| Optimal planning and operation of large hydropower systems, when realistically considered, usually result in a nonlinear, nonconvex optimization problems of high dimension which can be difficult to solve by any known optimization technique. In this research, five optimization algorithms have been vigorously evaluated based on applications on a hypothetical five-reservoir hydropower system. These algorithms are incremental dynamic programming (IDP), successive linear programming (SLP), feasible direction method (FDM), optimal control theory (OCT) and objective-space dynamic programming (OSDP). The performance of these algorithms have been comparatively evaluated using unbiased, objective criteria which include accuracy of results, rate of convergence, smoothness of resulting storage and release trajectories, computer time and memory requirements, robustness and other pertinent secondary considerations.; The results of the above studies have shown that all the algorithms, with the exception of OSDP converge to optimum objective values within 1.0% difference from one another. The highest objective value is obtained by IDP, followed closely by OCT. Computer time required by these algorithms, however, differ by more than two orders of magnitude, ranging from 10 seconds in the case of OCT to a maximum of about 2000 seconds for IDP. With a well-designed penalty scheme to deal with state-space constraints, OCT proves to be the most efficient algorithm based on its overall performance. The performance of SLP is also highly satisfactory. FDM converges to good results but computer time falls on the moderate to high scale. OSDP has performed poorly because of failure to comply with basic assumptions on uniqueness and finite countability of decision space.; SLP, FDM and OCT have also been applied to the case study of Mahaweli project, a ten-powerplant system in Sri Lanka. Two objective functions have been investigated, one on maximizing energy output and the other on minimizing deviations from a pre-specified energy demand pattern. The results of the case study further confirm the advantages and superiority of OCT as the most efficient, robust and flexible optimization algorithm for large-scale hydropower systems. The performance of SLP is slightly inferior to OCT but it should be an acceptable alternative for many practical applications. |
