Simulating heat load profiles in buildings using mixed effects models

The landscape of buildings is a diverse one and long-term energy system planning requires simulation tools that can capture such diversity. This work proposes a model for simulating the space-heating consumption of buildings using a linear mixed-effects model. This modelling framework captures the noise caused by the differences that are not being measured between individual buildings; e.g. the preferences of their occupants. The proposed model uses outdoor temperature and space-heating consumption measured at hourly resolution; thus, the model is able to predict the intra-day variations as well as longer effects. Given the stochastic nature of the simulation, the prediction interval of the simulation can be estimated, which defines a region where the consumption of any unobserved building will fall in. A whole year has been simulated and compared to out-of-sample measurements from the same period. The results show that the out-of-sample data is virtually always inside the estimated 90% prediction interval. This work uses data from Norwegian schools, although the model is general and can be built for other building categories. This amount of detail allows energy planners to draw a varied and realistic map of the future energy needs for a given location.

A Short-Term Hybrid Energy System Robust Optimization Model for Regional Electric-Power Capacity Development Planning under Different Pollutant Control Pressures

This paper is aimed at proposing a short-term hybrid energy system robust optimization model for regional energy system planning and air pollution mitigation based on the inexact multi-stage stochastic integer programming and conditional value-at-risk method through a case study in Shandong Province, China. Six power conversion technologies (i.e., coal-fired power, hydropower, photovoltaic power, wind power, biomass power, and nuclear power) and power demand sectors (agriculture, industry, building industry, transportation, business, and residential department) were considered in the proposed model. The optimized electricity generation, capacity expansion schemes, and economic risks were selected to analyze nine defined scenarios. Results revealed that electricity generations of clean and new power had obvious increasing risks and were key considerations of establishing additional capacities to meet the rising social demands. Moreover, the levels of pollutants mitigation and risk-aversion had a significant influence on different power generation schemes and on the total system cost. In addition, the optimization method developed in this paper could effectively address uncertainties expressed as probability distributions and interval values, and could avoid the system risk in energy system planning problems. The proposed optimization model could be valuable for supporting the adjustment or justification of air pollution mitigation management and electric power planning schemes in Shandong, as well as in other regions of China.

A column generation algorithm for solving energy system planning problems

Energy system optimization models are typically large models which combine sub-models which range from linear to very nonlinear. Column generation (CG) is a classical tool to generate feasible solutions of sub-models, defining columns of global master problems, which are used to steer the search for a global solution. In this paper, we present a new inner approximation method for solving energy system MINLP models. The approach is based on combining CG and the Frank Wolfe algorithm for generating an inner approximation of a convex relaxation and a primal heuristic for computing solution candidates. The features of this approach are: (i) no global branch-and-bound tree is used, (ii) sub-problems can be solved in parallel to generate columns, which do not have to be optimal, nor become available at the same time to synchronize the solution, (iii) an arbitrary solver can be used to solve sub-models, (iv) the approach (and the implementation) is generic and can be used to solve other nonconvex MINLP models. We perform experiments with decentralized energy supply system models with more than 3000 variables. The numerical results show that the new decomposition method is able to compute high-quality solutions and has the potential to outperform state-of-the-art MINLP solvers.