Abstract
Renewable sources can provide a clean and smart solution to the increased demands. Thus, photovoltaic and wind turbine are considered here as sources of distributed generation (DG). Allocation and sizing of DG have greatly affected the system losses. In this paper, ant lion optimization algorithm (ALOA) is proposed for optimal allocation and sizing of DG-based renewable sources for radial distribution system. First, the most candidate buses for installing DG are suggested using loss sensitivity factors. Then the proposed ALOA is employed to deduce the locations of DG and their sizing from the elected buses. The proposed algorithm is tested on 69 bus radial distribution system. The obtained results via the proposed algorithm are compared with others to highlight its benefits in reducing total power losses and consequently maximizing the net saving. Moreover, the results are introduced to verify the superiority of the proposed algorithm to enhance the voltage profiles for various loading conditions.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
1 Introduction
In recent years, the attention has shifted to projections of energy and related greenhouse gas emissions as a result of increasing environmental concern and global warming [1,2,3]. Renewable distribution generation (DG) such as wind turbine (WT) and photovoltaic (PV) systems presents a cleaner power production. The main advantages of DG are reduced line losses, increased efficiency, improved system reliability and minimized total costs [4,5,6].
The problem of DG placements and sizing was solved using various techniques. The authors in [7] used ant colony algorithm (ACA) with harmony search (HS) to solve the network reconfiguration problem. A cat swarm optimization is introduced in [8] for optimal location and sizing of DG units. Two ways to reach integration of multiple DG units in low- and medium-voltage distribution networks while optimizing many relevant objectives are discussed in [9]. Genetic algorithm (GA) combined with fuzzy programming to design multi-objective function for optimal sizing and siting of multiple DGs is illustrated in [10]. Mixed integer non-linear programming (MINLP) is introduced in [11] for multi-objective design to reduce both cost and losses effectively by optimal selection of DG size and location. GA is presented in [12] to determine the optimal size and locations of DGs taking into account system constraints; maximizes system loading margin and voltage profiles. In [13], GA and fuzzy are employed to transform original objectives and constraints into a fuzzy weighted single objective function to optimize DGs. Monte Carlo simulation embedded GA-based approach is displayed in [14] to minimize the DG cost, network loss cost, and capacity cost by optimally siting and sizing of DGs. A combination of GA and particle swarm optimization (PSO) for optimal sizing and siting of DG unit is addressed in [15]. PSO is presented in [16] for determining optimal DG locations, sizes and generated power contract price. Bacterial foraging optimization algorithm for optimal placement and sizing of distributed generation is illustrated in [17]. Firefly algorithm (FA) for optimal sizing and siting of voltage-controlled distributed generators in distribution system to reduce losses is considered in [18, 19]. A multi-objective optimization for sizing of DG using cuckoo search algorithm is discussed in [20]. Artificial bee colony (ABC) algorithm is employed in [21] to determine the optimal DG unit’s size, power factor and location to minimize the total system real power loss. Differential evolution (DE) is employed in [22, 23] to determine optimal DG capacity for minimum power losses. An effective method based on evolutionary programming (EP) and GA is presented in [24] to identify the switching operation plan for feeder reconfiguration and distributed generation size simultaneously. An imperialist competition algorithm (ICA) to maximize the benefits of distribution network, improve voltage stability and reduce costs is discussed in [25, 26]. Plant growth simulation algorithm (PGSA) is illustrated in [27, 28] for loss reduction and voltage profile improvement in distribution systems.
A new optimization algorithm known as ant lion optimization algorithm (ALOA) has been presented by Mirjalili [29]. It proves its superiority in many fields which are shown in [30,31,32,33]. ALOA optimizes DG in distribution system has not been considered yet. This encourages us to develop ALOA to deal with this problem. It is used to determine the optimal locations and sizing of DG in radial distribution systems. The results of the ALOA are compared with various techniques to detect its superiority in solving the problem of optimal locations and sizing of DG and thus reducing the active power losses and mitigating the voltage profiles for various loading conditions.
2 Loss sensitivity factors
LSFs are employed in this paper to assign the candidate buses for DG installation [34]. The area of search is greatly reduced and consequently the time consumed in optimization process using LSFs. A transmission line ‘l’ connected between ‘i’ and ‘k’ buses is given in Fig. 1:
The active power loss in this line is specified by \(I_l^2 R_{ik} \), which can be given by,
The LSFs can be computed from the following equation:
The normalized voltages are obtained by dividing the base case voltages by 0.95 [35]. If the values of these voltages are less than 1.01, they can be considered as candidate buses for installing DG.
3 Overview of ant lion optimization algorithm
Ant lion optimizer (ALO) is a novel nature-inspired algorithm presented by Mirjalili in [29]. The ALO mimics the hunting mechanism of ant lions in nature. An ant lion larva digs a cone-shaped pit in sand by moving along a circular path and throwing out sands with its massive jaw [36,37,38]. After digging the trap, the larva hides underneath the bottom of the cone and waits for insects to be trapped in the pit [39, 40]. The edge of the cone is sharp enough for insects to fall to the bottom of the trap easily. Once the ant lion realizes that a prey is in the trap, it tries to catch it. Then, it is pulled under the soil and consumed. After consuming the prey, ant lions throw the leftovers outside the pit and prepare the pit for the next hunt [30]. The pseudo code of the ALO algorithm is shown in appendix.
3.1 Operators of the ALO algorithm
The ALO algorithm mimics the interaction between ant lions and ants in the trap. To model such interactions, ants are required to move over the search space and ant lions are allowed to hunt them and become fitter using traps. Since ants move stochastically in nature when searching for food, a random walk is chosen for modeling ants’ movement as follows:
where cums calculates the cumulative sum and r(t) is defined as follows:
The location of ants are stored and used during optimization process in the following matrix:
The location of an ant refers the parameter for each solution. Matrix\(M_\mathrm{ant} \) is considered to save the position of each ant. The objective function is employed during optimization and the following matrix saves the fitness value for each ant:
In addition, the ant lions are hiding in the search space. The followings matrices are used to save their locations.
3.1.1 Random walks of ants
Ants change their positions randomly based on Eq. (3). To keep the random walks inside the search space, they are normalized using the following equation:
3.1.2 Trapping in ant lion’s pits
Random walks of ants are affected by ant lions’ traps. To model this supposition, the following equations are introduced:
Equations (10, 11) give that ants walk randomly in a hyper-sphere defined by the vectors C and D around a selected ant lion.
3.1.3 Building trap
A roulette wheel is used to model the ant lion’s hunting ability. The ALO algorithm is required to employ a roulette wheel operator for selecting ant lions based of their fitness during iterations. This mechanism shows high chances to the best ant lions for catching ants.
3.1.4 Sliding ants towards ant lion
With the previous mechanisms, ant lions can build traps relative to their fitness and ants are required to move randomly. However, ant lions shoot sands outwards the center of the pit once they sense that an ant is in the trap. This behavior slides down the trapped ant that is trying to escape. To model this behavior, the radius of ant’s random walk hyper-sphere is decreased adaptively. The following equations are presented in this regard:
3.1.5 Catching prey and re-building the pit
In this step, the objective function is calculated. If the ant has a better objective function than the selected ant lion then it changes its position to the latest position of the hunted ant to improve its chance of catching new one. The following equation is illustrated in this regard:
3.1.6 Elitism
It is important to maintain the best solution acquired at each step of optimization task. The best ant lion achieved so far in each iteration is saved as the elite. Since the elite is the best ant lion, it should be capable to affect the motions of all ants during iterations. Thus, it is assumed that every ant randomly walks around a selected ant lion by the roulette wheel and the elite simultaneously as follows:
4 Objective function
The proposed objective function is used to reduce the power losses and to improve the voltage profiles and Voltage Stability Index. The DG locations and their sizing can be obtained optimally by solving the following objective function [15, 41]:
where \(f_1 \) can be expressed as shown in the following equation:
\(f_2 \) can be defined as the following equation:
\(f_3 \) can be defined as:
where VSI is formulated as the following Eq. [15, 42]:
\(w_1 ,w_2\) and \(w_3\) are weighting factors. The sum of the absolute values of the weights assigned to all impacts should add up to one as shown in the following equation:
In this paper, \(w_1\) is taken as 0.5 while \(w_2\) and \(w_3 \) are taken as 0.25.
4.1 Equality and inequality constraints
Equation (16) is minimized whilst satisfying the following equality and inequality constraints.
4.1.1 Equality constraint
-
Power conservation constraint
The algebraic sum of all incoming and outgoing power flow over the distribution system should be equal [43]; thus,
4.1.2 Inequality constraints
-
Voltage constraint
The magnitude of voltage at each bus must be limited by the following equation:
where \(V_{\min }\) and \(V_{\max }\) are taken as 0.95 and 1.05 p.u, respectively, as given in [44].
-
DG limits constraint
To prevent reverse power flow, the installed capacity of DG in the network has been limited so as not to exceed the power supplied by the substation [43].
-
Line capacity constraint
The complex power through any line must be less than its rating value as given by the following equation.
5 Results and discussion
The effectiveness of the proposed ALOA with LSFs is examined. The results of 69 bus radial distribution systems are given below in details. The proposed algorithm has been performed via Matlab.
5.1 69 bus test system
The suggested algorithm is applied on the 69 bus system. Figure 2 shows the system diagram which consists of main feeders and seven branches. This system has a total load of 3800 kW and 2690 kVAr at 12.6 kV. The system data are given in [45]. The order of candidate buses for this system according to their LSF values is 57, 58, 61, 60, 59, 64, 17, 65, 16, 21, 19, 63, 20, 62, 25, 24, 23, 26, 27, 18 and 22 as appeared in Fig. 3. The superiority of the proposed technique to solve the problem of optimal location and sizing of DG compared with those obtained in [21, 43, 46,47,48,49,50,51,52,53] is confirmed.
Single DG location
For single DG installation, the optimal location and size are obtained via ALOA. Table 1 summarizes the developed results for installing single and two DGs. Bus number 61 is the best location for DG installation with a size of 1800 kW for PV type. A reduction in the total active power losses to 81.776 kW is resulted which illustrates a 63.645% reduction. The annual energy saving is 75,247$ via the proposed ALOA. The minimum voltage is grown from 0.9102 p.u to 0.9679 p.u. In addition, compared with [21, 43, 46, 48,49,50,51,52] and [53], the proposed algorithm introduces better results in terms of power losses and percentage reduction of power as displayed in Table 2. Moreover, the effects of DG installation on voltage profiles and VSI are given in Figs. 4 and 5, respectively. With WT type, the power losses are constringed to 23.1622 kW with percentage reduction of 89.703. The annual energy saving is 106,054.41$ via the proposed ALOA. The minimum voltage is increased to 0.9716 p.u. Thus, the proposed algorithm outlasts GA, CSA, SGA, PSO and BB–BC in minimizing losses and consequently improving saving. In addition, the designed WT type shows better results than PV type in terms of voltage profiles and VSI as clarified in Figs. 4 and 5.
Two DG locations
For two DG installation, the optimal location and size are gained using ALOA as given in Table 1. For PV type, bus numbers 17 and 61 are the best locations for DG installation with size of 538.777 and 1700 kW, respectively. The power losses are decreased to 70.75 kW with percentage reduction of 68.547. The annual energy saving is 81,042.26$ via the proposed algorithm. The minimum voltage is modified from 0.9102 p.u to 0.9801 p.u. In addition, compared with [47, 49, 51, 52], the proposed algorithm gives better results in terms of power losses and percentage reduction of power as reported in Table 3. Moreover, the effects of DG installation on voltage profiles and VSI are displayed in Figs. 6 and 7, respectively. With WT type, the power losses are lowered to 20.9342 kW providing a 90.69% reduction in total power losses. The annual energy saving is 107,225.44$ via the proposed ALOA. Thus, the proposed algorithm outperforms CSA, SGA and PSO in diminishing losses and enhancing saving. The minimum voltage is grown to 0.9742 p.u. In addition, the designed WT type gives superior results than PV type in terms of voltage profiles and VSI as mentioned in Figs. 6 and 7. In addition, the reactive power capability of WT has a considerable effect on reducing power losses and improving voltage profiles.
5.2 Effect of variable load
A constant load over the year is a hypothetical case as the load profile has the impact of seasonal and time variations. To mimic this effect, the load of the entire year has been considered as combination of three load levels of different durations as given in Table 4. ALOA finds the optimal sizes of DG for different load levels. The values of losses, installed DG and minimum and maximum voltage profiles are displayed for 69 bus system in Table 5 with variable loads. It can be seen that the losses are reduced at different loads as the number of locations increase. Moreover, the voltages are within the specified limits.
6 Conclusions
In this paper, ALOA has been successfully implemented with LSFs for optimal location and sizing of DG-based renewable sources in 69 bus radial distribution system. The designed problem has been formulated as an optimization task with computing of power losses, voltage profiles and VSI. The results have been compared with those obtained using other algorithms. It is obvious from the comparison that the proposed approach provides a notable performance in terms of power losses and saving. Moreover, the proposed ALOA is robust and it can be applied for variable loads demand. Applications of the proposed algorithm to large-scale distribution power systems and unbalanced one are the future scope of this study.
Abbreviations
- \(P_k ,Q_k \) :
-
The total effective active and reactive power supplied behind the bus ‘k’
- \(V_k \) :
-
The magnitude of voltage at bus k
- \(R_{ik} ,X_{ik} \) :
-
The resistance and reactance of transmission line between bus ‘i’ and ‘k’
- \(V_i \) :
-
The magnitude of voltage at bus i
- \(K_P \) :
-
The cost per kW-Hours
- n :
-
The maximum number of ants
- r(t):
-
A stochastic function
- t :
-
The step of random walk (current iteration in this paper)
- \(M_\mathrm{ant} \) :
-
The matrix for saving the position of each ant
- \(\mathrm{Ant}_{i,j} \) :
-
The value of the jth variable of ith ant
- d :
-
The number of variables
- \(M_\mathrm{oa} \) :
-
The matrix for saving the fitness of each ant
- \(M_{\text {ant lion}} \) :
-
The matrix for saving the position of each ant lion
- \({\text {Ant lion}}_{i,j} \) :
-
The value of the jth variable of ith ant lion
- \(M_\mathrm{oal} \) :
-
The matrix for saving the fitness of each ant lion
- \(A_i \) :
-
The minimum of random walk of ith variable
- \(C_i^t \) :
-
The minimum of ith variable at tth iteration
- \(C^{t}\) :
-
The minimum of all variables at tth iteration
- \(C_j^t \) :
-
The minimum of all variables for ith ant
- \(D_i^t \) :
-
The maximum of ith variable at tth iteration
- \(D^{t}\) :
-
The vector including the maximum of all variables at tth iteration
- \(D_j^t \) :
-
The maximum of all variables for ith ant
- \(\mathrm{Ant\, lion}_j^t \) :
-
The position of the selected jth ant lion at tth iteration
- I :
-
This ratio equals to \(10^{w}\frac{t}{T}\)
- T :
-
The maximum number of iterations
- w :
-
To adjust the accuracy level of exploitation
- \(r_a^t \) :
-
The random walk around the ant lion selected by the roulette wheel at tth iteration
- \(r_e^t \) :
-
The random walk around the elite at tth iteration
- \(\mathrm{Ant}_i^t \) :
-
The position of ith ant at tth iteration
- \(P_\mathrm{Loss} \) :
-
The total power losses after compensation
- \(F_t \) :
-
The total objective function
- \(f_1 \) :
-
The part of \(F_t \) that express the minimization of power losses
- \(f_2 \) :
-
The part of \(F_t \) that express the enhancement of voltage profiles
- \(f_3 \) :
-
The part of \(F_t \) that express the improvement of VSI
- \(w_1 ,w_2 ,w_3 \) :
-
The weighting factors
- \(P_\mathrm{Swing} \) :
-
The active power of swing bus
- \(Q_\mathrm{Swing} \) :
-
The reactive power of swing bus
- L :
-
The number of transmission line in a distribution system
- Pd(q) :
-
The demand of active power at bus q
- Qd(q) :
-
The demand of reactive power at bus q
- N :
-
The number of total buses
- \(V_{\min } \) :
-
The minimum voltage at bus i
- \(V_{\max } \) :
-
The maximum voltage at bus i
- \(P_\mathrm{DG} \) :
-
The installed active power of the DG
- \(Q_\mathrm{DG} \) :
-
The installed reactive power of the DG
- \(N_\mathrm{DG} \) :
-
The number of installed unit of the DG
- \(P_\mathrm{DG}^{\min }, P_\mathrm{DG}^{\max }\) :
-
The minimum and maximum real outputs of the DG unit
- \(Q_\mathrm{DG}^{\min },Q_\mathrm{DG}^{\max } \) :
-
The minimum and maximum reactive outputs of the DG unit
- \(S_\mathrm{Li} \) :
-
The actual complex power in line i
- \(S_{\mathrm{Li}(\mathrm{rated})} \) :
-
The rated complex power in that line i
- ALOA:
-
Ant lion optimization algorithm
- DG:
-
Distributed generation
- LSFs:
-
Loss sensitivity factors
- PV:
-
Photovoltaic system
- WT:
-
Wind turbine
- GA:
-
Genetic algorithm
- PSO:
-
Particle swarm optimization
- PGSA:
-
Plant growth simulation algorithm
- CSA:
-
Cuckoo search algorithm
- ABC:
-
Artificial bee colony
- ACO:
-
Ant colony optimization
- FA:
-
Firefly algorithm
- MINLP:
-
Mixed integer non-linear programming
- HS:
-
Harmony search
- ICA:
-
Imperialist competitive algorithm
- BF:
-
Bacteria foraging
- VSI:
-
Voltage Stability Index
- MTLBO:
-
Modified teaching learning-based optimization
- BB–BC:
-
Big Bang–Big Crunch
- SGA:
-
Standard genetic algorithm
- NR:
-
Not reported
References
Feng YY, Zhang XL (2012) Scenario analysis of urban energy saving and carbon abatement policies: a case study of Beijing City. China Procedia Environ Sci 13:632–644
Craig P, Gadgil A, Koomey J (2002) What can history teach us? A retrospective examination of long-term energy forecasts for the United States. Annu Rev Energy Environ 27:83–118
Aydin G (2014) The modeling of coal related CO2 emissions and projections into future planning. Energy Sources Part A Recovery Util Environ Eff 36(2):191–201
Sing RK, Goswami SK (2009) Optimum siting and sizing of distribution generations in radial and networked systems. Electr Power Compon Syst 37(2):127–145
Sing RK, Goswami SK (2011) Multi-objective optimization of distributed generation planning using impacts indices and trade-off technique. Electr Power Compon Syst 39:1175–1190
Vionthkumar K, Selvan MP (2012) Distributed generation planning: a new approach based on goal programming. Electr Power Compon Syst 40:497–512
Abdalaziz AY, Osama RA, Elkhodary SM (2012) Distribution systems reconfiguration using ant colony optimization and harmony search algorithms. Electr Power Compon Syst 41:537–554
Kumar Deepak S, Samantaray R, Kamwa I, Sahoo NC (2014) Reliability constrained based optimal placement and sizing of multiple distribranuted generators in power distribution network using cat swarm optimization. Electr Power Compon Syst 42:149–164
Haesen E, Driesen J, Belmans R (2007) Robust planning methodology for integration of stochastic generators in distribution grids. IET Renew Power Gener 1(1):25–32
Kim KH, Song KB, Joo SK, Lee YJ, Kim JO (2008) Multiobjective distributed generation placement using fuzzy goal programming with genetic algorithm. Int Trans Electr Energy Syst 18(3):217–230
Porkar S, Poure P, Abbaspour Tehrani Fard A, Saadate S (2011) Optimal allocation of distributed generation using a two stage multi-objective mixed integer nonlinear programming. Int Trans Electr Energy Syst 21(1):1072–1087
Akorede MF, Hizam H, Aris I, Ab MZA (2011) Effective method for normal allocation of distributed generation units in meshed electric power systems. IET Gener Transm Distrib 5(2):276–287
Vinothkumar K, Selvan MP (2011) Fuzzy embedded genetic algorithm method for distribution generation planning. Electr Power Compon Syst 39:346–366
Liu Z, Wen F, Ledwich G (2011) Optimal siting and sizing of distributed generators in distribution systems. IEEE Trans Power Deliv 26:2541–2551
Moradi M, Abedini M (2012) A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems. Int J Electr Power Energy Syst 34(1):66–74
Ameli A, Bahrami S, Khazaeli F, Haghifam MR (2014) A multiobjective particle swarm optimization for sizing and placement of DGs from DG owner’s and distribution company’s viewpoints. IEEE Trans Power Deliv 29:1831–1840
Devi S, Geethanjali M (2014) Application of modified bacterial foraging optimization algorithm for optimal placement and sizing of distributed generation. Expert Syst Appl 41(6):2772–2781
Othman MM, Hegazy YG, Abdelaziz AY (2015) A modified Firefly algorithm for optimal sizing and siting of voltage controlled distributed generators in distribution system. Period Polytech Electr Eng Comput Sci 59(3):104–109
Nadhir K, Chabane D, Tarek B (2013) Distributed generation location and size determination to reduce power losses of a distribution feeder by Firefly algorithm. Int J Adv Sci Technol 56:61–72
Zaid NM, Mokhtar MK, Musirin I, Rahmat NA (2015) Multi-objective optimization for sizing of distributed generation using cuckoo search algorithm. Appl Mech Mater 785:34–37
Abu-Mouti FS, El-Hawary ME (2011) Optimal distributed generation allocation and sizing in distribution systems via artificial bee colony algorithm. IEEE Trans Power deliv 26(4):2090–2101
Nayak MR, Dash SK, Rout PK (2012) Optimal placement and sizing of distributed generation in radial distribution system using differential evolution algorithm. Swarm, evolutionary, and memetic computing, vol 7677 of the series Lecture notes in computer science, pp 133–142
Abbagana M, Bakare GA, Mustapha I (2011) Optimal placement and sizing of a distributed generator in a power distributed system using differential evolution. 1st International technology, education and environment conference, pp 536–549
Dahalan WM, Mokhlis H, Ahmad R, Abu Bakar AH, Musirin I (2014) Simultaneous network reconfiguration and DG sizing using evolutionary programming and genetic algorithm to minimize power losses. Arabian J Sci Eng 39(8):6327–6338
Soroudi A, Ehsan M (2012) Imperialist competition algorithm for distributed generation connections. IET Gener Transm Distrib 6(1):21–29
Ghasemi D, Ebrahimi R (2015) Use of the imperialist competitive algorithm in determining the optimal location and capacity of distributing generation units to improve voltage stability and reduce costs of loss in radial distribution networks. Indian J Fundam Appl Life Sci 5:5099–5106
Baghipourr R, Hosseini SM (2013) Optimal placement and sizing of distributed generation and capacitor bank for loss reduction and reliability improvement in distribution systems. Majlesi J Electr Eng 7:59–66
Heydari SA, Heydarzadeh T, Tabatabaei NM (2016) A combined approach for loss reduction and voltage profile improvement in distribution systems. Int J Tech Phys Probl Eng 8:30–35
Mirjalili S (2015) The ant lion optimizer. Adv Eng Softw 83:80–98
Nischal MM, Mehta S (2015) Optimal load dispatch using ant lion optimization. Int J Eng Res Appl 5(8):10–19
Petrović M, Petronijević J, Mitić M, Vuković N, Plemić A, Miljković Z, Babić B (2015) The ant lion optimization algorithm for flexible process planning. JPE 18(2):65–68
Yamany W, Tharwat A, Hassanin MF, Gaber T, Hassanien AE, Kim TH (2015) A new multi-layer perceptrons trainer based on ant lion optimization algorithm. 2015 Fourth international conference on information science and industrial applications (ISI), 20–22 September 2015
Talatahari S (2016) Optimum design of skeletal structures using ant lion optimizer. Int J Optim Civ Eng 6(1):13–25
Hung D, Mithulananthan N (2013) Multiple distributed generator placement in primary distribution networks for loss reduction. IEEE Trans Ind Electron 60(4):1700–1708
Abdelaziz AY, Ali ES, Abd-Elazim SM (2016) Flower pollination algorithm and loss sensitivity factors for optimal sizing and placement of capacitors in radial distribution systems. Int J Electr Power Energy Syst 78C:207–214
Scharf I, Subach A, Ovadia O (2008) Foraging behaviour and habitat selection in pit building antlion larvae in constant light or dark conditions. Anim Behav 76(6):2049–2057
Griffiths D (1986) Pit construction by ant-lion larvae: a cost–benefit analysis. J Anim Ecol 55(1):39–57
Grzimek B, Schlager N, Olendorf D, Dade MC (2004) Grzimek’s animal life encyclopedia. Gale Farmington Hills, Michigan
Goodenough J, Mc Guire B, Jakob E (2009) Perspectives on animal behavior, 3rd edn. Wiley, United Kingdom
Scharf I, Ovadia O (2006) Factors influencing site abandonment and site selection in a sit-and-wait predator: a review of pit-building antlion larvae. J Insect Behav 19(2):197–218
Ghadimi N (2013) A method for placement of distribution generation (DG) units using particle swarm optimization. Int J Phys Sci 8(27):1417–1423
Das D, Kothari D, Kalam A (1995) Simple and efficient method for load flow solution of radial distribution network. Int J Electr Power Energy Syst 17(5):335–346
Hassan A, Fahmy F, Nafeh A, Abuelmagd M (2015) Genetic single objective optimisation for sizing and allocation of renewable DG systems. Int J Sustain Energy. doi:10.1080/14786451.2015.1053393
Abd-Elaziz AY, Ali ES, Abd-Elazim SM (2016) Optimal sizing and locations of capacitors in radial distribution systems via flower pollination optimization algorithm and power loss index. Eng Sci Technol Int J (JESTCH) 19(1):610–618
Baran M, Wu F (1989) Optimal capacitor placement on radial distribution systems. IEEE Trans Power deliv 4(1):725–734
Acharya N, Mahat P, Mithulananthan N (2006) An analytical approach for DG allocation in primary distribution network. Int J Electr Power Energy Syst 28:669–678
Shukla T, Singh S, Srinivasaraob V, Naik K (2010) Optimal sizing of distributed generation placed on radial distribution systems. Electr Power Compon Syst 38(3):260–274
Gozel T, Hocaoglu M (2009) An analytical method for the sizing and siting of distributed generators in radial systems. Int J Electr Power Syst Res 79:912–918
Pisica I, Bulac C, Eremia M (2009) Optimal distributed generation location and sizing using genetic algorithms. 15th International conference on intelligent system applications to power systems. ISAP ’09, Curitiba, pp 1–6
Wong LY, Rahim SRA, Sulaiman MH, Aliman O (2010) Distributed generation installation using particle swarm optimization. 4th International conference on power engineering and optimization, 23–24 June 2010, Shah Alam, pp 159–163
Tan W, Hassan M, Majid M, Rahman H (2012) Allocation and sizing of DG using cuckoo search algorithm. IEEE International conference on power and energy, pp 133–138
García J, Mena A (2013) Optimal distributed generation location and size using a modified teaching–learning based optimization algorithm. Int J Electr Power Energy Syst 50:65–75
Abdelaziz A, Hegazy Y, El-Khattam W, Othman M (2015) A multi-objective optimization for sizing and placement of voltage-controlled distributed generation using Supervised Big Bang-Big Crunch method. Electr Power Compon Syst 43(1):105–117
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
The pseudo code of the ALO algorithm is defined as follows:
- Step 1: :
-
Initialize the first population of ants, ant lions randomly, LSFs and DG. Run load flow and calculate the fitness of ants and ant lions.
- Step 2: :
-
Find the best ant lions and assume it as the elite.
- Step 3: :
-
For each ant, select an ant lion using roulette wheel
3.1 Create a random walk and normalize it to keep it inside the search space,
3.2 Update the position of ant,
3.3 Update the values of c and d,
End for
- Step 4: :
-
Run load flow and calculate the fitness of all ants,
- Step 5: :
-
Replace an ant lion with its corresponding ant it if becomes fitter,
- Step 6: :
-
Update elite if an ant lion becomes fitter than the elite,
- Step 7: :
-
Repeat from step 3 until a stopping criteria is satisfied. ALOA parameters: Number of ant lions \(=\) 30, maximum number of iterations \(=\) 500.
Rights and permissions
About this article
Cite this article
Ali, E.S., Abd Elazim, S.M. & Abdelaziz, A.Y. Optimal allocation and sizing of renewable distributed generation using ant lion optimization algorithm. Electr Eng 100, 99–109 (2018). https://doi.org/10.1007/s00202-016-0477-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00202-016-0477-z