Reduction of Line Losses and Enhancement of Voltage Stability in a Radial Distribution System with Renewable Distributed Generation

Reduction of line losses in a distribution system is very important and cannot be overlooked in the modern distribution systems which have been expanded to meet the increased load demand. This is because line losses have an undesirable effect on the voltage profile of the power system especially when electrical power has to be transmitted over long distances due to increased line resistance. Consequently this results to increased voltage drop along the lines and voltage compensation has to be employed to avoid voltage collapse. Introduction of Renewable Distributed Generation (RDG) in the distribution network has been deployed in addressing this problem in the recent past. However, interconnection of these RDGs to the grid has to be properly done to enhance the performance of the system by reducing line losses and improving the system’s voltage profile. A formulation of the multi-objective problem of reducing line losses and enhancing voltage stability of the distribution system with RDGs is very important for proper system operation. This paper presents a three method approach of optimally locating and sizing RDGs using Voltage Stability Index (VSI), Adaptive Genetic Algorithm (AGA) and Simulated annealing (SA) to solve this problem. Researchers have solved this problem by; using under frequency load shedding, optimally locating Flexible AC Transmission systems (FACTS) and by use of capacitor banks to achieve reactive power compensation. Over the last decade optimal DG placement and sizing has been an emergent trend. This paper contains a review of the methods applied by other researchers in solving the problem, a detailed formulation of the multi-objective problem and an analysis of the solutions obtained from the standard IEEE 33 Bus test system using MATLAB. Results from the proposed method are compared with Particle Swarm Optimization (PSO) method and Optimal Power Flow and Improved Harmony Search (OPF and IHS) hybrid. Obtained results indicate that properly located and sized RDGs reduce line losses and increase voltage stability in a radial distribution network.


INTRODUCTION
Owing to the increase in electrical load at the distribution level of a power system, distribution network expansion has proofed to be inevitable. It is therefore, critical to ensure that the system remains stable and reliable. Renewable Distributed Generation has been an emerging trend in curbing the problem of line losses and voltage stability in expansive distribution networks by having RDGs located near the consumer centers. This reduces transmission line losses and eliminates the cost of transmission network expansion that would be required to cater for the additional electrical load. RDGs have been adopted because they pose minimal environmental effects and cannot be depleted unlike fossil fuel Distributed Generators. Following the increased advocacy on environmental conservation worldwide, RDG has become an active emergent trend over the last decade. Contribution:-This research paper gives a review of various methods used in placing and sizing grid interconnected DGs, a detailed formulation of the multi-objective problem aimed at reducing line losses and improving voltage stability of a radial distribution system with Renewable Distributed Generation and a two method hybrid optimization technique of solving this problem using a proper blend of wind and Photovoltaic solar sources. Paper organization:-This paper has five major parts; part II contains literature review, Part III has the problem formulation, part IV consists of the methodology, part V contains the results and a detailed analysis and part VI is made up of the conclusion.

II. LITERATURE REVIEW
Renewable distributed Generation refers to renewable energy sources that are located at load centers either individually or with grid integration so as to meet increased electrical load. Grid Interconnected Renewable Distributed Generation is an emerging trend in modern power systems and it is therefore important to study their effects in the distribution system and also how to improve system performance. Previous research works have found out that incorporation of RDGs in to the grid may affect the system's power factor, line losses and voltage profile due to the fluctuation of power output from the sources. Consequently, system protection may be affected because RDGs may cause reverse active power flow in the feeders [1] [2]. Non-optimally sized and located RDGs results in increased losses, costs and system instability.

International Journal of Engineering Research & Technology (IJERT)
ISSN: 2278-0181 http://www.ijert.org Researchers have used bus stability indices to determine the lines that are susceptible to voltage instability. These include Voltage Stability Index (VSI) [3] [4]. This paper contains a three method approach of solving the multi-objective problem of reducing line losses and total voltage deviation of a radial distribution system on the IEEE 33 Bus system.

III. PROBLEM FORMULATION
The following single objectives were formulated and later combined into the multi-objective function.
A. Total line losses, .
Equation 1 is used to calculate the base values without any RDG penetration into the grid.
Where i=1, 2, 3,….,N buses, R k and X k are resistance and reactance of the kth branch respectively, P k and Q k are the real and reactive power at the sending end of the kth branch, P kDG and Q kDG are the real and reactive powers of the RDGs connected to the sending end of the kth branch and |V k | is the magnitude of the voltage at the sending end of the kth branch.
Where P DG min and P DG max are the minimum and maximum active power limits and Q DG min and Q DG max are the minimum and maximum reactive power limits respectively.
Where P Gi − P Di gives the real power injected and Q Gi − Q Di is the reactive power injected at a bus, and are the conductance and susceptance of the line between buses i and k. [5].

E. Voltage Stability Index formulation
( ), is the voltage stability index of the receiving end bus, is the magnitude of the sending-end voltage, and represent the line resistance and line reactance respectively. and are the real and reactive power loads connected to the jth bus.
The voltage of all buses and currents at all the branches can be determined from load flow studies. Consequently, and at the receiving end of each line can be calculated. Thus bus with the minimum VSI is more proximate to voltage collapse [6] [5].

IV. METHODOLOGY
The following is the process undertaken during the three method optimization technique.
Step 1: The IEEE 33 Bus system data was obtained.
Step 2: Candidate buses were determined using the VSI.
Step 3: The buses with the least VSI were taken as the candidate buses for RDG placement. RDG sizes were determined using Adaptive Genetic Algorithm ad Simulated Annealing (AGA-SA). The candidate bus with the results that greatly enhance system performance is selected as the first RDG location and size.
Step 4: Determine the second RDG size for the remaining candidate buses with the bus data updated with the first RDG size using Adaptive Genetic Algorithm and Simulated Annealing.
Step 5: Determine the third RDG size for the remaining candidate buses with bus data updated with the first and second RDG sizes using Adaptive Genetic Algorithm and Simulated Annealing.
Step 6: Steps 3, 4 and 5 were carried out for Photo voltaic Solar generators (generates real power only) and wind generators (generates both real and reactive power) separately.
Step 6: Results were tabulated and analyzed. They were compared with other research works. Tables 1 and 2 show the mapping of the Adaptive Genetic Algorithm and Simulated Annealing parameters used in the optimization.    Table 3 shows the base values of JTLL and JTVD before RDG integration into the system.  Figure 1 shows Voltage stability indices for each bus based on equation 9 using Newton Raphson method.  Table 4 shows the optimal RDG size, the total line losses and total voltage deviation after incorporating one real power generating RDG. The proposed method gives a 62.4% reduction on the total line losses which is greater compared to the losses from the other comparative works. It also gives a 61.8% reduction in the total voltage deviation and the system performance is therefore, enhanced by having a 3.56 MW Photovoltaic Solar generator placed at bus 33. Table 5 shows the optimal RDG sizes, the total line losses and total voltage deviation after incorporating two real power generating RDGs. The proposed method gives a 62.1% reduction in total line losses with incorporation of two real power generating RDGs at buses 33 and 18. There was 73.2% improvement in the total voltage deviation from the base value with two real power generating RDGs incorporated as compared to the 61.8% improvement with only one real power generating RDG. Table 6 shows the optimal RDG sizes, the total line losses and total voltage deviation after incorporating three real power generating RDGs. The proposed method gave a higher total line loss reduction as compared to PSO method only. However, it gave a lower reduction in total line losses as compared to OPF and IHS. There were no changes in the total line losses and the total voltage deviation when three real power generating RDGs were incorporated compared to when two real power generating RDGs were incorporated. Therefore only two properly sized RDGs can be incorporated to achieve better system performance that would be achieved with three RDGs sized using PSO only or using OPF and IHS. This would save on the cost of setting up the third RDG. Table 7 shows the optimal RDG sizes, the total line losses and total voltage deviation after incorporating one real and reactive power generating RDG. The proposed method gave a 71.6% reduction in JTLL in comparison with PSO only and a hybrid of OPF and IHS algorithms which had a 68% reduction in total line losses. The total voltage deviation was reduced by 59.1%. The proposed method gave smaller RDG sizes compared to PSO and OPF and IHS methods. Table 8 shows the optimal RDG sizes, the total line losses and total voltage deviation after incorporating two real and reactive power generating RDGs. Incorporation of two RDGs generating both real and reactive power using the proposed method gives a 75.7% reduction in total line losses compared to incorporation of only one RDG which reduced the total line losses by 71.6%. It also gives a better voltage profile by reducing the total voltage deviation by 70.1% as compared to incorporation of one RDG which reduces the total voltage deviation by 59.1%. Table 9 shows the optimal RDG sizes, the total line losses and total voltage deviation after incorporating three real and reactive power generating RDGs.  Incorporation of a third real and reactive power generating RDG did not have any considerable effect on the reduction of line losses compared to the system with two such RDGs integrated. However, the voltage profile deteriorated from a 70.1% reduction in total voltage deviation with two RDGs to 59.1% reduction with three RDGs. The results in table 7 and 8 indicate that the system achieves enhanced performance with only two RDGs incorporated. Integration of a third RDG would result to increased costs of setting up the third RDG unit which would cause a distortion of the system's performance. Therefore the proposed method would be used in optimally siting ad sizing two RDG units.

VI. CONCLUSION
This paper has presented a three method approach of solving the multi-objective problem of reducing total line losses and total voltage deviation in IEEE 33 bus system. The optimal locations were obtained using Voltage Stability Index and a hybrid of Adaptive Genetic Algorithm and Simulated Annealing was used to achieve the optimal RDG sizes while solving both objectives simultaneously because it has the better convergence. Results show that having one and two optimally placed and sized RDGs would improve the system performance. A third RDG would not be required with the propose algorithm because it would distort the system performance. Further work can be done on applying this method on larger interconnected test systems and also tested on a network with a variable loading profile.