Distributed generation (DG) is small generating plants which are connected to consumers in distribution systems to improve the voltage profile, voltage regulation, stability, reduction in power losses and economic benefits. The above benefits can be achieved by optimal placement of DGs. A novel nature-inspired algorithm called Dragonfly algorithm is used to determine the optimal DG units size in this paper. It has been developed based on the peculiar behavior of dragonflies in nature. This algorithm mainly focused on the dragonflies how they look for food or away from enemies. The proposed algorithm is tested on IEEE 15, 33 and 69 test systems. The results obtained by the proposed algorithm are compared with other evolutionary algorithms. When compared with other algorithms the Dragonfly algorithm gives best results. Best results are obtained from type III DG unit operating at 0.9 pf. Keywords: Dragonfly algorithm, Loss sensitivity factor method, Distributed generation placement, Radial distribution system, Loss reduction typically situated in remote areas, requiring the opera- Introduction tion systems that are fully integrated into transmission Interconnection of generating, transmitting and distribu- and distribution network. The aim of the DG is to inte - tion systems usually called as electric power system. Usu- grate all generation plants to reduce the loss, cost and ally distribution systems are radial in nature and power greenhouse gas emission. The main reason for using DG flow is unidirectional. Due to ever growing demand units in power system is technical and economic benefits modern distribution networks are facing several prob- that have been presented as follows. Some of the major lems. With the installation of different distributed power advantages are (Reddy et al. 2016, 2017c) sources like distributed generations, capacitor banks etc, several techniques have been proposed in the literature for the placement of DGs. Most of the losses about 70% • Reduced system losses losses are occurring at distribution level which includes • Voltage profile improvement primary and secondary distribution system, while 30% • Frequency improvement losses occurred in transmission level. Therefore, distribu - • Reduced emissions of pollutants tion systems are main concern nowadays. The losses tar - • Increased overall energy efficiency geted at distribution level are about 7.5%. • Enhanced system reliability and security By installing DG units at appropriate positions, the • Improved power quality losses can be minimized. Photovoltaic (PV) energy, wind • Relieved Transmission & Distribution congestion turbines, and other distributed generation plants are Some of the major economic benefits *Correspondence: firstname.lastname@example.org • Deferred investments for upgrades of facilities Department of EEE, S V College of Engineering, Tirupati, Andhra Pradesh, • Reduced fuel costs due to increased overall efficiency India Full list of author information is available at the end of the article © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Suresh and Belwin Renewables (2018) 5:4 Page 2 of 8 • Reduced reserve requirements and the associated for sizing of DGs. In most of the studies economic analy- costs sis has not been taken. • Increased security for critical loads. A novel nature-inspired algorithm called Dragon- fly algorithm is used to find the optimal DG size in this paper. The optimal size of DGs at different power factors Different types of distributed generations and their defi - are determined by DA algorithm to reduce the power nitions have been discussed in Ackermann et al. (2001). losses in the distribution system as much as possible and An analytical approach was proposed by Acharya et al. enhancing the voltage profile of the system. The eco - (2006) and Hung et al. (2010) with out taking voltage nomic analysis of DG placement is also considered in this constraint. The uncertainties in operation including paper. varying load, network configuration and voltage control devices have been considered in Su (2010). Sensitivity- Problem formulation based simultaneous optimal placement of capacitors and Objective function DG was proposed in Naik et al. (2013). In this paper ana- In distribution system more losses are there due to low lytical approach is used for sizing. voltage compared to transmission system. Copper losses Abu-Mouti and El-Hawary (2010) proposed ABC to predominant in distribution system, this can be calcu- find the optimal allocation and sizing of distributed gen - lated as follows eration. Distributed generation uncertainties (Zangiabadi et al. 2011) have been taken in account for the placement of DG. P = I R loss i i (1) Alonso et al. (2012), Rahim et al. (2012), Doagou- Mojarrad et al. (2013) and Hosseini et al. (2013) proposed where I is current, R is resistance and n is number of evolutionary algorithms for the placement of distributed i i buses. Objective taken in this paper is real power loss generation. Nekooei et al. (2013) proposed Harmony minimization. Search algorithm with multi-objective placement of DGs. A novel combined hybrid method GA/PSO is pre- Constraints sented in Moradi and Abedini (2011) for DG placement. The constraints are With unappropriated DG placement, can increase the system losses with lower voltage profile. The proper size of DG gives the positive benefits in the distribution sys - • Voltage constraints tems. Voltage profile improvement, loss reduction, dis - 0.95 ≤ V ≤ 1.05 i (2) tribution capacity increase and reliability improvements are some of the benefits of system with DG placement • Power balance constraints (Rahim et al. 2013; Ameli et al. 2014). Embedded Meta Evolutionary-Firefly Algorithm P + P = P + P DG d loss (3) (EMEFA) was proposed in Rahim et al. (2013) for DG k=1 allocation. Here how losses are varied with popula- tion size are considered. Simultaneous placement of • Upper and lower limits of DG DGs and capacitors with reconfiguration was proposed by Esmaeilian and Fadaeinedjad (2015) and Golshan- 60 ≤ P ≤ 3500 DG (4) navaz (2014). Dynamic load conditions have been taken in Gampa and Das (2015). Big bang big crunch method where the limits are in kW, kVAr and kVA for Type I, II was implemented for the placement of DG in Hegazy and III DG, respectively. et al. (2014). Murty and Kumar (2014) uses mesh distri- bution system analysis for the placement of distributed Loss sensitivity factors method generation with time varying load model. Probabilistic Optimal locations for DG placement are identified based approach with DG penetration was discussed in Kolenc on the losses at the nodes and their sensitivity after com- et al. (2015). The backtracking search optimization algo - pensation using the loss sensitivity factors method. Real rithm (BSOA) was used in DS planning with multi-type and reactive power losses are calculated at all the buses DGs in El-Fergany (2015), BSOA was proposed for DG and then the locations corresponding to the bus which placement with various load models. has the highest loss is selected as the best location for Reddy et al. (2017a) and Reddy et al. (2017b) proposed DG placement. The buses with high losses give maxi - whale optimization and Ant Lion optimization algorithm mum loss reduction when DG are placed in the distribu- tion system. Loss sensitivity is referred to as the change Suresh and Belwin Renewables (2018) 5:4 Page 3 of 8 in losses corresponding to the compensation provided by placing the DGs. Loss sensitivity factors (LSF) deter- mine the best locations for DG placement. These factors reduce the search space by finding the few best locations which saves the cost of the DGs in optimizing the losses in the system as a whole. Consider a line with impedance Fig. 1 A distribution line with connected load (R + jX) between buses i and j and a load in the distribu- tion system as shown in Fig. 1. Real power loss in the kth line considered in Fig. 1 is given by [I ]×[R ] and can also be expressed as follows power delivering capacity is enhanced. The value 1.01 is 2 2 selected as the maximum value of the normalized voltage (P (j) + Q (j)) × R PL(j) = (5) at the buses where compensation is required. V (j) Similarly reactive power loss in the kth line is given by Algorithm [I ]×[X ] and can also be expressed as follows The algorithm to find the optimal locations for DG place - 2 2 ment using LSF is explained in detail in the following (P (j) + Q (j)) × X QL(j) = (6) steps V (j) where I is the current flowing through k line; R and k th k Step 1 Re ad line and load data of the system and X are the resistance and reactance of the kth line; V[j] solve the feeder line flow for the system using is the voltage at the bus j; P[j] = Net Active power sup- the branch current load flow method. plied beyond the bus j; Q[j] = Net Reactive power sup- Step 2 C alculate the real and reactive power losses plied beyond the bus j. using Eqs. (5) and (6). After finding the real and reactive power losses for all Step 3 F ind the loss sensitivity factors using Eq. (7). the buses, the loss sensitivity factors can be calculated Step 4 S tore the buses with loss sensitivity fac- using the following equations. tors arranged in decreasing order in a vector ∂PL (2 × Q(j)) × R k according to their positions. (7) ∂Q V (j) Step 5 Nor malize the magnitudes of the voltages for all the buses using Eq. (9). ∂QL (2 × Q(j)) × X Step 6 S elect the buses with normalized voltage mag- (8) ∂Q V (j) nitudes less than 1.01 as the best suitable loca- tions for DG placement. Identification of optimal locations using loss sensitivity factors LSF method is applied to 15-bus, 33-bus and 69-bus The loss sensitivity factors for all the buses from load IEEE systems and the locations are given in the tables flows are calculated using Eq. (7) and the buses are stored below (Tables 1, 2, 3). in a vector according to their positions such that these 15-bus system factors are arranged in the decreasing order. Voltage From above table first best location for DG placement magnitudes are normalized by assuming the minimum is 6. voltage value as 0.95 at these buses using the following 33-bus system equation From above table first best location for DG placement | V (i) | is 6. Vnorm[i]= (9) 0.95 69-bus system From above table first best location for DG placement where V[i] is the base voltage at the ith bus. The opti - is 61. mal locations for DG placement are determined based on the normalized voltage magnitudes and the loss sen- The Dragonfly algorithm (DA) sitivity factors calculated as described above, the former The DA algorithm was proposed by Mirjalili (2015). It decides the requirement of compensation and the latter has been developed based on swarm intelligence and the gives the order of priority. The buses with Vnorm ≤ 1.01 peculiar behavior of dragonflies in nature. This algorithm are selected as the best suitable locations for the place- mainly focused on the dragonflies how they look for food ment of DGs in order to reduce the real power losses and or away from enemies. improve the voltage profile simultaneously so that the Suresh and Belwin Renewables (2018) 5:4 Page 4 of 8 Table 1 Loss sensitivity factors for 15-bus system The mathematical model of DA algorithm can be mod - eled with the following five behaviors of dragonflies. ∂PL Bus number VNorm[i] Base voltage V[i] ∂Q (decreasing) Separation In the static swarm no collision is there between any dragonflies. The mathematical model S of 2966.2 2 1.0224 0.9713 th the i individual is given by 1643.7 6 1.0087 0.9582 1548.5 3 1.0070 0.9567 852.6 11 1.0000 0.9500 S =− X − X i k (10) 618.2 4 1.0010 0.9509 k=1 526.6 12 0.9956 0.9458 Here 413.4 9 1.0189 0.9680 314.1 15 0.9984 0.9484 Position of current dragonflies is represented by X 292.6 14 0.9985 0.9486 th X represents position of k neighboring dragonflies 281.1 7 1.0063 0.9560 N is the total number of neighboring dragonflies 167.8 13 0.9942 0.9445 161.3 8 1.0073 0.9570 Alignment Individual dragonflies velocities will match 134.2 10 1.0178 0.9669 with the other in same neighborhood. This can be mod - 125.6 5 0.9999 0.9499 eled as k=1 (11) A = Table 2 Loss sensitivity factors for 33-bus system th ∂PL where V is the velocity of the k neighboring individuals Bus number VNorm[i] Base voltage V[i] ∂Q (decreasing) Cohesion All the dragonflies will move toward the cen - 1678 6 0.9995 0.9495 tre of mass of the neighborhood. This can be modeled as 1365 28 0.9827 0.9335 k=1 1325 3 1.035 0.9829 (12) C = − X Food For survival all the dragonflies will move toward the food. The attraction for food can be modeled as Table 3 Loss sensitivity factors for 69-bus system ∂PL Bus number VNorm[i] Base voltage V[i] F = X − X i F (13) ∂Q (decreasing) where X is the position of food location. 2664.8 57 0.9896 0.9401 Enemy All the dragonflies will move away from an 1344.9 58 0.9779 0.9290 enemy. To move away from the enemy located at a posi- 935.7 7 1.0324 0.9808 tion X can be modeled as 882.9 6 1.0422 0.9901 848.3 61 0.9604 0.9123 E = X + X i E (14) 635.0 60 0.9681 0.9197 All the above five motions will influence the behavior of 571.8 10 1.0236 0.9724 dragonflies in the swarm. The new position update of 526.9 59 0.9734 0.9248 dragonflies can be obtained with the following step func - 456.8 55 1.0178 0.9669 tion ∆X which is modeled as i+1 449.7 56 1.0132 0.9626 ∆X = (sS + aA + cC + fF + eE ) + w∆X i+1 i i i i i i (15) where separation, alignment, cohesion weights, food, The static behavior of dragonflies, i.e, looking for food enemy factors and inertia factor are represented by s, a, c, can be treated as exploitation phase and evade from f, e and w, respectively enemies can be treated as exploration phase. The static With the above step function the new position of X i+1 swarm dragonflies consist of small group of dragonflies is given by which are hunting the preys in small space. The direc - X = X + ∆X i+1 i i+1 (16) tion and velocity of this dragonflies are small and abrupt changes will be there in the direction. Dynamic swarm The best and worst solutions are taken from food source with constant direction and more number of different and enemy. If there is no neighboring solution, DA can be dragonflies moves to another place over a long distance. Suresh and Belwin Renewables (2018) 5:4 Page 5 of 8 modeled through random walk. New position of dragon- Cost of energy losses (CL) flies is updated with following equations. The annual cost of energy loss is given by (Murthy and Kumar 2013) X = X + Levy(x) × X i+1 i i r ×σ CL = (TRPL) ∗ (Kp + Ke ∗ Lsf ∗ 8760) $ Levy(x) = 0.01 × (18) |r | where TRPL, total real power losses; Kp, annual demand � � (17) �β Ŵ(1+β)×sin cost of power loss ($/kW); Ke, annual cost of energy � � σ = � � β−1 loss($/kW h); Lsf, loss factor 1+β Ŵ ×β×2 Loss factor is expressed in terms of load factor (Lf ) as where random numbers r ,r ε [0,1] , i is current iteration, below 1 2 d is dimension and β is equal to 1.5. Lsf = k ∗ Lf + (1 − k) ∗ Lf (19) Ŵ(x) = (x − 1)! The values taken for the coefficients in the loss factor cal - Implementation of DA culation are: k = 0.2, Lf = 0.47, Kp = 57.6923 $/kW, Ke = The detailed algorithm is as follows. 0.00961538 $/kWh. Cost component of DG for real and reactive power Step 1 F eeder line flow is solved by branch current load flow method. Step 2 F ind the best DG locations using the index C(Pdg) = a ∗ Pdg + b ∗ Pdg + c $/MWh (20) vector method. Cost coefficients are taken as: Step 3 Initi alize the population/solutions and itmax = 100, Number of DG locations a = 0, b = 20, c = 0.25 d=1,dg = 60, dg = 3500. min max Cost of reactive power supplied by DG is calculated Step 4 G enerate the population of DG sizes ran- based on maximum complex power supplied by DG as domly using equation population = (dg − dg ) × rand() + dg max min min 2 2 C(Qdg) = Cost(Sg max) − Cost Sgmax − Qg ∗ k where dg and dg are minimum and max- min max imum limits of DG sizes. (21) Step 5 D etermine active power loss for generated Pg max population by performing load flow. Sgmax = (22) Step 6 S elect low loss DG as current best solution. cos φ Step 7 U pdate the position of the dragonflies using Pgmax = 1.1*pg, the power factor, has been taken 1 at Eqs. 11–13. unity power factor and 0.9(lag) at lagging power factor to Step 8 D etermine the losses for updated population carry out the analysis. k = 0.05 − 0.1 . In this paper, the by performing load flow. value of factor k is taken as 0.1. Step 9 Re place the current best solution with the updated values if obtained losses are less than IEEE 15‑bus system the current best solution. Otherwise go back The single-line diagram of IEEE 15-bus distribution sys - to step 7 tem (Baran and Wu 1989) is shown in Fig. 2. Table 4 shows the real,reactive power losses and mini- Step 10 If ma ximum number of iterations is reached mum voltages after the placement of different types of then print the results. DGs. The optimal location for 15 bus test system is 6. The minimum voltage is more in case of type III DG operat- ing at 0.9 pf. The losses are also lower with DG type III Results and discussion operating at 0.9 pf when compared to DG operating at DA algorithm in the application of DG planning problem upf in Table 4. This is due to both real and reactive pow - to obtain DG size and economic analysis is presented in ers are supplied by the DG at lagging pf. Reactive power this section. IEEE 15, 33 and 69 bus test systems are eval- is not supplied by type III DG when operating at Unity pf. uated using MATLAB. Hence, losses are higher when compared to DG operat- ing at 0.9 pf lagging. Economic analysis Cost of energy losses, cost of PDG and cost of QDG The mathematical model is given below for cost are also shown in Table 4. From table the cost of energy calculations. Suresh and Belwin Renewables (2018) 5:4 Page 6 of 8 losses is reduced from 4970.3 $ to 2685.3 $ when DG is operating at 0.9pf lag and it reduced to 3684.1 $ when operating at unity pf. Cost of energy losses are less when DG is operating at 0.9pf. Results for 33 bus The single-line diagram of IEEE 33-bus distribution sys - tem (Baran and Wu 1989) is shown in Fig. 3. Without installation of DG, real and reactive power losses are 211 kW and 143 kVAr, respectively. With installation of DG at unity pf, real, reactive power losses are 111.0338 kW and 81.6859 kVAr, respectively. With DG at 0.9 pf lag, real, reactive power losses are 70.8652 kW and 56.7703 kVAr, respectively. The losses obtained are lower when lagging power fac - tor DG is used when compared to unity power factor DG. This is due to reactive power available in lagging power factor DG. Cost of energy losses, cost of PDG and cost of QDG are also shown in Tables 5 and 6. From table the cost Fig. 2 Single-line diagram of 15-bus system of energy losses is reduced from 16,982.57 $ to 5700.1 $ when DG is operating at 0.9pf lag and it reduced to 8930.65 $ when operating at unity pf. Cost of energy losses are less when DG is operating at 0.9pf. Table 4 Results for 15 bus system With out DG With DG at 0.9pf With DG at UPF Results for 69 bus The IEEE 69-bus distribution system with 12.66-kV base DG location – 6 6 voltage (Baran and Wu 1989) is shown in Fig. 4. DG size (kVA) – 907.785 675.248 Without DG real, reactive power losses are 225 kW and TLP (kW ) 61.7933 33.385 45.8035 102.1091 kVAr, respectively. With the installation of DG TLR (kVAR) 57.2969 29.89 41.88 at unity pf, the real and reactive power losses are 83.2261 Vmin (p.u.) 0.9445 0.959 0.9527 kW and 40.5754 kVAr, respectively. With DG at 0.9 pf lag Cost of Energy 4970.3 2685.31 3684.18 losses ($) real, reactive power losses are 27.9636 kW and 16.4979 Cost of PDG ($/ – 16.5404 13.754 kVAr. MW h) The losses obtained are lower when lagging power fac - Cost of QDG ($/ – 1.8656 – tor DG is used when compared to unity power factor DG. MVAR h) This is due to reactive power available in lagging power factor DG. Cost of energy losses, cost of PDG and cost of QDG are also shown in Tables 5 and 6. From table the cost of energy losses is reduced from 18,101.7 $ to 2249.2 $ when DG is operating at 0.9pf lag and it reduced to 6694 $ when operating at unity pf. Cost of energy losses are less when DG is operating at 0.9pf. The results obtained are given in Tables 7, 8. Better results are obtained while considering reactive power of DG when comparison with unity pf. Fig. 3 Single-line diagram of 33-bus system Suresh and Belwin Renewables (2018) 5:4 Page 7 of 8 Table 5 Results for 33 bus system with DG at upf Table 7 Results for 69 bus system with DG at upf Without Voltage sensitivity Proposed Without Voltage sensitivity Proposed DG index method (Murthy method DG index method (Murthy method and Kumar 2013) and Kumar 2013) DG location – 16 6 DG location 65 61 DG size (kW ) – 1000 2590.2 DG size (kW ) 1450 1872.7 Total real power loss 211 136.7533 111.0338 TLP (kW ) 225 112.0217 83.22 ( TLP) (kW ) TLR (kVAR) 102.1091 55.1172 40.57 Total reactive power 143 92.6599 81.6859 Vmin (p.u.) 0.909253 0.9660621 0.9685 ( TLR)loss (kVAR) Cost of energy 18,101.7621 9017.2139 6694 Vmin (p.u.) 0.904 0.9318 0.9424 losses ($) Cost of energy 16,982.5724 11,007.9901 8930.65 Cost of Pdg ($/ – 29.25 37.7 losses ($) MW h) Cost of PDG ($/ 20.25 52.05 MW h) Table 8 Results for 69 bus system with DG at 0.9 pf Table 6 Results for 33 bus system with DG at 0.9 pf With DG With DG Voltage sensitivity Proposed index method (Murthy method Voltage sensitivity Proposed and Kumar 2013) index method (Murthy method and Kumar 2013) DG location 65 61 DG size (kVA) 1750 2217.3 DG location 16 6 TLP (kW ) 65.4502 27.9636 DG size (kVA) 1200 3073.5 TLR (kVAR) 35.625 16.4979 TLP (kW ) 112.7864 70.8652 Vmin (p.u.) 0.969302 0.9728 TLR (kVAR) 77.449 56.7703 Cost of Energy losses ($) 5268.4297 2249.2 Vmin (p.u.) 0.9378 0.9566 Cost of PDG ($/MW h) 31.75 40.1 Cost of Energy losses ($) 9078.7686 5700.01 Cost of QDG ($/MVAR h) 3.083 4.48 Cost of PDG ($/MW h) 21.85 55.5 Cost of QDG ($/MVAR h) 2.1207 6.2 proposed optimization technique has been applied on typical IEEE 15, 33 and 69 bus radial distribution systems with different two types of DGs and compared with other algorithms. Better results have been achieved with com- bination of loss sensitivity factor method and DA algo- rithm when compared with other algorithms. Best results are obtained from type III DG operating at 0.9 pf. Authors’ contributions MCVS: carried out the literature survey, participated in DG location section. MCVS and EJB: participated in study on different nature-inspired algorithm for DG sizing. MCVS: carried out the DG sizing algorithm design and mathemati- cal modeling. MCVS and EJB: participated in the assessment of the study and performed the analysis. MCVS and EJB: participated in the sequence alignment and drafted the manuscript. Both authors read and approved the Fig. 4 Single-line diagram of 69-bus system final manuscript. Author details Department of EEE, S V College of Engineering, Tirupati, Andhra Pradesh, Conclusions India. Department of EEE, School of Electrical Engineering, VIT University, A novel nature-inspired algorithm called Dragonfly algo - Vellore, India. rithm is used to determine the optimal DG units size in Competing interests this paper.It has been developed based on the peculiar The authors declare that they have no competing interests. behavior of dragonflies how they look for food or away Consent for publication from enemies. Reduction in system real power losses Not applicable. with low cost are chosen as objectives in this paper. This Suresh and Belwin Renewables (2018) 5:4 Page 8 of 8 Ethics approval and consent to participate Moradi, M. H., & Abedini, M. (2011). A combination of genetic algorithm and Not applicable. particle swarm optimization for optimal dg location and sizing in distri- bution systems. International Journal of Electrical Power & Energy Systems, 33, 66–74. Publisher’s Note Murthy, V. V. S. N., & Kumar, A. (2013). 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