Optimal placement and sizing of pvdg units in a distribution system

ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 11(132).2018, QUYỂN 2 69 OPTIMAL PLACEMENT AND SIZING OF PVDG UNITS IN A DISTRIBUTION SYSTEM TỐI ƯU VỊ TRÍ VÀ CÔNG SUẤT CÁC PVDG UNITS TRONG HỆ THỐNG PHÂN PHỐI Thai Dinh Pham Thu Duc College of Technology; phamdinhthai9x@gmail.com Abstract - This paper presents a meta-heuristic optimization algorithm which is based on the intelligent foraging behavior of honey bee swarm and called artificial bee colony (ABC). This algorithm is applied to find out optimal placement and sizing of Solar Photovoltaics Distributed Generation (PVDG) units under considering multiple objective functions in a distribution system. Considerations of the objective function include total power loss reduction and voltage profile improvement while harmonic distortions (THD and IHD) comply with harmonic standard IEEE-519. The simulation study is implemented on the distribution system of IEEE 33 node test feeder. Obtained results show that suitable PVDG units can bring more benefit in both economic and technical prospects. Tóm tắt - Bài báo này trình bày một thuật toán tối ưu hóa dựa trên hành vi tìm kiếm thức ăn thông minh của đàn ong và được gọi là bầy ong nhân tạo (ABC). Thuật toán này được áp dụng để tìm ra vị trí và công suất tối ưu của các đơn vị máy phát điện mặt trời (PVDG Units) dưới sự xem xét nhiều hàm mục tiêu trong một hệ thống phân phối. Hàm đa mục tiêu bào gồm việc giảm tổng tổn thất điện năng trên lưới và cải thiện điện áp ở các điểm nút trong khi sóng hài (THD và IHD) được giữ tuân theo tiêu chuẩn sóng hài cho phép của IEEE-519. Nghiên cứu mô phỏng này được thực hiện trên hệ thống phân phối của IEEE 33 node test feeder. Kết quả thu được cho thấy các đơn vị PVDG được lắp phù hợp có thể mang lại nhiều lợi ích cả về kinh tế lẫn kỹ thuật. Key words - ABC; optimization algorithm; PVDG; power loss; voltage profile; harmonic. Từ khóa - ABC; thuật toán tối ưu; PVDG; công suất mất mát; điện áp; sóng hài. 1. Introduction Nowadays, the integration of renewable energy based distributed generation (PVDG) units are common in the distribution network due to many potential benefits. PVDG units are connected to the system with its optimal location and size and they can reduce total power losses, improve voltage and power quality However, incorrect location and sizing can cause significant damage such as increased losses, voltage flicker, fault current, and increased harmonic distortion in the power system which has nonlinear loads. Therefore, an effective solution needs to perform under considering the multiple objective functions to identify suitable location and sizing of PVDG units. The received benefits depend on how optimally DG units are installed. Most of the approaches in finding optimal location and sizing of DG units are considered for loss reduction and voltage improvement. There are many presented approaches such as PSO, Fuzzy logic, ABC, GA or method based sensitivity analysis. In Ref. [1], a Particle Swarm Optimization (PSO) methodology has been applied. PSO is one of the useful and popular methods. In that paper, the author found the optimal DGs with objective function as minimum total power loss and voltage in the constraints. It is necessary to take suitable place and size DGs before connecting DGs into the distribution system. However, that paper only consider a single objective function are power losses. A biology-based optimization method which is very common as a genetic algorithm (GA) also presented in Ref. [2] and [3]. These authors used GA as a method of determining the placement and sizing of DGs. This paper considers improving voltage as well as power loss reduction with calculation in power generation and power losses. The voltage stability and loss reduction are really enhanced after properly installing DGs in the distribution system. Besides, the author of Ref. [4] has found suitable DGs by using Big Bang-Big Crunch method. That paper tries to minimum power loss as well as energy loss in a distribution system. A multi-objective particle swarm optimization (MOPSO) is applied for optimal placement and sizing of DGs under economic and technical analysis [5]. Suitable DGs can bring significant benefits from saving the cost of power losses and purchasing power. Most previous researches have overlooked an important element of harmonics. Actually, when connecting DG units to the distribution system, the harmonic (THD, IHD) will be changed. According to the paper in [6], this is a nice paper which presented under study some types of DGs in the small distribution system. By using a genetic algorithm (GA), the location, the type, and the sizes of DGs are successfully found in a distribution system. The suitable location DG units can reduce many problems related to power quality. In this paper, power loss, voltage deviation, and harmonic become the main issue which needs to be minimized. However, with the distribution system and many nonlinear loads, it will be a real-world problem. In addition, with considering another aspect, THD and IHD are not necessary to reduce to a minimum, because it will not bring many benefits instead of minimum other factors as power losses, emissions In this paper, a meta-heuristic algorithm which is called artificial bee colony (ABC) has been presented. ABC’s optimization technique was motivated by biogeography, under the study of operation from employed bees, onlookers, and scout bees in the natural environment. ABC is applied to find optimal location and sizing of DG units for total power loss and voltage profile index reduction while total harmonic distortion (THD) and individual harmonic distortion (IHD) reduction are maintained at harmonic standard. 70 Thai Dinh Pham To evaluate the multiple objectives, a sum of the weighted method is applied for deciding the fitness of multi-objective function to obtain the best solution. The weighted factor depends on the importance level between the components in the objective function. In this research, harmonic flow is solved based on the exact three-phase component models, and combined with forward/ backward sweep technique which is presented in [7]. In the test cases, the different harmonic sources are injected into some loads. With using the applied methodology (ABC), it will become a strong optimization technique for finding optimal location and sizing of multiple PVDGs in a distribution system. This paper introduced and applied a methodology which is called artificial bee colony (ABC) in finding optimal location and sizing of PVDG units in a distribution system IEEE 33 node test feeder while maintaining harmonic follow the standard IEEE-519. 2. Problem Formulation The optimal location and sizing of PVDG units for multiple objective functions are challenging which need to solve. This paper focus on the main issue is total power loss, voltage profile while maintaining total harmonic in standard limits. 2.1. Opjective Function The objective function includes 3 components: Total power loss, voltage profile and harmonics (THD and IHD). 2.1.1. Total Power Loss The total power loss (TPL) is an important factor for economic and technical evaluation. The total active power loss needs to be minimized and can be written by 1 ( ) Nbr L n TPL P n = = (1) where LP is the power loss of line in the distribution system and Nbr is the number of the branches. The ratio of total power loss with PVDG units and without PVDG unit is shown as: 1 withDGs withoutDG TPL F TPL = (2) 2.1.2. Voltage profile Index Voltage profile index (VPI) is one of the elements to evaluate in the distribution system. VPI can be calculated from Eq.(3). 1 |1 | n i i V VPI n = − =  (3) where iV is the voltage of each node (p.u), n is the total number of node in the system. The ratio of VPI before and after connecting PVDG units is shown as 2 withDGs withoutDG VPI F VPI = (4) 2.1.3. Harmonic This article researches the system which has many nonlinear loads and this is the cause of the harmonics. When PVDG units are connected to the system, THD and IHD will be changed dramatically. This change depends entirely on the PVDG units location. Total harmonic distortion (THD) is defined: 2 1/2 1 1 ( | | ) (%) 100 | | H h i i h i V THD V       =         (5) where iTHD is the total harmonic distortion at the ith node, h iV is the “h” order harmonic voltage at the i th node and 1 iV is the fundamental voltage at the ith node. Individual harmonic distortion (IHD) is defined: 1 | | (%) 100 | | h i i i V IHD V =  (6) Where, IHD is the individual harmonic distortion at the ith node. By the harmonic standard IEEE-519, the total harmonic distortion (THD) and individual harmonic distortion (IHD) should not exceed 5 % and 3 %. In this work, F3 will be divided into 2 parts: F3-THD and F3-IHD which are defined as: For F3-THD, 3_ 1 1 ,THDF e = − (7) where max( ) , max( ) 5 5 0, max( ) 5 i i i THD if THD if THD    =    =  (8) For F3-IHD, 3_ 1 1 ,IHDF e = − (9) where max( ) , max( ) 3 3 0, max( ) 3 i i i IHD if IHD if IHD    =    =  (10) Eq.(7) and Eq.(9) are divided into 2 parts. If THD or IHD violates the harmonic standard limit, they will be gradual convergence and help to reduce THD and IHD to limits. But if THD and IHD are in the harmonic limits, the convergence tends to focus on the rest of objective functions (F1 & F2). This can help to obtain the best solution. F3 will be averaged of F3-THD and F3-iHD as: 3_ 3_ 3 2 THD IHDF F F + = (11) Finally, the objective function of the optimization will be defined as below: F= min(aF1+bF2+cF3) (12) In this paper, a sum of the weighted method for multi- objective optimization is used for deciding the fitness value ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 11(132).2018, QUYỂN 2 71 of the multi-objective function to obtain the best solution. Minimizing the weighted sum depends on the components that constitute the objective function. Because the total power loss reduction has a highest impact on economic and technology, the weight factor of F1 is the highest. Harmonic is also quite important and to help reduce harmonic in the limits quickly, the weight factor of F3 will be higher than F2. 2.2. Constraints The constraints of the objective function (Eq.12) should be kept in the limits as below: 2.2.1. The voltage limits The voltage at each node should be kept with voltage constraint as follows: min maxiV V V  , i = 1, 2, , N (13) where Vi is the voltage at node ith and N is the node number; Vmin and Vmax equal to 0.95 p.u and 1.05 p.u, respectively. 2.2.2. Total harmonic voltage distortion & Individual harmonic voltage distortion limits Following the harmonic standard IEEE-519, total harmonic voltage distortion and individual harmonic voltage distortion should be met in the constraints as: max(%) (%) 5%iTHD THD = (14) max(%) (%) 3%iIHD IHD = (15) where maxTHD and maxIHD are the maximum values of total harmonic distortion and individual harmonic distortion which are accepted in IEEE Std. 519. 2.2.3. The PVDGs capacity limits The active power of DGs should be kept in the limits as follows: min max , , 1 , DG DG DG j DG N DG j load j P P P P P =    (16) where, 0 1   , min ,DG jP and max ,DG jP are the minimum and maximum PVDG sizing, Pload is total active power of load demand and NDG is the number of PVDG units. 3. Applied Methodology 3.1. PVDG units modeling issue With the strong growth in the connection of PVDG units into the distribution system, several methods have been given to solve the optimization problems under considering the different objective functions. Actually, PVDG planning is one of the important issues which have a significant impact on economic and technical prospects. In this paper, PVDG units supply the active power directly for the loads. With the optimal location and sizing, PVDG units have the ability to reduce the power loss, voltage profile index and maintain harmonic in the standard limits. 3.2. The characteristic of Applied Optimization Algorithm This paper presents a meta-heuristic algorithm that is called artificial bee colony (ABC) and was introduced by Haraboga in 2005 [8]. Actually, ABC has common features with other biology-based optimization methods as PSO, GAs but it has more outstanding features. The algorithm is found based on optimization technique inspired by the intelligent foraging behavior of the honeybee swarm in natural phenomenon. The colony of artificial bees includes three kinds of bees: employed bees, onlookers, and scout bees. The employed bees are generated randomly for finding food-sources (solutions). Due to dancing, these bees share the food source's information with the Onlookers which are waiting in the dance area of the hive. Food-sources will be evaluated for each dancing (fitness values). Onlookers will observe the quality of food-source that employed bees shared. Realistically, with a good quality food- source, it really attracts the attention of many bees rather than a bad food- source. For onlookers and scout bees, once it discovers a new food-source, it becomes the employed bee. Also, when employed bees are abandoned, they become onlookers and scout bees to find new food-sources. Employed bees, after being generated to find food sources, will remember the location of the food sources and continue to find new food sources in the vicinity. If it discovers a new food source that is evaluated to be of higher quality, it will remember the location of the new food source and forget the poor quality source of food. Once all employed bees have completed the task, they will share the food source location with Onlookers. Onlookers make the evaluation for all received food sources and they will select a food source with a probability related to quality [9]. 3.3. Artificial bee colony optimization algorithm Artificial bee colony optimization algorithm is applied to solve the optimization problem in finding the suitable placement and sizing of PVDG units. In this algorithm, each food-source position is a solution to the problem. This algorithm generates a randomly distributed initial population of solution and the initial population of solution xi can be defined by Eq.(17): )(*)1,0( minmaxmin iiii xxrandxx −+= (17) where xmin i and xmax i are lower bound and upper bound of parameter xi, respectively. Each employed bee xi generates a new solution vi in around of curent position as: )(* jkikikikik xxxv −+=  (18) where xj is a randomly selected candidate solution (i≠j), k is a random dimension index, and ik is random within [-1 1]. If the fitness of vi is better than its parent xi, then update xi which has great vi. All employed bees share information with onlooker bees. Onlooker bees make the evaluation with probabilistic selection which is based on a roulette wheel selection mechanism as defined: 72 Thai Dinh Pham 1 i i fit i n fit i F p F = =  (19) where Ffit i is the fitness value of xi solution and n is the swarm number. Assume that the abandoned source is xi and the scout bee finds out a new solution, it will be replaced with ith as: (0,1)*( )ik i i ix lb rand ub lb= + − (20) where ub and lb are opper and lower boundaries of the ith dimension, respectively. Initialize parameters, bus limit, sizing limit of unit, population Random Initial solution within limit Solve power flow and harmonic flow Satisfied criterion ? i>imax ? Calculate the fitness value Update to neighbor solution Solve power flow and harmonic flow Satisfied criterion ? Calculate the fitness value and retain best solution Ob>Obmax ? Calculate Pi value and determine solution with high Pi value Modify the determined solution, count (Ob) Solve power flow and harmonic flow Satisfied criterion ? Limit reached ? Generate new solution ramdomly Solve power flow and harmonic flow Satisfied criterion ? Calculate the fitness value Compare and save the best one Iter >Itermax ? Optimal solution No Yes No Yes No Yes Yes No Yes No Yes No No Yes No Yes Figure 1. Flowchart of ABC’s algorithm The process of implementation is shown in the flowchart (Figure 1). In the above flowchart, variable values (i, Ob, Iter) will be updated by one unit after each individual loop cycle. 4. Simulation Results The purpose of this research is to find optimal location and sizing of PVDG units to improve voltage profile, reduce total active power loss while maintaining harmonic at IEEE standard 519. IEEE 33 node test feeder is selected as an experienced case. Figure 2. IEEE 33 node test feeder As mentioned above, the total harmonic distortion and individual harmonic distortion will be considered with IEEE standard 519. The harmonic sources are directly injected to loads of the distribution system with the detailed information of harmonic spectrums which are shown in Table 1. In this paper, the weight factors of multiple objective functions are used with parameters (a, b, and c) equal to 0.70, 0.10 and 0.20, respectively. There are 2 PVDG units connected to the system. The maximum of active power is equal to 2.0 MW per PVDG unit; the maximum power factor of DG units equals to 1. In this research, nonlinear load positions at node 9, 14, 19, 23, 26 and 31 in the distribution system are shown in Table 1. Table 1. Harmonic spectrum Harmonic number Harmonic order Magnitude (%) Angle (degree) 5 5; 7; 11; 13; 17 0.765; 0.627; 0.248; 0.127; 0.071 28; -180; -59; 79; -253 Table 2. The results for applied method Without PVDG With PVDGs Location – Sizing of PVDGs Node 14 - 0.8368 MW Node 30 - 1.3098 MW Node volt (min) 0.9131 p.u 0.9732 p.u THD (max) 6.0331 % 3.9247 % IHD (max) 3.9133 % 2.5465 % Total power loss 0.2027 MW 0.0868 MW Based on the obtained simulation results, 2 PVDG units need to be connected to the system at node 14 and node 30 with capacity equal to 0.8368 and 1.3098 MW, respectively. The total power loss is significantly reduced from 0.2027 to 0.0868 MW. Figure 3. Convergence of ABC’s algorithm (50 iterations) 0 5 10 15 20 25 30 35 40 45 50 0.33 0.335 0.34 0.345 0.35 0.355 0.36 0.365 0.37 0.375 Iter No. F itn es s ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 11(132).2018, QUYỂN 2 73 The convergence of the algorithm seems pretty fast. This is one of the outstanding features of this algorithm. Figure 4. Volt profile without and with PVDG units Volt profile is significantly improved after connecting PVDG units and all node voltages are within acceptable limits. Figure 5. THD without and with PVDG units Figure 6. Highest order IHD without and with PVDG units THD and IHD (%) are reduced to the acceptable limits thanks to the optimal connection of PVDG units and this is one of the benefits of PVDG units properly installed. 5. Conclusion Artificial bee colony (ABC) method is applied to find the optimal location and sizing of PVDG units. The main idea in this algorithm is based on bee behavior. In this research, the multiple objective functions are to minimize total power loss and improve voltage profile while maintaining harmonic in standard limit. This paper does not focus on reducing harmonics to a minimum; it only maintains THD and IHD in the harmonic standard limits. This will open more opportunity for finding the greater fitness value. The suitable location and sizing of PVDG units are successfully found out in the distribution system. REFERENCES [1] Krischonme Bhumkittipich and Weerachai Phuangpornpitak, “Optimal placement and sizing of distributed generation for power loss reduction using Particle Swarm Optimization”, 10th Eco-Energy and Materials Science and Engineering, Energy Procedia 34, 2013. [2] M. Sedighizadeh, and A. Rezazadeh, “Using Genertic Algorithm for Distributed Generation Allocation to Reduce Losses and Improve Voltage Profile”, International Scholarly and Scientific Research & Innovation, Vol.2, No.1, 2008. [3] R. Sulistyowati, D. C. Rianwan, and M. Ashari, “PV Farm Placement and Sizing Using GA for Area Development Plan of Distribution Network”, International Seminar on Intelligent Technology and Its Application, 2016. [4] M.M. Othman, W. El-Khattam, Y. G. Hegazy and A. Y. 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Padmavathy, “Optimal allocation and sizing of distributed generation using artificial bee colony algorithm”, International Research Journal of Engineering and Technology (IRJET), vol. 03, Iss. 2, Feb. 2016. (The Board of Editors received the paper on 01/10/2018, its review was completed on 26/10/2018) 0 5 10 15 20 25 30 35 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 Bus No. pu Without DG With DGs