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The art of estimating future values of a random process, based upon previously observed or estimated values, is usually known as a priori estimation, prediction, or forecasting. Power system state estimation process can be enhanced if state/measurement forecasts are incorporated into it. Important research efforts have been made in this direction bringing a fresh perspective to the state estimation problem. This paper (Part I) presents a comprehensive survey of forecasting-aided state estimators. It gathers up-covering a period of three decades-research results on the main benefits achieved by state estimators with forecasting capability regarding: data redundancy, innovation analysis, observability, filtering, bad data, and network configuration and parameter error processing. Aspects of modeling, forecasting techniques, and computational effort are also addressed. The second of this two-paper series presents the results of the implementation of a forecasting-aided state estimator in the energy management system of the LIGHT Services of Electricity, a company which provides electric energy to Rio de Janeiro, Brazil.