This paper addresses very short-term (10 s) forecasting of power demand of highly variable loads. The main purpose of this study is to develop methods useful for this type of forecast. We have completed a comprehensive study using two different time series, which are very difficult to access in practice, of 10 s power demand characterized by big dynamics of load changes. This is an emerging and promising forecasting research topic, yet to be more widely recognized in the forecasting research community. This problem is particularly important in microgrids, i.e., small energy micro-systems. Power demand forecasting, like forecasting of renewable power generation, is of key importance, especially in island mode operation of microgrids. This is due to the necessity of ensuring reliable power supplies to consumers. Inaccurate very short-term forecasts can cause improper operation of microgrids or increase costs/decrease profits in the electricity market. This paper presents a detailed statistical analysis of data for two sample low voltage loads characterized by large variability, which are located in a sewage treatment plant. The experience of the authors of this paper is that very short-term forecasting is very difficult for such loads. Special attention has been paid to different forecasting methods, which can be applied to this type of forecast, and to the selection of explanatory variables in these methods. Some of the ensemble models (eight selected models belonging to the following classes of methods: random forest regression, gradient boosted trees, weighted averaging ensemble, machine learning) proposed in the scope of choice of methods sets constituting the models set are unique models developed by the authors of this study. The obtained forecasts are presented and analyzed in detail. Moreover, qualitative analysis of the forecasts obtained has been carried out. We analyze various measures of forecasts quality. We think that some of the presented forecasting methods are promising for practical applications, i.e., for microgrid operation control, because of their accuracy and stability. The analysis of usefulness of various forecasting methods for two independent time series is an essential, very valuable element of the study carried out. Thanks to this, reliability of conclusions concerning the preferred methods has considerably increased.