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2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

Allocation and Sizing of DG Using Cuckoo Search Algorithm W. S. Tan 1, M. Y. Hassan 2, M. S. Majid 3, and H. A. Rahman 4 Centre of Electrical Energy Systems (CEES), University of Technology Malaysia (UTM), Johor, Malaysia. 1 Email: [email protected], 2 Email: [email protected], 3 Email: [email protected], 4 Email: [email protected]

Abstract— Recent years, penetration of distributed generation in the distribution system is one of the most attractive studies along with the creation of retail electricity markets and pressure place on countries to exploit the renewable resources. For exploiting the DG potential, the optimal allocation and sizing of DG are essential. In this paper, a novel Cuckoo Search algorithm is presented for optimal location and sizing of distributed generation on a radial distribution system. The objectives are to minimize the total real power losses and improve voltage stability within the system at the same time improve voltage profile within the voltage constrains. Cuckoo Search algorithm toolbox which coded in Matlab generates both optimal distributed generation site and size as outputs. Two case studies are carried out on 69 bus radial distribution systems and compare to the Standard Genetic Algorithm and Particle Swarm Optimization to verify the efficiency of the proposed methodology. The results show that Cuckoo Search algorithm outperforms other algorithms in terms of solution quality and standard deviation values.

    

One of the essential parts of DG research study is related to its suitable siting and sizing in power systems, which allow electric utility to reduce investments such as decreasing the power or energy losses, and reducing the operational costs by improving the reliability of the system [4]. DG application basically formulated as mixed integer based optimization problem, which can be solved by any optimization methods. As more objectives and constraints included in the problem formulation, the application becomes more challenging because more data is required to generate results. There have been a significant number of techniques applied to solve the DG placement problems, such as, Genetic Algorithm (GA) [5], and Particle Swarm Optimization (PSO) [6], which gives promising result and still evolving. Some of the algorithms have been modified to overcome their limitation and to improve the quality of their solution. Additionally, most of the optimization methods have many parameters to be tuned.

Keywords-distributed generation; radial distribution system; optimal location; Cuckoo Search algorithm

I.

INTRODUCTION

One of the most significant attractions for the studies regarding the integration of distributed energy resources to the power system is the exploitation of the renewable-energy resources such as solar, wind, biomass, hydro, geothermal, and ocean energy. The renewable basically consists of clean, primary or inexhaustible energy which smaller in size and scattered around the world [1]. Accordingly, these resources can only be tapped through integration into the distribution network by means of distributed generation (DG).

An analytical method was presented by C. Wang et al. to verify the optimal location for DG placement in radial along with networked systems; the aim was to reduce the power losses of the system [7]. Gautam et al. proposed two new methodologies for DG allocation with an optimal power flow based wholesale electricity market. Optimal placement and size are identified and classified for social welfare along with a profit maximization problem [8]. G. Celli et al. proposed a multi-objective expression based on GA and an ɛ-constrained method to minimize cost for the DG resources siting and sizing problem [5]. Another multi-objective formulation was proposed by Hajizadeh et al. to minimize the cost of energy not supplied and the cost of power losses based on PSO [6].

Despite the fact that there is no agreement on the exact definition of DG, there are some noteworthy attempts, in the literature [2], to define the concept. DG is small scale sources (10 to 10,000 kW) which not centrally planned or dispatched, and it is generally directly connected to the power system near the point of the end users. DG is expected to play an important role, and become one of the most attractive research areas in the power-generation study. This ever-increasing attention can be related to several important reasons such as DG great capabilities and advantages, increasing of electrical demands, technical and economic constraints in construction of new power plants and new transmission lines. The major reasons for the progressively widespread usage of DG can be described as follows [3]:

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Small generators like DG are easy to find the site for installation. Modern technology has made existing plants ranging in capacities from 10 KW to 15 MW. DG units are nearer to customers; Transmission and Distribution (T&D) costs can be ignored or reduced. Natural gas, regularly used as fuel in DG is distributed almost everywhere, and stable prices are expected for it. The investment risks of DG are low and require shorter installation times. DG offers wide ranges of combination in terms of cost and reliability to choose by engineer planners.

With the intention of mimic animal abilities in problem solving, a branch of nature inspired meta-heuristics, which are

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2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

A. Objective Functions In this study, the total real power losses are selected as one of the objective functions, which is expressed as the sum of all nodes injections of power in the distribution system, the first objective function, formulated as power losses indices is given by:

recognized as swarm intelligence become gradually popular. Particle Swarm Optimization [6], Artificial Bee Colony [9], Ant Colony Optimization [10], etc. are some of the famous algorithms that mimic animal behavior in problem modeling and solution. In this paper, a new population-based search algorithm called Cuckoo Search algorithm (CS), inspired by the interesting brood parasitic breeding behavior of certain species of cuckoos, is presented to evaluate the DG site and size in the distribution network. Using the CS, the optimization can be solved efficiently, partly because there are fewer parameters to be fine-tuned in CS than in other optimization algorithms. Simulation work is carried out on a 69 bus radial distribution feeder to validate the effectiveness of the proposed method. Results showed that CS is capable of handling complex optimization problems, and gives better quality solution and higher precision factor compare to GA and PSO methods.

f1  PLDG / PL

where PL and PLDG are the total real power losses of distribution system before and after installation of DG respectively, and express as: N

ni 1

where Ini is the current magnitude and Rni is the resistance. Ini can be obtained from the load flow analysis. In a radial distribution system, each receiving node is supply by only one sending node. When DG is connected to distribution network, the voltage stability index (VSI) which was presented by Charkravorty and Das [12], will be changed. Equations used to formulate this index are presented in [13], to solve the load flow for radial distribution systems. By using Eq. (6) and Eq. (7), Eq. (8) which represents the VSI is formulated as:

PROBLEM FORMULATION

Proposed methodology in this paper is aimed to find the optimal siting and sizing of DG implementation by minimizing the power losses, while improving the voltage stability in the system. The multi-objectives (MO) method proposed in this paper is the Weight Method. The main strength of this method is its efficiency and suitability to produce a strongly non-dominated solution which can be used as an initial solution for other techniques [11]. Weight Method converts the MO optimization problem into a traditional problem. Mathematically, the objective function is formulated as:

min f  w1 f1  w2 f 2

I ni 

k

w  1 i 1

i

Vmi  Vni Rni  jX ni

(6) (7)

Pni (ni)  jQni (ni)  Vni* I ni VSI (ni)  Vmi

4

 4Pni (ni) Rni  Qni (ni) X ni Vmi

 4Pni (ni) Rni  Qni (ni) X ni 

2

(8)

2

where Vmi, is the sending node voltage; while Vni, Pni, Qni, Rni, and Xni are voltage, real power, reactive power, resistance, and impedance for the receiving node.

(2)

The index is modified to become an objective function for improving VSI, as follow:

where f1 is the total real power losses while f2 is the voltage stability index (VSI), and wi are the weighting coefficients representing the relative importance of the objectives. It is usually assumed that

0  wi  1 and

(5)

PL ( DG )   I ni2 Rni

This paper is structured as follows: First, Section II describes about the problem formulation. The fundamental concepts of CS along with the implementation to DG placement are proposed in Section III. Finally, simulation results are discussed in Section IV to demonstrate the efficiency of CS, with conclusions given in Section V. II.

(4)

f2 

(3)

1 min(VSI (ni))

n i  2,3,, n n

(9)

where VSI(ni) > 0 for i = 2, 3... ,n, so that a feasible solution is existed. It is very essential to recognize weak buses for nodes with minimum VSI that are disposed to voltage instability. Inspecting the VSI performance exposes that the buses which undergoing huge voltage drops are weak and within the condition of corrective actions.

The choice of weighing factors depends on the objective function which is more crucial. If DG is implementing to mitigate a certain objective to overcome a specific problem, the corresponding weighing factor is increased. The real power losses received significant weight (0.7), while VSI takes a weight of 0.3 due to its power quality impacts. To minimize the objective function, CS has been chosen due to its effectiveness in solving complex optimization problems.

B. Constraits The occurrence of the voltage rise that regularly arises due to reverse flow of power after DG implementation is

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2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

considered throughout this study. Consequently, the voltage profile is retained within standard limits at each bus, which expressed as: Vi  Vi max Vi  Vi

min

Vi max  1.05 p.u. Vi

min

• •

(10)

 0.95 p.u.

As DG capacity is naturally limited by the energy resources at any given location, the active and reactive power for DG is formulated as a discrete value with 100 KW increment, and restricted by lower and upper limits, as: Pdg  Pdgmax

Pdgmax  5MW

Pdg  P

min dg

min dg

max Qdg  Qdg

Qdg  Q

min dg

P

min dg

Q

When generating new solutions x(t+1) for a cuckoo i, a Lévy flight is performed. xi(t 1)  xi(t )    Levy( )

(11) (12)

 0M var

C. Case study In fact, two test cases are considered in this study. Two different types of DG applications represent first test case and second test case respectively. Type 1: DG is capable of supplying only real power, for instant, photovoltaic and micro turbines. Type 2: DG is capable of supplying real and reactive power. Gas turbines based synchronous generator such as biomass can be included. In this study, the type 2 DG is assumed to have 0.98 (lagging) power factor, therefore it is providing real and reactive power support. Both test cases also include single and multiple DG unit installation. In this study, the maximum DG allowed to be implemented within the network is only two units. III.

(13)

The random step length of Lévy flight, which fundamentally provides a random walk, is derived from a Lévy distribution with an infinite variance and infinite mean. Levy ~ u  t 

(14)

Here, the sequential jumps of a cuckoo fundamentally form a random walk process with a power law step length distribution with a heavy tail. [15] Numerous new solutions should be generated by Lévy walk near the best solution obtained, since this procedure will speed up the local exploration. However, to confirm the algorithm will not be trapped in a local optimum, a substantial part of the new solutions must be generated through far field randomization, so that the locations would be sufficiently far from the current best solution. [14]

CUCKOO SEARCH ALGORITHM

Cuckoo search (CS) is an optimization algorithm inspired by the brood parasitism of cuckoo species, which lay their eggs in the nests of other host birds. CS is proposed by Yang and Deb in 2009 [14], and it has been applied into the engineering optimization problems and shown its promising efficiency. For instant, in solving the welded beam design and spring design problems, CS achieved better quality solutions compare to existing algorithms in [15]. If a host bird discovers foreign eggs in its nest, it will either abandon the nest and build a new nest elsewhere or simply throw the foreign eggs away. A cuckoo egg represents a new solution while each host bird egg in a nest represents a solution. The aim is to replace a worst solution in the nests with the new and possibly better solutions. In this study, the simplest approach is used where each nest has only a single egg, even though the algorithm can be extended to handle multiple eggs case.

A. Cuckoo Search for Distributed Generation placement The implementation of CS for optimal siting and sizing DG problem entailed the determination of several steps of procedure as presented in Fig. 1. For the CS parameters setting, number of nests, n=20, step size, α=1, and the probability to discover foreign eggs, Pa=0.6 have been applied in this study. On the other hand, network topology based on forward/backward sweep algorithm was used for load flow analysis to evaluate the objective function, due to its computational effectiveness, low memory consumptions, and robust convergence characteristic [16].

For ease in describing CS, the three idealized rules are described as follows [15].





where > 0 is the step size which should be associated to the problem of interests scales; α can be set to value 1 in most situations. Eq. (13) is basically the stochastic equation for random walk, which is a Markov chain whose next status or location only depends on the current status or location, and the transition probability, which are the first and second term respectively. The product  represents the entry wise multiplication, which is similar to those used in PSO. In terms of exploring the search space, random walk via Lévy flight is more efficient as its step length is much longer in the long run. [15]

 0MW

max Qdg  1M var

The algorithm will carry over the best nests with highquality eggs (solutions) to the next generations; A host bird can discover a foreign egg with a probability, pa = [0, 1] while the number of available host nests is fixed. In this case, the host bird can either abandon its nest and build a completely new nest elsewhere or simply throw the eggs away.

1) Step 1: Initialize population The CS must be provided with the population number, n and the initial range of host nests at the start, which can be

At one time, each cuckoo only lays one egg, and leaves it in a randomly chosen nest;

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2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

specified by the user. If the user not suggests any initial range, the algorithm will create an initial population with the default value. The initial population will be evaluated using the objective function, which is the driving force behind CS. 2) Step 2: Generation of cuckoo A cuckoo is randomly generated by Lévy flight. The cuckoo is evaluated using the load flow and objective functions to determine the quality of the solution. 3) Step 3: Replacement A nest is selected among n randomly, if the quality of new solution in the selected nest is better than the old solution, it will be replaced by the new solution (cuckoo). 4) Step 4: Generation of new nest The worse nests are abandoned based on the probability (Pa) and new ones are built.

Figure 2: Single line diagram of a 69 bus radial distribution network [17].

IV.

5) Step 5: Termination In this study, the stopping criterion is set to tolerance value of 1e-6 and maximum generation of 100 iterations. After satisfied the stopping criterion, the iteration will be stopped and the result of CS will be obtained.

SIMULATION RESULTS

The proposed method is verified on a 69 bus radial distribution system as illustrated in Fig. 2. The power of all network buses are assumed to be delivered by the substation placed at node 1. The total real power loads and reactive power loads on the 69 radial distribution system are 3.80MW and 2.69 Mvar respectively. The objective functions values before installation of DG, which include the total power losses and VSI values, are 0.2250 MW and 0.6883 respectively. In order for directly obtained the optimal siting and sizing of DG in the distribution system with the target of minimizing the total real power losses and improve voltage stability while maintain the acceptable voltage limit, the Cuckoo Search algorithm was used, which is a self-developing code, built using Matlab script functions. TABLE I COMPARISON OF RESULT BETWEEN ALGORITHMS FOR TEST CASE 1. Method CS SGA PSO

Bus no.

DG size (MW)

Ploss (MW)

61 22, 61 61 17, 61 61 14, 62

2.0 0.6, 2.1 2.3 1.0, 2.4 2.0 0.7, 2.1

0.0838 0.0764 0.0894 0.0829 0.0838 0.0788

Loss reduction % 62.8 66.0 60.3 63.1 62.8 65.0

Min(VSI) 0.8840 0.9612 0.8882 0.9756 0.8840 0.9682

TABLE II COMPARISON OF RESULT BETWEEN ALGORITHMS FOR TEST CASE 2. Method

Figure 1: The CS method for optimal siting and sizing of DG.

CS SGA PSO

136

Bus no.

DG size (MVA)

Ploss (MW)

61 18, 61 61 18, 62 61 18, 62

2.3 0.8, 2.0 2.6 0.6, 2.3 2.3 0.9, 1.9

0.0526 0.0399 0.0644 0.0440 0.0526 0.0424

Loss reduction % 76.7 82.3 71.4 80.4 76.7 81.2

Min(VSI) 0.8947 0.9771 0.9009 0.9771 0.8947 0.9731

2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

installation. After DG is installed, the VSI values are improved. Furthermore, voltage profile values of both cases indicate identical pattern, which illustrated in Fig. 4 and Fig. 6. The results show different voltage levels throughout pre and post installation of DG. Before installation of DG, voltage level of bus 65 was very low; the voltage shows improvement after DG installation. In brief, the placement and size proposed by CS and PSO gives better VSI and improvement in voltage profile than the SGA outcome.

Figure 3: Voltage stability index for test case 1 (multiple DG).

Figure 5: Voltage stability index for test case 2 (multiple DG).

Figure 4: Voltage profile for test case 1 (multiple DG).

The CS is compared to well-known Standard Genetic Algorithm (SGA) and Particle Swarm Algorithm (PSO) to verify the effectiveness and quality of the results generated; all corresponding outputs are given in Table I and Table II for test case 1 and test case 2 respectively. Based on the outputs, it clearly shows that CS generates better quality solutions most of the time, while SGA results are the poorest among the algorithms. For single DG placement and sizing, the optimum placement and size of DG determined by CS and PSO are in close agreement, while SGA gives lower quality solutions. However, different trends can be observed for multiple DG cases for both types of DG. All three algorithms give different output for multi DG cases. However, CS still outperforms SGA and PSO in terms of solution quality.

Figure 6: Voltage profile for test case 2 (multiple DG). TABLE III SIMULATION RESULTS OF ALGORITHMS OVER 30 INDEPENDENT RUNS FOR MULTIPLE DG AT TEST CASE 2. Method CS SGA

Fig. 3 and Fig. 5 illustrated the voltage stability index for 69 bus distribution systems, test case 1 and test case 2 respectively. It clearly shows that VSI values for all modes in the radial distribution systems were poor before the DG

PSO

137

Statistic Obj. Func., f Obj. Func., f Obj. Func., f

Best

Worst

Mean

Std. Dev.

0.4279

0.4745

0.4369

0.0088

0.4313

1.3691

0.5816

0.2229

0.4308

0.9956

0.5845

0.2103

2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

combination with other algorithms may also create an interesting area for further research. ACKNOWLEDGMENT This work was supported by Ministry of Higher Education Malaysia (MOHE) and University Teknologi Malaysia (UTM) through Research University Grant (GUP) vot 00J67. REFERENCES [1]

[2]

[3]

[4] [5]

Figure 7: Convergence characteristic of three different methods (test case 2, multiple DG).

[6]

Table III shows the mean and standard deviation values for all algorithms over 30 independent runs of simulation for multi DG in test case 2. It illustrations that CS is very precise, with standard deviation values of 0.0088; while SGA and PSO have higher standard deviation values, which are 0.2229 and 0.2103 respectively. This indicates the output consistency for CS and inconsistency for other’s algorithm. The convergence characteristic of all three artificial intelligence algorithms is shown in Fig. 7. It can be observed that SGA performs faster in terms of convergence. However premature convergence arises, which cause a lower-quality result. Additionally, PSO converges slowest among the three algorithms. V.

[7]

[8]

[9]

[10] [11]

CONCLUSION

A Cuckoo Search algorithm (CS) for DG placement and sizing problem in the radial distribution system to reduce total real power losses and improve voltage stability with imposed voltage constraint is presented in the paper. The CS provides both optimal location and sizing of DG as the outputs. It is demonstrated that the proposed method is capable of saving a significant amount of power, attain improvement in voltage stability, and voltage profile by comparing the results among pre and post installation of DG. On the other hand, CS outperforms SGA and PSO in terms of generating high-quality solutions. However, in practice, the best location or size may not always be possible due to other practical constraints. For example, the optimum size for certain resources of DG may not be available in the market. In the present study, the other advantages such as the economic and environmental aspects of DG are not considered. In addition, the application of CS in

[12]

[13]

[14]

[15]

[16]

[17]

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