مسئله تعهد واحد با رمپ نرخ محدودیت با استفاده از الگوریتم ژنتیک باینری واقعی رمزی

The unit commitment problem (UCP) is a nonlinear mixed-integer optimization problem, encountered as one of the toughest problems in power systems. The problem becomes even more complicated when dynamic power limit based ramp rate constraint is taken into account. Due to the inadequacy of deterministic methods in handling large-size instances of the UCP, various metaheuristics are being considered as alternative algorithms to realistic power systems, among which genetic algorithm (GA) has been investigated widely since long back. Such proposals have been made for solving only the integer part of the UCP, along with some other approaches for the real part of the problem. Moreover, the ramp rate constraint is usually discussed only in the formulation part, without addressing how it could be implemented in an algorithm. In this paper, the GA is revisited with an attempt to solve both the integer and real parts of the UCP using a single algorithm, as well as to incorporate the ramp rate constraint in the proposed algorithm also. In the computational experiment carried out with power systems up to 100 units over 24-h time horizon, available in the literature, the performance of the proposed GA is found quite satisfactory in comparison with the previously reported results.

The unit commitment problem (UCP) involves the optimum scheduling of power generating units as well as the determination of the optimum amounts of power to be generated by committed units, so as to meet the forecasted demand at minimum production cost over a daily to weekly time horizon. The problem is subject to various generator- and system-based constraints. Since the size of the discrete search space increases exponentially with the increasing number of units to be scheduled, the UCP is known as one of the most difficult problems encountered in power systems. The problem becomes even more complicated if the ramp rate constraint is also taken into account. It is a dynamic constraint, which imposes restriction on drastic change in power generation by a unit in successive time instants. The inclusion of the ramp rate constraint requires the modification of the range of generated power for each unit at every time instant. The exact solution of the UCP can be obtained by complete enumeration. But the approach is not applicable to realistic power systems due to its excessive computational time requirement [39]. This has motivated to investigate alternative algorithms, which can be applied to realistic power systems in order to obtain approximate solutions of the UCP in reasonable computational time. Such alternative algorithms studied for the UCP include both deterministic methods and metaheuristic techniques. However, two major drawbacks are observed with such approaches. Firstly, no single algorithm can handle both the integer and real parts of the UCP. Secondly, although the ramp rate constraint is discussed in the theoretical part of many works, the algorithms are silent on its implementation. It is observed that the genetic algorithm (GA) in different forms is being studied for the UCP since long back. However, it is also used only for scheduling the units of the UCP, along with some other techniques for the load dispatch part of the problem. Further, the ramp rate constraint is discussed only in the theoretical part, without any mention about its experimental implementation. This has motivated the present work to revisit the GA for handling both the integer and real parts of the UCP by a single algorithm, as well as to investigate if the ramp rate constraint can also be incorporated in the algorithm. For this purpose, a binary-real-coded GA is proposed here, in which the binary part deals with the scheduling of units and the real part determines the amounts of power generated by committed units. Since the UCP is a hard mixed-integer problem, some mechanisms (including a new one) are also incorporated in the GA for forcibly steering an infeasible solution into the feasible region. Moreover, the algorithmic difficulties and remedies in handling both binary and real variables of the UCP by a single algorithm, as well as handling the ramp rate constraint, are discussed in detail. A set of power systems up to 100 units, available in the literature, are used to evaluate the effectiveness of the approach over 24-h time horizon. A comparison is made between the proposed method and other similar proposals made in last four years. Computational results show the potential of the proposed approach under different scenarios of the problem. The rest of the article is organized as follows: the related specialized literature is reviewed in Section 2. The formulation of the UCP is presented in Section 3, followed by the repairing mechanisms in Section 4 and the binary-real-coded GA for the UCP in Section 5. The computational results and discussion are presented in Section 6. Finally, the article is concluded in Section 7 with the present findings and future scope of the current theme.

The mixed-integer unit commitment problem (UCP), encountered in power systems, is a combination of two linked optimization processes, namely integer-valued unit scheduling and real-valued load dispatch. Due to the inadequacy of deterministic methods in handling large-size instances of the UCP, various metaheuristics are being investigated, including genetic algorithm (GA), in order to obtain approximate solutions of the UCP in reasonable computational time. However, GA is normally used only for scheduling units, and it is incorporated with some other techniques for determining the amounts of power to be generated by committed units. Moreover, the dynamic ramp rate constraint is also not included in those approaches. Such issues motivated the present work to propose a binary-real-coded GA, in which the binary part deals with the scheduling of units and the real part determines the amounts of power to be generated by committed units. The ramp constraint is also successfully incorporated in the proposed GA. The technical difficulties and their remedies in incorporating the ramp rate constraint as well as handling both integer and real parts of the problem by a GA are also addressed in detail. Both the cases, without and with the consideration of the ramp rate constraint, are studied through their application to a set of six power systems up to 100 units over a 24-h time horizon. The obtained results without the consideration of the ramp rate constraint are found very much comparable with those produced by some other similar approaches. As the major future scope, an attempt may be made for further improvement in the performance of the GA, such as incorporation of some problem information in the used GA operators. Further, other practical aspects of the problem may also be studied.