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Optimal Allocation of Water for Irrigation and Power Generation―A Case Study of Hirakud Reservoir,

Odisha, India

最佳的灌溉與發電用水分配―以印度奧里薩邦Hirakud水庫為例

Ashutosh Rath, Prof. Prakash Chandra SwainDepartment of Civil Engineering, VSS University of Technology, Odisha, Burla768018, India

ABSTRACT

This study presents a case study of optimal allocation of water for Irrigation and power generation at Hirakud reservoir with the application of meta-heuristic algorithm. Wefocus on reservoir operation of Hirakud reservoir, which is situated in the Sambalpur district of Odisha state, in India. It is a multipurpose reservoir. This work deals with the maximizationboth hydropower generation and irrigation. As the inflow to the reservoir is uncertain, it creates difficulties and complexities in dealing with the reservoir operation. Therefore,we attempt to build a policy for reservoir operation in Hirakud multipurpose reservoir with a view to satisfy the dual needs of both irrigation and hydropower generation given uncertainty intrinsic to this system. A number of optimization techniques such as Genetic algorithms (GA), particle swarm optimization (PSO), ant colony optimization (ACO), etc., have been applied to find optimal release for irrigation and hydropower generation. The analysis indicates that the performance of ACO, a meta-heuristics based algorithm,provides better resultsthan other methods.

Keywords: Genetic algorithms, Particle swarm optimization, Ant colony optimization, Hydropower generation, Irrigation release.

摘　　　　　要

本研究採用巨集啟發式演算法，對Hirakud水庫的灌溉和發電用水之最佳分配進行了案例研究。我們著重在Hirakud水庫的運營，該水庫位於印度奧里薩邦的Sambalpur區，為一個多功能水庫。這份研究涉及水力發電和灌溉的最大化。由於進入水庫的流量具有不確定性，在處理水庫運行模式時會產生困難和復雜度。因此，我們試圖在Hirakud多用途水庫建立運行策略，以滿足灌溉和水力發電的雙重需求以及其固有的不確定性。許多優化技術，如遺傳演算法(GA)，粒子群最佳化(PSO)，蟻群優化(ACO)等，已被應用於尋找灌溉和水力發電的最佳量體。分析表明，基於巨集啟發式演算法的蟻群優化較其他方法而言，提供了更好的結果。

關鍵詞： 遺傳演算法，粒子群最佳化，蟻群優化，水力發電，灌溉。

*Corresponding author. E-mail: erashutoshrath@gmail.com ; pcswain.vssut@hotmail.com

臺灣水利　第 66 卷　第 3 期民國 107 年 9 月出版

Taiwan Water ConservancyVol. 66, No. 3, September 2018

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1. INTRODUCTION

Development of available water resources plays an important role in the growth of a country’s economy. A considerable proportion of the Indian economy depends on the development of agriculture. Water resources and their development depend on various factors such as industrialization, c l imat ic changes , popula t ion growth, e tc . Scientifically based reservoir management that considers the spatiotemporal variation of water availability would better cater to various needs such as the municipal and industrial supply of water, irrigation, generation of the hydroelectric power and navigation, etc. throughout the year. Reservoir operation strategies are often based on traditional approaches like standard operating polices such as simple rule curves, which may not consider the optimal release of water for various uses especially during non-monsoon and dry periods. The rule curve for the Hirakud reservoir has not been revised for more than 50 years. Hence, scientific approaches that maximize benefits are required to develop effective reservoir operational practices. There are various types of reservoirs depending on the nature of operation. A Storage reservoir stores the extra amount of water during the monsoon or heavy flow. A Flood Control reservoir stores excess flood waters during the monsoon season thereby reducing the risk of flooding in downstream areas. As the name suggests, multipurpose reservoirs serve multiple purposes such as flood control, hydropower generation, irrigation, navigation, water supply etc.

Optimization techniques can be applied to find optimal solutions for a problem by considering the initial conditions as input using some constraints and variables. Many optimization techniques have been applied in the past for intelligent reservoir operation. Linear programming (LP), non-linear programming (NLP) and dynamic programming (DP) have been used to deal with reservoir operational problems. Optimization method

selection is based on the complexity of the problem, fitness function, decision variables and types of constraints. Each technique has some advantages and disadvantages. Optimization techniques such as genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO), etc. have been used for both single and multiple reservoirs systems to meet various objectives. Reservoir operational problems are complex as determining factors like inflow; rainfall and reservoir release rates and storage capacity are uncertain. A number of authors have investigated this subject. Butcher (1971) worked on Wataheamu dam situated at the California-Nevada border to find the reservoir operation rule by applying a discrete stochastic dynamic behaviour method. Benedito et al. (1991) used stochastic dynamic programming in the Lower Tiete river basin, a Brazilian multi-reservoir system, for reservoir operation with particular emphasison hydroelectric purposes. Wardlaw et al. (1992) applied and analysed the genetic algorithm for multi-reservoir operations. Panigrahi et al. (2000) and Mousavi et al. (2004) studied the application of fuzzy logic in reservoir operation. Chandramouli et al. (2001) applied dynamic programming and artificial neural network for efficient multipurpose reservoir operations. They used three alternative formulations of ACO algorithms for testing a single purpose reservoir operation. Raju et al. (2004) investigatedthe operation of Sri Ram Sagar Project and its irrigation policy by using GA. Kumar et al. (2006) studied an integrated model for multiple crop planning and optimal reservoir operations using GA. Kumar et al. (2007) and Cheng et al. (2009) used PSO and GA methods for reservoir operation problems. Ostadrahimi et al. (2012) solved multi-reservoir operation rules by using a multi-swarm PSO based optimization by applying various mathematical equations.Srinivas et al. (2017) conducted a study on the development of a comprehensive fuzzy based approach for evaluating sustainability and self-purifying capacity of the

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river Ganges. Rath. et al. (2018) conducted the performance evolution of two canals of Hirakud canal system using a benchmarking technique.

The main objective of this study is to develop an optimal reservoir operation policy for Hirakud multipurpose reservoir to meet the demand of irrigation and hydropower generation, so that hydropower generation can be maximized and the gap between the supply and demand for irrigation can be bridged. This work will be helpful for the development of irrigation and power generation and also significantly contributes to water management policies of the study area.

2. MATERIALS AND METHODS

Optimization techniques have been applied in various sectors to find suitable solutions. The first step is to develop a model by considering the modelling environment. This is important since although new optimization methods have been introduced over the years, from slight modifications of classical methods to evolutionary algorithms, there is little consensus on a blanket solution for all situations sincethe efficiency and effectiveness of these methods vary with scale. Therefore, optimization and optimization method selection is still an active area of research with a broad range of researchattempting to improve the efficiency and performance of these methods, or at least identify the appropriatenessof different optimization algorithms given particular circumstances.

2.1 Particle Swarm Optimization

Kennedy and Eberhart (1995) developed a new meta-heuristic optimization technique known as the Particle Swarm Optimization (PSO) technique, which is based on the concept of swarm intelligence. In this technique, the particle represents an “individual” in a group of insects or birds that work as a group.This technique considers both the individual and group behaviour of the swarm. It is

considered to be a global optimization technique in finding the best local solution as well as the best solution of n dimensional space.

Concept of Particle Swarm Optimization

i- The Individual swarms always searches for the best solution. ii- Each individual adjusts its flight in accordance with its own experience and the experience of others. iii- Collectiveflightchanges of the particles represent changes in solution. iv-Search areasof potential solutions are considered. v-The global optimum is considered as per swarm movement. vi-For each particle the individual best value and global best value are considered. vii-Velocities and positions adjust based on the distance of the particles from the goal. viii-Possible solutions within the search area are considered. ix-Movement towards the goal is the global optimum. ix-Each particle considers its individual best value and the global best value. x- Position and velocity are modified by the individuals on the basis of the distance between the goal and itself. Iteration details are illustrated in Fig. 1.

Advantages and disadvantages of Particle Swarm optimization can be described as follows: i-implementation is easy.ii- Parameter requirements

Fig. 1. Flow Chart indicating working principle of Particle

Swarm Optimization.

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are low. iii- It can be easily applied to find the global optimum.iv- Mathematical functions such as derivatives and integrals are not required. v- It can be used for multidimensional and large-scale problems. vi- The probability of overlapping is minimal. While the disadvantages are: i- in some cases it gives premature convergence.ii- It may suffer from partial optimization.iii-It has difficulty in finding the local optimum.

2.2 Ant Colony Optimization

Dorigo et al. (1992) developed the concept of ant colony optimization to solve various types of optimization problems. The flow chart at Fig. 2 described the concept of ant colony optimization. Destination – i-ants moves from source to the place where food is available. ii-Pheromone trails help to find the shortest path traced by the ants. iii- The ants move randomly. iv-At the time of movement of ants the pheromone is deposited on the path. v-The deposit helps the ants find the paths. vi- More pheromone on the path increases the probability of the path being followed. vii-The entire process is repeated until the shortest path is found.

2.3 Genetic algorithm

The concept of Genetic algorithm based on biology, Darwin’s principle: survival of the fittest. This concept is based on bio-inspired processessuch

as mutation, crossover and selection. A genetic algorithm provides a set of highprobability solutions from which a good feasible solution for a particular problem can be obtained. Figure 3 highlights how the evolution process of a genetic algorithm works, with base units represented by chromosomes based on encoding of the search space.

Working Principle

i GA starts with the selection of a set of populations. ii-A new population is found on the basis of higher empirical fitness than the previousone. iii-The solution is based on the fitness value since this dictatesproductive success and contributions to the next generation. iv-The process is continued till the termination criteria is satisfied.

2.4 Problem Formulation

Problem formulation plays an important role in finding a solution for an optimization problem, as it decides a structure for the research and explains the problem logically. In this work the problem has been formulated to get a minimum irrigation deficit whilemaximizinghydropower production. Therefore, in this investigationirrigation and hydropower generation has been optimized.

Irrigation release and Hydropower generation

The main aim of any water resource project is

Fig. 2. Flow Chart indicating working principle of ACO.

Fig. 3. Flow Chart indicating working principle of genetic algorithm.

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to attain minimum irrigation deficits by bridging the gap between the demand and release for irrigation whilemaximizing hydropower production. These two objectives are contradictory to each other. For minimizing irrigation deficit, more release of water is required and for hydropower generation more water should be stored for maintaining high water levels to meet the demand. It is crucial to determine this for the non-monsoon season, when irrigation release and power generation are conflicting the most. Layout of water flow from inflow to the reservoir and to outflow is indicated in Fig. 4.

Objective function for irrigation release and hydropower generation

For irrigation release operationThe square deficit should be minimized

Minimize F = ∑T=1T (DT ‒ IRT)2......................(1)

Where,F = Squared deviation of irrigation demand and

releasesDt = Irrigation demands in period t (106) m3

IRt = Water Releases for irrigation in the period t (106) m3

t = 1, 2…………For hydropower production operationMaximizing the production of energy

EP = ∑t=1T P Qt • Ht ........................................(2)

Where,EP = Energy produced

p = it is the coefficient of power productionQt = it is the amount of water release to the turbine

during the period t (106) m3

Ht = net heads available (m), (gross head –head loss due to friction)

For combining irrigation release and hydropower generation operation

According to the basis of priority, objectives are fixed for multipurpose reservoir, the final fitness function is:

Minimize the objective function

F = k1∑T

t = 1((DT ‒ IRT)2 / DT2 + k2 ∑

Tt = 1 (EMAX ‒

P Qt • Ht) / EMAX .......................................(3)

k1 and k2 = Constants are used according to the priority,

Dt = Irrigation demands in period t (106) m3,IRt = Water release for irrigation in period t (106)

m3, Emax = Maximum energy produced (KW),p = power production coefficient, Qt = Release made to river bed turbine in period t (106) m3,Ht = Design head (m).

Constraints for irrigation release and hydropower generation

(a) Continuity constraints of the reservoir:

S(t+1) = S(t) + I(t) ‒ Q t ‒ IR(t) ‒ E(t) ‒ O(t)……...................……………(4)

For all t = 1, 2......., TWhere;St = Reservoir storage at time t (106) m3,St+1 = Reservoir storage at next time period (106) m3 It = Inflow to the reservoir at time period t (106) m3

Qt = Reservoir release for power generation for time period t (106) m3

IRt = Irrigation release for time period t (106) m3

E(t) = Evaporation at time period t (106) m3

O(t) = Overflow at time period t (106) m3

Fig. 4. Layout of water flow from inflow to the reservoir to outflow.

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(b) Constraints of release from the reservoir:

Dmin(t) ≤ IRt ≤ Dmax(t)......................................(5)

Dmax(t) = Maximum irrigation demand (106) m3.Dmin(t) = Minimum irrigation demand (106) m3.

(c) Maximum power production limits

pQH ≤ Emax ....................................................(6)

Where;p = Power production coefficient, Q = Discharge for the hydropower generation,H = Net head available (m), Emax = Maximum energy produced.

(d) Canal capacity limits

IRt ≤ Camax .....................................................(7)

Where;Camax =Maximum canal capacity

(e) Discharge from the reservoir through penstocks

Q = A*V ........................................................(8)

Where Q = πd2/4 *(2gH)0.5

Q = Discharge from the reservoir for hydropower production

d = Diameter of the penstocksg = Acceleration due to gravity,H = Design head in meters for hydropower

generation and it is a function of time.

3. STUDY AREA

Hirakud reservoir is indicated in Fig. 5, which comes under the Mahanadi catchment basin. Mahanadi drains into the Bay of Bengal. The total length of the river is 851 Km, out of which 357 km come under Chhattisgarh region and the rest 494 km flow in Odisha. A part of the basin also covers Jharkhand, Maharashtra and Madhya Pradesh. The main tributaries are Tel, Ong, Mand, Jonk, Hasdeo and Seonath. The total catchment area of the Mahanadi river basin is 1,41,589 sq Km. There are different types of soil throughout the basin such

as red soil, yellow soil, black soil, laterite soil and sandy soil etc. The properties of soil can provide information regarding the cropping pattern and water requirements for crops etc. Most of the soil throughout the basin is red soil. Its colour is red due to the presence of iron oxide. The Mahanadi river basin gets 90% of water from rainfall due to formation of a depression in the Bay of Bengal.

Maximum temperature is recorded during in the month of May, whereas the minimum temperature is in the month of December. In winter temperature varies from 5o to 14o and in summer it is recorded between 47o and 49o. In the system Inflow and storage is the inputs whereasthe irrigation and hydropower is the outputs. The main objective is to make proper use of storage to fulfil both irrigation and hydropower generation requirements as well as control floods. Hirakud dam consists of 83,400 square kilometre of the total basin. Total flood discharge is 1,500,000 cusecs. Minimum, maximum and average annual rainfalls are 691.46 mm, and 1928.42 mm, 1122.28 mm, respectively. Minimum, maximum, and average annual runoffs are 1.133 Million-HaM, 9.09 M.HaM and 3.313 Million-HaMrespectively. The total storage capacity is 5,896 Million HaM out of which 1,073 million m3 is dead storage. Theheight of the dam is 60.96 m. The spillway capacity is 42,450 cumecs. We used data over 35 years based on measurements takenonce every ten daysfrom 1983 to 2017. Inflow, storage, demands for irrigation, hydropower release, evaporation, and spill over are taken as inputs for

Fig. 5. Basin map of River Mahanadi (source-Google).

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finding the release for irrigation and determining the hydropower production. To determine the operation rule for reservoir or flood control, we calculated the outflows from the reservoir. For that, we considered the ten day time interval average records of the discharge from Khairmal and Barmul, storage, inflow, spill and evaporation data forthe monsoon period from 2008 to 2017.

4. DATA COLLECTION AND INTERPRETATION

Optimizations of hydropower generation and irrigation release for the non-monsoon period in Hirakud reservoir depend on the storage of water during the monsoon period. The reserve inflow variable and climatic factors like rainfall, evaporation suffer from uncertainty. So these data can be treated as the constraints for the optimization model, i.e., to optimize the release of water for irrigation, and power generation.

The data have been collected on a ten day basis. Figure 6 shows the volume of water for irrigation demand with respect to the non-monsoon season on a ten day basis of the year 2017. By considering the irrigation demand, the release for the irrigation has been calculated to fulfil the demand. Similarly data from 1983 to 2017 have been taken as inputs. Figure 7 shows the relationship between hydropower release and time period of non-monsoon season

from 1st January to 20th June and from 21st October to 31st December of the year 2017 on a ten-day basis. By using the hydropower release and storage data, hydropower generation can be calculated. Due to shortages in storage water, it is difficult to fulfil the requirement of irrigation demand and hydropower from April to June. Thus these have been used as constraints for the optimization model. Figure 7 shows the variation of Irrigation demand for the non-monsoon period.

5. RESULTS AND DISCUSSIONS

5.1 Result from the application of Ant Colony Optimization

The Ant Colony Optimization model is based on the foraging behaviour of ants. As per this behaviour, a chemical substance is deposited on the path of ants so that they can move from source to destination. Thereafter, the parameters for ant colony optimization are initialised. Subsequently, the solution is constructed using the proportionality rule andlocal and global updating is done. The length of the optimal path and the amount of pheromone deposited is calculated. This process is continued until the objective is reached. In the objective function, the irrigation release and design head for the power generation (KW) is calculated. Then by using the following formula the power generation is calculated.

Fig. 6. Irrigation demand for ten-day time interval for non-monsoon season.

Fig. 7. Irrigation demand at ten day intervals for the non-monsoon season.

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Energy generated = 9.81 *ƞ*Q*H= 9.81*0.8*Q*H= 7.84*Q*H...................................................(9)

Where,Ƞ = efficiency of turbine which is taken as 80%,Q = Discharge for power generation,H = Design head for power generation.

5.2 By Genetic algorithm

Use of genetic algorithm

Pertaining to the methodology, the process of genetic algorithm is based on selection, crossover and mutation. At first, a set of populationsare fixed. For the selection process, some are randomly chosen for the reproduction of the next generation. The main objective of this method is the selection of good results by considering the fitness function. The populations withhigh fitness value reproduce more and represent a greater proportion of the next generation. By determining the fitness of individuals, the selection operation is derived. The next step after selection is crossover. The objectives are to attain a new solution from the existing one present in the mating pool after the selection process. After using the crossover operation, the next step is mutation. It is the process of addition of new features to the solution. Mutation is also used for finding the optimum solution in the string. Finally, after selection, mutation and cross over, the next part is to set the number of generations and iterationsrequired to attain the results. The main part is to find the fitness value of each individual as per the iteration calculated by using the objective functions and constraints as given in the problem formulation for minimizing the deficit of irrigation release and maximizing power generation.

The iteration is taken as 150;Probability of crossover is taken as 0.55;Probability of mutation is taken as 0.2;The fitness value for each iteration is given in

Figure 8. The fitness value takes a particular value for an objective function for a given iteration. It is updated during each iteration and after a number of iterationsquickly converges to a constant value. Further, it can be concluded that in the genetic algorithm, after the 2nd iteration, it converges to a very low fitness value. Its fitness value varies from 0.035 to 0.252.

Fig. 9 represents the irrigation release value for the non-monsoon period of 2017 on a ten-day basis. Irrigation demand is greater during the pre-monsoon period than the post-monsoon period. From Fig. 10 it is clear that for the pre-monsoon period the release of irrigation is more than that of the post-monsoon period. This is due to differences in climatic and soil conditions during the months of November and December. The total release is 1724.624 million m3; the minimum release is 2.78 MCum and maximum release is 138.67 MCum.

Fig. 8. Fitness value over 150 iterations with genetic algorithm.

Fig. 9. Temporal variation of irrigation release for 2017 with genetic algorithm.

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Figure 10 is the representation of generation of hydropower for the non-monsoon period of 2017. There is a lot of variation in the generation of the hydropower from the pre-monsoon period to the post-monsoon period. Here the maximum generation of power from Burla power house is equal to 235.5 MW and the generation of hydropower should not exceed the installed capacity. Before the monsoon period the amount of water stored in the reservoir is less. Hence the generation of the power is less during the months of May and June. Before the monsoon the storage is considered dead storage.

For the genetic algorithm selection, mutation and cross over operators are fixed with changing hydroelectric generation. The final result is based on the probability of mutation and crossover at 0.55 and 0.2, respectively, and 150 generations. In order to identify the optimal water allocation for irrigation and hydropower generation, the objective function is used, i.e., equation 3. Equation 4 to 8 indicates the constraints. In equation 8, d refers to the diameter of the penstocks. In Hirakud reservoir, there are 7 penstocks out of which 4 are of 7.6 m in diameter whereas 3 are of a 7 m diameter. As described in equation 8, discharge for hydropower generation is directly proportional to H, which is the design head for power generation. H is a function of time period, i.e., H(t). In equation 3, m, the irrigation release, is optimized and, similarly, the design head

is also optimized to get hydropower generation. In the objective function, there are two constants k1 and k2 which are used on the basis of priority of the purpose. Various trail values of k1 and k2 are taken to get the final values which would yield optimal release for irrigation and power generation.

5.3 By Particle Swarm Optimization

Use of particle swarm optimization

This solution is based on swarm intelligence. Initially the parameters are set by introducing the number of swarms, number of iterations, cognitive constants, social constants and inertia weights. The ranges of the variables are then assigned. Fitness values of the objective functions are calculated based on the p Best and g. The best for each iteration is identified and the best fitness will be determined. The velocity and the position of the particle is updatedat each step according to the most recent fitness value. This process is continued until meeting the objective. By considering the number of iterations as 100 and the swarm size as 50, the optimum result is obtained by using the weight inertia as 1 and the acceleration coefficient as 1.49445 and 1.49445, respectively.

Fig. 11 shows the fitness value with respect to the number of iterations for PSO. It shows that after the 16th iteration the fitness value converges to a constant of approximately 0. Particle swarm optimization has an advantage of

Fig. 10. Temporal variation of hydropower generation for

2017 by genetic algorithm.

Fig. 11. Fitness value over iteration with Particle swarm optimization.

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rapid convergencesince its convergence rate is high. Before arriving at an optimal solution many other trialsolutionshave resulted but by using 100 iterationsan optimum solution has been achieved.

Fig. 12 shows the calculated irrigation release for the non-monsoon period of 2017. The requirement for irrigation is more from January to March. In the post-monsoon period, there is a lower water requirement because during that periodsoil moisture is adequate for crop growthand the ground water level is higher. Conversely, the irrigation demandsare higher in the pre-monsoon period rather than the post-monsoon period. Therefore, irrigation levelsduringthe pre-monsoon period should be greater than that of the post monsoon period. From figure 12 it is clear that the release of water for irrigation is greater during the pre-monsoon period than post-monsoon period. The calculated release value varies from 4 MCum to 127 MCum. The average release throughout thenon-monsoon period is 1774.281 MCum.

Figure 13 shows the generation of hydropower for the non-monsoon per iod of 2017. The requirement of electricity is greater during the pre-monsoon period. This Figure also shows that the generation of electricity is greater during the period from the last week of October to the last week of November. The main reason behind this is the high storage levels. In addition, less hydropower is

required during the winter season from December to February. From the months of March to June, the requirement of hydropower is greater than the other months but due to lower storage levels, the generation of hydropower is not satisfied. Power production varies from 3.09 MW to 189.0561 MW. The total power generation throughout the non-monsoon period is 741.7488 MW.

5.4 By ant colony optimization

Figure 14 represents the fitness value for each iteration. This Figure shows that after the 11th iteration, the fitness value converges, which israpid. By going through different iterations and antsizes the optimum results finally occurred at iteration 40.

Figure 15 shows irrigation for the non-monsoon period of 2017. The irrigation demands throughout the year is as per the need of cultivation. More water is required from May onwards. The main objective

Fig. 12. Temporal variation of irrigation release for 2017 by particle swarm optimization.

Fig. 13. Temporal variation of Hydropower release for 2017 by particle swarm optimization.

Fig. 14. Fitness value over iteration by ACO.

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is to fulfil the irrigation demand. For some weeks in the post-monsoon period the release is lower due to climatic and soil condition of the area. During the rainfall, the ground water level becomes higher which leads to lower irrigation requirements. Thus, more release of irrigation is unnecessary. Due to maintenance purposes during the month of April, the release is lower as compared to other months of the year. Overall, the release is greater in the pre-monsoon period than that of the post-monsoon period. The release varies from 13 MCum to 200 MCum. The total release for irrigation is 2040.624 MCum.

Fig. 16 represents the generation of hydropower on a ten day basis for the non-monsoon period of 2017. Consumption of electricity increases day by day with respect to the increase in the number of industries and population density. Further, it leads to the increase in the demand for hydropower

generation since there are so many industries; institution buildings and societies that avail the power generated from the Hirakud reservoir. As the demand for hydropower continues throughout the year, so the generation of the hydropower is ensured to meet the requirements. For the summer season, the need of hydropower is greater, but due to lower storage hydropower generation is not as high as that of the monsoon season. The generation of hydropower during the period just after the monsoon is more than the month of January, February, November and December. Greater storage allows for greater hydropower generation. The generation of hydropower varies from 3.201 MW to 174.0713 MW. The total power generated is 753.6561 MW. For example, if Q is equal to 134.56 Million m3, H = 10 m, then according to eq. (9) the power generated is equal to10560.26 KW.

Comparisons among GA, PSO and ACO

The meta-heuristic methods have been applied to solve the reservoir operation model for a 35 year period with a ten day time interval. From the fitness comparison, it is clear that the fitness of ant colony optimization is greater than the other two with a higher rate of convergence. The results show that annual irrigation release obtained for ten day intervals by ant colony optimization is higher than other methods for almost all years with a 70% higher priority for release. The ten day models give more realistic solution, which can be very useful for real time operations. The calculated releases from the models are much greater than the requirements. From the comparison, as shown in Table 1, it is evident that after some iterations the fitness converges to a single value. All three meta-heuristic algorithms have high convergence rates but the fitness value is greatestfor the ant colony optimization. This shows that the ant colony optimization technique gives better result than the other two techniques.

Figure 17 presents the box plot comparison

Fig. 15. Temporal variation of irrigation rates for 2017 by ant colony optimization.

Fig. 16. Temporal variation of Hydropower production for 2017 by ant colony optimization.

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of optimization techniques for the release of hydropower generation over the historical data from 1983 to 2017 for the non-monsoon seasons. From the comparison, it is clear that by using genetic algorithm the minimum release is 47 MCum and the maximum release is 650 MCum. However, by using particle swarm optimization, the minimum release is 57 MCum and the maximum release is 661.15 MCum and by using ant colony optimization the obtained minimum release is 68 MCum and the maximum release is 689 MCum. The connection line between the green box and purple one shows the median of the data. The bottom of the green box demarcates the 25% bound of the data and the top of the purple green box shows 75% bound of the data. The lower point shows the minimum value and the higher point shows the maximum value.

Figure 18 represents the irrigation levels as per particle swarm optimization, ant colony optimization and genetic algorithm with respect to the non-monsoon season for 35 years in box plot. The connection line between the green box and blue one shows the median of the data. The bottom of

the green box demarcates the 25% bound of the data and the top of the purple box shows the 75% bound of the data. The lower point shows the minimum value and the higher point shows the maximum value.From the comparison, it is clear that the end storage is less for the ACO technique as the release is greater. According to the rule curve, the storage level in the reservoir is at the highest level during the end of the monsoon period, i.e., during the month of October because during the non-monsoon period the water can be used for different purposes. The reservoir level is at dead storage during the end of non-monsoon period, i.e., during the end of June. The details are described in Table 2 and Table 3.

The above tables show the release of water for irrigation from 1983 to 2017 by using genetic algorithm, particle swarm optimization and ant colony optimization. From the fitness comparison it is clear that the fitness of ant colony optimization is more than the other two. Its performance is better than the other two techniques. From this analysis, we can see that the release value obtained from ant colony optimization is greater than the other two.

Table 1. comparison table of three methods

optimization Genetic Algorithm Particle Swarm Ant ColonyTechniques Optimization Optimization

No. of iteration 150 100 40Size of Population 100 30 10

Constants P cross = 0.3 c1 = 1.49445 alpha = 1P mutation = 0.1 c2 = 1.49445 beta = 1;

w = 1 rho = 0.05

Fig. 17. Comparison of hydropower release for 35 years by using optimization techniques.

Fig. 18. Comparison of Irrigation release for 35 years by using optimization techniques.

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6. Conclusions

The following conclusions are derived from the results based on the effectiveness of models for irrigation release and hydropower generation:

i-In this work the optimization techniques such as genetic algorithm, particle swarm optimization and ant colony optimization have been applied for finding irrigation release and hydropower generation.

ii-The demand for irrigation depends upon the season. During the non-monsoon season more water is required for irrigation. Maximum demand of water for irrigation is about 138.054 million m3. By using ant colony optimization the optimal release of 138 million m3 was obtained.

iii-The installed capacity of Burla power house is 235.5 MW. By using ant colony optimization method up to 220 MW power generations has been obtained with 657 million m3 of release and 41 m design head.

iv-In the summer season, the average power generation required is 100 MW. By using ant colony optimization the optimal result of a 95 MW average was obtained.

References

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Table 2. Irrigation release for the historical years of the non-monsoon season from 1983 to 2017 in Hirakud reservoir system from ACO, PSO and GA methods for 10-day interval time periods (in Million m3)

STATISTICAL PARAMETERSMODELS FOR RESERVOIR OPERATION

ACO PSO GAMaximum value (Million m3 ) 138 135 130Minimum value (Million m3 ) 25 20 15Average value (Million m3 ) 89.72 87.55 74.48

Standard deviation (Million m3 ) 681.74 734.26 767.31

Table 3. Hydropower production for the historical years for the non-monsoon season from 1983 to 2017 in Hirakud reservoir system from ACO, PSO and GA methods for 10-day interval time periods (in KW)

STATISTICAL PARAMETERSMODELS FOR RESERVOIR OPERATION

ACO PSO GAMaximum value (KW) 203715.9 185915.5 183730.3Minimum value (KW) 1369.864 1178.432 1061.016Average value (KW) 32387.5 29441.22 27887.11

Standard deviation (KW) 442031.6 463615.4 483136.68

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Received: 107/02/10

Revised: 107/04/25

Accepted:107/05/25