Quantum binary particle swarm optimization for optimal on-load tap changing and power loss reduction

Over time, there has been a continuous surge in the demand for electrical energy, necessitating the development of larger and more intricate electrical power networks. These extensive networks pose a significant challenge, primarily in the form of considerable loss of electrical energy, which, if not effectively addressed


INTRODUCTION
With the passage of time, the demand for electrical energy continues to surge.This escalating need necessitates larger and more complex electrical power networks.However, as these extensive networks evolve, they bring forth a significant challenge.One such challenge is the substantial loss of electrical energy within the network, which, if left unaddressed, can lead to ongoing and imperceptible losses.
The growing demand for electricity due to population expansion has necessitated the installation of power systems with a larger capacity.However, as the capacity of a power system increases, so does its power loss and operational cost [1]- [3].Numerous approaches have been proposed to reduce power loss, such as preventing voltage drop, reducing unbalanced phase loads, correcting power factors using capacitor banks, and optimizing the loading of power transformers [4]- [6].Photovoltaics (PVs) have also been integrated into power systems to control voltage level fluctuations and reduce power loss [7]- [9].Static compensator distribution [10] and voltage control on the transformer using on-load tap changers (OLTC) can  Quantum binary particle swarm optimization for optimal on-load tap changing and … (Aji Akbar Firdaus) 489 also be used to achieve the same objective [11].Distributed generators (DGs), wind turbines, and PVs can additionally support extra power demand and stabilize supplied voltages [12]- [16].However, OLTC coordination and the exchange of reactive power from DGs, wind turbines, and PVs are time-consuming and expensive to install and maintain.
In this research, we propose the utilization of quantum binary particle swarm optimization (QBPSO) to facilitate OLTC coordination and minimize power losses within a distribution network.The choice of particle swarm optimization (PSO) as the optimization technique is rooted in its advantageous qualities, including speed and efficiency, ease of implementation, scalability, adaptiveness, and a balanced explorationexploitation trade-off.This paper delves into issues related to power losses within distribution systems and elaborates on the proposed approach for OLTC coordination.Experimental results stemming from the implementation of the suggested method are presented, and a concise conclusion is provided.

METHOD 2.1. Transformer
The electromagnetic induction principle is utilized by an electrical device known as a transformer to transfer alternating voltage from one level to others [17].The transformer comprises two types of coils, the primary and secondary coils, which are electrically separated but magnetically connected, as depicted in Figure 1.The working principle of a transformer is based on Ampere's law, which states that an electrical current can generate a magnetic field, and Faraday's law, which states that a magnetic field can generate an electric current [18], [19].When the primary coil is connected to an alternating voltage supply, alternating flux is generated inside the laminated core.This flux induces self-induction in the primary coil and mutual induction in the secondary coil, resulting in magnetic flux in the secondary coil.If the load is connected to the secondary coil, the secondary current flows.
A simple transformer is composed of two insulated coils or wires and an iron core.The ratio of turns on a transformer can be determined using (1) and the number of turns on the transformer can impact the voltage and current produced on the secondary side.This concept is related to the calculation of the number of transformers turns using (2), where  and  represent the number of primary and secondary turns, and Vp and Vs are the voltages on the primary and secondary sides, respectively.Lastly,  and  indicate the currents on the primary and secondary sides.

Problem formulation in the radial distribution network
The primary objective of this paper is to enhance the efficiency and economic viability of a distribution system by minimizing power loss while ensuring that the output voltage remains within specified limits.The overarching goal is to optimize the overall performance of the system by addressing both real and reactive power losses.Real power, which represents the actual energy consumed or dissipated as heat, and reactive power, associated with the phase difference between voltage and current in AC circuits, are targeted for reduction.In (3) and (4), as referenced from sources [20], [21], play a pivotal role in guiding the minimization process.By focusing on these equations, the paper aims to provide a systematic approach to achieving optimal power management, thereby contributing to the economic efficiency and sustainability of the distribution system.(3)

Power flow in the distribution system
The power flow solution in a distribution system diverges from that in a transmission system due to the radial-connected network characteristic of distribution systems.A method commonly employed for power flow calculations in radial distribution systems is the bus injection to branch current-branch current to bus voltage (BIBC-BCBV) method, as outlined in references [22], [23].This technique facilitates the accurate determination of power flow dynamics in the context of radial distribution networks.Figure 2 allows for the arrangement of the bus injection to bus current (BIBC) matrix, which can then be used to simplify ( 5) into (6).
(5) The branch current to bus voltage (BCBV) matrix can be formulated from the voltage equation, as shown in (7).
If ( 6) is substituted into (8), then  can be expressed as (9) which in turn can be simplified to (10): The complete power change can be obtained by iterating (5) through (13).
TELKOMNIKA Telecommun Comput El Control  Quantum binary particle swarm optimization for optimal on-load tap changing and … (Aji Akbar Firdaus) 491

Quantum binary particle swarm optimization
The PSO algorithm, developed by Kennedy and Eberhart in 1995, draws inspiration from bird and fish colony intelligence [22]- [25].In ( 14) and ( 15) are representative of the standard PSO algorithm.The introduction of the inertia weight as a diversity controller in the original PSO modifies the particle update equation.
( + 1) =   () +   ( + 1) The standard procedure for implementing the PSO algorithm includes initializing the velocity, position, and PSO parameters, updating the velocity and position of the particles using ( 14) and ( 15), evaluating the fitness function with  and  update, comparing each candidate  from the fitness function value to get the best  value, and returning to step 2 if the value of  is not the best value.The iteration limit is performed to get  with the least or the best fitness function [26], [27].The binary particle swarm optimization (BPSO) algorithm updates  and  in the swarm, with a difference in the interpretation of the velocity compared to the PSO standard.The range of the velocity in BPSO is limited to [0,1].In ( 16) is used to obtain the new position of the particle, while its velocity is determined by (17).
The integration between quantum computing and BPSO is known as QBPSO [28]- [30].The use of the contraction-expansion coefficient is one of the parameter differentiators in QBPSO to control the convergence velocity from the particles.The first search, which is more global and dynamic, is accommodated by using an initial βmax value of 1.Then, the beta () value is gradually decreased until it reaches  = 0.4.This is done to complete the QBPSO algorithm search with a better local search.In (18) gives the evolution of β.

𝛽(𝑡) = 𝛽 𝑚𝑎𝑥 − ( 𝛽 𝑚𝑎𝑥 −𝛽 𝑚𝑖𝑛 𝑖𝑡𝑒𝑟 𝑚𝑎𝑥
) .() The new positions in quantum particle swarm optimization (QPSO) are provided by (19) and (20) respectively, using the Monte Carlo method.It is noteworthy that time units are used for particles to move.Additionally, in the migration process, there is an evaluation process, where the best position is represented by mbest.From the QPSO result, the velocity value will be converted to binary by using ( 16) and (17).

RESULTS AND DISCUSSION
In this research, a 20 kV 34-bus radial network is utilized with the OLTC's location on the IEEE 34 bus system depicted in Figure 3.The net and load data on each bus are presented in Tables 1 and 2. The bus data table includes a load-type column where the value 1 denotes constant power, 2 denotes constant current, and 3 represents constant impedance.In the system, there are 34 buses and five transformers, positioned between specific buses.The power flow in the radial distribution system is calculated using the BIBC-BCBV method with average lines and loads taken from (13).The total active power of the loads is 428.638399kW.Without OLTC optimization, the power loss from the distribution system is 21.756107 kW, and the average  The voltage drops and current values in every bus and line obtained from the power flow simulation in Table 1 represent the condition or characteristic of the IEEE 34 bus system and are used to calculate the power loss.Figure 4 shows the bus voltage of the system within the defined tolerance range of ± 5% of the base voltage of 20 kV, where buses 16 to 34 experience under voltage.Tap formation for transformer 1 to transformer 5 is performed in a sequence of -1, 0, 2, -1, 0. The current at the line between bus 3 and 4 for transformer 1 is 20.7 A with tap transformer -1.Similarly, for transformer 2, the current at line 9 between bus 9 and 13 is 20.7 A with tap transformer 0. For transformer 3, the current at the line between bus 15 and bus 16 is 20.7 A with tap transformer 2. The current at the line between bus 21 and bus 25 for transformer 4 is 11.27A with tap transformer -1, while for transformer 5, the obtained current is 0.57 A with tap transformer 0.  The power loss simulation was performed to determine the active and reactive power losses in the transformer lines.The results showed that the active power losses in transformers 1, 2, and 3 were relatively high at 3.29 kW, 1.5 kW, and 3.01 kW, respectively, while the losses in transformers 4 and 5 were lower at .24 kW and 0 kW, respectively.The reactive power losses in all transformers were also recorded, with the highest value of 3.28 kVAR in transformer 1 and the lowest value of 0 kVAR in transformer 5.These losses were attributed to the large current flowing through the transformers.Furthermore, the voltage drop analysis revealed that the lines between bus 3 and bus 4, bus 15 and bus 16, and bus 21 and bus 25 had relatively high voltage drops of 0.23 kW, 0.19 kV, and 0.03 kV, respectively.The findings from this study provide valuable insights into the power loss and voltage drop characteristics of the IEEE 34 bus system, which could be useful for improving the system's overall efficiency and performance.
The QBPSO optimization simulation was utilized to obtain optimal OLTC tap coordination to minimize power loss and maintain voltage within a predetermined standard.The result of the OLTC simulation using QBPSO is presented in Table 2, which brings changes to the power flow in the system as shown in Table 3.The power loss obtained from this optimization is 19.157321 kW, with an average voltage of 19.93068 kV. Figure 5 indicates that there is no under-voltage bus, and the minimum voltage obtained is 19.099 kV.The required time for the optimization is 3.858783 seconds, as presented in Table 4.The tap formation for transformers 1 to 5 in sequence is used: -1, 1, 3, -3, 3. The current in the line between bus 3 and bus 4 is lowered from 20.7 A to 19.47 A with tap transformer -1 at transformer 1.The current in the line between bus 9 and bus 13 is lowered from 20.7 A to 19.47 A with tap transformer 1 at transformer 2. The current in the line between bus 15 and bus 16 is lowered from 20.7 A to 19.47 A with tap transformer 3 at transformer 3. The current in the line between bus 21 and 25 is increased from 11.27 A to 11.37 A with tap transformer -3 at transformer 4. The current from 0.57 A to 0.52 A is obtained with tap transformer 3 at transformer 35.From the obtained current with the tap transformer, it can be seen that the current flowing can be reduced, resulting in a decrease in power losses.
The simulated power loss in the lines with transformers shows that the active power loss in the line of the transformer 1 decreased from 3.29 kW to 3.09 kW and the reactive power loss decreased from 3.28 kVAR to 3.09 kVAR.The active power loss in the line of transformer 2 decreased from 1.5 kW to 1.14 kW and the reactive power loss decreased from 1.1 kVAR to 0.07 kVAR.The active power loss in the line of transformer 3 decreased from 3.01 kW to 2.36 kW and the reactive power loss decreased from 2.24 kVAR to 1.55 kVAR.The active power loss in the line of the transformer 4 decreased from 0.27 kW to -0.26 kW and the reactive power loss decreased from 0.2 kVAR to 0.03 kVAR.The active power loss in the line of transformer 5 decreased from 0 kW to -0.02 kW and the reactive power loss decreased from 0 kVAR to -0.02 kVAR.The voltage drops across the lines between bus 3 and bus 4 decreased from 0.23 kV to 0.22 kV, the voltage drops in the line between bus 9 and bus 13 remained at 0.09 kV, the voltage drops in the line between bus 15 and bus 16 decreased from 0.19 kV to 0.18 kV, the voltage drops in the line between bus 21 and bus 25 remained at 0.03 kV, and the voltage drop in the line between bus 30 and bus 31 remained at 0.0 kV.Table 5 presents a comparison of simulation results using various artificial intelligence methods.In this paper, GA, BPSO, QDE, and QBPSO are compared to QBPSO.Based on Table 5, it is shown that QBPSO converges faster than the other methods, as demonstrated in Table 4.In the first experiment, QBPSO was able to directly find the minimum power loss of 19.1573 kW, while GA produced a simulation result of 19.3016 kW.

Table 1 .
Power flow result without OLTC optimization using QBPSO TELKOMNIKA Telecommun Comput El Control  Quantum binary particle swarm optimization for optimal on-load tap changing and … (Aji AkbarFirdaus)493

Table 3 .
Power flow result with OLTC optimization using QBPSO Figure 5. Voltage profile with OLTC optimization using QBPSO TELKOMNIKA Telecommun Comput El Control  Quantum binary particle swarm optimization for optimal on-load tap changing and … (Aji Akbar Firdaus) 495

Table 4 .
Comparison of time running program results

Table 5 .
Comparison of running program results