(471i) Dynamic Optimization of Li-Ion Battery Systems for Grid-Connected High Current Density Operation

­­Title: Dynamic Optimization of Li-Ion Battery Systems for Grid-Connected High Current Density Operation

Authors: Chungho Suh, Chrysanthos E. Gounaris, Debangsu Bhattacharyya

Traditionally, energy generation has relied heavily on fossil fuels. However, in order to achieve the goals set out by the Paris Agreement, reliance on fossil fuels must be dramatically diminished by increasing renewable energy penetration. One of the greatest challenges with the renewable energy sources is due to their intermittency. This not only causes an increased cycling operation of the power plants leading to efficiency loss, higher emissions, and an adverse effect on plant health, but also prevents higher penetration of renewables to the grid [1]. To promote higher penetration of renewables to the grid, development of efficient energy storage technologies is absolutely critical. While many candidate energy storage technologies are being investigated, grid-level Li-ion batteries have great promise as a storage technology due to their wide-ranging power ratings, high cycle efficiency, and fast response times. While dynamics and charging/discharging characteristics of Li-ion batteries have been investigated earlier for applications in electric cars, dynamic optimization of these batteries for grid-level applications is yet to be thoroughly investigated [2][6]. Grid-level operation has some distinct characteristics compared to electric car applications including extremely fast yet uncertain charging/discharging requirements, very high current density operation, and resource constraints (i.e. if excess energy is not available, the battery may not be desired even if the state of charge is low). In addition, it is desired to maximize the roundtrip efficiency [5].

As a first step to the model-based dynamic optimization problem, a 1-D dynamic model of a Li-ion battery stack is developed [3][4]. Governing equations for the conservation of both Li-ion species and charge are considered. These equations are applied to both the electrolyte and solid phases. Polynomial approximation and volume-averaging are used to eliminate the radial dependence of the solid-phase concentration, resulting in a system of partial differential equations (PDEs). Coordinate transformation, spatial discretization and orthogonal collocation are used for developing a system of equations that are used for optimization [3].

For grid-connected systems, battery packs can be charged when there is excess energy available while discharging them when there is discrepancy between the demand and supply [5]. Given the current cost of the Li-ion batteries, it is unlikely that in the near-future, battery packs that can provide grid-level power for long duration will be economically viable. They are likely to be deployed for addressing discrepancy between the demand and supply that are high but of shorter duration [7]. Such scenarios have considerable uncertainty in the magnitude of discrepancy, its duration, and time of the day/night. Thus it is desired to solve a multi-scenario nonlinear programming (NLP) problem. Furthermore, high current density operation can cause overheating and fire. High current density operation can also significantly reduce the battery efficiency while improving the grid resiliency and reducing the ramp rate for the fossil-fired generators. Therefore it is desired to solve a multi-objective dynamic optimization problem. If the rating of the battery pack is increased, operating current density at any instant of time can be reduced for the same level of discrepancy. While a lower current density operation can improve the cell efficiency, it also increases the capital cost. Therefore rating of the battery pack is a critical decision variable. In addition to rating, cell dimensional variables and its charging/discharging profiles are also optimized. Overall, a multi-scenario, multi-objective dynamic optimization problem is solved for optimal rating, design and operation of the grid-connected Li-ion batteries. For tractability of this large scale NLP, sparsity in the structure of the system of equations is exploited.

References

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