Objective functions

The optimal solution of any model is optimal only with respect to the model itself, not necessarily with respect to the real system (Loucks and Van Beek, 2005). Also in this study, subjectively chosen loss functions were used. The results are dependent on this selection and thus, precise conclusions should be avoided. For example, both reservoir systems could probably be operated more efficiently with respect to hydropower

production if the whole live capacity could be utilised through the year without any objective water levels. In practice, water level limits decrease the live capacity of the system.

The basis for the selection of the loss functions was the current operation policy of the system. The objective water levels were set on the basis of the recent studies on River Kymijoki, but in the case study of Lake Pyhäjärvi they were mainly set subjectively. The absolute water level limits are set in the regulation licenses except for the lower water level limit in Lake Ruotsalainen and limits in Lake Päijänne. These limits were subjectively set. In the case study of River Kymijoki, the loss functions were similar for each of the lakes. By putting more weight on the water level violations in Lake Päijänne, the flood and drought problems downstream had probably been larger. Now, the capacity of Lake Päijänne was used to avoid larger water level violations downstream.

The objective water levels were set for the 1st and the 15th of each month. At the same

time, an update frequency of 15 days was used for the forecasts. Thus, during the simulation period the forecast dates varied between, for example, the first, tenth or,

say 28th, of any month. As a consequence, the objective water levels are not at exactly

the same spot for every optimisation problem, and sometimes only a single objective water level falls into the period of 30 days. If the forecast period is long, the effect on the results is insignificant, but for the short forecast lengths, it might underline the importance of hydropower production by using the maximum capacity of the hydropower plants at the expense of the water levels of the studied lakes. However, the most relevant results are related to the longer forecasts and therefore, this drawback is not considered that significant.

In the River Kymijoki basin, the financial costs caused by the high water levels have been studied (Eskola, 1999). The financial losses caused by floods for agriculture, forestry and buildings have been approximated. The curves relating these variables to the water level limits in the River Kymijoki basin were available, but they were not used. It is obvious that the whole system is operated much more strictly than on the basis of purely economic values. The absolute water level limits are obeyed although the economic losses caused by the violations would not be large.

The price of electricity has recently risen and this increases the financial value of the inflow forecasts. In this study, constant prices were used and an assumption was made that all produced electricity can always be sold immediately at the given price. In reality, the price of electricity is dependent on the market situation and that should also be taken into account in the release optimisation. In addition, one of the biggest benefits of hydropower production is the easy usage of power plants to control the variations in electricity consumption. Hydropower plants are easily shut down and turned on again. In this study, the usage of hydropower plants for control is not taken into account. This is a drawback, but the effects of using hydropower for control could not be taken into account because the electricity markets were not modelled. This is also the reason why the additional value of the inflow forecasts in the light of non-firm and firm electricity markets was not studied. As shown by Hamlet et al. (2002), earlier inflow forecasts can increase the possibility of making non-firm electricity delivery deals with a large additional economical value for hydropower companies.

The efficiency factors of the power plants were set constant in the study. Constant values were also used for the heads of the different plants except for the Vuolenkoski

power plant. Hence, the need for hydraulic models was avoided. If these were taken into account, it is probable that slightly higher water levels would have been aimed at especially in the case study of Lake Pyhäjärvi. It is reasonable to assume that neither of these simplifications has affected the general results. This is supported by the fact that by using the observed release sequences, the hydropower production of the simulation model was close to the production reported by the power companies. The results are analysed only in the light of the water level and release limit violations and hydroelectric power production. Ecological aspects such as breeding of fishes and nesting of birds are not studied in detail. It is supposed that the objective water levels that are set to take into account these matters, guarantee a good state of the lakes for breeding of different species. It is possible, however, that large forecast errors occurring in springtime may cause severe problems for nesting of birds although only occasional violations of the water level limits would occur. The value of the inflow forecasts for different seasons was not studied separately. For example, it might be reasonable to use longer forecasts for the seasons with a low inflow because the live capacity of the lake is larger compared with the average inflow of the period in question.

Despite the limitations and simplifications of the methodology discussed in the previous chapters, the results are in line with the outcomes of similar international studies. High accuracy of forecasts should be aimed at if reservoirs are small compared with annual inflow (Lake Päijänne). With large reservoirs, long-term forecasts should be utilised without focusing too much on accuracy (Lake Pyhäjärvi). Similar conclusions have been presented in the studies of Kim and Palmer (1997) and Takeuchi and Sivaarthitkul (1995).