A Method of Multi-Stage Reservoir Water Level Forecasting Systems: a Case Study of Techi Hydropower in Taiwan

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Article A Method of Multi-Stage Reservoir Water Level Forecasting Systems: A Case Study of Techi Hydropower in Taiwan

Hao-Han Tsao 1 , Yih-Guang Leu 1,*, Li-Fen Chou 2 and Chao-Yang Tsao 2

1 Department of Electrical Engineering, National Taiwan Normal University, Taipei 106, Taiwan; [email protected] 2 Taiwan Power Company, Taipei 100, Taiwan; [email protected] (L.-F.C.); [email protected] (C.-Y.T.) * Correspondence: [email protected]

Abstract: Reservoirs in Taiwan often provide hydroelectric power, irrigation water, municipal water, and flood control for the whole year. Taiwan has the climatic characteristics of concentrated rainy seasons, instantaneous heavy rains due to typhoons and rainy seasons. In addition, steep rivers in mountainous areas flow fast and furiously. Under such circumstances, reservoirs have to face sudden heavy rainfall and surges in water levels within a short period of time, which often causes the water level to continue to rise to the full level even though hydroelectric units are operating at full capacity, and as reservoirs can only drain the flood water, this results in the waste of hydropower resources. In recent years, the impact of climate change has caused extreme weather events to occur more frequently, increasing the need for flood control, and the reservoir operation has faced severe challenges in order to fulfil its multipurpose requirements. Therefore, in order to avoid the waste of hydropower resources and improve the effectiveness of the reservoir operation, this paper proposes a real-time 48-h ahead water level forecasting system, based on fuzzy neural networks with multi-stage Citation: Tsao, H.-H.; Leu, Y.-G.; Chou, L.-F.; Tsao, C.-Y. A Method of architecture. The proposed multi-stage architecture provides reservoir inflow estimation, 48-h ahead Multi-Stage Reservoir Water Level reservoir inflow forecasting, and 48-h ahead water level forecasting. The proposed method has been Forecasting Systems: A Case Study of implemented at the Techi hydropower plant in Taiwan. Experimental results show that the proposed Techi Hydropower in Taiwan. method can effectively increase energy efficiency and allow the reservoir water resources to be fully Energies 2021, 14, 3461. https:// utilized. In addition, the proposed method can improve the effectiveness of the hydropower plant, doi.org/10.3390/en14123461 especially when rain is heavy.

Academic Editors: Helena M. Ramos Keywords: hydropower; reservoir water level forecasting; multi-stage architecture and Chirag Trivedi

Received: 7 April 2021 Accepted: 7 June 2021 1. Introduction Published: 11 June 2021 Hydropower is a clean and non-exhaustive energy source, and it is relatively more

Publisher’s Note: MDPI stays neutral stable than other renewable energies, such as solar and wind energy. As the operation of with regard to jurisdictional claims in the hydroelectric units can start and stop instantly, it provides flexibility for operation. It published maps and institutional affil- can adjust the voltage and frequency of a power system with the instantaneous change of iations. the load and has always played an essential role in ensuring the safety of power supply and maintaining the quality of power. At present, there are many studies on hydroelectric power generation and the integration of other renewable energy sources. The authors of [1] analysed the revenue evaluation of reservoirs in terms of water flow in the surrounding Amazon basin from an economic perspective, the authors of [2] discussed the benefits Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. and drawbacks of reservoir-regulated water for livelihood farming from the perspective This article is an open access article of irrigation and flood regulation, the authors of [3] discussed the subsequent impacts distributed under the terms and of power industry components and investment costs, and the authors of [4] designed conditions of the Creative Commons a simulation system to evaluate the impact of future climate change on power system Attribution (CC BY) license (https:// operations and regional dependencies, emphasizing the influence of the climate on hy- creativecommons.org/licenses/by/ dropower. This study in [5] investigated how hydroelectricity under climate change affects 4.0/). the ability of the grid to integrate high wind and solar capacities, using California as an

Energies 2021, 14, 3461. https://doi.org/10.3390/en14123461 https://www.mdpi.com/journal/energies Energies 2021, 14, 3461 2 of 21

example. The impact of higher capacity green energy installations on the power system and the importance of increased hydro capacity are emphasized. In [6], the long-term ensemble rainfall forecast, and the one-week rainfall forecast were considered to assess the daily inflow forecast for the coming month and to plan the daily discharge to maintain the downstream livelihood water consumption during drought conditions. In [7], the physical model of flow prediction with a long prediction interval was proposed, which is not a suitable choice for Taiwan with its extreme weather with frequent typhoons. In [8], a decision system was developed to make decisions on the timing of electricity and water release by considering flow forecasting and energy prices. In [9], a hybrid support vector machine and an artificial neural networks approach for monthly incoming flow prediction was proposed. The authors of [10] proposed a model-based approach for assessing the impact of climate change on hydropower potential in the Nanliujiang River basin of China. The authors of [11] discussed the optimal scheduling of hydroelectric power generation, considering the status of renewable energy systems such as solar and wind energy. The authors of [12] systematically reviewed the drivers, benefits, and governance dynamics of transboundary dams. With the increasing global climate change, the phenomenon of extreme rainstorms and rapid rainfall in recent years has become more frequent. To efficiently generate electricity while taking into account flood prevention and water supply tasks at the same time is a significant challenge. Traditionally, the operators of hydroelectric power plants refer to their experience on the reservoir’s water level to decide the power generation operation. Considering the water demand of multiple goals and multiple conditions, if the reservoir water level forecast information for the next few coming days can be provided, it will significantly help the operators to manage the reservoir. If the trend of reservoir inflow changes can be known in advance, it will greatly improve the optimization of power dispatch and reduce reservoir flood discharge. In general, there are two types of forecasting models for reservoir inflow: statistical models and mathematical models. Mathematical models require huge calculation costs and physical parameter data. The runoff model [13,14] needs to consider many parameters, such as evapotranspiration, infiltration, and soil storage, which has a good impact on the results. However, it is not easy to obtain this information for reservoirs that contain many watersheds upstream. On the other hand, the statistical approach is to find the correlation between a large amount of data and the output result, and it uses various statistical methods to find the best forecast result. For the statistical model’s training process, the calculation cost is relatively high. However, the actual operation does not require too much computation. In recent years, the neural network of the statistical models has played an important role in system identification, mainly due to the progress in neural network development, which enables it to learn the relationship between data input and output without involving mathematical conversion functions to complete complex nonlinear mapping, association, data classification, knowledge processing. The study in [15] designed a method of adaptive fuzzy class neural controllers for nonlinear dynamical systems and demonstrated the usability of the method through simulation results. The study in [16] applied a fuzzy neural network to short-term rainfall prediction in Zhejiang, China, and showed that the fuzzy neural network can have good results in rainfall prediction. The study in [17] discussed the effect of training methods on hydropower prediction using neural networks and proposed many optimization suggestions in the overall training process of neural networks. The study in [18] proposed an adaptive fuzzy neural network system for weekly and monthly inflow prediction of the Guardialfiera dam in Italy. The study in [19] used a neural network for future inflow prediction, which illustrated the effectiveness of inflow prediction without the use of meteorological data. In [20,21], an artificial neural network model considering the historical time was applied to water level prediction and acceptable results were achieved. The study in [22] investigated which neural network architectures could be used to achieve better hydropower prediction. The study in [23] used artificial neural networks and multiple regression to predict rainfall in a watershed, the study in [24] Energies 2021, 14, 3461 3 of 21

used rainfall forecasting to forecast the cross-river inflow, and the authors of [25] used observations, weather forecasts and climate indices in stream flow forecasting. These methods have good results for inflow and rainfall forecasting, but they do not consider the actual power generation situation and the trend of hourly changes in the daily operation of the hydropower. In rainfall forecasting, the addition of numerical meteorological forecasts has a significant benefit on the forecast’s accuracy. Regarding the numerical meteorological forecasts, grid-based ensemble forecasts are usually applied. There are so many applications and improvements for ensemble forecasts [26–33]. The study in [26] used the Fifth-Generation Penn State/NCAR Mesoscale Model (MM5) to simulate typhoon tracks. The study in [27] proposed the Weather Research and Forecasting (WRF) model to have a good grasp of the weather system in Taiwan, and analysed 20 years of historical data to compare the effectiveness of the WRF and MM5 models and to calibrate the forecasting model. The study in [28] proposed a quantitative precipitation forecasting technique to be applied to the rainfall forecasting system. In [29,30], a numerical dynamical model was applied to analyse the climate of Taiwan by considering the geomorphological and hydrological characteristics of the Techi Reservoir catchment area, and the spatial statistical theory of the kriging method [31,32] was used to downscale the numerical dynamical model grid rainfall forecast data to a specific area. A typhoon quantitative precipitation forecasting model was proposed in [33], and the average water withdrawal was defined based on the typhoon trajectory of the ensemble forecasting system to produce a quantitative rainfall forecast for the whole of Taiwan. In recent years, the development of the numerical dynamics model has expedited. The application of the WRF model has accelerated and gradually replaced the MM5 model [34,35]. Currently, MM5 is only used for numerical simulation and analysis in some studies. The design concept of the WRF model is to link academic research results with the need for real-time forecasting of data users. The WRF model can be used to simulate changes in the ideal atmosphere and the real atmosphere. The literatures have also pointed out that numerical forecasting is very helpful for rainfall forecasting [36]. With the improvement of rainfall forecasting accuracy and reliability, the inclusion of rainfall forecasting values in the inflow forecasting model will be of great help to forecasting accuracy, especially in Taiwan, where the weather changes dramatically in all seasons. Due to Taiwan’s island climate, rainfall mainly comes from the topographical rain in the southwest during the summer monsoon season, the northeast monsoon in winter, thunderstorms in summer, typhoon rain in summer and autumn, and frontal cyclone rain in spring and summer. Taiwan’s climate is mostly affected by the rainy season, and the water level of reservoirs often increases substantially during the rainy season. Because of the reasons, rainfall forecasts play an important role in the prediction of river flow. The effect of introducing climatic data on the prediction of river flow has been studied in [37,38]. In [37], Mann-Kendall nonparametric tests for streamflow analysis were used, and the authors of [38] experimentally demonstrated the feasibility of introducing meteorological forecasting grid point data for basin water flow prediction. There are many studies in this area of hydropower forecasting. In [39], a long-term forecast system for average reservoir inflow with a time scale interval of 10 days was built, but this forecast interval may not be able to produce real-time forecast results for seasons with large rainfall variability, which may limit the short-term power dispatch. In [40], a rainfall runoff model was designed considering soil infiltration, and the results are suitable for application to the prediction of inflow volume. The study in [41] proposed a method to predict the downstream reservoir water level in real time using the upstream reservoir. The study in [42] analysed and compared the neural network for the one-hour ahead streamflow forecasting for the Lan-Yang river in Taiwan. The study in [43] designed a power generation prediction system for a small hydropower turbine and selected a non-gradient descent trade-off algorithm for the neural network training rule. In [44], a heuristic algorithm was used to train fuzzy neural networks to predict hydroelectricity. Energies 2021, 14, 3461 4 of 21

Currently, these algorithms have good results for rainfall and inflow forecasts. However, they do not consider the conditions of the local hydroelectric plants. Hydroelectric power plants are more concerned about future water level changes which are affected by the generation schedule of the plant, irrigation water, municipal water, flooding, etc. The development of a reservoir water level forecasting system that takes into account the plant conditions will help the operators of the plant to dispatch power and may even become the basis of a plant energy management system. Techi reservoir in Taiwan provides hydroelectric power, irrigation water, municipal water, and flood control for the whole year. In recent years, the impact of climate change has caused flood control in extreme weather events more frequently. During the rainy season in May and June, or during typhoons from July to September, large amounts of rainfall can be achieved in a short period of time, and with Taiwan’s steep topography and fast flowing rivers, rainfall responds to water level quite quickly. If there is no reservoir water level forecasting system, when the water level starts to rise and the hydroelectric units are operating at full capacity, it will still not be able to cope with the large inflow, which can cause losses of several GWh. To cope with the management of reservoirs, this paper proposes a reservoir water level forecasting system using fuzzy neural networks for Techi Reservoir in Taiwan. The forecasting system is a 48-h ahead forecast system that considers the numerical characteristics of meteorological rainfall forecasts, analyses the correlation and delay between rainfall forecasts and rainfall observations on reservoir inflow in major upstream river basins, and considers the relationship between real-time flood discharge and power and water use in the plant area. The fuzzy neural networks are a three-stage architecture. The first stage generates the reservoir inflow estimation of Techi Reservoir, and the power to water ratio of the hydroelectric units and the flood discharge are considered to estimate the immediate inflow to the reservoir. The second stage predicts the 48-h ahead reservoir inflow, which considers the effect of observed and numerical predicted rainfall in the upper basin on future inflow and the current inflow estimation measurements to forecast the 48-h ahead inflow of Techi Reservoir. The third stage outputs the water level of Techi Reservoir. The rest of the paper is structured as follows: Section2 gives the background knowledge of Techi Reservoir in Taiwan. Section3 describes the design of the reservoir water level forecasting system. Section4 describes in detail the data analysis, experimental results, and discussions. Section5 draws a final research summary.

2. Techi Reservoir in Taiwan Techi Reservoir originates in Heping District, Taichung City, Taiwan, and is located in the uppermost reservoir of the Dajia River. The Dajia River originates from the Central Mountain Range. It has a total length of 124.2 km from the source to the estuary. It has abundant rainfall and numerous upstream rivers. The drainage area is 1235.73 square kilometres. It is currently the river with the most abundant water resources in Taiwan. In addition, the middle and upper reaches of the riverbed are steep. The distance from below Techi Reservoir to Shigang is about 70 km, with a height drop of 1000 m above sea level. It is the river with the most favourable conditions for hydroelectric power generation. Taiwan is abundant in steep rivers, slopes, and water resources. The technical available hydro-energy resources of 30 major rivers are 5040 MW, and the electric energy is 20.15 billion kWh [45]. The conventional hydroelectric power plant completed in Taiwan at the end of 2020 has a total installed capacity of 2093.37MW and an annual power generation of approximately 3.02 billion kWh. The Techi branch of Dajiaxi Power Plant is located underground on the left bank of Techi Dam. It is 77 m long, 33 m high, and 17.5 m wide. The plant is equipped with a Francis turbine. There are 3 hydroelectric units with a design head of 143.1 m, a maximum water consumption of 72.5 cubic meters per second (CMS), a single unit capacity of 78,000 kW, and 3 hydroelectric units totalling 234,000 kW. It is the second largest hydroelectric power plant in Taiwan, with an average annual power generation of approximately 360 million kWh. The main structures of Techi Reservoir include dams, Energies 2021, 14, x FOR PEER REVIEW 5 of 23

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second largest hydroelectric power plant in Taiwan, with an average annual power generation of approximately 360 million kWh. The main structures of Techi Reservoir include floodingdams, flooding structures, structures, flood tunnels, flood tunnels, waterways, waterways, an underground an underground power plant power and plant Zhilexi and diversionZhilexi diversion tunnel. tunnel. The dam The was dam built was in built Techi in Gorge,Techi Gorge, and it and is a doubleit is a double curvature curvature thin archthin dam.arch dam. TheThe inflow inflow of of Techi Techi Reservoir Reservoir is is mainly mainly affected affected by by the the rainfall rainfall in thein the upstream upstream waters, wa- andters, the and location the location of rainfall of rainfall observation observation stations stations in the in relevantthe relevant upstream upstream watershed watershed is shownis shown in Figurein Figure1. The1. The rainfall rainfall of of each each upstream upstream river river will will affect affect the the inflow inflow of of Techi Techi ReservoirReservoir by by the the topographytopography of of the the upstream upstream river river and and the the distance distance between between the the river river and and thethe reservoir. reservoir. Among Among them, them, because because of of the the flow flow rate rate of of the the river, river, there there will will be be a a time time delay delay forfor the the upstream upstream rainfall rainfall to to affect affect the the reservoir reservoir inflow. inflow.

FigureFigure 1. 1.The The locationlocation ofof TechiTechi Reservoir Reservoir and and upstream upstream rainfall rainfall observation observation stations. stations.

TheThe inﬂowinflow ofof TechiTechi Reservoir Reservoir is is mainly mainly from from the the Dajiaxi Dajiaxi River, River, considering considering that that the the rainfallrainfall in in the the Dajiaxi Dajiaxi drainage drainage basin basin between between April April and and September September accounts accounts for about for about 80% of80% the of annual the annual rainfall, rainfall, and theand dry the seasonsdry seasons between between October October and and March March of the of the following follow- yearing accountsyear accounts for about for 20%.about There 20%. areThere seven are rainfall seven observationrainfall observation stations in stations Techi Reservoir in Techi andReservoir its upstream and its catchment upstream area.catchment The seven area. rainfallThe seven stations rainfall are stations located are atTechi located Reservoir, at Techi Siyuan,Reservoir, Pingyan, Siyuan, Songmao, Pingyan, Songmao, Lishan, Songfeng Lishan, Songfeng and Hehuan. and Hehuan. This paper This uses paper the uses seven the rainfallseven rainfall stations, stations, their meteorological their meteorological forecast forecast data, and data, the and water the levelwater of level Techi of ReservoirTechi Res- toervoir develop to develop the 48-h the ahead 48-h water ahead level water forecast level forecast system. system.

3.3. TheThe DesignDesign ofof ReservoirReservoir WaterWater Level Level Forecasting Forecasting System System ThisThis sectionsection discussesdiscusses thethe architecturearchitecture ofof fuzzy fuzzy neural neural networks networks and and the the 48-h 48-h ahead ahead reservoirreservoir water water level level forecasting forecasting system. system. 3.1. The Architecture of Fuzzy Neural Networks 3.1. The Architecture of Fuzzy Neural Networks In recent years, artificial neural network (ANN) has been very important in the field In recent years, artificial neural network (ANN) has been very important in the field of system identification in intelligent forecast models. Artificial neural networks have of system identification in intelligent forecast models. Artificial neural networks have ex- excellent learning ability and it is easy to find the relationship between system input and cellent learning ability and it is easy to find the relationship between system input and output to build a model of the actual system, such as physical dynamic systems, nonlinear output to build a model of the actual system, such as physical dynamic systems, nonlinear systems, and data-driven systems. ANN also has parallel computing capabilities to provide systems, and data-driven systems. ANN also has parallel computing capabilities to pro- fast computing functions, and it is easy to complete multiple model predictions in real time. vide fast computing functions, and it is easy to complete multiple model predictions in ANN is a mathematical model that imitates the structure of the brain neuron. ANN uses a setreal of time. massive ANN data is toa obtainmathematical the relationship model that between imitates input the and structure output data.of the In brain the learning neuron. process,ANN uses we a don’t set of need massive to provide data to the obtain corresponding the relationship mathematical between functions.input and Thisoutput feature data. isIn suitable the learning for application process, we in forecasting don’t need systems to provide with the variable corresponding inputs of differentmathematical properties. functions.In This scientific feature research, is suitable fuzzy for theory application provides in aforecasting logical system systems to deal with with variable the process inputs ofof human different logic properties. inference and can be used to design intelligent systems to analyse semantics or analyseIn scientific descriptive research, language. fuzzy The theory fuzzy provides architecture a logical consists system of fuzzification, to deal with fuzzythe process logic rules,of human inference logic mechanism,inference and and can defuzzification. be used to design The intelligent applications systems of fuzzy to analyse logic systems seman- includetics or analyse control descriptive systems, graphics language. recognition, The fuzzy voice architecture recognition, consists diagnostic of fuzzification, programs, fuzzy time series forecasting, intelligent robots, decision-making systems, and other fields.

Energies 2021, 14, 3461 6 of 21

With the fuzzy neural network architecture [15,46,47], which is a neural network with fuzzy architecture, it is easy to model the input and output relationship of the real systems to establish the model characteristics of the actual system, and it also has the characteristics of easy integration of expert knowledge (fuzzy theory) and increases learning efficiency. The study in [46] proposed an observer-based direct adaptive fuzzy neural control scheme for nonlinear systems in the presence of unknown nonlinear structures. In [47], many architectures and examples of fuzzy neural networks were introduced. The configuration of fuzzy logic systems is comprised of a fuzzifier, some fuzzy IF-THEN rules, a fuzzy inference engine, and a defuzzifier [15]. The fuzzifier converts a crisp input to a fuzzy value, and defuzzification converts a fuzzy set to a crisp value. The fuzzy inference engine combines the fuzzy IF-THEN rules to make a map from an input linguistic vector to an output linguistic vector. The ith fuzzy IF-THEN rule can be written as:

(i) i i i i R : if x1 is A1 and ... and xn is An , then y1 is B1 and ... and ym is Bm (1)

i i i i i i T n where A1, A2, ... , An and B1, B2, ... , Bm are fuzzy sets, x = [x1x2 ··· xn] ∈ < is an input T m vector, and y = [y1y2 ··· ym] ∈ < is an output vector. Let z be the number of the fuzzy IF-THEN rules. By using product inference, centre-average, and singleton fuzziﬁer, the kth output of the fuzzy logic system can be expressed as: z i n ∑ = y ∏ = µ i xj i 1 k j 1 Aj yk(x) = (2) z n ∑ = ∏ = µ i xj i 1 j 1 Aj

T = θk ϕ(x) (3) i where µ i (xj) is the membership function value of the fuzzy variable xj, and y is the point Aj k i T h 1 2 zi T 1 2 z at which µBi yk = 1. θk = ykyk ··· yk is a weighting vector, and ϕ = ϕ ϕ ··· ϕ is a fuzzy basis vector, where ϕi is deﬁned as: n ∏j=1 µAi xj i j ϕ (x) = (4) z n ∑ = ∏ = µ i xj i 1 j 1 Aj

The fuzzy logic system (3) can be implemented using neural network. Figure2 shows the conﬁguration of the fuzzy neural network [15], and it has four layers. The nodes of T layer I stand for input vector x = [x1x2 ··· xn], the nodes of layer II represent the values of the membership function of total linguistic variables, and the nodes of layer III are the values of the fuzzy basis vector ϕ. The links between layer III and layer IV are fully T h 1 2 zi connected by the weighting factors θk = ykyk ··· yk . The nodes of layer IV is the output T vector y = [y1y2 ··· ym]. Therefore, this paper uses fuzzy neural network architecture to integrate meteorological rainfall data, rainfall observation data, water level and power generation to forecast reservoir inﬂow and water level, where the membership functions are selected as gauss functions.

integrated, the accuracy of the long lead time forecast will be improved. Moreover, too many feature inputs for a neural network increase the model complexity and learning difficulty. Therefore, this paper proposes a forecasting mechanism with three-stage fuzzy neural networks, as shown in Figure3, to predict the water level of the reservoir. The fuzzy neural networks of the forecasting mechanism are a three-stage architecture. Among them, the first stage generates the reservoir inflow estimation of the reservoir by using real-time water level value, power generation of hydroelectric units and reservoir flood discharge as inputs. The purpose of the first stage is to find out the effect of actual plant operation on the reservoir inflow, which is important information for the establishment of the inflow observation and prediction system. The current water level and the power to water ratio curve can be used to find out the effect of the current power generation on the inflow rate. The current power generation, water level and flood discharge can derive the current reservoir inflow. On the basis of the reservoir inflow, observation rainfall data and meteorological rainfall data, the second stage predicts the 48-h ahead reservoir inflow. Finally, the third stage uses the total power generation, flood discharge and inflow forecast value to output the 1 to 48 h forecasting results of the reservoir water level. For Techi Reservoir, the input of the second stage neural network includes the inflow data of the past 9 h, the observation rainfall data of 7 rainfall observation stations in the past 6 h, and the Energies 2021, 14, x FOR PEER REVIEWmeteorological rainfall data of 7 rainfall stations in the next 3 h. These inputs take7 of into 23

account the delay of rainfall from the Techi watershed to the reservoir.

Layer I Layer II Layer III Layer IV x φ1 1 1 y1 y i 1 A1 2 y1 z y1 φ 2 x2 y i 2 A2

φ z xn ym Ai n z ym Energies 2021, 14, x FOR PEER REVIEW 8 of 23

FigureFigure 2. 2.TheThe configuration conﬁguration of of a afuzzy fuzzy neural neural network. network.

Therefore, this paper uses fuzzy neural network architecture to integrate meteorological rainfall data, rainfall observation data, water level and power generation to forecast reservoir inflow and water level, where the membership functions are selected as gauss functions.

3.2. The 48-h Ahead Reservoir Water Level Forecasting System In general, the traditional forecasting mechanism often only uses historical data to predict the future value. For example, using the historical data of water level, rainfall observation station, power generation and flood discharge predicts the water level change of Techi Reservoir in the next 1 to 48 h. However, its prediction accuracy will deteriorate asFigure Figurethe forecast 3.3. ForecastingForecasting lead time mechanism becomes with with longer. thr three-stageee-stage If the fuzzy fuzzy meteorological neural neural networks. networks. rainfall data can be effectively integrated, the accuracy of the long lead time forecast will be improved. Moreover, too4.4. many Analysis,Analysis, feature Results inputs and and for Discussions Discussions a neural network increase the model complexity and learning difficulty.InIn thisthis Therefore, section,section, wethis we first ﬁrstpaper discuss discuss proposes the the correla correlationa forecastingtion between between mechanism 7 rainfall 7 rainfall with observation observation three-stage stations stations fuzzy neuralandand the thenetworks, waterwater level as shownof of the the Techi Techiin Figure Reservoir. Reservoir. 3, to Secondly, predict Secondly, the the the waterrelationship relationship level betweenof betweenthe reservoir. water water level The level fuzzyand reservoirneural networks inflow will of be the presented. forecasting The correlationmechanism between are a reservoirthree-stage water architecture. level and Amongmeteorological them, the rainfall first stage data generates from the the Ta reserviwan Typhoonoir inflow and estimation Flood Research of the reservoir Institute by using(TTFRI) real-time will also water be analysed.level value, Finally, power the generation typhoons betweenof hydroelectric 2013 and units 2014 andare usedreservoir as floodcases discharge to show theas inputs.forecast The results purpose of the ofproposed the firs tmethod stage is in to this find paper. out the effect of actual plant operation on the reservoir inflow, which is important information for the establish- 4.1. The Relationship between Water Level, Inflow and Rainfall of Techi Reservoir ment of the inflow observation and prediction system. The current water level and the power Into orderwater to ratio find curve out the can time be delayused tobetween find out rainfall the effect observation of the current stations power in the catch-genera- tionment on thearea inflow and the rate. water The level current of Techi power Reservoir, generation, Pearson water product-moment level and flood correlation discharge iscan deriveused theand current shown reservoirin (5)–(6). inflow. On the basis of the reservoir inflow, observation rainfall data and meteorological rainfall data,∑( the𝑥 −𝑥second̄)(𝑦 −𝑦stagē) predicts the 48-h ahead reser- 𝑆 = (5) voir inflow. Finally, the third stage uses the total𝑛−1 power generation, flood discharge and inflow forecast value to output the 𝑠1 to 48 h fo∑(recasting𝑥 −𝑥̄)(𝑦 results −𝑦̄) of the reservoir water level. 𝑟 = = (6) 𝑠 𝑠 For Techi Reservoir, the input of the second ∑( st𝑥age −𝑥 neural̄) ∑( network𝑦 −𝑦̄) includes the inflow data of the past 9 h, the observation rainfall data of 7 rainfall observation stations in the past 6 where 𝑆 is the covariance of the two inputs, 𝑟 is the correlation coefficient of the two h, inputs.and the From meteorological April to September rainfall datain 2013, of 7the rainfall total ofstations 7 rainfall in theobservation next 3 h. stations These inputsand takethe into water account level observation the delay of of rainfall Techi Reservoir from the areTechi shown watershed in Figure to the4. According reservoir. to Pear- son product–moment correlation, the correlation between the water level and the total of 7 rainfall observation stations at different delay times can be obtained as shown in Figure 5. In Figure 5, it is shown that the time delay with the highest correlation is 6 h. In other words, when rainfall occurs, it takes about six hours for the total of the rainfall observation stations to affect the inflow of Techi Reservoir.

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and reservoir inﬂow will be presented. The correlation between reservoir water level and meteorological rainfall data from the Taiwan Typhoon and Flood Research Institute (TTFRI) will also be analysed. Finally, the typhoons between 2013 and 2014 are used as cases to show the forecast results of the proposed method in this paper.

4.1. The Relationship between Water Level, Inﬂow and Rainfall of Techi Reservoir In order to ﬁnd out the time delay between rainfall observation stations in the catchment area and the water level of Techi Reservoir, Pearson product-moment correlation is used and shown in (5)–(6). ∑(x − x)(y − y) S = i i (5) xy n − 1

sxy ∑(xi − x)(yi − y) rxy = = q q (6) sxsy 2 2 ∑(xi − x) ∑(yi − y)

where Sxy is the covariance of the two inputs, rxy is the correlation coefﬁcient of the two inputs. From April to September in 2013, the total of 7 rainfall observation stations and the water level observation of Techi Reservoir are shown in Figure4. According to Pearson product–moment correlation, the correlation between the water level and the total of 7 rainfall observation stations at different delay times can be obtained as shown in Figure5 . Energies 2021, 14, x FOR PEER REVIEW In Figure5, it is shown that the time delay with the highest correlation is 6 h. In other9 of 23

Energies 2021, 14, x FOR PEER REVIEW words, when rainfall occurs, it takes about six hours for the total of the rainfall observation9 of 23 stations to affect the inﬂow of Techi Reservoir.

Figure Figure4. Comparison 4. Comparison of water of level water change level change of Techi of Reservoir Techi Reservoir and the and total the of total seven of rainfall seven rainfall observation observation stations. stations. Figure 4. Comparison of water level change of Techi Reservoir and the total of seven rainfall observation stations.

Figure Figure5. The correlation 5. The correlation between between the water the level water and level the and total the of total seven of sevenrainfall rainfall observation observation sta- stations. tions. Figure 5. The correlation between the water level and the total of seven rainfall observation sta- 4.2.tions. Design of Neural Network of Water Level and Reservoir Inflow The influencing factors of water level changes have been introduced in the previous section.4.2. Design Among of them,Neural the Network curves of Waterwater leLevelvel volume and Reservoir and power Inflow to water ratio can be trained Thethrough influencing neural networks, factors of and water the approximationlevel changes resultshave been are shown introduced in Figure in the 6. previous Powersection. generation Among and them, flood the discharge curves are of pre-arranged,water level volume and the scheduleand power for theto waternext two ratio can be days can be known in advance. After knowing the relationship between reservoir inflow trained through neural networks, and the approximation results are shown in Figure 6. and water level volume and the power to water ratio curves, the relationship among res- ervoirPower inflow, generation power and and water flood level discharge can be obtained.are pre-arranged, and the schedule for the next two days can be known in advance. After knowing the relationship between reservoir inflow and water level volume and the power to water ratio curves, the relationship among reservoir inflow, power and water level can be obtained.

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4.2. Design of Neural Network of Water Level and Reservoir Inflow The influencing factors of water level changes have been introduced in the previous section. Among them, the curves of water level volume and power to water ratio can be trained through neural networks, and the approximation results are shown in Figure6. Power generation and flood discharge are pre-arranged, and the schedule for the next Energies 2021, 14, x FOR PEER REVIEW two days can be known in advance. After knowing the relationship between reservoir10 of 23

inﬂow and water level volume and the power to water ratio curves, the relationship among reservoir inﬂow, power and water level can be obtained.

FigureFigure 6. (a 6.) The(a) The water water level level volume volume curve curve approximation; approximation; ( b(b)) The The power power to waterto water ratio ratio curve curve approximation. approximation. 4.3. Correlation Analysis of Reservoir Water Level and Meteorological Rainfall Data from TTFRI 4.3.in Correlation Catchment Area Analysis of Reservoir Water Level and Meteorological Rainfall Data from TTFRI in CatchmentMany studiesArea have pointed out that renewable energy forecasts are more severely affectedMany by studies weather have [6,48 pointed,49]. The out study that in renewable [48] introduced energy the forecasts current situation are more in theseverely WRF mode of rainfall forecasting mainly used in Taiwan. The model in [49] integrated a affectedvariety by of meteorologicalweather [6,48,49]. data and The responded study in well[48] to introduced instantaneous the inflows, current reflecting situation the in the WRFimportance mode of of rainfall rainfall forecastsforecasting for flowmainly prediction. used in The Taiwan. reservoir The inflow model is affectedin [49] integrated by the a varietyrainfall. of meteorological It is currently known data and that theresponded rainfall datawell of to the instantaneous upstream rainfall inflows, observation reflecting the importancestations is of closely rainfall related forecasts to the for reservoir flow prediction. inflow. If the The meteorological reservoir inflow rainfall is affected data are by the rainfall.included It inis thecurrently forecasting known system, that the the forecasting rainfall accuracydata of the will upstream increase. In rainfall order to observation obtain stationsthe meteorological is closely related rainfall datato the in thereservoir Techi Reservoir inflow. catchment If the meteorological area, this paper rainfall cooperated data are with TTFRI. Since 2010, the TTFRI centre has developed and implemented the experience included in the forecasting system, the forecasting accuracy will increase. In order to ob- of Taiwan Cooperative Precipitation Ensemble Forecast Experiment (TAPEX). In addition, tainin the order meteorological to consider the rainfall geological data and in hydrological the Techi Reservoir characteristics catchment of the Techi area, Reservoir this paper co- operatedcatchment with area, TTFRI. the TTFRI Since centre 2010, uses the the TTFRI Kriging centre method has [34 developed,35] in spatial and statistical implemented theory the experienceto convert of the Taiwan gridded Cooperative rainfall data Precipitation of the numerical Ensemble model to Forecast the Dajiaxi Experiment meteorological (TAPEX). In rainfalladdition, data in of order seven to rainfall consider observation the geological stations. and The hydrological seven meteorological characteristics rainfall of the Techistations Reservoir include catchment Techi Reservoir, area, Songmao,the TTFRI Siyuan, centre Lishan, uses the Songfeng, Kriging Hehuan method Mountain, [34,35] in spa- and Pingyan Mountain. The meteorological rainfall data from TTFRI are provided every tial statistical theory to convert the gridded rainfall data of the numerical model to the 6 h, and it provides hourly cumulative rainfall forecast data from 1 to 78 h for each Dajiaxirainfall meteorological station. rainfall data of seven rainfall observation stations. The seven me- teorologicalIn order rainfall to confirm stations the accuracyinclude Techi of meteorological Reservoir, Songmao, rainfall data, Siyuan, this paper Lishan, analyses Songfeng, Hehuanthe periods Mountain, of abundant and rainfallPingyan from Mountain. April to SeptemberThe meteorological 2013 in Taiwan. rainfall First, data we analyse from TTFRI arethe provided delay correlation every 6 h, among and it the provides water level,hourly Techi cumulative rainfall observation rainfall forecast station data and from the 1 to 78 meteorologicalh for each rainfall rainfall station. data of Techi, and the results are shown in Figure7. From Figure7, it canIn order be seen to that confirm the water the level accura is delayed.cy of meteorological Moreover, the correlationrainfall data, coefficient this paper between analyses the periods of abundant rainfall from April to September 2013 in Taiwan. First, we analyse the delay correlation among the water level, Techi rainfall observation station and the meteorological rainfall data of Techi, and the results are shown in Figure 7. From Figure 7, it can be seen that the water level is delayed. Moreover, the correlation coefficient between TAPEX forecast data and reservoir water level is worse than that of rainfall observation data, but there are similar rainfall trends. Then, according to the meteorological rainfall data and the actual value of the reservoir catchment area, error analysis is carried out using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) as in (7) and (8), respectively. The MAE, RMSE and Mean Square Error (MSE), as in (9), are commonly used to assess the accuracy of prediction. 1 MAE = |𝑓 −𝑦| (7) 𝑛

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1 RMSE = (𝑓 −𝑦) (8) 𝑛 1 MSE = (𝑓 −𝑦) (9) 𝑛 Energies 2021, 14, 3461 The error analysis of meteorological rainfall data and Techi rainfall observation10 of 21 station is shown in Figure 8, and the errors are also within a certain degree of acceptable range. This meteorological rainfall data should be able to provide an important reference basisTAPEX for the forecast long-term data and lead reservoir water level water forecasting. level is worse than that of rainfall observation data, but there are similar rainfall trends.

FigureFigure 7. (a) 7. The(a) Thecorrelation correlation between between the the water water level level and and meteorological meteorological rainfall rainfall data data of Techi;of Techi; (b) The(b) The correlation correlation between between the waterthe water level level and and Techi Techi rainfall rainfall observation observation station. station. Then, according to the meteorological rainfall data and the actual value of the reservoir catchment area, error analysis is carried out using Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) as in (7) and (8), respectively. The MAE, RMSE and Mean Square Error (MSE), as in (9), are commonly used to assess the accuracy of prediction.

1 n MAE = ∑| fi − yi| (7) n i=1

s n 1 2 RMSE = ∑( fi − yi) (8) n i=1 n 1 2 MSE = ∑( fi − yi) (9) n i=1 The error analysis of meteorological rainfall data and Techi rainfall observation station is shown in Figure8, and the errors are also within a certain degree of acceptable range. This meteorological rainfall data should be able to provide an important reference basis for the long-term lead water level forecasting.

4.4. Experimental Results Figure 8. The error analysisIt is assumedof Techi meteorological that only the historical and observation water level rainfall, change (a) ofRMSE; Techi ( Reservoirb) MAE. is considered, and the neural network is used to predict the 6-h lead water level change of Techi 4.4.Reservoir. Experimental The neuralResults network is trained by using the water level measurement data from 1 JanuaryIt is assumed 2012 to that 30 June only 2013 the ofhistorical the Techi water Reservoir, level and change the water of Techi level Reservoir measurement is consid- data from 1 October 2013 to 30 December 2013 of the Techi Reservoir are used as the testing ered, and the neural network is used to predict the 6-h lead water level change of Techi data after the learning of the neural network. The neural network consists of 5 input layer Reservoir.neurons, The 7 hidden neural layer network neurons, is trained 1 output by layer using neuron, the water 5 inputs level (4 historical measurement water leveldata from 1 Januarydata and 2012 1 water to 30 level June difference 2013 of data) the Techi and 1 outputReservoir, (predicted and the water water level level value measurement for the datanext from 1 hour). 1 October The training 2013 to method 30 December uses a gradient 2013 of descent the Techi algorithm. Reservoir The are learning used resultas the test- ingof data training after data theand learning the forecasting of the neural result netw of testingork. dataThe areneural shown network in Figure consists9. The MSEof 5 input of the training results is 0.0324. The MSE of the testing results is shown in Table1.

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1 RMSE = (𝑓 −𝑦) (8) 𝑛 1 MSE = (𝑓 −𝑦) (9) 𝑛 The error analysis of meteorological rainfall data and Techi rainfall observation station is shown in Figure 8, and the errors are also within a certain degree of acceptable range. This meteorological rainfall data should be able to provide an important reference basis for the long-term lead water level forecasting.

EnergiesFigure2021 7. (a, 14) The, 3461 correlation between the water level and meteorological rainfall data of Techi; (b) The correlation between11 of 21 the water level and Techi rainfall observation station.

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layer neurons, 7 hidden layer neurons, 1 output layer neuron, 5 inputs (4 historical water level data and 1 water level difference data) and 1 output (predicted water level value for the next 1 hour). The training method uses a gradient descent algorithm. The learning result of training data and the forecasting result of testing data are shown in Figure 9. The MSE of the training results is 0.0324. The MSE of the testing results is shown in Table 1.

Table 1. The MSE of the testing results.

Lead-Time (Hour) t + 1 t + 2 t + 3 t + 4 t + 5 t + 6 MSE 0.0437 0.0558 0.0825 0.1229 0.1724 0.2078 FigureFigure 8. The 8. The error error analysis analysis of of Techi Techi meteorological meteorological and and observation observation rainfall, rainfall, (a) RMSE;(a) RMSE; (b) MAE. (b) MAE.

4.4. Experimental Results It is assumed that only the historical water level change of Techi Reservoir is considered, and the neural network is used to predict the 6-h lead water level change of Techi Reservoir. The neural network is trained by using the water level measurement data from 1 January 2012 to 30 June 2013 of the Techi Reservoir, and the water level measurement data from 1 October 2013 to 30 December 2013 of the Techi Reservoir are used as the testing data after the learning of the neural network. The neural network consists of 5 input

FigureFigure 9. ( 9.a) ( Thea) The learning learning result result of of training training data; data; ( b(b)) The The forecasting forecasting resultresult of testing data. data.

Table 1.ThisThe MSEpaper of uses the testingMATLAB results. as the development platform to develop a 48-h ahead reservoir water level forecasting system using fuzzy neural networks. The purpose of this Lead-Time (Hour) t + 1 t + 2 t + 3 t + 4 t + 5 t + 6 system is to predict the trend of water level changes 48 h ahead, and update the forecasting resultsMSE every hour. This 0.0437 system 0.0558automatically 0.0825 retrieves0.1229 power generation 0.1724 of hydroe- 0.2078 lectric units, water level of Techi Reservoir, seven rainfall observation stations and TAPEX meteorologicalThis paper usesdata every MATLAB hour asfor thewater development level forecasting. platform To illustrate to develop the validity a 48-h of ahead the reservoirprediction water results, level typhoons forecasting in Taiwan system from using 2013 fuzzy to 2014 neural are networks.used as the The experimental purpose of thisdata system in this is paper. to predict The typhoon the trend data of are water derived level from changes the typhoon 48 h ahead,database and of the update Central the forecastingWeather Bureau results (CWB) every hour.in Taiwan This [ system50], as shown automatically in Table retrieves2, to obtain power the past generation typhoon of hydroelectriclanding time units, and related water levelinformation. of Techi Reservoir, seven rainfall observation stations and TAPEXFor meteorological Typhoons Tammei, data every Kongrey, hour for Usagi water and level Matmo forecasting. in Table To2, illustratethe water thelevel validity and of theinflow prediction forecasting results, results typhoons of Techi in Reservoir Taiwan from are shown 2013 to in 2014 Figures are used 10–17, as therespectively. experimental In dataFigures in this 10–17, paper. the The blue typhoon lines with data square are derived symbol from represent the typhoon the observed database values of the and Central the Weatherred lines Bureau with plus (CWB) symbol in Taiwan represent [50 ],the as fore showncasting in Tablevalues.2, It to can obtain be seen the pastfrom typhoonFigures landing10–17 timethat the and forecasting related information. values have a similar trend to the actual future values. For Typhoons Tammei, Kongrey, Usagi and Matmo in Table2, the water level and inﬂowTable forecasting 2. From results2013 to 2014, of Techi typhoons Reservoir landing are in Taiwan. shown in Figures 10–17, respectively. In Figures 10–17, the blue lines with square symbolMaximum represent Wind the Speed observed of Central values andPressure the red Typhoon Name Duringlines Typhoon with plus Landing symbol represent Typhoon theIntensity forecasting values. It can be seen from Figures 10–17 (m/s) that the forecasting values have a similar trend to the actual future values. Matmo 21 July–23 July 2014 middle typhoon 38 Hagibis 14 June–15 June 2014 light typhoon 20 Fitow 4 October–7 October 2013 middle typhoon 38 Usagi 19 September–22 September 2013 strong typhoon 55 Kongrey 27 August–27 August 2013 light typhoon 25 Trami 20 August–22 August 2013 light typhoon 30 Cimaron 17 July–18 July 2013 light typhoon 18

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Table 2. From 2013 to 2014, typhoons landing in Taiwan.

Typhoon Name During Typhoon Landing Typhoon Intensity Maximum Wind Speed of Central Pressure (m/s) Matmo 21 July–23 July 2014 middle typhoon 38 Hagibis 14 June–15 June 2014 light typhoon 20 Fitow 4 October–7 October 2013 middle typhoon 38 Usagi 19 September–22 September 2013 strong typhoon 55 Kongrey 27 August–27 August 2013 light typhoon 25 Energies 2021Trami, 14, x FOR PEER REVIEW 20 August–22 August 2013 light typhoon 30 13 of 23 Energies 2021Cimaron, 14, x FOR PEER REVIEW 17 July–18 July 2013 light typhoon 18 13 of 23

Figure 10. Forecasting results of water level at 00:00 on 21 August 2013 (during Typhoon Trami). FigureFigure 10. 10. ForecastingForecasting results results of of water water level level at at 00:00 00:00 on on 21 21 August August 2013 2013 (dur (duringing Typhoon Typhoon Trami). Trami).

Figure 11. Forecasting results of reservoir inflow at 00:00 on 21 August 2013 (during Typhoon Trami). Figure 11. Forecasting results of reservoir inflow at 00:00 on 21 August 2013 (during Typhoon Trami). Figure 11. Forecasting results of reservoir inﬂow at 00:00 on 21 August 2013 (during Typhoon Trami).

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Figure 12. Forecasting results of water level at 06:00 pm on 28 August 2013 (during Typhoon Kongrey). Figure 12.FigureForecasting 12. Forecasting results results of water of water level level at at 06:00 06:00 pm pm on on 28 28August August 2013 2013(during (during Typhoon Typhoon Kongrey). Kongrey).

Figure 13. Forecasting results of reservoir inflow at 06:00 pm on 28 August 2013 (during Typhoon Kongrey). Energies 2021,Figure 14, x FOR 13. PEER Forecasting REVIEW results of reservoir inflow at 06:00 pm on 28 August 2013 (during Typhoon Kongrey). 15 of 23 Figure 13. Forecasting results of reservoir inﬂow at 06:00 pm on 28 August 2013 (during Typhoon Kongrey).

Figure 14. Forecasting results of water level at 02:00 am on 22 September 2013 (during Typhoon Usagi). Figure 14. Forecasting results of water level at 02:00 am on 22 September 2013 (during Typhoon Usagi).

Figure 15. Forecasting results of reservoir inflow at 02:00 am on 22 September 2013 (during Typhoon Usagi).

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Figure 14. Forecasting results of water level at 02:00 am on 22 September 2013 (during Typhoon Usagi).

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Figure 15. Forecasting results of reservoir inflow at 02:00 am on 22 September 2013 (during Typhoon Usagi). Figure 15. Forecasting results of reservoir inﬂow at 02:00 am on 22 September 2013 (during Typhoon Usagi).

Figure 16. Forecasting results of water level at 00:00 on 22 July 2014 (during Typhoon Matmo). Figure 16. Forecasting results of water level at 00:00 on 22 July 2014 (during Typhoon Matmo).

The MAE of the 48-h ahead reservoir inflow forecasting in 2012 and 2013 can be obtained, and the results are shown in Figures 18 and 19. It can be seen from Figures 18 and 19 that the forecasting accuracy will gradually decrease as the lead time increases, and there will be a relatively large error in the sudden change of rainfall. This is partly due to the influence of the accuracy of the meteorological rainfall data, and the other part is that the training data with sudden rainfall changes account for a relatively small proportion of the training data. This will affect the forecasting accuracy during the typhoon landing. As the water level changes significantly in the rainy season, this paper evaluates the accuracy of the forecasting performance by observing events with reservoir inflow greater than 100 CMS. The results of the RMSE and MAE in 2012 and 2013 are shown in Figures 20 and 21, respectively. Figure 20 shows that the RMSE value for the first 24 h in 2012 is about 160 CMS, and Figure 21 shows that the RMSE value for the first 24 h in

Figure 17. Forecasting results of reservoir inflow at 00:00 on 22 July 2014 (during Typhoon Matmo).

The MAE of the 48-h ahead reservoir inflow forecasting in 2012 and 2013 can be obtained, and the results are shown in Figures 18 and 19. It can be seen from Figures 18 and 19 that the forecasting accuracy will gradually decrease as the lead time increases, and there will be a relatively large error in the sudden change of rainfall. This is partly due to the influence of the accuracy of the meteorological rainfall data, and the other part is that the training data with sudden rainfall changes account for a relatively small proportion of the training data. This will affect the forecasting accuracy during the typhoon landing. As the water level changes significantly in the rainy season, this paper evaluates the accuracy of the forecasting performance by observing events with reservoir inflow greater than 100 CMS. The results of the RMSE and MAE in 2012 and 2013 are shown in Figures 20 and 21, respectively. Figure 20 shows that the RMSE value for the first 24 h in 2012 is about 160 CMS, and Figure 21 shows that the RMSE value for the first 24 h in 2013 is about 120 CMS. In general, the designed fuzzy neural network model can obtain good water level forecasting results. However, the reservoir inflow during a typhoon or heavy rain

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2013 is about 120 CMS. In general, the designed fuzzy neural network model can obtain good water level forecasting results. However, the reservoir inflow during a typhoon or heavy rain may be hundreds of times different from the reservoir inflow during a normal period, and the water level of the reservoir may change by tens of meters. In addition, when the water level is predicted, the predicted reservoir inflow error value will continue to accumulate from 1 to 48-h, and the predicted water level will have a large error 48-h in Figure 16. Forecastingthe future. results of water level at 00:00 on 22 July 2014 (during Typhoon Matmo).

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may be hundreds of times different from the reservoir inflow during a normal period, and the water level of the reservoir may change by tens of meters. In addition, when the water

level is predicted, the predicted reservoir inflow error value will continue to accumulate Figure 17. Forecasting results of reservoir inflow at 00:00 on 22 July 2014 (during Typhoon Matmo). Figure 17. Forecastingfrom 1 to results48-h, and of reservoir the predicted inﬂow atwater 00:00 level on 22 will July 2014have (during a large Typhoonerror 48-h Matmo). in the future.

FigureFigure 18. MAE 18. MAE of reservoir of reservoir inflow inﬂow forecasting forecasting in 2012. in 2012.

Figure 19. MAE of reservoir inflow forecasting in 2013.

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may be hundreds of times different from the reservoir inflow during a normal period, and the water level of the reservoir may change by tens of meters. In addition, when the water level is predicted, the predicted reservoir inflow error value will continue to accumulate from 1 to 48-h, and the predicted water level will have a large error 48-h in the future.

Energies 2021, 14, 3461 16 of 21 Figure 18. MAE of reservoir inflow forecasting in 2012.

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FigureFigure 19. MAE 19. MAE of reservoir of reservoir inflow inﬂow forecasting forecasting in 2013. in 2013.

FigureFigure 20. 20. ForecastingForecasting error error of of observed observed reservoir reservoir inflow inﬂow greater greater than than 100 100 CMS CMS in in 2012. 2012.

In order to illustrate the relationship between reservoir level forecasting and hydroelectric power generation, this paper assumes the starting water level of 1400 m at the time of typhoon Matmo and conducts a simulation analysis. The impact on hydroelectricity generation is illustrated for the scenarios with and without the reservoir level forecasting system. It is assumed that without the forecast system, the dispatcher would normally start to operate the hydroelectric plant at full capacity when there is a large change in water level at 00:00 in the morning on 23 July 2014. Assuming that the forecast system is available, the dispatcher observes the predicted water level trend a day before and starts to operate the hydroelectric plant at full capacity immediately, based on the forecast system results. The results are shown as Figures 22 and 23, and it can be seen that if the dispatcher starts to operate the hydroelectric plant at full capacity without the reservoir level forecasting system when the typhoon hits, the water level will be raised to the full level and it is

Figure 21. Forecasting error of observed reservoir inflow greater than 100 CMS in 2013.

In order to illustrate the relationship between reservoir level forecasting and hydroelectric power generation, this paper assumes the starting water level of 1400 m at the time of typhoon Matmo and conducts a simulation analysis. The impact on hydroelectricity generation is illustrated for the scenarios with and without the reservoir level forecasting system. It is assumed that without the forecast system, the dispatcher would normally start to operate the hydroelectric plant at full capacity when there is a large change in water level at 00:00 in the morning on 23 July 2014. Assuming that the forecast system is available, the dispatcher observes the predicted water level trend a day before and starts to operate the hydroelectric plant at full capacity immediately, based on the forecast system results. The results are shown as Figures 22 and 23, and it can be seen that if the dispatcher starts to operate the hydroelectric plant at full capacity without the reservoir level forecasting system when the typhoon hits, the water level will be raised to the full level and it is necessary to discharge the flood, which is a loss of energy. From Figures 22 and

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Energies 2021, 14, 3461 17 of 21

necessary to discharge the ﬂood, which is a loss of energy. From Figures 22 and 23, if the operation of the hydroelectric plant at full capacity can be started 24 h before, the reservoir Figurecan avoid 20. Forecasting the ﬂood discharge.error of observed reservoir inflow greater than 100 CMS in 2012.

EnergiesEnergies 20212021,, 1414,, xx FORFOR PEERPEER REVIEWREVIEW 1919 ofof 2323

23,23, ifif thethe operationoperation ofof thethe hydroelectrichydroelectric plantplant atat fullfull capacitycapacity cancan bebe startedstarted 2424 hh before,before, thethe reservoirreservoir cancan avoidavoid thethe floodflood discharge.discharge. Next,Next, wewe analyseanalyse inin detaildetail thethe lossloss ofof genegenerationration causedcaused byby thethe dispatcher’sdispatcher’s hydroe-hydroe- lectriclectric operationoperation atat differentdifferent times.times. WhenWhen thethe predictedpredicted resultresult waswas generatedgenerated onon 2222 July,July, itit showedshowed thatthat thethe reservoirreservoir wouldwould reachreach fullfull levellevel inin 3333 h.h. InIn thisthis case,case, whenwhen thethe waterwater levellevel isis full,full, therethere isis nono wayway toto stopstop thethe waterwater levellevel fromfrom risingrising eveneven ifif thethe hydroelectrichydroelectric plantplant isis operatingoperating atat fullfull capacity.capacity. InIn casecase ofof highhigh initialinitial reservoirreservoir levellevel andand suddensudden heavyheavy rain,rain, thethe dispatcherdispatcher startsstarts toto operateoperate thethe hydroelectrichydroelectric plantplant atat fullfull capacitycapacity afterafter differentdifferent timetime pointspoints andand analysesanalyses thethe waterwater levellevel change.change. DuDuringring thethe process,process, thethe amountamount ofof floodflood dis-dis- chargecharge whenwhen thethe waterwater levellevel reachesreaches thethe highesthighest pointpoint ofof 14081408 mm isis recorded,recorded, andand thethe ac-ac- cumulatedcumulated powerpower generationgeneration lossloss ofof thethe hydroehydroelectriclectric unitsunits isis evaluatedevaluated accordingaccording toto thethe powerpower toto waterwater ratioratio value.value. TheThe resultsresults areare shshownown inin FigureFigure 24,24, andand itit isis clearclear thatthat thethe dispatcherdispatcher mustmust startstart toto operateoperate thethe hydroelectrichydroelectric plantplant atat fullfull capacitycapacity 2424 hh prior,prior, other-other- wisewise itit willwill causecause powerpower generationgeneration lossloss duedue toto floodflood discharge.discharge. FromFrom FigureFigure 24,24, thethe lossloss inin powerpower generationgeneration isis veryvery impressive,impressive, whichwhich alsoalso showsshows thethe importanceimportance ofof waterwater levellevel forecastingforecasting forfor thethe dispatcherdispatcher toto operateoperate thethe hydroelectrichydroelectric units.units. FigureFigure 21. 21. ForecastingForecasting error error of of observed observed reservoir reservoir inflow inﬂow greater than 100 CMS in 2013.

In order to illustrate the relationship between reservoir level forecasting and hydroelectric power generation, this paper assumes the starting water level of 1400 m at the time of typhoon Matmo and conducts a simulation analysis. The impact on hydroelectricity generation is illustrated for the scenarios with and without the reservoir level forecasting system. It is assumed that without the forecast system, the dispatcher would normally start to operate the hydroelectric plant at full capacity when there is a large change in water level at 00:00 in the morning on 23 July 2014. Assuming that the forecast system is available, the dispatcher observes the predicted water level trend a day before and starts to operate the hydroelectric plant at full capacity immediately, based on the forecast system results. The results are shown as Figures 22 and 23, and it can be seen that if the dispatcher starts to operate the hydroelectric plant at full capacity without the reservoir level forecasting system when the typhoon hits, the water level will be raised to the full level

and it is necessary to discharge the flood, which is a loss of energy. From Figures 22 and FigureFigure Figure 22.22. TheThe 22. effecteffectThe onon effect hydropowerhydropower on hydropower regulationregulation regulation withwith andand with withoutwithout and without forecastingforecasting forecasting (water(water (water level).level). level).

FigureFigure Figure 23.23. TheThe 23. effecteffectThe onon effect hydropowerhydropower on hydropower reregulationgulation regulation withwith andand with withoutwithout and without foforecastingrecasting forecasting (difference(difference (difference betweenbetween between reservoirreservoirreservoir inflowinflow inﬂow andand waterwater and cons waterconsumptionumption consumption forfor powerpower for power generation).generation). generation).

Energies 2021, 14, 3461 18 of 21

Next, we analyse in detail the loss of generation caused by the dispatcher’s hydroelectric operation at different times. When the predicted result was generated on 22 July, it showed that the reservoir would reach full level in 33 h. In this case, when the water level is full, there is no way to stop the water level from rising even if the hydroelectric plant is operating at full capacity. In case of high initial reservoir level and sudden heavy rain, the dispatcher starts to operate the hydroelectric plant at full capacity after different time points and analyses the water level change. During the process, the amount of ﬂood discharge when the water level reaches the highest point of 1408 m is recorded, and the accumulated power generation loss of the hydroelectric units is evaluated according to the power to water ratio value. The results are shown in Figure 24, and it is clear that the dispatcher must start to operate the hydroelectric plant at full capacity 24 h prior, otherwise Energies 2021, 14, x FORit PEER will REVIEW cause power generation loss due to ﬂood discharge. From Figure 24, the loss in 20 of 23 power generation is very impressive, which also shows the importance of water level forecasting for the dispatcher to operate the hydroelectric units.

Figure 24.FigureEffect 24. of Effect start-up of start-up time of hydroelectrictime of hydroelectric units on units ﬂood on discharge. flood discharge.

4.5. Discussions4.5. Discussions The effect ofThe rainfall effect onof rainfall the basin on inflow the basin can inflow be seen can from be bothseen thefrom physical both the runoff physical runoff model of [13model,14,40 of] and [13,14,40] the statistical and the model statistical of [16 model,24,44 ].of The[16,24,44]. fact that The rain fact in that the upstreamrain in the upstream catchmentcatchment increases the increases water levelthe water of the level Techi of Reservoirthe Techi Reservoir is well established. is well established. In order In order to to understandunderstand the delay the time delay of time the river of the confluence river conflu atence Techi at Reservoir, Techi Reservoir, the correlation the correlation be- between thetween rainfall the station rainfall and station reservoir and reservoir water level water was level analysed. was analysed. In Figure7 In, it Figure can be 7, it can be seen that theseen maximum that the maximum correlation correlation of the observed of the data observ oned the data reservoir on the inflow reservoir is at inflow 4 h, is at 4 h, while the predictedwhile the data predicted have adata more have significant a more effectsignificant at about effect 6 h.at Figureabout 46 alsoh. Figure reflects 4 also reflects the influencethe of influence the rainfall of the stations rainfall on stations the trend on of the water trend level of water variation. level Itvariation. can then It be can then be seen from Figureseen from6 that Figure the power–water 6 that the power–water ratio curve learnedratio curve by neurallearned networks by neural is networks similar is similar to the actualto curve, the actual and curve, the water and level the water volume level curve volume also hascurve a good also has learning a good result. learning result. Based on [16,17,19,24,25], they demonstrated the importance of rainfall forecasting Based on [16,17,19,24,25], they demonstrated the importance of rainfall forecasting for reservoir water level and inflow. For this purpose, we further analysed the correlation for reservoir water level and inflow. For this purpose, we further analysed the correlation between the predicted rainfall data and the actual water level changes. From Figure7a, between the predicted rainfall data and the actual water level changes. From Figure 7a, it it can be seen that the correlation between the rainfall forecasting and reservoir water can be seen that the correlation between the rainfall forecasting and reservoir water level level change is relatively low, compared to the observed rainfall values, and from Figure8, change is relatively low, compared to the observed rainfall values, and from Figure 8, the the accuracy of the rainfall forecasting is acceptable but can be further optimized. When accuracy of the rainfall forecasting is acceptable but can be further optimized. When ana- analysing the forecast data, it is found that sometimes the forecast data do not reflect the lysing the forecast data, it is found that sometimes the forecast data do not reflect the ac- actual rainfall trend. tual rainfall trend. Next, we conducted a typhoon case study. The dispatcher usually relies on experience Next, we conducted a typhoon case study. The dispatcher usually relies on experi- in scheduling hydroelectric units for hydroelectric power generation. In order to present the effectivenessence in of scheduling the proposed hydroelectric method, we units simulated for hydroelectric the inflow power of typhoon generation. Maghreb In order to pre- and addedsent the water the effectiveness consumption of of the the proposed hydroelectric meth powerod, we generation simulated into the theinflow reservoir of typhoon Ma- ghreb and added the water consumption of the hydroelectric power generation into the reservoir using the power–water ratio curve. In addition, in order to highlight the huge loss of power generation due to flood discharge, we assumed that the initial water level before the typhoon arrives is 1400 m and simulated that if the dispatcher can start to operate the hydroelectric plant at full capacity earlier, the loss of power generation due to flood discharge can be greatly reduced, which may reach 7GWh loss in a single typhoon, which is a very large energy loss. Finally, because of the characteristics of Taiwan’s island climate, the rainy season in Taiwan is concentrated between May and September, and there are often very drastic changes in reservoir inflow during this period. Based on [1,2,4], the impact of extreme rainfall on water resources can be understood. Obviously, it is not very objective to use RMSE and MAE directly to evaluate the annual reservoir inflow and water level. There- fore, this paper selected representative typhoons from 2013 to 2014 as experimental data, aiming to investigate whether the water level forecasting system can reflect the future water level trend in real time when heavy rainfall occurs. From Figures 10–17, it can be

Energies 2021, 14, 3461 19 of 21

using the power–water ratio curve. In addition, in order to highlight the huge loss of power generation due to flood discharge, we assumed that the initial water level before the typhoon arrives is 1400 m and simulated that if the dispatcher can start to operate the hydroelectric plant at full capacity earlier, the loss of power generation due to flood discharge can be greatly reduced, which may reach 7GWh loss in a single typhoon, which is a very large energy loss. Finally, because of the characteristics of Taiwan’s island climate, the rainy season in Taiwan is concentrated between May and September, and there are often very drastic changes in reservoir inflow during this period. Based on [1,2,4], the impact of extreme rainfall on water resources can be understood. Obviously, it is not very objective to use RMSE and MAE directly to evaluate the annual reservoir inflow and water level. Therefore, this paper selected representative typhoons from 2013 to 2014 as experimental data, aiming to investigate whether the water level forecasting system can reflect the future water level trend in real time when heavy rainfall occurs. From Figures 10–17, it can be seen that the forecasting system has a good ability to follow the water level in case of extreme rainfall. In addition, the accuracy of the inflow prediction was analysed for the case of reservoir inflow exceeding 100 CMS, i.e., a certain level of rainfall occurred. As can be seen in Figures 10 and 21, the forecasting system is able to provide good forecasting results for both special cases and rainfall events.

5. Conclusions Taiwan is blessed with abundant water resources. Among them, Techi Reservoir is the uppermost reservoir in the Dajiaxi Basin. The operation of the Techi branch of Dajiaxi Power Plant is critical to the power generation, and downstream water supply of power plants in the entire Dajiaxi River Basin, and its importance is beyond words. Therefore, for Techi Reservoir, based on the meteorological rainfall information and the rainfall stations in the catchment area, reservoir level, flood discharge, and power generation, this paper has developed a fuzzy neural network 48-h ahead reservoir water level forecasting system that is capable of predicting the hourly water level 1 h to 48 h ahead. The main objective of this paper is to enable the power plant operator to efficiently dispatch the hydroelectric units with the dynamic information of future water level in the reservoir in order to increase the power generation. If the proposed water level forecasting system can be integrated into the energy management system of hydroelectric power plant, the hydroelectric power, irrigation water, municipal water, and flood control can be managed more effectively to achieve the optimal use of energy. During the prior typhoon period, the actual reservoir inflow analysis also proved that the proposed forecasting system has a certain leading predictive ability and the ability to predict the changes in the reservoir’s inflow and water level when the offshore typhoon warning is issued. Therefore, the operators can refer to the real-time information on the dynamic changes of the reservoir water level to manage the water level. Besides retaining storage capacity for storing floods, reducing peaks, and stably supplying water for various downstream targets, the reservoir operator can also adjust the reservoir’s water level to increase the amount of power generated and increase power generation revenue. The most important part of the model training is that the training data should cover a complete range of local climatic characteristics, especially in the area of heavy rainfall, which is very important for a successful water level forecast system to be able to respond rapidly to drastic water level changes. In order to enhance the effectiveness of the water level forecast system, the accuracy of the meteorological data is also very important, in addition to the coverage of upstream rainfall observation stations. Since most meteorological data use tuned observations from nearby urban areas, this sometimes makes it impossible for them to reflect accurate rainfall values in mountainous areas due to many factors, such as topography and climate. In this case, if the rainfall observation stations in the upper watershed can be used to calibrate the meteorological data, the accuracy of water level prediction will be improved. Energies 2021, 14, 3461 20 of 21

Author Contributions: Investigation, H.-H.T., L.-F.C. and C.-Y.T.; data curation, H.-H.T. and L.-F.C.; conceptualization and methodology, Y.-G.L.; software, validation and formal analysis, H.-H.T. and Y.-G.L.; writing—original draft preparation, H.-H.T.; supervision, Y.-G.L. and C.-Y.T.; resources, L.-F.C. and C.-Y.T. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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