole-zero analysis. The requirements and constraints for achieving stable operation with enhanced bandwidth using negative capacitance as realized by a floating NIC network are derived. Furthermore, it is shown that it is nearly impossible to simultaneously implement a negative capacitor and a negative inductor to such structures. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2111–2114, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27019

A physical packing sequence algorithm for the container loading problem with static mechanical equilibrium conditions

The container loading problem (CLP) is a combinatorial optimization problem for the spatial arrangement of cargo inside containers so as to maximize the usage of space. The algorithms for this problem are of limited practical applicability if real-world constraints are not considered, one of the most important of which is deemed to be stability. This paper addresses static stability, as opposed to dynamic stability, looking at the stability of the cargo during container loading. This paper proposes two algorithms. The first is a static stability algorithm based on static mechanical equilibrium conditions that can be used as a stability evaluation function embedded in CLP algorithms (e.g. constructive heuristics, metaheuristics). The second proposed algorithm is a physical packing sequence algorithm that, given a container loading arrangement, generates the actual sequence by which each box is placed inside the container, considering static stability and loading operation efficiency constraints.

Upgrading of Transmission Lines in Areas of Severe Environmental Constraints

The need for increasing the loading capacity of transmission lines in a traditional way, by replacing or reinforcement of the structures and foundations on routes crossing areas considered of permanent environmental preservation, may require additional works that alter the environment. The present rigorous environmental legislation turns these changes and substitution unfeasible. One way to increase the capacity of these lines is the use of new conductor technology. The aim of this paper is to discuss the needs for upgrading a transmission line and minimize or eliminate the damage to the environment by using special conductors. Because the aluminum conductor composite reinforced technology is relatively new and considering the lack of information related to its effective performance in practical system, there is a need to verify the behavior of these conductors through monitoring procedures.

Integrins in human T cell function: Transdominant regulation, conformational constraints, and intracellular effectors

Integrin adhesion molecules have both positive and negative potential in the regulation of peripheral blood T cell (PB T cell) activation, yet their mechanism of action in the mediation of human T lymphocyte function remains largely undefined. The goals of this study then were to elucidate integrin signaling mechanisms in PB T cells.^ By ligating $\beta$1 integrins with mAb 18D3, it was demonstrated that costimulation of PB T cell proliferation induced by coimmobilizing antibodies specific for $\beta$1, $\beta$2, and $\beta$7 integrin subfamilies in conjunction with the anti-CD3 mAb OKT3 was inhibited. Costimulation of T cell proliferation induced by non-integrins CD4, CD26, CD28, CD44, CD45RA, or CD45RO was unaffected. Inhibition of costimulation correlated with diminished IL-2 production. In his manner, $\beta$1 integrins could regulate heterologous integrins of the $\beta$2 and $\beta$7 subfamilies in a transdominant fashion. It was also demonstrated that integrin costimulation of T cell activation was acutely sensitive to the structural conformation of $\beta$1 integrins. Using the cyclic hexapeptide CWLDVC (TBC772, which is based on the $\alpha4\beta1$ integrin binding site in fibronectin) in soluble form, it was shown that integrins locked into a conformation displaying a neo-epitope called the ligand induced binding site (LIBS) recognized by mAb 15/7 were inhibited from sending mitogenic signals to T cells. When BSA-conjugated TBC772 was coimmobilized with anti-CD3 mAb OKT3, costimulation of proliferation occurred. This suggested that temporally uncoupling integrin receptor occupancy from receptor crosslinking inhibited $\beta$1 integrin signaling mechanisms. When subsets of PB T cells were examined to determine those initially activated by integrins within 6 hours of activation, costimulation induced intracellular accumulation of IL-2 predominantly in the CD4$\sp+$ and CD45RO$\sp+$ T cell subsets. This was similar to a number of PB T cell costimulatory molecules including CD26, CD43, CD44. Only CD28 costimulated IL-2 production from both CD45RA$\sp+$ and CD45RO$\sp+$ subpopulations.^ The GTPase Rho has been implicated in regulating integrin mediated stress fiber formation and anchorage dependent growth in fibroblasts, so studies were initiated to determine if Rho played a role in integrin dependent T cell function. In order to perform this, a technique based on scrape-loading was developed to incorporate macromolecules into PB T cells that maintained their functional activity. With this technique, C3 exoenzyme from Clostridium botulinum was incorporated into PB T cells. C3 ADP-ribosylates Rho proteins on Asn$\sp{41},$ which is in close proximity to the Rho effector domain, rendering it inactive. It was demonstrated that functional Rho is not required for basal or upregulated PB T cell adhesion to $\beta$1 integrin substrates, however PB T cell homotypic aggregation induced by PMA, which is an event mediated predominantly by the integrin $\rm\alpha L\beta2,$ was delayed. PB T cells lacking Rho function displayed altered cell morphology on $\beta$1 integrin ligands, producing stellate, dendritic-like pseudopodia. Rho activity was also found to be required for integrin dependent costimulation of proliferation. When intracellular accumulation of IL-2 was measured, inactivation of Rho prevented both integrin and CD28 costimulatory activity. Rho was identified to lie upstream of signals mediating PKC activation and Ca$\sp{++}$ fluxes, as PMA and ionomycin activation of PB T cells was unaffected by the inactivation of Rho. ^