As our electric power distribution infrastructure has aged, considerable investment has been applied to modernizing the electrical power grid through weatherization and in deployment of real-time monitoring systems. A key question is whether or not these investments are reducing the number and duration of power outages, leading to improved reliability. Statistical methods are applied to analyze electrical disturbance data (from the Department of Energy, DOE) and reliability index data (from state utility public service commission regulators) to detect signs of improvement. The number of installed smart meters provided by several utilities is used to determine whether the number of smart meters correlate with a reduction in outage frequency. Indication emerged that the number of power outages may be decreasing over time. The magnitude of power loss has decreased from 2003 to 2007, and behaves cyclically from 2008 to 2014, with a few outlier points in both groups. The duration also appears to be decreasing between 2003-2014. Large blackout events exceeding 5 GW continue to be rare, and certain power outage events are seasonally dependent. There was a linear relationship between the number of customers and the magnitude of a power outage event. However, no relationship was found between the magnitude of power outages and time to restore power. The frequency of outages maybe decreasing as the number of installed smart meters has increased. Recommendations for inclusion of additional metrics, changes to formatting and semantics of datasets currently provided by federal and state regulators are made to help aid researchers in performing more effective analysis. Confounding variables and lack of information that has made the analysis diffcult is also discussed.

Master of Science / Department of Electrical and Computer Engineering / Sanjoy Das / Anil Pahwa / Outage management describes system utilized by electric distribution utilities to help restore power in event of an outage. The complexity of outage management system employed by different utilities to determine the location of fault could differ. First step of outage management is to know where the problem is. Utilities typically depend on customers to call and inform them of the problem by entering their addresses. After sufficient calls are received, the utility is able to pinpoint the location of the outage. This part of outage management is called trouble call analysis. In event of fault in a feeder of a radial distribution system, the upstream device or the device that serves to protect that particular zone activates and opens the circuit. This particular device is considered as the operated protective device. The knowledge of the activated protective device can help locate the fault. Repair crews could be sent to that particular location to carry out power restoration efforts. The main objective of this work is to study model of distribution system that could utilize the network topology and customer calls to predict the location of the operated protective device. Such prediction would be based on the knowledge of the least amount of variables i.e. network topology and customer calls. Radial distribution systems are modeled using the immune system algorithm and test cases with trouble calls are simulated in MATLAB to test the effectiveness of the proposed technique. Also, the proposed technique is tested on an actual feeder circuit with real call scenarios to verify against the known fault locations.

In this dissertation, power allocation approaches considering path loss, shadowing, and Rayleigh and Nakagami-m fading are proposed. The goal is to improve power consumption, and energy and throughput efficiency based on user target signal to interference plus noise ratio (SINR) requirements and an outage probability threshold. First, using the moment generating function (MGF), the exact outage probability over Rayleigh and Nakagami-m fading channels is derived. Then upper and lower bounds on the outage probability are derived using the Weierstrass, Bernoulli and exponential inequalities. Second, the problem of minimizing the user power subject to outage probability and user target SINR constraints is considered. The corresponding power allocation problems are solved using Perron-Frobenius theory and geometric programming (GP). A GP problem can be transformed into a nonlinear convex optimization problem using variable substitution and then solved globally and efficiently by interior point methods. Then, power allocation problems for throughput maximization and energy efficiency are proposed. As these problems are in a convex fractional programming form, parametric transformation is used to convert the original problems into subtractive optimization problems which can be solved iteratively. Simulation results are presented which show that the proposed approaches are better than existing schemes in terms of power consumption, throughput, energy efficiency and outage probability. Prioritized cell association and power allocation (CAPA) to solve the load balancing issue in heterogeneous networks (HetNets) is also considered in this dissertation. A Hetnet is a group of macrocell base stations (MBSs) underlaid by a diverse set of small cell base stations (SBSs) such as microcells, picocells and femtocells. These networks are considered to be a good solution to enhance network capacity, improve network coverage, and reduce power consumption. However, HetNets are limited by the disparity of power levels in the different tiers. Conventional cell association approaches cause MBS overloading, SBS underutilization, excessive user interference and wasted resources. Satisfying priority user (PU) requirements while maximizing the number of normal users (NUs) has not been considered in existing power allocation algorithms. Two stage CAPA optimization is proposed to address the prioritized cell association and power allocation problem. The first stage is employed by PUs and NUs and the second stage is employed by BSs. First, the product of the channel access likelihood (CAL) and channel gain to interference plus noise ratio (GINR) is considered for PU cell association while network utility is considered for NU cell association. Here, CAL is defined as the reciprocal of the BS load. In CAL and GINR cell association, PUs are associated with the BSs that provide the maximum product of CAL and GINR. This implies that PUs connect to BSs with a low number of users and good channel conditions. NUs are connected to BSs so that the network utility is maximized, and this is achieved using an iterative algorithm. Second, prioritized power allocation is used to reduce power consumption and satisfy as many NUs with their target SINRs as possible while ensuring that PU requirements are satisfied. Performance results are presented which show that the proposed schemes provide fair and efficient solutions which reduce power consumption and have faster convergence than conventional CAPA schemes. / Graduate

In this study, it was investigated how individual households could manage security of supply during an outage by installing a local energy system that could operate independently from the electricity grid. By installing local renewable off-grid energy systems, households could guarantee an uninterrupted supply of energy even during an outage on the electricity grid, while also increasing their energy autonomy during normal circumstances. The results showed that managing an outage during summer was fairly easy. Due to high electricity production, a small energy storage was enough to manage an outage during summer. However, managing an outage during winter was more critical. During winter, the systems needed to be almost fully reliant on the energy storage. This significantly increased the cost of these systems. Due to the high cost for the energy systems today, it was not considered a feasible solution to improve energy security at a national level. However, at a local level, this was considered to have the potential to improve energy security. First, it could to be of interest for people who already have installed solar panels, who could add a battery and thereby be able to manage an outage during summer. Second, it could be of interest for people who are more exposed to outages or have a low trust in the system to work properly. Lastly, this could be of interest for actors for whom backup energy is important, for instance for the industry.

Visible Light Communications (VLC) has recently emerged as a viable solution for solving the spectrum shortage problem. The idea is to use artificial light sources as medium to communicate with portable devices. In particular, the light sources can be switched on and off with a very high-frequency corresponding to 1s and 0s of digital communication. The high-frequency on-off switching can be detected by electronic devices but not the human eyes, and hence will not affect the light sources' illumination functions. In VLC, if a receiver is equipped with photodiodes that count the number of arriving photons, the channels can be modeled as Poisson channels. Unlike Gaussian channels that are suitable for radio spectrum and have been intensively investigated, Poisson channels are more challenging and are not that well understood. The goal of this thesis is to characterize the fundamental limits of various Poisson channels that models different scenarios in VLC. We first focus on single user Poisson fading channels with time-varying background lights. Our model is motivated by indoor optical wireless communication systems, in which the noise level is affected by the strength of the background light. We study both the single-input single-output (SISO) and the multiple-input and multiple-output (MIMO) channels. For each channel, we consider scenarios with and without delay constraints. For the case without a delay constraint, we characterize the optimal power allocation scheme that maximizes the ergodic capacity. For the case with a strict delay constraint, we characterize the optimal power allocation scheme that minimizes the outage probability. We then extend the study to the multi-user Poisson channels and analyze the sum-rate capacity of two-user Poisson multiple access channels (MAC). We first characterize the sum-rate capacity of the non-symmetric Poisson MAC when each transmitter has a single antenna. We show that, for certain channel parameters, it is optimal for a single-user to transmit to achieve the sum-rate capacity. This is in sharp contrast to the Gaussian MAC, in which both users must transmit, either simultaneously or at different times, in order to achieve the sum-rate capacity. We then characterize the sum-rate capacity of the Poisson MAC with multiple antennas at each transmitter. By converting a non-convex optimization problem with a large number of variables into a non-convex optimization problem with two variables, we show that the sum-rate capacity of the Poisson MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter. We further analyze the sum-rate capacity of two-user Poisson MIMO multiple-access channels (MAC), when both the transmitters and the receiver are equipped with multiple antennas. We first characterize the sum-rate capacity of the Poisson MAC when each transmitter has a single antenna and the receiver has multiple antennas. We show that similar to Poisson MISO-MAC channels, for certain channel parameters, it is optimal for a single user to transmit to achieve the sum-rate capacity, and for certain channel parameters, it is optimal for both users to transmit. We then characterize the sum-rate capacity of the channel where both the transmitters and the receiver are equipped with multiple antennas. We show that the sum-rate capacity of the Poisson MAC with multiple transmit antennas is equivalent to a properly constructed Poisson MAC with a single antenna at each transmitter.

The supply chain risk management discipline studies how to address daily and extraordinary risks to avoid vulnerability and to guarantee production continuity. In the case of the electricity sector, the economic impact of interrupting the power supply is depicted by an indicator called the deficit cost, measured in monetary unit per electricity consumption unit (for example, in Brazil, R$/MWh). This value is commonly applied to cost-benefit analysis that results in decisions about maintenance and investment in the electricity system in the medium and long term, in addition to composing the short-term energy price. Most countries in the world have a thermal energy matrix, and cases in which interruption problems occur are mainly due to punctual failures in generation or transmission and last a few hours or days until maintenance is concluded. Brazil, however, has been strongly dependent on hydrological conditions ever since the main generation source became hydroelectric. Since restricted energy supply scenarios last longer, from weeks to months, a better measure for the electricity structural deficit impact is the economic loss in the deficit-affected regional production, translated as the GDP (gross domestic product) region. This dissertation estimates the Brazilian GDP marginal loss due to power deficits by applying an input-output (I/O) matrix analysis methodology and concludes that the officially adopted deficit cost is underestimated. / Sem resumo em português.

Simulation methods are used when closed-form solutions do not exist. An interesting simulation method that has been widely used in many scientific fields is the Monte Carlo method. Not only it is a simple technique that enables to estimate the quantity of interest, but it can also provide relevant information about the value to be estimated through its confidence interval. However, the use of classical Monte Carlo method is not a reasonable choice when dealing with rare event probabilities. In fact, very small probabilities require a huge number of simulation runs, and thus, the computational time of the simulation increases significantly. This observation lies behind the main motivation of the present work. In this thesis, we propose efficient importance sampling estimators to evaluate rare events probabilities. In the first part of the thesis, we consider a variety of turbulence regimes, and we study the outage probability of free-space optics communication systems under a generalized pointing error model with both a nonzero boresight component and different horizontal and vertical jitter effects. More specifically, we use an importance sampling approach,based on the exponential twisting technique to offer fast and accurate results. We also show that our approach extends to the multihop scenario. In the second part of the thesis, we are interested in assessing the outage probability achieved by some diversity techniques over generalized fading channels. In many circumstances, this is related to the difficult question of analyzing the statistics of the sum of random variables. More specifically, we propose robust importance sampling schemes that efficiently evaluate the outage probability of diversity receivers over Gamma-Gamma, α − µ, κ − µ, and η − µ fading channels. The proposed estimators satisfy the well-known bounded relative error criterion for both maximum ratio combining and equal gain combining cases. We show the accuracy and the efficiency of our approach compared to naive Monte Carlo via some selected numerical simulations in both case studies. In the last part of this thesis, we propose efficient importance sampling estimators for the left tail of positive Gaussian quadratic forms in both real and complex settings. We show that these estimators possess the bounded relative error property. These estimators are then used to estimate the outage probability of maximum ratio combining diversity receivers over correlated Nakagami-m or correlated Rician fading channels

In wireless networks, communication links may be subject to random fatal impacts: for example, sensor networks under sudden power losses or cognitive radio networks with unpredictable primary user spectrum occupancy. Under such circumstances, it is critical to quantify how fast and reliably the information can be collected over attacked links. For a single point-to-point channel subject to a random attack, named as a dying channel, we model it as a block-fading (BF) channel with a finite and random channel length. First, we study the outage probability when the coding length K is fixed and uniform power allocation is assumed. Furthermore, we discuss the optimization over K and the power allocation vector PK to minimize the outage probability. In addition, we extend the single point to-point dying channel case to the parallel multi-channel case where each sub-channel is a dying channel, and investigate the corresponding asymptotic behavior of the overall outage probability with two different attack models: the independent-attack case and the m-dependent-attack case. It can be shown that the overall outage probability diminishes to zero for both cases as the number of sub-channels increases if the rate per unit cost is less than a certain threshold. The outage exponents are also studied to reveal how fast the outage probability improves over the number of sub-channels. Besides the information-theoretical results, we also study a practical coding scheme for the dying binary erasure channel (DBEC), which is a binary erasure channel (BEC) subject to a random fatal failure. We consider the rateless codes and optimize the degree distribution to maximize the average recovery probability. In particular, we first study the upper bound of the average recovery probability, based on which we define the objective function as the gap between the upper bound and the average recovery probability achieved by a particular degree distribution. We then seek the optimal degree distribution by minimizing the objective function. A simple and heuristic approach is also proposed to provide a suboptimal but good degree distribution.

The aggregate interference distribution in cognitive radio networks is studied in a rigorous and analytical way using the popular Poisson point process model. While a number of results are available for this model for non-cognitive radio networks, cognitive radio networks present extra levels of difficulties for the analysis, mainly due to the exclusion region around the primary receiver, which are typically addressed via various ad-hoc approximations (e.g., based on the interference cumulants) or via the large-deviation analysis. Unlike the previous studies, we do not use here ad-hoc approximations but rather obtain the asymptotic interference distribution in a systematic and rigorous way, which also has a guaranteed level of accuracy at the distribution tail. This is in contrast to the large deviation analysis, which provides only the (exponential) order of scaling but not the outage probability itself. Unlike the cumulant-based analysis, our approach provides a guaranteed level of accuracy at the distribution tail. Additionally, our analysis provides a number of novel insights. In particular, we demonstrate that there is a critical transition point below which the outage probability decays only polynomially but above which it decays super-exponentially. This provides a solid analytical foundation to the earlier empirical observations in the literature and also reveals what are the typical ways outage events occur in different regimes. The analysis is further extended to include interference cancelation and fading (from a broad class of distributions). The outage probability is shown to scale down exponentially in the number of canceled nearest interferers in the below-critical region and does not change significantly in the above-critical one. The proposed asymptotic expressions are shown to be accurate in the non-asymptotic regimes as well.

This thesis describes the research conducted on the use of historical performance data in assessing the financial risk for a power distribution utility in a performance based regulation (PBR) regime. The historical utility data used in this research are taken from the Canadian Electrical Association (CEA) annual reports. The individual utility data in these reports are confidential and only provided to the participating utilities. Thirteen utilities that participate in the CEA data reporting activity agreed to provide their individual utility data for the research described in this thesis. These utilities are anonymous and are referred to by numerical designations in accordance with the CEA protocol. This research could not have been conducted without the support of these utilities. The objectives of the research described in this thesis are to examine and analyze the variations in the annual performance indices of the thirteen participating utilities and the aggregated systems including the overall indices and the cause code contributions, and to examine the possible utilization of historic utility reliability indices to create suitable reward/penalty structures in a PBR protocol. The potential financial risk and actual financial payment analyses for these selected utilities are conducted using their historical performance data imposed on a number of possible reward/penalty structures developed in this thesis. An approach to recognize adverse utility performance in the form of Major Outage Years (MOY) is developed and the influence of the MOY performance in PBR decision making is examined.