Economic Dispatch Analysis Using Equal Incremental Cost Method with Linear Regression Approach

Arnawan Hasibuan 1,2, Robi Kurniawan3, Muzamir Isa4, Mursalin5 1Department of Electrical Engineering, Universitas Malikussaleh, Bukit Indah, Lhokseumawe, Indonesia, arnawan@unimal.ac.id School of Electrical System Engineering, Universiti Malaysia Perlis, Perlis, Malaysia (arnawan@unimal.ac.id 3Department of Electrical Engineering, Universitas Malikussaleh, Bukit Indah, Lhokseumawe, Indonesia, robikurniawan467@gmail.com School of Electrical System Engineering, Universiti Malaysia Perlis, Perlis, Malaysia muzamir@unimap.edu.my 5Department of Mathematics, Universitas Malikussaleh, Aceh Utara, Indonesia, mursalin@unimal.ac.id Corresponding author : arnawan@unimal.ac.id


Introduction
The use of fuel is one of the things that needs special attention in the operation of power plants, because about 60% of the total operational costs incurred are fuel costs (Marsudi, 2006). Changes in the demand for electrical energy on the load side will cause fluctuations in fuel costs. These fluctuations are very difficult to predict and are always changing, therefore we need a very fast system to cope with and respond to them (Syah et al., 2012). The analysis to produce the minimum cost at the generator is usually referred to as economic dispatch. Economic Dispatch is the distribution of loading on generating units in the system optimally and economically at a certain system load price. With the application of economic dispatch to the electricity generating unit, the minimum generation cost for electricity production will be obtained (Syah et al., 2012) (Pramudia, Hardiansyah and Junaidi, no date).
There are two methods of approach taken to solve the economic dispatch problem, namely the numerical method and the meta-heuristic method (Takeang and Aurasopon, 2019). Examples of numerical method solutions in economic dispatch problems include using the Lagrange method (Syah et al., 2012), Lambda Iteration (Dike, Adinfono and Ogu, 2013), Dynamic Programming Techniques (Nabila, 2017), Equal Incremental Cost (Hasibuan, no date) while the metaheuristic method solution, for example using the Particle Swarm Optimization method (Dewangan, Jain and Huddar, 2015), Cuckoo Optimization Algorithm (Iskandar, 2016), Artificial Bee Colony Algorithm (Pramudia, Hardiansyah and Junaidi, no date), Taguchi (Rusilawati, Penangsang and Soeprijanto, no date). Previous research conducted by Arnawan Hasibuan examined the Economical Operation of a Steam Power Plant Using the Equal Incremental Cost Method with a Linear Regression (Least Square) Approach, obtained savings are when compared with an even distribution of the total power output to the generating units (Hasibuan, no date). This research was conducted using the Equal Incremental Cost method with the Linear Regression (Least Square) approach to obtain the minimum power plant operating costs. The calculation of the Equal Incremental Cost method to calculate economic dispatch is carried out by using constrain equality and inequality constrain (Syah et al., 2012). Equality constraint is a power balance limitation, which requires that the total power generated by each generator must be equal to the total required load and transmission losses (Syah et al., 2012)(Nabila, 2017.Inequality constraint is a cost function that is not influenced by reactive power but on the real power balance in the system (Suman et al., 2016). efficiently, namely to meet the load at an optimal and economical cost by paying attention to reliability that meets environmental safety standards and can serve demand continuously from time to time 2018). The operation of the electric power system at a fixed frequency is said to be in a balanced power state if the total real power generated is equal to the total system load. In the form of an equ and Wijono, 2014). = + = ∑ Where: = The total power generated by the generator =total system load (MW) =Total loss -actual loss of power from the transmission line = The power generated by the ith generator =Number of generators in the system

Power Plant Economical Operation Considerations
Economic operation is the process of dividing or rationing the total load for each generating unit, all generating units are controlled continuously at certain time intervals so that optimal operation is achieved, so that the generator can be run in the most economical manner the power system can be divided into two parts, namely the economic dispatch and the unit commitment date).

Economic Dispatch
Economic Dispatch is a method used to divide the power generated by the generating uni requirements. This power plant aims to get the cheapest generation costs are two certain constraints that must be met, namely the Equality constraint and the Inequality constraint 2012) (Suman et al., 2016). Equality constraint can be expressed by equations 1 and 2. the following equation :

Generator Input-Output Characteristics
Each generator has its own characteristics in operation. The input characteristics that describe the relationship between the input in the f (liters/hour) and the output produced by the generator (MW) no date).

Journal of Renewable Energy, Electrical, and Computer Engineering, 1 (1) (2021) 16-22
meet the load at an optimal and economical cost by paying attention to reliability that meets environmental safety standards and can serve demand continuously from time to time (Pertiwi, Syahrizal and Siregar, The operation of the electric power system at a fixed frequency is said to be in a balanced power state if the total real power generated is equal to the total system load. In the form of an equation written as follows The total power generated by the generator (MW) actual loss of power from the transmission line (MW) The power generated by the ith generator (MW) Number of generators in the system

Power Plant Economical Operation Considerations
Economic operation is the process of dividing or rationing the total load for each generating unit, all generating units are controlled continuously at certain time intervals so that optimal operation is achieved, so that the generator can st economical manner (Hakimah, 2016). The considerations taken to achieve the economic operation of the power system can be divided into two parts, namely the economic dispatch and the unit commitment Economic Dispatch is a method used to divide the power generated by the generating uni requirements. This power plant aims to get the cheapest generation costs (Nabila, 2017). In the are two certain constraints that must be met, namely the Equality constraint and the Inequality constraint . Equality constraint can be expressed by equations 1 and 2.The inequality constraint is stated in thermal units committed to serve a load of Pload (Wood and Wollenberg, 1996) the configuration of multiple load serving generators. This system consists of N thermal generator units connected to one bus bar to serve the received electrical load Pload.The input for each unit is shown as representing the cost of fuel from the units whose total quantity is :

Output Characteristics
its own characteristics in operation. The input-output characteristics of a thermal generator are characteristics that describe the relationship between the input in the form of heat energy demand (MBtu by the generator (MW) (Pertiwi, Syahrizal and Siregar, 2018) Characteristic curves of the generator input-output meet the load at an optimal and economical cost by paying attention to reliability that meets (Pertiwi, Syahrizal and Siregar, The operation of the electric power system at a fixed frequency is said to be in a balanced power state if the total ation written as follows (Kristianto, Suyono (1) Economic operation is the process of dividing or rationing the total load for each generating unit, all generating units are controlled continuously at certain time intervals so that optimal operation is achieved, so that the generator can . The considerations taken to achieve the economic operation of the power system can be divided into two parts, namely the economic dispatch and the unit commitment (Mariang, no Economic Dispatch is a method used to divide the power generated by the generating unit to meet load . In the Economic Dispatch, there are two certain constraints that must be met, namely the Equality constraint and the Inequality constraint (Syah et al., The inequality constraint is stated in (3) (Wood and Wollenberg, 1996) This system consists of N thermal generator put for each unit is shown as output characteristics of a thermal generator are orm of heat energy demand (MBtu/hour) or fuel (Pertiwi, Syahrizal and Siregar, 2018)(Syafii and Monice,

Journal of Renewable Energy, Electrical, and Computer Engineering, 1 (1) (2021) 16-22
Linear Regression (Least Square) The linear regression equation is an equation model describes the relationship between one independent variable/predictor (X) and one non variable free/response (Y), which is usually represented by a straight line. Below is a straight line equation namely (Yuliara, 2016). λ = + (7) The magnitude of the constants a and b can be determined using equations: The above formula can be converted into a 2 × 2 matrix as below:

Equal Incremental Cost Method
The unit cost of additional fuel (Equal Incremental Cost) of a unit for each output is the limit on the ratio of the increase in fuel input cost in dollars per hour to the corresponding increase in power output in MW as the increase in power output approaches zero. Mathematically, Equal Incremental Cost can be calculated using the following equation: Where: = Input to unit i ($/h) = Unit output i (MW)

Research Methods
The stages carried out in this research are literature study or literature review, study guidance, data collection and processing, and calculation simulation with Matlab and Microsoft Excel. Below is a picture of a flow chart for calculating the Equal Incremental Cost method with the Linear Regression approach to obtain the minimum generation cost.

Results and Discussion
Operational Data of Pangkalan Susu PLTU

Modeling Generating Units with Linear Regression (Least Square)
This generating unit modeling aims to determine the input-output characteristic equation of a generating unit. Calculate the equation of the input-output characteristics of each generating unit with simulation matlab. The equation of the input-output characteristics of the unit one generator is obtained. = 42.5 + 1,052.1 And the equation for the input-output characteristic of the unit two generator is: = 40.1 + 1,194.9

Optimization Using Equal Incremental Cost Method
Optimization of costs when the load is 277 MW λ = . .

Journal of Renewable Energy, Electrical, and Computer
The power in each generating unit is: - For the next load optimization is done with the same calculation. The results of optimization calculations using the Equal Incremental Cost method using the Linear Regression approach can be seen in Table 4. The following is a graphic image of the comparison of the input cost of fuel ($ / h) and the output of power produced by the generator (MW).

Figure
The percentage of this fuel cost is obtained the actual cost in the field with the total cost of the incremental cost method and the actual cost in the field and then multiplied by 100%.The savings obtained using the Equal In is obtained from the reduction in actual fuel costs in the field, which is cheaper than the optimization result of the Equal Incremental Cost method. The following is a graphic image of the comparison of the input cost of fuel ($ / h) and the output of power produced by Graph of comparison of fuel costs and generation load before and after optimization above is a graph of the comparison of the input fuel costs ($ / h) and the power output generated by the ual costs in the field. This figure shows that the fuel costs from the optimization using the Equal Incremental cost method are greater than the actual costs incurred by generators in the field. Comparison of fuel costs ($ / h) between actual costs in the field and optimization costs using the Equal Incremental cost method for more details, can be seen in the following Figure 4. The percentage of this fuel cost is obtained from the quotient between the total cost of the incremental cost method and the actual cost in the field with the total cost of the incremental cost method and the actual cost in the field and then multiplied by 100%.The savings obtained using the Equal Incremental Cost method is -0.033% ($ / h). This minus value is obtained from the reduction in actual fuel costs in the field, which is cheaper than the optimization result of the Equal The following is a graphic image of the comparison of the input cost of fuel ($ / h) and the output of power produced by Graph of comparison of fuel costs and generation load before and after optimization above is a graph of the comparison of the input fuel costs ($ / h) and the power output generated by the ual costs in the field. This figure shows that the fuel costs from the optimization using the Equal Incremental cost method are greater than the actual costs incurred by generators in the field. Comparison of field and optimization costs using the Equal Incremental cost method for from the quotient between the total cost of the incremental cost method and the actual cost in the field with the total cost of the incremental cost method and the actual cost in the field and then 0.033% ($ / h). This minus value is obtained from the reduction in actual fuel costs in the field, which is cheaper than the optimization result of the Equal True Cost ($/h) EIC Method ($/h)