Intelligent Renewable Energy Systems. Группа авторов

       a) Unity power factor (UPF) DG,

       b) Lagging power factor (LPF) DG and

       c) Reactive power DG.

UPF DG injects active power only to the network whereas LPF DG injects both active and reactive power to the distribution network. On the other hand, reactive power DG generates only reactive power. An example of UPF DG is solar photovoltaic cells. Biomass and wind turbines can be considered as an example of LPF DG. The shunt capacitor injects reactive power to the network and it can be said as the reactive power DG.

      Proper incorporation of renewable distributed generation (RDG) may reduce the network power loss, improve the voltage profile, improve the voltage stability index (VSI), improve reliability, etc. Due to the various benefits of the incorporation of distributed generation to the distribution network, various researchers have considered this topic as their research interest. The literature review reveals that for the placement of DG to the distribution network, various researchers have considered different approaches to optimize the location and the size of the DG sources. The approaches include analytical, classical optimization methods as well as the metaheuristic optimization algorithm. In order to reduce the active power loss of the distribution network, Acharya et al. [1] have proposed an analytical approach to optimize the size and location of the DG source. Gozel and Hocaoglu [2] have proposed another analytical expression to determine the optimum size and location of DG. This approach is based on the current injection method with an objective to reduce the network power loss. Wang and Nehair [3] have proposed an analytical approach to optimize the size of UPF DG [3]. Wang and Nehair have considered different types of load demands of the distribution network [3]. On the other hand, Hung et al. [4] have proposed an analytical expression to optimize the location and size of LPF DG which is capable of supplying both active and reactive power to the distribution network. It may be observed that most of the researchers have developed analytical expressions to determine the optimum size of the DG in order to reduce the network loss. Aman et al. [5] have proposed an analytical approach for optimum placement of DG considering active power loss reduction and improvement of voltage profile of the network. They have considered a voltage sensitivity analysis approach based on the power stability index to determine the size of DG using a stepwise iterative approach. Some researchers [6] have also considered classical optimization methods to optimize the size of DG. At that same time, an analytical approach to determine the optimum location of DG in the distribution network may also be seen in [7]. Analytical methods can be implemented easily and take less computation time. But the direct formulation of complex problems using the analytical method is quite difficult. The application of an analytical approach, to solve complex problems, may lead to inaccurate solutions due to the assumptions made during the problem formulation process.

To overcome the problem, some of the researchers have adopted the linear and nonlinear programming approach for optimizing the DG size [8]. A considerable number of researchers have applied the metaheuristic optimization algorithm for the DG placement problem. Different nature-inspired algorithms like genetic algorithm (GA) [9], tabu search [41], particle swarm optimization (PSO) [42, 43], combined GA-PSO [44], artificial bee colony (ABC) algorithm [45], harmony search algorithm [46, 47], differential evolution (DE) [48], teaching-learning based optimization (TLBO) [49] may be found in the literature. The application of different hybrid optimization algorithms to solve the DG placement problem may also be noticed in the literature [50−53]. In [54], the authors proposed a multi-objective GA-based approach for the optimal positioning of multiple types of DG to reduce investment costs, cost due to annual energy loss and increase the system reliability. Many of the researchers have taken into account the VSI as the primary objective function while optimizing the DG size [55, 56]. Various objective functions have been considered by different researchers to determine the size and the locations of the DG. In [57], considering the probabilistic behavior of renewable resources, the authors attempted to solve the DG optimization problem. Singh and Goswami [58] have considered nodal pricing methodology for optimizing the DG locations and capacity. They have also studied the economical aspect of DG incorporation into the distribution network. At that same time, in [59], the authors have studied the power penetration by the DG sources considering the average hourly load demand. Some other research works on the optimum DG placement problem may also be noticed in the literature [60−65].

      In this current book chapter, placement of DG sources including RDGs (such as biomass, solar PV) and shunt capacitor has been considered for the study purpose. The study has been performed by considering a multi-objective function that includes reduction of active power loss, the betterment of voltage profile, and minimization of effective annual installation cost. To optimize the locations of considered DG sources, a novel optimizing technique named mixed-discrete student psychology-based optimization (SPBO) algorithm is used. The proposed algorithm is inspired by the natural behaviour of the students to be the best student in the class. The criteria to be the best student is to perform well in the examination and the student needs to give more effort to be the one. The study has been carried out considering the hourly average load demand of the distribution network for a day. In this book chapter, the proposed method is tested on two distribution networks namely 33-bus and 69-bus distribution networks.

The remaining book chapter is categorized as follows. In the next section, a new algorithm named mixed-discrete SPBO is presented. The problem formulation is discussed in Section 1.3. Section 1.4 presents the optimum DG placement in the distribution networks using the proposed mixed-discrete SPBO algorithm. Finally, the conclusions are drawn in Section 1.5.

1.2 Mixed Discrete SPBO

      1.2.1 SPBO Algorithm

      SPBO algorithm has been proposed by Das et al. [66]. Similar to other meta-heuristic methodology, SPBO also uses a set of populations. The population considered in SPBO is analogous to a group of students present in the class. In general, the performance of a student is analyzed based on the marks/grade obtained by the student in the examination. The student with the maximum marks/grade is considered as the best one in the class and the student is awarded accordingly. It is also very clear that in the test the students will aim to achieve the highest marks/grade for which they need to provide more effort in their study. The overall grade is the final score of the students in the examination. The overall grade of a student depends on the cumulative effort given by the student in each subject offered to them. The students enhance their performance in the examination by paying more attention and effort in their studies. SPBO is based on the psychology of the students who are trying to improve their performance in the examination as well as trying to get the highest marks/grade in the examination.

For the improvement of the overall performance, the students need to enhance their performance in each subject which are offered to them. However, the improvement of the students’ performance is not the same for all the students. Improvement of the students’ performance depends upon a few factors like the capability and efficiency of the student as well as how the student gets interested in the subject. If a student is interested in a subject, he/she will be more involved in that subject. As a result, the performance of the student will be improved in that subject. As the overall grades/marks depend on each subject, improvement in any subject will improve the student’s overall performance. To improve performance, some students use to give similar or better kind of effort as given by the best student while some use to give more effort than that of the average student. If a student is less interested in a subject, then he/she will try to give the subject an average effort to improve his/her overall performance in the exam. The effort of a student can’t be measured directly. Marks obtained by the student in a subject are the outcome of her/his effort given to that subject. So, it may be considered, in general, that the effort given by the student is equivalent to the marks/grade obtained. Considering all these facts and the psychology of the students, the students can be divided into four different categories (such as the best student, good student, average student, and the students trying