Multi-objective Optimization Problems in Power Systems

In this chart, no solution exists in some ranges and solutions are not provided uniformly. Like this chart, it was difficult to obtain a better Pareto front which had enough

simulations with these simulations. Although a brief trend of the Pareto front in the optimization problem can be found from this sample chart, in some simulation results, only a few solutions were able to be selected thus Pareto front was not able to be drawn.

4.2 Challenges in Hybrid Approach of Optimization Methods (2)

In order to solve the challenge in the

-- -objective optimization

methods was considered.

a. Utilization of the Adaptive Grid in IPESA-II

Grid division of an objective space was proposed in PESA-II [6-20] to maintain diversity of solutions, and this method has changed the existing individual-based selection process to the area-based selection process. IPESA-II [6-14], which is the enhanced version of PESA-II improved results by changing the adjusting method in the grid environment.

Therefore, utilization of the adaptive grid method in the IPESA-II, which is called - research, is considered for the effective management of

solutions generated in multi-

-b. - daptive Grid

-some basic simulations were executed by changing -some parameters. As the result, the following issue was clarified in our numeral simulations.

The mating-selecting method utilized in IPESA-II to create solutions in multi-objective space was not able to find Pareto front solutions effectively if enough solutions would not exist in the space.

Therefore, the following conditions were added to the hybrid approach.

If solutions in adaptive grid in the multi-objective space would be smaller than 2,

-mating-selection would be utilized.

Since the method was - SA-II, the method is called the hybrid ADE-IPESA-II (H-ADE-IPESA-II) in this research.

c. Optimization Testing using H-ADE-IPESA-II Method

Using H-ADE-IPESA-II, Pareto front for the multi-objective optimization problem was able to be found effectively.

Figure 6-9 shows the Pareto front of the multi-objective optimization problem which has two objectives of loss minimization and cost minimization with effective DG installation (3 DGs) using H-ADE-IPESA-II. A good set of the Pareto front was provided with respect to

for Figure 6-9 is 3, other cases (DGs=2, 4) also provided similar good results.

From the result, H-ADE-IPESA-II which is hybrid approach of Adaptive DE and IPESA-II is one of effective methods for constrained multi-objective optimization problems in power systems.

Figure 6-9 Pareto Front of the Multi-objective Optimization Problem Considering Variable Cost Only

Discussion of Multi-objective Optimization Results (3)

Using H-ADE-IPESA-II, various simulation scenarios for the multi-objective optimization problem were executed. Three simulation parameters for the minimization of power loss are considered by the installation of DGs: a. Variable cost; b. Fixed and variable cost; c. Discrete DG capacity.

a. Optimization of power loss and cost by the installation of 3 DGs considering variable cost

Figure 6-9 shows the Pareto front of both loss and cost optimization problem and only variable cost is considered using the proposed H-ADE-IPESA-II.

b. Optimization of power loss and cost by the installation of 3 DGs considering both fixed and variable cost

With respect to objective function for cost, both fixed and variable costs are considered and the Pareto front is created.

Figure 6-10 shows the Pareto front of the multi-objective optimization problem considering both fixed and variable costs. Under the influence of the fixed cost, the set of Pareto front does not converge to a single curve, but shows divided lines.

Figure 6-10 Pareto Front of the Multi-objective Optimization Problem Considering Both Fixed and Variable Cost

c. Optimization of power loss and cost by the installation of 3 DGs considering discrete DG capacity

With respect to objective function for loss minimization, discrete DG capacity settings are considerable. Therefore, the Pareto front using discrete DG capacity settings are also considered.

Figure 6-11 Pareto Front of the Multi-objective Optimization Problem Considering Variable Cost Only

Figure 6-11 shows the Pareto front of the multi-objective optimization problem for discrete DG capacity settings with variable cost only. Figure 6-12 shows the Pareto front of the multi-objective optimization problem for discrete DG capacity settings over non-discrete DG capacity setting with both fixed and variable cost. Basically, the Pareto front for the problem with discrete DG capacity settings does not show a clear difference from that with non-discrete DG capacity setting.

Figure 6-12 Pareto Front of the Multi-objective Optimization Problem Considering Both Fixed and Variable Cost

Summary 6.4.

The purpose of this chapter is to provide effective tools for evaluation of Smart Grid critical technologies and measures installation. In the chapter, two types evaluation method are proposed in order to correspond to actual project situations after the provision of value circulation model in Smart Grid and the periodical data preparation methods for business profitability evaluation.

The first one is a method of profitability priority approach and this is appropriate approach for general competitive companies in power market. In this method, an approach

been considered enough were considered, while many researches for energy reduction effect have been studied. As the result of simulations, it was clarified that energy reduction

in a company and power

consumers should understand that excess energy saving results in revenue or productivity reduction. Generally impact to energy cost by energy reduction is much smaller than that of profit of the company, so balanced energy utilization considering both environmental and business sustainability.

Another on is a method of both installation effect and money optimization approach which are suitable for regulated area in power market but it can be effective for competitive organizations. Because most of multi-objective optimization tools were prepared for non-constrained problems, it was difficult to have enough results for constrained problems using most of these methods in convergence, uniformity and extensity. Therefore some simulations using various optimization approaches and enough results were able to be provided by the hybrid approach between adaptive DE method and IPESA-II. Although this study deals with only two objectives optimization problems, it is assumed that the approach can be applied to more than three objectives optimization problems and these problems should be conducted in future works. In addition, test data were used in all simulations in this study, but real multi-objective optimization problems should have additional constraints related to electrical and economical aspects.

Comparison works between the results of the Pareto frontier provided by the proposed approach and actual decision making and its results in some actual project in the future.

Chapter References

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