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Optimal sizing and sitting of DG with load models using soft computing techniques in practical distribution system

2016; Institution of Engineering and Technology; Volume: 10; Issue: 11 Linguagem: Inglês

10.1049/iet-gtd.2015.1034

1751-8695

Aashish Kumar Bohre, Ganga Agnihotri, Manisha Dubey,

Electric Power System Optimization

IET Generation, Transmission & DistributionVolume 10, Issue 11 p. 2606-2621 ArticleFree Access Optimal sizing and sitting of DG with load models using soft computing techniques in practical distribution system Aashish Kumar Bohre, Corresponding Author Aashish Kumar Bohre aashu371984@gmail.com Electrical Engineering Department, MANIT, Bhopal, IndiaSearch for more papers by this authorGanga Agnihotri, Ganga Agnihotri Electrical Engineering Department, MANIT, Bhopal, IndiaSearch for more papers by this authorManisha Dubey, Manisha Dubey Electrical Engineering Department, MANIT, Bhopal, IndiaSearch for more papers by this author Aashish Kumar Bohre, Corresponding Author Aashish Kumar Bohre aashu371984@gmail.com Electrical Engineering Department, MANIT, Bhopal, IndiaSearch for more papers by this authorGanga Agnihotri, Ganga Agnihotri Electrical Engineering Department, MANIT, Bhopal, IndiaSearch for more papers by this authorManisha Dubey, Manisha Dubey Electrical Engineering Department, MANIT, Bhopal, IndiaSearch for more papers by this author First published: 01 August 2016 https://doi.org/10.1049/iet-gtd.2015.1034Citations: 61AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In the deregulated power market environment, distributed generation (DG) is an effective approach to manage performance, operation and control of the distribution system. Methods available in the literature for DG planning are often not able to simultaneously provide technical and economical benefits. Therefore an effective methodology is developed to improve the technical as well as economical benefits as compared with the existing approaches. This study reports the optimal installation of multi-DG in the standard 33-bus, 69-bus radial distribution systems and 54-bus practical radial distribution system. Several performance evaluation indices such as active and reactive power loss indices, voltage deviation index, reliability index and shift factor indices are used to develop a novel multi-objective function (MOF). A new set of equations is developed for representing different practical load models. A novel MOF has been solved to find optimal sizing and placement of DGs using genetic algorithm and particle swarm optimisation technique. The comparative result analysis is also discussed for both techniques. The result analysis reveals that system losses, energy not supplied, system MVA intakes are reduced, whereas available transfer capability, voltage profile, reliability and cost benefits are improved for the case with-DGs in the distribution system. Nomenclature DG distributed generation PLI active power loss index QLI reactive power loss index VDI voltage deviation or profile index RI reliability index SFI sensitivity factor or shift factor or PTDF indexes Pj, Qj active and reactive power flow of jth bus PDj, QDj active and reactive power demand of jth bus PLj, QLj active and reactive power losses at jth bus Vi, Vj voltage magnitude values at ith and jth buses PDGj, QDGj real and reactive power of DG placed at jth bus λPj, λQj prices of real and reactive powers at bus j. Ik kth branch current Rk, Xk resistance and reactance of kth line Pji real power flow between buses j and i ΔPji change in real power flow between buses j and i SF sensitivity factor PTDF power transfer distribution factor ENS energy not supplied Ikp peak load branch current Vrated rated voltage of system α load factor β loss factor d repair duration λk failure rate R reliability PD power demand Csubstation substation power supply cost Cdg DG power supply cost PLDG active power loss with DG of system PLNo−DG active power loss with-out DG of system QLDG reactive power loss with DG QLNo−DG reactive power loss with-out DG N total number of buses Vreff reference voltage of the system VDGj system voltage value with-DG Xinj amount of power injection at bus Δx change in power amount 1 Introduction In the distribution system network, several ways are available to maintain performance, operation, economy and reliability of the distribution system such as network reconfiguration, placement of distributed generations (DGs) and placement of capacitors and so on. The genetic algorithm (GA)-based optimisation technique is presented in [1–3] and the standard or conventional particle swarm optimisation (PSO)-based optimisation approach is proposed in [4–6]. The concept of the butterfly- PSO technique is given by Bohre et al. in [6, 7]. The power flow and optimal power flow problems are solved with the Matpower tool, which is described in [8]. The basic concepts related to DG technology are described in [9]. The performance-based multi-objective function (MOF) approach for optimal DG planning in distribution systems with load models using GA and PSO have implemented in [10, 11]. Ochoa et al. [12] analysed several performance indices for MOF approach in distribution networks with different power factor (PF) of DG. The location and sizing of different types of DGs using PSO in the primary distribution system to enhance the loadability is proposed in [13]. The analytical methods for allocation of different types of multi-DGs in primary distribution networks are investigated in [14, 15]. A co-ordinated local control approach that allows distribution system operator and independent power producers to obtain benefits is presented in [16]. The method for optimal planning of radial distribution networks on the basis of combining the steepest descent and the simulated annealing approach is investigated in [17]. The direct solution method to find the radial paths existing in a distribution system and the cost calculation associated with the paths has given in [18]. A new concept for the network reconfiguration problem considering the DG is introduced in [19]. The effects of load models for DG planning in the distribution system are investigated in [20]. The exhaustive load flow method to find optimal size, location and PF of four types of DG units to achieve higher loss reduction is described in [21]. The mitigation of power loss by installing DGs in distribution system using PSO is proposed in [22]. The MOF formulation for sizing and siting of DG into an existing distribution system is proposed in [23]. A methodology to allocate the active and reactive powers cost of the generators is analysed in [24]. The reliability of future distribution systems and impacts of conventional and renewable DGs are introduced in [25]. The reliability model for distribution system planning studies in the new competitive environment to determine the DG facility is proposed in [26]. The concept of segments for reliability studies in distribution system with DG placement is reported in [27]. Mitra et al. [28] and Patra et al. [29] have introduced concept of reliability in terms of expected energy not supplied (ENS) also defined energy index of reliability. The calculation of available transfer capability (ATC) for a transmission system with the new set of distribution factors is reported in [30–32]. The different load models such as constant, industrial, residential, commercial and mixed loads are explained in [33–36]. The optimal location and size of DG in the distribution network providing with a comparison of various methods are presented in [37]. The differential evolution algorithm for finding the optimal planning of various models of DG units is performed in [38]. An analytical approach for optimal sizing and siting of DG in radial distribution system to minimise the power losses is introduced in [39]. The optimisation problem for optimal placement and size of DGs using bat algorithm is proposed in [40]. The integration of dispatchable and non-dispatchable type of DG units to minimise annual losses is reported in [41]. This paper is organised with seven different sections as follows: in Section 1, introduction of the optimal installation of DGs using various techniques are described. Section 2 gives the different type of DG models. The modelling of different type of load models is described in Section 3. Section 4 includes the detailed description of the proposed methodology. The soft computing techniques used in this work are explained in Section 5. The results and discussions are reported in Section 6. Finally, conclusions are drawn in Section 7. 2 Distributed generation The electric power generation units placed near to the load and connected directly to the distribution networks is defined as DG. On the basis of the power delivering capability, the classification of DG majorly of four types [13, 14] based on their real and reactive power delivering capabilities are as [21] Type-1: DG delivers only active power at unity PF of DG (PFDG = 1). Examples include photovoltaic, micro-turbines, and fuel cells and so on. Type-2: DG delivers only reactive power at zero PF of DG (PFDG = 0). Examples include synchronous compensators such as gas turbine. Type-3: DG delivers active power but consumes or absorbs reactive power (Q is negative) at PF range between 0 and 1 (i.e. 0 < PFDG < 1). For example induction generator (wind farm). Type-4: DG delivers both active and reactive powers at PF range between 0 and 1 (i.e. 0 < PFDG < 1). Examples include synchronous generators or synchronous machine (cogeneration, gas turbine, etc.). When DG is installed at optimal location then power factor (PFDG) of DG is considered as an optimal PF (OPFDG) which is given by the following equation (1)where PDG and QDG are active and reactive powers of DG, respectively. Different types of DGs consider the dispatchable, non-dispatchable or combinations of both with DG operation at OPF are optimally placed. The dispatchable and non-dispatchable generation are categorised on the basis of energy delivering capability. If output power can be controlled by varying the fuel consumption rate automatically, then DG units are considered as dispatchable such as small hydro power plants and biomass-based gas turbines and so on otherwise, DG units are considered as a non-dispatchable such as solar and wind generation (which totally depends on weather conditions) [41]. 3 Load models In the practical situation, loads are not explicitly residential, industrial and commercial; rather, load class mix may be seen by distribution system depending on the nature of area being supplied. Thus, a load model mix of residential, industrial and commercial load has also been investigated [10, 11, 20]. Practical voltage dependent load models, i.e. residential, industrial and commercial, given in [10, 11] have been adopted for investigations. The newly developed mathematical expression for practical and various type load models [33–36] in the system is given by the following equation (2) (3)where PDi and QDi are real and reactive power demand or load at bus i, PDoi and QDoi are the active and reactive demand operating points at bus i, Vo is the operating point voltage, Vi is the voltage at bus i and α and β are the active and reactive power exponents for constant, industrial, residential and commercial load models with subscript o, i, r and c, respectively. Table 1 gives the exponent value of the load models. The value of the active power weight coefficients a1, b1, c1, d1 and the reactive power weight coefficient a2, b2, c2, d2 are selected on the basis of weight of active and reactive power consumption of particular load or demand. The different type and mixed practical load model based on (2) and (3) can be given as: Load type-1: constant load: a1 = 1, b1 = 0, c1 = 0, d1 = 0 and a2 = 1, b2 = 0, c2 = 0, d2 = 0. Load type-2: industrial load: a1 = 0, b1 = 1, c1 = 0, d1 = 0 and a2 = 0, b2 = 1, c2 = 0, d2 = 0. Load type-3: residential load: a1 = 0, b1 = 0, c1 = 1, d1 = 0 and a2 = 0, b2 = 0, c2 = 1, d2 = 0. Load type-4: commercial load: a1 = 0, b1 = 0, c1 = 0, d1 = 1 and a2 = 0, b2 = 0, c2 = 0, d2 = 1. Load type-5: mixed or practical load: a1 = ta1, b1 = ta2, c1 = ta3, d1 = ta4 and a2 = tr1, b2 = tr2, c2 = tr3, d2 = tr4. Also, for the practical mixed load models ta1 + ta2 + ta3 + ta4 = 1, and tr1 + tr2 + tr3 + tr4 = 1. Table 1. Exponent values for load models Load type Exponents Load type Exponents constant load αo βo residential load αr βr 0 0 0.92 4.04 industrial load αi βi commercial load αc βc 0.18 6 1.51 3.4 The mixed practical load model for 33-bus and 69-bus radial distribution systems assumes that the system consists with industrial, residential and commercial load models only. As there is no constant loads, a1 and a2 get weight equal to 0. Let us assume that the industrial load demands or consumes 45% active and reactive powers of the total load demand, hence b1 and b2 get weight equals to 0.45 and 0.45, respectively. The residential load demands 40% active and reactive powers of the total load demand, hence c1 and c2 get weight equals to 0.4 and 0.4, respectively. The commercial load demands 15% active and reactive powers of the total load demand, hence d1 and d2 get weight equals to 0.15 and 0.15, respectively. The actual (mixed) load model is used for 54-bus practical radial system, no separate assumptions are considered in this case. 4 Proposed methodology 4.1 MOF-based problem formulation This part introduces the MOF-based problem formulation for optimal positioning and sizing of multi-DG uses GA and PSO techniques in different test system with MOF explained as (4)where k1, k2, k3, k4 and k5 are the indices weight factors and PLI, QLI, VDI, RI and SFI are active power loss, reactive power loss, voltage deviation or profile, reliability and sensitivity or shift factor indexes of system, respectively. The multi-DG approach considers the installation of three-DG in the test systems. The detailed concepts for selecting the weight factor of the indices are given in [10–12]. All these weight factors are decided on the basis of the individual impacts and importance of the particular index while installing the DG. The main aim is to minimise the overall power losses of the system, so the active PLI gets the highest weight of 0.38, after that QLI gets second highest weight of 0.25. The VDI gets a weight of 0.15, to maintain the power quality and voltage profile of the system. The RI indicates the reliability of the system hence it gets a weight of 0.12. The SFI decides the change in power at other buses due to particular injection of the DG size at the bus; hence it gets a weight of 0.10. 4.2 System parameter calculations Active power losses (PL) (5) Reactive power losses (QL) (6)where Ik is the branch current, Rk is the resistance, Xk is the reactance of kth branch or line. ATC of line at base case, between buses j and i using line flow limit criterion have been calculated using AC-power transfer distribution factors (PTDFs) as [31, 32] (7) is the MW power flow limit of a line between buses-j and -i, is the base case power flow in the line between buses-j and -i, are the power transfer distribution factors for the line between buses-j and -i, when an injection or transaction is taking place between bus/zone, Nbr is the total number of branches or lines. The ENS to the customers can be given as [17] (8)where Ikp is the peak load branch current, Rk is the resistance, Xk is the reactance, λk is the failure rate for kth branch or line and Vrated is the rated voltage of the system. The α and d are the load factor and repair duration, respectively. The reliability of the system is given as (9)where R is the reliability, ENS is the energy not supplied and PD is the total power demand. The capital recovery fixed cost (Cfix) of system is (10) The cost for energy not delivered or supply is (11) The cost of energy losses is (12)where β = 0.15α + 0.85α2, Nbr is the total number of branches or lines, Ik is branch current, Rk is the resistance for kth branch or line, ck is the cost of branch k of the main feeder, g is the yearly recovery rate of fixed cost, α is the load factor and β is the loss factor. Substation power supply cost is (13) (14) Distributed generator (DG) power supply cost is (15)where csubstation is the substation power supply cost ($/kVA), and cdg is the distributed generator (DG) power supply cost ($/kVA). 4.3 Evaluation of system performance indices The active power loss index (PLI) can be expressed by the following equation (16) The reactive power loss index (QLI) given by the following equation (17) This voltage deviation index (VDI) is given as (18)where n is the total no. of buses. The Vreff and VDGj are the reference voltage and the system voltage value with DG, respectively. The installation of DG with particular size will inject some power say xinj at bus and due to this injection the change in power is Δx, then SFI can be given as (19) The RI of the system is given by the following equation (20)where ENSDG is energy not supplied (ENS) with-DG and ENSNo−DG is ENS without-DG condition. 5 Soft computing techniques for optimal planning of DG The soft computing techniques used for the planning of DG in this work are GA and PSO which can be explained below. 5.1 Genetic algorithm The basic concept behind GA (by Holland in 1975 [1, 2]) optimisation is the ‘survival of the fittest’. The optimisation process of GA solution includes only one strong solution because they can survive and the weak one cannot survive in the process. The GA has the capacity to develop an initial population associated with probable optimum solutions. After that, GA recombines these individuals in such a way to steer their particular search towards the most favourable results in search space. The possible result is encoded to be a string or chromosome, as well as every chromosome is actually provided with a way of measuring fitness by using a fitness function or objective function. The particular fitness of a chromosome decides their capability to survive, as well as generate the new offspring. The GA maintains finite population of chromosomes throughout the process. The GA utilises probabilistic principles in order to develop the population in the progressive generations from one to another. The new solutions in the progressive generations are developed by recombination operators of GA. These operators are selection or reproduction, crossover and mutation operators. The crossover operator combines the ‘fittest’ chromosome which contributes in the next generation as superior genes. The mutation makes sure that the whole search space will probably be searched in a particular time, due to which the populations will be free from the occurrences of local minima. The important parameters used in genetics algorithm are: population size, evaluation of fitness function, crossover methodology and mutation rate. The process flowchart to find optimal location and sizing of DGs in the different test systems using GA is represented in Fig. 1. In this flowchart, the Pdg, Qdg and Ldg represent active power, reactive power and location of DG, which are converted and represented in populations. The general steps for the GA are given as [2, 3]. Step1: Generate an initial population of string or chromosome. Step2: Calculate fitness value of each member of population based on the problem type (minimisation or maximisation). Step3: Generate offspring string through reproduction, crossover and mutation and then evaluate. Step4: Calculate fitness value for each string. Step5: Check for convergence if required solution is obtained or number of generation is attained. Fig. 1Open in figure viewerPowerPoint Flowchart to find optimal location and sizing of DG using GA 5.2 PSO technique The PSO was first proposed by Kennedy and Eberhart in 1995 [5]. The PSO is a well-known optimisation algorithm based on population [5, 6]. Throughout the PSO, every particle within the search space follows a particular velocity and inertia with the related generations. The speed and direction of the velocity are adjusted based on the particle's previous best experience (self) and the historical best experience in its neighbourhood (social). So, the particle has a tendency to fly towards a promising area in the search space. The PSO includes each individual flies in the entire search space with a particular velocity which is updated according to its self-flying experience and its companions flying experience [4–6]. Fig. 2 shows the PSO algorithm process flowchart. The PSO optimisation process initialises the random population of particles and updates their particles position based on the personal and neighbours best experiences [6]. The updated value of the population depends on the updated values of the velocity in each generation (or iteration). The particle's population in the next iteration updates by summation of previous iteration population and the current iteration velocity. Let us assume total N populations (i = 1, 2, 3….N) and respective velocities. Consider vk and xk are the velocity and population, respectively, for kth iteration and also vk−1 and xk−1 velocity and population, respectively, for previous iteration. The equations for updated values of velocity and population for kth iteration are given as [3–6] (21) (22)where N is the number of swarm, k is the kth iteration number, w is the inertia weight, rl and r2 are the random numbers between 0 and 1, respectively, and c1 and c2 are the velocity coefficients, which are positive constant numbers [3, 5]. The process flowchart to find optimal location and sizing of DGs in the different test systems using PSO is given in Fig. 2. In this flowchart, the Pdg, Qdg and Ldg represent active power, reactive power and location of DG, respectively, which are converted and represented in swarm positions. Fig. 2Open in figure viewerPowerPoint Flowchart to find optimal location and sizing of DG using PSO 6 Results and discussions The multi-DG installation with MOF is presented in this work using different optimisation techniques. The type of DG and its PF is decided based on the optimal DG location requirement in particular system. All the results for the proposed methodology are carried out with MATLAB (2009a)/Matpower 4.1 tool with the system configuration windows-8.1, AMD-E1-1500APU, 1.48 GHz and 2.0 GB RAM. The population or swarm size and iterations are 30 and 50, respectively, for this work. 6.1 33-Bus radial distribution system The 33-bus radial distribution test system with total real and reactive power loads 3.72 MW and 2.30 MVAr, respectively, which is used in this section and the load and branch data of 33-bus system is given in [13, 15]. The results for optimal planning of multi-DG with different load models in the 33-bus radial system by using soft computing techniques such as GA and PSO are given in Tables 2–9 and Figs. 3–6. Table 2. MOF and indices for 33-bus radial system with multi-DG Load type Fitness (MOF) PLI QLI VDI RI SFI Optimal technology constant load 0.1639 0.0768 0.0901 0.0117 0.081 1.0068 PSO 0.1872 0.1061 0.1234 0.0122 0.0819 1.0439 GA industrial load 0.1727 0.0891 0.1101 0.0079 0.0395 1.0537 PSO 0.1998 0.121 0.1453 0.0118 0.0963 1.0413 GA residential load 0.1758 0.0974 0.1217 0.0059 0.0352 1.0324 PSO 0.1990 0.1112 0.1362 0.0127 0.1715 1.0024 GA commercial load 0.1953 0.133 0.1601 0.0062 0.0139 1.0212 PSO 0.2046 0.132 0.1554 0.0128 0.0888 1.0303 GA mixed load 0.1732 0.0947 0.118 0.0058 0.0308 1.031 PSO 0.1983 0.1201 0.1443 0.0121 0.0972 1.0312 GA Table 3. DG size and locations for 33-bus radial system with multi-DG Load type DG-1 DG-2 DG-3 Optimal bus location DG type Optimal technology P, MW Q, MVAR P, MW Q, MVAR P, MW Q, MVAR constant load 1.0823 1.1503 0.6476 0.2458 0.6478 0.6004 30, 15, 25 all type-4 PSO 1.4879 0.9880 0.9464 1.0982 0.4330 1.0573 3, 13, 30 all type-4 GA industrial load 1.1860 0.6596 0.9305 0.8473 0.8106 0.5738 24, 30, 14 all type-4 PSO 1.6667 1.1265 0.9784 1.1594 0.8124 0.3285 3, 30, 14 all type-4 GA residential load 1.2459 0.8901 0.6281 0.5974 1.0709 0.5816 30, 14, 24 all type-4 PSO 1.7462 0.8063 0.9706 0.9862 0.6940 0.3643 3, 30, 14 all type-4 GA commercial load 0.6710 0.3708 1.1473 0.9133 1.3156 1.3662 14, 30, 24 all type-4 PSO 1.1962 1.4069 1.0789 1.0004 0.7399 0.4308 3, 30, 14 all type-4 GA mixed load 0.7057 0.3951 0.9841 1.2087 1.5201 0.4490 14, 30, 24 all type-4 PSO 1.0289 1.0509 1.5634 1.1935 0.7401 0.4107 30, 3, 14 all type-4 GA Table 4. Active and reactive power losses for 33-bus radial system with multi-DG Load type Losses No-DG DG-PSO DG-GA constant load PL, MW 0.2027 0.0156 0.0215 QL, MVAR 0.1352 0.0122 0.0167 loss reduction, % PL – 92.30 89.39 QL – 90.98 87.65 industrial load PL, MW 0.1617 0.0144 0.0196 QL, MVAR 0.1075 0.0118 0.0156 loss reduction, % PL – 91.10 87.88 QL – 89.02 85.49 residential load PL, MW 0.1594 0.0155 0.0177 QL, MVAR 0.1059 0.0129 0.0144 loss reduction, % PL – 90.28 88.90 QL – 87.82 86.40 commercial load PL, MW 0.155 0.0204 0.0206 QL, MVAR 0.1029 0.016 0.0165 loss reduction, % PL – 86.84 86.71 QL – 84.45 83.96 mixed load PL, MW 0.1595 0.0151 0.0192 QL, MVAR 0.106 0.0125 0.0153 loss reduction, % PL – 90.53 87.96 QL – 88.21 85.57 Table 5. Energy not supplied (ENS) and reliability of 33-bus radial system with multi-DG Load type Parameters No-DG DG-PSO DG-GA constant load ENS, MW 0.1251 0.0101 0.0103 reliability 0.9663 (96.63%) 0.9973 (99.73%) 0.9972 (99.72%) industrial load ENS, MW 0.1044 0.0041 0.0101 reliability 0.9717 (97.17%) 0.9988 (99.88%) 0.9973 (99.73%) residential load ENS, MW 0.1071 0.0038 0.0184 reliability 0.97 (97.0%) 0.9989 (99.89%) 0.9948 (99.48%) commercial load ENS, MW 0.1071 0.0052 0.0095 reliability 0.9692 (96.92%) 0.9985 (99.85%) 0.9973 (99.73%) mixed load ENS, MW 0.1058 0.0033 0.0103 reliability 0.9706 (97.06%) 0.9991 (99.91%) 0.9971 (99.71%) Table 6. Fix, loss, ENS total and benefit cost of 33-bus radial system with multi-DG Load type Cost, $ No-DG DG-PSO DG-GA constant load fix 41465.38 41465.38 41465.38 loss 70321.53 5402.97 7461.08 ENS 500.58 40.57 41.01 total 112287.49 46908.92 48967.47 system cost benefit – 65378.57 63320.02 benefit, % – 58.23 56.39 industrial load fix 41465.38 41465.38 41465.38 loss 56101.12 4996.63 6789.36 ENS 417.53 16.48 40.23 total 97984.03 46478.49 48294.97 system cost benefit – 51505.54 49689.06 benefit, % – 52.57% 50.71% residential load fix 41465.38 41465.38 41465.38 loss 55280.58 5387.07 6148.82 ENS 428.31 15.09 73.47 total 97174.27 46867.54 47687.67 system cost benefit – 50306.73 49,486.6 benefit, % – 51.77% 50.93% commercial load fix 41465.38 41465.38 41465.38 loss 53753.37 7093.22 7150.26 ENS 428.48 20.86 38.05 total 95647.23 48579.46 48653.69 system cost benefit – 47067.77 46993.54 benefit, % – 49.21 49.13 mixed load fix 41465.38 41465.38 41465.38 loss 55319.01 5235.96 6644.47 ENS 423.39 13.05 41.17 total 97207.78 46714.39 48151.02 system cost benefit – 50493.39 49056.76 benefit, % – 51.94 50.47 Table 7. DGs, substation, total and benefits costs of power for 33-bus radial system with multi-DG Cost, $ No-DG DG-PSO DG-GA substation power 288908.09 86901.49 25485.30 DG1 0 94763.17 110956.67 DG2 0 41559.48 64719.84 DG3 0 52996.53 85137.37 Total 288908.09 276220.67 286299.17 generation cost benefit – 12687.42 2608.92 Benefit, % – 4.39 0.91 Table 8. System MVA intake with different cases for 33-bus radial system with multi-DG Parameter No-DG DG-PSO DG-GA MVAsys 4.710 4.389 4.3964 Table 9. ATC with different cases for 33-bus radial system with multi-DG Branch No. ATC No-DG ATC DG-PSO ATC DG-GA 1 0.7835 3.0958 2.958 2 0.6889 2.9904 2.904 3 0.4726 2.395 2.35 4 0.4446 2.3476 2.2476 5 0.4289 2.3134 2.3134 6 0.2191 0.9269 0.919 7 0.1787 0.8848 0.8548 8 0.1377 0.8392 0.812 9 0.1249 0.8225 0.815 10 0.1122 0.8066 0.7807 11 0.103 0.797 0.787 12 0.0909 0.7843 0.7743 13 0.0783 0.7705 0.7505 14 0.0542 0.0543 0.0553 15 0.0421 0.0422 0.0422 16 0.0301 0.0301 0.0301 17 0.018 0.018 0.018 18 0.0722 0.0722 0.0722 19 0.0542 0.0542 0.0542 20 0.036 0.036 0.036 21 0.018 0.018 0.018 22 0.1879 0.5193 0.503 23 0.1693 0.4987 0.487 24 0.0843 0.4106 0.406 25 0.1902 1.329 1.29 26 0.1776 1.3139 1.139 27 0.165 1.298 1.198 28 0.1507 1.2732 1.1732 29 0.1251 1.2406 1.206 30 0.0844 0.0846 0.0846 31 0.054 0.0541 0.0541 32 0.012 0.012 0.012