(373ah) A Methodology for Global Sensitivity Analysis for the Operation of Distributed Energy Systems Using a Two-Stage Approach

Optimisation-based models are often employed for the design and operation of distributed energy systems (DES). A two-stage approach often involves the optimisation of the design of a distributed energy system for a specified location or scale, and the subsequent optimisation of the operational model based on the structure recommended by the design model. The structure includes what types of generation and storage technologies should be used in the operation, related capacities and sizes, and potential locations. Often, both design and operational models are deterministic in nature, as either past or fictitious data is fed into the models to minimise an objective function such as the total cost or environmental impact due to carbon emissions. Consequently, the operational models encounter challenges when real-time data is fed, as time-variant input variables such as electricity demand, heating demand and solar insolation can be deemed uncertain. These variables could have unexpected and significant impacts on the total costs involved with the operation of distributed energy systems, leading to sub-optimality or even infeasibilities. Identifying these input variables, quantifying their uncertainties (which are then described in the models), and evaluating the influence of these variables on the outputs can lead to the design of more robust models. Such models can then be used to design and operate optimal distributed energy systems.

This paper presents a novel methodology for using global sensitivity analysis (GSA) on an operational optimisation-based model of a distributed energy system. The operational model also utilises Model Predictive Control (MPC) rolling horizon concepts (as done by [1]) to determine hourly total operational costs. The paper also addresses how some challenges and limitations encountered in the operational model can be attributed to the deterministic design model on which the structure of the operational model has been based. Furthermore, the research explores how the design can be improved to support more robust operation. Another novel aspect of this paper highlights the use of the optimisation tool GAMS alongside SobolGSA, a global sensitivity analysis software [2]. This software uses the variance-based Sobol method to generate N samples and perform global sensitivity analysis, allowing users to understand how variations in the inputs can influence the outputs, whilst accounting for the different combinations of the uncertain parameters without varying one uncertain parameter at a time.

Data from nine residential areas in the University of Surrey’s Stag Hill campus is used for the formulation of Mixed-Integer Linear Programming (MILP) design and operational models of a potential distributed energy system in this area. Electricity demand, heating demand and solar insolation are chosen as the uncertain input variables. Other input variables such as electricity buying and selling prices and generational tariffs associated with distributed energy resources are disregarded for uncertainty quantification and global sensitivity analysis, as these do not vary with each timestep, thereby having less impact than the those varying with each time step. Uncertainties in the chosen input variables are quantified using variance and characterised by assigning suitable distributions. The uncertain parameters for electricity and heating demand are assigned normal distributions, whilst solar insolation is assigned a beta distribution. SobolGSA is used for simultaneous generation of samples for the uncertain parameters based on their distributions. These are then fed into the optimisation model in GAMS, which then calculates the input variables from relevant mathematical expressions using the uncertain parameters. The twenty-four-hour operational model is looped such that the model is run once for each set of samples whilst unloading data into Microsoft Excel. The outputs of the operational model from GAMS are then fed back into the SobolGSA software for global sensitivity analysis, which generates quantitative sensitivity indices.

The proposed methodology is flexible and easy to use, as it can be modified easily for different designs and can include larger numbers of uncertain parameters or time periods if required (provided that computational resource is also available to process larger samples).

References

[1]. Mehleri, E., Papageorgiou, L.G., Markatos, N.C., Sarimveis, H., 2012, A model predictive control framework for residential microgrids, Computer Aided Chemical Engineering 30, 327-331

[2]. Kucherenko, S., 2013, SobolHDMR: A general-purpose modelling software, Methods Mol Biol. 1073, 191-224