Scholarly article on topic 'Distributed generations planning using flower pollination algorithm for enhancing distribution system voltage stability'

Distributed generations planning using flower pollination algorithm for enhancing distribution system voltage stability Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Eyad S. Oda, Abdelazeem A. Abdelsalam, Mohamed N. Abdel-Wahab, Magdi M. El-Saadawi

Abstract Distributed generations (DGs) have been utilized in some electric power networks. Power loss reductions, voltage improvement, increasing reliability, postponement of system upgrading and environmental friendliness are some advantages of DG-unit applications. This paper presents a new optimization approach that employs a flower pollination algorithm (FPA) to determine the optimal DG-unit’s size and location in order to minimize the total system real power loss and improve the system buses voltage. The FPA is a new metaheuristic optimization technique and it is inspired by the reproduction strategy of the flow pollination process of flowering plants. To reveal the validity of the FPA algorithm, IEEE 33-bus, 69-bus and 136-bus radial distribution test systems are examined with different test cases of the objective function using the MATLAB. Furthermore, the results obtained by the proposed FPA algorithm are compared with other metaheuristic optimization techniques such as backtracking search optimization algorithm, artificial bee colony, and selection algorithm. The outcomes verify that the FPA algorithm is efficient, robust, and capable of handling mixed integer nonlinear optimization problems.

Academic research paper on topic "Distributed generations planning using flower pollination algorithm for enhancing distribution system voltage stability"

Ain Shams Engineering Journal (2015) xxx, xxx-xxx

Ain Shams University Ain Shams Engineering Journal

www.elsevier.com/locate/asej www.sciencedirect.com

ELECTRICAL ENGINEERING

Distributed generations planning using flower pollination algorithm for enhancing distribution system voltage stability

Eyad S. Oda a, Abdelazeem A. Abdelsalam a*, Mohamed N. Abdel-Wahab a, Magdi M. El-Saadawib

a Department of Electrical Engineering, Faculty of Engineering, Suez Canal University, 41522 Ismailia, Egypt b Department of Electrical Engineering, Faculty of Engineering, Mansoura University, Mansoura, Egypt

Received 13 February 2015; revised 13 October 2015; accepted 4 December 2015

KEYWORDS

Distributed generation; Optimization; Flower pollination; Voltage stability

Abstract Distributed generations (DGs) have been utilized in some electric power networks. Power loss reductions, voltage improvement, increasing reliability, postponement of system upgrading and environmental friendliness are some advantages of DG-unit applications. This paper presents a new optimization approach that employs a flower pollination algorithm (FPA) to determine the optimal DG-unit's size and location in order to minimize the total system real power loss and improve the system buses voltage. The FPA is a new metaheuristic optimization technique and it is inspired by the reproduction strategy of the flow pollination process of flowering plants. To reveal the validity of the FPA algorithm, IEEE 33-bus, 69-bus and 136-bus radial distribution test systems are examined with different test cases of the objective function using the MATLAB. Furthermore, the results obtained by the proposed FPA algorithm are compared with other meta-heuristic optimization techniques such as backtracking search optimization algorithm, artificial bee colony, and selection algorithm. The outcomes verify that the FPA algorithm is efficient, robust, and capable of handling mixed integer nonlinear optimization problems.

© 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

* Corresponding author. Tel.: +20 102 193 0088; fax: +20 643 218 977.

E-mail addresses: eyad.oda@eng.suez.edu.eg (E.S. Oda), aaabdelsalam @eng.suez.edu.eg (A.A. Abdelsalam), mohamed_Nabil1973@yahoo.com (M.N. Abdel-Wahab), m_saadawi@mans.edu.eg (M.M. El-Saadawi).

1. Introduction

The interest in distributed generation (DG) in power system networks has been growing rapidly. This increase can be explained by factors such as environmental concerns, the restructuring of electricity businesses, and the development of technologies for small-scale power generation. DG can be alternative to the industrial, commercial and residential application. Several definitions are available for DG all over the world, depending upon plant rating, generation voltage level,

Peer review under responsibility of Ain Shams University.

http://dx.doi.org/10.1016/j.asej.2015.12.001

2090-4479 © 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

point of connection, etc. It can be concluded that the DG is an electrical power generation within distribution system or on the customer side of the system [1].

DGs are anticipated to play a great role in developing of electrical power systems. Studies have predicted that they are about 20% of the new generations being installed [2]. The increment in active power loss represents loss in savings to the utility as well as a reduction in feeder utilization. Studies have shown that 70% of power losses are due to distribution system and the losses resulting from Joule effect only account for 13% of the generated energy [3]. This non-negligible amount of losses has a direct impact on the financial results and the overall efficiency of the system.

DG affects the power flow and the voltage on the buses of the system. The non-optimal placement of DG can increase the system losses and thus make the voltage profile lower than the allowable limit. It must also be reliable of proper size so that it can give the positive impacts or be known as 'system support benefits'. These benefits include improved voltage profile, reduce the losses, increase the distribution capacity, and improve the reliability of utility system [4,5].

In practice, in the distribution network, load pattern is varying with time. The optimal location and size of DG determined under invariant loads may not be optimal under time-varying loads and the optimal DG size may vary with varying load demand. But in practice, it is not economically feasible to change the DG size with changing load demand. Therefore, for planning purpose, an optimal size and location of DGs can be determined by considering peak, average, or combination of the two loading conditions to get the maximum benefit of DGs [6].

Previously, different methodologies have been developed to determine the optimum size and location of DG [7]. A simple search algorithm for optimal sizing and placement of DG based on the minimization of losses in a radial distribution system is proposed in [8]. This method consumes more computational time to solve and is not valid for multi-objective optimization problem. Optimization based algorithm has also been proposed by [9] to find the optimal location for DG with maximum profit using dynamic based programming. In [10], Clonal selection algorithm (CSA) is proposed to determine the optimal DG-unit's size and location is determined by loss sensitivity index. Other studies have been conducted on DG installations which consider sizing and allocation using Embedded Meta Evolutionary-Firefly Algorithm (EMEFA) [11]. This method focused on the effect of population size on loss and cost minimization while improving the performance of the system. In [12], an optimization algorithm based on the genetic algorithm was introduced to address the optimal distributed generation sizing and siting for voltage profile improvement, power losses, and total harmonic distortion (THD) reduction in a distribution network with high penetration of nonlinear loads. The proposed planning methodology takes into consideration the load profile, the frequency spectrum of nonlinear loads, and the technical constraints such as voltage limits at different buses (slack and load buses) of the system, feeder capacity, THD limits, and maximum penetration limit of DG units. In [13] a probabilistic planning approach is proposed for optimally allocating different types of distributed generator (i.e. wind-based DG, solar DG and non-renewable DG) into a harmonic polluted distribution system so as to minimize the annual energy losses and reduce

the harmonic distortions. The performance of DG in distribution networks was also being studied in [5] using the technique of Hybrid Mutation-Evolutionary Programming (HM-EP) and Particle swarm Optimization (PSO). Calculation of location and size of the DG are determined separately, which means different method is applied for sizing and location. Thus, it may result in the solution trap in local optimum so Ref. [14] provides a solution to the output power and location of multiple DG sources by using modified Artificial Bee Colony algorithm to avoid this issue. Big bang big crunch method was used in [15] to find optimal site and size of DG to minimize power loss for balanced and unbalanced distribution systems. The backtracking search optimization algorithm (BSOA) was used in DS planning in [16] with multi type DGs while in [17], BSOA was used to study the impact of various load models on DG placement and sizing and also the time of calculation to find optimal size and location was obtained.

The flower pollination algorithm (FPA) is a new meta-heuristic optimization technique and it is inspired by the reproduction strategy of the flow pollination process of flowering plants [18-20]. The FPA is used to solve real optimization problems [21,22]. In [21] the FPA is used to select the optimal location of distribution transformers in a low-voltage grid, while in [22], the optimal control in multi-machine system with generalized unified power flow controller was discussed.

In this paper, the FPA is used to determine the optimal size and location of single and multi-DGs to minimizing the power losses of the distribution system as much as possible and enhancing voltage profile of the system using voltage index. IEEE 33-bus, 69-bus and 136-bus systems are examined as test cases with different scenarios of the objective function. The results in this paper are compared with performance of BSOA, artificial bee colony (ABC), and clonal selection algorithm (CSA).

2. Problem formulation

2.1. Load flow

On account of the some inherent features of distribution systems such as radial structure, large number of nodes and a high R/X ratio, the conventional techniques such as Newton-Raphson and fast decoupled method may fail or have problems when dealing with distribution networks. In this paper, the load flow is based on the forward/backward sweep technique because it is a powerful method and has been widely used in distribution [23].

2.2. Objective functions

The objective function proposed in this study is defined as follows:

OF = min{(WL *fi) + {Wv *f2)] (1)

where OF is the objective function, f1 is the total real power losses, f2 is the voltage index (VI), WL is the weighting factor for power loss and Wv is the weighting factor for VI.

WL and Wv are the weighting coefficients representing the relative importance of the objectives. It is usually assumed that [24]:

0 6 WL 6 1, and WL + Wv = 1

The value of weighing factors depends on the objective function which is more important. If DG is implementing to mitigate a certain objective to overcome a specific problem, the corresponding weighing factor is increased. In this paper different values of weighing factors for both real power losses and VI are studied.

Voltage limitation

Vmin 6 Vi 6 Vma

where Vmin and Vmax are the minimum and maximum allowed voltage (±10%) and Vi is the voltage at bus i.

Power balance constraints

2.2.1. Power losses

After electrical power is generated, it is transferred through the transmission line to many distribution circuits that the utility operates. So, distribution system will take the power and sent it to the consumer to serve their needs. However, not all the power are delivered hundred percent efficiently due to the losses occur at the transformer and distribution lines. Power lines or distribution lines connect the substation to the loads. Practically, all real power that is lost in distribution system is due to the copper losses. Thus, it can be calculated as equation below:

where Ij is current magnitude in ampere, Rj is resistance at branch j in ohm, n is number of buses.

From the equation, it can be said that amount of power loss in the line can be affected by the change of current or line resistance. Thus, minimizing the real power loss is considered for the placement and sizing of DG in distribution system as the equation shown below:

The whole power loss is divided by MVA base to be normalized (a value between 0 and 1).

To show the impact of installing WT at distribution feeder on power loss reduction (PLR) the following relation used:

PLR% =

^x 100

where PDG is system loss after DG installation

2.2.2. Voltage index VI

The main objective of voltage indices (VIs) is to estimate the distance from the current operating point to the system voltage marginally stable point. Numerical indices help operators to monitor how close the system is to collapse or to initiate automatic remedial action schemes to prevent voltage collapse. Most of the VIs that have been proposed are based on steady state power flow. An index, which can be evaluated at all buses in radial distribution systems, was presented in [25]. The Equation represents the voltage index VI is given by the following:

= 1 » /|Vi - vDg|

j n^-fK Vi

where VDG is the voltage at bus i after DG installation. 2.3. Constraints

The operating constraints are defined as follows:

Ps + £ PDG — Pd + ploss (8)

• Size of each DG

0.1 6 Pdg 6 2.00 MW for 33 and 69 bus systems 0.1 6 Pdg 6 5.00 MW for 136 bus system

where NDG is total number of DGs, Ps is feeder power, and

Pd is load power.

3. The optimization methodology

3.1. Flower pollination algorithm (FPA)

Flower pollination algorithm is a meta-heuristic search algorithm which has been proposed recently by Yang and Deb [18-20]. The algorithm is inspired by the reproduction strategy of the flow pollination process of flowering plants. For simplicity, the following four rules are used:

• Rule #1: Biotic and cross-pollination can be considered processes of global pollination, and pollen-carrying pollinators move in a way that obeys Levy flights.

• Rule #2: For local pollination, abiotic pollination and self-pollination are used.

• Rule #3: Pollinators such as insects can develop flower constancy, which is equivalent to a reproduction probability that is proportional to the similarity of two flowers involved.

• Rule #4: The interaction or switching of local pollination and global pollination can be controlled by a switch probability p 2 [0,1], slightly biased toward local pollination.

To formulate the updating formulas, these rules have to be converted into proper updating equations. Rule #1 and flower constancy, Rule #3, can be represented mathematically as follows:

XT1 = X + yL(k)(g.- <

where Xf1 is the solution vector xi at iteration t, g„ is the current best solution found among all solutions at the current generation/iteration, y is a scaling factor and L(k) is a step-size parameter. A Levy flight can be used to mimic this characteristic efficiently. That is, L >0 is drawn from a Levy distribution.

kC(k) sin(pk/2)

, (S >> S > 0)

C(k) is the standard gamma function, and this distribution is valid for large steps S > 0. Mantegna algorithm is used for drawing step size S by using two Gaussian distributions U and V by the following transformation:

U ~ N(0, r2), V ~ N(0,1)

U ~ N(0, r2) means that the samples are drawn from a Gaussian normal distribution with a zero mean and a variance of r2. The variance can be calculated by the following:

r C(1 f k)

U C((1 4 k)/2)

sin(pk/2)

For the local pollination, both Rule #2 and Rule #3 can be represented as follows:

Xt+1 = X +2(x' - .

where xj and x'k are pollen from different flowers of the same plant species and 2 is drawn from a uniform distribution in [0,1].

3.2. Implementation of FPA

Flower pollination algorithm is developed by the idea of flower pollination process. There are only two parameters in this algorithm, the population size n, and probability switch (p 2 [0,1]). Once n is fixed, p essentially controls the pollinators and the balance of the randomization and local search. Few parameters make an algorithm less complex and thus potentially more generic. In this paper p = 0.8 and n = 25 [18], the mechanism of proposed FPA is shown in Fig. 1. In this formulation, the DG units are assumed to operate at unity power factor.

4. Simulation results

4.1. The test systems

To evaluate the performance of the FPA in the application of DG allocation, IEEE 33-bus, 69-bus and 136-bus test systems are simulated using Matlab environment software. The FPA is used to select the optimal location and site with two case studies:

• Case #1: allocation of a single DG.

• Case #2: allocation of multi DGs.

Each case study has six scenarios of the objective function based on weighted factors value, stated in Eq. (1), as listed below:

• Scenario #1: this is a reference scenario, in which no DG units are connected to the system (base case).

• Scenario #2: WL = 1.0 and Wv = 0.0.

• Scenario #3: WL = 0.7 and Wv = 0.3.

• Scenario #4: WL = 0.5 and Wv = 0.5.

• Scenario #5: WL = 0.3 and Wv = 0.7.

• Scenario #6: WL = 0.0 and Wv = 1.0.

The values of weighting factors are chosen to show the effect of objective function target on size and location of DG in DS.

4.1.1. IEEE 33-bus system

The single line diagram, shown in Fig. 2, of IEEE 33-bus distribution system is used. The system voltage is 12.66 kV and total system active and reactive loads are 5084.26 kW and 2547.32 kVAr, respectively, and the complete system parameters are in [27].

4.1.1.1. Case #1: allocation of single DG unit. In this case study, the optimization process is introduced to select the best location for locating single DG. The optimal location, optimal size of DG, the minimum and maximum buses voltage, the active and reactive system losses and the percentage power loss reduction are summarized in Table 1.

In scenario#1 (base case) the system loss is 210.8 kW, and minimum voltage (Vmin) is 0.9098 pu at bus 18. After installing DG in the system based on senario#2, the loss decreases to 112.10 kW (PLR% equal to 46.48) and minimum voltage becomes 0.9434 pu at bus 18. As WL decreases and WV increases, the system voltage will enhance while the system loss will increase as shown in Table 1. In scenario #6, the loss reaches 139.20 kW (PLR% is 34.0) and minimum voltage 0.9436 pu at bus 33.

4.1.1.2. Case #2: Allocation of Multi DGs. In this case, the voltage profile is improved with increasing WV and the system loss is increased with decreasing WL, scenarios from #2 to #6. Table 2 summarizes the results of determining the size, and location of multi-DG in 33-bus. The evaluation of the convergence of objective functions of scenario #2 is shown in Fig. 3. The objective function of case #1 reaches to the best value after four iterations while for case #2, it reaches to the best value after sixty-two iterations.

4.1.2. IEEE 69 bus system

The IEEE 69-bus distribution system [28], which is 12.5-kV system, shown in Fig. 4, is employed in this paper. It consists of one slack bus and 68 load buses. The total real and reactive power demand is 3.8 MW and 2.69 MVAr, respectively.

The selection is achieved by developing two case studies. In each case, a DG unit is installed at a certain bus, according to specific OF scenario and the changes of the system voltages and power loss are observed.

4.1.2.1. Case #1: Allocation of single DG unit. The results of the six scenarios which are presented in this section are stated in Table 3. These results are obtained by the optimization formulation which is proposed in previous section. It demonstrates the optimal size and location of DG unit, the minimum and maximum voltage of the system buses, power losses, and PLR% in each scenario.

Fig. 5 shows the impact of the DG unit on voltage profile of the system. The DG unit is installed at different buses according to the scenario of OF as listed in Table 3. In the first scenario the worst value of bus voltage is 0.9091 pu and it is at bus 65. By installing DG according to scenario #2 (WL = 1 & Wv = 0), the optimal size of PDG is 1.8768 MW and the

Figure 1 The proposed algorithm flowchart.

Figure 2 The single line diagram of IEEE 33-bus radial network.

optimal location is bus 61 and the minimum value of the bus voltage is 0.9683 and it appears at bus 27. While according to scenario #6 (WL = 0 & Wv = 1), the optimal size and location of PDG is 2.000 MW at bus 64 and also the minimum value of bus voltage appears at bus 27 and is equal to

0.9690. The results show that optimal site and size of DG depends on the OF priorities according to the weight factors.

The system loess at scenario #1 (base case) is 224.95 kW. In scenario #2, the losses decreased to 83.221 Kw, and this

Table 1 Results of FPA of case #1 (single DG) in IEEE 33-bus system.

Scenario Scenario Scenario Scenario Scenario

#1 #2 #4 #6

DG size, - 2.000 1.9707 1.9872

DG location - 7 10 12

Vmin, pu 0.9098 0.9434 0.9435 0.9436

Vmax, pu 1.0000 1.0000 1.0000 1.0000

Ploss, kW 210.80 112.10 132.00 139.20

Qloss, kVAr 140.60 78.30 91.50 94.00

PLR, % 0.00 46.82 37.38 34.0

Table 2 Results of FPA of case #2 (Multi-DG) in IEEE 33-bus system.

Scenario Scenario Scenario Scenario Scenario

#1 #2 #4 #6

DG size, - 1.0339, 1.0047, 1.3249,

MW 1.0866 1.3004 1.6481

DG - 12, 30 13, 30 13, 30

location

Vmin, pu 0.9098 0.9675 0.9742 0.9801

Vmax, pu 1.0000 1.0000 1.0000 1.0000

Ploss, kW 210.80 89.20 91.50 122.2

Qloss, kVAr 140.60 60.70 62.90 87.60

PLR, % 0.00 57.70 56.70 42.03

means that PLR is 63%. Also the losses of the system increased as the WL is decreased until scenario #6, WL = 0, the system loss reaches 101.511 kW and the PLR decreased to 54.87%.

4.1.2.2. Case #2: Allocation of multi DGs. In this section, the results of case #2, six scenarios, are presented in Table 4.

Table 4 demonstrates the sizing and sitting of multi DG units, minimum and maximum voltage of the system, power loss, and % PLR in each scenario.

Fig. 6 shows the impact of the DG unit on voltage profile of the system. The DG units are installed at different buses according to the scenario of OF as listed in Table 4. In the first scenario, the minimum buses voltage (Vmin) is 0.9091 pu at bus 65. By installing multi-DG according to the second scenario (WL = 1 & Wv = 0), the optimal sizes and locations are 1.7710 MW and 0.46360 MW at bus 61 and bus 17, respectively, and the Vmin is 0.9780 at bus 65. On the other hand in scenario #6 (WL = 0 & Wv = 1), the optimal sizes and locations are 1.9534 MW at bus 64 and 1.0050 MW at bus 14 and the Vmin is 0.9910 at bus 60. The results shows that optimal site and size of DG depends on the OF priorities according to the weight factors.

The system loss at scenario #1 (base case) is 224.95 kW while in scenario #2, the loss decreased to 71.70 kW (PLR% = 68.13). The system loss increased as the WL is decreased until scenario #6 at which the system loss reaches to 95.83 kW (PLR% = 57.40). Fig. 7 shows the convergence curve of the objective functions of scenario #2.

4.1.3. 136-bus system

To insure the validity and the effectiveness of the FPA, this study employs the proposed method to determine optimal size and location using large, and real distribution system with 136-nodes with total active and reactive load of 18.314 MW and 7.933 MVAr, respectively. The data and single line diagram of the system are given in [17,29]. The results of the simulation with different OF scenarios are summarized in Table 5. The results ensure that both size and location vary according to OF scenarios. In case #1, the power loss in scenario #2 is 228.6 kW while in scenario #6 it reaches 308.7 kW. The minimum voltage is 0.9636 pu and 0.9711 pu in scenario #2 and scenario #6, respectively. Fig. 8 shows the convergence curve of the objective function for scenario #2 of the test system.

10 20 30 40 50 60

No of iterations

Figure 3 The convergence curve of OF for 33-bus system, scenario #2.

Figure 4 The single line diagram of IEEE 69-bus radial network.

Table 3 Results of FPA of case #1 in IEEE 69-bus system.

Scenario Scenario #1 Scenario #2 Scenario #3 Scenario #4 Scenario #5 Scenario #6

DG size, MW - 1.8768 2.0000 2.0000 2.0000 2.0000

DG location - 61 61 61 61 64

Vmin, Pu 0.9091 0.9683 0.9690 0.9690 0.9690 0.9690

Vmax, pu 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Ploss, kW 224.95 83.221 83.782 83.782 83.782 101.511

PLR, % 0.00 63.00 62.75 62.75 62.75 54.87

4.2. Comparison with other optimization algorithms

To insure the validity of proposed algorithm, a comparison with other optimization algorithms such as the backtracking search optimization algorithm (BSOA), artificial bee colony (ABC), and performance of clonal selection algorithm (CSA) is achieved. The comparison is based on the result of scenario #2 in each case study.

The proposed algorithm is coded using MATLAB R2014a/8.3 [26]. Simulation is carried out using Lenovo laptop with Intel ® Core™ i7-4702MQ CPU @ 2.20 GHz.

4.2.1. 33-bus system

In this system, the results are compared with the backtracking search algorithm BSOA [16]. The results show that the proposed algorithm has a small computational time compared with BSOA as shown in Table 6.

4.2.2. 69-bus system

In case #1, the comparison shows that the ABC, CSA and FPA give the optimal location at bus 61 but with different sizes while in case #2, the optimal locations are at 61 and 59 buses for the ABC and CSA algorithms and at 61 and 17 buses for

J_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_L

10 13 16 19 22 25 28

31 34 37 Bus No

40 43 46 49 52

58 61 64 67 69

Figure 5 Voltage profile of IEEE 69-bus system in scenarios #1, #2 and #6.

Table 4 Results of FPA for test case #2 in IEEE 69-bus system.

Scenario Scenario #1 Scenario #2 Scenario #3 Scenario #4 Scenario #5 Scenario #6

DG size, MW - 0.4636 1.7710 0.6918 2.0000 0.7067 2.000 0.9931 1.9830 1.0050 1.9534

DG location - 17 16 15 14 14

61 61 61 61 64

Vmin, pu 0.9091 0.9780 0.9858 0.9875 0.9881 0.9910

Vmax, pu 1.0000 1.0000 1.0000 1.0020 1.0045 1.0030

Ploss, kW 224.95 71.70 73.70 76.39 79.15 95.83

PLR, % 0.0 68.13 67.24 66.04 64.81 57.40

Qloss, kVAr 102.15 35.95 36.55 37.45 38.35 46.92

1.01 1

0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91

- Scenario 1

- Scenario 2

- Scenario 3

- Scenario 4

- Scenario 5

- Scenario 6

Bus No

Figure 6 Voltage profile of IEEE 69-bus system with different Scenarios.

"Single DG ■ Multi DG

10 20 30 40 50 60

No of iterations

Figure 7 The convergence curve of OF for 69-bus system, scenario #2.

Table 5 Results of FPA for 136-bus system.

Scenario Base case Case 1: Single DG Case 2: Multi-DG

Scenario #1 Scenario #2 Scenario #4 Scenario #6 Scenario #2 Scenario #4 Scenario #6

DG size, MW - 2.8391 2.9251 5.00 2.6243, 2.8753 2.0521, 3.1166 4.4818, 5.000

DG location - 106 106 108 11, 106 11, 106 28, 108

Vmin, pu 0.9306 0.9636 0.9645 0.9711 0.9640 0.9665 0.9711

Vmax, pu 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0003

Ploss, kW 320.40 228.60 228.70 308.70 194.80 195.4 315.2

Qloss kVAr 702.90 491.50 491.70 643.50 415.4 418.1 653.7

PLR, % 0.00 28.65 28.62 3.652 39.20 39.00 1.623

■ Single DG -Multi-DG

0.75 -

»-------------1

0.65 -

No of Iteration

Figure 8 The convergence curve of OF for 136-bus system, scenario #2.

Table 6 Results of comparing FPA with BSOA for 33-bus system.

Optimization method DG location and size Vmin, pu Ploss, kW Elapsed time (s)

Single DG Multi DG Single DG Multi DG Single DG Multi DG Single DG Multi DG

BSOA [16] The proposed algorithm 8, 1.8575 7, 2.0000 13, 0.880 31, 0.924 12, 1.0014 30, 1.1417 0.9441 0.9434 0.9665 0.9675 118.12 112.10 89.34 89.20 20.40 5.660 23.54 5.564

Table 7 Results of comparing FPA with ABC and CSA for 69-bus system.

Optimization method DG size and location Vmin, pu Ploss, kW Elapsed time (s)

Single DG Multi DG Single DG Multi DG Single DG Multi DG Single DG Multi DG

Artificial Bee Colony (ABC) [10] 1.787, 61 1.569, 61 0.9708 0.9712 91.21 90.51 --

0.263, 59

Clonal Selection Algorithm (CSA) [10] 1.787, 61 1.474, 61 0.9708 0.9713 91.21 90.47 --

0.374, 59

The proposed algorithm 1.8768,61 1.771, 61 0.9683 0.9782 83.2 71.9 13.343 13.854

0.4636, 17

Table 8 Results of comparing FPA with BSOA for 136-bus system.

Optimization method DG location and size Vmin, pu Ploss, kW Elapsed time (s)

Single DG Multi DG Single DG Multi DG Single DG Multi DG Single DG Multi DG

BSOA [17]a (2.824 + j1.199) = 3.068-106 - 0.9712 - 213.06 - - -

The proposed algorithm 2.8391, 106 2.6243, 11 2.8753, 106 0.9636 0.9640 228.60 194.80 41.149 40.880

a The reference calculates optimal active and reactive power of DG.

FPA. Also from Table 7, the minimum bus voltage is enhanced and the system power loss is reduced using FPA in comparing with ABC and CSA algorithms.

4.2.3. 136-bus system

Table 8 shows a comparison of proposed algorithm and BSOA [17], and the results ensure the validity and accuracy of FPA for large system optimization. Even if the BSOA was interested in studying DG type injects active and reactive power and FPA considers the DG as active power source the optimal location was the same in both techniques.

5. Conclusions

A modern optimization technique based on a flower pollination algorithm is presented in this paper for DGs placement and sizing problem in radial distribution systems. The objective function of the proposed technique is to reduce system power losses and improve voltage profile of system buses. This proposed optimization technique has been applied on typical IEEE 33-bus, IEEE 69-bus, and 136-bus radial distribution systems with different scenarios of the objective function weighted factors. The simulation results using Matlab programming environment show that the proposed method is capable of selecting the optimal location and size of DGs with a significant saving of power losses, and improvement of voltage profile of the system with a small convergence time. Furthermore, the results obtained by the proposed FPA algorithm are compared with other metaheuristic optimization techniques such as backtracking search optimization algorithm, artificial bee colony, and selection algorithm. The outcomes verify that the FPA algorithm is efficient, robust, and capable of handling mixed integer nonlinear optimization problems.

References

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Eyad S. Oda is an assistant lecturer at Suez Canal University, Egypt. He received his B.Sc and M.Sc. degrees in Electrical Engineering from Suez Canal University, Egypt, in 2006, and 2012. His current research areas include power quality issues, distributed energy resources planning and application of artificial intelligent techniques on power systems.

Abdelazeem A. Abdelsalam is an Assistant Professor at Suez Canal University, Egypt. He was a post doctorate fellow at University of Ontario Institute of Technology (UOIT), Canada. He received his B.Sc., M.Sc. and Ph. D. degrees in Electrical Engineering from Suez Canal University, Egypt, in 2001, 2005 and 2011, respectively. His current research areas include power quality issues, FACTS technology, distributed energy resources interface and control and application of artificial intelligent techniques on power systems.

Mohamed N. Abdel-Wahab had his B.Sc. from Zagazig University, and then he had his M.Sc. and Ph.D. from Mansoura University, Egypt. He worked as a super-intended engineer in (Naval Medical Research Unit) NAMRU-3 in Cairo then he participated in upgrading electrical network of Abu Hamad Air Base as an external electrical officer engineer then he moved to Egyptian Electricity Transmission Company (EETC) as a consultant engineer. Eventually, Dr. Abdel-Wahab had been appointed as an assistant professor in Electrical Engineering Department, Faculty of Engineering, Suez Canal University, Egypt. He published fourteen papers in international journals, national and international conferences.

Magdi M. El-Saadawi was born in Mansoura, Egypt in 1959. He received his B.Sc. and M.Sc. from Mansoura University, Egypt in 1982 and 1988, respectively, and his Ph.D. from Warsaw University of Technology in 1997. He was a teaching assistant at Mansoura University from 1983-1992. From 1997, he was a staff member of the Electrical Engineering Department, Mansoura University, and has been a professor since May 2011. His fields of interest include power system analysis, Renewable energy applications, DG systems, and AI applications in power systems.