Optimal Operation Of Multi-reservoir System Research Articles

Introducing improved atom search optimization (IASO) algorithm: Application to optimal operation of multi-reservoir systems

Nowadays, optimal reservoir operation is regarded as one of the most important issues in water resources management. In this regard, several optimization algorithms have been used to evaluate the issue of optimal reservoir operation. To increase the accuracy and proximity of the solutions to the absolute optimal solution, the improved atom search optimization (IASO) algorithm was introduced with a mutation strategy to improve its global search capability, as an important factor in preventing trapping in a locally optimal solution. This article implemented the atom search optimization (ASO) algorithm and its improved model to improve the results of the objective function in multi-reservoir systems. Comparing the IASO algorithm with the basic ASO algorithm on the mathematical benchmark functions revealed good accuracy and the superiority of the IASO algorithm. Then, sensitivity analysis was performed on the effective coefficients of both algorithms, in which alpha and beta, as the depth and weight coefficients used in the calculation of atoms acceleration, were considered 50 and 0.5, respectively. The results showed the relatively good accuracy of the ASO algorithm in the case of multi-reservoir systems, but implementing and comparing the results of the improved algorithm, showed improvement so that the best IASO results were improved from 95.33% to 99.99% as close to the global four-reservoir system response of 308.29 and from 89.67 to 94.36% with the solution of the ten-reservoir system in the amount of 1194.44.

Optimal operation of multi-reservoir system for flood control and hydroelectric generation

In this research, a flood control operating strategy is developed based on a simulation-optimization model to reduce flood damage downstream of multi-reservoir systems by using spillway gates. For this purpose, an optimization algorithm is introduced, in which the maximum water level of the downstream control points and hydropower potential generation in the flood season are objective functions, and the level of the stages of spillway gates are the decision variables. A global optimization tool, Shuffled Complex Evolution (SCE) algorithm implemented in the AUTOCAL software was coupled with the Mike 11 from DHI simulation model for optimizing stages level of spillway gates. As a case study, the Vu Gia Thu Bon rivers catchment including multi-reservoirs of A Vuong, Song Tranh 2, Dak Mi 4 and Song Bung 4 is analyzed. The proposed method was demonstrated to provide an effective tradeoff between flood control and hydropower generation.

Application of Cellular Automata in Bi-Objective Operation of Multi Reservoir Systems

Optimal operation of multi-reservoir systems is one the most challenging problems in water resource management due to their multi-objective nature and time-consuming solving process. In this paper, Multi-Reservoir Parallel Cellular Automata-Simulated Annealing (MPCA-SA), a hybrid method based on cellular automata and simulated annealing is presented for solving bi-objective operations of multi-reservoir systems problems. The problem considers the bi-objective operation of a multi-reservoir system with the two conflicting objectives of water supply and hydropower generation. The MPCA-SA method uses two single-objective cellular automata acting in parallel to explore the problem search space and find the optimal solutions based on the probabilistic interaction with each other. Bi-objective operation of the Dez-Gotvand-Masjed Soleyman three-reservoir system, as a real-world system in southwestern Iran for a period of 60 months, is considered in order to evaluate the ability of the proposed method. In addition, a Non-dominated Sorting Genetic Algorithm (NSGAII) is also used to solve the problems and the results are compared with those of MPCA-SA, indicating the capabilities of the proposed MPCA-SA method. The results show that the MPCA-SA method is able to produce solutions comparable to those of NSGAII with a much-reduced computational cost equal to 1.2% of that required by the NSGAII, emphasizing the efficiency and practicality of the proposed method.

Optimal operation of multi-reservoir systems for increasing power generation using a seagull optimization algorithm and heading policy

Power supply is a key issue for decision-makers. The reservoir operation of multi-reservoir systems is an important aspect to consider in efforts to increase power generation. This research studies a multi-reservoir system comprising of the Khersan-I (KHI), Karoon-III (KAIII) and Karoon-IV (KAIV) with the intent being to increase power generation. To achieve this, the Two-Point Heading Rule was integrated with a new optimization algorithm, namely the Seagull Optimization Algorithm (SEOA). The Two-Point Heading Rule was used based on four distinct scenarios, namely Two-Point Heading Rule (1), Two-Point Heading Rule (2), Two-Point Heading Rule (3) and Two-Point Heading Rule (4). The Seagull Optimization Algorithm was then used to find two heading parameters of the TPHRs. The Seagull Optimization Algorithm was subsequently benchmarked against the Salp Swarm Algorithm (SSA), Bat Algorithm (BA) and the Shark Optimization Algorithm (SOA). Various inflow scenarios consisting of the first inflow scenario (dry condition), the second inflow scenario (normal) and the third inflow scenario (wet condition) were considered for the optimal operation of this multi-reservoir system. The results indicated that the global solution of the MSOO based on NLP for Two-Point Heading Rule (1) under the first inflow scenario and was 3.22 while the average solution of Seagull Optimization Algorithm, Salp Swarm Algorithm, Shark Optimization Algorithm, and Bat Algorithm in respective order was 3.25, 3.93, 4.87 and 6.03. The results indicated that the global solution of the MSOO based on NLP for Two-Point Heading Rule (1) under the second inflow scenario was 2.14 while the average best solution of Seagull Optimization Algorithm, Salp Swarm Algorithm, Shark Optimization Algorithm, and Bat Algorithm in respective order was 2.16, 2.98, 3.96, and 4.89. It can be concluded that the SEOA outperformed all of the other algorithms. It was also found that the SEOA based on the Two-Point Heading Rule (3) under the third inflow scenario provided the most power generation for the KHI and KAIV systems. A multi-criteria decision was utilized to choose the best algorithm and heading policy. The ensuing results indicate that the SEOA had the best performance out of all the algorithms based on Two-Point Heading Rule (3) and the third inflow scenario.

Optimal operation of multi-reservoir systems: comparative study of three robust metaheuristic algorithms

Abstract In this study, the capability of the recently introduced moth swarm algorithm (MSA) was compared with two robust metaheuristic algorithms: the harmony search (HS) algorithm and the imperialist competitive algorithm (ICA). First, the performance of these algorithms was assessed by seven benchmark functions having 2–30 dimensions. Next, they were compared for optimization of the complex problem of four-reservoir and 10-reservoir systems operation. Furthermore, the results of these algorithms were compared with nine other metaheuristic algorithms. Sensitivity analysis was performed to determine the appropriate values of the algorithms’ parameters. The statistical indices coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), normalized MSE (NMSE), mean absolute percentage error (MAPE), and Willmott’s index of agreement (d) were used to compare the algorithms’ performance. The results showed that MSA was the superior algorithm for solving all benchmark functions in terms of obtaining the optimal value and saving CPU usage. ICA and HS were ranked next. When the dimensions of the problem were increased, the performance of ICA and HS dropped but MSA has still performed extremely well. In addition, the minimum CPU usage and the best solutions for the optimal operation of the four-reservoir system were obtained by MSA, with values of 269.7 seconds and 308.83, which are very close to the global optimum solution. Corresponding values for ICA were 486.73 seconds and 306.47 and for HS were 638.61 seconds and 264.61, which ranked them next. Similar results were observed for the 10-reservoir system; the CPU time and optimal value obtained by MSA were 722.5 seconds and 1,195.58 while for ICA they were 1,421.62 seconds and 1,136.22 and for HS they were 1,963.41 seconds and 1,060.76. The R2 and RMSE values achieved by MSA were 0.951 and 0.528 for the four-reservoir system and 0.985 and 0.521 for the 10-reservoir system, which demonstrated the outstanding performance of this algorithm in the optimal operation of multi-reservoir systems. In a general comparison, it was concluded that among the 12 algorithms investigated, MSA was the best, and it is recommended as a robust and promising tool in the optimal operation of multi-reservoir systems.

Optimal Operation of Multi-reservoir System for Hydropower Production Using Particle Swarm Optimization Algorithm

The determination of optimal operation rules for water storage systems will provide a good perception on the ability of these systems to achieve their objective functions. This study aims to identify optimal operation policies by maximizing the annual hydropower generation of a multi-reservoir system that consists of two reservoirs with different functions in flood risk management. These reservoirs, namely, Mosul and Badush, are located in the Tigris River, Northern Iraq. The Mosul Dam was constructed to protect the cities located downstream, and the Badush Dam is building to absorb flood waves in case the Mosul Dam collapses. The particle swarm optimization model for a single reservoir (PSOS) was formulated to determine optimal operation policies during real operation time to maximize annual hydroelectric generation. PSOS was approved during these operations and developed to specify ideal operation rules for a multi-reservoir system (PSOM), which consists of two reservoirs, through three modes of annual inflows. Results of PSOS indicated its superiority during real-time operation. The annual hydropower generation was achieved by the optimal operation rules of PSOM during the three styles of inflows. These optimal policies will provide good insights into the potential of this multi-reservoir system in supplying the national electricity network with hydropower energy, which is considered environmentally friendly, in addition to achieving the original goals of its construction.

Optimal Operation of Multireservoir Systems by Enhanced Water Cycle Algorithm

In this article, an enhanced water cycle algorithm (EWCA) is proposed and applied to optimize the operation of multireservoir systems. Three improvements have been made to the water cycle algorithm (WCA). They refer to high-quality initial solutions obtained by the chaos-based method, balancing of exploration of streams using a dynamic adaptive parameter, and dynamic variation of sub-water system size using the fitness value of rivers. For the purpose of verifying the improvements, three typical benchmark functions were selected as test functions. It has shown that EWCA performs better than WCA and water cycle algorithm with evaporation rate (ER-WCA). And then these three algorithms were also applied to optimize the operation of a multireservoir system with complex constrains as the case study. By comparing the results, it is found that the EWCA has higher ability to find a feasible solution in a narrow searching space. The effectiveness of the improvements is confirmed.

Optimal Allocation of Flood Control Capacity for Multi-Reservoir Systems Using Multi-Objective Optimization Approach

Operation of multi-reservoir systems during flood periods is of great importance in the field of water resources management. This paper proposes a multi-objective optimization model with new formulation for optimal operation of multi-reservoir systems. In this model, the release rate and the flood control capacity of each reservoir is considered as decision variable and the resulting nonlinear non-convex multi-objective optimization problem is solved with e-constraint method through the mixed integer linear programming (MILP). Objective functions of the model are minimizing the flood damage at downstream sites and the loss of hydropower generation. The developed model is used to determine optimal operating strategies for Karkheh multi-reservoir system in southwestern Iran. For this purpose, the model is executed in two scenarios based on “two-reservoir” and “six-reservoir” systems and for floods with return periods of 25 and 50 years. The results show that in two-reservoir system, flood damage is at least about 114 million dollars and cannot be mitigated any further no matter how hydropower generation is managed. But, in the case of developing all six reservoirs, optimal strategies of coordinated operation can mitigate and even fully prevent flood damage.

Coupled Operating Rules for Optimal Operation of Multi-Reservoir Systems

Due to the complexity of multi-reservoir system operation problems, researchers usually prefer to assume lumped demands located downstream of such systems. Consequently, distributed local demands through the system are neglected or supplied completely (e.g. using Standard operating policy, SOP), in order to simplify the problem. In this study, Coupled Operating Rules (COR) as a simple and suitable operating policy is applied for optimal operation of multi-reservoir systems with local demands. The applied policy includes two types of linear rules, which are defined to determine total releases and local water allocations in decision points. This policy is adopted within a simulation-optimization approach to optimally operate a three-reservoir system in the Karkheh river basin. Obtained results indicate that the proposed strategy reduces the intensity of demand deficits and distributes the occurred shortages throughout the system properly. Moreover, the system losses are managed appropriately and big unbalanced local shortages are prevented. Although COR strategy decreases the reliability of local demands compared to SOP, it is a reasonable operating policy for systems with distributed local demand sites. Moreover, in this study an effective Improved Melody Search (IMeS) algorithm is proposed to achieve the optimum values of operating rules’ parameters. The efficiency of the optimization method is compared to the results achieved by other selected well-known heuristic search methods. Based on the experimental results, it is revealed that the proposed algorithm is more effective in finding precise solutions over a long-term period, comparing with the other conventional algorithms.

Modeling Total Dissolved Gas for Optimal Operation of Multireservoir Systems

AbstractOne important environmental issue of hydropower in the Columbia and Snake River Basins (Pacific Northwest region of United States) is elevated total dissolved gas (TDG) downstream of a dam,...

Optimal Operation of Multi-reservoir Systems Considering Time-lags of Flood Routing

Operations of multi-reservoir systems are nonlinear and high-dimensional problems, which are difficult to find the optimal or near-optimal solution owing to the heavy computation burden. This study focuses on flood control operation of multi-reservoir systems considering time-lags caused by Muskingum flood routing of river channels. An optimal model is established to jointly minimize the flood peak on the downstream flood control station for the multi-reservoir systems. A hybrid algorithm, Progressive Optimality Algorithm and Successive Approximation (POA-SA), is improved to solve the multi-reservoir operation model by modifying the POA. The POA-SA uses the DPSA to reduce the spatial dimensionality due to the multiple reservoirs, and adopts an improved POA to alleviate the temporal dimensionality caused by the time-lags of the Muskingum flood routing. Linear programming is then implemented to verify the solution of the POA-SA method with a linear approximation of the discharge capacity curve. The multi-reservoir systems of China’s Xijiang River is selected for a case study. Results show that the flood peak of Wuzhou station can be averagely decreased by 6730 m3/s (12.8 %) for the 100-year return period floods, indicating that the proposed method is efficient to operate the multi-reservoir systems and resolve the time-lags issues.

Optimal Operation of Multi-Reservoir System Based-On Cuckoo Search Algorithm

Efficient utilization of water resources by reservoir operation in arid and semi-arid regions has been a traditional and important approach to mitigate water and energy scarcity. As the complexity of water resources system increases, there are urgent needs to apply effective optimization techniques to derive better operation rules. The meta-heuristic algorithms have been an alternative to the optimal operation of multi-reservoir system (OOMRS) for their parallel search capabilities. This paper presents the application of the cuckoo search (CS) algorithm to OOMRS with the objective to maximize the energy production. The penalty method was used to handle the physical and operational constraints. To make the CS more efficient, the optimized parameters of the CS were selected based on the parameter sensibility analysis. Finally, the performance of the CS was accessed by comparison with the genetic algorithm (GA) and the particle swarm optimization (PSO) under the same objective function evaluations (FEs). A case study of China’s Wujiang multi-reservoir system reveals that the CS can provide better and more reliable optimal results with average energy production of 12.31 billion kW∙h, 10.43 billion kW∙h, and 10.02 billion kW∙h for three different scenarios, which are approximately 0.52, 0.32, and 1.64 % higher than that of the GA, respectively. Meanwhile, the convergence performance of the CS is also satisfying. Therefore, it can be concluded that the CS is quite promising in handling complex reservoir operation optimization problem in terms of its simple structure, excellent search efficiency, and strong robustness.

Extension of the constrained particle swarm optimization algorithm to optimal operation of multi-reservoirs system

Three constrained versions of Particle Swarm Optimization (PSO) algorithm are presented in this paper for the efficient optimal operation of multi-reservoir systems using storage/release volumes as decision variables of the problem. Proposed algorithms are based on identifying and excluding the infeasible region of the search space before and during the search which has already proposed and used by the author for the operation of single reservoirs [5]. In the first version named Partially Constrained Particle Swarm Optimization I (PCPSO1), the sequential nature of the solution building procedure of PSO is used to explicitly enforce the release/storage constraints of the problem during solution construction. For this, the continuity equation is used at each period of the operation of each reservoir to define a new set of bounds for decision variable of the next period which satisfy release/storage constraints of the problem. Particles of the swarm are, therefore, forced to fly in the feasible region of the search space except for some rare cases. In the second version named Partially Constrained Particle Swarm Optimization Two (PCPSO2), the periods of the operations for upstream reservoirs, reservoirs with known inflow, are treated in a reverse order prior to the PCPSO1 search to define new set of bounds for storage volumes such that PCPSO1 algorithm is not given any chance of producing infeasible operations regarding upstream reservoirs. In the third version, the PCPSO2 search is augmented with a mechanism similar to that used in PCPSO2 for all downstream reservoirs by which all the infeasible operation of the downstream dams are also excluded from the search process and, hence, the name of Fully Constrained Particle Swarm Optimization (FCPSO) algorithm. Proposed methods are used to solve two benchmark problems of hydropower operations of multi-reservoir system namely Four and Ten reservoir systems and the results are presented and compared with those of the conventional unconstrained PSO and other methods in the literature. The methods are shown to be very effective in locating optimal or near optimal solutions and efficient in terms of the convergence characteristics of the resulting algorithms. Proposed algorithms are also shown to be relatively insensitive to the swarm size and initial swarm compared to the original algorithm.

Optimal operation of multi-reservoir system by multi-elite guide particle swarm optimization

With increasingly scarce of fossil fuel resources required for energy demand, hydropower has become one of the most important energy resources. As a renewable and sustainable energy, hydropower system has developed rapidly during recent decades. The unprecedented rate of expansion and development scale of hydropower has posed a challenge to the operation of multi-reservoir system (OMRS). The optimal operation of multi-reservoir system is a large-scaled, non-linear and multi-stage problem which subject to a series of hydraulic constraints. The main objective of OMRS is to find out the optimal hourly water discharge rate of each hydro station in the multi-reservoir system to minimize the power deficit and distribute the uniformly deficit if any. In order to solve OMRS problem effectively, in this paper, a multi-elite guide particle swarm optimization (MGPSO) is proposed by introducing archive set into standard particle swarm optimization. External archive set which can preserve elite solutions along the evolution process is employed to provide multi-elite flying directions for particles. Meanwhile, an effective constrain handling method is proposed to handle the operational constraints of OMRS problem. This proposed method is applied to a multi-reservoir system consisting of 10 cascaded hydro plants for case study. Compared with several previous methods, the simulation results of MGPSO can get better solutions with smaller energy deficit, which proves it is an alternative method to deal with OMRS problem.

Extension of the constrained ant colony optimization algorithms for the optimal operation of multi-reservoir systems

This paper extends the application of Constrained Ant Colony Optimization Algorithms (CACOAs) to optimal operation of multi-reservoir systems. Three different formulations of the constrained Ant Colony Optimization (ACO) are outlined here using Max-Min Ant System for the solution of multi-reservoir operation problems. In the first two versions, called Partially Constrained ACO algorithms, the constraints of the multi-reservoir operation problems are satisfied partially. In the third formulation, all the constraints of the underlying problem are implicitly satisfied by the provision of tabu lists to the ants which contain only feasible options. The ants are, therefore, forced to construct feasible solutions and hence the method is referred to as a Fully Constrained ACO algorithm. The proposed constrained ACO algorithms are formulated for both possible cases of taking storage/release volumes as the decision variables of the problem. The proposed methods are used to optimally solve the well-known problems of four- and ten-reservoir operations and the results are presented and compared with those of the conventional unconstrained ACO algorithm and existing methods in the literature. The results indicate the superiority of the proposed methods over conventional ACOs and existing methods to optimally solve large scale multi-reservoir operation problems.

Applying Simulated Annealing For Optimal Operation of Multi-Reservoir Systems

Applying Simulated Annealing For Optimal Operation of Multi-Reservoir Systems

Applying Simulated Annealing For Optimal Operation of Multi-Reservoir Systems

The need to optimize the operation of water reservoirs is an issue that is becoming increasingly a concern for water resources planners in developing countries. This issue particularly becomes more significant in large systems with multiple reservoirs where operation of one reservoir has an impact on the others. In other word, the set of reservoirs in these systems act like a united series and require specific methods to handle various modeling issues. Problem statement: Sirvan River basin in west of Iran, standing in fifth order in respect of discharge, is an example of such a complex system. The project of water transfer from western tropical regions which is one of the large-scale projects in water resources management in Middle East, consists of a number of reservoirs and transfer systems. The matter of optimum operation of such a collection is one of the complicated and outstanding issues in water resources management. Approach: It was found that, due to increasing decision-making variables, conventional models used in optimizing water resources systems were not any longer capable of obtaining a desired solution, either because of low precision or time constraints. Hence, the intelligent random research approach "Simulated Annealing" has been used which in recent, decades has revealed appropriate results in solving major problems. Results: The results of this research indicate that the annealing approach is capable of solving such complex problems in water resources management with good precision in a reasonable period of time. Conclusions/Recommendations: The results were also compared with outputs of MODSIM which is a widely known model for solving complex water resources systems problems and benefits from "out of kilter" algorithm. The results indicate SA as a very robust and effective model in optimization of large real multi-reservoir systems.

Stochastic optimization of multireservoir systems via reinforcement learning

Although several variants of stochastic dynamic programming have been applied to optimal operation of multireservoir systems, they have been plagued by a high‐dimensional state space and the inability to accurately incorporate the stochastic environment as characterized by temporally and spatially correlated hydrologic inflows. Reinforcement learning has emerged as an effective approach to solving sequential decision problems by combining concepts from artificial intelligence, cognitive science, and operations research. A reinforcement learning system has a mathematical foundation similar to dynamic programming and Markov decision processes, with the goal of maximizing the long‐term reward or returns as conditioned on the state of the system environment and the immediate reward obtained from operational decisions. Reinforcement learning can include Monte Carlo simulation where transition probabilities and rewards are not explicitly known a priori. The Q‐Learning method in reinforcement learning is demonstrated on the two‐reservoir Geum River system, South Korea, and is shown to outperform implicit stochastic dynamic programming and sampling stochastic dynamic programming methods.

Closure to “Optimal Operation of Multireservoir Systems: State-of-the-Art Review” by John W. Labadie

Closure to “Optimal Operation of Multireservoir Systems: State-of-the-Art Review” by John W. Labadie

Discussion of “Optimal Operation of Multireservoir Systems: State-of-the-Art Review” by John W. Labadie

A large and long-existing literature employs analytical optimization methods to derive reservoir operating rules for multireservoir systems. These date back to rules for minimizing spill from parallel reservoirs by Bower et al. 1966 and Clark 1950 . Lund and Guzman 1999 summarize such analytically derived optimal operating rules for some simple multireservoir systems under specific conditions and criteria. Lund 2000 uses analytical optimization for hydropower operations with multiple reservoirs. More complex multireservoir problems have been examined analytically and partially analytically using interesting extensions of Varlet’s 1922 and Masse’s 1946 single reservoir methods MorelSeytoux 1999 .