(179f) Identification-Based Optimization of Thermal Energy Storage Systems Under Uncertainty
The operation of a chemical process faces multiple uncertainties, including changes in feed quality, environmental conditions, and fluctuations in process demand. As a result, these variables should be specified at the design stage in terms of probability density functions, rather than as exact values, and the process design problem should be formulated and solved as an optimization problem under uncertainty. The typical approach for addressing this class of problems consists of sampling the probability distributions of the uncertain variables to generate a number of probability-weighted scenarios, which are then used to calculate an average value of the design objective function to be minimized. The number of scenarios increases substantially with the number of uncertain variables, which in turn increases the computational resources required to solve this problem.
Focusing in particular on the case of dynamical systems operating under uncertainty, we have recently  introduced the concept of identification-based optimization (IBO). The IBO principle relies on representing the uncertain variables as time varying pseudo-random multi-level signals (PRMS), which are imposed on the differential-algebraic equation (DAE) model of the system during the optimization iterations to efficiently sample the uncertainty space. The PRMSs are generated from the probability distributions of the uncertain variables using concepts from system identification theory. IBO thus converts the infinite dimensional optimization problem under uncertainty into a dynamic optimization problem.
Motivated by the need to provide rigorous design optimization solutions for thermal energy storage systems– whose operation is inherently transient and uncertain – in this paper provides a critical investigation of two numerical frameworks that are appropriate for solving the dynamic optimization problem associated with IBO. We first consider a full discretization approach , whereby the DAE model is converted using orthogonal collocation on finite elements. Then, we consider a sequential strategy, in which a DAE solver and a nonlinear programming algorithm (NLP) work in tandem. We propose initialization methods for both algorithms, focused specifically on IBO problems.
Finally, we demonstrate these concepts in the design of a thermal energy storage system based on phase-change materials, which is used for leveling the grid load of buildings . We provide optimal design results, showing in the meantime that IBO is significantly more computationally efficient than scenario-based methods.
 S. Wang and M. Baldea. Identification-based optimization of dynamical systems design under uncertainty. Comput. Chem. Eng., 64(7):138-152, 2014.
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