Optimal Power Flow Using Particle Swarm Optimization Hybrid Inertia Weight and Constriction Factor Algorithm (PSOHIC) Case Study: Thermal Generator System of 150 kV Sulbagsel

. The increasing use of electricity encourages electricity scientists to create or build mathematical models to improve the quality of electric power. This study uses IEEE 26 bus system data to validate the method and 150 kV thermal generator data from the South Sulawesi (Sulbagsel) system as a case study. The method used is PSOHIC. The simulation results for the 150 kV Sulbagsel system data show that PSOHIC converges more quickly, namely in the 8th iteration. The standard PSO converges at the 25th iteration. The IPSO algorithm converges at the 20th iteration. At the same time, the MIPSO algorithm converges at the 12th iteration. The power flow simulation results show that with PSOHIC, the power loss of 16.48 MW is smaller than the current system of 19.10 MW, that is, the power loss is reduced by 0.1613%. The production cost with PSOHIC is IDR 281,860.91/hour, cheaper than MIPSO, IPSO and PSO.


Introduction
The fulfillment of electricity needs plays an important role in the development of the country in general and in particular as a driver of economic activity in realizing a just and prosperous society.Electricity demand increases from time to time along with increased economic activity in a region and the welfare of the population.The dynamics of electricity consumption growth can also be used as an indicator of regional development.Electricity needs that continue to increase absolutely must be prepared by offering a more appropriate electrical system in terms of quantity and quality.
Calculation of power flow is basically a calculation of the magnitude of the voltage and voltage phase angle at each substation at steady state and the three phases are balanced.Based on the results of these calculations, the amount of active and reactive power of each transmission device, the amount of active and reactive power of each generation center and the amount of power loss in the system are calculated.Each bus has 4 (four) operating variables, namely active power, reactive power, voltage magnitude and voltage phase angle.To calculate the power flow equation of each bus, 2 (two) of the 4 (four) variables above must be known, the remaining 2 (two) variables are calculated.The load bus is a known variable that is active power, reactive power.Voltage magnitude and voltage phase angle are calculated.Generator bus active power and voltage are known variables, while reactive power and voltage phase angle are the result of calculation.The slack bus is a known variable consisting of the magnitude of the voltage and the phase angle of the voltage, which is the reference angle, while the active power and reactive power to be compensated are the result of the calculation.There are two general methods used to solve power flow, namely the Gauss-Seidel method and the Newton-Raphson Method [1], [2].

Input output characteristics of thermal plants
This characteristic shows the relationship between the input of the generator as a function of the output of the generator.The equation of the input-output characteristics of a generator expresses the relationship between the amount of fuel required to produce a certain power of a power plant.

Fig.1. Thermal plant input-output curve
The figure above shows the input-output characteristics of an ideal thermal plant, which is represented as a continuous nonlinear curve.The generator input is indicated on the vertical axis, that is, the thermal energy required in MBtu/h, since the British thermal unit is used (if SI is used, it becomes MJ/h or kcal/h), which can also be expressed as the total price per hour (Rp/h).The horizontal axis shows the limit minimum and maximum generator powers [1], [3], [4].

Gauss Seidel Method
Mathematically, the Gauss Seidel method can be illustrated as follows [1], () = 0 (1) The above function is reformulated and written as  = () (2)   () is the initial estimate of the variable x, then the following iterative sequence can be formed as  (+1) = ( () ) (3) A completion can be obtained when the difference between the absolute values of successive iterations is less than the specified accuracy, i.e., | (+1) −   | ≤  (4)

Newton Raphson Method
Newton Raphson method is formulated as [1], [5], [6].() =  (5) If  (0) is an initial approximation of the solution, and ∆ (0) as a small difference from the proper solution, then ( (0) + ∆ (0) ) =  (6) if the left side in the Taylor series above is extended then maka  (0) yields (∆ (0) ) 2 + … =  (7) with a very small approximate error of ∆ (0) , then the higher order terms can be ignored and produce The addition of ∆ (0) to the initial estimate can produce a second estimate Successive applications of the above methods can produce the Newton-Raphson algorithm as follows.
where: = Gbest, the best group to iteration k
2 Material and Method

IEEE 30-bus System Data
In this study, IEEE 30-bus [1] data was used as validation of PSOHIC method used in the case study.

Method
The method used in this study is particle swarm optimization hybrid inertia weight and constriction factor (PSOHIC).
The stages of research can be seen in the following flow chart.

Results and Discussion
The results of the study present the IEEE system data as validation of the model used, and the 150 kV Sulbagsel system data.The first step in this study is to test the power flow solution with IEEE 30 bus data as validation of PSOHIC method, the second step is to calculate the power flow solution using particle swarm optimization hybrid inertia weight algorithm and constriction factor algorithm as a case study.

Results of 30-bus IEEE data simulation
30-bus IEEE data used as validation of PSOHIC method by comparing the standard PSO, update velocity using inertia weight and update velocity using constriction factor.For more details can be seen in the convergence graph of each of the following methods.

Fig. 3 .
Fig.3.Comparison of data simulation results IEEE update velocity standard PSO, IWA, CFA, and PSOHIC.The graph of the research results shows that PSOHIC (Hybrid Inertia Weight with Constriction Factor) converges faster in the 11th iteration.The standard PSO converges on the 23rd iteration.The IPSO algorithm converges at the 20th iteration.At the same time, the MIPSO algorithm converges at the 15th iteration.The power flow simulation results are shown in the following table.

Tabel 6 .
26-bus IEEE data power flow comparisonThe results of the IEEE 30-bus system power flow study show that the power flow is within the generation limit.The results of the convergence of each update velocity are different, namely: the standard PSO converges at the 23rd iteration, the IPSO algorithm at the 20th iteration, the MIPSO algorithm converges at the 15th iteration.At the same time, the 11th iteration of the PSOHIC (Particle Swarm Optimization Hybrid Inertia Weight and Constriction Factor) algorithm converges.The power loss using the PSOHIC method is 12.81 MW/hour, less than 15.53 MW/hour in the current system (Hadi Saadat), or the power loss is reduced by 0.1751%.The cost of generation using the PSOHIC method is $ 15,446.74per hour, lower than the current system of $ 16,760.73 per hour (Hadi Saadat) or a cost savings of 0.0789%.PSOHIC's success in the IEEE system power flow solution will be used as an indicator for testing or use in a case study of the Sulbagsel 150 kV system.

Table 2 .
Daytime peak load bus data 150 kV 29 bus Sulbagsel system

Table 4 .
Thermal generator cost function

Table 5 .
Thermal generating power limitation