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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 3He 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, 3He 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 3He.

In a companion manuscript (Frolov et al 2014 New J. Phys. 16 art. no.) , we developed a novel optimization method for the placement, sizing, and operation of flexible alternating current transmission system (FACTS) devices to relieve transmission network congestion. Specifically, we addressed FACTS that provide series compensation (SC) via modification of line inductance. In this sequel manuscript, this heuristic algorithm and its solutions are explored on a number of test cases: a 30-bus test network and a realistically-sized model of the Polish grid (∼2700 nodes and ∼3300 lines). The results from the 30-bus network are used to study the general properties of the solutions, including nonlocality and sparsity. The Polish grid is used to demonstrate the computational efficiency of the heuristics that leverage sequential linearization of power flow constraints, and cutting plane methods that take advantage of the sparse nature of the SC placement solutions. Using these approaches, we can use the algorithm to solve a Polish transmission grid in tens of seconds. We explore the utility of the algorithm by analyzing transmission networks congested by (i) uniform load growth, (ii) multiple overloaded configurations, and (iii) sequential generator retirements.

We explore optimization methods for planning the placement, sizing and operations of flexible alternating current transmission system (FACTS) devices installed to relieve transmission grid congestion. We limit our selection of FACTS devices to series compensation (SC) devices that can be represented by modification of the inductance of transmission lines. Our master optimization problem minimizes the l1 norm of the inductance modification subject to the usual line thermal-limit constraints. We develop heuristics that reduce this non-convex optimization to a succession of linear programs (LP) that are accelerated further using cutting plane methods. The algorithm solves an instance of the MatPower Polish Grid model (3299 lines and 2746 nodes) in 40 seconds per iteration on a standard laptop—a speed that allows the sizing and placement of a family of SC devices to correct a large set of anticipated congestions. We observe that our algorithm finds feasible solutions that are always sparse, i.e., SC devices are placed on only a few lines. In a companion manuscript, we demonstrate our approach on realistically sized networks that suffer congestion from a range of causes, including generator retirement. In this manuscript, we focus on the development of our approach, investigate its structure on a small test system subject to congestion from uniform load growth, and demonstrate computational efficiency on a realistically sized network.