BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT THÀNH PHỐ HỒ CHÍ MINH LUẬN VĂN THẠC SĨ NGUYỄN THANH NHÀN TÁI CẤU TRÚC LƯỚI BA PHA KHƠNG CÂN BẰNG CĨ XÉT ĐẾN ẢNH HƯỞNG CỦA PIN MẶT TRỜI NỐI LƯỚI CÔNG SUẤT NHỎ NGÀNH: KỸ THUẬT ĐIỆN - 8520201 SKC008012 Tp Hồ Chí Minh, tháng 3/2023 BỘ GIÁO DỤC VÀ ĐÀO TẠO TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT THÀNH PHỐ HỒ CHÍ MINH LUẬN VĂN THẠC SĨ NGUYỄN THANH NHÀN TÁI CẤU TRÚC LƯỚI BA PHA KHƠNG CÂN BẰNG CĨ XÉT ĐẾN ẢNH HƯỞNG CỦA PIN MẶT TRỜI NỐI LƯỚI CÔNG SUẤT NHỎ NGÀNH: KỸ THUẬT ĐIỆN - 8520201 Hướng dẫn khoa học: PGS.TS TRƯƠNG VIỆT ANH Tp Hồ Chí Minh, tháng 03/2023 Reduction of Power Losses Using Phase Load Balancing Method in Power Networks Based on the Selective Probabilistic Discrete Particle Swarm Optimization Viet-Anh Truong1 , Pham Quoc Khanh2(B) , Minh Thuyen Chau2 , and Nguyen Thanh Nhan3 Faculty of Electrical and Electronics Engineering, University of Technology and Education, Ho Chi Minh City, Vietnam Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City (IUH), Ho Chi Minh City, Vietnam phamquockhanh@iuh.edu.vn Hochiminh City Power Corporation, Ho Chi Minh City, Vietnam Abstract Reducing power losses using Phase Load Balancing Method (PLBM) in the distribution network is a mandatory requirement for electricity companies The goal of reconfiguration is to minimize active power loss and improve voltage profile Many methods have been proposed to solve this problem because of its significant economic and technical significance The paper presents a phase loadbalancing method based on the Selective Probabilistic Discrete Particle Swarm Optimization (SPD-PSO), a metaheuristics algorithm to minimize power loss and simplicity in operation The obtained results demonstrate the algorithm’s effectiveness in reducing power loss considering the phase load balancing cost of the unbalanced power network to find the operating states with the higher efficiency Keywords: Phase load balancing method · Unbalanced distribution networks · Metaheuristics algorithm · Selective probabilistic discrete particle swarm optimization Introduction A single-phase usually powers electrical appliances in the home However, civil electrical equipment is mostly single-phase loads, so when connecting multiple loads, the total power of the phases will be unbalanced, thereby appearing a power imbalance between the phases of the distribution power system Furthermore, electricity use is not continuous with electricity consumers, and the power consumption is always different from time to time Therefore, the consuming households will create an imbalance of total power in the phases Power quality and reducing power loss of the distribution networks are technical and economic problems for power companies Unlike the transmission grid, the distribution © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 Y.-P Huang et al (Eds.): GTSD 2022, LNNS 567, pp 413–422, 2023 https://doi.org/10.1007/978-3-031-19694-2_37 414 V.-A Truong et al networks have a phase imbalance that worsens the power quality and increases the power loss of the neutral line The larger the phase unbalance, the worse the power quality and the corresponding increase in power loss There are many ways to reduce power loss and improve voltage profile in the distribution network, such as reactive power compensation, operating voltage increase, load balancing, and conductor cross section increase These methods are technically feasible but require a lot of investment On the other hand, the phase load balancing method effectively reduces power loss and dramatically improves the voltage profile in the power system without requiring much investment The phase load balancing method is implemented by opening/closing switches to form a new network topology to reduce power loss while meeting operating constraints Merlin and Back [1] first proposed a method for this problem, where the discrete branching and constraint method is used to find the electrical structure resulting in minimal power loss The branch exchange method [2, 3] is used to solve the problem of minimizing power loss and balancing load demand The Heuristic method [4–6] is applied in finding loss-minimizing configurations based on selective trial and error Metaheuristics are used to improve the efficiency of finding suitable candidates based on optimization algorithms such as the Cuckoo Search Algorithm [7], Fractal Chaotic Search Algorithm [8], and Fractal Chaotic Search Algorithm Harmony search [9] One direction of research to improve the efficiency of the phase load balancing method is to combine optimization algorithms and artificial intelligence methods such as Fuzzy Logic [10–12] or Neural Network [13, 14] The article proposes applying the phase load-balancing method based on the PSDPSO algorithm to reduce power losses The PSD-PSO algorithm is a discrete metaheuristic that quickly determines the power supply lock for single-phase electrical loads to minimize the power loss on the phases and neutrals The paper results are verified through simulation modeling on a power network configuration at a power company In addition to the introduction presented above, the paper includes the following parts: Part introduces the unbalanced power grid reconstruction problem, Part presents the SPD-PSO algorithm, and Part shows the results after the applied phase load balancing method and the final part is the conclusion Loss Calculation for Unbalanced Three-Phase Grid Let SA , SB , SC be the apparent power of phase A, B, and C, respectively: SA = PA + jQA (1) SB = PB + jQB (2) SC = PC + jQC (3) There will be current on the neutral wire due to the asymmetric loads − → − → − → − → In = IA + I B + I C (4) Reduction of Power Losses Using Phase Load Balancing 415 Fig Mathematical model of 3-phase electrical circuit Fig Power conversion diagram PN , QN are active power and reactive power on the neutral phase, respectively Based on the vector diagram in Fig showing the relationship between the three phases A, B, C, the following formula is suggested (Fig 2): √ √ 3 1 QB + QC PN = P = PA − PB − PC − (5) 2 2 416 V.-A Truong et al √ √ 3 1 PB − PC QN = Q = QA − QB − QC + 2 2 (6) The formula for determining the power loss on phases A, B, C, and the neutral line is PA = PB = PC = PN = PA2 + QA2 UP2 PB2 + QB2 UP2 PC2 + QC2 UP2 PN2 + QN2 UP2 · RA (7) · RB (8) · RC (9) · RN (10) The total active power loss of an unbalanced three-phase power network: P = PA + PB + PC + PN (11) The formula for determining the reactive power loss on phases A, B, C, and the neutral line is: QA = QB = QC = QN = PA2 + QA2 UP2 PB2 + QB2 UP2 PC2 + QC2 UP2 PN2 + QN2 UP2 · XA (12) · XB (13) · XC (14) · XN (15) The total reactive power loss of an unbalanced three-phase power network: Q = QA + QB + QC + QN (16) To minimize P and Q, PN and QN must be minimized, which leads to PA = PB = PC and QA = QB = QC We cannot arrange the load to ensure PA = PB = PC and QA = QB = QC , but we can only try to put the most reasonable load, such as PA ≈ PB ≈ PC and QA ≈ QB ≈ QC The phase load balancing method uses optimization algorithms to determine load switching locations for each phase Reduction of Power Losses Using Phase Load Balancing 417 Begin Initialization of swarm Update Pbest and Gbest satisfy the convergence condition Yes No X kt +1 = X kt + I Q (Vkt +1 ) Evaluation of Particle Fitness Vkt +1 = I Q1≥ Q ( Pbest , k − X kt ) + I Q1< Q ( Gbest − X kt ) Vk0 = a random velocity Updates position of particle for next iteration X 0k = a random solution Record the best Particle End Fig Flowchart of the SPD-PSO algorithm Selective Probabilistic Discrete Particle Swarm Optimization Algorithm SPD-PSO is proposed and detailed in [15] However, the following is a brief outline of the main ideas for implementing the SPD-PSO approach Particle position X and velocity V of the proposed SPD-PSO algorithm are matrices The particle and velocity update equations have been modified as shown in the pseudocode of the SPD-PSO algorithm given in Fig According to this representation scheme, a particle k in the proposed SPD-PSO algorithm is stored as a binary matrix m × n ì k with the following properties: ã All elements in the matrix are either or The value indicates the allocation of a group of respondents to the interviewer, while indicates no assignment 418 V.-A Truong et al • In each row, only one element has a value of 1, while all the remaining elements along the same row are 0, indicating that each cluster was assigned to only one interviewer (Fig 4) Fig Representation of a swarm particle in the SPD-PSO algorithm Equations (17) and (18) illustrate the process of updating the velocity and position of the k particle in the SPD-PSO, where t represents the iteration step in the search (17) Vkt+1 = IQ1 ≥ Q2 · Pbest,k − Xkt + IQ1 < Q2 · Gbest − Xkt Xkt+1 = Xkt + IQ3 Vkt+1 (18) Simulation Result 4.1 Distribution Grid Diagram Phu Lam substation is used to evaluate the proposed algorithm’s efficiency in reducing power losses using the phase load balancing method Phu Lam substation includes source and 47 buses; this location is in Ward 13, District 6, Ho Chi Minh City, and has a diagram of the electrical system presented in Fig 4.2 The Fitness Function of the Phase Load Balancing Method in Power Networks Two goals are set, including reducing power loss on the distribution network and optimizing the cost of load redeployment in phases The load of an unbalanced distribution network constantly changes according to the time of day The load phase cannot be changed from time to time but can only change with a power cycle The capacity of the load is calculated by the average power consumption of the consumer in year Every time a load is switched from one phase to another, there is an implementation cost To accurately evaluate the benefits of changing the load phase, we must include this cost Now, the fitness function is expressed as (19): F = Ktd ∗ (Pt − Ps ) · T − Kdp ∗ N where: (19) Reduction of Power Losses Using Phase Load Balancing 419 Fig Configuration of Phu Lam F Ktd Kdp T Pt Ps N fitness function value; Amount saved over kWh; Phase inversion cost for load; One load cycle time (h); Power loss without phase load balancing method; Power loss after applied phase load balancing method; Total load needs to change phase for phase load balancing of distribution network The Eq (19) shows how the different measures/factors introduced above are combined to form an objective function for the SPD-PSO algorithm to solve the problem 4.3 Calculation Results on the LDPP of Phu Lam If the loss is reduced in the unbalanced distribution network, this amount of electricity can be sold at a high price in the electricity price list Therefore, the electricity-saving price is 2500 (VND), and each load phase reversal cost is 25000 (VND) The SPD-PSO algorithm is used to determine the load configuration on the phases of the distribution network so that the total cost of saving electricity minus the total cost of phase change for the load is the highest Parameters to execute the SPD-PSO algorithm in distribution network reconstruction are given in Table Figure shows the efficiency obtained through each loop when performing the phase load balancing method The phase change results for loads during the phase load balancing method are presented in Table 420 V.-A Truong et al Table Parameters of the SPD-PSO algorithm Parameters Value Maximum number of repetitions 100 Number of individuals in the population 20 ϕ 0.5 δ 0.5 Fig Maximum electrical energy savings by phase load balancing method based on SPD-PSO Table Result of phase change for the load on the distribution network Position of load Bus From phase To phase 4A A C 31 14A A B 32 14A B A 63 4A-7A C A 71 4A-15A C B 105 8A-6A C B 121 8A-9A A B Reduction of Power Losses Using Phase Load Balancing 421 The power loss of the distribution network before reconstruction is determined based on the proposed algorithm with the value Pt = 3511.82 (W) After performing the load balancing method, the system’s power loss is Ps = 3309.26 (W) As a result, active power loss was reduced by 5.77% Thus, the electric energy saved in a year is calculated by (20): A = (3511.82 − 2209.26) ∗ 24 ∗ 365 = 1774.38 (kWh) (20) When considering the cost of phase change for the loads, the amount obtained after applying the load balancing method will be determined according to (19) and have the results shown in (21) F = 2500 ∗ 1774.38 − 25000 ∗ = 4260953 (VND) (21) The results show that just restructuring the distribution network after each year of operation of a substation can reduce the power loss on the transmission line caused by phase imbalance Conclusions The article has proposed a load balancing method for the unbalanced distribution network to reduce active power loss based on the SPD-PSO algorithm The results show that the 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