# Literature Review On Distributed Generation Allocation Engineering Essay

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Distribution system is a component of the system between transmission and end user dedicated to deliver energy to end user. In general, distribution system losses are predominant compared to transmission losses; for example distribution losses vary up to about 75% of the overall system losses in India [137]. Further, poor voltage regulation is the norm usually at peak hours which further aggravates the losses. Causes for these deficiencies are overloading of system elements like transformers, feeders, conductors; ill maintained equipment and substations; ageing transforms etc. [142] It is imperative to cut down the losses and improve voltage profile for general well-being of the society. Even though there is significant scientific development in the field of generation and transmission, distribution was not given due care till recent times. However, significant work is in progress in this area since 2000. Several loss reduction methods such as capacitor placement, network reconductoring, network reconfiguration and load balancing and load management are being used in distribution systems. Employing DG placement results in the highest loss reduction and improved voltage profile apart from improving system reliability and security. Hence in this work DGs are used to reduce losses and the experiments shown significant improvement.

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This section deals with literature review on Distributed Generation, Network Reconfiguration, wind speed modeling and Distributed Generation planning under realistic Load and Generation Scenario. The literature is presented chronologically, chapter wise.

## Literature review on Distributed Generation allocation

In recent years several researchers tried to explore different possibilities for optimal allocation of DG, which are reviewed in this section. Benefits of DG from economical point of view include reduction or avoidance of the need to build new T&D lines and up gradation of existing power lines.

Kim et al. [63] presented an approach based on Hereford ranch algorithm (HRA) to optimally allocate DGs in a meshed network. Proposed algorithm was used to optimally allocated DGs to achieve maximum benefits by minimizing active power losses in the network. Results of this algorithm were compared with those of conventional second order method and genetic algorithm (GA) and the proposed method was found to be superior.

Ackermann [5] provided a general definition for distributed generation in competitive electricity markets. In addition, terms such as distributed resources, DG penetration, distributed capacity and utility were discussed. Connection and network issues of distributed generation were also presented. Technologies available for distributed generation based on fossil fuels as well as renewable energy based were presented in this paper.

Rosehart et al. [90] used a lagrangian based approach to find optimal locations for the installation of DGs. Optimization formulations for determining DG locations based on minimizing clearing/operating costs and enhancing voltage stability were considered in this paper.

Bhowmik et al. [16] formulated analytical methods to predict permissible distributed generation resources on a radial distribution feeder without exceeding voltage harmonic limits. These methods are suitable for typical radial distribution feeders with linearly increasing, linearly decreasing and uniform load patterns.

Greatbanks et al. [51] used both loss sensitivity and voltage sensitivity analysis of power flow equations to identify optimal locations for DG placement.

El-Khattam and Salama [38] reviewed different distributed generation technologies, definitions and their operational constraints. Benefits of distributed generation from economical point of view and operational point of view were discussed in this paper. The authors presented DG classification based on their electrical application, supply duration and power type, DG capacities, generated power type and technology.

Wang and Nehrir [118] presented an analytical method based on phasor current to identify optimal location of DG in both mesh and radial systems for power loss minimization. Since the proposed approach is a non-iterative, there is no convergence problems associated with it. The drawback of this method is that it finds location for a fixed DG size only.

Mithulananthan et al. [73] presented a genetic algorithm based distributed generator placement technique for reducing total power losses in a radial distribution system.

Chiradeja and Ramkumar [30] discussed the benefits of employing DGs and proposed a general approach and a set of indices to evaluate and measure some of the technical benefits of DG in terms of line loss reduction, voltage profile improvement and environmental impact reduction.

Chiradeja [31] proved analytically that, inclusion of DG results in loss reduction by considering a simple distribution line with concentrated load at one end and a DG. It was shown that operating power factor, rating and location of DG are crucial for maximizing the benefits of DG.

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Le et al. [66] developed an index to determine near optimal location of DG for maximum voltage improvement in a distribution system feeder. Operating point of DG which injects real and reactive power in maximum voltage sensitivity line was obtained based on voltage sensitivity.

Gandomkar et al. [46] presented a new algorithm which is a combination of Simulated Annealing (SA) and Genetic Algorithms for optimal allocation of DG in distribution systems. In this optimization problem, power loss minimization was the objective function which was solved considering certain equality and inequality constraints.

Celli et al. [23] proposed a multi-objective formulation for siting and sizing of DG in a distribution system which was solved using GA. The proposed methodology allows the planner to decide the best compromise among cost of power losses, cost of network upgrading, cost of unsupplied energy, and cost of energy required by the served customers.

Ochoa et al. [79] presented a multi-objective performance index to evaluate DG impacts in distribution networks. Real and reactive power losses, voltage, current capacity of conductors and three-phase and single-phase-to-ground short circuit currents were the network impact indices considered for studies. Based on the performance index, DG location problem was solved considering three fixed DG sizes.

KariÂ Alanne and Arto Saari [61] discussed the definitions of a distributed energy system and evaluated various social, economic, political and technological dimensions associated with introduction of DG in regional distribution systems. They concluded that for sustainable development distributed energy system is a good option in long run and also it is environmental friendly.

Nazari and Parniani [78] investigated the effects of DG on power losses of a distribution network feeder with a combination of lumped and uniformly distributed loads. Analytical expressions for power loss reduction in terms of feeder parameters and DG were extracted. Optimum DG unit allocation was determined using the derived loss reduction.

Freitas et al. [45] presented an exhaustive analysis about the impact of connecting synchronous and induction generators in distributed systems. It was concluded that, from voltage stability and transient stability perspective, usage of constant voltage synchronous generators permits to improve the acceptable distributed generation penetration level. Using induction motors lead to reduction of system stability margins. Usage of induction generators or constant power factor synchronous generators leads to very poor voltage regulations as these machines are not voltage self regulated.

Quezada et al. [87] presented an approach to calculate annual energy loss variations when different concentration and penetration levels of DG are connected to a radial distribution network. In addition, the impact on energy losses of different DG technologies, such as wind power, combined heat and power, fuel-cells and photovoltaic was studied. It is shown that energy loss Vs DG penetration level, exhibits a U-shape characteristic. They proved that better loss reduction can be achieved if DG is more dispersed along distribution network feeders.

Carmen and Djalma [18] presented a method for determining optimal DG units location and sizes to maximize the benefit/cost relation, where the benefit was quantified by diminution of power losses and the cost dependend on investment and installation. Constraints to guarantee acceptable voltage profile and reliability level along the distribution feeders were incorporated.

Acharya et al. [4] calculated optimal size and location of the DG to minimize active power loss based on exact loss formula. This method is applicable for single DG unit placement when only active power is supplied by DG. Also LSF based method is employed to select the candidate locations for single DG placement to reduce the search space. Results indicate that loss sensitivity factor (LSF) based approach may not lead to the best placement for loss reduction.

Andreas Poullikkas [11] did cost-benefit analysis pertaining to the use of DG technologies use in isolated systems. Results indicated that wind energy can be a competitive substitute for internal combustion engines or small gas turbines, provided the capital cost is less than 1000 â‚¬/kW with a wind turbine capacity factor of 18%. He also proved that Fuel cells using hydrogen from natural gas reforming can be a competitive alternative to photovoltaic systems for all the range of capital cost under study.

Falaghi and Haghifam [41] proposed a cost based model to obtain the optimal location and size of distributed generation units in a distribution system with an objective to minimize DG investment and operating cost of the system. Cost based objective function and its constraints form an optimization problem, which was solved using Ant Colony optimization algorithm.

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Examples of our workAlemi and Gharehpetian [8] proposed an analytical method based on loss sensitivity factor for optimal DG allocation in order to improve voltage profile and minimize losses.

Farnaz et al. [42] employed Ant Colony Search Algorithm for optimal allocation of DG with an objective to minimize losses. Obtained results are then compared with GA method and proved to be superior.

Prommee and Ongsakul [86] proposed an adaptive weight particle swarm optimization (APSO) algorithm to solve optimal DG allocation problem. APSO has the ability to control velocity of particles. The objective was to minimize the active power losses without violating voltage limits. Four DG types considered for analysis were:

DG injecting active power only

DG injecting reactive power only

DG injecting active power and consume reactive power

DG capable of supplying both active and reactive powers

Singh and Verma [101] formulated the problem of optimal DG allocation using an objective function that includes the cost and energy loss minimization under time varying load conditions. Three load levels were used to model a typical daily load profile of a residential consumer. Minimization of objective function was done using GA under line loading and voltage constraints.

Tuba and Hocaoglu [115] employed an analytical loss sensitivity factor method for determination of optimum site and size of the DG to minimize power losses, based on equivalent current injection method, which uses bus-injection to branch-current (BIBC) and branch-current to bus-voltage (BCBV) matrices developed using topological structure of the distribution systems. Though the computation time is less for this method, only single DG placement and sizing were considered.

Koutroumpezis and Safigianni [65] proposed a method to find the optimum allocation of maximum dispersed generation penetration in medium voltage distribution systems considering technical constraints such as short circuit level, thermal rating and system voltage profile.

Shukla et al. [99] used genetic algorithm to solve multi-location distributed generation placement problem which aims to minimize the total power loss of radial distribution systems. Optimal locations of DG were found using loss sensitivity factors and corresponding DG sizes were obtained using genetic algorithm. The objective function was formulated as a cost function in terms of cost involved toward installing DG and loss cost.

Duong Quoc Hung and Nadarajah Mithulananthan [36] proposed an analytical method for determining optimal size and location of four different DG types viz.,

DG capable of delivering both real and reactive power

DG capable of delivering only active power

DG capable of delivering real power and absorbing reactive power

DG capable of delivering reactive power only

It was shown that operating power factor of DGs for minimizing power losses found to be nearer to the power factor of combined load in the respective system.

Sudipta et al. [109] developed a simple method for the optimal placement and sizing of distributed generators. A conventional iterative search technique along with Newton Raphson method was implemented on different IEEE test systems with an objective to bring down both cost and loss effectively. This paper further focuses on optimizing the weighing factor, which balances both loss and cost factors and helps in achieving desired objectives with maximum benefits.

Sedighizadeh et al. [95] proposed a method which uses a combination of PSO and Clonal Selection Algorithm for optimal allocation of DGs. As system size increases this approach may not lead to optimal location and size.

Sookananta et al. [103] utilized PSO to search for an optimal solution of the DG allocation problem with an objective of minimizing total power losses of the radial distribution system.

Ziari et al. [124] solved DG optimal placement problem using the combination of Discrete Particle Swarm Optimization (DPSO) and GA. The objective of optimization process was to minimize loss and to improve reliability with minimal cost, subjected to the constraints viz., feeder current, bus voltage and the reactive power flowing back to the supply side.

Hosseini and Kazemzadeh [54] proposed an analytical approach to determine optimal placement and sizing of a single DG by considering its power factor in radial distribution networks. Results obtained are also compared with Acharya's method [4] and improved particle swarm optimization method (IPSO).

Amanifar [10] used Particle Swarm Optimization (PSO) algorithm to obtain optimal size of DG considering an objective function which encompasses the total cost of the total active power loss and that of the DG installation cost. Loss sensitivity analysis was used to identify some candidate buses for DG placement to reduce search space that will improve convergence of PSO algorithm.

Raj and Goswami [89] presented a multi-objective formulation to obtain optimal DG sizes and locations. Objectives considered in the study are reliability of service, cost of purchased energy, system operational efficiency, and power quality and system security. Multi-objective formulation was solved using an interactive trade-off algorithm to obtain most satisfactory non-inferior solutions.

Abu-Mouti and El-Hawary [3] used a new population based Artificial Bee Colony (ABC) algorithm to determine the optimal DG-units' size and location in order to minimize the total system active power losses subjected to equality and inequality constraints. The advantage with ABC algorithm is that, only two parameters need to be tuned.

Moradi and Abedini [75] presented a novel combined GA/PSO for optimal siting and sizing of DG in distribution systems. The authors considered only real power injection of DG whose optimal location was found using GA. The solution obtained based on the GA method is then used in the PSO algorithm to obtain optimal DG size to minimize losses and improve voltage regulation index.

Rajkumar et al. [88] reviewed DG technologies, DG applications and benefits of DG such as technical, environmental and economic. Various DG planning methodologies have been reviewed and compared in this paper. Benefits of DG on voltage profile betterment, loss minimization and reliability for a distribution system were also reviewed in this paper.

Florina et al. [44] developed a method which composes of two stage nested calculation. The external stage is carried out by selecting a set of candidate buses employing a clustering-based approach based on normalized loss sensitivity factors and normalized node voltages. The internal stage uses exhaustive search driven by the computation of an objective function with energy losses and voltage profile components, directed at finding upgraded optimal DG sizes at the candidate buses from a set of available discrete sizes.

Chandrasekhar et al. [25] presented a new methodology which uses a population based meta-heuristic approach viz. Shuffled frog leaping algorithm for allocation of DGs in radial distribution systems to reduce the active power losses and DG cost. This paper also concentrates on optimizing the weighing factor, which balances the cost and the loss factors and helps to attain desired objectives with maximum benefit.

Duong Quoc Hung and Nadarajah Mithulananthan [37] proposed an Improved Analytical method (IA) for multiple DG units allocation. In this method each DG is added one by one in which the location and its size are determined in sequence. Further Exhaustive load flow (ELF) method is implemented which demands excessive computational time compared to IA since it searches exhaustively around the solution obtained from IA method.

## Literature review on Network Reconfiguration with DG

In recent years, a little research has been carried out on loss minimization using network reconfiguration of distribution systems with DG. Network reconfiguration of a power distribution system is defined as "altering the topological structures of distribution network by changing open/closed states of sectionalizing and tie switches".

Shirmohammadi and Hong [98] modified the work proposed by Merlin and Back [72] and they included the feeder voltage and current constraints using compensation based power flow technique by ensuring that the behavior of the weakly meshed distribution network was accurately modeled.

Chang et al. [26] presented a modified simulated annealing (SA) technique to solve network reconfiguration problem to reduce power losses in distribution networks. An efficient perturbation scheme and initialization procedure was adapted to ensure better starting temperature for the SA technique. They integrated simplified line flow equations with efficient perturbation scheme which resulted in reduction of computation for solution convergence and thereby gave a near optimal solution.

Sarfi and Chikhani [93] proposed a method which partitions the network into groups of buses such that the line section power losses between the groups of buses are reduced. By virtue of partitioning the buses, this method overcame the network size limitations imposed by earlier reconfiguration techniques. This method facilitated on-line distribution network reconfiguration for power loss reduction.

Young and Jae [122] presented an efficient hybrid algorithm based on Simulated Annealing and Tabu Search for loss minimization by automatic sectionalizing switch operation in large scale radial distribution systems. Simulated annealing is well suited for large combinational optimization problems, but its usage also requires excessive computational time. Tabu search tries to find a better solution in the manner of a greatest-descent algorithm, but it cannot guarantee convergence. Hybridization of these two algorithms with some adaptations was used to improve the computation time and convergence property. Proposed methodology was effective in large-scale radial distribution networks, and its search capacity became more significant as the network size increases.

Ji-Pyng et al. [60] proposed a variable scaling hybrid differential evolution (VSHDE) method to solve optimal network reconfiguration problem for power loss reduction and voltage profile improvement of distribution systems. Variable scaling factor based on the 1/5 success rule was used in this method to overcome the drawback of random and fixed scaling factor thereby alleviate the problem of selection of a mutation operator in the hybrid differential evolution (HDE).

Ching et al. [32] introduced an ant colony search (ACS) algorithm to solve network reconfiguration problem for loss reduction. ACS algorithm employs the state transition rule, local pheromone and global pheromone updating rule to facilitate the computation. Obtained results were compared with those obtained using GA and SA to prove the superiority of this algorithm.

Calderaro et al. [17] presented a GA based reconfiguration methodology that aims to maximize DG penetration in order to exploit renewable sources in a distribution network. Two scenarios were considered for studies: in the first scenario, three DGs were added in sequence and the obtained first DG optimal size was assumed to be fixed while obtaining the second DG optimal size. This approach was repeated to obtain the third DG size also. In the second scenario three DGs were added simultaneously whose sizes were optimized in one go. Based on the simulation results, it was shown that the first-come first-served policy (Scenario 1) for DG connection is a hindrance to maximum DG penetration. However, DG location optimization was not considered for studies.

Debapriya [34] presented an algorithm for distribution network reconfiguration based on the heuristic rules and fuzzy multi-objective approach. Multiple objectives were considered for network reconfiguration problem while maintaining a radial network structure in which all the loads were energized. The objectives were modeled with fuzzy sets to assess their inaccurate nature and one can furnish anticipated value of each objective. Heuristic rules were also incorporated in the algorithm to minimize the number of tie-switch operations.

Yasin and Rahman et al. [119] investigated the effect of location and sizing of DGs on real power loss and network voltage profile during network reconfiguration for service restoration in the event of a three-phase fault. Voltage stability indices were used to identify candidate DG locations and corresponding sizes were optimized using evolutionary programming.

Zhang et al. [126] presented an improved Tabu Search (ITS) algorithm which is a meta-heuristic algorithm to reconfigure large scale distribution systems for power loss minimization. In ITS algorithm, global search ability was improved by introduction of mutation operation, which undermines the dependence of global search ability on Tabu length.

Olamaei et al. [82] presented a new approach to DFR with addition of DGs. The main objectives of the DFR were to minimize the total number of switching operations, the deviance of the bus voltage, and the entire cost of the real power. Since DFR is a non-linear optimization problem, PSO algorithm was used to solve it. Feasibility of the proposed approach was proved and compared with evolutionary methods such as differential evolution, GA and Tabu search (TS) over a realistic distribution test network to demonstrate its superiority.

Li et al. [67] presented an algorithm for reconfiguration with DG based on branch exchange algorithm and sensitivity to minimize losses in distribution systems. It was shown that DG has effects of voltage profile improvement, loss reduction over feeders and network structure optimization.

Mojdehi et al. [74] presented an algorithm to determine optimal distribution network configuration, which minimizes power loss in the absence of DGs and maximize social welfare by reduced power cost in the presence of DGs.

Abdelaziz et al. [1] presented a modified particle swarm optimization algorithm to solve network reconfiguration problem for power loss minimization. PSO algorithm was introduced with some changes such as employing an inertia weight that decreases linearly from 0.9 to 0.2 during the course of iterations which allows the PSO to explore a large area at the beginning of the simulation. Further, a modification in the population size and the number of iterations was presented.

Yuan-Kang et al. [123] proposed a network reconfiguration methodology based on Ant Colony Algorithm (ACA) to achieve minimum power loss and increment the load balance factor of a radial distribution system with DGs. Simulation results indicated that improved load balancing and lower power loss were attained in a distribution network with DG compared to a network without DG.

Abdelaziz et al. [2] presented a modified Tabu Search algorithm for distribution network reconfiguration to minimize active power losses by turning on/off tie switches and sectionalizing switches. To broaden the search toward unexplored regions, random multiplicative move was used in the search process. In order to check the radiality condition of the distribution network, Kirchhoff algebraic method was used.

Rung-Fang et al. [91] employed ordinal optimization (OO) technique in conjunction with a PSO method to solve a network reconfiguration problem that intends to maximize DG penetration in a distribution network. Good solutions obtained from OO method were taken as the initial PSO population in order to speed up solution efficiency in subsequent iterations to reduce the computational burden of PSO.

Jie Chen et al. [59] introduced a reconfiguration method based on simulated annealing immune algorithm to solve optimal network reconfiguration problem for loss minimization. In the algorithm, hyper-mutation and immune supplement assure diversity and avoid local optimal solution. Vaccine inoculation and extraction maintain the excellence info and hence both the convergence and performance of solution were improved.

Olamei et al. [83] presented a hybrid evolutionary optimization algorithm based on ACO and SA for distribution feeder reconfiguration (DFR) considering DGs. Objective function chosen was summation of electrical energy generated by DGs and Sub-station bus in the next day. However, the DG location and size were not optimized.

Zidan et al. [125] proposed a network reconfiguration approach for both balanced and unbalanced systems with DG. Branch currents were utilized as switching index to find the open or closed states of the sectionalizing and tie switches, with an objective of network loss reduction. However, the DG location and size were not optimized.

Rao et al. [105] proposed Harmony Search Algorithm to solve the network reconfiguration problem to obtain optimal switch combinations in the radial network which results in minimum power loss while satisfying operating constraints. The algorithm used a stochastic random search instead of a gradient search which makes derivative information unnecessary.

Tahir NiKnam et al. [112] presented a multi-objective modified Honey Bee Mating Optimization (MHBMO) algorithm to solve the network reconfiguration problem considering the effect of renewable energy sources (RES). Proposed algorithm found a set of pareto optimal solutions and a fuzzy based decision maker was adopted to find the best compromised solution among the non-dominated solutions. Minimization of loss, voltage deviation, cost of power produced by RES and grid and total emissions were the objectives chosen to solve this problem. RES chosen for the analysis were fuel cells, photo voltaic and wind turbines. It was assumed that the location and installed capacity of RES were fixed.

Hao Zhang et al. [52] solved network reconfiguration problem with consideration of random output power of wind based DG by using ant colony algorithm. They used graph theory to generate the state graph of network and employed probability based scenario approach to obtain optimal reconfiguration scheme under multi-scenario and mono-scenario.

Syahputra et al. [111] presented a fuzzy multi-objective based approach for network reconfiguration to achieve minimum real power loss and maximum voltage magnitude with DGs. Multi-objective function was considered for minimization of the active power loss, load balancing between the feeders, deviation of bus voltages, and branch current constraint when subjected to a radial structure in which all the loads need to be energized.

Nasiraghdam and Jadid [76] presented a new multi-objective ABC algorithm to solve network reconfiguration and hybrid (wind turbine/ photo voltaic/fuel cell) energy system sizing problem. The objectives of optimization problem include total real power loss reduction, total energy cost minimization, total emission minimization, and maximization of the voltage stability index (VSI) of distribution network.

## Literature review on Wind speed modeling

Wind energy comes from natural processes and hence any amount of energy drawn will be replenished incessantly. The strong increase in usage of wind based generation worldwide is due to awareness about depleting oil and gas reserves, raising public consciousness in adopting emission less and clean energy technologies, and improvements in wind turbine technology [56]. Lu et al. [68] presented an analysis which indicates that potential of wind energy is five times total global use of energy in all forms. The potential of wind energy as a global source of electricity is assessed by using wind speed data derived through assimilation of data from various meteorological sources. Accurate wind speed modeling is critical in estimating wind energy potential for harnessing wind power effectively which is done using Probability density functions (PDF).

Luna and Church [69] used lognormal function to satisfactorily model wind speed distributions.

Garcia et al. [47] used Weibull and lognormal functions to represent wind speed data in the form of wind frequency distribution curves by making use of hourly data. Suitability of both the distributions was judged employing R2 coefficient and it was shown that Weibull provides better fit to wind data.

Seguro et al. [96] compared the accuracy of maximum likelihood estimator (MLE), graphical and modified MLE methods in estimating the parameters of Weibull function. They recommended MLE when wind data is in time series format and shown that graphical method is less robust than MLE since its accuracy depends on bin size used in cumulative frequency distribution (CDF). Modified MLE was recommended for use with wind data in frequency distribution format.

Celik [21] analyzed wind energy potential of Iskenderun of Turkey using Rayleigh and Weibull statistical distribution functions. It was shown that Weibull model is better in fitting the measured monthly probability density distributions than the Rayleigh model.

Ali [9] showed that Weibull-representative data estimated wind energy output accurate enough and hence suggested that, it can be an alternative to the measured data in time-series format.

Meishen and Xianguo [70] developed maximum entropy principle (MEP)-type distributions by introducing a pre-exponential term to the theoretical MEP distribution that was deduced from the maximization of the Shannon's entropy. They showed that MEP distribution represents a variety of measured wind data closely than the empirical Weibull distribution.

Generalized Extreme Value (GEV) distribution that combines the Gumbel, Frechet and Weibull extreme value distributions were used to model extreme wind speeds [121].

Carta and Ramirez [19] used two-component mixture Weibull distribution In order to represent heterogeneous wind regimes in which there is a proof of bimodality, bitangentiality or simply unimodality. Three methods viz., least square, method of moments and maximum likelihood estimators were used to assess fitness of the distribution.

Kiss and Imre [64] employed Weibull, Rayleigh and gamma distributions in order to model wind speed distributions both over sea and land. They observed that generalized gamma distribution function, which has independent shape parameters for both tails, renders a unified and adequate description nearly everywhere.

Akpinar and Akpinar [7] used Weibull distribution, MEP, singly truncated normal Weibull mixture distribution (TNW) and two component mixture Weibull distribution for wind speed studies. They concluded that TNW PDF was better compared to other three PDFs in describing wind speed data at different wind stations due to smaller values of chi-square and RMSE errors.

Carta et al. [20] reviewed the suitability of different PDFs available in literature such as three parameter generalized gamma, two parameter gamma, two parameter Weibull, one parameter Rayleigh, two parameter square-root normal , two parameter normal truncated, two parameter lognormal, two parameter inverse Gaussian distribution, three parameter beta distribution, two component mixture Weibull distribution, singly truncated normal Weibull mixture distribution and maximum entropy for wind distribution analysis. A review of parameter estimation methods such as method of moments (MOM), least squares methods (LSM) and maximum likelihood method (MLM) which need to be employed to check distribution models fitness was also done. It was shown that Weibull distribution cannot represent wind regimes with bimodal distributions. They demonstrated that singly truncated normal Weibull mixture distribution and two component Weibull distribution are suitable for bimodal wind regimes.

Celik et al. [22] modeled observed wind speed distributions using the models found in the literature, namely, Lognormal, Rayleigh, two-parameter Weibull, three parameter Weibull, and bimodal Weibull PDFs. A new statistical tool was developed using four statistical parameters viz., slope, R2, mean bias error, and root mean squared error to evaluate relative performance of the above mentioned PDFs; since any single statistical parameter cannot adequately indicate the goodness of a model.

Akdag et al. [6] checked the suitability of two-parameter Weibull distribution (W-PDF) function and two-component mixture Weibull distribution (WW-PDF) function to fit wind speed data in order to estimate wind energy potential.

Tian Pau Chang [113] incorporated PSO technique in MLE method to assess Weibull parameters. It was shown that PSO technique is a viable option for wind energy applications owing to its speedy convergence.

Valerio et al. [116] employed Rayleigh, Weibull, Gamma, Lognormal, Pearson type V, Inverse Gaussian and Burr PDFs to depict wind speed frequency distributions. MLM was used to estimate parameters of the PDFs and Kolmogorov-Smirnov (K-S) test was employed to assess the fitness of PDFs.

Feng et al. [43] defined an objective function based on the moments of wind distribution and solved it using GA to obtain shape and scale parameters of Weibull function.

Tian Pau Chang [114] proposed two new PDFs viz., mixture Gamma-Weibull function (GW) and mixture truncated normal function (NN) to estimate wind energy potential. Based on the results, it was depicted that GW PDF performed better than two component mixture Weibull and NN PDFs. For estimating wind energy potential, GW PDF was shown to be a useful alternative to the conventional Weibull function.

## Literature review on DG planning involving time-varying generation and load demand

Most of the methods formulated for optimal allocation of DGs so far assumed an unrealistic constant DG output and constant network load profile. Optimal DG locations and sizes found with the above assumptions may not result in minimum annual energy loss when employed in a realistic scenario i.e., with variability in the DG output power generation and loads. This section presents a review of work done on DG planning involving time-varying generation and load demand.

Wang and Nehrir [118] introduced an analytical method to identify optimal location of DG in meshed and radial networks for loss minimization with time varying as well as time invariant loads. To depict the time varying nature of loads, a typical daily average demand profile was considered for the entire year. The drawbacks of this method were that, DG size was not optimized and seasonal daily averaged demand profiles were not considered for analysis.

Dan Zhu et al. [127] discussed two criteria for optimal placement of a single DG for time-varying loads. The two criteria are maximizing the reliability and minimizing power losses. The actual load curve was approximated into different load windows, in which loading condition of each window is assumed to be relatively constant. Complexity of the method increases with the number of load windows (states) representing the load curve since exhaustive search was used.

Khattam et al. [39] proposed a novel algorithm to evaluate the performance of distribution system which includes distributed generation. Monte Carlo-based power flow algorithm was used to estimate the steady-state hourly variation values of the system generated scheduled power, the system bus voltages and angles, the distribution sub-station power, the primary distribution feeder section currents, and the total system power loss taking in to account the power transferred to the system by DG units independent of their stochastic operation. The number of DG units in their "on state," the buses to which these DGs are associated and their corresponding generated power which is delivered to the distribution system, are the three random parameters of interest that are modified in each experiment. These values can be used for short time forecasting in electricity spot market. However, the drawbacks are:

for each hour number of experiments to be conducted is high and hence this algorithm is computationally demanding

optimization of DG sizes and locations were not considered

Ochoa et al. [80] presented a multi-objective performance index which includes indices such as losses, voltages, short circuit levels and reserve capacity of conductors in order to find suitable DG location for maximizing the benefits. The inherent time-varying behavior of distributed generation (particularly when renewable sources are used) and demand were taken into account while evaluating the impact of DG. In the analysis a fixed wind based DG size was assumed.

Ochoa et al. [81] presented a multi-objective programming approach using non-dominated sorting genetic algorithm (NSGA) to find DG locations that maximizes the integration of distributed wind power generation (DWPG) while satisfying voltage and thermal limits. Time-series steady-state analysis of technical issues such as losses, energy export to the grid, and short-circuit levels were presented which considered both load and generation patterns.

Atwa et al. [12] studied the impact of wind speed uncertainty and seasonality on the system energy losses. Optimum DG sizes and locations were found using two methods with an objective to minimize energy loss. In the first method wind based DG power was calculated using a proper PDF while regarding a constant load profile. In the second method, a common monthly wind speed profile and two common load profiles (weekday and weekend) for a month were generated.

Atwa et al. [13] presented a methodology for optimal allocation of different types of renewable DG sources to minimize energy loss. A probabilistic generation-load model that mixes all possible operating conditions of the renewable DG units along with their probabilities was proposed and accommodated this model in a deterministic planning problem.

Atwa and Saadany [14] proposed a method to allocate DGs optimally with an objective of minimizing annual energy loss. They developed a probabilistic generation -load model that combines all possible load levels and operating conditions of wind based DG units with their probabilities. The problem was formulated as mixed integer non-linear programming under GAMS taking in to account network constraints such as discrete DG size of DG units, voltage limits, feeder capacity and maximum DG penetration limit. However, the drawbacks of proposed method are:

DG location optimization was not considered

While obtaining generation model, Rayleigh PDF was used for wind speed modeling which was not accurate

Zhang et al. [120] proposed a probabilistic framework of reliability modeling to integrate wind energy conversion system with the electric power system. Different stochastic characteristics in wind energy conversion system such as resource availability, transmission availability and generation facility outage were investigated in this work.

## Conclusion

This chapter presents a fairly exhaustive literature review on various types of DG allocation methods. Literature survey of various papers on network reconfiguration with DG is done. Review of different papers which considered variability in load profile and/or variability in DG output are presented in this chapter. Further, literature work related to wind speed modeling meant for wind based DG modeling have been reviewed. The following observations were made based on the review:

As per literature, analytical methods for DG allocation which follow two step procedures may not lead to optimal solution which is a major disadvantage. Further, each DG is added one by one, in case of multiple DG allocation, which may result in missing the optimal solution. Most of the existing meta-heuristic methods considered optimization of DG locations and corresponding sizes sequentially which may not lead to optimal solution. Even in some methods where sizes and locations were optimized simultaneously, all the buses of the network were considered which increases the search space for locations leading to sub optimal solutions. Hence, a novel method which optimizes both DG sizes and locations simultaneously is required with a reduced search space for DG locations for improved efficiency.

In existing methods for network reconfiguration with DG, reconfiguration and DG installation were not dealt simultaneously which will not lead to maximum loss reduction. Hence, a new approach which simultaneously reconfigures the network and finds optimal DG sizes and locations is needed.

Most of the existing methods for optimal allocation of DG units did not account for variability in load profile. Hence the DG sizes and locations obtained with the above assumptions may not lead to minimum annual energy loss when employed in realistic scenario where there is variability in network load profile. Hence, a new method which considers time varying load profile while determining optimal DG sizes and locations is required.

Based on the gaps identified during literature survey, the objectives of this work are formed which are mentioned in introduction chapter.