Scott Backhaus

Petr Šulc, Scott Backhaus, Michael Chertkov

We formulate the control of reactive power generation by photovoltaic inverters in a power distribution circuit as a constrained optimization that aims to minimize reactive power losses subject to finite inverter capacity and upper and lower voltage limits at all nodes in the circuit. When voltage variations along the circuit are small and losses of both real and reactive powers are small compared to the respective flows, the resulting optimization problem is convex. Moreover, the cost function is separable enabling a distributed, on-line implementation with node-local computations using only local measurements augmented with limited information from the neighboring nodes communicated over cyber channels. Such an approach lies between the fully centralized and local policy approaches previously considered. We explore protocols based on the dual ascent method and on the Alternating Direction Method of Multipliers (ADMM) and find that the ADMM protocol performs significantly better.

Deepjyoti Deka, Scott Backhaus, Michael Chertkov

Distribution grids represent the final tier in electric networks consisting of medium and low voltage lines that connect the distribution substations to the end-users. Traditionally, distribution networks have been operated in a radial topology that may be changed from time to time. Due to absence of a significant number of real-time line monitoring devices in the distribution grid, estimation of the topology is a problem critical for its observability and control. This paper develops a novel graphical learning based approach to estimate the radial operational grid structure using voltage measurements collected from the grid loads. The learning algorithm is based on conditional independence tests for continuous variables over chordal graphs and has wide applicability. It is proven that the scheme can be used for several power flow laws (DC or AC approximations) and more importantly is independent of the specific probability distribution controlling individual bus power usage. The complexity of the algorithm is discussed and its performance is demonstrated by simulations on distribution test cases.

Sidhant Misra, Michael W. Fisher, Scott Backhaus et al.

Natural gas transmission pipelines are complex systems whose flow characteristics are governed by challenging non-linear physical behavior. These pipelines extend over hundreds and even thousands of miles. Gas is typically injected into the system at a constant rate, and a series of compressors are distributed along the pipeline to boost the gas pressure to maintain system pressure and throughput. These compressors consume a portion of the gas, and one goal of the operator is to control the compressor operation to minimize this consumption while satisfying pressure constraints at the gas load points. The optimization of these operations is computationally challenging. Many pipelines simply rely on the intuition and prior experience of operators to make these decisions. Here, we present a new geometric programming approach for optimizing compressor operation in natural gas pipelines. Using models of real natural gas pipelines, we show that the geometric programming algorithm consistently outperforms approaches that mimic existing state of practice.

Krishnamurthy Dvijotham, Scott Backhaus, Misha Chertkov

As the penetration level of transmission-scale time-intermittent renewable generation resources increases, control of flexible resources will become important to mitigating the fluctuations due to these new renewable resources. Flexible resources may include new or existing synchronous generators as well as new energy storage devices. The addition of energy storage, if needed, should be done optimally to minimize the integration cost of renewable resources, however, optimal placement and sizing of energy storage is a difficult optimization problem. The fidelity of such results may be questionable because optimal planning procedures typically do not consider the effect of the time dynamics of operations and controls. Here, we use an optimal energy storage control algorithm to develop a heuristic procedure for energy storage placement and sizing. We generate many instances of intermittent generation time profiles and allow the control algorithm access to unlimited amounts of storage, both energy and power, at all nodes. Based on the activity of the storage at each node, we restrict the number of storage node in a staged procedure seeking the minimum number of storage nodes and total network storage that can still mitigate the effects of renewable fluctuations on network constraints. The quality of the heuristic is explored by comparing our results to seemingly "intuitive" placements of storage.

Sejun Park, Deepjyoti Deka, Scott Backhaus et al.

Efficient operation of distribution grids in the smart-grid era is hindered by the limited presence of real-time nodal and line meters. In particular, this prevents the easy estimation of grid topology and associated line parameters that are necessary for control and optimization efforts in the grid. This paper studies the problems of topology and parameter estimation in radial balanced distribution grids where measurements are restricted to only the leaf nodes and all intermediate nodes are unobserved/hidden. To this end, we propose two exact learning algorithms that use balanced voltage and injection measured only at the end-users. The first algorithm requires time-stamped voltage samples, statistics of nodal power injections and permissible line impedances to recover the true topology. The second and improved algorithm requires only time-stamped voltage and complex power samples to recover both the true topology and impedances without any additional input (e.g., number of grid nodes, statistics of injections at hidden nodes, permissible line impedances). We prove the correctness of both learning algorithms for grids where unobserved buses/nodes have a degree greater than three and discuss extensions to regimes where that assumption doesn't hold. Further, we present computational and, more importantly, the sample complexity of our proposed algorithm for joint topology and impedance estimation. We illustrate the performance of the designed algorithms through numerical experiments on the IEEE and custom power distribution models.

Deepjyoti Deka, Scott Backhaus, Michael Chertkov

Traditionally power distribution networks are either not observable or only partially observable. This complicates development and implementation of new smart grid technologies, such as those related to demand response, outage detection and management, and improved load-monitoring. In this two part paper, inspired by proliferation of metering technology, we discuss estimation problems in structurally loopy but operationally radial distribution grids from measurements, e.g. voltage data, which are either already available or can be made available with a relatively minor investment. In Part I, the objective is to learn the operational layout of the grid. Part II of this paper presents algorithms that estimate load statistics or line parameters in addition to learning the grid structure. Further, Part II discusses the problem of structure estimation for systems with incomplete measurement sets. Our newly suggested algorithms apply to a wide range of realistic scenarios. The algorithms are also computationally efficient -- polynomial in time -- which is proven theoretically and illustrated computationally on a number of test cases. The technique developed can be applied to detect line failures in real time as well as to understand the scope of possible adversarial attacks on the grid.

Soumya Kundu, Karanjit Kalsi, Scott Backhaus

With increasing availability of communication and control infrastructure at the distribution systems, it is expected that the distributed energy resources (DERs) will take an active part in future power systems operations. One of the main challenges associated with integration of DERs in grid planning and control is in estimating the available flexibility in a collection of (heterogeneous) DERs, each of which may have local constraints that vary over time. In this work, we present a geometric approach for approximating the flexibility of a DER in modulating its active and reactive power consumption. The proposed method is agnostic about the type and model of the DERs, thereby facilitating a plug-and-play approach, and allows scalable aggregation of the flexibility of a collection of (heterogeneous) DERs at the distributed system level. Simulation results are presented to demonstrate the performance of the proposed method.

Mowen Lu, Harsha Nagarajan, Emre Yamangil et al.

In recent years, there have been increasing concerns about how geomagnetic disturbances (GMDs) impact electrical power systems. Geomagnetically-induced currents (GICs) can saturate transformers, induce hot spot heating and increase reactive power losses. These effects can potentially cause catastrophic damage to transformers and severely impact the ability of a power system to deliver power. To address this problem, we develop a model of GIC impacts to power systems that includes 1) GIC thermal capacity of transformers as a function of normal Alternating Current (AC) and 2) reactive power losses as a function of GIC. We use this model to derive an optimization problem that protects power systems from GIC impacts through line switching, generator redispatch, and load shedding. We employ state-of-the-art convex relaxations of AC power flow equations to lower bound the objective. We demonstrate the approach on a modified RTS96 system and the UIUC 150-bus system and show that line switching is an effective means to mitigate GIC impacts. We also provide a sensitivity analysis of optimal switching decisions with respect to GMD direction.

Md Umar Hashmi, Deepjyoti Deka, Ana Busic et al.

The importance of reactive power compensation for power factor (PF) correction will significantly increase with the large-scale integration of distributed generation interfaced via inverters producing only active power. In this work, we focus on co-optimizing energy storage for performing energy arbitrage as well as local power factor correction. The joint optimization problem is non-convex, but can be solved efficiently using a McCormick relaxation along with penalty-based schemes. Using numerical simulations on real data and realistic storage profiles, we show that energy storage can correct PF locally without reducing arbitrage profit. It is observed that active and reactive power control is largely decoupled in nature for performing arbitrage and PF correction (PFC). Furthermore, we consider a real-time implementation of the problem with uncertain load, renewable and pricing profiles. We develop a model predictive control based storage control policy using auto-regressive forecast for the uncertainty. We observe that PFC is primarily governed by the size of the converter and therefore, look-ahead in time in the online setting does not affect PFC noticeably. However, arbitrage profit are more sensitive to uncertainty for batteries with faster ramp rates compared to slow ramping batteries.

Konstantin Turitsyn, Scott Backhaus, Maxim Ananyev et al.

We introduce and analyze Markov Decision Process (MDP) machines to model individual devices which are expected to participate in future demand-response markets on distribution grids. We differentiate devices into the following four types: (a) optional loads that can be shed, e.g. light dimming; (b) deferrable loads that can be delayed, e.g. dishwashers; (c) controllable loads with inertia, e.g. thermostatically-controlled loads, whose task is to maintain an auxiliary characteristic (temperature) within pre-defined margins; and (d) storage devices that can alternate between charging and generating. Our analysis of the devices seeks to find their optimal price-taking control strategy under a given stochastic model of the distribution market.

Deepjyoti Deka, Scott Backhaus, Michael Chertkov

Distribution grids refer to the part of the power grid that delivers electricity from substations to the loads. Structurally a distribution grid is operated in one of several radial/tree-like topologies that are derived from an original loopy grid graph by opening switches on some lines. Due to limited presence of real-time switch monitoring devices, the operating structure needs to be estimated indirectly. This paper presents a new learning algorithm that uses only nodal voltage measurements to determine the operational radial structure. The algorithm is based on the key result stating that the correct operating structure is the optimal solution of the minimum-weight spanning tree problem over the original loopy graph where weights on all permissible edges/lines (open or closed) is the variance of nodal voltage difference at the edge ends. Compared to existing work, this spanning tree based approach has significantly lower complexity as it does not require information on line parameters. Further, a modified learning algorithm is developed for cases when the input voltage measurements are limited to only a subset of the total grid nodes. Performance of the algorithms (with and without missing data) is demonstrated by experiments on test cases.

Line Roald, Sidhant Misra, Michael Chertkov et al.

Over the past years, the share of electricity production from wind power plants has increased to significant levels in several power systems across Europe and the United States. In order to cope with the fluctuating and partially unpredictable nature of renewable energy sources, transmission system operators (TSOs) have responded by increasing their reserve capacity requirements and by requiring wind power plants to be capable of providing reserves or following active power set-point signals. This paper addresses the issue of efficiently incorporating these new types of wind power control in the day-ahead operational planning. We review the technical requirements the wind power plants must fulfill, and propose a mathematical framework for modeling wind power control. The framework is based on an optimal power flow formulation with weighted chance constraints, which accounts for the uncertainty of wind power forecasts and allows us to limit the risk of constraint violations. In a case study based on the IEEE 118 bus system, we use the developed method to assess the effectiveness of different types of wind power control in terms of operational cost, system security and wind power curtailment.

Harsha Nagarajan, Russell Bent, Pascal Van Hentenryck et al.

As illustrated in recent years (Superstorm Sandy, the Northeast Ice Storm of 1998, etc.), extreme weather events pose an enormous threat to the electric power transmission systems and the associated socio-economic systems that depend on reliable delivery of electric power. Besides inevitable malfunction of power grid components, deliberate malicious attacks can cause high risks to the service. These threats motivate the need for approaches and methods that improve the resilience of power systems. In this paper, we develop a model and tractable methods for optimizing the upgrade of transmission systems through a combination of hardening existing components, adding redundant lines, switches, generators, and FACTS and phase-shifting devices. While many of these controllable components are included in traditional design (expansion planning) problems, we uniquely assess their benefits from a resiliency point of view. More importantly, perhaps, we evaluate the suitability of using state-of-the-art AC power flow relaxations versus the common DC approximation in resilience improvement studies. The resiliency model and algorithms are tested on a modified version of the RTS-96 (single area) system.

Vladimir Frolov, Priyanko Guha Thakurta, Scott Backhaus et al.

Decentralized electricity markets and more integration of renewables demand expansion of the existing transmission infrastructure to accommodate inflected variabilities in power flows. However, such expansion is severely limited in many countries because of political and environmental issues. Furthermore, high renewables integration requires additional reactive power support, which forces the transmission system operators to utilize the existing grid creatively, e.g., take advantage of new technologies, such as flexible alternating current transmission system (FACTS) devices. We formulate, analyze and solve the challenging investment planning problem of installation in an existing large-scale transmission grid multiple FACTS devices of two types (series capacitors and static VAR compensators.) We account for details of AC character of the power flows, probabilistic modeling of multiple-load scenarios, FACTS devices flexibility in terms of their adjustments within the capacity constraints, and long term practical tradeoffs between capital vs operational expenditures (CAPEX vs OPEX). It is demonstrated that proper installation of the devices allows to do both - extend or improve feasibility domain for the system and also decrease long term power generation cost (make cheaper generation available). Nonlinear, nonconvex, and multiple-scenario-aware optimization is resolved through an efficient heuristic algorithm consisting of a sequence of quadratic programmings solved by CPLEX combined with exact AC PF resolution for each scenario for maintaining feasible operational states during iterations. Efficiency and scalability of the approach is illustrated on the IEEE 30-bus model and the 2736-bus Polish model from Matpower.

Deepjyoti Deka, Michael Chertkov, Scott Backhaus

Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This paper discusses a theoretical framework to jointly estimate the operational topology and statistics of injections in radial distribution grids under limited availability of nodal voltage measurements. In particular we show that our proposed algorithms are able to provably learn the exact grid topology and injection statistics at all unobserved nodes as long as they are not adjacent. The algorithm design is based on novel ordered trends in voltage magnitude fluctuations at node groups, that are independently of interest for radial physical flow networks. The complexity of the designed algorithms is theoretically analyzed and their performance validated using both linearized and non-linear AC power flow samples in test distribution grids.

Deepjyoti Deka, Harsha Nagarajan, Scott Backhaus

The transient response of power grids to external disturbances influences their stable operation. This paper studies the effect of topology in linear time-invariant dynamics of different power grids. For a variety of objective functions, a unified framework based on $H_2$ norm is presented to analyze the robustness to ambient fluctuations. Such objectives include loss reduction, weighted consensus of phase angle deviations, oscillations in nodal frequency, and other graphical metrics. The framework is then used to study the problem of optimal topology design for robust control goals of different grids. For radial grids, the problem is shown as equivalent to the hard "optimum communication spanning tree" problem in graph theory and a combinatorial topology construction is presented with bounded approximation gap. Extended to loopy (meshed) grids, a greedy topology design algorithm is discussed. The performance of the topology design algorithms under multiple control objectives are presented on both loopy and radial test grids. Overall, this paper analyzes topology design algorithms on a broad class of control problems in power grid by exploring their combinatorial and graphical properties.

Krishnamurthy Dvijotham, Michael Chertkov, Scott Backhaus

Deviations of grid frequency from the nominal frequency are an indicator of the global imbalance between genera- tion and load. Two types of control, a distributed propor- tional control and a centralized integral control, are cur- rently used to keep frequency deviations small. Although generation-load imbalance can be very localized, both controls primarily rely on frequency deviation as their in- put. The time scales of control require the outputs of the centralized integral control to be communicated to distant generators every few seconds. We reconsider this con- trol/communication architecture and suggest a hybrid ap- proach that utilizes parameterized feedback policies that can be implemented in a fully distributed manner because the inputs to these policies are local observables at each generator. Using an ensemble of forecasts of load and time-intermittent generation representative of possible fu- ture scenarios, we perform a centralized off-line stochas- tic optimization to select the generator-specific feedback parameters. These parameters need only be communi- cated to generators once per control period (60 minutes in our simulations). We show that inclusion of local power flows as feedback inputs is crucial and reduces frequency deviations by a factor of ten. We demonstrate our con- trol on a detailed transmission model of the Bonneville Power Administration (BPA). Our findings suggest that a smart automatic and distributed control, relying on ad- vanced off-line and system-wide computations commu- nicated to controlled generators infrequently, may be a viable control and communication architecture solution. This architecture is suitable for a future situation when generation-load imbalances are expected to grow because of increased penetration of time-intermittent generation.

Sai Krishna Kanth Hari, Kaarthik Sundar, Harsha Nagarajan et al.

In recent years, microgrids, i.e., disconnected distribution systems, have received increasing interest from power system utilities to support the economic and resiliency posture of their systems. The economics of long distance transmission lines prevent many remote communities from connecting to bulk transmission systems and these communities rely on off-grid microgrid technology. Furthermore, communities that are connected to the bulk transmission system are investigating microgrid technologies that will support their ability to disconnect and operate independently during extreme events. In each of these cases, it is important to develop methodologies that support the capability to design and operate microgrids in the absence of transmission over long periods of time. Unfortunately, such planning problems tend to be computationally difficult to solve and those that are straightforward to solve often lack the modeling fidelity that inspires confidence in the results. To address these issues, we first develop a high fidelity model for design and operations of a microgrid that include component efficiencies, component operating limits, battery modeling, unit commitment, capacity expansion, and power flow physics; the resulting model is a mixed-integer quadratically-constrained quadratic program (MIQCQP). We then develop an iterative algorithm, referred to as the Model Predictive Control (MPC) algorithm, that allows us to solve the resulting MIQCQP. We show, through extensive computational experiments, that the MPC-based method can scale to problems that have a very long planning horizon and provide high quality solutions that lie within 5\% of optimal.

Scott Backhaus, Russell Bent, Daniel Bienstock et al.

Direct methods can provide rapid screening of the dynamical security of large numbers fault and contingency scenarios by avoiding extensive time simulation. We introduce a computationally-efficient direct method based on optimization that leverages efficient cutting plane techniques. The method considers both unstable equilibrium points and the effects of additional relay tripping on dynamical security\cite{01SH}. Similar to other direct methods, our approach yields conservative results for dynamical security, however, the optimization formulation potentially lends itself to the inclusion of additional constraints to reduce this conservatism.

Andrey Y. Lokhov, Nathan Lemons, Thomas C. McAndrew et al.

Cyber-physical systems are critical infrastructures that are crucial both to the reliable delivery of resources such as energy, and to the stable functioning of automatic and control architectures. These systems are composed of interdependent physical, control and communications networks described by disparate mathematical models creating scientific challenges that go well beyond the modeling and analysis of the individual networks. A key challenge in cyber-physical defense is a fast online detection and localization of faults and intrusions without prior knowledge of the failure type. We describe a set of techniques for the efficient identification of faults from correlations in physical signals, assuming only a minimal amount of available system information. The performance of our detection method is illustrated on data collected from a large building automation system.

Changhong Zhao, Michael Chertkov, Scott Backhaus

We consider joint control of a switchable capacitor and a D-STATCOM for voltage regulation in a distribution circuit with intermittent load. The control problem is formulated as a two-timescale optimal power flow problem with chance constraints, which minimizes power loss while limiting the probability of voltage violations due to fast changes in load. The control problem forms the basis of an optimization problem which determines the sizes of the control devices by minimizing sum of the expected power loss cost and the capital cost. We develop computationally efficient heuristics to solve the optimal sizing problem and implement real-time control. Numerical experiments on a circuit with high-performance computing (HPC) load show that the proposed sizing and control schemes significantly improve the reliability of voltage regulation on the expense of only a moderate increase in cost.

Deepjyoti Deka, Michael Chertkov, Scott Backhaus

Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being at the root of any tree. The operational topology/forest may change from time to time, however tracking these changes, even though important for the distribution grid operation and control, is hindered by limited real-time monitoring. This paper develops a learning framework to reconstruct radial operational structure of the distribution grid from synchronized voltage measurements in the grid subject to the exogenous fluctuations in nodal power consumption. To detect operational lines our learning algorithm uses conditional independence tests for continuous random variables that is applicable to a wide class of probability distributions of the nodal consumption and Gaussian injections in particular. Moreover, our algorithm applies to the practical case of unbalanced three-phase power flow. Algorithm performance is validated on AC power flow simulations over IEEE distribution grid test cases.

Arthur Barnes, Harsha Nagarajan, Emre Yamangil et al.

In the electrical grid, the distribution system is themost vulnerable to severe weather events. Well-placed and coordinatedupgrades, such as the combination of microgrids, systemhardening and additional line redundancy, can greatly reduce thenumber of electrical outages during extreme events. Indeed, ithas been suggested that resilience is one of the primary benefitsof networked microgrids. We formulate a resilient distributiongrid design problem as a two-stage stochastic program andmake use of decomposition-based heuristic algorithms to scaleto problems of practical size. We demonstrate the feasibilityof a resilient distribution design tool on a model of an actualdistribution network. We vary the study parameters, i.e., thecapital cost of microgrid generation relative to system hardeningand target system resilience metrics, and find regions in thisparametric space corresponding to different distribution systemarchitectures, such as individual microgrids, hardened networks,and a transition region that suggests the benefits of microgridsnetworked via hardened circuit segments.

Deepjyoti Deka, Scott Backhaus, Michael Chertkov

Distribution grids include medium and low voltage lines that are involved in the delivery of electricity from substation to end-users/loads. A distribution grid is operated in a radial/tree-like structure, determined by switching on or off lines from an underling loopy graph. Due to the presence of limited real-time measurements, the critical problem of fast estimation of the radial grid structure is not straightforward. This paper presents a new learning algorithm that uses measurements only at the terminal or leaf nodes in the distribution grid to estimate its radial structure. The algorithm is based on results involving voltages of node triplets that arise due to the radial structure. The polynomial computational complexity of the algorithm is presented along with a detailed analysis of its working. The most significant contribution of the approach is that it is able to learn the structure in certain cases where available measurements are confined to only half of the nodes. This represents learning under minimum permissible observability. Performance of the proposed approach in learning structure is demonstrated by experiments on test radial distribution grids.

Deepjyoti Deka, Scott Backhaus, Michael Chertkov

Physical Flow Networks are different infrastructure networks that allow the flow of physical commodities through edges between its constituent nodes. These include power grid, natural gas transmission network, water pipelines etc. In such networks, the flow on each edge is characterized by a function of the nodal potentials on either side of the edge. Further the net flow in and out of each node is conserved. Learning the structure and state of physical networks is necessary for optimal control as well as to quantify its privacy needs. We consider radial flow networks and study the problem of learning the operational network from a loopy graph of candidate edges using statistics of nodal potentials. Based on the monotonic properties of the flow functions, the key result in this paper shows that if variance of the difference of nodal potentials is used to weight candidate edges, the operational edges form the minimum spanning tree in the loopy graph. Under realistic conditions on the statistics of nodal injection (consumption or production), we provide a greedy structure learning algorithm with quasilinear computational complexity in the number of candidate edges in the network. Our learning framework is very general due to two significant attributes. First it is independent of the specific marginal distributions of nodal potentials and only uses order properties in their second moments. Second, the learning algorithm is agnostic to exact flow functions that relate edge flows to corresponding potential differences and is applicable for a broad class of networks with monotonic flow functions. We demonstrate the efficacy of our work through realistic simulations on diverse physical flow networks and discuss possible extensions of our work to other regimes.

Misha Chertkov, Michael Fisher, Scott Backhaus et al.

The development of hydraulic fracturing technology has dramatically increased the supply and lowered the cost of natural gas in the United States, driving an expansion of natural gas-fired generation capacity in several electrical inter-connections. Gas-fired generators have the capability to ramp quickly and are often utilized by grid operators to balance intermittency caused by wind generation. The time-varying output of these generators results in time-varying natural gas consumption rates that impact the pressure and line-pack of the gas network. As gas system operators assume nearly constant gas consumption when estimating pipeline transfer capacity and for planning operations, such fluctuations are a source of risk to their system. Here, we develop a new method to assess this risk. We consider a model of gas networks with consumption modeled through two components: forecasted consumption and small spatio-temporarily varying consumption due to the gas-fired generators being used to balance wind. While the forecasted consumption is globally balanced over longer time scales, the fluctuating consumption causes pressure fluctuations in the gas system to grow diffusively in time with a diffusion rate sensitive to the steady but spatially-inhomogeneous forecasted distribution of mass flow. To motivate our approach, we analyze the effect of fluctuating gas consumption on a model of the Transco gas pipeline that extends from the Gulf of Mexico to the Northeast of the United States.

Irina Stolbova, Scott Backhaus, Michael Chertkov

We analyze the dynamics of a distribution circuit loaded with many induction motor and subjected to sudden changes in voltage at the beginning of the circuit. As opposed to earlier work \cite{13DCB}, the motors are disordered, i.e. the mechanical torque applied to the motors varies in a random manner along the circuit. In spite of the disorder, many of the qualitative features of a homogenous circuit persist, e.g. long-range motor-motor interactions mediated by circuit voltage and electrical power flows result in coexistence of the spatially-extended and propagating normal and stalled phases. We also observed a new phenomenon absent in the case without inhomogeneity/disorder. Specifically, transition front between the normal and stalled phases becomes somewhat random, even when the front is moving very slowly or is even stationary. Motors within the blurred domain appears in a normal or stalled state depending on the local configuration of the disorder. We quantify effects of the disorder and discuss statistics of distribution dynamics, e.g. the front position and width, total active/reactive consumption of the feeder and maximum clearing time.

Michael Chertkov, Vladimir Lebedev, Scott Backhaus

The revolution of hydraulic fracturing has dramatically increased the supply and lowered the cost of natural gas in the United States driving an expansion of natural gas-fired generation capacity in many electrical grids. Unrelated to the natural gas expansion, lower capital costs and renewable portfolio standards are driving an expansion of intermittent renewable generation capacity such as wind and photovoltaic generation. These two changes may potentially combine to create new threats to the reliability of these interdependent energy infrastructures. Natural gas-fired generators are often used to balance the fluctuating output of wind generation. However, the time-varying output of these generators results in time-varying natural gas burn rates that impact the pressure in interstate transmission pipelines. Fluctuating pressure impacts the reliability of natural gas deliveries to those same generators and the safety of pipeline operations. We adopt a partial differential equation model of natural gas pipelines and use this model to explore the effect of intermittent wind generation on the fluctuations of pressure in natural gas pipelines. The mean square pressure fluctuations are found to grow linearly in time with points of maximum deviation occurring at the locations of flow reversals.

Scott Backhaus, Russell Bent, James Bono et al.

Recent years have seen increased interest in the design and deployment of smart grid devices and control algorithms. Each of these smart communicating devices represents a potential access point for an intruder spurring research into intruder prevention and detection. However, no security measures are complete, and intruding attackers will compromise smart grid devices leading to the attacker and the system operator interacting via the grid and its control systems. The outcome of these machine-mediated human-human interactions will depend on the design of the physical and control systems mediating the interactions. If these outcomes can be predicted via simulation, they can be used as a tool for designing attack-resilient grids and control systems. However, accurate predictions require good models of not just the physical and control systems, but also of the human decision making. In this manuscript, we present an approach to develop such tools, i.e. models of the decisions of the cyber-physical intruder who is attacking the systems and the system operator who is defending it, and demonstrate its usefulness for design.