02 Nov 2017

The major challenge for power system engineers is to meet the ever increasing load demand with available generating capacities. Creating additional generation capacity involves huge capital investments and hence it is imperative to operate the existing power system network with optimal utilization. This requires systematic methods of planning and should employ suitable control strategies to reduce the energy losses and to improve the power quality supplied to the consumers. The major components of a power system are Generating stations interconnected through high voltage transmission network and low voltage distribution network to the different points of utilization of electrical energy. The planning, design and operation of Generating systems and Transmission systems has been systematically analyzed and suitable control strategies to optimize the performance have been put into practice. Especially in the systematic planning and design of distribution systems much attention is needed to improve the power quality supplied to the consumers.

The distribution system is generally characterized into Primary distribution network and Secondary distribution network [15]. A primary distribution network delivers power at higher than utilization voltages from the substation to the point where the voltages are further stepped down to the value at which the energy is utilized by the consumers. The secondary distribution network supplies power to the consumer premises at levels of utilization voltages. Based on the scheme of connection the primary distribution system may be a Radial distribution system or a Mesh system.

Most of the primary distribution systems are designed as radial distribution systems having exclusively one path between consumer and substation and if it is interrupted results in complete outage of power to the consumers. The main advantages of radial system are simplicity of analysis, simpler protection schemes, lower cost and easy predictability of performance.

A mesh system has two paths between substation and every consumer and it is more complicated in design and requires complex protection schemes which involves higher investment than in radial systems. The radial distribution systems are inherently less reliable than mesh systems but reliability can be improved with good design.

Recently many researchers have suggested different strategies to effectively reduce the energy losses in the distribution network and maintain a good voltage profile at various buses in the network. Basically, the researchers have suggested various reactive compensation methods to reduce the reactive component of currents in the feeders thereby reduce the energy losses, kVA demand on the feeders and improve the voltage profile in the distribution system. The different methods suggested to optimize the performance of distribution system are optimal sizing and placement of Capacitors, reconductoring of feeders, employing Voltage Regulators at proper locations and Distributed Generators at suitable locations. In investigating the above strategies to improve the overall performance of the distribution network, an efficient and robust load flow technique suitable for distribution systems is required.

The conventional load flow methods used for power system networks such as Newton â€“ Raphson and Fast Decoupled load flow methods cannot provide solution for the distribution system because of high R/X ratio (ill conditioned systems). Hence an efficient load flow method of solution for solving distribution systems with balanced and unbalanced load configuration is required. To ensure good quality of supply to consumers it is necessary to limit the voltage drops and reduce power losses by proper choice of compensation techniques such as capacitor placement, voltage regulators, distributed generators, network reconfiguration and grading of conductors.

In radial distribution systems it is common to employ uniform conductor over the entire length of the feeder. From the consideration of current carrying capacity it is not necessary to employ uniform conductors in radial distribution systems and hence the size of conductor should reduce as we proceed from substation to tail end of the feeder. In planning radial distribution systems grading of conductors is employed which will reduce the losses, kVA demand and cost of the conductor besides improving the voltage profile.

It is apparent that it will be economical if transmission lines are used to transfer only active power and the reactive power requirements of the loads are met in the distribution system itself either at the consumer premises or at the substation level. Series and shunt capacitors are employed in power system to improve system stability, power factor and voltage profile thereby enhancing the system capacity and reducing the losses. In distribution systems it requires careful planning to meet the reactive power requirements by suitably placing the shunt capacitors. The benefits that can be derived from shunt capacitor installation in the distribution systems are

Reduces lagging component of current

Increases voltage level at the load

Improves voltage regulation if the capacitor units are properly switched

Reduces power losses in the system because of reduction in current

Reduces kVA demand where power is purchased

Reduces investment in system facilities per kW of load supplied

The extent of these benefits depends on the location, size, type and number of capacitors as well as on their control settings. The capacitor placement problem is formulated as an optimization problem for determining the location and size of the capacitor with an objective to maximize the net savings.

Another method of improving the voltage profile in distribution systems is to employ required number of voltage regulators with suitable tap settings at proper locations. Installation of voltage regulators on distribution network will help in reducing the energy losses, peak demand losses and in addition improves system stability and power factor. To achieve these objectives, the problem is formulated as an optimization problem to reduce the losses and hence maximize the net savings with suitable constraints.

In planning distribution systems, the present trend is installation of distributed (or local) generators other than central generating stations closer to consumer premises preferably at high load density locations. Distributed Generators (DGs) are small modular resources such as photo voltaic cells, fuel cells, wind generators, solar cells. Such locally distributed generation has several merits from the point of environmental restrictions and location limitations.

The main reason for increasingly wide spread deployment of DG can be summarized as follows:

DG units are closer to customers so that Transmission and Distribution costs are reduced or avoided.

Reduced line losses

Voltage profile improvement and power quality improvement

Enhanced system reliability and security

It is easier to find sites for small generators.

Reduced fuel cost due to increased overall efficiency

Usually DG plants require shorter installation times and the investment risk is not high.

DG plants yield fairly good efficiencies especially in cogeneration and in combined cycles (larger plants).

The liberalization of the electricity market contributes to create opportunities for new utilities in the power generation sector.

The costs of Transmission and Distribution costs have increased while costs of DG have reduced and hence, the overall costs are reduced with the installation of DGs.

In fact, the distribution systems are not planned to support installations of Distributed Generators at various locations. Installation of DGs on one hand improves the overall performance of the distribution system where as on the other hand poses new problems. To mention few problems with DGs are their grid connections, pricing and change in protection schemes. To achieve maximum benefit from installation of DGs, it is formulated as an optimization problem to locate and fix the size of DGs with the constraint on total injection of installed DGs in a radial distribution system.

Recently, a large number of Artificial Intelligent techniques have been employed in power systems. Nowadays, Fuzzy logic is used to solve the problem of distribution systems more efficiently. Fuzzy logic is a powerful tool in meeting challenging problems in power systems. This is so because fuzzy logic is the only technique, which can handle imprecise, â€˜vague or fuzzyâ€™ information. The benefits of such fuzzification include greater generality, higher expressive power, an enhanced ability to model real world problems and a methodology for exploiting the tolerance for imprecision. Hence, Fuzzy logic can help to achieve tractability, robustness, and lower solution cost.

A power system consists of power stations of various types which are interconnected by transmission lines, sub-transmission lines and distribution networks to supply different types of loads to different consumers. A distribution system is that part of electrical power system with sole objective of delivering electrical energy to the end user. There has been significant scientific development in planning of power generation and transmission systems but little interest is shown in systematic planning of distribution systems.

Distribution system failures have severely affected the power supply to the consumers. In practice the distribution lines has been stretched too long unscientifically resulting in poor voltage regulation and high energy losses especially at peak load conditions. Indeed the need of the hour is to deliver a better quality of power to the consumers by overcoming the various deficiencies.

Hence, of late much attention has been paid on electrical distribution systems by suggesting the improved methods for optimizing the performance namely

Optimal conductor selection for RDS

Optimal voltage regulator placement

Optimal capacitor placement

Distributed generator placement

Network reconfiguration

The modern power distribution network is constantly being faced with an ever-growing load demand. Distribution networks experience distinct change from a low to high load level conditions every day. In order to evaluate the performance of a distribution system and to examine the effectiveness of proposed modifications to a system in the planning stage, it is essential that a load flow analysis of the system is to be repeated for different operating conditions. Certain applications, particularly in the distribution automation (i.e., VAr planning, state estimation, etc.) require repeated load flow solutions. It basically gives the steady state operating condition of a distribution system corresponding to a specified load on the system.

Any load flow method must be able to model the special features of the distribution systems in sufficient detail. The traditional load flow methods used in transmission systems, such as Newton â€“ Raphson and Gauss â€“ Seidel techniques, failed to meet the requirements in both convergence and robustness aspects for the distribution system applications. Generally distribution networks have high R/X ratio. Due to this reason, popularly used Newton â€“ Raphson [2] and Fast Decoupled load flow algorithms [3] may provide inaccurate results and may not converge. Many researchers have suggested modified versions of the conventional load flow methods for solving distribution networks with high R/X ratio [39, 54, 104]. Kersting [6, 11] has developed a load flow method for solving radial distribution networks by converting distribution networks based on ladder network theory into a working algorithm. In this method, update currents and voltages during the forward sweep and backward sweep give directly voltage correction.

Baran and Wu [18] have proposed a method based on iterative solution of three fundamental equations representing voltage, real and reactive power. They have computed system Jacobian matrix using chain rule. They have also proposed decoupled and fast decoupled distribution load flow algorithms. Chiang [21, 22] has proposed decoupled load flow method for distribution networks and also proposed the effect of convergence criteria for the solution of distribution systems. In fact, the decoupled and fast decoupled methods proposed by Chiang [22] are similar to that of Baran and Wu [18]. However, very fast decoupled distribution load flow proposed by Chiang is very attractive because it does not require any Jacobean matrix construction and factorization but more computations are involved because it solves three fundamental equations in terms of active power, reactive power and voltage magnitude.

Das et al. [32, 38] have proposed load flow technique for solving radial distribution networks, in which they have proposed a unique bus, branch and lateral numbering scheme which help to evaluate exact real and reactive power loads fed through any bus and to obtain bus voltages. These methods involve only the evaluation of simple algebraic expression of receiving end voltage which does not involve any trigonometric terms, as in the case of conventional load flow method. Haque [41] has proposed load flow solution of radial distribution systems for different load models which are dependent on voltage magnitude. Rajicic and Taleski [48] have proposed two load flow methods for the radial and weakly meshed distribution networks. The first is an admittance method and the second is an extension of the current summation method. Both are developed under an assumption that network branches are ordered according to the known rules.

Ghosh and Das [52] have presented another method for solving radial distribution networks by evaluating a simple algebraic expression of receiving end voltages. Ranjan et al. [71] have proposed a new load flow method using power convergence characteristic. This method can easily accommodate the composite load modeling if the composition of load is known. Venkatesh and Ranjan [72] have proposed load flow method which uses concept of data structure to define the topology of distribution system. In this, dynamic data structure for distribution system is defined to obtain a computationally efficient solution.

Aravindhababu [74] has proposed a fast decoupled power flow method for distribution systems based on equivalent current injections. In this method, the assumptions on voltage magnitudes, angles and R/X ratios necessary for decoupling the network as in the conventional FDLF are eliminated. Ranjan et al. [76, 77] have proposed load flow method for radial distribution system and has extended it to different load models to analyze voltage stability of the system. Sathish Kumar et al. [131] have proposed a new technique which uses modified forward substitution method to solve radial distribution systems.

Chen et al. [24, 25] have proposed three phase power flow method for unbalanced distribution system using YBus and also proposed detailed models of three phase generator and transformer to incorporate in load flow method for analyzing unbalanced distribution systems. Chen and Chang [26] have proposed Open wye/open delta and open delta/open delta transformer models which are commonly used in analysis of three phase unbalanced distribution systems. Zimmerman and Chiang [39] have proposed fast decoupled load flow technique for unbalanced radial distribution systems. Thukaram et al. [50] have proposed robust three phase power flow algorithm for unbalanced radial distribution networks. This method uses forward and backward propagation to calculate branch currents and bus voltages. Garcia et al. [53] have proposed three phase current injection method (TCIM) to solve unbalanced radial distribution system. TCIM is based on the current injection equations written in rectangular coordinates and is a full Newton method, which gives quadratic convergence to obtain the solution.

Lin and Teng [54] have proposed fast decoupled load flow method to solve unbalanced radial distribution systems. In this, constant G â€“ matrix has been developed based on equivalent current injections which needs to be inverted only once to obtain the solution. Teng [55] has presented a network topology method to obtain the solution of unbalanced distribution system. In this method, two matrices have been developed; one is Bus Injection to Branch Current (BIBC) and second is Branch Current to Bus Voltage (BCBV) matrix to find the solution. Kersting [56] has proposed modeling of transformer and other components of distribution systems. Jen-Hao Teng [78] has proposed direct method of load flow solution of unbalanced radial distribution networks. Garcia et al. [79] have presented a procedure to implement PV buses in three phase distribution load flow of unbalanced radial distribution systems.

Peng Xiao et al. [96] have proposed unbalanced distribution load flow method to solve unbalanced distribution networks. In this, the unified three phase transformer model has been developed to obtain the solution of unbalanced distribution systems. Subrahmanyam [100, 132] has proposed three phase load flow method to solve three phase unbalanced radial distribution system. This algorithm uses basic principles of circuit theory and solves simple algebraic recursive expression of voltage magnitude to obtain the solution. Many researchers [78, 93, 114, 127] have proposed different methods to solve unbalanced radial distribution systems. Literature survey shows that good amount of work has been carried out for the load flow solution of balanced and unbalanced radial distribution systems.

Attention was given to the problem of optimal conductor selection as early as 1950â€™s [1]. Funkhouser and Huber [1] have proposed a method for determining economical Aluminum Conductor Steel Reinforced (ACSR) conductor sizes for distribution systems. Adams and Laughton [4, 5] have proposed a method based on mixed integer programming for optimal planning of radial distribution systems. The selection of type of conductor is based on the current carrying capacity of the optimal feeder configuration. Wall et al. [7] have proposed a method which goes one step further, i.e. based on the need for feeder voltage support as well as the current carrying capacity requirement. Kiran and Alder [9] have proposed a dynamic model for the development of primary and secondary circuits supplying a residential area. Features of this model, which support optimal conductor sizing and the evaluation of annual reserve requirements associated with capital requirement and energy losses.

Ponnavaikko and Prakasa Rao [8, 10] have proposed a model (PPR model) for optimal conductor grading for radial distribution feeders. This model is flexible and can handle the variations in the load growth rate, load factor, and cost of energy over the planned period. The PPR model considers the conductor-grading problem as optimization problem of minimizing the sum of the cost of the feeder and the cost of the feeder energy losses. However, major drawback of this method is that it cannot handle the lateral branches. Tram and Wall [17] have developed a practical computer algorithm for optimal selection of conductors of radial distribution feeders. Many researches [23, 29, 43, 133] have formulated the optimal conductor selection as a planning problem using Genetic, Evolutionary programming and Differential Evolution algorithm.

Zhuding Wang et al. [58] have proposed a new approach to find the selection of optimal conductor size for radial distribution system. In this a multisection, branching feeder model with non-uniform load distribution has been considered to obtain the best solution. Sivanagaraju et al. [65] have proposed a method for selecting the optimal size of conductor for radial distribution networks, and the conductor selected by this method will satisfy power quality constraints. Rakesh Ranjan et al. [69] have presented a method using voltage deviation index and power quality index for selecting optimal branch conductor of radial distribution feeders based on evolutionary programming.

Mandal and Pahwa [70] have presented a systematic approach for selection of an optimal conductor set, by considering several financial and technical factors in the solution, which will be the most economical when both capital and operating costs are considered. Prasad et al. [103] have proposed an algorithm for selecting the optimal branch conductor of radial distribution systems using Genetic Algorithm. Rama Rao and Sivanagaraju [116] have proposed a method to select optimal branch conductor for radial distribution systems to minimize the losses, using Plant Growth Simulation Algorithm. Sivanagaraju and Viswanatha Rao [128] have proposed to select optimal conductor of radial distribution system by using discrete particle swarm optimization technique. It can be observed that good amount of work has been carried out for the selection of optimal branch conductor of radial distribution systems.

The use of shunt capacitors in electrical distribution system is a common practice and has been investigated by many authors in the past. A review of the literature on reactive power compensation in distribution feeders indicates that the problem of capacitor allocation for loss reduction in electric distribution systems has been extensively researched over the past several decades.

Reactive currents in a distribution system produce losses and result in increased ratings for various distribution components. Shunt capacitors can be installed in a distribution system to reduce energy and peak demand losses, release the kVA capacities of distribution apparatus, which improves power factor and the system voltage profile [33]. Thus, the problem of optimal capacitor placement consists of determining the locations, sizes and number of capacitors to be installed in a distribution system such that the maximum benefits are achieved while operational constraints are satisfied.

Erstern and Tudor [16] proposed a method to determine the optimal size of capacitor using non-linear dynamic programming. A nonlinear model has been developed based on the bus impedance reference frame, and takes into account the uncertainty of the load. Pattern recognition technique and sensitivity analysis are used to minimize the number of variables of the model. Salama and Chikani [27, 28] have developed a method for the control of reactive power in distribution systems for fixed and varying load conditions, giving generalized equations for calculating the peak power and energy loss reductions, the optimal locations and rating of the capacitors.

Abdul-Salam et al. [31] have proposed a heuristic technique, which brings about the identification of the sensitive buses that have very large impact on reducing the losses in the distribution systems. This method is relatively fast, very effective and gives considerable saving in energy and in net saving when the cost of the capacitors and their installations are taken into account. Sundharajan and Pahwa [35] have proposed a method to select optimal size of capacitors using genetic approach and a sensitivity analysis based method is used to find the sensitive locations for installing the capacitors. Laframboise al. [36] and Ananthapadmanabha et al. [42] have proposed a method based on expert system to identify the bus in distribution system to place capacitor and thereby reduce the losses in the system. In these methods, approximate reasoning using fuzzy set theory is used for placement of capacitor in a radial distribution system.

Chis et al. [45] proposed a heuristic method in which only a number of critical buses, named as sensitive buses, are selected for installing capacitors in order to achieve a large overall loss reduction in the system combined with optimum savings. The sensitive buses are selected based on the losses caused in the system by the reactive components of the load currents. Lee [46] has proposed a method to find the optimal size of a capacitor based on evolutionary programming. A comparative study has been carried out with genetic algorithm and linear programming. Haque [51] has suggested an analytical method for capacitor placement for loss reduction in radial distribution systems. Levitin et al. [57] formulated the capacitor allocation problem as complicated combinatorial problem and solved using Genetic Algorithm.

Bhaskar et al. [60] presented a system approach to the problem of capacitor allocation on radial distribution feeders. A genetic algorithm was used to determine the optimal placement and control of capacitors, so that the economic benefits achieved from system capacity release, overall peak load power and energy losses reductions are maximized. Calovic and Saric [64] have proposed a new integrated fuzzy concept for multi-objective solution of the optimal capacitor placement and compensation planning problem in distribution networks. Sivanagaraju et al. [68, 102] presented a method of minimizing the cost of loss associated with the reactive component of branch currents by placing optimal capacitors at proper locations. Mekhamer et al. [73] have proposed a method for reactive power compensation using fuzzy logic in RDSs. Khodr et al. [124] have presented computationally efficient methodology for the optimal location and sizing of static and switched capacitors in radial distribution systems. The optimization problem has been formulated as mixed integer linear programming problem.

However, few papers reported capacitor allocation problem in combination with network reconfiguration or voltage regulator placement in the system to improve the voltage profile [19, 20, 30, 40, 95, 111]. In view of this, to include uncertainties of the system data a fuzzy logic approach is suggested to determine the optimal location of capacitor in radial distribution systems.

One of the other methods to reduce losses and to improve voltage profile is by placing voltage regulators at suitable locations in a distribution system. It is a device that keeps a predetermined voltage in distribution networks in spite of load variations within its rating. Voltage regulators are mainly employed in extensive and loaded feeders, where the reactive compensation does not have a satisfactory effect. The optimization problem involves the determination of the number and optimal locations of VRs and their tap positions, in order to minimize the peak power and energy losses and provide a smooth voltage profile along a distribution network with lateral branches.

Grainger and Civanlar [12-14] have proposed an integrated method for the reactive power and voltage control of radial distribution system using combination of capacitors and voltage regulators. In these papers, they decouple the capacitor problem from the VR problem and propose VRâ€™s for a network completely compensated with capacitors. Also the network voltage is the criterion for the selection of the optimal number of VRs and their locations and tap positions. Salis and Safigianni [37, 59] have proposed a method to locate voltage regulator and its tap setting in a radial distribution system based on voltage drop criterion. Gu and Dizy [44] have presented a method using neural networks for combined control of capacitor banks and voltage regulators in distribution systems. In this method, loss equation is considered as objective function with voltage inequalities as constraints to obtain the optimal number, location and tap position of VR. Kagan et al. [83] have proposed for integral control of Volt / VAr using capacitors and voltage regulators in radial distribution system.

Souza et al. [84, 85] have proposed a method using genetic algorithm for optimal location of voltage regulators in distribution networks. Augugliaro et al. [86] have suggested a method using evolutionary programming to fix the tap positions of VRâ€™s to minimize the losses and to improve the voltage regulation. Mendoza et al. [88] have presented a method using genetic algorithm to define the number of voltage regulators and their optimal position in radial networks based on the minimization of energy losses. The proposed method separates the original problem into two parts, the first part consists in determining the optimal position of VRs in the system, by solving a multi-objective optimization problem and second part, consists in choosing the number of VRâ€™s, by using the benefits index as the decision making process.

Lopez et al. [101] have presented the problem of voltage regulation and minimization of power loss for radial distribution systems with new approach of micro-genetic algorithm. Rao and Sivanagaraju [113] have proposed Discrete Particle Swarm Optimization technique for the voltage regulator placement problem in radial distribution systems with an objective of maximizing the net savings. Pereia and Castro [125] have proposed an analytical method to find optimal placement of voltage regulator in distribution systems. Ganesh and Sivanagaraju [126] have proposed a method for placement of voltage regulators in unbalanced radial distribution system using genetic algorithm. Rama Rao and Sivanagaraju [129] have proposed a method, which deals with initial location of voltage regulator buses by using Power Loss Indices (PLI) and Plant Growth Simulation Algorithm (PGSA) is used for determining optimal number and location along with their tap setting, which provides a smooth voltage profile along the network. The main objective of this method is to minimize the number of voltage regulators which in turn reduces the overall cost. From the above discussion it can be observed that good amount of work has been carried out for the selection of optimal number and location of VRs on radial distribution systems. However, literature survey on voltage regulator clearly shows that hardly any attempt is made to find optimal location and number of VRs directly without sequential or recursive algorithm.

Due to the increasing interest on renewable sources in recent times, the studies on integration of distributed generation to the power grid have rapidly increased. In order to minimize line losses of power systems, it is very important to determine the optimal size and location of local generation in radial distribution system. The benefits of DG are numerous and the reasons for implementing DGs are rational use of energy, deregulation policy, diversification of energy sources, ease of finding sites for smaller generators, shorter construction times and lower capital costs of smaller plants and proximity of the generation plant to heavy loads. Many researchers have proposed different methods to evaluate the benefits from DGs in a distribution system in the form of loss reduction and reduction in loading level [90, 97].

Kim et al. [47] have presented power flow algorithm to find the optimum DG size at each load bus assuming every load bus can have DG source. Such methods are, however, inefficient due to a large number of load flow computations. Celli and Pilo [62] have proposed method to find sizing and placing of DG using GA, in order to achieve a good compromise between costs of network upgrading and power losses. A method is presented to identify the optimal location and size of DG based on Tabu search algorithm [63, 75]. Nara et al. [63] have proposed a method using Tabu search algorithm to identify optimal location and number of DG. The size of DG is calculated using analytical method. Rosehart and Nowicki [66] have proposed Lagrangian based method to determine optimal location for placing DG, considering economic limits and stability limits.

Genetic algorithm (GA) based distributed generator placement techniques to reduce overall power loss in distribution system are presented in [61, 67, 82, 87, 105, 107-108, 112, 119, 120] but the problems with GA are that it is computationally intensive and suffers from excessive convergence time and premature convergence.

Wang and Nehrir [80] have proposed analytical methods to find the optimal location and size of DG to place in radial as well as meshed systems with respect to the reduction of power losses. This technique is basically concerned with finding the optimal location but not the optimal size. EI-Khattam et al. [81, 91] have proposed an optimization model to solve the distribution system planning problem and determine optimal sizing and placing of DG. Harrison and Wallace [89] have proposed repeated power flow method to find optimal size of DG in continuous functions of capacity. Celli et al. [90] have proposed a method based on multi evolutionary algorithm in terms of pre-specified sizes of DG at the best locations to reduce losses in the distribution system.

Khattam et al. [91] have developed an optimization model to solve distribution planning problem and determine optimal sizing and placing of DG. Iyer et al. [92] have proposed an analytical method to improve voltage profile of radial distribution system by optimally placing DG. Mallikarjuna and Mitra [94] have proposed a method for determination of optimal size and location of a distributed generator for microgrid system. Khoa et al. [98] have proposed an algorithm using the Primal dual interior point method for solving nonlinear optimal power flow problem. The main aim is to optimize location and sizing of DG in distribution systems for line loss reduction. Le et al. [99] have proposed a method to find placement of optimal Distributed Generator to reduce losses in radial distribution systems. Lakshmi Devi and Subramanyam [106, 109] have presented a case study to minimize the loss associated with the absolute value of branch currents by placing DG operating with any power factor at suitable locations using Fuzzy logic and the size of DG at any power factor is calculated by analytical method.

Harrison et al. [108] have proposed a hybrid approach to find optimal number and size of DG. In this method, GA is used to search a large range of combinations of locations, then employing optimal power flow to define available capacity for each combination. Raj et al. [110] have proposed particle swarm optimization technique to identify the optimum generation capacity of the DG and its location based on indices to provide maximum power quality improvement. Alemi and Gharehpetian [115] have proposed an analytical method which is based on sensitivity factors for optimal allocation and sizing of DG units in order to minimize losses and to improve the voltage profile in distribution systems. The sensitivity factor method helps to reduce the search space by the linearization of nonlinear equations around the initial point.

Ahmadigorji et al. [117] have incorporated the benefits of cost of DG in their method to find the optimal location and size of DG and also have considered constraints on voltage limits and operational limits of DG in the calculation of objective function. Firouzi et al. [118] have proposed Ant Colony Optimization Based Algorithm for finding optimal location and size of DG in distribution networks. Shayeghi and Mohammadi [121] have proposed probabilistic model for optimal location and sizing of DG for loss reduction and voltage profile improvement in power distribution networks. Lee and Park [122] have proposed a method to select the optimal locations of multiple DGs by considering the power loss in steady state operation. Thereafter, their optimal sizes are determined by using Kalman Filter Algorithm.

Padma Lalitha et al. [130] have proposed new technique known as Artificial Bee Colony (ABC) algorithm to find the optimal size of DG by taking number and location of DG as inputs. The location of DG is identified by single DG placement method [123], which is an analytical method. The advantages of ABC method for determination of locations of DGs are improved convergence characteristics and less computation time with voltage and thermal constraints being considered. From the above discussion, it can be seen that lot of work has been carried out on DG placement to reduce the real power losses of the system. But in most of the methods analytical approach has been adopted to find the optimal location of DG and hardly any attempt is made to find optimal location and number by using Fuzzy Expert System (FES).

The recent trends in power system studies emphasize the importance of FES [34, 49].Due to the advantage of FES, the optimal location and number of voltage regulating devices that are to be employed to reduce the system losses and to improve the voltage profile in RDS can be directly determined instead of using recursive or sequential approaches. In addition the variation in bus voltages and power losses are simultaneously taken into consideration for determining the optimal locations.

The objective of the thesis is to reduce power losses and to improve the voltage profile of radial distribution systems by using conductor grading and other voltage regulating devices. The following methods are suggested to minimize the losses and hence maximize the objective function, which consists of net savings in terms of cost of conductor or voltage regulating equipment and cost of energy losses.

Conductor grading of RDS

Optimal capacitor placement and its sizing

Optimal voltage regulator placement and its tap position

Optimal distributed generator placement and its rating

The above proposed methods are investigated with 15, 33, 69 bus radial distribution systems. A load flow technique using data structures is developed for balanced and unbalanced radial distribution systems and is employed in the above studies.

In the above optimization studies, to find optimal conductor grading or optimal placement of voltage regulating device a fuzzy logic approach is employed.

The various features of distribution systems in general and survey of the past work concerning Load flow methods for distribution networks, grading of conductors in distribution system, optimal capacitor size with its location, optimal voltage regulator location with its tap position and optimal size of distributed generator with its location, are presented in Chapter 1. The objectives and motivations of the research work presented in the thesis are discussed further in subsequent chapters.

A simple method is presented for obtaining the load flow solution of balanced and unbalanced radial distribution systems in Chapters 2 and 3 respectively. The proposed method involves the solution of algebraic equation of receiving end voltages and also makes use of Data Structure to identify the structure of distribution system. This method can handle system data with any random bus and line numbering scheme except the slack bus being numbered as 1. In this method a Bus Incidence Matrix (BIM) is constructed and is then processed to reflect the structure of the RDS. The proposed method is demonstrated through different balanced and unbalanced radial distribution systems and the results are presented.

There is a need to reduce the system losses and improve the voltage profile by suitable methods in distribution systems. Some of these methods to improve the overall performance of the distribution systems are presented in subsequent chapters.

A method is proposed using fuzzy expert system for obtaining the optimal branch conductor type in Chapter 4. The conductor, which is determined by this method, will satisfy the maximum current carrying capacity and simultaneously maintains voltage levels of the distribution system within the acceptable limits. The above method also determines the period for which the optimal conductor selected will be suitable even taking the annual load growth into consideration. The proposed method is tested with two different practical radial distribution systems and results are presented.

A simple method for minimizing the loss associated with the reactive component of branch currents by placing capacitors using fuzzy expert system is presented in Chapter 5. In this method, first identify the suitable locations to place capacitors using fuzzy logic and the size of the capacitors is found using an analytical method. The efficacy of the proposed method is tested with different examples of radial distribution systems and the results are presented.

The automatic voltage regulators help to reduce energy losses and to improve the power quality of electric utilities, compensating the voltage drops in distribution systems. In Chapter 6, two different methods are presented to determine optimal number of voltage regulators and their optimal tap position. In the first method, the suitable location and tap position of voltage regulator is determined by using Back Tracking Algorithm. In the second method, the suitable location is determined by using fuzzy logic and its tap position is obtained using analytical method. The two proposed methods are demonstrated through different radial distribution systems and the comparison of results obtained from both these methods is presented.

In Chapter 7, a method is proposed for loss reduction by injecting power locally at load centers. In this method, optimally located distributed generator is used to minimize losses and to improve the voltage profile of the radial distribution system. The optimal locations of distributed generators are determined with the help of fuzzy logic and its size is calculated using an analytical method. The proposed method is tested with different radial distribution systems and results are presented.

The significant contributions of the entire work and the scope for future research in this area are presented in Chapter 8.

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