Using Predictive Model of Mean Monthly Flows for Large Open Reservoirs Hydropower Control

Procedia Engineering 89 ( 2014 ) 1486 – 1492 1877-7058 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of WDSA 2014 doi: 10.1016/j.proeng.2014.11.435 ScienceDirect Available online at www.sciencedirect.com 16th Conference on Water Distribution System Analysis, WDSA 2014 Using Predictive Model of Mean Monthly Flows for Large Open Reservoirs Hydropower Control P. Menšíka, * , M. Starýa, D. Martona aBrno University of Technology, Faculty of Civil Engineering, Inst. of Landscape and Water Management, Brno 602 00, Czech Republic Abstract Conventional hydropower reservoir operations are mostly based on rules or rule curves. The paper describes algorithm which has been created on idea of adaptive control theory. The adaptive control approach uses repeatedly generated medium-term water flow predictions on a several months ahead as inflows into the large open reservoirs. Values of control outflows are searched by evolution algorithm optimization methods. Principle of the predictive model of average monthly flows is introduced in this paper. The algorithm is applied to the operation hydropower control of selected reservoir. © 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Organizing Committee of WDSA 2014. Keywords: Adaptive; evolution algorithms; hydropower function; large open reservoir; operative control; optimization; predictive model 1. Introduction The more frequent occurrence of extreme hydrological events points to climate changes in the Czech Republic, as well. The occurrence of extreme flood events and the occurrence of extensive periods of drought are more frequent. The extreme flood events were observed in 1997, 2002, 2006, 2010 and 2013. The years 2000, 2003, 2012 and 2013 were identified as the dry years [1]. From the long-term observations it may be stated that the occurrence of both extremes is more frequent. This may cause danger to the storage function of some large open reservoirs. Most of large open reservoirs are designed for the versatile utilization. Their main purpose consists in the storage and protective function. These functions are often completed with the hydroenergetic function. However, a small change in the active * Corresponding author. Tel.: +420-541-147-773; fax: +420-541-147-771. E-mail address: [email protected] © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of WDSA 2014 1487 P. Menšík et al. / Procedia Engineering 89 ( 2014 ) 1486 – 1492 storage zone of the reservoir may affect the water power station operation. Then, the decrease of produced energy may be caused. The conventional operations of hydropower function of reservoirs predominantly comes out from the rules or rule curves [2] that are based on the generalization of historical processes of water inflow into reservoirs represented by historical time series [3]. Nevertheless, in the period of expected climate changes the courses of flow series begin to alter and it is necessary to search for other ways of the control methods. In the following text the means of the intelligent control that enables to react to the topical hydrological situation is described. The intelligent control of the water reservoir operation emanates from the adaptive approach. Adaptability is one of the methods of Artificial Intelligence. The knowledge of hydrological predictions of water inflows into reservoirs is essential for the adaptive control. In practice, by means of adaptability it is partly possible to eliminate an inaccuracy of the prediction emerging from the fact that the solution is carried out in the conditions of considerable uncertainty. In the publication the algorithm of the control is depicted [4] that uses the repeatedly specified predictions of water inflows into reservoirs issued several months in advance. Different methods for the creation of medium-term to long-term predictions of mean monthly flows have been described abroad. The algorithms based on stochastic modelling of time series are used. The model ARMA (autoregressive moving average) or the model ARIMA (autoregressive integrated moving average) are the most frequently used for the stationary stochastic modelling of time series. For instance in [5] the models ARMA and ARIMA are used for the creation of the long-term prediction of the discharge on the Danube River. A large part of predictive models is built up on the model of neural networks. The application of the model of neural network for the discharge prediction is described, for instance in [6]. In [7] the comparison of the three predictive models of mean monthly inflows into the reservoir Dez based on the model ARMA, the model ARIMA and neural networks is carried out. Next, it is possible to use the theory of Fuzzy Sets for the formation of the predictive model. The combination of fuzzy and neural networks is depicted in [8]. When creating predictive models, a lot of authors mutually combine the mentioned methods. Nowadays, the method of Vector Machines is used for the formation of the prediction. The application of the method of Vector Machines is described into details, for instance in [9] and in [10]. There are many other methods that may be looked up in the scientific literature. In general, it may be stated that the use of the mentioned approaches is possible in the conditions with the regular hydrological cycle. In the complex hydrological conditions of the Czech Republic the use of these models is complicated and practically hard to be used. In the article the own predictive model is described and it will be possible to be used for the creation of the prediction of the mean monthly flows even in these complicated hydrological conditions. In the following text the model is called the Zone Probabilistic Predictive Model. 2. Methods 2.1. Zone Probabilistic Predictive Model The predictive model is based on the theory of probability and it enables to predict the sequence of mean monthly water inflows into reservoirs in the specified duration, usually 1 to 12 months. The mean monthly inflows into reservoirs are predicted on the basis of the topical inflow. The knowledge of historical discharge series of mean monthly inflows is necessary when creating the predictive model. Then, the model works with the monthly step. It is suitable to use series of the largest duration for the successful creation of the predictive model. The advantage of the model is the fact that the knowledge of the other hydrological, climatic and meteorological quantities is not essential for the formation of the prediction as it is usual for other types of predictive models. 2.2. Algorithm of Predictive Model Formation and Creation of Prediction From the perennial discharge series the particular years ݕ ൌ ͳǡʹǡǥǥǡܻ are allocated, where ܻ is the number of years. From the whole number of years ܻ for each month of the year ݉ ൌ ͳǡʹǡǥǥ ǡͳʹ is allocated the set of ܳ௠ inflow. The set ܳ௠ is thus created by mean monthly water inflows into the reservoir ݍ௠ǡ௬ of all ܻ years of corresponding inflows in the month ݉. For each calendar month in the year the set of mean monthly inflows is allocated. In the set ܳ௠ is found the maximum ݉ܽݔܳ௠ and minimum ݉݅݊ܳ௠ historical value of the inflow. The 1488 P. Menšík et al. / Procedia Engineering 89 ( 2014 ) 1486 – 1492 interval between values ൏݉݅݊ܳ௠ǡ݉ܽݔܳ௠൐ is divided into the selected number of zones. In general, it is possible to mark the zone sequence by means of the letter ݖ and it applies ݖൌͳǡʹǡǥǥǡܼ, where ܼ is the number of zones. The number of zones ܼ is for each month ݉ equal but the zone interval ൏݉݅݊ܳ௠ ௭ǡ݉ܽݔܳ௠ ௭൐ may be different. The size of each zone ݖ is for the month ݉ determined on the basis of the requirement so that each zone contains approximately the equal number ݍ௠ǡ௬. The elements ݍ௠ǡ௬ ranked to the particular zone ݖ create the subset ܳ௠ ௭. Based on the initial mean value of the water inflow ܳ௠ ௖ in the month ݉, in which the decision on the control is made, the zone ݖ is selected, for which it is ܳ௠ ௖א൏ ݉݅݊ܳ௠ ௭ǡ݉ܽݔܳ௠ ௭൐. Through the zone ݖ the selected set of the historical series ݏൌͳǡʹǡǥǥǡܵ goes, where ܵ is the total number of series going through the zone ݖ. For each historical series ݏ in the set ܵ applies that ݍ௠ǡ௦ אܳ ௠ ௭. The following members of the historical series ݏ of the set ܵ represented by mean monthly inflows ݍ௠ା௧ǡ௦ in the months ݉൅ݐ, where ݐ is the sequence of the month of the prediction, are subsequently used to determine the interval of the prediction zone ݖ݌ . For ݐ is applied ݐൌ ͳǡʹǡ ǥ ǥǡ ܶܲ, where ܶܲ is the number of predicted steps (months) and ݍ௠ା௧ǡ௦ אܳ ௠ା௧ ௭௣ . For the sequence of the months ݉൅ݐ൐ͳʹ applies ݉൅ݐെͳʹ. For each month of the prediction ݉൅ݐ only one zone of the prediction ݖ݌ is determined. The predicted value of the mean monthly water inflow into the reservoir ܳ௠ା௧ ௣ in the month ݉൅ݐ equals the value occurring in the interval of the prediction zone ݖ݌ with the highest probability (modus). The average monthly inflow is predicted as follows. For all the elements ݍ௠ା௧ǡ௦ אܳ ௠ା௧ ௭௣ the density of the probability division ݂൫ݍ௠ା௧ǡ௦൯ is created. The form of the continuous function ݂൫ݍ௠ା௧ǡ௦൯ is for simplification triangle (small number of elements in). The base of the triangle is formed by the interval ൏݉݅݊ܳ௠ା௧ ௭௣ ǡ݉ܽݔܳ௠ା௧ ௭௣ ൐ and the vertex of the triangle corresponds with the presupposed position of the modus ܯ݋݀൫ݍ௠ା௧ǡ௦൯ of the quantity ݍ௠ା௧ǡ௦ אܳ ௠ ௭௣. For the estimation of the modus position the assumption is used that applies:  max ,, min 1, zp mt zp mt Q mts mts Q fq dq    ³ (1) Fig. 1. The procedure of the location of the modus position. The procedure of the location of the modus position on the interval ൏݉݅݊ܳ௠ା௧ ௭௣ ǡ݉ܽݔܳ௠ା௧ ௭௣ ൐ is graphically displayed in the Fig. 1. For the predicted value of water inflow into the reservoir in the month ݉൅ݐ is applied: 1489 P. Menšík et al. / Procedia Engineering 89 ( 2014 ) 1486 – 1492  , p mt mts QModq  (2) The algorithm of the prediction creation ܳ௠ା௧ ௣ for more steps (months) is shown in the Fig. 2. Fig. 2. The algorithm of the prediction creation. 2.3. Adaptive Control Algorithm The verification of the suitability of the predicative model on the existing reservoir would be practically impossible and that is why a simulation model (global model) is used for its testing. It is the classic simulation model in which the rules of control are replaced by optimization. The step of the simulation model is ܶ ൌ ͳǡʹǡǥ ǥǡܯ, where ܯ is the total number of steps (months). It is possible to describe the algorithm of control in the three steps that gradually repeats. In the first step on the basis of the topical flow ܳ௠ ௖ in the month ݉ the prediction of the mean monthly water inflow into the reservoir on the selected number of the predicted months ܶܲ is created. In the second step the optimization model of the reservoir control is compiled. By means of optimization in each time step of the local model ߬ ൌ ͳǡʹǡǥǥǡܰ, where ܰ is the total number of steps, turbine discharges ்ܳ ఛ on the controlled period are looked for. The method of differential evolution [11] is used for the finding of ்ܳ ఛ. Maximum possible value of the discharge in the hydropower plant ்ܳ ఛ is generally determined by the absorption capacity of turbine. The higher flow is distributed, so called flow above the maximum possible value is released directly into the watercourse under the reservoir. The number of steps ܰ is equal with the number of the predicted months ܶܲ. Marginal conditions of the solution are then created by the predicted water inflows into the reservoir. The initial condition of the solution is the volume in the reservoir at the end of the time step ߬ൌͲ. In reality it corresponds with the measured value of the volume in the reservoir. The criterion of optimization is the sum of squared deviations between the required electric power ܲௐ ఛ and the actual controlled electric power ܲ௉ ఛ of the hydropower plant, which minimizes (3).  2 1 . NTP WP PP MIN WW W S ªº o «» ¬¼ ¦ (3) Actual controlled electric power ܲ௉ ఛ in each time step ߬ is calculated according to: 1490 P. Menšík et al. / Procedia Engineering 89 ( 2014 ) 1486 – 1492 , PT Pg QH WWW UK    (4) where g is gravitational acceleration, ߩ is density of water, ܪத is head the turbine in the time step ߬ and ߟ is coefficient of hydraulic losses which is equal to 0.9. In the third step on the basis of the actual inflow and found controlled outflow which corresponds with the first step of the local model ߬ൌͳ the simulation of the reservoir behaviour is carried out in time step ܶൌͳ by means of the simulation model. The resulting size of the volume of water in the reservoir at the end of the first time is the initial condition for the solution of another optimization of the control on the next local model that is shifted by one time step. The model gradually adapts to the new conditions by means of the repetition of the steps 1 to 3, for each step of the global model ܶ – newly created predictions of water inflows. The process of adaptation is terminated when reaching the time step ܶൌܯ. The software SOMVS (Simulation and Optimization Model of Multi-reservoir Systems) is used for the adaptive control [12]. The software has been created at Brno University of Technology (BUT), Faculty of Civil Engineering, Institute of Landscape Water Management. In general, the software enables to create the simulation and optimization model of the multi-reservoir systems. Models may be used for the solution of tasks of optimal development and tasks of optimal control of the system of water supply. The mathematical model is written in the programming language FORTRAN and the graphical user interface in the language C#. 3. Application The evaluation of the results of the application of the predictive model to simulate the control of the operation of the specific hydropower function of the reservoir is used for the assessment of the predictive model quality. Control is applied to the hydro energetic function of the water reservoir Mostiště. The reservoir Mostiště is situated in the Czech Republic in the catchment area of the Svratka River. The reservoir lies on the watercourse Oslava and serves for the production of electric energy, for the decrease of flood discharges, water withdrawal and for ensuring of the minimum discharge. The volume of the dead storage zone equals 1.045 million m3 and the active storage zone volume equals 9.339 million m3. The maximum turbine absorption capacity equals the value 1.5 m3.s-1. Historical flow series of mean monthly water inflows into the reservoir has the duration of 86 years. The first 76 years are used for the formation (calibration) of Zone Probabilistic Predictive Model (ܻൌ͹͸). The number of the zones of the model ݖ equals 5. The predictive model is validated on the remaining 10 years. The control is applied to the period of the duration 10 years, where the number of steps of the simulation model ܯ equals 120. The number of the predicted months is chosen gradually ܶܲ ൌͳǡʹǡǥǥǡͳʹ. The objective function is expressed in the additive form by means of the technical indicators (3). The effort is always to approximate the actual controlled electric power to the required electric power ܲௐ ఛൌʹͲͲܹ݇ for the whole solved period ܰ. The size of the value of the required electric power is determined so as not to be possible to achieve the value at least in one time step ܶ. The adaptive control is performed for twelve variants. The individual variants differ in the number of the predicted months ܶܲ ൌͳǡʹǡǥǥǡͳʹ. The twelve variants are completed with the other two variants for the comparison of the success of the procedure for the predicted values (variants 13 and 14). In the thirteenth variant the control is solved from month to month based on the current water inflow into the reservoir. It is the simulation model, where the discharges through the hydropower plant are determined gradually in the individual months so as to be ensured the production of the required electric power. This way of control does not use the prediction and it currently corresponds to the most frequent means of the control. In the fourteenth variant the adaptive control is performed in the historical flow series. From the perspective of the predicted values we work with the prediction that has 100% accuracy – corresponds to reality. The number of the predicted months is ܶܲ ൌͳʹ. Control success in each time step ܶ can be expressed using: . TTT WP PPP'  (5) Control success over the whole period ܯ can then be expressed by: 1491 P. Menšík et al. / Procedia Engineering 89 ( 2014 ) 1486 – 1492 1 . M T T PP ' ¦¦ (6) In the case of the sufficient size of the mean monthly inflows the value ο்ܲ and σܲ would be equal to the value 0. This case would be ideal. The resulting control success over the whole period ܯ for the variants 1 to 12 is stated in the Table 1. The resulting control over the whole period ܯ for the variant 13 is σܲൌ͵͸ͷͶͶʹܹ and for the variant 14 is σܲൌ͹Ͷ͸ͳ͹ܹ. The graphic comparison of control success for each time step ܶ for variants 4, 13 and 14 can be seen in the Fig. 3. Table 1. The resulting control success over the whole period M for the variants 1 to 12. Variant ܶܲ σܲ [W] Variant ܶܲ σܲ [W] 1 1 148 848 7 7 117 456 2 2 117 174 8 8 119 862 3 3 116 586 9 9 119 510 4 4 116 437 10 10 121 533 5 5 116 618 11 11 126 802 6 6 117 148 12 12 124 247 Fig. 3. The graphic comparison of control success for each time step T for variants 4, 13 and 14. 4. Conclusion When compiling the predictive model, the part of the historical series of mean monthly inflows of water into the reservoir with the duration of 76 years was only used to build the model. The remaining part of the series (10 years) was used for the own application of the operation control of the hydropower function of the reservoir – for the validation of the model. The objective control of the predictive model quality was ensured by this procedure. Within the mutual comparison of the control success of all the investigated variants it is possible to notice that control success of the variants 1 to 12 is better than the variant 13. These results could be expected. The variant 13 does not consider the prediction and corresponds to the simplest way of control. There is an effort to achieve the required electric power 1492 P. Menšík et al. / Procedia Engineering 89 ( 2014 ) 1486 – 1492 in each time step of the global model ܶ for this variant. The effort to achieve the required electric power may lead to the emptying of the significant portion of the active storage zone resulting in a significant increase in the value ο்ܲ. The above-mentioned fact is seen in the shape of ο்ܲ in the Fig. 3. The control of the reservoir operation is performed in the historical flow series for the variant 14 (100% accuracy of prediction). The results of this variant are only theoretical and in practice they will never be achievable. The variant serves only for the determination of the theoretical control success and corresponds to the best possible way of the control. Based on the fact that the control success of the variants 1 to 12 is better than the variant 13 and slightly worse than the variant 14, it can be concluded that the adaptive control in the combination with the predictive model of inflows of water into the reservoir makes sense. The described prediction model allows creating sufficiently successful predictions. From the results of the control it is obvious that the number of predicted steps (months) has a significant impact on the overall control success. It is evident from Table 1. In the used application of control the biggest control success is achieved in the variant 4. The variant considers the prediction for four months in advance. For simplification it can be concluded that the less regular the hydrological cycle is, the shorter prediction is suitable for the adaptive control. It can be assumed on the basis of the fact that the reservoir Mostiště is situated in the upper part of the catchment area. In the future it will be appropriate to examine the influence of the number of steps of the prediction on the quality of the resulting control in details. It will also be appropriate to carry out the analysis of the impact of the number of zones on the control quality. It will be advisable to verify the predictive model within the control of the storage function of the reservoir as well as the control of multi-reservoir systems. Acknowledgements The article is the result of project CZ.1.07/2.3.00/30.0039 “Excellent young researcher at Brno University of Technology of Brno University of Technology” and result of specific research project FAST-S-14-2454 “Operation control of storage function of large open reservoirs system by using optimization model”. References [1] E. Soukalova, R. Muzikar, Periodicity and predictions drought in groundwater, in: Drought and management strategies, Czech Water Management Society, T. G. Masaryk Water Research Institute, public research institution, Czech Hydrometeorological Institute, Prague, 2013, pp. 27–32. [2] S. K. Jain, Reservoirs-Multipurpose, Water Encyclopedia, 2005, pp. 382–387. [3] L. Votruba, V. Broza, Water Management in Reservoirs, New York: Elsevier Science Ltd, 1989. [4] M. Stary, Reservoir and Reservoir system, Brno University of Technology, Faculty of Civil Engineering, Brno, 1986. [5] P. Pekarova, J. Pekar, Long-term discharge prediction for the Turnu Severin station (the Danube) using a linear autoregressive model, Hydrol. Process. 20 (2006) 1217–1228. [6] K.P. Sudheer, K. Srinivasan, T.R. Neelakantan, V.V. Srinivas, A nonlinear data-driven model for synthetic generation of annual stream-flows, Hydrol. Process. 22(12) (2008) 1831–1845. [7] M. Valipour, M. E. Banihabib, S. M. R. Behbahani, Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir, Journal of Hydrology 476 (2013) 433–441. [8] F. Chang, Y. Chen, A counterpropagation fuzzy-neural network modeling approach to real time streamflow prediction, Journal of Hydrology 245 (2001) 153–164. [9] J. Lin, C. Cheng, K. Chau, Using support vector machines for long-term discharge prediction, Hydrological Sciences J. 51 (2006) 599–612. [10] S. Huang et al., Monthly streamflow prediction using modified EMD-based support vector machine, J. of Hydrology 511 (2014) 764–775. [11] J. Lampinen, Differential Evolution – New naturally parallel approach for engineering design optimization, in: Developments in computational mechanics with high performance computing, 1999, vol. 3, pp. 217–228. [12] P. Mensik, M. Stary, SOMVS – Simulation and Optimization Model of Multi-reservoir Systems, url: http://uvhk.fce.vutbr.cz/somvs.php.