With the construction of major hydro plants, more and more large-scale hydropower systems are taking shape gradually, which brings up a challenge to optimize these systems. Optimization of large-scale hydropower system (OLHS), which is to determine water discharges or water levels of overall hydro plants for maximizing total power generation when subjecting to lots of constrains, is a high dimensional, nonlinear and coupling complex problem. In order to solve the OLHS problem effectively, an improved decomposition–coordination and discrete differential dynamic programming (IDC–DDDP) method is proposed in this paper. A strategy that initial solution is generated randomly is adopted to reduce generation time. Meanwhile, a relative coefficient based on maximum output capacity is proposed for more power generation. Moreover, an adaptive bias corridor technology is proposed to enhance convergence speed. The proposed method is applied to long-term optimal dispatches of large-scale hydropower system (LHS) in the Yangtze River basin. Compared to other methods, IDC–DDDP has competitive performances in not only total power generation but also convergence speed, which provides a new method to solve the OLHS problem.
Hydropower is a kind of renewable and clean energy when compared with traditional fossil fuel, which leads to widespread construction of hydro plants in many countries. As constructed hydro plants are put into operation, the optimization of these hydro plants becomes a challenge to researchers and operators. The optimization of large-scale hydropower system (OLHS) [1], [2], [3], [4], [5] and [6] is to determine water discharges or water levels of overall hydro plants for maximizing optimal objective while considering various constrains, including hydraulic connection, water balance equation, water level and water discharge limits et al. Due to these coupled constrains and system scale, OLHS is a high dimensional, nonlinear and coupling complex problem [7], [8] and [9].
In order to solve the OLHS problem, lots of methods have been proposed and discussed by researchers in the past decades, including linear programming (LP) [10] and [11], non-linear programming (NLP) [2] and [12], dynamic programming (DP) [13], [14] and [15], progressive optimal algorithms (POA) [16], [17] and [18] and dynamic programming successive approximation (DPSA) [19] and [20]. Besides these mathematical programming methods, kinds of heuristic algorithms have been proposed, such as genetic algorithm (GA) [21] and [22], ant colony optimization (ACO) [23] and [24], differential evolution (DE) [25] and [26] and particle swarm optimization (PSO) [27], [28] and [29]. These mathematical programming methods and heuristic algorithms have received various degrees of success in OLHS. However, because of hydraulic connection and water balance equation, the operational state of current hydro plant influences other hydro plants and future periods. Moreover, kinds of limits aggravate the complexity of OLHS. These characteristics lead to high dimension, nonlinearity and complexity. LP is not suitable for OLHS because hydropower system is nonlinear. NLP has problems that it cannot handle non-convexity and the convergence efficiency is bad [9]. DP is a widely used method, while it suffers from “curse of dimensionality” in OLHS. POA hardly finds feasible initial solution of complex system, and it is easily trapped in local optimum when system scale is huge [17]. DPSA has the similar drawbacks with POA when it is applied to OLHS. Due to huge optimizing space of OLHS, heuristic algorithms will hardly obtain optimal solution while trapped in local optimum [5] and [28].
Decomposition–coordination (DC), also called “two level” algorithm, has been widely utilized in OLHS [30], [31] and [32] and other complex system optimizations [33], [34], [35] and [36]. It divides the complex system into some non-coupling subsystems and coordinates them to realize optimization. By decomposing and decoupling, the complexity of original system is reduced sharply. Meanwhile, the subsystems’ coordination realizes overall optimization of the complex system. Discrete differential dynamic programming (DDDP) is an improved DP method to solve “curse of dimensionality”, and it has achieved a certain degree of success in OLHS [37], [38], [39], [40] and [41]. It splits the searching space of large-scale hydropower system (LHS) into some small searching spaces for reducing calculation. Due to incremental search mechanism, DDDP will hardly obtain optimal solution if the searching space is too huge [42]. On the contrary, DC is a good method to overcome drawbacks of DDDP by combining them because of the powerful globe optimization capacity. Therefore, an improved DC and DDDP method (IDC–DDDP) is proposed to solve the OLHS problem in this paper. It combines DC and DDDP, with DC for overall optimization and DDDP for local optimization. Meanwhile, some improvement strategies are proposed to overcome drawbacks of DC and DDDP. A stochastic strategy is adopted to reduce generation time of initial solution. An adaptive bias corridor technology is proposed to improve convergence speed of DDDP. Moreover, a relative coefficient based on maximum output capacity is proposed to enhance optimization of DC. Finally, the proposed novel method is applied to long-term optimal dispatches of LHS in the Yangtze River basin. Compared with other methods, IDC–DDDP has competitive performances in optimal objective and convergence speed.
The rest of this paper is organized as follows: Section 2 introduces the long-term optimization model of LHS. The improvement strategies of IDC–DDDP are presented in Section 3, following by brief descriptions of DC and DDDP. In Section 4, IDC–DDDP is applied to optimal dispatches of LHS in the Yangtze River basin, and the optimal results are analyzed. Finally, conclusions followed by acknowledgements are summarized in Section 5.
In this paper, an improved decomposition–coordination and discrete differential dynamic programming (IDC–DDDP) is proposed, to solve the optimization of large-scale hydropower system (OLHS) problem. In order to reduce generation time, initial solution is generated randomly in feasible space. Meanwhile, a relative coefficient based on maximum output capacity is proposed for subsystem coordination. Moreover, an adaptive bias corridor technology is presented to enhance convergence speed. The novel improved method is applied to optimal dispatches of LHS in the Yangtze River basin, with some other optimal methods.
In the performance testing of IDC–DDDP, the improvement strategy that initial solution is generated randomly can reduce generation time sharply. The coordination factor which is calculated by relative coefficient can increase the total power generation of LHS. The adaptive corridor and bias corridor can enhance the convergence speed of optimization. Compared to DC–DDDP and POA, IDC–DDDP has better evolution process although convergence is not well during early stage. Meanwhile, the results of Case study 1 show that IDC–DDDP can obtain more total power generation than EGPSO, DC–DDDP and DPSA in typical years. In addition, IDC–DDDP has the best performance among IDC–DDDP, DC–DDDP and POA in Case study 2. These results reveal that the proposed IDC–DDDP has pretty well performances in total power generation and convergence speed, which indicates that IDC–DDDP is a competitive method to solve the OLHS problem.
