Optimizing Three Power Plants’ Output Power Using Firefly Method

— Continuing the previous article that use merit order, the simplest method in economic dispatch, this article pursue to optimize the output of three power plants using more advanced algorithm, the firefly. The plants used are similar to the previous paper which are three generators used to supply a load of 975 MW. Simulation is used by taking into account losses. The results show that in spite of having higher losses, firefly algorithm managed to calculate a better result than merit orders did by 0,15%.


I. INTRODUCTION
Managing power plant output has become an interesting issue for electric and power plant companies as it will reduce the total cost of the electric they use. The amount of power every power plant produce can be engineered easily without sacrificing the other parameters such as the load. This engineering process is called economic dispatch of power plants.
There are several methods to determine the power plant produced power that already used widely, and the most popular one is merit order method. This method was already used in the previous article [9] to determine the power of three power plants. This method offers a very simply algorithm as it only make an order of the existing power plant based on the heat rate and function cost of the particular power plants. Moreover, this method is also widely used especially in Perusahaan Listrik Negara, the Indonesian electric company, to determine the output of each power plant. However, there is one disadvantage of this method which is its inability to represent the real valid order because it simplifies the main function cost into an average number.
This paper tries to implement firefly algorithm to solve the same problem as the initial article. The total cost and total losses between the proposed method and merit order will be compared in this article.

II. METHODS
This paper combined firefly algorithm and power flow equation. The firefly algorithm is used to determine the best output power of the power plant, and the losses, voltage, and other parameters is calculated using power flow equation.

A. Power Plants Parameters
There are three power plants that are used in this article. Each of the power plant share a different parameter such as minimum and maximum power capacity and cost function. Table 1 depicts the parameters of each power plant.

B. Line Parameters
The simulation that considers the losses uses a 4 bus configuration consisting of 3 generator buses and 1 load bus. Network configuration and data can be seen in table 2.
To obtain the value of losses, the power flow equation is used, which in this simulation uses software from Hadi Saadat's book [10].

C. Firefly Algorithm
A basic firefly algorithm is inspired from firefly behavior in the nature. Each firefly will fly into particular direction, based on the brightness of the other fireflies. The less bright firefly will move to brighter firefly whereas the brightest firefly will move randomly. Basic of firefly movement can be calculated using following equation [7]: (1) Xi and Xj represent a less bright firefly of i and a brighter firefly j position, respectively. β represent firefly attractiveness factor or firefly speed movement. Light absorption coefficient is represented by γ coefficient. The parameter α represent random coefficient, and ϵ represent random vector. In this article, each firefly represents the power of power plant, and the objective function that represent firefly brightness is total cost of the power plant.

B. Proposed Method
The main idea of the proposed method is use the firefly algorithm to determine the power output instead of using https://jurnal.polines.ac.id/index.php/eksergi Copyright © EKSERGI Jurnal Teknik Energi ISSN 0216-8685 (print); 2528-6889 (online) merit order method. There are two parameters in a single firefly used in this simulation which represent power plant 2 and 3. The first power plant will be selected as the slack bus. The proposed firefly then will be applied in power flow calculation that will produce both total generations cost as well as losses. The total generation cost will be used as the firefly brightness or the objective function of this simulation. The next step is firefly movement step using equation (1). The less bright firefly will move towards the brighter one whereas the brightest will move randomly. This step will take place in maximum 200 iterations. The flowchart of proposed algorithm is presented in fig 2 followed by the source code. for iff=1:jff ff(iff,1) = round(rand*(Ub(2,1)-Lb(2,1)))+Lb(2,1); ff(iff,2) = round(rand*(Ub(3,1)-Lb(3,1)))+Lb(3,1); end while iterff<itermff iterff = iterff+1 ff; for iff=1:jff iff;  From the simulation result above, the comparison between proposed method and merit order can be presented. Despite having higher losses, the proposed algorithm produces a better solution in terms of total cost without scarifying the load. It means that the power plants success to supply the load with a lower cost. The total cost has been lowered from 8.3026e+03 to 8.2903e+03, which is 0,15 % from the initial total cost.
. IV. CONCLUSION Ensure that the conclusion is related to the title, purpose, and contribution of the paper.