Mohsen Saadat

Optimal trajectories for a liquid piston compressor/expander in a Compressed Air Energy Storage system with consideration of heat transfer and friction

For a Compressed Air Energy Storage (CAES) approach to be viable, the air compressor/expander must be sufficiently powerful and efficient. Since efficiency is governed by heat transfer, there is a generally a tradeoff between efficiency and compression/expansion time (or power). In this paper, we determine Pareto optimal compression/expansion profiles for a liquid piston air compressor/expander that maximizes efficiency (power) for a given power (efficiency). Compared to previous works, a numerical optimization approach is proposed that allows for more general heat transfer model, the consideration of the viscous friction, and system limitations in the optimization. The resulting optimal profiles are compared to other trajectories. At compression ratio of 10, the optimal profile results in 10%-40% increase in power density relative to other methods. Optimal geometries that trades off friction and heat transfer improvement can also be determined using this method.

Heat Transfer in a Long, Thin Tube Section of an Air Compressor: An Empirical Correlation from CFD and a Thermodynamic Modeling

Heat transfer during compression of air in a long, thin tube is studied by CFD. The tube represents one of the many in a honeycomb geometry inserted in a liquid piston air compressor to minimize temperature rise. A dimensionless number for the heat flow rate that includes the changing heat transfer area between the tube wall and air during compression is used. From the CFD results, alinear relation between the inverse of this dimensionless heat flow rate and the Stanton number is found. Using thisrelation, the transient volume-averaged temperature, and heat flow rate from the air can be well predicted by thermodynamic modeling.With the heat transfer model, a non-linear ODE is solved numerically todetermine the average temperature and pressure. The application of this study can be found in liquid piston air compressors for compressed air energy storage systems.Copyright

Combined Optimal Design and Control of a Near Isothermal Liquid Piston Air Compressor/Expander for a Compressed Air Energy Storage (CAES) System for Wind Turbines

The key component of Compressed Air Energy Storage (CAES) system is an air compressor/expander. The roundtrip efficiency of this energy storage technology depends greatly on the efficiency of the air compressor/expander. There is a trade off between the thermal efficiency and power density of this component. Different ideas and approaches were introduced and studied in the previous works to improve this trade off by enhancing the heat transfer between air and its environment. In the present work, a combination of optimal compression/expansion rate, optimal chamber shape and optimal heat exchanger material distribution in the chamber is considered to maximize the power density of a compression/expansion chamber for a given desired efficiency. Results show that the power density can be improved by more than 20 folds if the optimal combination of flow rate, shape and porosity are used together.Copyright

Revenue maximization of electricity generation for a wind turbine integrated with a Compressed Air Energy Storage system

A high-level supervisory controller is developed for a Compressed Air Energy Storage (CAES) system integrated with a wind turbine. Complementary to the low-level controllers in our previous works to track generator power and pressure, this controller coordinates different subsystems to optimize the system performance. The control strategy is obtained by solving an optimal storage/regeneration problem in order to maximize the achievable total revenue from selling electricity to the electric grid. Dynamic Programming (DP) approach is used to solve the corresponding optimal control problem that accounts for all the major losses in the CAES system as well as its nonlinear dynamics. Results show that an increase of 51% in total revenue is achievable by using the CAES system for a conventional wind turbine. Furthermore, a case study has been conducted to investigate the effect of storage system sizing on the maximum revenue.

Nonlinear Controller Design With Bandwidth Consideration for a Novel Compressed Air Energy Storage System

Maintaining the accumulator pressure regardless of its energy level and tracking the power demanded by the electrical grid are two potential advantages of the Compressed Air Energy Storage (CAES) system proposed in [1, 2]. In order to achieve these goals, a nonlinear controller is designed motivated by an energy-based Lyapunov function. The control inputs of the storage system include displacement of the pump/motor in the hydraulic transformer and displacement of the liquid piston air compressor/expander. While the latter has a relatively low bandwidth, the former is a faster actuator with a higher bandwidth. In addition, the pneumatic path of the storage vessel that is connected to the liquid piston air compressor/expander has a high energy density, whereas the hydraulic path of the storage vessel is power dense. The nonlinear controller is then modified to achieve a better performance for the entire system according to these properties. In the proposed approach, the control effort is distributed between the two pump/motors based on their bandwidths: the hydraulic transformer reacts to high frequency events, while the liquid piston air compressor/expander performs a steady storage/regeneration task. As a result, the liquid piston air compressor/expander will loosely maintain the accumulator pressure ratio and the pump/motor in the hydraulic transformer will precisely track the desired generator power. This control scheme also allows the accumulator to function as a damper in the storage system by absorbing power disturbances from the hydraulic path generated by wind gusts.© 2013 ASME

MODELING AND TRAJECTORY OPTIMIZATION OF WATER SPRAY COOLING IN A LIQUID PISTON AIR COMPRESSOR

An efficient and sufficiently power dense air compressor/expander is the key element in a Compressed Air Energy Storage (CAES) approach. Efficiency can be increased by improving the heat transfer between air and its surrounding materials. One effective and practical method to achieve this goal is to use water droplets spray inside the chamber when air is compressing or expanding. In this paper, the air compression cycle is modeled by considering one-dimensional droplet properties in a lumped air model. While it is possible to inject water droplets into the compressing air at any time, optimal spray profile can result in maximum efficiency improvement for a given water to air mass ratio. The corresponding optimization problem is then defined based on the stored energy in the compressed air and the required input works. Finally, optimal spray profile has been determined for various water to air mass ratio using a general numerical approach to solve the optimization problem. Results show the potential improvement by acquiring the optimal spray profile instead of conventional constant spray flow rate. For the specific compression chamber geometry and desired pressure ratio and final time used in this work, the efficiency can be improved up to 4%.

Optimal Control Experimentation of Compression Trajectories for a Liquid Piston Air Compressor

Air compressor is the critical part of a Compressed Air Energy Storage (CAES) system. Efficient and fast compression of air from ambient to a pressure ratio of 200-300 is a challenging problem due to the trade-off between efficiency and power density. Compression efficiency is mainly affected by the amount of heat transfer between the air and its surrounding during the compression. One way to increase heat transfer is to implement an optimal compression trajectory, i.e., a unique trajectory maximizing the compression efficiency for a given compression time and compression ratio. The main part of the heat transfer model is the convective heat transfer coefficient (h) which in general is a function of local air velocity, air density and air temperature. Depending on the model used for heat transfer, different optimal compression profiles can be achieved. Hence, a good understanding of real heat transfer between air and its surrounding wall inside the compression chamber is essential in order to calculate the correct optimal profile. A numerical optimization approach has been proposed in previous works to calculate the optimal compression profile for a general heat transfer model. While the results show a good improvement both in the lumped air model as well as Fluent CFD analysis, they have never been experimentally proved. In this work, we have implemented these optimal compression profiles in an experimental setup that contains a compression chamber with a liquid piston driven by a water pump through a flow control valve. The optimal trajectories are found and experimented for different compression times. The actual value of heat transfer coefficient is unknown in the experiment. Therefore, an iterative procedure is employed to obtain h corresponding to each compression time. The resulted efficiency versus power density of optimal profiles is then compared with ad-hoc constant flow rate profiles showing up to %4 higher efficiency in a same power density or %30 higher power density in a same efficiency in the experiment.

Iterative optimal and adaptive control of a near isothermal liquid piston air compressor in a compressed air energy storage system

The power density and efficiency of high compression ratio (~200:1) air compressors/expanders are crucial for the economical viability of a Compressed Air Energy Storage (CAES) system such as the one proposed in [1]. There is a trade-off between power density and efficiency that is strongly dependent on the heat transfer capability within compressor/expander. In previous papers, we have shown that the compression or expansion trajectory can be optimized so that for a given power, the efficiency can be optimized and vice versa. Theoretically, for high compression ratios, the improvement over ad-hoc trajectories can be significant- for example, at the same efficiency of 90%, the power can be increased by 3-5 folds [2], [3], [4], [5]. Yet, the optimal trajectories depend on the heat transfer coefficient profile that is often unknown. In this paper, we focus on the experimental study of an iterative control algorithm to track a compression trajectory that optimizes the efficiency-power trade-off in a liquid piston air compressor. First, an adaptive controller is developed to track any desired compression trajectory characterized by the temperature-volume profile. The controller adaptively estimates the unknown heat transfer coefficient. Second, the estimated heat transfer coefficient from one iteration is then used to estimate the optimal compression trajectory for the next iteration. As the estimate of the heat transfer coefficient improves from one iteration to the next, the quality of the estimated optimal trajectory also improves. This leads to successively improved efficiency. The experimental results of optimal trajectories show up to 2% improvement in compression efficiency compared to linear trajectories in a same power density.

Air compression performance improvement via trajectory optimization - Experimental validation

In an isothermal compressed air energy storage (CAES) system, it is critical that the high pressure air compressor/expander is both efficient and power dense. The fundamental trade-off between efficiency and power density is due to limitation in heat transfer capacity during the compression/expansion process. In our previous works, optimization of the compression/expansion trajectory has been proposed as a means to mitigate this tradeoff. Analysis and simulations have shown that the use of optimized trajectory can increase power density significantly (2-3 fold) over ad-hoc linear or sinusoidal trajectories without sacrificing efficiency especially for high pressure ratios. This paper presents the first experimental validation of this approach in high pressure (7bar to 200bar) compression. Experiments are performed on an instrumented liquid piston compressor. Correlations for the heat transfer coefficient were obtained empirically from a set of CFD simulations under different conditions. Dynamic programming approach is used to calculate the optimal compression trajectories by minimizing the compression time for a range of desired compression efficiencies. These compression profiles (as function of compression time) are then tracked in a liquid piston air compressor testbed using a combination of feedforward and feedback control strategy. Compared to ad-hoc constant flow rate trajectories, the optimal trajectories double the power density at 80% efficiency or improve the thermal efficiency by 5% over a range of power densities.