No abstract

An energy hub, which receives, converts, stores and delivers different energy carriers by means of variety of energy converters and/or storage elements, is one of the most important concepts in multi-carrier energy systems. For cost-effective and reliable supply of energy to loads in multi-carrier energy systems, the problem of selecting different components forming the hub (referred to as hub design) and their operation is of great importance. In this paper, a comprehensive linearized model for optimal design and operation of energy hubs considering reliability constraints is proposed. Adequacy indices and maximum allowable loss of load probability (LOLP) in case of single contingency are checked and different reliability constraints are introduced in the optimization process to satisfy the required level of reliability for different load types. Finally, the proposed method is applied on a test case considering electrical and thermal loads. Obtained results show the ability of the proposed method in meeting energy demand while respecting reliability constraints.Index terms--Adequacy, energy hub, energy storage, reliability NOMENCLATURE The main notation used throughout this paper is stated below. Other symbols are defined as needed. Indices: UB ELNS Upper bound of ELNS. UB EENS Upper bound of EENS. UB LOLE Upper bound of LOLE.

Sequential model-based design of experiments (MBDoE) uses information from previous experiments to select new experimental conditions. Computation of MBDoE objective functions can be impossible due to a noninvertible Fisher information matrix (FIM). Previously, we evaluated a leave-out (LO) approach that designed experiments by removing problematic model parameters from the design process. Unfortunately, the LO approach can be computationally expensive due to its iterative nature. In this study, we propose a simplified Bayesian approach that makes the FIM invertible by accounting for prior parameter information. We compare the proposed simplified Bayesian approach to the LO approach for sequential A-optimal design. Results from a pharmaceutical case study show that the proposed approach is superior, on average, for design of experiments. We suggest that simplified Bayesian MBDoE should be combined with a subset-selection-based approach for parameter estimation. This combined methodology gave the best results on average for the case study.

The sequential model-based optimal design of experiments (e.g., A-, D-, and E-optimal design) is a well-known technique for selecting experimental conditions that lead to informative data for obtaining reliable parameter estimates and model predictions. An important computational step for selecting new model-based experiments is to compute the inverse of the Fisher information matrix (FIM) which may not be invertible. In this study, three different methodologies for selecting new experiments are compared for situations where the FIM is noninvertible. The first approach finds and leaves out problematic parameters that make FIM noninvertible and then designs experiments using a reduced FIM (LO approach). The second approach uses a Moore-Penrose pseudoinverse of the FIM in A-optimal design calculations (PI approach). The third methodology is an ad hoc approach which does not require optimization. In this MS approach, the modeler selects settings at corners of the specified design space. Comparisons are made using two linear regression models and a nonlinear dynamic model for production of a pharmaceutical agent. Monte Carlo simulation results show that experimental settings obtained by LO and PI approaches give better parameter estimates on average than the MS approach, with the LO approach giving the best estimates in 20 of 24 linear situations studied. The LO approach also gives the best parameter estimates on average for the nonlinear pharmaceutical model.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights Sequential model-based design of experiments results in informative experimental data for estimating parameters and making predictions using fundamental models.  Inversion of Fisher Information Matrix (FIM) is required for model-based design of experiments. The FIM may be noninvertible for complex chemical and pharmacological process models. Parameter subset selection leaves out problematic parameters, resulting in a reduced FIM that is effective for experimental design.