2. Optimization of Short-Term Scheduling

Gea et al. ^[5] considered the optimization of the water time delay, which is continuously changing and creates a difficult problem in dealing with the corresponding mathematical models. This study shows that the suggested model with a delay period for the water may enhance the operational ability and profitability of scheduling utilization. Catalão et al. ^[6] proposed a modern mixed-integer non-linear programming (MINP) technique, taking into account a non-linear function to release water and the net head. An improved approach is implemented because of the more reliable modeling and executed positively on cascaded hydro units with an ignored computational time condition. In Catalão et al. ^[7], they also consider not only head dependency but intermittent operating regions and water release limitations as well. Numerical results show the good performance of the suggested technique. Moreover, in Catalão et al. ^[8], they propose a new non-linear method to solve the problem of hydro scheduling with constraints satisfied, taking into account the head dependency. The results show that the suggested non-linear method is efficient.

Belsnes et al. ^[9] presented a model for operational stochastic hydropower scheduling. The proposed approach is based on stochastic successive linear programming. From this study, enhancements achieve the objective function value and reduce the risk of spills from reservoirs. Ge et al. ^[10] proposed a model that contains a non-linear function connected with the water delay time, which is based on a successive approximation method. The suggested method is verified with two-reservoir and ten-reservoir units. The numerical results prove that the suggested method provides realistic results.

Ma et al. ^[11] utilized the population initialization stage to improve the best individuals in the culture algorithm with differential evolution (DE). For a constant water release operation, there is a better base to choose an operation strategy in which the net head for hydropower generation is optimized and distributed economically for plant internal operation. Mo et al. ^[12] presented a hybrid algorithm utilizing the multi ant colony system and the DE method that are used to solve the sub-problems: unit commitment and economic load dispatch. The simulation results demonstrate that the suggested technique has the best convergence features and computational proficiency with less consumption for water discharge. Glotić et al. ^[13] considered the multi-population strategy to fulfil system requests with a reduced amount of water used in each generated unit. The initial and final statuses of the reservoirs were fulfilled as well.

Yuan et al. ^[14] suggested a new hybrid chaotic GA. Simulation results have verified that the solution method is possible and efficient for the applications. Chuanwen and Bompard ^[15] proposed a new self-adaptive chaotic PSO algorithm for the hydropower plant dispatch model according to the base of optimum utilization. The results show the proficiency and durability of the suggested approach in comparison with the original PSO algorithm. Li et al. ^[16] selected the support vector machine with GA since it displays several benefits in handling non-linear and high dimensional pattern recognition. By comparing its achievements, it is proven that the proposed model is a possible candidate for the optimum forecast of hydropower generation. Mu et al. ^[17] highlighted an effective method to enhance the operation solutions of hydropower plants in flood seasons. Three operation bases are validated with a numerical model by using the GA. Operation solutions with bases executed may be obtainable with better objective values and higher optimization proficiencies.

Séguin et al. ^[18] presented a new technique to resolve the unit commitment and loading problem for a determined hydropower system. The DP is employed to calculate the optimum output generated by a hydropower plant. Yuan and Zhou ^[19] discussed how to process the problems produced by doubts and achieve self-optimization for real-time hydropower operation. The results show that system dynamics simulation is a significant technique to model a composite cascaded hydropower plant with feedback and specific loops. Changing et al. ^[20] proposed multiple stages of discharge towards the outside of the upstream reservoir simultaneously with the discharge towards the inside of the downstream reservoir, which can be computed by the Muskingum model. The result of the operation of the proposed model produces additional advantages over realistic operation.

Jiekang et al. ^[21] presented a dynamic generation flow plan using the dynamically organizing net head of water in the reservoir and the consumption quantity of water. The results show that this new approach can improve the synthesis generation utilization of cascaded hydropower plants. Xin-Yu ^[22] composed the multi-objective optimal peak shaving model. It minimizes the maximum remaining loads per energy grid, which is an integral part of distributing the energy of a plant among some energy grids. A case study shows that the solution method is realistic, flexible and strong to get near-optimal results proficiently. Lu et al. ^[23] suggested a real binary bee colony optimization algorithm that is used to resolve parallel sub-problems of unit commitment and economic load dispatch. The simulation results prove that the suggested approach can obtain top-advantage solutions with shorter computing times and less water consumption. Marchand et al. ^[24] proposed a proficient model as a mixed-integer linear program, which shows a three-phase method based on a cost analysis that produces, rapidly, close optimal solutions to real-world cases. Ellen et al. ^[25] presented a model for hydropower bidding according to the OGS from a stochastic model. Furthermore, they presented a heuristic algorithm for decreasing the bid matrix into a size desired by a market operator. The results show how unchecked inflows may change the bids.

Naresh and Sherma ^[26] presented a proposed technique using two phases of a neural network. The results show that the suggested technique with a convenient choice of control parameters can generate and satisfy the optimal solution. Xu et al. ^[27] focused on the entire price of operating a cascaded reservoir system for the corresponding power demand that includes the price for the power source and the alternative price related to spillage. The results show that when immensely rainy hydrological circumstances are predictable, a compromise method is a superior plan. Castro et al. ^[28] highlighted the influence of operational choices on the market prices and the capability of regulating the tailwater level and the generation and pumping proficiencies as a function of the water inflow. As a result, the advantage of the operation of the hydro systems is assessed in a more realistic way, since market prices increase when pumping overrides generation and decrease if generation overrides pumping.

A summary of the research studies executed previously on the overall optimization methods used for the operation of short-term hydro scheduling is presented in Table 1.

In daily-term scheduling optimization, Mengfei et al. ^[29] proposed a hybrid approach that merges discrete differential DP with the progressive optimality algorithm. To correspond to the realistic operational requirements of the power grid, a utilization maximization model is developed, in which the peak shaving requirements are used as constraints. With this unit-commitment plan, the calculation speed may be faster, and the estimated optimal solutions may be obtained in a sensible period. Yuan et al. ^[30] suggested a chaos concept to get self-adaptive parameter settings in the DE method. The suggested approach is verified with four interconnected cascaded hydropower units, and the experience results are validated with those obtained by the conjugate gradient and two-phase neural network technique to prove the superiority of the proposed solution. Moreover, they proposed an enhanced PSO algorithm using chaotic sequences ^[31]. The simulation results show that both of the suggested approaches can get top quality solutions. Moreno and Kaviski ^[32] highlighted an adjusted PSO algorithm. It is executed to achieve the maximum water benefit and with all constraints associated with synchronous water discharge. Computational evidence and comparisons with other heuristics approaches such as simulated annealing proved the efficiency of the solution method. A summary of the research studies executed previously on overall optimization methods used for the operation of daily-term hydro scheduling is presented in Table 2.

3. Optimization of Mid-Term Scheduling

Shrestha et al. ^[33] addressed the optimal organization of hydropower properties based on optimizing the expected profits of a provider, and the decision variables are generation and future contracts per interval of time. Baslis et al. ^[34] presented a stochastic self-scheduling model for a hydro cost provider. The provider intends to optimize revenues in the daily markets. The results indicate the possibility of getting a unique commercial solver. Catalão et al. ^[35] proposed a new contribution to market volatility, which is presented in a model using cost strategies and risk management via conditional value-at-risk concept to prevent revenue volatility. Furthermore, plant scheduling and pool contribution by hydropower providers are concurrently considered to provide a solution for practically cascaded hydro units.

Flatabø et al. ^[36] established a plan to operate the generation system for a period of time. The arrangement of the turbine and spill capacities of water is such that it minimizes the predictable operational expenses. Huber et al. ^[37] presented a modeling method, in which the real accessible electricity market provides the source of data for the model. A benefit of this modeling method includes the normal consideration of power future that provides hourly price curves. Besides, the model can unify the optimizations. Moreover, they proposed a method to contain the capability of contribution to secondary control. The output is an approximation of water quantities for use in the optimization and optimal contribution of secondary control ^[38]. They also proposed an approach based on Lagrangian relaxation, which is employed to discover realistic quantities of water ^[39]. Arild et al. ^[40] described an approach for optimal scheduling, a revenue optimizing, price-taking approach with neutral risk to the provider for the exported energy and the ability to isolate and serially clear markets. Martin et al. ^[41] assessed the quantity for producing initial reserves and how significant correct modeling is for selling ability. It was discovered that the predictable revenue from selling ability decreased by 40% when the simulator results are compared with the planning model.

Aquino et al. considered a recurrent ^[42] and hybrid intelligent ^[43] two-phase optimization neural network to resolve the economic dispatch of power that minimizes the total cost of production with the corresponding load demand. The results show that the enhanced model delivers optimal scheduling that gives orientation to the minimal cost of operation. Lotfi and Ghaderi ^[44] proposed a new possibilistic price according to the MILP method. The result shows the capability and suitability of the suggested method, and it may be simply executed for a regulated environment. A summary of the research studies executed previously on overall optimization methods used for the operation of mid-term hydro scheduling is presented in Table 3.

4. Optimization of Long-Term Scheduling

Zhao et al. ^[45] proposed a constrained Markov decision method for managing the water discharge to satisfy water supply conditions and the system requirements for electric power and to minimize the entire expenses of energy production. Numerical results prove the activity and the proficiency of the configuration and the solution method. Scarcelli et al. ^[46] presented the Markovian stochastic DP by modeling monthly discharges based on possibility distribution functions. The results demonstrate that the production of regular and proposed programs is very similar, corresponding to an average of spillage and power generation but with cheaper costs. Scarcellia et al. ^[47] proposed monthly discharges based on possibility distribution functions. The results show that the solution method produces spillage that decreases and increases in electrical energy production, which reduces operational costs by up to 2.1%.

Birger Mo et al. ^[48] presented a method of operation scheduling and economic hedging by future contracts that are combined in a unique model. The method may be valuable for hydropower firms that cover cost risks as well as the discharge volatility. In ^[49], they described the structure of the cost model and its identification that is employed in the stochastic optimization of hydro operation and adjustable contracts. The result shows how the cost model is employed to combine hydro operation and economic hedging. Hongling et al. ^[50] assessed state-of-the-art techniques like Tree Captures (TC), the Clustering Method (CM), the Heuristic Method (HM), the Stochastic of the DP, and Monte-Carlo Simulation (MCS), in which considerations focus on the revenue produced by volatility in instant costs and reservoir discharge. Moreover, generation sources can also be employed to control risk to some extent. Larsen et al. ^[51] proposed a linear time series model based on stochastic discharge that considers flood season and lag-one autocorrelation as well as the strategy of decrease based on reducing the size of a conventional strategy set while retaining the wasted stochastic information included. The results show that the selection of the strategy of decrease technique affects the solution to the planning problem of hydropower operation considerably. Hjelmeland et al. ^[52] proposed a stochastic DDP scheduling model according to mixed integer programming (MIP). The predictable revenue from the selling ability of the linear stochastic DDP model was 29.2% greater than that from the simulator model. The total revenue wasted reduces by 0.93%, quantifying the overestimation of revenue in the proposed model.

Baohong et al. ^[53] introduced three optimization approaches including the progressive optimization algorithm, the PSO, and the GA. The minimum rate of water inflow consumption is selected as the objective function. After comparing the effects of the three approaches, the progressive optimization algorithm is discovered to be more suitable for the Zhelin reservoir. Mengfei et al. ^[54] considered the prediction error that occurs in monthly forecasting of the flow of watercourses and suggested an approach named the predicting dispatching chart for Xiluodu and Xiangjiaba cascaded hydro plants. The chart has been verified for realistic operations and realizes enough production.

Cheng et al. ^[55] proposed a new chaotic GA. The results show that the average yearly power is the largest, and its convergent speed is not only quicker than the DP but exceeds that of the GA as well. Therefore, the solution method is possible and efficient for the optimal operations of composite reservoir units. Yao-Yao et al. ^[56] presented a new chaotic PSO algorithm and makes a comparison between the proficiency of one- and three-dimensional chaotic charts within a regular range. Statistical results and validations prove the influence and speed of various algorithms for a realistic hydro-system. Hammid and Sulaiman ^[57] focused on the enhancement of the optimization model by using the PSO and Firefly Algorithm (FA) approaches to obtain a steady utilization of power generation at its optimum level. The results show the robustness of the FA, its proficiency and its excellence. They have made a new strategy to improve PSO and FA via a series division method as well. The results show that the Series Division Firefly Algorithm is robust and has good efficiency and superiority ^[58]. Lia et al. ^[59] proposed a multi-core parallel PSO algorithm. The results show the enhancement of the efficiency, the dependability of the optimal production, and its low execution price. The proposed method has a high possibility for future optimal operation.

Zhang et al. ^[60] proposed a multi-objective adaptive DE with a chaotic neural network. The proficiency of the proposed algorithm is obtained to compare with multi-objective optimization algorithm and demonstrates that it can be an assuring choice and deliver optimal trade-offs for multi-objective reservoir operation. Wang et al. ^[61] proposed multi-population ant colony optimization for a continuous domain. The effectiveness and steady state of the proposed algorithm are validated by its further acceptable outcomes. The system can get more power generation gain than other choices during a wet, normal and dry year.

Liao et al. ^[62] formulated an economic dispatch of hydropower systems and analyzed the accomplishments of three various principles of the control parameter adjustment standard. Then, the accomplishment of the suggested algorithm is compared with that of different algorithms like the PSO. Liao et al. ^[63] presented a modern multi-objective evolutionary algorithm called the multi-objective artificial bee colony algorithm. Statistical results prove the performance and proficiency of the suggested algorithms, which have better convergence speed and satisfy the distribution of the Pareto front.

Zambelli et al. ^[64] proposed a yearly discharge predicting model in an open-loop feedback control operational strategy. In Zambelli et al. ^[65], they proposed a predictive control according to deterministic non-linear optimization and yearly discharge predicting models. The production of the suggested method is compared with that of the stochastic DP method. The results illustrate that both solution methods indicate an operational production nearer to that of an excellent solution, producing higher average hydropower generation and lower spillages of the reservoir. Moreover, in Zambelli et al. ^[66], they proposed a novel deterministic method based on adaptive model predictive control. In comparison, the suggested method is discovered to deliver a better product because of the increased effective utilization of water sources, causing a safer and cost-effective operation.

Mantawy et al. ^[67][68] proposed a Tabu search algorithm and introduced novel concepts for generating possible solutions with a flexible stage vector orientation. The statistical results illustrate an enhancement in the introduced solution compared with earlier solutions.

Nabona ^[69] employed deterministic discharges for the case of the discharge that is delivered as possibility density functions via multicommodity network discharges. It has been illustrated that problems including numerous reservoir units with incomplete reliance on discharges can be passably modeled as well. Fosso et al. ^[70] created a model based on maximizing generation by taking into account the spot market cost. The result shows how to implement the management computations for water value. Fleten et al. ^[71] presented a multi-stage stochastic MIP model that has a current tax time decision and a harsher decision in the future. It treats cost as a stochastic parameter and considers deterministic water discharge as it is designed for treatment in the wintertime period. Grønvik et al. ^[72] proposed linear decision rules that optimize the market price from the energy production sale in a good performance market. The uncertainty concept is included in market costs and reservoir discharges. The results show that the suggested estimation is efficient at reducing the complexity of computations. Guisández et al. ^[73] considered water discharge as another case variable to determine the problem case description. The results of the water discharge as a state variable does not illustrate an important influence in the expected yearly profits, but assured variations are recognized for specified time intervals of the year that might prove its deliberation in fewer period prospects. Xiaolin et al. ^[74] aimed to explore the possibility of power generation and load requests. The results show that the cost-effectiveness of the system is developed when power generation and load requests are combined in the scheduling.

Sharma et al. ^[75] presented the optimum exploitation of accessible hydro sources in all parts of the country with minimum ecological influences. It not only satisfies the country’s power demand but also provides power to the north grid to support the general progress of the country. Zhao et al. ^[76] determined the optimum ability endurance of storage between tight, minimal cost increment and reduced minimal return. The results support the analytical decisions and show that the minimal return from the ability endurance of storage is larger than the minimal cost. Molina and Soares ^[77] presented the evaluation efficiency of a simulation model that proves a scientific application using two fundamental comparisons of the model: a hydropower generation function and the balanced equation of water. The results show that the simulation model may be exaggerating, by more than 3%, the hydropower production of the recognized plants. A summary of the research review executed on the overall optimization methods used for the operation of long-term hydro scheduling is presented in Table 4.