Probabilistic analysis of heat demand in district heating supply

Fifth-generation district heating systems have appeared in the heating supply of modern cities. There is a growing demand for the use of renewable energy sources, the most significant of which is geothermal energy. Implementing district heating systems is very costly, and reducing investment and operating costs requires accurate forecasting of expected heating demands and uncertainty analysis. The design of district heating systems begins with determining the heat demand to be supplied. The heating demand maximum occurring with a 1% frequency (24-h duration) is called the representative heating demand. In our study, we deal with the probability theory of heating demands. Heating demands are also uncertain primarily due to the uncertainties in meteorological and weather characteristics and, in a mathematical sense, are random variables. We must emphasize that any description that follows a deterministic approach in determining heating demands does not meet the criteria of modern science and can lead to severe planning and operational errors. In our study, following a probabilistic approach, we present a mathematical model that allows the determination of heating demands using probabilistic tools. With the help of the model, we can determine the low-risk representative heat demand and, through this, assess whether the available heat production capacity is sufficient with the prescribed safety or whether its expansion is necessary. Furthermore, in operation, we can prepare with the least risk of the short- and long-term forecasted values of meteorological factors. In our study, using the presented probabilistic method, we proved that for the most common prefabricated housing units in Hungary (approximately 500,000), there is a 30% uncertainty in the representative-previously accepted as 5000 W-heat demand, which, if considered in operation, can avoid significant costs. Our investigations showed that under representative meteorological conditions, the standard deviation of the expected heat demand is 1119 W, while the expected value is 3700 W. With the help of the presented model, the errors and uncertainties in the parameters used to calculate heat demand can be extensively analyzed.