Pulse tube refrigerators are a critical enabling technology for many disciplines that require low temperatures. These refrigerators dominate the total power consumption of most modern cryostats, including those that reach millikelvin temperatures using additional cooling stages. In state-of-the-art commercial pulse tube refrigerators, the acoustic coupling between the driving compressor and the refrigerator is fixed and optimized for operation at base temperature. We show that this optimization is incorrect during the cooldown process, which results in wasted power consumption by the compressor and slow cooldown speed. After developing analytic expressions that demonstrate the need for acoustic tuning as a function of temperature, we dynamically optimize the acoustics of a commercial pulse tube refrigerator and show that the cooldown speed can be increased to 1.7 to 3.5 times the original value. Acoustic power measurements show that loss mechanism(s)-and not the capacity of the compressor-limit the maximum cooling available at high temperatures, suggesting that even faster cooldown speeds can be achieved in the future. This work has implications for the accessibility of cryogenic temperatures and the cadence of research in many disciplines such as quantum computing. Pulse tube refrigerators are a critical enabling technology for many disciplines that require low temperatures, including quantum computing. Here, the authors show that dynamically optimizing the acoustic parameters of the refrigerator can improve conventional cooldown speeds up to 3.5 times.

A wide variety of science is performed at temperatures near and below 4 K. Such low temperatures are commonly achieved using the pulse tube refrigerator, a type of cryocooler that cyclically compresses and expands helium gas to pump heat from the cold end. Here, we discuss three topics demonstrating that thermoacoustic analysis enables substantial gains in the understanding and performance of these refrigerators. We begin by showing that dynamic acoustic optimization of pulse tube refrigerators can lead to a tremendous increase in their cooldown speed (up to 3.5 times the status quo speed). This is a novel technique that is currently being commercialized. Second, we discuss the development of mass flow meters for the study of pulse tube refrigerator compressor efficiency. The flow meters are used to validate a thermoacoustic expression that more simply finds the flow rate using only pressure transducers. Third, we show that a large amount of cooling power may be extracted from the regenerators of these refrigerators without impacting the cooling power available at the cold end. Thermoacoustic analysis reveals that the real-fluid properties of helium are responsible for this capability.

Under some circumstances, pulse tube refrigerator regenerators operating in the real-fluid regime can absorb a large amount of heat between their warm and cold ends without a decrease to cooling power at their cold heat exchanger. Experiments and analysis show that this extra source of cooling is available because real-fluid thermodynamics modify the temperature profile to direct this additional heat flow toward the warm rather than the cold heat exchanger. Intermediate cooling capacity measurements in a two-stage, dual-inlet pulse tube refrigerator show that the cooling available is larger than commonly appreciated, 2 W at 7.5 K for the particular cryocooler investigated—almost nine times the 0.23 W available at the 3 K cold end. An analytical model is developed that predicts the dependence of injection temperature versus amount of injected heat and location along the regenerator; results from the model agree well with those from experiment and those generated using common numerical codes. This model is also used to explore strategies to increase the available intermediate cooling. For very high amounts of regenerator cooling, the shape of the temperature profile fundamentally changes and power flow changes occur at the cold—rather than warm—heat exchanger. Our results can guide users on how to best utilize this source of cooling and inspire designers to plan for large amounts of intermediate cooling.

The expansion of distribution power systems and the growing penetration of distributed energy resources present new challenges for situational awareness. Calibrating the extended system model with sensor system measurements and maintaining usability is one critical task. This paper presents a distribution network parameter estimation (DNPE) approach using machine learning (ML) and metering data to improve extended distribution system model quality. The reliability model can improve the ability of endpoint data to be translated into network-level situational awareness in real-time and help distribution system operators (DSOs) solve branch flow and voltage problems. In addition, a data analytic and automated processing scheme is proposed to improve the sensor data quality and prevent misleading information. The effectiveness of the proposed method is verified with advanced metering infrastructure (AMI) data on an actual utility feeder model while considering the higher penetration of photovoltaic power generation. The test of DNPE and study results are demonstrated in this paper.

The second-stage regenerators of pulse tube refrigerators are routinely used to intercept heat in cryogenic systems; however, optimal methods for heat sinking to the regenerator have not been studied in detail. We investigated intermediate cooling methods by densely instrumenting a commercial, two-stage pulse tube refrigerator with thermometers and heaters. We then experimentally emulated heat loads from common sources such as arrays of electrical cables (a single-point conductive load) and 3 He return gas for dilution refrigerators (a distributed load). Optimal methods to absorb these heat loads, whether applied independently or simultaneously, are presented. Our study reveals the importance of understanding the response of the regenerator temperature profle for optimal thermal integration of heat loads along the regenerator, i.e., temperatures and heat fows at all heat sink locations. With optimal utilization of regenerator intermediate cooling, 3 He fow rates of up to 2 mmol/s can be cooled from 50 K to 3 K and fully condensed using this pulse tube refrigerator; alternatively, the heat leak from over 100 electrical cables can be cooled across that same temperature span while simultaneously condensing 1.4 mmol/s of 3 He.

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 article 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 is validated using both linearized and nonlinear ac power flow samples in test distribution grids.

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 article 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, and 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 important, 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.

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.

Power distribution grids are structurally operated radially, such that energized lines form a collection of trees with a substation at the root of each tree. The operational topology 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 the radial operational structure of the distribution grid from synchronized voltage measurements. 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, and in particular Gaussian, for injections. We validate the algorithm through extensive experiments on ac three-phase IEEE distribution grid test cases.

This work considers the task of finding an ac-feasible operating point of a severely damaged transmission network while ensuring that a maximal amount of active power loads can be delivered. This AC maximal load delivery (AC-MLD) task is a nonconvex nonlinear optimization problem that is incredibly challenging to solve on large-scale transmission system data sets. This work demonstrates that convex relaxations of the AC-MLD problem provide a reliable and scalable method for finding high-quality bounds on the amount of active power that can be delivered in the AC-MLD problem. To demonstrate their effectiveness, the solution methods proposed in this work are rigorously evaluated on 1000 N-k scenarios on seven power networks ranging in size from 70 to 6000 buses. The most effective relaxation of the AC-MLD problem converges in less than 20 seconds on commodity computing hardware for all 7000 of the scenarios considered.

` Electrical distribution systems are often vulnerable to severe weather. Upgrades, such as microgrids, system hardening, and line redundancy, can greatly reduce the number of electrical outages during such extreme events. More recently, the networking of microgrids has received attention as a solution to further improve the resilience of distribution feeders. Although these upgrades have the potential to improve resilience, a barrier to their execution is a lack of tools and approaches that support systematic exploration of the underlying parameters of these upgrades and their cost vs. resilience tradeoffs.To address this gap, we develop a method for designing resilient distribution grids, including networked microgrids, by posing the problem as a two-stage stochastic program. When resilience is defined as the ability of a network to supply load immediately following a storm event, we show that a decomposition-based heuristic algorithm scales to a 1200-node distribution system. We also vary the study parameters, i.e., the cost of microgrids relative to system hardening and target resilience metrics. In this study, we find regions in this parametric space that correspond to different resilient distribution system architectures, such as individual microgrids, hardened networks, and a transition region that suggests the benefits of microgrids networked via hardened circuit segments.

This paper presents a new co-optimization formulation for energy storage for performing energy arbitrage and power factor correction (PFC) in the time scale of minutes to hours, along with peak demand shaving in the time scale of a month. While the optimization problem is non-convex, we present an efficient penalty based convex relaxation to solve it. Furthermore, we provide a mechanism to increase the storage operational life by tuning the cycles of operation using a friction coefficient. To demonstrate the effectiveness of energy storage performing multiple tasks simultaneously, we present a case study with real data for a time scale of several months. We are able to show that energy storage can realistically correct power factor without significant change in either arbitrage gains or peak demand charges. We demonstrate a real-time Model Predictive Control (MPC) based implementation of the proposed formulation with AutoRegressive forecasting of net-load and electricity price. Numerical results indicate that arbitrage gains and peak demand shaving are more sensitive to parameter uncertainty for faster ramping battery compared to slower ramping batteries. However, PFC gains are insensitive to forecast inaccuracies.

Decentralized electricity markets and greater 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, for example, 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 existing large-scale transmission grid multiple FACTS devices of two types (series capacitors and static var compensators). We account for details of the ac character of 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 versus operational expenditures. It is demonstrated that proper installation of the devices allows to do both-extend or improve the feasibility domain for the system and 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 power flow resolution for each scenario for maintaining feasible operational states during iterations. Efficiency and scalability of the approach are illustrated on the IEEE 30-bus model and the 2736-bus Polish model from Matpower.

This paper outlines the design of an intraday market-based mechanism for coordinated scheduling of gas-fired electric generation, intra-day natural gas purchases, sales and deliveries, and underlying pipeline operation. The mechanism is based on an exchange of physical and pricing data between participants in each market, with price formation in both markets being fully consistent with the physics of energy flow. In organized nodal electricity markets, prices are consistent with the physical flow of electric energy in the power grid because the economic optimization used to clear the market accounts for the physics of power flows. In the gas system, the proposed physical operation and pricing will be based on the transient optimization approach that accounts for physical and engineering factors of pipeline hydraulics and compressor station operations. The paper provides theoretical foundations for the market mechanism.

Traditional power distribution networks suffer from a lack of real-time observability. 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 paper, inspired by proliferation of metering technology, we discuss topology estimation problems in structurally loopy but operationally radial distribution grids from measurements, for example, voltage data, which are either already available or can be made available with a relatively minor investment. The primary objective of this paper is to learn the operational layout of the grid. Further, the structure learning algorithm is extended to cases with missing data, where available observations are limited to a fraction of the grid nodes. The algorithms are computationally efficient-polynomial in time-which is proven theoretically and illustrated in numerical experiments on a number of test cases. The techniques 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.

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.

The large size of multiscale, distribution and transmission, power grids hinders fast systemwide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable for fast simulations and follow-up applications. While the classical Kron reduction has been successful in reduced order modeling of power grids with traditional, hierarchical design, the selection of reference nodes for the reduced model in a multiscale, distribution and transmission, network becomes ambiguous. In this work we extend the use of the iterative Kron reduction by utilizing the electric grid's graph topology for the selection of reference nodes, consistent with the design features of multiscale networks. Additionally, we propose further reductions by aggregation of coherent subnetworks of triangular meshes, based on the graph topology and network characteristics, in order to preserve currents and build another power-flow equivalent network. Our reductions are achieved through the use of iterative aggregation of subgraphs that include general tree structures, lines, and triangles. Important features of our reduction algorithms include that (i) the reductions are either equivalent to the Kron reduction or otherwise produce a power-flow equivalent network; (ii) due to the mentioned power-flow equivalence, the reduced network can model the dynamic of the swing equations for a lossless, inductive, steady state network; (iii) the algorithms efficiently utilize hash tables to store the sequential reduction steps. The third feature allows for easy reintroduction of detailed models into the reduced, conceptual network and makes the final reduced order model backward compatible with a sequence of intermediate, partially reduced networks with varying resolution-the ordered sequence of iterative reductions corresponds to a sequence of reduced order models. The performance of our graph reduction algorithms and features of the reduced grids are discussed on a real-word transmission and distribution grid. We produce visualizations of the reduced models through open source libraries and release our reduction algorithms with example code and toy data.

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.

The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes more significantly in real-time. In this paper, we aim at developing control policies that are able to track the optimal set-point with high probability. The approach is based on the observation that the OPF solution corresponding to a certain uncertainty realization is a basic feasible solution, which provides an affine control policy. The optimality of this basis policy is restricted to uncertainty realizations that share the same set of active constraints. We propose an ensemble control policy that combines several basis policies to improve performance. Although the number of possible bases is exponential in the size of the system, we show that only a few of them are relevant to system operation. We adopt a statistical learning approach to learn these important bases, and provide theoretical results that validate our observations. For most systems, we observe that efficient ensemble policies constructed using as few as ten bases, are able to obtain optimal solutions with high probability.

The recent and rapid shift towards the increased use of natural gas for power generation has convinced both power grid operators and regulators that additional coordination between electric power and natural gas transmission is needed to ensure the reliable operation of both systems. We report on an ongoing modeling effort for joint gas-grid expansion planning. We develop a Combined Electricity and Gas Expansion (CEGE) planning model that determines least-cost network expansions for power and gas transmission in a way that endogenizes the effects of expansion decisions on locational costs for electric power and natural gas deliveries. The CEGE model, which leverages recent advances in convex approximations for large-scale nonlinear systems, is illustrated on a new gas-grid test system topologically similar to the Northeastern United States. We show that the CEGE model is computationally tractable, and how the model might be used to jointly plan infrastructures to avoid extreme events such as the coincident gas-electric peaks experienced during the 2014 polar vortex.