Keywords

1 Introduction

With the constant increase in demand of power, burden on transmission lines, losses in the lines also increases, Das and Roy (2018) [1]. Measures must be taken such that transmission line losses are minimized instead of generating an additional power to meet the required demand which leads to effective usage of the input fuel and economically advantageous by Anbarasan and Jaya bharathi (2017) [2]. By dispatching the reactive power optimally even voltages are maintained in the rated limits. Along with conventional optimization methods, many heuristic techniques were also implemented as seen in below. Sundaram Pandya and Ranjith Roy (2015) recalled with ORPD with the main objective of declination of real power loss [3]. The same was applied to IEEE—14, 30, 57 and IEEE—39 New England bus test systems and are compared with various optimization techniques.

Rebecca Ng Shin Mei, Mohd Herwan Sulaiman, Zuriani Mustaffa, Hamdan Daniyal (2017) introduced a newly surfaced optimization known as moth-flame optimization technique which is addressed to solve the problem of ORPD [4]. This technique makes use of moment of moths that travel during dark time and is applied to IEEE bus systems 30, 57. B. Shaw, V. Mukherjee, S. P. Ghoshal (2014) gave a solution for ORPD [5] by using an opposition based gravitational search algorithm which is based on the gravity and masses interaction which is further modified to opposition-based gravitational search algorithm and this study is applied on IEEE test systems −30 and 57. N. Sinsuphan, U. Leeton, T. Kulworawanichpang (2013) [6] discussed the overall power flow using Improved Harmony Search algorithm inspired by musicians improvisation formulated by Geem and was tested on five standard IEEE systems. K. Valipour and A. Ghasemi (2017) took harmony search algorithm further as modified harmony search algorithm for better results [7]. Dr. K. Lenin (2018) contributed to minimization of real power loss using upgraded red shaver swarm optimization algorithm based on the red shaver behavior and this was implemented on IEEE 30 bus system [8].

In this paper authors presents the usage of other nature inspired methodology known as Firefly algorithm is implemented which serves as the alternative to the present optimization techniques. Firefly algorithm is advantageous due to its ability of automatic sub division and dealing with multimodality. The paper presented is organized as stated:

  • Section 2: Formulation of ORPD problem

  • Section 3: Firefly Algorithm

  • Section 4: Simulation results

  • Section 5: Conclusions.

2 Problem Formulation

2.1 Objective Function

For minimization of real power loss the objective function is expressed as

$$F_{1} = {\text{Min}}\left\{ {P_{\text{Loss}} (a,b)} \right\} = \sum\limits_{m = 1}^{{N_{l} }} {P_{\text{loss}} }$$
(1)

For reliable operation of any system, the voltages must be within the acceptable limits. In order to minimize the total voltage deviation, then the objective function is expressed as

$$F_{2} = {\text{Min}}\left\{ {V_{\text{deviation}} (a,b)} \right\} = \sum\limits_{n = 1}^{{N_{b} }} {\left| {V_{n} - V_{\text{spec}} } \right|}$$
(2)

For multi objective function above stated 2 functions in Eqs. (1) and (2) are given equal weight age such that

$$F_{3} = 0.5*F_{1} + 0.5*F_{2}$$
(3)

2.2 Constraints

In order to achieve all the above objectives, the following restraints must be contended. The equality constraint is the basic load flow equation which states that generation of power must meet its demand and losses which is shown in Eqs. 4 and 5 below

$$P_{Gz} - P_{Dz} - V_{z} \sum\limits_{i = 1}^{{N_{b} }} {V_{i} } \left( {\begin{array}{*{20}c} {G_{zi} } & {\cos \theta_{zi} } \\ {B_{zi} } & {\sin \theta_{zi} } \\ \end{array} } \right) = 0$$
(4)
$$Q_{Gz} - Q_{Dz} - V_{z} \sum\limits_{i = 1}^{{N_{b} }} {V_{i} } \left( {\begin{array}{*{20}c} {G_{zi} } & {\sin \theta_{zi} } \\ {B_{zi} } & {cos\theta_{zi} } \\ \end{array} } \right) = 0$$
(5)

The inequality constraints are

$$P_{Gm,\hbox{min} } \le P_{Gm} \le P_{Gm,\hbox{max} } ;m \in N_{g}$$
(6)
$$Q_{Gm,\hbox{min} } \le Q_{Gm} \le Q_{Gm,\hbox{max} } ;m \in N_{g}$$
(7)
$$V_{Gm,\hbox{min} } \le V_{Gm} \le V_{Gm,\hbox{max} } ;m \in N_{g}$$
(8)
$$T_{m,\hbox{min} } \le T_{m} \le T_{m,\hbox{max} } ;m \in N_{t}$$
(9)
$$Q_{cm,\hbox{min} } \le Q_{cm} \le Q_{cm,\hbox{max} } ;m \in N_{c}$$
(10)

\(N_{l} ,N_{b} ,N_{g} ,N_{t} ,N_{c}\) denotes number of lines, buses, generators, Transformers, Capacitors.

3 Firefly Algorithm

Xin-She Yang (2008) developed an algorithm based on its flashing nature of fireflies [9]. Firefly’s stands in the superiority compared to other developed meta heuristics techniques because of its three intrinsic idealized properties [10,11,12].

3.1 Implementation of FA for ORPD

  1. (1)

    Initialize

    • Number of fireflies

    • Number of iterations

    • Set the values of α, β and

    • In this, the values of α, β and γ are considered as 0.2, 0.1 and 1 respectively.

  2. (2)

    Set the iteration counter i = 0 and increase the iteration by i = i + 1.

  3. (3)

    Calculate the fitness result of each firefly by substituting in the objective function stated in Eqs. (1), (2) and (3).

  4. (4)

    Sort the fireflies depending on their light intensities and for every iteration find the best firefly. Light intensity is varied based on the distance between them.

  5. (5)

    Move the fireflies (control variables) based on their light intensity.

  6. (6)

    Continue the process till stopping criteria is reached.

4 Simulation Results and Discussions

4.1 IEEE 30 Bus System

This IEEE 30 bus system comprises of 6 generator buses including slack bus, 4 transformers with tap setting values and 3 reactive power compensation devices. These values are given in Sundaram Pandya and Ranjith Roy (2015) [3]. So, totally in 30 bus system have 13 control variables whose limits are stated below in Table 1.

Table 1 Limits of control variables
Full size table

Case 1—Minimizing real power loss (RPL)

The control variables in this objective are tuned in order to minimize the real power losses of IEEE 30 bus system. The control variables values are shown in Table 2 along with its convergence characteristics in Fig. 1. Minimum, maximum, mean and standard deviations are shown in Tables 3 and 4.

Table 2 Parameters of control variables and power loss
Full size table
Fig. 1
figure 1

Graph of convergence for minimization of losses in IEEE 30 bus system with FA

Full size image
Table 3 Mean and standard deviation of Real Power losses in IEEE 30 bus system with FA
Full size table
Table 4 Comparison of real power loss with different optimization techniques
Full size table

Case 2—Minimizing voltage deviation (VD)

The bus voltages with its deviated value form 1 p.u are shown in Table 5. More voltage deviation in the system results in weak behavior of the system. Convergence characteristics of the system are shown in Fig. 2.

Table 5 Optimal values of bus voltage deviation of IEEE 30 bus system with FA by minimizing voltage deviation
Full size table
Fig. 2
figure 2

Convergence curve of minimization of voltage deviation with FA

Full size image

Case 3—Multi objective function

The multi objective function is considered here. The optimal values that control both the objectives and the convergence curve are shown in Table 6 and Fig. 3 respectively.

Table 6 Optimal values of active power loss and voltage deviation by considering multi objective optimization with FA
Full size table
Fig. 3
figure 3

Convergence characteristics for multi objective function with FA

Full size image
$${\text{Optimal value}} = 0. 5*0. 1 9 50 + 0. 5*0. 2 3= 0. 2 1 2 5\;{\text{p}}.{\text{u}}$$

Thus, control of variables for minimization of real power losses, voltage deviation and for multi objective is discussed. Through multi objective loss are said to be better than second objective and voltage deviation is reduced considerably compared to the first case thus satisfying control of both the objectives.

5 Conclusions

In this paper, multi objective function for minimization of real power losses and voltage deviation is performed for IEEE 30 bus systems using FA. The obtained results for minimization of losses are compared with other stated papers and values achieved through FA are found to be superior and it is widely used because of its efficiency.