The performance of electrostatic precipitators has been predicted by the Deutsch equation and its modifications over a long period, and ESP index is a good tool among them which considers the importance of electrical discharge. The present work shows the theoretical development of ESP index and the relevant model. The collection process considering migration induced by both electrostatic attraction and deposition is simulated. Subsequently, the model is applied to calculate grade collection efficiency for particles larger than 0.02 mu m in electrostatic precipitators. The physical meaning of two coefficients, alpha (relative to particle charging and migration) and beta (relative to particle deposition) in the model is clarified. By integrating and averaging the alpha and beta values, the overall collection efficiency is obtained. The present predictions agree well with experimental data. The model is also able to predict variations of particle collection at different gas temperature. The particle mass emissions at the ESP outlets decrease linearly with the ESP index or its square root. It is expected that the present model can facilitate the design and sizing of the ESPs. (C) 2019 Elsevier B.V. All rights reserved.