A Novel Approach for Optimal Allocation of a Distributed Generator in a Radial Distribution Feeder for Loss Minimization and Tail End Node Voltage Improvement during Peak Load

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The steps involved in this GA scheme for optimization are explained below ^{[14, 15]}:

1. Generate initial population – the first generation is randomly generated, by selecting the genes of the chromosomes among the allowed alphabet for the gene. Because of the easier computational procedure it is accepted that all populations have the same number (N) of individuals.

2. Calculation of the fitness values of the function that we want to minimize or maximize.

3. Check for termination of the algorithm – it is possible to stop the genetic optimization by:

• Value of the function – the value of the function of the best individual is within defined range around a set value. It is not recommended to use this criterion alone, because of the stochastic element in the search procedure, the optimization might not finish within sensible time;

• Maximal number of iterations – this is the most widely used stopping criteria. It guarantees that the algorithms will give some results within some time, whenever it has reached the extremum or not;

• Stall generation – if within initially set number of iterations (generations) there is no improvement of the value of the fitness function of the best individual the algorithms stops.

4. Selection – between all individuals in the current population are chose those, who will continue and by means of crossover and mutation will produce offspring population. At this stage elitism could be used – the best n individuals are directly transferred to the next generation. The elitism guarantees, that the value of the optimization function cannot get worst (once the extremum is reached it would be kept).

5. Crossover – the individuals chosen by selection recombine with each other and new individuals will be created. The aim is to get offspring individuals that inherit the best possible combination of the characteristics (genes) of their parents.

6. Mutation – by means of random change of some of the genes, it is guaranteed that even if none of the individuals contain the necessary gene value for the extremum, it is still possible to reach the extremum.

7. New generation – the elite individuals chosen from the selection are combined with those who passed the crossover and mutation, and form the next generation.

4. Proposed Methodology

The proposed technique based on multi objective GA for optimal allocation of a DG unit in radial distribution feeder is as follows:

Step 1: Input load data & line data of distribution network.

Step 2: Using forward-backward method of load flow analysis ^[16], calculate distribution system power loss.

Step 3: Generate initial population of chromosomes with random size and position and set iteration count to zero. Each chromosome is associated with a bus position & real power rating of DG.

Step 4: Fix the maximum limits on DG size and its position. Limit on position of DG depends on no. of buses in test system under consideration.

Step 5: For each chromosome check the bus voltage with specified limits and in any case if it is exceeding limit then the chromosome is infeasible and discarded.

Step 6: For each chromosome, calculate fitness function value which is value of objective function F in present case given in (5).

Step 7: Arrange the objective function values from minimum to maximum and discard the unfit values and retain most fit values.

Step 8: Perform Mutation and Mating operations on retained chromosomes to generate new set of chromosomes.

Step 9: Calculate fitness values of new set of chromosomes generated.

Step 10: Increase iteration count by 1 & repeat step 5 to 9 until iteration count reaches maximum iteration.

The solution obtained after completion of step 10 is optimal solution to the problem. The value of the chromosome at the end includes optimal size & location of the DG for the given distribution system.

5. Results and Discussion

The proposed methodology is tested on IEEE-33bus radial distribution system shown in Figure 2 having following characteristics: Number of buses = 33; Number of lines = 32; Slack Bus no = 1; Base Voltage = 12.66KV; Base MVA = 100 MVA;

The test system is simulated in MATLAB 2008 & the proposed methodology has been tested, whose results are as shown below. The loads are assumed to be peak load.

Figure 2. Single line diagram of IEEE-33 bus RDS

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Figure 3. Base Case Voltage

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As per the proposed methodology with 90% weightage given to power loss reduction and 10% weightage to tail end node voltage improvement in multi objective function, the optimal location of DG is found to be bus number 30 with optimal size of 1.7622 MW and 0.8535 MVAR. The result tabulated in Table 2 clearly shows that there is 62.83% reduction in real power loss of system and more importantly there is considerable improvement in tail end node voltage given in Table 1. Hence the proposed method gives better tail end node voltage along with loss minimization as shown in Figure 4, The voltage profile of the distribution system with DG and without DG is shown in Figure 5.

Figure 4. Comparison of Tail End Node Voltages with and without DG

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Table 1. Tail End Node Voltage Improvement with DG

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Table 2. Real Power Loss Reduction with DG

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Figure 5. Comparison of Voltage Profile with DG

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Table 3. GA parameters

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The Genetic Algorithm (GA) parameters used in this proposed DG allocation methodology for test system is shown in Table 3. Each population consists of three chromosomes representing Location, Real power of DG and Reactive power of DG respectively. At each iteration, each population is evaluated for its fitness from (5). After maximum number of iterations specified in Table 5, the optimal solution is obtained.

The performance of the proposed optimal DG allocation method when applied to IEEE 33 bus radial distribution system is compared with the other methods in Table 4. In all the methods, it is observed that the distribution system real power loss is going to be reduced after allocating a DG unit in distribution system. In order to quantify the most effective DG unit, the improvement in the loss reduction is compared with the DG size in MVA injection. This gives loss savings in Kw per Unit DG MVA injection, a better value indicates the allocation results in high loss reduction whereas a poor value of which indicates the allocation results in less loss reduction comparatively.

It is very clear from Table 4 that, the proposed method yields loss reduction of 67.977 KW/MVA DG injection and hence the proposed method tries to bring down the distribution system real power loss to a lower value comparatively and thereby benefits the utility in terms of revenue improvement.

Table 4. Comparison of performance parameters

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Table 5 illustrates the improvement of critical tail end nodes voltage profile with the proposed method. It is evident that the proposed method provides considerable improvement in the voltage comparatively especially with the bus no 33. The proposed methodology while reducing the power loss of the distribution system with the lesser size of a DG unit comparatively as shown in Table 4, it will improve the tail end nodes voltage profile also.

Table 5. Comparison of Tail End Node Voltages

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