This report considers load scheduling for decentralized combined heat and power plants where the revenue from selling power to the transmission company and the fuel cost may be time-varying. These plants produce both heat and power with a fixed ratio between these outputs. A heat storage facility is used to be able to deviate from this restriction. The load scheduling must be performed with only approximate knowledge about the future. At present in Denmark this uncertainty is only associated with the heat demand, but in the future revenues of produced energy and the fuel costs might also be uncertain and dependent on time. It is suggested to use a combination of background knowledge of the operator and computer tools to solve the scheduling problem. More specificly it is suggested that the plant is equipped with (i) an automatic on-line system for forecasting the heat demand, (ii) an interactive decision support tool by which optimal schedules can be found given the forecasts or user-defined modifications of the forecasts, and (iii) an automatic on-line system for monitoring when conditions have changed so that rescheduling is appropriate. In this report the focus is on methods applicable for items (ii) and (iii). For item (i). The approach taken in this report is explicitly to describe how the total revenue from running the plant depends on the schedule for the heat and power producing units of the plant. Hereafter optimization theory, in this case dynamic programming, is applied to find the optimal schedule. To take the uncertainties into account it might be considered to use stochastic dynamic programming. However, it is argued that this is unpractical because the forecasting system will need to be integrated into the optimization system, whereby a modular design of the software cannot be obtained. Furthermore, we believe that all relevant forecasting methods are far too complicated to allow for this integration; both uncertainties originating from the dependence of heat load on climate and from meteorological forecasts need to be taken into account. Instead we suggest that the decision support system allows the operator to investigate the sensitivity of the optimal schedule to variations in the input. Furthermore, we suggest that the system is equipped with the possibility to simulate realistic realizations of the heat demand based on the actual forecast and previous forecast errors. By letting the system find optimal schedules for each of these realizations the operator can gain some insight into the importance of the uncertainties. It is shown that with modern personal computers (e.g. 1 GHz Pentium III), operating systems (e.g. RedHat Linux 6.0), and compilers (e.g. GNU C 2.91) the calculations can be performed quickly enough to allow use to be applicable in practice. One optimal schedule covering one week can easily be found within 5 to 10 seconds. When considering many possible realizations of the future heat demand some techniques are needed to reduce the amount of CPU time required. The results indicate that it is possible to find optimal schedules for 100 realizations of heat demand using less than 3 minutes of CPU time. Furthermore, the methods allow for massive use of parallel processing.
optimization; dynamic programming
Main Research Area:
Informatics and Mathematical Modelling, Technical University of Denmark, DTU, 2000