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Many European countries aim for a low-carbon electricity system, mainly by replacing fossil fuels with renewable electricity. This structural change might redistribute the associated benefits and burdens. Some regions may benefit from positive impacts, such as new employment linked to new low-carbon infrastructures and reduced air pollution. Other regions may become disproportionally burdened by negative impacts, such as increased land use from new low-carbon infrastructures and economic losses from divestment of fossil-fuel infrastructures. The distribution of these benefits and burdens and associated regional equity implications are uncertain due to the complexity and long-term time horizon of transitioning the electricity system. Yet, anticipating and improving such regional equity implications matters, as this could foster the success of implementing the transition, reduce social and economic inequities, and reduce the need for policy mechanisms to compensate for inequitable outcomes. Given the increased policy interest in equity, finding new ways to anticipate and mitigate the regional equity implications and uncertainties around implementing a low-carbon electricity system has become a new research frontier. Representing regional impacts, equity implications, and uncertainties in conventional electricity system models is challenging due to the narrow scope, aggregated geographic scale, and computational complexity of existing models. Regarding scope, conventional models typically only focus on assessing the technical and economic feasibility of future low-carbon electricity systems. These models ignore other aspects that matter to society that could limit feasibility, such as employment impacts. Regarding scale, continent-scale models rarely account for sub-national regions. However, missing these spatial details would overlook the regions that may become disproportionally burdened. Regarding computation, conventional models often only quantify a handful of scenarios to keep models solvable within a reasonable time, and these scenarios typically only aim to minimize costs. Such scenarios can potentially produce misleading results and underplay the large degree of freedom for cost-efficiently implementing a low-carbon electricity system. What is still missing in current research is a modeling framework that investigates regional impacts, equity implications, and uncertainties. Here, I develop such a holistic modeling framework and investigate the following three conceptual, methodological, and case study questions. For the conceptual questions, I review existing energy justice frameworks and develop new conceptual frameworks and equity metrics for guiding the quantitative analysis of regional equity with electricity system models. For the methodological questions, I demonstrate how to quantify regional equity implications with electricity system models, including an analysis of multi-dimensional regional impacts and uncertainties. Finally, for the case study questions, I quantify the regional impacts, equity implications, and uncertainties of implementing a low-carbon electricity system in 2035 for four case studies in Switzerland, Central Europe, and Europe as a whole.