Optimal Placement of Distributed Generation Based on Power Quality Improvement Using Self-Adaptive Lévy Flight Jaya Algorithm

Abstract

The optimal placement of distributed generation (DG) is a critical task for distribution companies in order to keep the distribution network running smoothly. The optimal placement of DG units is an optimization problem. In this paper, minimization of the voltage deviation from flat voltage is considered as an objective function. The self-adaptive Lévy flight-based Jaya algorithm is used as an optimization technique to determine the best location and size of distributed generation units. In the MATLAB environment, the proposed algorithm was implemented on IEEE 15 and PG and E 69 bus distribution systems. According to the simulation results, distribution networks can supply more quality power to customers by minimizing the voltage deviation from the flat voltage profile if the DG units are properly placed and sized.

1. Introduction

The incorporation of distributed generation (DG) into the distribution system has grown at a rapid pace due to its technical, economic, and environmental benefits [1,2], such as power quality improvement, loss reduction, emission reduction and increase in the financial growth margin for distribution companies (DISCOs), leading to an increase in the integration of DG units over the last decade [3]. This integration may have a positive or negative impact on the distribution system. The positive benefits built into the distribution network are achieved by optimal positioning and sizing of the DG units. Incorrect positioning of DG units has a negative impact on the distribution network.

The optimal placement and sizing of DG units is a common issue in radial distribution systems. Determining the optimal location and size of DG units to maximise the voltage profile, while maintaining the required high quality operating conditions, is critical. Power quality (PQ) refers to the ability to maintain the power distribution bus voltages near to the flat voltage profile. It is commonly used to express the voltage quality. However, voltage quality and power losses are the fundamental factors that influence other factors [4]. In this paper, the optimal placement of DG units in distribution system is determined based on power-quality improvement using a self-adaptive Lévy flight-based Jaya algorithm.

Many optimization algorithms and objective functions have been proposed to determine the ideal location and size of DG units so that distribution businesses can profit from DG unit integration. DG placement in IEEE 15 bus and PG and E 69 bus radial distribution systems based on loss reduction using the genetic algorithm, the firefly algorithm and the hybrid genetic dragonfly are discussed in [5,6,7]. DG placement in IEEE 15 bus and PG and E 69 bus radial distribution systems based on benefit to DISCOs using black widow optimization is discussed in [8]. DG placement in IEEE 33 bus and PG and E 69 bus radial distribution systems based on a voltage stability index using butterfly optimization is discussed in [9].

DG placement in IEEE 33 bus and PG and E 69 bus radial distribution systems based on minimization of active power losses using grasshopper optimization and the cuckoo search technique is discussed in [10]. DG placement in IEEE 33 bus and PG and E 69 bus radial distribution systems based on minimization of active power losses and voltage deviation using an enhanced genetic algorithm is discussed in [11]. DG placement in IEEE 33 bus and PG and E 69 bus radial distribution systems based on minimization of active power losses using heuristic algorithms is discussed in [12]. DG placement in IEEE 38 bus radial distribution systems based on economic and operational issues using a lightning search algorithm is discussed in [13]. Event-trigger-based distributed cooperative energy management for multi-energy systems is proposed in [14]. Automated distribution network reliability optimization in the presence of DG units considering the probability of customer interruption is discussed in [15]. The optimal placement and sizing of DG units using an improved non-dominated sorting genetic algorithm is proposed in [16].

DG placement in IEEE 14 bus and 30 bus radial distribution systems based on transmission costs using the MW-Mile method is discussed in [17]. DG placement in an IEEE 33 bus radial distribution system based on voltage profile enhancement using an equilibrium optimizer is discussed in [18]. DG placement in an IEEE 14 bus radial distribution system based on LMP and congestion using a GA-GSF algorithm is discussed in [19]. DG placement in an IEEE 6 bus radial distribution system based on minimization of active power losses using a fuzzy expert system is discussed in [20]. DG placement in an IEEE 33 bus radial distribution system based on minimization of active power losses using GA, PSO and BWO is discussed in [21]. DG placement in IEEE 33 and PG and E 69 bus radial distribution systems based on minimization of active power losses using the firefly algorithm is discussed in [22]. DG placement in IEEE 33 and PG and E 69 bus radial distribution systems based on node power mismatches using the soccer game optimization is discussed in [23].

DG placement in a Park–Umngeni 11kV feeder radial distribution network based on active and reactive power losses using simulated annealing optimization is discussed in [24]. DG placement in a PG and E 69 bus radial distribution system based on minimization of active power losses using the honey badger optimization is discussed in [25]. DG placement in an IEEE 14 bus radial distribution system based on minimization of active power losses and voltage deviation using the battle royale optimization, accelerated PSO and the genetic algorithm is discussed in [26]. DG placement in IEEE 16 and 33 bus and PG and E 69 bus radial distribution systems based on minimization of active power losses using mixed-integer linear programming is discussed in [27]. DG placement in an IEEE 33 bus radial distribution system based on minimization of active power losses and enhancement of voltage profile using PSO is discussed in [28]. DG placement in IEEE 33 bus and PG and E 69 bus radial distribution systems based on minimization of active power losses using an iterative algorithm is discussed in [29].

DG placement in an IEEE 33 bus radial distribution system based on minimization of active power losses and operational cost using GA and PSO is discussed in [30]. DG placement in 15, 118 and 51 bus radial distribution systems based on emission, cost and voltage deviation using the manta ray foraging optimization is discussed in [31]. DG placement in an IEEE 33 bus radial distribution system based on voltage stability, loss and cost using PSO is discussed in [32]. DG placement in a PG and E 69 bus radial distribution system based on the voltage stability index and loss using an iterative procedure is discussed in [33]. DG placement in a 34 bus radial distribution system based on voltage profile and loss using GA, SA, HGA and VNS is discussed in [34]. DG placement in a 33 bus radial distribution system based on voltage stability and loss using Advanced-PSO is discussed in [35]. DG placement in 37 and 119 bus radial distribution systems based on voltage profile and loss using an exhaustive iterative method is discussed in [36]. DG sizing in IEEE 15 bus and PG and E 69 bus radial distribution systems based on losses, emission and reliability using game theory, the point estimation method and hybrid heuristic algorithms is discussed in [37,38,39,40].

The main contributions of this paper are as follows:

• Determination of optimal location and size for multiple DG units based on power quality in terms of voltage deviation from the flat voltage profile
• A self-adaptive Lévy flight Jaya algorithm (SALFJA) representing an improved version of the Jaya algorithm by the addition of Lévy flight for extensive search is used for optimal DG placement
• The performance of the proposed method is validated in a stochastic environment
• The power quality of the distribution system is mathematically modeled as a sum of squares of voltage deviation at each bus from the flat voltage profile

The remainder of the paper is organized asfollows: Section 2 discusses the formulation of the problem and describes the optimization algorithm. Section 3 provides an analysis of the simulation results. Section 4 presents the conclusions.

2. Methodology

2.1. Mathematical Modeling of DG Placement

DG placement in a radial distribution system is an optimization problem. In this paper, power quality enhancement is considered as an objective by keeping DG units in a proper location with appropriate size. Power quality in the network is measured in terms of the total voltage deviation from the flat voltage profile that is mathematically modeled as shown in Equation (1).

$$MinVoltageDeviation=\sum _{i=1}^n{(1-v\left(i\right))}^2$$

(1)

The DG placement problem as a constrained optimization problem, and the equality constraint as a power balance constraint, is represented in Equation (2). The inequality constraint as a thermal limit of the feeder is represented in Equation (3),

$$\sum _{i=1}^{n}P\left(i\right)=P_D+P_{loss}$$

(2)

$$S_l\le S_{max}$$

(3)

In this optimization problem, the DG unit location and size are the decision variables; the boundaries are represented in Equations (4) and (5), respectively.

$$2\le D{G}_{loc}\le n$$

(4)

$$0\le D{G}_{size}\le 1MW$$

(5)

In this paper, two DG units were considered for study and both were considered to be PQ models.

2.2. Self-Adaptive Lévy Flight Jaya Algorithm (SALFJA)

Meta-heuristic algorithms are created because traditional optimization approaches are unsuitable for handling non-linear problems and are extremely sensitive to initial guesses [41]. The Jaya algorithm [42] was designed with the intention that the solution should move away from the worst solution and towards the best solution. In this study, Lévy flight is employed in conjunction with the Jaya algorithm to increase search capabilities—by avoiding the solution from becoming trapped in the local optimum, an effective search utilising Lévy flight may be obtained. The Lévy flight search improves the capacity to perform both global and local searches at the same time. The Lévy flight is modeled mathematically as shown in Equations (6) and (7).

$$Lvy=0.01\times \frac{r_1\sigma }{|r_2{|}^{\frac{1}{\beta }}}$$

(6)

$$\sigma ={\left(\frac{\Gamma (1+\beta )\times sin\left(\frac{\pi \beta }{2}\right)}{\Gamma \left(\frac{1+\beta }{2}\right)\times \beta \times 2\left(\frac{\beta -1}{2}\right))}\right)}^{\frac{1}{\beta }}$$

(7)

where $r_1$ and $r_2$ are random numbers in [0, 1] produced by a normal distribution. A complete flowchart representing SALFJA for optimal DG placement based on power quality enhancement is presented in Figure 1.

3. Results Analysis

The SALFJA algorithm to address the proposed DG placement optimization problem was implemented on IEEE 15 bus and PG and E 69 bus distribution systems. The line and load data for the test systems were drawn from [43]. In this study, two PQ modeled DG units, each with a capacity of 1 MW and a 0.9 lagging power factor, were used and simulated in a MATLAB environment.

3.1. Case Study—01: IEEE 15 Bus Radial Distribution System

To identify the placement and generating capacity of the DG units, the proposed SALFJA algorithm was simulated ten times in MATLAB. The best of ten simulations, in terms of minimum total square voltage deviation in the test system, was used to determine the placement and generating capacity of the DG units.

Table 1. Stochastic behaviour of SALFJA on IEEE-15 bus test system.

Simulation	TSVD	Simulation	TSVD
1	0.00018	6	0.00018
2	0.00018	7	0.00018
3	0.00018	8	0.00018
4	0.00018	9	0.00018
5	0.00018	10	0.00018
Min	0.00018	Max	0.00018
Mean	0.00018	Std.	0

shows the performance of the proposed method in a stochastic setting. The standard deviation was 0 since the suggested approach produced the same amount of total square voltage deviation (TSVD)) across all runs, i.e., 0.00018. A standard deviation of zero indicates that the suggested SALFJA algorithm produced a solution that was free of ambiguity.

Figure 2 depicts the performance curves of the proposed SALFJA for optimal placement of DG units throughout ten simulations. According to Figure 2, the suggested method converged at an TSVD value of 0.00018 for all ten simulations.

Table 2. Optimal location and size of DG units.

DG1		DG2
Location	Size	Location	Size	TSVD	Base Case TSVD
2	1 MW	3	1 MW	0.00018	0.0283

shows the ideal location and capacity for the two DG units in the IEEE 15 bus distribution network. According to Table 2, the distribution network will run with a TSVD value of 0.00018 if two DG units with generating capacities of 1MW each are linked at bus 2 and 3, respectively.

The proposed SALFJA algorithm for optimal placement of DG units in the IEEE 15 bus distribution network was validated by comparing it to the genetic algorithm [44], the Jaya algorithm [42] and the particle swarm optimization [45]. Because all of these meta-heuristic algorithms are stochastic in nature, a comparison of all of them for the DG optimum placement issue was conducted in a stochastic setting. Each algorithm was simulated ten times on the IEEE 15 bus network and its performance was assessed using statistical characteristics, such as the mean and standard deviation, as shown in

Table 3. Stochastic validation of proposed SALFJA algorithm for DG placement.

Simulation	SALFJA	Jaya	GA	PSO
1	0.00018	0.00018	0.00087	0.00090
2	0.00018	0.00018	0.00057	0.00093
3	0.00018	0.00018	0.00095	0.00054
4	0.00018	0.00018	0.00077	0.00095
5	0.00018	0.00018	0.00021	0.00079
6	0.00018	0.00018	0.00078	0.00232
7	0.00018	0.00018	0.00055	0.00074
8	0.00018	0.00018	0.00084	0.00106
9	0.00018	0.00018	0.00051	0.00056
10	0.00018	0.00018	0.00094	0.00091
Min	0.00018	0.00018	0.00021	0.00054
Max	0.00018	0.00018	0.00095	0.00232
Mean	0.00018	0.00018	0.000699	0.00097
Std	0	0	0.000235	0.000503
p-value	-	-	3.18 × 10${}^{-5}$	0.000388

. The proposed SALFJA algorithm had a standard deviation of zero, as shown in Table 3. However, compared to SALFJA, the remaining meta-heuristic algorithms, i.e., GA and PSO, had higher standard deviation values, indicating that SALFJA exhibited more robust behaviour with respect to determining the optimal location and size for DG units. The performance of SLAFJA for optimal DG placement was confirmed statistically using the Wilcoxon rank sum test [46]; the resulting p-values are shown in Table 3. The p-value of less than 0.05 obtained for SALFJA indicated a higher level of statistical significance than for GA or PSO. However, on a small distribution system, the IEEE 15 bus system, both the Jaya algorithm and SALFJA performed similarly.

Figure 3 shows a comparison of the proposed SALFJA algorithm with different meta-heuristic algorithms in terms of convergence characteristics. In comparison to GA and PSO, the proposed SALFJA exhibited smoother convergence properties. SALFJA was faster than GA and PSO in reaching the optimal position, i.e., the least TSVD value.

Figure 4 depicts the voltage at each bus in the IEEE 15 bus test system. The voltage at each bus was lower in the absence of DG units in the system than in the presence of DG units owing to reverse power flow, which reduced losses and improved the voltage profile. The voltage profile with SALFJA was superior to GA and PSO, being closer to unity. A voltage profile closer to unity indicates that optimizing the location and size of DG units leads to enhanced power quality operation of the distribution system.

When the optimal simulation was used, the effectiveness of SALFJA for optimal DG allocation on an IEEE 15 bus distribution system was shown to be better than both GA and PSO in a stochastic setting, which is important because all algorithms are stochastic in nature.

3.2. Case Study—02: PG & E 69 Bus Radial Distribution System

To identify the placement and generating capacity of DG units, the proposed SALFJA algorithm was simulated ten times in MATLAB. The best of ten simulations in terms of minimum TSVD was used to determine the placement and generating capacity of the DG units.

Table 4. Stochastic behaviour of SALFJA on PG and E 69 bus test system.

Simulation	TSVD	Simulation	TSVD
1	0.01161	6	0.01158
2	0.01142	7	0.01142
3	0.01139	8	0.01147
4	0.01138	9	0.01147
5	0.01155	10	0.01152
Min	0.01138	Max	0.01161
Mean	0.011481	Std.	0.000081

shows the performance of SALFJA in a stochastic setting. The standard deviation was 0.000081 since the proposed approach produced the same TSVD value across all runs. A standard deviation close to zero indicates that the suggested SALFJA provided a solution that was free of ambiguity.

Figure 5 depicts the performance curves of the proposed SALFJA for optimal DG unit placement throughout ten simulations. According to Figure 5, the SALFJA algorithm converged close to the optimal TSVD value of 0.01138 for all ten simulations.

Table 5. PG and E 69 bus test system: Optimal placement of DG units.

DG1		DG2
Location	Size	Location	Size	TSVD	Base Case TSVD
61	1 MW	15	0.82 MW	0.01138	0.0993

shows the best position and size for the two DG units in the PG and E 69 bus test system. According to Table 5, the distribution network will run with a lower TSVD value, i.e., 0.01138, if two DG units with 1000 kW and 824 kW generating capacity are linked at bus 61 and 15, respectively.

The proposed SALFJA algorithm for optimal placement of DG units in the PG and E 69 bus test system was validated by comparing it to the genetic algorithm [44], the Jaya algorithm [42] and the particle swarm optimization [45]. Because all of these meta-heuristic algorithms are stochastic in nature, a comparison of all of them for the DG optimum placement issue was performed in a stochastic setting. Each algorithm was simulated ten times on the PG and E 69 bus test system and its performance was assessed using statistical characteristics, such as the mean and standard deviation, as shown in

Table 6. PG and E 69 bus test system: Stochastic validation of proposed SALFJA algorithm for DG placement.

Simulation	SALFJA	Jaya	GA	PSO
1	0.01161	0.01580	0.05750	0.02131
2	0.01142	0.01155	0.02872	0.02424
3	0.01139	0.01187	0.01618	0.02001
4	0.01138	0.01187	0.05025	0.02135
5	0.01155	0.01667	0.02419	0.01241
6	0.01158	0.01986	0.03762	0.01301
7	0.01142	0.01187	0.04480	0.01187
8	0.01147	0.01187	0.04259	0.01187
9	0.01147	0.01489	0.04805	0.01727
10	0.01152	0.01187	0.01612	0.02989
min	0.01138	0.01155	0.01612	0.01187
max	0.01161	0.01986	0.05750	0.02989
mean	0.01148	0.01381	0.03660	0.01832
std	0.00008	0.00286	0.01457	0.00612
p-value	NA	0.013664	0.0002	0.00321

. The proposed SALFJA algorithm had a standard deviation close to zero, as shown in Table 6. However, compared to SALFJA, the remaining meta-heuristic algorithms, i.e., GA, Jaya and PSO had higher standard deviation values, indicating that SALFJA exhibited more robust behaviour with respect to determining the optimal location and size for the DG units. The proposed SALFJA’s performance for optimal DG placement was confirmed statistically using the Wilcoxon rank sum test [46]; the resulting p-values are shown in Table 3. The p-values for GA and PSO were less than 0.05 in comparison with SALFJA; the results obtained for SALFJA, were more statistically significant than for GA and PSO.

Figure 6 shows a comparison of the proposed SALFJA algorithm with different meta-heuristic algorithms in terms of convergence characteristics. In comparison to GA, Jaya and PSO, the proposed SALFJA exhibited smoother convergence properties in achieving results closer to the global optimum TSVD value, i.e., 0.01138.

Figure 7 depicts the voltage at each bus in the PG and E 69 bus test system. The voltage at each bus was lower in the absence of DG units in the system than in the presence of DG units owing to reverse power flow, which reduced losses and improved the voltage profile. The voltage profile with SALFJA was superior to GA. The Jaya and PSO results were close to unity. A voltage profile closer to unity shows that DG units having optimal location and size result in better power quality operation of the distribution system.

When the optimal simulation was used, the effectiveness of SALFJA for optimal DG allocation on a PG and E 69 bus system was better than GA, Jaya and PSO in a stochastic setting, which is important because all algorithms are stochastic in nature. However, for a small test system, the IEEE 15 bus, both SALFJA and Jaya performed identically.

4. Conclusions

A modified Jaya algorithm, denoted SALFJA, was created by adding Lévy flight to the Jaya algorithm to improve the search capability for finding the optimal location and size of DG units. The SALFJA algorithm was implemented to address the DG placement optimization issue by dealing with the appropriate objective function, i.e., minimization of the total square voltage deviation, and by considering the maximum line loading capacity as a constraint.

With regard to the simulation findings, the proposed method performed well, producing a solution that was closer to the global optimum point and which also worked well statistically with a standard deviation close to zero. The proposed algorithm was validated statistically by comparing it with well-known meta-heuristic algorithms, including GA, Jaya and PSO in both large test systems, such as the PG and E 69 bus system, and smaller systems, such as the IEEE 15 bus system.

The DG placement problem may be extended to include emissions and reliability as objectives, as well as the influence of load modeling, and by taking into account load and renewable energy uncertainty.