Keywords

1 Introduction

Distribution networks have the highest rate of power loss in power system which has been approximated in the studies about 13% [1, 2]. Hence many efforts have been taken to decrease the power loss in the RDS. The optimal placement of DG has valid effect on decreasing network losses and improving the voltages between the each bus in the distribution networks. The term “Distributed” or “Dispersed” Generation (DG) is used to define as small level power generation that is directly linked to the electric distribution systems.

Distributed Generation consists of synchronous and induction generators, fuel cells, solar photovoltaic installations, combustion and reciprocating engines, micro turbines, wind turbines and other small power generation sources. There are several reasons for a consumer to place a DG in the distribution system. The power supply to the consumers is generated by DG for peak saving or emergency generation or standby purpose. The installation cost of DGs are usually less in compare with construction of new power plants and distribution and transmission lines. The installation of DG exhibits numerous advantages over conventional generations such as power quality, high reliable energy related solutions, economic and environmental friendly [3, 4].

The problem of optimal allocation of DGs in the RDS is become a big challenging task for power system engineers. Till now the numbers of research works have been carried out for optimum allocation of DG in RDS using various optimization algorithms. Bee Colony Algorithm [5], PSO and Monte Carlo simulation [6], GA [7], Honey Bee Mating Optimization Algorithm [8], Quasi-oppositional teaching learning based optimization [9], Backtracking search optimization algorithm [10] have been considered for DG allocation in RDS with different objective function.

In this paper an efficient methodology proposed by considering drawbacks exists in the other optimization techniques to determine the optimal allocation for DG in the RDS for reduction of power loss and bus voltage profile enhancement. Recently developed bio-inspired Bat Algorithm is used to identify the candidate DG location and amount of kW/kVAr injection in the RDS. In the proposed method different types of DG models are considered and analyzed for reduction of power loss and enhancement of bus voltage profile.

2 Power Flow Analysis

Radial distribution networks have high resistance to reactance (R/X) ratio. Therefore traditional load flow studies such as Newton Raphson, fast decoupled and Gauss-Seidal load flow solution methods are not appropriate for finding the voltages between the buses and line flows in the RDS.

The Distribution power flow solution is one of the most efficient methods for load flow analysis of RDS [11]. The main feature of this power flow study is that there is no difficulty of convergence in the solution of radial distribution networks with high ratio of resistance to reactance. The Model radial distribution system is depicted in Fig. 1.

Fig. 1
figure 1

Model radial distribution system

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The equivalent current injection at bus i can be calculate using Eq. (1).

$$I_{i} = \left( {\frac{{P_{i} + jQ_{i} }}{{V_{i} }}} \right)^{*}$$
(1)

where the \(P_{i}\) and \(Q_{i}\) are represented the loads of the active and reactive powers at bus i, respectively.

From Fig. 1, the branch current \(J_{i,i + 1}\) between the buses i and i + 1 can be computed by using KCL, which is given by

$$J_{i,i + 1} = I_{i + 1} + I_{i + 2}$$
(2)

By using the Bus Injected to BIBC, the above equation is derived in matrix format

$$\left[ J \right] = \left[ {\text{BIBC}} \right]\left[ I \right]$$
(3)

where BIBC is Branch Current matrix. From Fig. 1, the bus i + 1 voltage can be calculated by using Kirchhoff’s voltage law, which can be expressed as

$$V_{i + 1} = V_{i} - J_{i,i + 1} (R_{i,i + 1} + jX_{i,i + 1} )$$
(4)

where \(X_{i,i + 1}\) and \(R_{i,i + 1}\) are the Reactance and Resistance of the line segment between buses i and i + 1, respectively. The computation of the real \(\left( {P_{{{\text{Loss(}}i,i + 1 )}} } \right)\) and reactive power loss in the line segment between buses i and i + 1 are listed as follows:

$$P_{L(i,i + 1)} = \left( {\frac{{P_{i,i + 1}^{2} + Q_{i,i + 1}^{2} }}{{\left| {V_{i,i + 1} } \right|^{2} }}} \right)*R_{i,i + 1}$$
(5)

By considering the all line losses in each bus, we can calculate the total active power losses \({P}_{\text{TL}}\).

$$P_{\text{TL}} = \sum\limits_{t = 1}^{nb} {P_{L(i,i + 1)} }$$
(6)

2.1 Objective of the Problem

The objective of the present work is adapted to reduce the total active power loss of the RDS. The objective function can be formulated as

$${\text{Minimize}}\;(F) = {\text{Min}}\,(P_{\text{TL}} )$$
(7)

3 Bat Algorithm

Nowadays, nature inspired algorithms play a major role in distribution system optimization. Xin-Sha Yang developed a nature inspired algorithm known as bat algorithm in the year of 2010 [12, 13]. Echolocation behavior is the main tool of bat algorithm. Bats are alluring animals, these are only the mammals having wings and innovative echolocation ability to find their prey. Generally it radiates a sound signal named echolocation to sense the objects nearby them and identify their technique even in the night times.

Based on the BA idealization rules, the step by step execution of BA for the proposed DG allocation work is described in the following steps.

  1. Step 1:

    First, initialize the system bus and load data.

  2. Step 2:

    Find out the uncompensated system losses, and voltage between the buses with help of distribution load flow.

  3. Step 3:

    The different types of DG placement can be done by using bat algorithm.

  4. Step 4:

    Set the minimum and maximum bounds for the constraints, bat algorithm control parameters (pulse frequency, pulse rates and loudness) and maximum no of iteration.

  5. Step 5:

    Randomly produce the first bat population in the possible area. Each bat indicates an encouraging optimal size for DG in the RDS.

  6. Step 6:

    Calculate the fitness (objective) function. In this step, the predictable value of the power losses and the voltage values can be determined by using Direct Load Flow method for each solution or bat.

  7. Step 7:

    Pick the finest bat in the population (minimum objective function value).

  8. Step 8:

    Update the bat population.

  9. Step 9:

    Run the power flow again and note down the power losses and voltages for updated population.

  10. Step 10:

    Verify the termination criterion. Terminate the algorithm, if the objective function reaches to minimum value otherwise go to step number 5.

  11. Step 11:

    Display the optimal solutions.

To achieve the objective the above steps have been followed to entire optimization process.

4 Results and Discussion for IEEE 33-Bus

To verify the effectiveness of the proposed method, the implementation steps of proposed algorithm and other optimization algorithms have been coded using MTALAB, by considering various test conditions. To verify this; a standard IEEE 33-bus test system is considered and two types of DG models (Type-I and Type-II) also taken into consideration. The base case power losses and voltage between each bus is obtained by using direct distribution load flow method.

4.1 IEEE 33-Bus System

Here in this case, active and reactive loads of medium scale 33-bus system is given as 3.72 MW and 2.3 MVAr respectively. The bus and line data have been obtained from [14]. The uncompensated system active power loss and minimum voltage are 210.98 kW and 0.9037 respectively. In the present work; Type I and II DGs have been taken for the consideration. The 33-bus system schematic diagram is depicted in Fig. 2.

Fig. 2
figure 2

Schematic diagram of IEEE 33-bus system

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In this test system, three DGs (Type-I or Type-II) are optimally located in 13th, 24th and 30th buses. The optimum allocation of the different kinds of DGs are obtained by using bat optimization algorithm. The simulation results obtained by implementing this method are given in Table 1, that depicts the candidate locations, sizes of the DGs, real power loss, minimum voltage between the buses and minimum VSI values. Voltage profile of comparison of 33-bus network is shown in Fig. 3. From Table 1 and Fig. 3, it can be noted that Type-II DG placement is more beneficial as the power loss decrease and bus voltage profile enhancement than the Type-I DG placement. To validate the effectiveness of the present optimization approach, it is compared with the other algorithms such as BSA [10], and QOTLBO [9]. The obtained simulation values are presented in Table 1. From the examining the Table 1 clearly, it can be confirm that, the proposed method gives better results in terms of power loss reduction and bus voltage improvement.

Table 1 Comparison and performance of 33-bus test system
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Fig. 3
figure 3

Comparison of voltage profile for 33-bus network

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5 Conclusion

From the literature and work carried out it is understood that optimal allocation of DGs is one of the major issues in the RDS. It is important to place the DGs at candidate locations with optimal kW and kVAr to ensure the maximum benefits of the system. Different types of DG candidate placements and sizing is determined by implementing BA to achieve the objective function in the RDS. The benchmark 33-bus test system has been considered for analysis in the present work. The results presented in result section shows the effectiveness of the present work in finding best locations. Further, the BA can be recommended as a talented nature inspired algorithm to resolve difficult problems in the engineering fields for the upcoming researchers.