A variety of optimization methods exists in the literature for solving power system problems, such as capacitor planning, DG planning, and switches planning. These optimization methods can be divided into two main groups: analytical-based methods and heuristic-based methods.
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The simplest analytical method is linear programming which is employed when the objective function and constraints are linear. This method has been applied to various problems such as, power system planning and operation [106], optimal power flow [107], and economic dispatch [108]. Since some or all variables are discrete, the integer and mixed-integer programming techniques were introduced into power system analysis. These techniques have been used for hydro scheduling [109], TCSC planning [110], and planning and expansion of distribution and transmission networks [47,111]. The objective function associated with most of the power system problems contains nonlinearity. This resulted in the use of NLP for optimizing a variety of issues, such as stability analysis [112], optimal power flow [113], and DG planning [114]. The analytical techniques are highly sensitive to initial values and frequently get trapped in local minima particularly for the complex problems which have nonlinearity and discreteness. In addition to the convergence problem, algorithm complexity is another disadvantage associated with the NLP methods [115]. This has led to the need for developing another class of optimization methods, called heuristic methods. GA is a search technique for finding the approximate solutions to the optimization problems. This technique is inspired by evolutionary biology, such as mutation and crossover. PSO is another evolutionary computation technique which is inspired by the social behavior of bird flocking and fish schooling. This method is not highly sensitive to the size and nonlinearity of the problem and can converge to reasonable solution where analytical methods fail [51]. That is why a number of papers have been published in the past few years based on this optimization method, such as in allocation of switches in distribution networks [89], planning of capacitors [116], planning of harmonic filters [117],
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economic dispatch [118], optimal power flow [119], and loss minimization [120]. Comparing with other similar optimization techniques like GA, PSO has some advantages [50,51]:
1. In PSO, each member remembers its previous best value and the next value for each member is calculated using this memory.
2. There are fewer parameters to be set in PSO compared with other methods. 3. Implementation of PSO is easier than some other methods.
4. The diversity of variables is maintained in PSO, while in some other methods like GA, the worse solutions are discarded.
The main aim of distribution networks planning is to minimize an objective function composed of the line loss cost, reliability cost, and the investment cost. Since the line loss and system reliability values have a nonlinear relation with the element sizes and that the size of elements is discrete, the planning problem is highly nonlinear and discrete. Additionally, a large number of variables should be optimized during the planning procedure. All these characteristics ensure that the planning problem is a complex problem.
Given that PSO is a reliable optimization method in the literature, this optimization method is employed in this research for solving the distribution system planning problem. Figure 2.1 shows the flowchart of PSO method. The parameters and variables in this figure will be described in Chapter 4 of this report. In Chapter 4, a modification is applied to PSO method to increase the diversity of the optimizing variables. The results demonstrate that the MDPSO has higher robustness and accuracy compared with some other heuristic methods, such as GA and conventional PSO.
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Figure 2.1. Algorithm of PSO method
Considering the literature review done in this report, it is clear that a comprehensive algorithm is required to develop the planning of distribution networks. In this algorithm, the location and size of the transformers and feeders, the location and size capacitors and DGs in different load levels, the location and operation of VRs in different load levels, and the location of CCs should be optimized while the voltage drop and feeder current constraints are satisfied and the load growth is supported.
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2.9. Summary
In this chapter, a brief review is presented based on the previous published research works on the planning issues. Some papers propose methods for basic planning. In these papers, the effort is on determination of the location and rating of transformers as well as the route and type of feeders. Almost all papers focus mainly on MV or LV network. However, consideration of both these networks simultaneously is required since the MV feeder is a common element is both these networks which can influence the final outcome.
For planning a distribution network, some characteristics should be considered such as minimizing the line loss, improving the voltage profile, maximizing the system reliability, and including the load growth. Supporting each of these aspects needs to install some other electrical devices rather than only transformers and feeders.
Electrical devices have normally discrete size. Additionally, the line loss, system reliability, bus voltage and feeder current values have a nonlinear relation with these electrical devices’ size and location. This makes the engineers to employ the optimization methods, which can deal appropriately with discrete and nonlinear objective function. Therefore, different optimization methods are employed for this objective. A reliable optimization method should have some main characteristics such as high accuracy and robustness. These highlight the need for an optimization method which has these key factors.
The basic planning methods are improved mainly by inclusion of capacitors and partly by inclusion of VRs. Capacitors decrease the line loss and improve the voltage profile significantly and VRs mainly maintain the bus voltage into the standard range as
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presented in many papers. However, integration of these two elements needs to be studied for improving both line loss and voltage profile to decrease the total investment cost.
Capacitors improve line loss and voltage profile but they cannot influence the system reliability. On the other hand, DGs increase system reliability significantly. However, improving system reliability as well as the line loss and voltage profile all should be included in a reliable planning. Since DGs are expensive, using these devices is not justified for minimizing the line loss and voltage profile. Hence, capacitors, as less expensive devices, are integrated in DG-based planning to minimize the total cost. Since the loads in a distribution network are growing rapidly, this factor should be considered in the planning procedure. For supporting this factor, the transformers and feeders are conventionally upgraded which applies a large investment cost. For alleviating this issue, DGs are employed along with the capacitors to avoid extra upgrades of the transformers and feeders as the system reliability, line loss and voltage profile are improved.
Although DGs significantly reduce the reliability cost, their investment cost is an issue. On the other hand, CCs are less expensive than DGs but they cannot support the load growth. Therefore, using these elements for decreasing reliability cost under load growth can significantly reduce the required investment cost.
Selection of an appropriate optimization method for solving the planning problem is another issue. Since the planning problem is composed of nonlinear elements such as system reliability and line loss and discrete elements such as investment cost, a number of local minima exist in the resulting problem. The use of analytical methods such as
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nonlinear programming results in trapping in local minima. Therefore, heuristic methods like GA and PSO are mainly employed in the literature for solving these problems. The MDPSO is employed in this research. For this purpose, PSO is modified using two operators of GA to increase the diversity of variables. The results illustrate that the MDPSO is more accurate and robust compared with conventional PSO and GA.
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