Optimal Distributed Generator Sizing and Placement by Analytical Method and Fuzzy Expert System: a Case Study in Tezpur University, India
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Abstract
Loss minimization in a distribution network is a vital component for enhancing the efficiency and reliability of a power system. Integration of Distributed Generators (DGs) in the existing power system is comparatively an efficient method for loss reduction than other known solutions. Challenges lie in the optimal sizing and placement of distributed generator. Installation of DGs of higher size at non optimal buses leads to higher system losses. In this paper a two stage methodology is proposed for optimal sizing and placement of DGs. At first, the sizing of DGs is done by analytical approach based on exact loss formula for minimum loss at the allied buses. After that Fuzzy expert system (FES) is used for optimal Placement using Distribution Loss Reduction Index (DLRI) and Voltage Deviation Reduction Index (VDRI) as its input parameters. The proposed methodology is tested for a practical distribution system of Tezpur University, India. The results show the effectiveness of the algorithm in terms of the loss reduction and voltage profile improvement of the distribution system.
Keywords
Distributed generator (DG) Power loss Voltage deviation Analytical method Load flow Fuzzy expert systemIntroduction
Electricity generation in the developing countries is growing at a rapid rate, but a majority of people in these countries are yet without electricity. In addition to inadequate generation of electricity, high transmission and distribution loss is one of the major causes of gap in the supply and demand of electricity. For example, the reported T&D losses in India are around 24%. However most of the developed countries are consuming electricity with less than 10% of T&D losses. Further, distribution losses account for up to 80% of total T&D loss. Therefore the need to reduce distribution losses has drawn global attention in the last decade. Distributed Generation (DG) is one of the most attractive options to solve many such modern power system issues such as high transmission and distribution loss, poor voltage regulation etc [1]. Also there is a requirement for providing economically feasible environment for the integration of distributed resources [2]. An economically feasible design model for sizing and placement of gridinterconnected Distributed Generators based system has to be formulated [3]. Smaller generator units which are equal to or less than 1 or 2 MW and installed in distribution systems are referred to as ‘distributed generation’ (DG) [4]. Distributed generators (DGs) are technically defined as the small scale generation units, which are based either on renewable energy sources (e.g., wind, solar photovoltaic, biomass etc.) or conventional energy sources (e.g., diesel generator, small scale gas engine etc.) and are connected near to the load in the distribution network. The consolidation of smart distribution grids is predictably related with the growth and actual employment of different functionalities proposed for future electric grids that includes DG’s functionalities also [5].
Integration of DGs in the existing power systems has been slowly increasing in the last few years. The increasing integration of renewable power and the transition from a centralized electricity production model to distributed generation would pose many challenges to the reliable and sustainable operation of future power systems [6]. According to an IEEE survey, DG penetration in power sector is expected to reach 32% and 26% in Europe and Asia Pacific regions, respectively over the next five years [7]. Installation of solar photovoltaic (SPV) based DGs in countries like India is a suitable energy option, where solar radiation is available all over the region. Implementation of SPV based DGs in distribution network would result in power loss reduction and improvement of voltage profile. Maintaining voltage stability is vital for an efficient power system operation, as the system losses are directly related to the voltage profile. Running cost of SPV based DGs that may be installed for improving the voltage profile of the distribution network, is quite low. Moreover, SPV generator installation would also provide environmental benefits as it does not cause greenhouse gas emission.
Smart Power Grids incorporates superior abilities envisioned to encounter present and future energy demands. These demands comprise enhanced implementation connected with the concepts of reliability, resiliency, environmentally friendly generation, transmission, and distribution as well as turning consumers into prosumers. A smart power grid also relates the stateoftheart technologies to optimize the usage of its resources. For instance, optimized size is achievable with dynamic ratings, which permit resources to be expended at larger loads by constantly detecting and evaluating their capacities [2]. Two important aspects in this area of resource optimizations, are (i) Sizing and (ii) Placement of DGs that require attention to ensure reliable supply of electricity at minimum distribution loss. The size of the DG is decided by the load. Location of DGs should be optimally decided as it influences the distribution loss. Thus, the issue of DG Placement and sizing is of great importance. Present investigation has considered these two aspects for analysis.
Various methods have been proposed to find out the optimum size and location of DGs in a distribution network. Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Fuzzy Logic, Tabu search algorithm are some of the popular computational tools that used in such optimization problems [11]. Genetic algorithm (GA) is a search heuristic method which is used to generate useful solutions to optimization and search problems. GA is used for optimal DG placement using different load models and multiple DG placement to evaluate the loss reduction [8, 9]. The energycost savings due to loss reduction by DG placement using GA is addressed in [10]. PSO is another technique to find out the optimal size and placement of DG by changing location and varying sizes of DGs [11, 12]. PSO method possesses some disadvantages in terms of regulation of particle velocity and hence sometimes leads to the inaccuracy. Hybrid Differential Evaluation Particle Swarm Optimization (HPSO) and Enhanced multiobjective particle swarm optimization (EMOPSO) are two methods proposed to overcome the disadvantages of PSO [13, 14].
Analytical approach and Fuzzy logic have some advantages over PSO [15] as PSO is computationally demanding and slow in convergence. Analytical approach based on exact loss formula along with loss sensitivity factor method can be effectively used for optimal sizing and placement of DGs [16, 17, 18]. Fuzzy logic is a popular computational tool for solving the optimization problems targeting capacitor Placement in distribution system to maximize the energy savings and minimize the loss [19, 20]. This logic is also found to be effectively applicable for DGs Placement and is addressed in recent literatures for similar areas [21, 22]. In this research work, analytical method based on “exact loss formula” is used for optimal sizing of DG and then most suitable bus location for DGs is estimated using Fuzzy Expert System. The bussystem considered in this analysis is an actual Existing Practical Distribution Power System of Tezpur University Campus in North Eastern India with original substation data. The factors of optimal Sizing and Placement of DGs have been addressed specifically as per the minimum loss formulae and by a novel algorithm designed by us since, that is the design requirement and critical issues to be addressed for the electrification of a remote rural location like Tezpur town where DG resources are limited along with limited T&D infrastructure, so using the actual Tezpur University bus system is the practical need of the research since, rural electrification is one of the identified objective for the development of smart microgrids [23].
This paper is organized in six sections “Introduction” gives the introduction. Section “Objectives for the Research Problem” comprises of objectives of the research problem along with constraints. Section “Methodology” discusses the analytical method based on “exact loss formula” and Fuzzy Expert system (FES) respectively, for optimal sizing and Placement of DG to reduce the distribution loss. Electrical distribution system of a University located in India with a connected load of 13 MW is considered as case study to investigate the prospect of DG installation. Description of the test system is given in the “Configuration of Test System”. This section is followed by results and discussion in “Results and Discussion”. Finally, recommendations and conclusions are summarized in “Conclusions”.
Objectives for the Research Problem
Proper voltage profile and availability of power supply as per the demand are the main requirements for a reliable distribution system [24]. Distribution system receives the power from the transmission system and delivers it to the end user. Normally the distribution systems are radial in nature because of their simple structure. Distribution system consists of feeders and distributors. The feeder originates from the substation and passes through the consumer load. It is impossible to deliver power from the sending end to the receiving end without any losses. Major losses in the distribution system are I^{2}R losses which are dissipated as heat in the conductor. Placement of distributed generators of proper size at proper place results in the reduction in I^{2}R losses as it can be placed near to the load. Initially, as the size of a distributed generator at a particular bus or location increases, the distribution loss decreases. It reaches a minimum (optimum) value at optimum size of DG and then again increases with further increase in size of DG. Therefore, optimal Placement and sizing of DG is very important, since the installation of DG of any size higher than its optimal size at improper place may result in higher system losses [25].
A Distributed Generator could be of either type, either renewable energy source based (e.g., wind, solar photovoltaic, biomass etc.) or conventional energy source based (e.g., diesel generator, small scale gas engine etc.). Since, in the northeastern part of India, solar energy is available in abundance, solar photovoltaic (SPV) based DG is an attractive option. Implementation of SPV generator in distribution network would result power loss reduction and improvement of voltage profile along with environmental benefit as it does not cause greenhouse gas emission. Keeping in mind the “OffGrid & Decentralized Solar Applications” Scheme in the 2^{nd} Phase of the Jawaharlal Nehru National Solar Mission (JNNSM, any discrepancies in the size and placement of PV based DGs would ruin the underlying objective of this mission of developing sustainable solar power to rural areas. Moreover, the cost of SPV power produced is substantially higher than the conventional power, and it in turn depends upon the size of the SPV DG panel installed at an optimum location. Thus an oversized SPV panel placed at non optimal power bus will not only lead to more system loss but will also increase the per unit cost of solar power, making it an unattractive option for distributed generation schemes. Thus, this research work aims at optimizing the size and placement of PV based DGs for sustainable and reliable power supply.

Optimal sizing of DG by considering the distribution loss and voltage deviation at each bus

Optimal placement of the DGs in the distribution network
Methodology
Optimal Sizing of Distributed Generator at Particular Bus
r_{ij} + jx_{ij} = Z_{ij} is the ij th element of [Zbus] impedance matrix;
P_{i} and P_{j} active power injections at the i th and j th buses, respectively;
Q_{i} and Q_{j} reactive power injections at the i th and j th buses, respectively;
N number of buses
Placement of Distributed Generator Using Fuzzy Expert System
Fuzzy expert system (FES) uses the fuzzy logic which deals with approximate rather than fixed and exact reasoning. Unlike the classical Boolean set allowing only 0 or 1 value, the fuzzy set is a set with a smooth boundary allowing partial membership. The degree of membership in a set is expressed by a number between 0 and 1, with 0 indicating entirely not in the set, 1 indicating completely in the set and a number in between meaning partially in the set. A fuzzy set can be defined by a function that maps objects in the domain of concern. Such a function is called the membership function. The two most widely used membership functions are the triangular and trapezoidal functions[26].
DL(min) is the minimum distribution real power loss when DG is connected to any bus
other than slack bus
DL(base) is the distribution real power loss without DG
VDI(min) is the minimum voltage deviation index when DG is connected to any of the
buses
other than slack bus
VDI(base) is the voltage deviation index without DG
V_{i,,sp} is the specified voltage magnitude
Fuzzy decision matrix for DG placement
AND  VDRI  

High  HighMedium  Medium  LowMedium  Low  
DLRI  High  High  High  HighMedium  Low  Low 
Medium  Medium  Medium  LowMedium  Low  Low  
Low  LowMedium  LowMedium  Low  Low  Low 
Constraints of DG Placement

Power balance constraint: After installation of DG the power in the i th bus is should satisfy the following power balance equation.
P_{Gi} is the real power generation in the i th bus
P_{Dgi} is the real power injected from DG ati th bus
P_{L} is the load connected to the i th bus respectively

DG capacity constraint: To ensure the reliability every country has DG penetration limit. For India DG penetration factor is considered as 30% and hence second constraint is determined as follows,
Configuration of Test System
The electrical energy demand of Tezpur University is fulfilled through a 33KV/11 KV power station. It has a connected load of 13.042 MW. Electrical energy is supplied to entire university through a distribution network, consisting of two feeders and distribution transformers. Voltage is stepped down by using 11KV/0.433 KV distribution transformers. It is a six bus system. Diesel Generators are used to deliver power during power outage.
For installation of Distributed Generator of optimal size at optimal place, the knowledge of entire test distribution system is required. The present status of existing distribution network, which includes voltage magnitude, power angle and existing distribution loss can be obtained by performing Load flow study. Estimation of Bus data and line parameters are required for the Load flow study.
Estimation of Bus Data

Personally visit to all the departments and hostels to calculate the total connected load of each building.

Data regarding power consumptions of buildings was collected from the main control panel of power supply from the substation.

The details of usage of the appliances were collected by surveying.
Estimation of Line Parameters
Line parameters include resistance and reactance of the line connecting the buses. Resistance and reactance of the conductor used can be calculated by using standard formulae of power system. Data required for calculation of resistance and reactance between the buses of the test system includes conductor properties as well as installation practices. Conductor properties include the type of conductor used, resistivity of the material of the conductor, temperature coefficient of the conductor etc. The conductor properties are estimated from the electrical engineering handbook after collecting information about existing conductor installation. Information comprises of existing conductor type along with cross sectional area, spacing between conductors, frequency of operation, axial spacing between two conductors are collected from the substation of Tezpur University.
The resistance and reactance calculated by adopting proposed methodology gives resistance and reactance of the conductor for one kilometer. The actual length of the conductor is required for the estimation of actual line parameters between two buses. Geographic information system (GIS) is used to estimate the distance between two buses and then length of the conductor estimated by considering 5% sag. Finally, line parameters of the TU distribution network are estimated from available data.
Results and Discussion
Active and reactive power demand at different bus
Bus  Active power demand (kW)  Reactive power demand (kW) 

1  0  0 
2  2548  1589 
3  1138  710 
4  3739  2331 
5  1680  1048 
6  3937  2455 
Line parameters of TU distribution system
Starting bus  Terminating  Line  Distance  Resistance  Reactance 

bus  (m)  (ohm)  (ohm)  
1  2  1  367.11  0.552  0.686 
2  3  2  472.70  0.711  0.883 
3  6  3  946.18  1.423  1.768 
1  4  4  315.29  0.474  0.589 
4  5  5  494.66  0.743  0.924 
 1)
The projected optimal size of DG at bus 2, bus 4 and bus 6 are 1245.7 kW, 1718.4 kW and 1660 kW respectively.
 2)
The Bus 3 and 5 are lightly loaded and hence the need of DG interconnection at these buses does not exist.
Ranking of buses from FES
Bus  DLRI  VDRI  DGAI  Ranking 

2  0.5846  0.83  0.913  3 
4  0.3765  0.89  0.908  2 
6  0.0000  0.00  0.081  1 
Effect of system loss due to single DG placement
Bus No  DG size (kW)  Power loss without DG(kW)  Power loss with DG(kW)  Reduction of power loss due to DG(kW)  Total loss reduction (%) 

6.00  1660.00  812.50  602.30  210.20  25.85 
4.00  1718.40  812.50  659.80  152.70  18.79 
2.00  1245.70  812.50  725.20  87.30  10.74 
Effect on real power loss due to DG placement at multiple buses
DG at bus 2,4  DG at bus 2,6  DG at bus 4,6  

Total loss  Total loss  Total loss  Total loss  Total loss  Total loss 
reduction  reduction  reduction  reduction  reduction  reduction 
(kW)  (%)  (kW)  (%)  (kW)  (%) 
240.00  29.54  297.50  36.62  362.90  44.66 
Along with these technical benefits DG integration reduces the energy import from transmission system and supports the financial returns of the distribution system. It also opens the scope for renewable energy penetration in conventional power system. Thus, DG integration in a distribution network is a viable option for loss reduction and enhancing the power system efficiency.
Conclusions
The present study aims to develop a methodology for integrating Distributed Generator of optimal size at optimal place in any existing electrical distribution network. Methodology comprises of fundamental laws of electricity and optimization techniques including Fuzzy logic. This is also applicable for deciding the parameters of any new electrical network. For a given electrical distribution network the size and placement of DG governs the performance of electricity supply (distribution loss, voltage profile). The application of analytical method integrated with Fuzzy expert system (FES) enables to determine optimal size and optimal location of potential DG. The prospect of distributed renewable energy sources like SPV, wind, biomass have been prime consideration. The methodology for selection of optimal size and optimal location of DG is expected to be useful for deciding the location and sizes of DG for microgrids and offgrid –cumdecentralized power systems. The proposed method is tested on a practical electrical distribution network by considering power loss minimization and voltage profile improvement as decision parameters. The results of the study indicates the effectiveness of the proposed methodology in optimal sizing and placement of DGs based on better voltage profile and loss reduction in the tested system.
The futureresearchwork would be based on optimizing the size and location of DGs for a better steady state voltage stability index using modified teaching–learning based optimization algorithm and Genetic Algorithm bases Particle Swarm optimization (GAPSO) and compare the results of the two since, previously these techniques have not been widely researched for the same purpose and they overcome the disadvantage of a regular PSO algorithm when applied for sizing and placement of DGs.
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