The neural networks and their application to optimize energy production of hydropower plants system K Nachazel, M Toman Department of Hydrotechnology, Czech Technical University, Thakurova 7, 66 9 Prague 6, Czech Republic EMail: tomanm@fsv.cvut.cz Abstract This study presents results of the artificial neural network (ANN) application aimed at the optimization of utilizating the hydropower plants system on the Moravice River for energy production. The objective of this research included a proposal of operational rules of reservoir management in real time in order to obtain maximum hydropower energy. The research results indicate that the proposed technique based upon ANN employment and other methods of artificial intelligence can be more effective and rapid than other methods. Introduction The water resources system consisting of three reservoirs constructed on the Moravice River supplies the Ostrava agglomeration with drinking water. Due to the economic transition to a market-oriented economy, demands for the drinking water supply have currently fallen considerably. Consequently, efforts have been made to use the free capacity of the reservoirs for electrical energy production. The goals of this research included the completion of a proposal of the operation of the whole system. This would lead to the maximum production of electrical energy while maintaining all purposes of the system and its limiting conditions. In order to solve this problem, we first employed the simulation modelling technique. However, its application has the following well-known drawbacks: the finding of the global extreme of the objective function requires multiple
repetition of simulation experiments; convergence towards the optimal area can be very slow resulting in a higher consumption of machine time. Therefore, in the following research stage, we tried to apply ANN principles which enabled to examine the complex dynamic system behaviour and the parallel behaviour of interacting elements. The selection of this methodology was based on the real arrangement and nature of the hydropower plants system. Figure shows the scheme of the system. The complexity of the solution of the optimization problem is caused by installation of different turbines in the hydropower plants, and the interaction of turbines during operation. Two different Francis turbines have been installed in the upper, carryover Slezska Harta Reservoir. There, energy production depends on the absorption capacity and head of the turbines which changes considerably during operation. Maximum energy production may not be achieved by parallel operation of the two turbines using their whole storage capacity, i.e. the whole head, and may not even correspond to the global maximum production in the whole system. Figure Scheme of the water resources system In the central Kruzberk Reservoir, two small Banki turbines of equal absorption capacity, ensuring only the minimum required outflow under the dam, and one larger Francis turbine, working in peak times have been installed. The lower Podhradi Reservoir, which is the smallest, has an equalizing function. A Kaplan turbine and a Banki turbine have been installed there. This system of seven turbines in three hydropower plants is a dynamic, non-linear, and stochastic system whose functioning depends above all on changeable hydrological conditions. In applying the ANN, we had to solve two complex problem. Firstly, we had to find a transformation of stochastic network inputs, i.e. inflows into the reservoir, which would give the objective function global extreme which is not known in advance. Secondly, in addition to the cooperation of the turbines in various hydropower plants, we had to consider the interaction of turbines in one hydropower plant.
Research Methods The ANN problem is often formulated as the problem of learning formalism by which inputs x,..., x n are transformed into the required outputs f(w x +... + w n x n ), where f is a non-linear function, and w i is the adjustable weight. The bibliography presents various methods of determining this function (Turban 5, Kosko, Narendra 4, Hertz, Krogh, Palmer, etc.). In our problem, inputs into the hydropower plants system x,..., x n were average monthly inflows into the upper Slezska Harta Reservoir. These random quantities were observed during a limited time interval. In order to raise the solution reliability, we applied methods of the time series theory to generate 500-year random sequence. The sequence maintain the same stochastic characteristics as the actual measured flow series. In the theory of reservoirs, the target release from the reservoir during dry periods is derived from these generated flow series while considering the capacity of the reservoir. Inputs into the ANN are actual absorption capacities of turbines. They are in a certain relation to the derived target release. The theory of water reservoirs and water resources systems solves these relations. They are not solved within the theory of the ANN. In this case, we defined the objective function as a quantity of electrical energy produced in the whole hydropower plants system. For energy production in the hydropower plant, the following expression generally applies: E= 98. η Q H t, () where E is energy [kwh], η is the efficiency of the turbine, Q is the immediate absorption capacity of the turbine [m 3 s - ], H is the head of the turbine [m], t is the operation period [h]. The solution of the extreme of the objective function () appears inefficient even if we consider only one turbine. It is caused by the fact that the efficiency η changes with the absorption capacity Q as well as with the head H; both Q and H decrease with the drop of water level; therefore, the function () is non-linear. During parallel operation of several turbines, energy production E depends on the volume of water utilized by individual turbines in their operation period t. Physically, we can imagine the input of each turbine as its absorption capacity on the amount of which the quantity of produced energy depends. This energy also depends on the operation period t which can be considered as the weight of the neuron to be optimized in order to achieve maximum production. Each ANN neuron has two basic functions. The summation function for one turbine in the following form yi = Qi ti [m 3 ], () expresses the volume of water utilized in the period t. For several turbines, the following expression applies
n y = Q t i= i i [m 3 ] (3) The transfer function transforms the output value of the summation function into the output function of the neuron. The bibliography presents various linear and non-linear types of these functions, sigmoid function, and others. Figure shows the scheme of the turbines installed on real hydropower plants. The most important problem was to algorithm the process of learning in the network so that the convergence could approximate the searched objective function extreme and be numerically more effective compared to the classical simulation model. First, we analyzed possible employment of the most widely used learning algorithm of back-propagation. In the given training sequence of inputs, the application of this method would require experimental, successive selection of various output values E and the choice of appropriate weights. Figure Scheme of the turbines system Obviously, this process of learning of the network could converge very slowly towards the maximum E. In a larger system of hydropower plants, it is impossible to make reliable predictions in advance as to which operations are optimal, or close to optimal during the interaction of the plants. Such a procedure would undoubtedly comprise drawbacks which would be similar to the simulation model. For these reasons we decided to divide our research into two main parts. Within the first part, we used the genetic algorithm in addition to the usual simulation model for the solution of maximum energy production and we compared the results which we obtained. In Nachazel and Toman s 3
paper, we studied a possible application of the genetic algorithm to the exploration of utilization of maximum hydropower energy production in one reservoir. The interaction of the turbines in the same hydropower plant (see Figure for horizontal linking) can bring about deterioration of working conditions of the turbines during their parallel operation (as the head and the effectiveness of the turbines diminish during emptying of the reservoir) as compared to their individual operation. The diagram in Figure 3 shows that in a certain time period, such as one month, head conditions can deteriorate during operation of both turbines so much that during their parallel operation, less electrical energy may be produced than during the operation of one effective turbine. Figure 3 Scheme of head conditions We solved this optimization problem so that conditions for making decisions about the parallel operation of turbines were introduced into the process of learning at each discrete step in the following form IF E(t) = E, (t) < E (t) OR E, (t) < E (t) THEN E(t+) = E (t+) OR E(t+) = E (t+) (4) In these expressions, E, (t) denotes parallel operation of turbines, E (t) or E (t) means the operation of individual turbines. Decision making conditions (4) can also be formulated for more turbines. The optimal time of parallel operation of the turbines can be derived from them. Within the second part of this research, we investigated the potential employment of the ANN in the planned yearly energy production depending on stochastic hydrological conditions. In the phase of the network learning, we simulated these conditions by means of a synthetic 500-year sequence of average monthly inflows which we generated using the linear regression model (i.e. Markov chain). Thus, we obtained 500 learning samples made of twelfths of average monthly inflows in each year for the process of network learning. We then assigned average yearly energy production values to these stochastic vectors. The ANN thus answers a practically important question of the relation
of changing hydrological conditions and electrical energy production in each year under optimal operation of the whole system. However, we do not consider the research into the process of learning finished. As it is difficult to determine criteria for the learning strategy and quality of numerical setting of weights in advance, more effective methods of network convergence may be found in further research. 3 Research Results We considered 500-year synthetic series of average monthly water flows in all the three dam profiles as discrete sequences. A sample set of calculations of electrical energy produced in the Slezska Harta hydropower plant while considering the absorption capacity of the turbines Q and their operation period t is shown in Table. The absorption capacity of the larger turbine F was selected to fit within the range of 4,050-5,00 m 3 s -. The absorption capacity of the smaller turbine F fitted within the range of 0,650-0,750 m 3 s -. The maximum average yearly energy production in individual stages A, B, and C varied considerably, while the extremes remained in a comparatively narrow range of 8,445-8,46 GWh/year, which proves that the optimization area is very narrow in this case. During these calculations, the quantity of energy produced in the other hydropower plants was calculated additionally for full absorption capacities of turbines without optimizing operation in these hydropower plants, i.e. in these layers of the network. Results presented in Table prove that the maximum yearly production in the whole system varies within a narrow range of 34,67-34,756 GWh/year. In further sets of calculations, we optimized energy production in the next layer, i.e. turbines in the Kruzberk hydropower plant. The calculation methodology was again based on search of the maximum considering network weights, i.e. the time period of utilization and absorption capacity of turbines. This time, the top network layer was optimized. Iterations were facilitated by two small Banki turbines which continually ensured the minimum required outflow and did not affect energy production. Therefore, it was necessary to optimize only the energy production by the peak Francis turbine. Table 3 shows a sample set of calculations. The extremes in energy production obtained in stages A, B, and C varied within the range of 5,455-5,548 GWh/year which again proved a very narrow optimization area. The energy production values in Table 4, including the third network layer - the Podhradi hydropower plant, correspond to numerical experiments given in Table 3. The extreme values vary within the range of 34,67-34,756 GWh/year. They do not differ from the range of production in the first step of the solution. This accordance can be explained by the increase and decrease in the absorption capacity of the peak turbine which diminish energy production. Thus, the greatest production in the whole hydropower plants system
corresponds to the maximum production in the Slezska Harta hydropower plant. Table Optimization of hydropower generation on the reservoir Slezska Harta Var. 3 4 5 6 7 8 A a 5.00 0.750 4369 59 5.09 3.004 8.096 00.00 b 5.085 0.750 4467 5905 5.9 3.00 8.30 00.00 c 4.970 0.750 4637 5899 5.7.9 8.50 00.00 d 4.855 0.750 4733 5908 5.377.944 8.3 00.00 e 4.740 0.750 488 597 5.490.970 8.460 00.00 f 4.65 0.750 330 59 9.787.967.753 99.80 g 4.50 0.750 396 590 9.653.993.646 99.80 h 4.395 0.750 343 587 9.45.904.354 99.0 i 4.80 0.750 3374 5883 9.0.937.047 99.40 j 4.65 0.750 363 5898 8.659.98.64 99.80 k 4.050 0.750 358 5876 8.353.986.339 99.80 B a 5.00 0.700 44 5905 5.70.84 8. 00.00 b 5.085 0.700 4507 590 5.466.850 8.36 00.00 c 4.970 0.700 4677 597 5.397.768 8.65 00.00 d 4.855 0.700 4768 5934 5.534.788 8.3 00.00 e 4.740 0.700 486 599 5.654.80 8.455 00.00 f 4.65 0.700 335 598 9.938.846.784 99.80 g 4.50 0.700 33 5930 9.50.895.397 99.80 h 4.395 0.700 3450 5887 9.546.799.346 99.0 i 4.80 0.700 334 5899 8.990.84.83 99.60 j 4.65 0.700 358 599 8.687.883.570 00.00 k 4.050 0.700 389 5890 8.73.90.76 99.80 C a 5.00 0.650 4454 595 5.435.680 8.5 00.00 b 5.085 0.650 4540 5934 5.606.69 8.98 00.00 c 4.970 0.650 473 5906 5.56.595 8.56 00.00 d 4.855 0.650 4809 595 5.696.6 8.308 00.00 e 4.740 0.650 490 5934 5.836.64 8.46 00.00 f 4.65 0.650 395 5940 9.85.749.575 99.80 g 4.50 0.650 39 5938 9.430.789.9 99.80 h 4.395 0.650 3394 5894 9.45.697.49 99.40 i 4.80 0.650 374 5896 8.90.733.634 99.80 j 4.65 0.650 333 596 8.687.786.473 00.00 k 4.050 0.650 3099 59 8.077.80 0.888 00.00 Legend: - intake for the turbine Francis [m 3 s - ], - intake for the turbine Francis [m 3 s - ], 3 - frequency t of intakes for the turbine Francis [months], 4 - frequency t of intakes for the turbine Francis [months], 5 - quantity of the hydropower generation by the turbine Francis [GWh/year], 6 - quantity of the hydropower generation by the turbine Francis [GWh/year], 7 - quantity of the hydropower generation on the hydropower plant Sl. Harta per year [GWh/year], 8 - reliability of the water supply according to repetition on the reservoir Sl. Harta [%].
Table Maximum anual quantity of hydropower generation in the cascade on the river Moravice (the generation on the hydropower plant Slezska Harta is only optimized - var. e) Maximum anual quantity of hydropower generation Var. [GWh/year] Slezska Harta Kruzberk Podhradi Total A 8.460 5.548 0.748 34.756 B 8.455 5.496 0.75 34.70 C 8.46 5.455 0.755 34.67 Table 3 Optimization of hydropower generation on the reservoir Kruzberk (when the generation on the hydropower plant Slezska Harta is optimized - var. e) Var. 3 4 5 6 7 8 9 0 A -0.0 0.550 0.550 3.053 6000 6000 4838 0.767 0.767 3.97 5.50 5 0.00 0.550 0.550 3.063 6000 6000 5680 0.767 0.767 4.0 4 5.54 8 +0.0 0.550 0.550 3.07 6000 6000 6000 0.749 0.749 3.94 6 5.44 4 e +0.0 0.550 0.550 3.08 6000 6000 6000 0.76 0.76 3.83 7 5.8 9 +0.03 0.550 0.550 3.09 6000 6000 6000 0.700 0.700 3.7 0 5. 0 +0.04 0.550 0.550 3.0 6000 6000 6000 0.673 0.673 3.57 4.9 9 +0.05 0.550 0.550 3.0 6000 6000 6000 0.649 0.649 3.46 5 B -0.0 0.550 0.550 3.04 6000 6000 487 0.767 0.767 3.9 8 0.00 0.550 0.550 3.05 6000 6000 5680 0.767 0.767 3.96 +0.0 0.550 0.550 3.06 6000 6000 6000 0.749 0.749 3.89 5 e +0.0 0.550 0.550 3.070 6000 6000 6000 0.76 0.76 3.78 9 +0.03 0.550 0.550 3.080 6000 6000 6000 0.70 0.70 3.66 3 +0.04 0.550 0.550 3.089 6000 6000 6000 0.674 0.674 3.53 6 +0.05 0.550 0.550 3.098 6000 6000 6000 0.650 0.650 3.4 4 C -0.0 0.550 0.550 3.033 6000 6000 499 0.767 0.767 3.87 8 5 4.76 3 5.45 5.49 6 5.39 3 5.4 5.06 5 4.88 4 4.7 4 5.4 0.00 0.550 0.550 3.04 6000 6000 5695 0.767 0.767 3.9 5.45
5 +0.0 0.550 0.550 3.05 6000 6000 6000 0.750 0.750 3.85 5 5.35 5 e +0.0 0.550 0.550 3.06 6000 6000 6000 0.77 0.77 3.75 4 5.0 8 +0.03 0.550 0.550 3.07 6000 6000 6000 0.70 0.70 3.63 4 5.03 8 +0.04 0.550 0.550 3.080 6000 6000 6000 0.676 0.676 3.5 4.86 3 +0.05 0.550 0.550 3.090 6000 6000 6000 0.65 0.65 3.40 4.70 5 Legend: - increment of the absorption capacity of the turbine Francis SVE [m 3 s - ], - average intake for the turbine Banki [m 3 s - ], 3 - average intake for the turbine Banki [m 3 s - ], 4 - average intake for the turbine Francis SVE [m 3 s - ], 5 - frequency of intakes for the turbine B [months], 6 - frequency of intakes for the turbine B [months], 7 - frequency of intakes for the turbine F-SVE [months], 8 - quantity of the hydropower generation by the turbine B [GWh/year], 9 - quantity of the hydropower generation by the turbine B [GWh/year], 0 - quantity of the hydropower generation by the turbine F-SVE [GWh/year], - quantity of the hydropower generation on the hydropower plant Kruzberk per year [GWh/year]. Table 4 Optimization of hydropower generation on the whole cascade (when the generation on hydropower plants Slezska Harta and Kruzberk is optimized - var. e) Var. Maximum anual quantity of hydropower generation [GWh/year] Slezska Harta Kruzberk Podhradi Total A -0.00 8.460 5.505 0.748 34.73 0.000 8.460 5.548 0.748 34.756 +0.00 8.460 5.544 0.748 34.65 e +0.00 8.460 5.89 0.749 34.498 +0.030 8.460 5.0 0.749 34.39 +0.040 8.460 4.95 0.750 34.35 +0.050 8.460 4.763 0.750 33.973 B -0.00 8.455 5.45 0.75 34.658 0.000 8.455 5.496 0.75 34.70 +0.00 8.455 5.393 0.75 34.599 e +0.00 8.455 5.4 0.75 34.448 +0.030 8.455 5.065 0.75 34.7 +0.040 8.455 4.884 0.753 34.09 +0.050 8.455 4.74 0.753 33.93 C -0.00 8.46 5.4 0.755 34.68 0.000 8.46 5.455 0.755 34.67 +0.00 8.46 5.355 0.756 34.57 e +0.00 8.46 5.08 0.756 34.45 +0.030 8.46 5.038 0.757 34.56 +0.040 8.46 4.863 0.757 34.08 +0.050 8.46 4.705 0.758 33.93
Legend: - increment of the absorption capacity of the turbine Francis SVE [m 3 s - ] - Kruzberk The above results show that production optimization in the third layer, Podhradi, has no practical significance. This hydropower plant is the smallest, it has only an equalizing function for peak outflows from the Kruzberk hydropower plant. It has no effect on the global extreme of the system. In further step of the solution we investigated other ways of a finer search of the energy production extreme in the Slezska Harta hydropower plant, which is the most important element of the system. These analyses aimed at the assessment of a possible shift, i.e. difference between extremes in individual network layers and the global extreme of the entire system. These differences have proved to be very small, having a theoretical rather than practical importance. In Table 5 are given only numerical experiments near the extreme of Slezska Harta hydropower plant. For example, for the optimized absorption capacities of turbines from Table, F = 4,740 m 3 s - and F = 0,750 m 3 s -, we searched for values of energy produced in their close vicinity. The extreme of 8,47 GWh/year did not differ considerably from the result of preceding iterations. Table 5 Dependance of hydropower generation on Slezska Harta and on the whole cascade (near vicinity of the extreme) Var. 3 4 5 6 7 8 ea 4.740 0.750 488 597 5.490.970 8.460 00.00 eb 4.735 0.750 489 5934 5.49.974 8.466 00.00 ec 4.739 0.745 483 593 5.505.956 8.46 00.00 ed 4.737 0.745 4834 599 5.5.950 8.46 00.00 ee 4.737 0.735 484 598 5.54.98 8.46 00.00 ef 4.736 0.735 484 5930 5.549.9 8.47 00.00 eg 4.735 0.735 4844 59 5.546.97 8.463 00.00 eh 4.74 0.730 4843 598 5.565.903 8.468 00.00 Var. 9 0 3 4 5 6 7 8 ea 0.550 0.550 3.063 6000 6000 5680 0.767 0.767 4.04 5.548 eb 0.550 0.550 3.06 6000 6000 568 0.767 0.767 4.007 5.54 ec 0.550 0.550 3.06 6000 6000 568 0.767 0.767 4.00 5.544 ed 0.550 0.550 3.06 6000 6000 5678 0.767 0.767 4.007 5.54 ee 0.550 0.550 3.059 6000 6000 5677 0.767 0.767 3.998 5.53 ef 0.550 0.550 3.058 6000 6000 5683 0.767 0.767 3.994 5.58 eg 0.550 0.550 3.059 6000 6000 5683 0.767 0.767 3.996 5.530 eh 0.550 0.550 3.058 6000 6000 5683 0.767 0.767 3.994 5.58 Var. 9 0 3 4 ea.68.045 0.58 0.0 0.748 34.756 eb.69.045 0.58 0.0 0.748 34.755 ec.69.046 0.58 0. 0.749 34.754 ed.70.046 0.58 0. 0.749 34.75 ee.7.048 0.58 0. 0.749 34.743
ef.7.048 0.58 0. 0.749 34.748 eg.7.048 0.58 0. 0.749 34.74 eh.7.048 0.58 0. 0.749 34.745 Legend: - intake for the turbine Francis [m 3 s - ], - intake for the turbine Francis [m 3 s - ], 3 - frequency t of intakes for the turbine Francis [months], 4 - frequency t of intakes for the turbine Francis [months], 5 - quantity of the hydropower generation by the turbine Francis [GWh/year], 6 - quantity of the hydropower generation by the turbine Francis [GWh/year], 7 - quantity of the hydropower generation on the hydropower plant Sl. Harta per year [GWh/year], 8 - reliability of the water supply according to repetition on the reservoir Sl. Harta [%], 9 - average intake for the turbine Banki [m 3 s - ], 0 - average intake for the turbine Banki [m 3 s - ], - average intake for the turbine Francis SVE [m 3 s - ], - frequency of intakes for the turbine Banki [months], 3 - frequency of intakes for the turbine Banki [months], 4 - frequency of intakes for the turbine Francis - SVE [months], 5 - quantity of the hydropower generation by the turbine Banki [GWh/year], 6 - quantity of the hydropower generation by the turbine Banki [GWh/year], 7 - quantity of the hydropower generation by the turbine Francis - SVE [GWh/year], 8 - quantity of the hydropower generation on the hydropower plant Kruzberk per year [GWh/year], 9 - average intake for the turbine Kaplan - MVE [m 3 s - ], 0 - average intake for the turbine Banki - MVE [m 3 s - ], - quantity of the hydropower generation by the turbine Kaplan - MVE [GWh/year], - quantity of the hydropower generation by the turbine Banki - MVE [GWh/year], 3 - quantity of the hydropower generation on the hydropower plant Podhradi per year [GWh/year], 4 - quantity of the hydropower generation in the whole system per year [GWh/year]. The presented optimization method of the utilization of the hydropower plants cascade for energy production using the ANN has proved that the global extreme can be found more effectively than in cases when we used a simulation model. Moreover, the suggested operation in the whole system increased the extreme by 0,558 GWh/year (,6 %) in average as compared to the extreme derived from the simulation model. This can be considered the practical contribution of the suggested solution. In Figure 4, we showed the method of utilization of the optimized system in the training sequence using the course of filling and emptying the Slezska Harta and Kruzberk reservoirs. The course of the supply volume indicates that the Slezska Harta reservoir and the Kruzberk reservoir manage water in multiple-year cycles.
Figure 4 Example of utilization of the optimized system in the part of the training sequence Figure 5 Sample of the selection and crossing process in genetic algorithm method As we mentioned earlier in the methodology of this research, the objective function extreme can be obtained more rapidly using the genetic algorithm. In Figure 5, sample application of the process of combining two different turbines in Slezska Harta s dam and a fast convergence towards extreme values of energy production are shown. Out of eight performed experiments of combining turbines, we give a graphic representation of four experiments which brought results quite close to each other. The variation dispersion of produced energy values, i.e. maximums and minimums, for all experiments and generations is given in Table 6. Numeric results of the solution show a very good accordance with the solution obtained by means of the simulation model. Within the second part of this research, we focused on numeric modelling of the ANN which transformed the twelfths of average monthly inflows in each year to the produced energy values. This transformation was performed in a
sequence of 500 learning samples, i.e. years. Figure 6 shows the diagram of the basic version of the ANN in which only one hidden layer of neurons was used in addition to the input neuron layer. Table 7 presents an example of a few learning years which were close to average values of energy production. The back-propagation algorithm was utilized in the network learning. This network model provided very satisfactory results at the output layer. These results are fully sufficient for practical purposes of the planned hyropower energy production. Table 6 Hydropower generation on the hydropower plant Slezska Harta by the genetic algorithm method (generation in the synthetic series of 500 years of average monthly flows) Experiment No Generation No max. E year [GWh/year] min. E year [GWh/year] 0 0 3 0 3 4 0 5 0 3 6 0 3 7 0 8 0 3 4 8.46 8.465 8.465 8.459 8.460 8.460 8.96 8.68 8.96 8.96 8.459 8.465 8.465 8.66 8.59 8.66 8.66 8.465 8.453 8.465 8.465 8.453 8.457 8.457 8.96 8.64 8.64 8.64 8.64 3.330.376 8.338 3.097.3 8.378 3.370 7.953 8.0 8.08 3.37.748 8.338 3.349.65.758 8.089 3.370.648 8.3 8.338 3.355.34 8.73 3.353.686 8.60 8.60 8.60
Figure 6 Basic version of the ANN Table 7 The sample of average monthly flows from 500 training years Number Energy The sample of average monthly flows [m 3 s - ] of year [GWh/year ] XI XII I II III IV 30 34.406.3 3.656.689 6.73 4.75 4.603 30 34.373.676 3.63 3.445.965 9.637 7.98 303 34.66.900.43.864 4.49 6.44 3.949 304 34.098 3.096 8.84 4.986 0.960 8.47 9.378 305 34.080.338 3.399 5.089 6.76 0.960 9.958 Number Energy The sample of average monthly flows [m 3 s - ] of year [GWh/year ] V VI VII VIII IX X 30 34.406 9.8 8.75.35.74.803 4.798 30 34.373.63 3.49.37.30.847.06 303 34.66 4.73 5.0 3.949 3.03.433 0.950 304 34.098 6.446.8.85.398.0.935 305 34.080 8.59 3.445 5.57 3.59.94.39
Figure 7 Percentage of dependence of deviations of actual energy values from the required output values Figure 7 shows the percentage of the dependence of deviations of actual energy values generated by network from the required output values throughout the 500-year learning sequence. This sequence was ordered in descendent way according to corresponding values of the year energy production. The graph shows the network learned best in the year 49 in which it achieved almost zero deviation at the output layer. The relatively highest deviations of up to - % after this year correspond to dry years at the end of the learning sequence. This research is currently continuing. We are looking for year groups, i.e. clusters, with a similar division of water bearing during the year in which the network would learn faster and would achieve lower deviations. It is obvious that, in this case, practical utilization of the results obtained in this research depends on the predicted inflow into the reservoir which is not known in advance in real time management. It is also clear that the more reliable this prediction, the more reliable the estimated energy production using the ANN. In order to solve this problem, it will need a useful co-operation of experts in the field of the ANN, climatology, hydrology, and power production. 4 Conclusion The results achieved in the research prove that ANN methodological principles and procedures enable to solve relatively complex dynamic systems with many links among their elements. They also enable to explore their optimal function. In this research, we succeeded in algorithming not only links among elements of various network layers, but also links among elements of the same layer. This research has also proved the usefulness of combining of various methods of artificial intelligence which can express the function of the whole
system more precisely. We consider this integration of various methods as very promising also for other types of problems. The suggested operation in the whole system lead to the global extreme of the objective function faster than in the simulation model. It can be considered a specific contribution for practice. According to the results of this research, we will be able to adapt the operation rules of the water resources system. With a view to the topicality of this problem, its research continues and concentrates on further types of ANN models and procedures which serve for fast convergences of weights towards the required outputs of the network. This research has shown that ANN applications in water management are very promising. In this field of study, a lot of important issues must be tackled in a system within large water resources systems. This problem encompasses water supply systems for inhabitants and industry, flood protection, irrigation optimization, and utilization of hydropower plants systems for energy production. Thus, ANN s are becoming relevant methodological means for planning, design, and optimal operation of these systems. Therefore, it is purposeful to support and further develop the research into this application area of the ANN. References. Hertz, J., Krogh, A., Palmer, R. G. Introduction to the Theory of Neural Computation, Addison-Wesley Publishing Company, Redwood City, CA, 99.. Kosko, B. Neural Networks and Fuzzy Systems. A Dynamical Systems Approach to Machine Intelligence, Prentice-Hall International Editions, Englewood Cliffs, NJ, 99. 3. Nachazel, K., Toman, M. The genetic algorithm and its application to optimise energy utilization of a water reservoir (ed G. Rzevski, R. A. Adey, C. Tasso), pp. 53-59, Proceedings of the 0th Conference on Applications of Artificial Intelligence in Engineering X, Udine, Italy, 995, Computational Mechanics Publications, Southampton, Boston, 995. 4. Narendra, K. S.: Neural Networks for Identification and Control. Proceedings of the 33rd IEEE Conference on Decision and Control, Workshop No 6, Florida USA, December -3, 994. 5. Turban, E.: Expert Systems and Applied Artificial Intelligence, Macmillan Publishing Company, New York, 99. Acknowledgement This research was supported by Grant Agency of the Czech Republic, Grant No 03/97/006.