Harris hawks optimization algorithm based power loss minimization in micro grid incorporated with distributed generation

In this paper, Harris hawks optimization algorithm is used to solve the distributed generation placement problem in the micro grid. Distributed generation will effectively mitigate the loss of a real power system and improve the voltage profile. Thus, reducing actual power loss is viewed as a fitness function to optimally locate and rate the distributed generation in the micro grid. The method presented is applied in the IEEE test systems, such as the 33-bus and 69-bus micro grids. Simulation analyses are performed in MATLAB simulation software and simulation results are compared with existing PSO and ES-PSO algorithms. The results show the superiority and consistency of the Harris hawks optimization algorithm in terms of power loss minimization, voltage profile, and execution time.


Introduction
Electricity is one of the most commonly used energies in the world. Power generation comes from a variety of devices, and the key source has a simple rule of rotational motion to extract energy from the generator. The aim of the power generation system is to generate the power that needs to be used over a time span, by considering the different levels of voltage provided and the energy loss associated with the micro grid [1]. The globalization of energy would greatly increase demand for electricity and will involve community awareness of the environmental effects of the broader power generation industry on more conventional or centralized power generation. With this in mind, it has led to numerous developments in micro grids, with a particular interest in distributed generation (DG) or decentralized generation [2]. DG is a small-scale power generation system, also known as an embedded power source, a decentralized power source, or a distributed power source, which generates electricity from 3 kW to 10,000 kW from wind, solar, biomass, micro-turbines, fuel cells, and so on [3]. The DG unit is more closely interconnected with the loads and is employed for commercial, domestic, and industrial applications. The key benefits of using the DG unit are reduced active power loss, improved voltage stability, improved reliability, enhanced grid, and reduced gas emission. Although DG has many advantages, the choice of the best size and position for the DG unit is an important problem in DG optimization. Studies have shown that inappropriate rating and positioning of DG units 1070 (2021) 012099 IOP Publishing doi: 10.1088/1757-899X/1070/1/012099 2 can result in increased transmission losses, increased costs, and voltage fluctuations due to reverse current flow from mounted DGs. Therefore in order to minimize the loss of control, it is necessary to consider options for the availability of resources to find the optimum position and capability of DG [4]. Renewable energy applications such as solar photovoltaic (PV) system, wind, biomass, and hydro demand better power efficiency, higher reliability, higher versatility, lower cost, and less environmental effects [5]. Renewable energy sources (RES) are projected to play a major role with a prosperous future in electricity boards of developed countries [6]. Many developing countries have also started the shift to a higher share of green energy in their power supply systems by encouraging the business adoption and growth of these technologies. Changes aimed at improving the environment are becoming globally politically accepted, particularly in developed countries. Society is moving slowly towards more sustainable generation techniques, generation of distributed energy, reduction of greenhouse gas emissions, minimization of waste, reduction of vehicle air pollution, and conservation of primeval forests. Meanwhile, DG is expected to bring a vital function in potential energy supplies and minimizing the polluted NOx, SOx, CO2 emissions [7]. Nonetheless, as DG's integration into grid conditions progresses, it presents various disruptions to the safe and effectual service of the micro grid. These issues can be partially solved by DGs optimally placed in the micro grid. The approaches employed to manage and control the behavior of micro grids are therefore constantly altering to optimize and maintain the system active [8]. Therefore, there is an immediate need to focus on more precise scheduling of DGs on micro grids with different objectives. These types of DGs have various benefits but there are several factors to consider. Incorporating the DGs to the micro grid presents a series of various operating constraints that can seriously affect the overall system operation, including voltage limits, power generation limits, power balance constraints, harmonic distortion, fault levels, and system stability issues [9]. This severely impacts the operation and control of micro grids when the system operates without proper attention. The future benefits of DG power generation rely on the rating and location of the DG units in a micro grid [10], [11]. The appropriate evaluation and placement of the DGs can reduce energy loss and improve the reliability level of the entire network. Nevertheless, determining the optimum location and capacity of the DG units is a complicated task and requires computational research on the parameters, while considering the intermittentness and unpredictability with RES [12]. The underlying research of this option should be conducted to meet system constraints while minimizing DG operating costs or other objectives in the functioning of the DG deployment. As the adoption of DGs in the grid increases, optimal operation and planning of the distribution system can enable the deployment of a smart micro grid. It is one of the considerable interests in the global power market today. The DG placement problem can be solved using analytical or artificial intelligent techniques like ant colony optimization (ACO), cuckoo search algorithm (CSA), particle swarm optimization (PSO), simulated annealing (SA), intelligent water drops (IWD), eagle strategy with particle swarm optimizer (ES-PSO), genetic algorithm (GA), firefly algorithm (FA), and hybrid intelligent techniques [1], [9], [13]. Many researchers have suggested new artificial intelligence methods in recent years to explore the optimum position and rating of DGs for the minimization problem in the micro grids based on the real power loss and operating cost of micro grid [13]. In [4], combined GA and IWD are applied for reduction of micro grid's power loss, improvement of voltage profile, and enhancing the voltage stability in the micro grids with subject to security and system operating limitations. In [14], the loss sensitivity factors (LSF) are employed for the detection of DG sites with the aid of the bus voltages. Further, the invasive weed optimization algorithm (IWOA) has been implemented to find DG size. Many researchers have considered the voltage profile enhancement and real power loss minimization as objective functions and solved using modified plant growth simulation technique [1], [9], [13], [14]. In the above approaches, the key disadvantages are low convergence speed and achieve near-optimal solutions only. This paper is aimed to overtake all the disadvantages in the existing methods by implementing a recently developed Harris hawks optimization algorithm (HHOA) to solve the DG placement problem in micro grids with objective function as minimization of active power loss, with subject to various constraints such as DG location, DG power generation limits and voltage limit  [15]. The HHOA is employed to optimize the location and size of DG in a micro grid test system, inspired by nature, to compete with other optimizers. Roused from the attacking nature and accommodative conduct of Harris' hawks, a novel technique called Harris hawks optimization algorithm was formulated by Heidari and co-authors [15]. A portion of the hawks means to astound the prey by pouncing it from various ways. It is noted that the hawks choose the attacking way to depend on the prey's flying path. In this proposed work, HHOA is employed to explore the optimal position and operating rating of DG in IEEE 33-bus and 69-bus micro grids [9]. Thus, the real power loss minimization problem of the micro grid is optimized using the HHOA technique and the obtained results are compared to that of the existing methods, providing helpful conclusions conceiving the effectuality and skillfulness of the proposed HHOA technique. After the introduction, a description of the DG placement issue colligated with its mathematical problem formulation is detailed in Section 2. Section 3 explains the implementation of the purported HHOA technique to determine the optimal bus position and rating of DG in the micro grid. Simulation analyses are discussed in Section 4. At last, Section 5 depicts the conclusion of the purported work.

Real power loss equation
The backward forward sweep technique is employed to solve the power flow in the micro grid. The real power loss equation for the micro grid with and without DG is given as [9], where, PL,DG is the total system real power loss of the micro grid with DG installed; PL is the total system real power loss of the micro grid without DG; P 1 is the total real power injected from the substation or main grid at the main feeder (bus 1) of the micro grid without DG; P 1 withDG is the total real power injected at the main feeder of the micro grid incorporated with DG source; P i D is the real load demand at bus i; P i DG is the real power produced from k th DG installed at bus i, P i DG = Pg k ; and nb is the total number of buses in the micro grid. In case of no DG is installed at bus i or only reactive power supporting DG is installed at bus i, P i DG = 0. The objective of the purported work is to reduce the real power loss of the micro grid installed with optimal DG. Hence, the objective function of this work can be formulated as,

Reactive power loss equation
The reactive power loss equation with and without DG for the micro grid is given as [9], where, QL,DG is the total system reactive power loss of the micro grid with DG installed; QL is the total system reactive power loss of the micro grid without DG; Q 1 is the total reactive power injected from the substation or main grid at the main feeder (bus 1) of the micro grid without DG; Q 1 withDG is the total reactive power injected at the main feeder of the micro grid incorporated with DG source; Q i D is the reactive load demand at bus i; and Q i DG is the reactive power produced from k th DG installed at bus i, Q i DG = Qg k . In case of no DG is installed at bus i or only real power supporting DG is installed at bus i,

Percentage of reduction in real power loss
The percentage of reduction in real power loss is the ratio between the system's real power loss with DG to that of the system without DG.

Percentage of reduction in reactive power loss
The percentage of reduction in reactive power loss is the ratio between the system reactive power loss with DG to that of the system without DG.

Subject to constraints DG real power generation limit
The active power P i DG produced from the DG unit at bus i must be within the lower and upper generation capacity.  (8) where, PDG,max is the upper operating range for active power generated from the DG units; and PDG,min is the lower operating range for active power generated from the DG units. In this study, the upper and lower limits are considered as,

DG reactive power generation limit
The reactive power Q i DG produced from the DG unit at bus i must be within the lower and upper generation capacity.
where, QDG,max is the upper operating range for reactive power generated from the DG units; and QDG,min is the lower operating range for reactive power generated from the DG units. In this study, the upper and lower limits are considered as,

Bus voltage constraint
The bus voltage must be within the voltage lower and upper range.
where V i is the voltage at bus i; Vmax is the maximum voltage limit of the micro grid; and Vmin is the minimum voltage limit of the micro grid. The values are considered as,

DG location constraint
The DG must be located between bus 2 and the last bus of the micro grid.
where, Bus k DG is the bus location of k th DG.

Load model
Different load models are obtained by varying the factors α and β in the mathematical equation (18) and (19) which give the relation between the real & reactive power and the voltage at bus i.
where, V i base is the i th bus voltage at base case; P i D,base is the active base load at bus i; Q i D,base is the reactive base load at bus i; ρ is the load factor is varied by which the load demand is increased or decreased; α and β are load coefficients. The above factors are varied, in order to validate the usefulness of the purported HHOA algorithm in the practical execution. The values are given in Table 1.

Harris hawks optimization algorithm (HHOA)
Roused from the attacking nature and accommodative conduct of Harris' hawks, a novel technique called Harris hawks optimization algorithm (HHOA) was formulated by Heidari and co-authors [15]. A portion of the hawks means to astound the prey by pouncing it from various ways. It is noted that the hawks choose the attacking way to depend on the prey's flying path. HHOA is a population-based exploration technique that optimizes the problem with respect to three significant phases such as exploration, exploitation, and transition that are clarified in the following sections [15].

Exploration stage
In the exploration stage, it is resolved to numerically pause, explore, and find the ideal chase. The position of hawks at iter+1 is numerically computed as, where, iter indicates the current iteration, rabit represents the position of rabbit, rand is the haphazardly chosen hawk in the group of Harris hawks, 1, 2, 3 and 4 are randomly distributed numbers between 0 to 1, and m depicts the mean location of all Harris hawk and is estimated as, where N is the population size of Harris hawks and refers to the location of i th hawks.

The transition between exploration and exploitation
Let T is the maximum iteration count and 0 ∈ (−1, 1) is the initial energy of the rabbit at each iteration, HHOA computes the rabbit's escape energy E as, Based on the rabbit's escape energy, the exploitation and exploration stage of HHOA can change, i.e., when | | ≥ 1, the exploration stage begins; or else the algorithm moves to the exploitation stage.

Exploitation stage
Contingent upon the availability of the rabbit's escape energy, Harris hawks can conceive a hard or soft blockade for chasing it from a different side. A parameter r is characterized to quantify the rabbit's escape possibility. If escape possibility < 0.5, then the rabbit escapes without any trouble. Likewise, if | | ≥ 0.5, HHOA uses a soft surround, and if | | < 0.5, the hard surround is employed. This can be significant that regardless of whether the rabbit gets escape i.e., | | ≥ 0.5, the prey's successful escape relies upon r also. The chasing process is affected by the pursuing and escaping schemes of the Harris hawks and rabbits correspondingly.
In this sense, four significant algorithmic steps are analyzed that are extensively clarified as follows.
More insights regarding the four stages of the exploitation stage in the HHOA technique are detailed as follows.
1. Soft surround [15], if | | ≥ ½, and ≥ ½, then the position of hawks at iter+1 is numerically computed as, where the term ΔX stands for the distance between the rabbit location and the variable J represents the rabbit jump severeness. 2. Hard surround [15], if | | < ½, and r ≥ ½, then the present location is estimated as, 3. Advanced rapid jumps during soft surrounding [15], if | | ≥ ½, and < ½, the following activity of the hawks is computed as, Then, the plunging of the hawks is estimated as, where LF is the Levy's flight; 1xD represents the stochastic vector; and D is the problem dimension. Let and be randomly distributed numbers in the range [0, 1], then LF is determined as, Subsequently, the location of hawks is refreshed as, where β =1.5. 4. Advanced rapid jumps during hard surrounding [15]: if < ½, | | < ½, then the conduct of the Harris hawks that are assumed as close to the rabbit. Hence, the location of hawks is determined as, In the above equation, Y and Z ought to be determined as,

Decision variables
In the DG placement problem, the position of each Harris hawk comprises of DG's location and rating with subjective to constraints (8), (11), and (17). where k is the number of DGs installed in the micro grid. Thus, the dimension of the problem is 3 x k.

Fitness value
For Harris hawks Xi, place all DGs at Bus j DG, j = 1, 2, …, k; in the micro grid and treat DGs' power Pg j and Qg j as negative load. Run the backward forward sweep load flow solution on the micro grid installed with k number of DGs to estimate the system's real power loss using (1). The estimated real power loss is considered as the fitness value of the i th Harris hawks.

Simulation results and analysis
In order to verify the performance of the purported HHOA technique, the simulation case studies are implemented on two test systems such as 33-bus and 69-bus micro grids. The m-script coding is developed in MATLAB simulation software. The control factors employed in the purported HHOA for the DG placement problem are shown in Table 2. The purported HHOA approach may be employed to install many DGs, but in this study, the number of DG is constrained to one. For both the micro grids, the main feeder is assumed as a slack bus for backward forward sweep load flow analysis.

33-bus micro grid
The case study consists of an IEEE 33-bus test micro grid with 32 branches. The total power demand of the micro grid is about 3.715 MW and 2.3 MVAR with 12.66 kV base voltage. The total real power loss of the micro grid without DG is about 210.9876 kW for base loading conditions (base case). The optimum rating and location of DG obtained from the presented HHOA technique are depicted in Table 3. In Table 3, it is seen that the system's real power loss is diminished to 111.0198 kW when a DG unit is located at the 6 th bus of the micro grid with an operating rating of 2.5817 MW. In addition, to validate the efficacy of the presented HHOA algorithm for discovering the optimum location and rating of DG in the micro grid, the proposed HHOA is employed on the same network with different load conditions such as half loading condition of 50% CP and heavy loading condition of 160% CP. The simulation outcomes for all loading conditions are depicted in Table 3. The convergence property of the proposed HHOA, ES-PSO, and PSO is depicted in Figure 1. As shown in Figure 1, the proposed HHOA technique achieves the optimal solution within the 5 th iteration, whereas ES-PSO achieves the same optimal solution at the 38 th iteration. Thus the proposed algorithm converges much quicker than the existing methods. The graphical representation of voltage profile with and without DG is portrayed in Figure 2. Table 4 gives the comparison results of the proposed algorithm and the existing methods [9]. As per Table 4, it is clearly seen that the results obtained from the HHOA provide a better solution than the existing methods. The simulation outcome of the ES-POS algorithm provides a similar optimal solution obtained from the proposed HHOA algorithm. However, the execution time taken to obtain the optimal solution for 100 iterations is about 1.128 sec for the ES-PSO technique where the proposed HHOA technique takes 0.992 sec and which is much lesser than that of both PSO and ES-PSO algorithms.   Table 5. In Table 5, it is seen that the system active power loss is diminished to 83.1476 kW when a DG unit is located at the 61 st bus of the micro grid with an operating rating of 1.8725 MW.
In addition, to validate the efficacy of the presented HHOA approach for discovering the optimum location and rating of DG in the micro grid, the proposed HHOA is employed on the same network with different load conditions such as half loading condition of 50% CP and heavy loading condition of 160% CP. The simulation outcomes for various loading conditions are depicted in Table 5. The convergence property of the proposed HHOA is depicted in Figure 3. As shown in Figure 3, the proposed HHOA technique achieves the optimal solution within the 7 th iteration, whereas ES-PSO achieves the same optimal solution at the 87 th iteration. Thus the proposed algorithm converges much quicker than the existing methods. The graphical representation of the voltage profile with and without DG is depicted in Figure 4. Table 6 gives the comparison results of the proposed algorithm and the existing methods [9]. As per Table 6, it is clearly seen that the results obtained from the HHOA provide a better solution than the existing methods. As like seen in the 33bus micro grid, the simulation outcome of the ES-POS algorithm provides a similar optimal solution obtained from the proposed HHOA algorithm. However, the execution time taken to obtain the optimal solution for 100 iterations is about 5.143 sec for the ES-PSO technique where the proposed HHOA technique takes 1.51 sec and which is much lesser than that of both PSO and ES-PSO algorithms.  The presented HHOA technique has enhanced local and global positions at the end of each generation. For both 33-bus and 69-bus micro grids, the percentage of loss reduction in the proposed HHOA is much better than the existing PSO algorithm. Similarly, the bus voltage profile of the micro grid is also enhanced quite well in the presented algorithm when compared to the PSO algorithm. The computational time of the proposed HHOA technique is also less than that of the existing PSO and 1070 (2021) Table 4 and 6. Moreover, the presented procedure takes a very less number of generations to achieve the optimal rating of DG in micro grids.

Conclusion
Metaheuristic techniques influenced by nature have in recent days gained growing prominence. Metaheuristic techniques have the versatility and potential to solve any issues in engineering optimization. This paper underlines the significance of the main components of exploration and exploitation in the presented Harris hawks optimization algorithm for power system DG placement problem in the micro grid. The proposed technique has been implemented to discover the optimal rating and location of DG in 33-bus and 69-bus micro grids using the Harris hawks optimization algorithm. The simulated studies have been carried out in a MATLAB simulation environment. It is also clear that the proposed Harris hawks optimization algorithm depicts the advantages and superiority over the existing algorithms in terms of real power loss minimization and execution time.
The approach presented can thus be applied in future work to a large-scale power system to find DG's optimal rating and location. Similarly, the approach presented with Harris hawks optimization algorithm can also be expanded with the usage of multi-DG positioning in micro grids to minimize power loss and voltage profile enhancement.