Energy system optimization models (ESOMs) have been used extensively in providing insights to decision makers on issues related to climate and energy policy. However, there is a concern that the uncertainties inherent in the model structures and input parameters are at best underplayed and at worst ignored. Compared to other types of energy models, ESOMs tend to use scenarios to handle uncertainties or treat them as a marginal issue. Without adequately addressing uncertainties, the model insights may be limited, lack robustness, and may mislead decision makers. This paper provides an in-depth review of systematic techniques that address uncertainties for ESOMs. We have identified four prevailing uncertainty approaches that have been applied to ESOM type models: Monte Carlo analysis, stochastic programming, robust optimization, and modelling to generate alternatives. For each method, we review the principles, techniques, and how they are utilized to improve the robustness of the model results to provide extra policy insights. In the end, we provide a critical appraisal on the use of these methods.

Introduction

Energy models can be categorized in various ways [1]. A comprehensive review by Jebaraj and Iniyan [2] on existing energy models in 2006 classifies energy models into energy planning models, energy supply–demand models, forecasting models, renewable energy models, emission reduction models, and optimization models. Gargiulo and Ó Gallachóir [3] classify long term energy models based on underlying methodology (simulation, optimisation, economic equilibrium), analytical approach (top-down, bottom-up, hybrid [4]), and sectoral coverage (energy system [5], power system [6]). As an important branch of energy models, energy system optimization models (ESOMs) can be characterised as technology-rich, optimization models covering an entire energy system. ESOMs have been widely used to offer critical climate and energy policy insights at national, global, and regional scales [7]. These models provide an integrated, technology-rich representation of the whole energy system for analysing energy dynamics over a long-term, multi-period time horizon. Optimal solutions are computed using linear programming techniques. The results are used to explore the least cost energy system pathways for an energy secure and low carbon future, offering insights on energy transition, economic implications and environmental impacts. One of the widely used ESOM model is the MARKAL/TIMES family of models [8] developed and maintained by the Energy Technology Systems Analysis Programme (ETSAP) under the aegis of the International Energy Agency (IEA) since the 1970s. Other ESOM models include MESSAGE [9], ESME [10], OSeMOSYS [11] and TEMOA [12]. The schematic of a typical ESOM model is shown in Fig. 1. The model inputs including energy supply, energy demand and associated economic parameters are shown on the sides, and the model outputs are shown on the top and bottom. While models are becoming increasingly more complex and sophisticated, projecting 50 or 100 years into the future is inherently uncertain [13]. Edenhofer et al. [14] categorizes uncertainties into parametric and structural. Parametric uncertainties arise due to lack of knowledge about empirical values associated with model parameters, and structural uncertainties refer to uncertainties in the model equations that collectively define the model structure – examples of the latter include the default ESOM formulation that ignores the heterogeneity among decision makers in the energy system, the manner in which non economic considerations factor into energy purchasing decisions, and the role that politics, social norms, and culture play in shaping public policy. Due to model complexity, computational intensity, and the time pressure to produce relevant policy, many ESOMs have been used in a deterministic fashion with limited attention paid to uncertainty. A review of energy system models by Pfenninger points out that assessing uncertainties has become one of the major challenges of ESOMs [15]. When formalizing best practices for using ESOMs, DeCarolis et al. [16] highlight the importance of quantifying uncertainties. Ignoring uncertainty is problematic as many of the issues that ESOM analyses consider are deeply uncertain.