Efficient operation of modern energy distribution systems often requires forecasting future energy demand. This paper proposes a strategy to estimate forecasting risk. The objective of the proposed method is to improve knowledge about expected forecasting risk and to estimate the expected cash flow in advance, based on the risk model. The strategy combines an energy demand forecasting model, an economic incentive model and a risk model. Basic guidelines are given for the construction of a forecasting model that combines past energy consumption data, weather data and weather forecast. The forecasting model is required to estimate expected forecasting errors that are the basis for forecasting risk estimation. The risk estimation strategy also requires an economic incentive model that describes the influence of forecasting accuracy on the energy distribution systems' cash flow. The economic model defines the critical forecasting error levels that most strongly influence cash flow. Based on the forecasting model and the economic model, the development of a risk model is proposed. The risk model is associated with critical forecasting error levels in the context of various influential parameters such as seasonal data, month, day of the week and temperature. The risk model is applicable to estimating the daily forecasting risk based on the influential parameters. The proposed approach is illustrated by a case study of a Slovenian natural gas distribution company.