A clear understanding of the monetary value that customers place on reliability and the factors that give rise to higher and lower values is an essential tool in determining investment in the grid. The recent National Transmission Grid Study recognizes the need for this information as one of growing importance for both public and private decision makers. In response, the U.S. Department of Energy has undertaken this study, as a first step toward addressing the current absence of consistent data needed to support better estimates of the economic value of electricity reliability. Twenty-four studies, conducted by eight electric utilities between 1989 and 2002 representing residential and commercial/industrial (small, medium and large) customer groups, were chosen for analysis. The studies cover virtually all of the Southeast, most of the western United States, including California, rural Washington and Oregon, and the Midwest south and east of Chicago. All variables were standardized to a consistent metric and dollar amounts were adjusted to the 2002 CPI. The data were then incorporated into a meta-database in which each outage scenario (e.g., the lost of electric service for one hour on a weekday summer afternoon) is treated as an independent case or record both to permit comparisons between outage characteristics and to increase the statistical power of analysis results. Unadjusted average outage costs and Tobit models that estimate customer damage functions are presented. The customer damage functions express customer outage costs for a given outage scenario and customer class as a function of location, time of day, consumption, and business type. One can use the damage functions to calculate outage costs for specific customer types. For example, using the customer damage functions, the cost experienced by an ''average'' customer resulting from a 1 hour summer afternoon outage is estimated to be approximately $3 for a residential customer, $1,200 for small-medium commercial and industrial customer, and $82,000 for large commercial and industrial customer. Future work to improve the quality and coverage of information on the value of electricity reliability to customers is described.
Ambient backscatter communications (AmBackComs) have been recognized as a spectrum- and energy-efficient technology for the Internet of Things, as it allows passive backscatter devices (BDs) to modulate their information into the legacy signals, e.g., cellular signals, and reflect them to their associated receivers while harvesting energy from the legacy signals to power their circuit operation. However, the co-channel interference between the backscatter link and the legacy link and the nonlinear behavior of energy harvesters at the BDs have largely been ignored in the performance analysis of AmBackComs. Taking these two aspects, this article provides a comprehensive outage performance analysis for an AmBackCom system with multiple backscatter links, where one of the backscatter links is opportunistically selected to leverage the legacy signals transmitted in a given resource block. For any selected backscatter link, we propose an adaptive reflection coefficient (RC), which is adapted to the nonlinear energy harvesting (EH) model and the location of the selected backscatter link, to minimize the outage probability of the backscatter link. In order to study the impact of co-channel interference on both backscatter and legacy links, for a selected backscatter link, we derive the outage probabilities for the legacy link and the backscatter link. Furthermore, we study the best and worst outage performances for the backscatter system where the selected backscatter link maximizes or minimizes the signal-to-interference-plus-noise ratio (SINR) at the backscatter receiver. We also study the best and worst outage performances for the legacy link where the selected backscatter link results in the lowest and highest co-channel interference to the legacy receiver, respectively. Computer simulations validate our analytical results and reveal the impacts of the co-channel interference and the EH model on the AmBackCom performance. In particular, the co-channel interference leads to the outage saturation phenomenon in AmBackComs, and the conventional linear EH model results in an overestimated outage performance for the backscatter link.
We propose a new method of power control for interference-limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explicitly takes into account the statistical variation of both the received signal and interference power and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair. We establish several results for this type of problem. We establish tight bounds that relate the outage probability caused by channel fading to the signal-to-interference margin calculated when the statistical variation of the signal and interference powers is ignored. This allows us to show that well-known methods for allocating power, based on Perron-Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (i.e., minimal) outage probability. We show that the problems of minimizing the transmitter power subject to constraints on outage probability and minimizing outage probability subject to power constraints can be posed as a geometric program (GP). A GP is a special type of optimization problem that can be transformed to a nonlinear convex optimization problem by a change of variables and therefore solved globally and efficiently by interior-point methods. We also give a fast iterative method for finding the optimal power allocation to minimize the outage probability.
This article compares statistical methods for modeling power outage durations during hurricanes and examines the predictive accuracy of these methods. Being able to make accurate predictions of power outage durations is valuable because the information can be used by utility companies to plan their restoration efforts more efficiently. This information can also help inform customers and public agencies of the expected outage times, enabling better collective response planning, and coordination of restoration efforts for other critical infrastructures that depend on electricity. In the long run, outage duration estimates for future storm scenarios may help utilities and public agencies better allocate risk management resources to balance the disruption from hurricanes with the cost of hardening power systems. We compare the out-of-sample predictive accuracy of five distinct statistical models for estimating power outage duration times caused by Hurricane Ivan in 2004. The methods compared include both regression models (accelerated failure time (AFT) and Cox proportional hazard models (Cox PH)) and data mining techniques (regression trees, Bayesian additive regression trees (BART), and multivariate additive regression splines). We then validate our models against two other hurricanes. Our results indicate that BART yields the best prediction accuracy and that it is possible to predict outage durations with reasonable accuracy.
In this paper, we study a probabilistically robust transmit optimization problem under imperfect channel state information (CSI) at the transmitter and under the multiuser multiple-input single-output (MISO) downlink scenario. The main issue is to keep the probability of each user's achievable rate outage as caused by CSI uncertainties below a given threshold. As is well known, such rate outage constraints present a significant analytical and computational challenge. Indeed, they do not admit simple closed-form expressions and are unlikely to be efficiently computable in general. Assuming Gaussian CSI uncertainties, we first review a traditional robust optimization-based method for approximating the rate outage constraints, and then develop two novel approximation methods using probabilistic techniques. Interestingly, these three methods can be viewed as implementing different tractable analytic upper bounds on the tail probability of a complex Gaussian quadratic form, and they provide convex restrictions, or safe tractable approximations, of the original rate outage constraints. In particular, a feasible solution from any one of these methods will automatically satisfy the rate outage constraints, and all three methods involve convex conic programs that can be solved efficiently using off-the-shelf solvers. We then proceed to study the performance-complexity tradeoffs of these methods through computational complexity and comparative approximation performance analyses. Finally, simulation results are provided to benchmark the three convex restriction methods against the state of the art in the literature. The results show that all three methods offer significantly improved solution quality and much lower complexity.
This paper evaluates the outage probability of cognitive relay networks with cooperation between secondary users based on the underlay approach, while adhering to the interference constraint on the primary user, i.e., the limited amount of interference which the primary user can tolerate. A relay selection criterion, suitable for cognitive relay networks, is provided, and using it, we derive the outage probability. It is shown that the outage probability of cognitive relay networks is higher than that of conventional relay networks due to the interference constraint, and we quantify the increase. In addition, the outage probability is affected by the distance ratio of the interference link (between the secondary transmitter and the primary receiver) to the relaying link (between the secondary transmitter and the secondary receiver). We also prove that cognitive relay networks achieve the same full selection diversity order as conventional relay networks, and that the decrease in outage probability achieved by increasing the selection diversity (the number of relays) is not less than that in conventional relay networks.
This paper deals with a full-duplex relay (FDR) system over Rayleigh fading channels. The exact outage probability of FDR is derived as a closed form to consider interferences from full duplex. Then, we obtain the conditions of the signal-to-noise ratio (SNR) and the signal to interface ratios (SIRs) for cases of FDR showing a lower outage probability than that of the half-duplex relay (HDR) system under the target outage probability. According to this condition, FDR is superior to HDR with lower SIRs in the low-SNR region rather than in the high-SNR region. In addition, the target outage probability is only satisfied when the SNR and SIRs are within the boundaries. These boundaries vary due to the target rate, the channel states of each link, and the target outage probability.
Fast and accurate unveiling of power-line outages is of paramount importance not only for preventing faults that may lead to blackouts, but also for routine monitoring and control tasks of the smart grid, including state estimation and optimal power flow. Existing approaches are either challenged by the combinatorial complexity issues involved and are thus limited to identifying single and double line-outages or they invoke less pragmatic assumptions such as conditionally independent phasor angle measurements available across the grid. Using only a subset of voltage phasor angle data, the present paper develops a near real-time algorithm for identifying multiple line outages at the affordable complexity of solving a sparse signal reconstruction problem via either greedy steps or coordinate descent iterations. Recognizing that the number of line outages is a small fraction of the total number of lines, the novel approach relies on reformulating the DC linear power flow model as a sparse overcomplete expansion and leveraging contemporary advances in compressive sampling and variable selection. This sparse representation can also be extended to incorporate available information on the internal system and more general line-parameter faults. Analysis and simulated tests on 118-, 300-, and 2383-bus systems confirm the effectiveness of identifying sparse power line outages.
Hurricanes regularly cause widespread and prolonged power outages along the U.S. coastline. These power outages have significant impacts on other infrastructure dependent on electric power and on the population living in the impacted area. Efficient and effective emergency response planning within power utilities, other utilities dependent on electric power, private companies, and local, state, and federal government agencies benefit from accurate estimates of the extent and spatial distribution of power outages in advance of an approaching hurricane. A number of models have been developed for predicting power outages in advance of a hurricane, but these have been specific to a given utility service area, limiting their use to support wider emergency response planning. In this paper, we describe the development of a hurricane power outage prediction model applicable along the full U.S. coastline using only publicly available data, we demonstrate the use of the model for Hurricane Sandy, and we use the model to estimate what the impacts of a number of historic storms, including Typhoon Haiyan, would be on current U.S. energy infrastructure.
Distribution factors play a key role in many system security analysis and market applications. The injection shift factors (ISFs) are the basic factors that serve as building blocks of the other distribution factors. The line outage distribution factors (LODFs) may be computed using the ISFs and, in fact, may be iteratively evaluated when more than one line outage is considered. The prominent role of cascading outages in recent blackouts has created a need in security applications for evaluating LODFs under multiple-line outages. In this letter, we present an analytic, closed-form expression for and the computationally efficient evaluation of LODFs under multiple-line outages
With wavelength-division multiplexing (WDM) rapidly nearing its scalability limits, space-division multiplexing (SDM) seems the only option to further scale the capacity of optical transport networks. In order for SDM systems to continue the WDM trend of reducing energy and cost per bit with system capacity, integration will be key to SDM. Since integration is likely to introduce non-negligible crosstalk between multiple parallel transmission paths, multiple-input multiple output (MIMO) signal processing techniques will have to be used. In this paper, we discuss MIMO capacities in optical SDM systems, including related outage considerations which are an important part in the design of such systems. In order to achieve the low-outage standards required for optical transport networks, SDM transponders should be capable of individually addressing, and preferably MIMO processing all modes supported by the optical SDM waveguide. We then discuss the effect of distributed optical noise in MIMO SDM systems and focus on the impact of mode-dependent loss (MDL) on system capacity and system outage. Through extensive numerical simulations, we extract scaling rules for mode-average and mode-dependent loss and show that MIMO SDM systems composed of up to 128 segments and supporting up to 128 modes can tolerate up to 1 dB of per-segment MDL at 90% of the system's full capacity at an outage probability of 10(-4).
We develop and analyze low-complexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals' relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplify-and-forward and decode-and-forward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signal-to-noise ratio (SNR) regime. Except for fixed decode-and-forward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., second-order diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to half-duplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks-wherever space constraints preclude the use of physical arrays-the performance characterizations reveal that large power or energy savings result from the use of these protocols.
Cooperative communication is an emerging paradigm where multiple mobiles share their resources (bandwidth and power) to achieve better overall performance. Coded cooperation is a mechanism where cooperation is combined with-and operates through-channel coding, as opposed to the repetition-based methods. This work develops expressions for outage probability of coded cooperation. In this work, each node acts as both a data source as well as a relay, i.e., only active (transmitting) nodes are available to assist other nodes, and each node operates under overall (source + relay) power and bandwidth constraints. Outage expressions confirm that full diversity is achieved by coded cooperation. This shows that despite superficial similarities, coded cooperation is distinct from decode-and-forward, which has been shown to have diversity one. The outage probability expressions developed in this work characterize coded performance at various rates. Furthermore, outage probabilities yield bounds that are arguably more insightful than the bit-error rate (BER) results previously available for coded cooperation. Numerical comparisons shed light on the relative merits of coded cooperation and various repetition-based methods, under various inter-user and uplink channel conditions.
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Although phasor measurement units (PMUs) have become increasingly widespread throughout power networks, the buses monitored by PMUs still constitute a very small percentage of the total number of system buses. Our research explores methods to derive useful information from PMU data in spite of this limited coverage. In particular, we have developed an algorithm which uses known system topology information, together with PMU phasor angle measurements, to detect system line outages. In addition to determining the outaged line, the algorithm also provides an estimate of the pre-outage flow on the outaged line. To demonstrate the effectiveness of our approach, the algorithm is demonstrated using simulated and real PMU data from two systems—a 37-bus study case and the TVA control area. </para>
We investigate the performance and design of free-space optical (FSO) communication links over slow fading channels from an information theory perspective. A statistical model for the optical intensity fluctuation at the receiver due to the combined effects of atmospheric turbulence and pointing errors is derived. Unlike earlier work, our model considers the effect of beam width, detector size, and jitter variance explicitly. Expressions for the outage probability are derived for a variety of atmospheric conditions. For given weather and misalignment conditions, the beam width is optimized to maximize the channel capacity subject to outage. Large gains in achievable rate are realized versus using a nominal beam width. In light fog, by optimizing the beam width, the achievable rate is increased by 80% over the nominal beam width at an outage probability of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> . Well-known error control codes are then applied to the channel and shown to realize much of the achievable gains.
Hurricanes can cause extensive power outages, resulting in economic loss, business interruption, and secondary effects to other infrastructure systems. Currently, power companies are unable to accurately predict where outages will occur. Therefore, it is difficult for them to deploy repair personnel and materials, and make other emergency response decisions in advance of an event. This paper describes negative binomial regression models for the number of hurricane-related outages likely to occur in each one square kilometer grid cell and in each zip code in a region due to passage of a hurricane. The models are based on a large Geographic Information System database of outages in North and South Carolina from three hurricanes: Floyd (1999), Bonnie (1998), and Fran (1996). The most useful explanatory variables are the number of transformers in the area, the company affected, maximum gust wind speed, and a hurricane effect. Wind speeds were estimated using a calibrated hurricane wind speed model. Pseudo R-squared values and other diagnostic statistics are developed to facilitate model selection with generalized negative binomial models.
In this paper, we present simple opportunistic relaying with decode-and-forward (DaF) and amplify-and-forward (AaF) strategies under an aggregate power constraint. In particular, we consider distributed relay-selection algorithms requiring only local channel knowledge. We show that opportunistic DaF relaying is outage-optimal, that is, it is equivalent in outage behavior to the optimal DaF strategy that employs all potential relays. We further show that opportunistic AaF relaying is outage-optimal among single-relay selection methods and significantly outperforms an AaF strategy based on equal-power multiple-relay transmissions with local channel knowledge. These findings reveal that cooperation offers diversity benefits even when cooperative relays choose not to transmit but rather choose to cooperatively listen; they act as passive relays and give priority to the transmission of a single opportunistic relay. Numerical and simulation results are presented to verify our analysis.
This paper proposes a probabilistic load flow method considering random branch outages as well as uncertainties of nodal power injections. Branch outages are simulated by fictitious power injections at the corresponding nodes. A unified procedure is given to deal with random branch outages, generating unit outages, and load uncertainties by their moments and cumulants. The variations of nodal voltages and line flows produced by normally and discretely distributed input variables are handled separately. The method proposed by Von Mises is employed to solve the discrete distribution part of each state and output variable. The final distribution of a desired variable is obtained by simply convoluting its continuous and discrete distribution part. Results of 24-bus IEEE Reliability Test System are analyzed and compared to those obtained by Monte Carlo simulation. A numerical test on a real power system shows the effectiveness of the proposed method.
In slow-fading scenarios, cooperation between nodes can increase the amount of diversity for communication. We study the performance limit in such scenarios by analyzing the outage capacity of slow fading relay channels. Our focus is on the low signal-to-noise ratio (SNR) and low outage probability regime, where the adverse impact of fading is greatest but so are the potential gains from cooperation. We showed that while the standard Amplify-Forward protocol performs very poorly in this regime, a modified version we called the Bursty Amplify-Forward protocol is optimal and achieves the outage capacity of the network. Moreover, this performance can be achieved without a priori channel knowledge at the receivers. In contrast, the Decode-Forward protocol is strictly suboptimal in this regime. Our results directly yield the outage capacity per unit energy of fading relay channels
In mobile networks, distance variations caused by node mobility generate fluctuations in the channel gains. Such fluctuations can be treated as another type of fading besides multipath effects. In this paper, the interference statistics in mobile random networks are characterized by incorporating the distance variations of mobile nodes to the channel gain fluctuations. The mean interference is calculated at the origin and at the border of a finite mobile network. The network performance is evaluated in terms of the outage probability. Compared to a static network, the interference in a single snapshot does not change under uniform mobility models. However, random waypoint mobility increases (decreases) the interference at the origin (at the border). Furthermore, due to the correlation of the node locations, the interference and outage are temporally and spatially correlated. We quantify the temporal correlation of the interference and outage in mobile Poisson networks in terms of the correlation coefficient and conditional outage probability, respectively. The results show that it is essential that routing, MAC, and retransmission schemes need to be smart (i.e., correlation-aware) to avoid bursts of transmission failures.