The multiplicative data envelopment analysis (DEA) model is an effective tool for efficiency measurement. Using piecewise log-linear technologies, it flexibly captures key production characteristics (convexity, linearity, and concavity) of production functions. However, many existing studies have not taken into account data uncertainty and have not allowed for the distribution of uncertain data to be unknown. Therefore, this paper adopts a robust optimization approach to model uncertainties in both input and output data of decision-making units, thereby ensuring stable and reliable performance evaluation. Based on the constructed budget uncertainty set with multiplicative features, this paper proposes two robust multiplicative DEA models and reformulates them as equivalent linear programming problems through duality. To solve the problem of efficiency score not reaching 1, a new robust multiplicative DEA model is proposed, and the probability bound of constraint violation is provided. This paper measures the operational efficiency of power systems in 31 provinces and cities in China, and the results show that the developed robust multiplicative DEA models perform well in terms of efficiency scores under uncertainty.