Optimization (PSO) and Clonal Selection Algorithm. (CLONALG) are two methods which have been applied to optimize different objective functions in previous ...
2010 IEEE International Conference on Power and Energy (PECon2010), Nov 29 - Dec 1, 2010, Kuala Lumpur, Malaysia
Optimal Placement of Distributed Generation Using Combination of PSO and Clonal Algorithm M. Sedighizadeh2, M. Fallahnejad1, M. R. Alemi1, M. Omidvaran1, D. Arzaghi-haris 1-Faculty of Electrical and Computer Engineering, Shahid Beheshti University, Tehran, Iran 2-Faculty of Engineering and Technology, Imam Khomeini International University, Qazvin, Iran
Abstract-The optimal placement of Distributed Generation (DG) has attracted many researchers’ attention recently due to its ability to obviate defects caused by improper installation of DG units, such as rise in system losses, decline in power quality, voltage increase at the end of feeders and etc. This paper presents a new advanced method for optimal allocation of DG in distribution systems. In this study, the optimum location of DG units is specified by introducing the power losses and voltage profile as variables into the objective function. Particle Swarm Optimization (PSO) and Clonal Selection Algorithm (CLONALG) are two methods which have been applied to optimize different objective functions in previous studies. In this paper, the Combination of Particle Swarm Optimization and Clonal Selection Algorithm (PCLONALG) is utilized as a solving tool to acquire superior solutions. Considering the fitness values sensitivity in PCLONALG process, it is necessary to apply load flow for decision making. Finally, the feasibility of the proposed technique is demonstrated for a typical distribution network and is compared with the PSO and CLONALG methods. The experimental results illustrate that the PCLONALG method has a higher ability in comparison with PSO and CLONALG, in terms of quality of solutions and number of iterations. The approach method has the preferences of both previous methods. Via immunity operation, the diversity of the antibodies is maintained and; the speed of convergence is ameliorated by operating particle swarm intelligence.
•
The liberalization of the electricity market contributes to creating opportunities for new utilities in the power generation sector; • DG offers greater values as it provides a flexible way to choose a wide range of combinations of cost and reliability. DG impacts different parameters of a power system, comprising voltage profile, line losses, short circuit current, amount of injected harmonic, and system reliability and stability. These parameters have to be appropriately investigated prior to installation of DG units. The problem of allocating DG units to optimal places and also sizing of them is of higher priority amongst all issues which affect on the mentioned parameters. However, installation of DG units in non-optimal places may results in an increase in system losses and a bad effect on voltage profile and other parameters which may lead to a growth of costs, and consequently an opposite effect on what is expected. Selecting the best places for installation of DG units and their preferable sizes in large distribution systems is a complex multimodal and combinatorial optimization problem. Thus, using an optimization method which is capable of indicating the best solution for a given distribution network, would help system planning engineers [2], [3]. The optimal placement and sizing of DG units in distribution networks have been vastly studied in order to achieve different targets. The intent may be the minimization of active losses of the feeders [4], [5], the minimization of total network supply costs, which includes generators operation and losses compensation [1], [6], the best utilization of available generation capacity [7], THD reduction [8], and improving voltage profile [9]. Many conventional optimization techniques such as gradient method, linear programming, dynamic programming, Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Clonal Selection Algorithm (CLONALG) have been employed to attain the aforementioned goals. Nevertheless, due to complexity of the problems, these methods may fail to find the global optimal solution and also may converge in an unreasonable time [2], [3]. In this paper a new method of optimization algorithms is proposed to minimize active losses of feeders and improve voltage profile. This technique, called PCLONALG, is combination of PSO and CLONALG, which is applied to
Index Terms--Distributed Generation, Optimal Placement, PCLONALG Method, Power Losses, Voltage Profile
I.
INTRODUCTION
Distributed Generation (DG) is a kind of electricity production which is on-site or close to the load center and is interconnected to the distribution system. The plenitude of the advantages of DG justifies the planning of electric systems at presence of DG. Some important reasons for the increasingly widespread use of DG could be summarized as follows [1]: • DG units are closer to customers. Therefore Transmission and Distribution (T&D) costs are reduced; • The latest technology has made available plants with high efficiency and extended ranging in capacity; • It is easier to find sites for small generators; • Natural gas as fuel in DG stations is easily accessible and prices are more stable; • Usually DG plants require shorter installation times and the investment risk is not too high; • DG plants yield fairly good efficiencies especially in cogeneration and in combined cycles (larger plants);
978-1-4244-8946-6/10/$26.00 ©2010 IEEE
1
neighbors’ flying experience, seeking a better position for itself. In the PSO, each particle keeps track of its own best position. The best position is associated with the best fitness. Furthermore, parallel with the acquiring best position of the particles, the global best position is also retained. The velocity vectors are updated according to recorded data which is mentioned above. The particles change their positions respect to their velocity vectors [2], [10]. More details of the PSO method could be found in [11].
satisfy defined conditions and eliminate the faults occurring in previous methods. The outline of the paper is as follows: In section II, an introduction to the PCLONALG technique is presented. Problem formulation is performed in section III, and the proposed algorithm is discussed in section IV. In section V and VI, an applied example is studied and numerical results are presented, respectively. Finally, conclusions come in section VII. II. PCLONALG TECHNIQUE
C.
PCLONALG In the hybrid optimization algorithm, the improving idea of the particle swarm intelligence is embedded into the immunity clone algorithm. The CLONALG can achieve more accurate results than PSO in a haphazard way. However, there is a large redundancy in repeating its search for the optimal solution, which significantly reduces the convergence speed of this algorithm. Consequently, the PCLONALG gathers the ideas from the PSO and incorporates an improvement operator in the CLONALG to ameliorate this method. The proposed hybrid optimization algorithm is composed of four operators: improvement operator, cloning operator, hyper mutation operator and finally, receptor editing operator. The improvement operator is inspired by the particle swarm intelligence. More precisely, after determining affinity of antibodies, a user defined number of best individuals is selected. Before cloning these antibodies, they must be reformed by the improvement operator. Based on the particle swarm principles, the following (1) and (2) are applied to these antibodies:
A.
Basic principles of CLONALG Clonal Selection Algorithm was put forward by Burnet in 1959. This mechanism explains how the immune system reacts against antigens by generating antibodies and, how it enhances its capability of recognizing and eliminating antigens. In this method, each candidate solution is considered as an antibody, and its distance from global optimal solution is assumed as an antigen. The solution population consists of a finite number of antibodies and each antibody represents a point in the search space. Every single antibody is appraised by the evaluation mechanism to procure its affinity. After sorting based on affinity values and undergoing immune operators, a new population is generated iteratively. The CLONALG employs three immune operators, including cloning, hyper mutation, and receptor editing, to refresh the composition of populations. The cloning operation refers to the act of producing copies of every individual in an antibody population proportional to its fitness with the antigen. That is to say, the higher the antigenic affinity, the higher the number of clones generated for each antibody. During hyper mutation operation, the cloned population is subjected to an affinity maturation process inversely proportional to the antigenic affinity. The receptor editing operation is the process of procreating a given number of new antibodies randomly and replacing them with the antibodies with the lowest antigenic affinity. Receptor editing enables the algorithm to escape from local optima on an affinity landscape [10].
1
(1) ,
1
1 ,
(2)
where cl and c2 are two positive learning factor constants, and are two uniformly distributed random numbers on the interval [0,1], pi(t) is the best position of ith particle, and pg(t) is the overall best position of the population. If the improved antibody is the offspring produced by the parents of the previous generation, vi(t) will be set randomly on the interval [0,1], and pi(t) will be set to xi(t). After (2), the affinity value of the antibody may exceed the preset range, and it shall be reassigned the nearest reasonable value to it. In the cloning operation, the clones are the identical copies of their parents. At the outset, the antibodies in the current population are sorted in an ascending order according to their affinities, for minimizing objective function. Then, the sorted antibodies are duplicated. The number of generated clones for each antibody is given by: . , (3)
B. Basic principles of PSO Particle Swarm Optimization is one of the Evolutionary Computation (EC) techniques which was primarily introduced by Kennedy and Eberhart in 1995. The PSO algorithm is an adaptive algorithm based on a social– psychological metaphor, that is, each individual in the swarm called particle is adapted by returning haphazardly toward previously successful regions in the search space and; is influenced by the successes of its topological neighbors. Initially, a population of particles which conceptually is similar to the antibodies in the CLONALG, is randomly generated. This initial population comprises finite members. The fitness of each particle is determined by the evaluation mechanism. Afterward, each particle relocates its position in search space and updates its velocity according to its own and
2
and
where β is a multiplying factor, N is total number of antibodies, round(.) is the operator that rounds its argument toward the closest integer, and i is the position of the parent antibody. The clones thereafter undergo the hypermutation operator, which is inversely proportional to the affinity value of each clone based on (4) and (5):
exp
0,1 ,
(4)
,
(5)
.
is defined as: ∑
min
∑
,
,
(8)
in which: k: Ri : Ii : Ii :
where c' is a mutated antibody of c, N(0,1) is a Gaussian random variable of zero mean and standard deviation σ = 1, ρ is a parameter that controls the decay of the inverse exponential function, and f is the fitness of an individual normalized in the interval [0,1]. A mutation is only accepted if the c' is within its preset range, otherwise the nearest reasonable value shall be reassigned to it as aforementioned. In order to increase the diversity of the antibodies, receptor editing operator is also employed. That is, a user defined number of new antibodies is randomly generated, and is utilized to replace the same number of antibodies with the lowest affinities [10], [12].
is the number of network lines, is the ith branch resistance, is the current of ith branch, is the current of ith branch without DG resource,
subject to: 0.9 p.u. ≤ Vi ≤ 1.1 p.u.
(9)
IV. PROPOSED ALGORITHM The flowchart of the proposed algorithm is illustrated in Fig. 1. Start
Input data of network
III. PROBLEM FORMULATION In order to solve DG placement problem, the determination of the optimal number, location and sizes of DG units which must be installed in a network is vital. These data should maximize cost savings, subject to operating constraints. Because of the complexity of the problem, some simplifying hypothesises are introduced [3]: • The capacity of DG units shall be selected from specified capacity candidate; • One DG could be allocated to one candidate position; • The maximum number of installable DG units is given. This paper specifically concentrates on minimization of power losses and improvement of voltage profile. These items should be composed with constraints to obtain a proper objective function. The overall objective function, with composing constraints and goals, is determined as following: . where
.
and
∑
, ,
,
Run load flow to calculate affinities Improve antibodies by particle swarm intelligence Run load flow to calculate affinities Clone antibodies
Maturate clones Run load flow to calculate affinities
(6)
are weighting factors; and ∑
min
,
Initialize antibody production
is defined as:
,
Generate next population
(7)
Antibody receptor editing
in which: n: Vi : Vi,ref : Vi,noDG :
Terminate?
is the number of network buses, is the voltage of ith bus, is the specified voltage for ith bus, is the voltage of ith bus without DG resource;
Yes End Fig. 1. The computation procedure
3
No
TABLE II BUS INFORMATION
According to this flowchart, at the opening, data of buses and branches of the network is entered to the algorithm. Then, PCLONALG algorithm as the core of this optimization process is run and load flow algorithm is used wherever the evaluation process is essential. These processes are programmed by MATLAB software [2]. V. CASE STUDY A test case is selected from a section of Tehran distribution network. The single line diagram of the network is illustrated in Fig. 2. This is a MV feeder with 13 buses from 63/20 KV Khoda-Bande-Loo substation. Table I and II provide the data of lines and buses [2].
Fig. 2. Single line diagram of case study
TABLE I LINE INFORMATION
Bus Number
P (KW)
Q (KVAR)
1
0
0
2
890
468
3
628
470
4
1112
764
5
636
378
6
474
344
7
1342
1078
8
920
292
9
766
498
10
662
480
11
690
186
12
1292
554
13
1124
480
VI. NUMERICAL RESULTS
From
To
R (ohm)
X (ohm)
1
2
0.176
0.138
2
3
0.176
0.138
3
4
0.045
0.035
4
5
0.089
0.069
5
6
0.045
0.035
5
7
0.116
0.091
7
8
0.073
0.073
8
9
0.074
0.058
8
10
0.093
0.093
7
11
0.063
0.050
11
12
0.068
0.053
7
13
0.062
0.053
Initially, a load flow is run for the test case. The base condition of system voltage profile and power losses is investigated. Mean voltage of buses is 0.9302 p.u. and sum of power losses is 800 KW. For installing DG units in the network, the available capacities are 500, 1000, 1500 and 2000 KW, and the maximum number of units is three. To show the effect of installation of DG units on operating parameters of the test system, one DG is installed in the first step. The prepared program is run and specifies that the best place and the best capacity of DG unit are bus 11 and 2000 KW, respectively. In this case, mean value of bus voltages is 0.9787 p.u. and amount of power losses is 524 KW. The results clarify that installing a DG unit could significantly improve voltage profile and reduce power losses. In the next step, two DG units are considered for installing in the network. In this case, connecting two DG units with 2000 KW capacity to the bus 9 and bus 10, is the best solution of the problem. Once again, the mean value of bus voltages rises and the sum of line losses drops. The Mean voltage of buses and the sum of power losses reach to 0.9911 p.u. and 400 KW, respectively. The solution of allocating three DG units to the network, is installation of three units of 2000 KW in buses 8, 12, and 13.
4
The presented charts display the power of PCLONALG in converging in the primary iterations. This ability is attained by several embedded maturation levels in the algorithm. In order to have a clear comparison, bus voltages in the base case and also after installation of DG units are illustrated in Table III and Fig. 6. The outcomes represents that installation of DG unit considerably improves the voltage profile.
The mean value of bus voltages climbs to 0.9973 p.u. and the sum of active power losses reduces to 172 KW. The convergence processes of the algorithm for allocating one, two and three DG units to the network are shown in Fig. 3, 4, and 5.
TABLE III COMPARISON OF VOLTAGE PROFILES Bus Number
Base Case
1 DG Unit
2 DG Units
3 DG Units
1
1.0000
1.0000
1.0000
1.0000
2
0.9709
0.9885
0.9925
0.9954
3
0.9441
0.9796
0.9874
0.9932
4
0.9378
0.9778
0.9866
0.9931
5
0.9268
0.9759
0.9865
0.9944
6
0.9265
0.9755
0.9862
0.9941
7
0.9146
0.9755
0.9886
0.9982
8
0.9117
0.9728
0.9959
1.0000
9
0.9108
0.9719
1.0000
0.9991
10
0.9106
0.9717
1.0000
0.9989
11
0.9129
0.9800
0.9870
0.9988
12
0.9116
0.9788
0.9858
1.0000
13
0.9136
0.9746
0.9876
1.0000
Mean Voltage
0.9302
0.9787
0.9911
0.9973
Fig. 3. The process of convergence with one DG unit
Fig. 4. The process of convergence with two DG units
Fig. 6. Voltage profile in the base case and after installation of DG units
Fig. 5. The process of convergence with three DG units
5
[9]
Y. Alinejad-Beromi, M. Sedighizadeh, M.R. Bayat, and M.E. Khodayar, “Using genetic algorithm for allocation to reduce losses and improve voltage profile,” Universities Power Engineering Conference UPEC, 2007, UK. [10] W. Qiaoling, W. Changhong, and X.Z. Gao, “A Hybrid optimization algorithm based on clonal selection principle and particle swarm intelligence,” Sixth International Conference on Intelligent Systems Design and Applications, 2006. [11] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proc. of the IEEE International Conference on Neural Networks, Australia, pp. 1942-1948, November-December 1995. [12] L.N. de Castro and F.J. Von Zuben, “Learning and optimization using the clonal selection principle,” IEEE Trans. on Evolutionary Computation, pp. 239-251, June 2002.
In Table IV, sum of line power losses in the base case and after installation of DG units is presented. It is obvious that installation of DG units leads to reduction in total power losses. TABLE IV COMPARISON OF POWER LOSSES Base Case
1 DG Unit
2 DG Units
3 DG Units
Power Losses (KW)
800
524
400
172
Reduction of Power Losses (KW)
-
276
124
228
VII. CONCLUSIONS In this paper, PCLONALG as a novel approach at the cutting edge of optimization methods was implemented to resolve DG allocation problem in the distribution networks. The Khoda-Bande-Loo distribution test feeders of Tehran city were analyzed and the outcomes of applying proposed PCLONALG to the problem were presented. The experiments indicated that this hybrid optimization algorithm improves the accuracy of the solution and is considerably faster than other techniques and, is capable of escaping from local minima and finding the global one effectively. The numerical results illustrated that PCLONALG reveals better characteristics in comparison with PSO and CLONALG techniques in all trials, particularly in terms of quality of solutions and number of iterations. REFERENCES [1] [2]
[3]
[4] [5] [6]
[7] [8]
G. Celli and F. Pilo, “Optimal distributed generation allocation in MV distribution networks,” in Proc. 2001 IEEE PICA Conference, pp. 8186. Y. Alinejad-Beromi, M. Sedighizadeh, and M. Sadighi, “A particle swarm optimization for sitting and sizing of Distributed Generation in distribution network to improve voltage profile and reduce THD and losses,” 43rd International Universities Power Engineering Conference, 2008. M.R. Aghaebrahimi, M. Amiri, S.H. Zahiri, “An immune-based optimization method for distributed generation placement in order to optimize voltage profile,” International Conference on Sustainable Power Generation and Supply, 2009. K. Nara, Y. Hayashi, K. Ikeda, and T. Ashizawa, “Application of tabu search to optimal placement of distributed generators,” in Proc. 2001 IEEE Power Engineering Society Winter Meeting, pp. 918-923. T.K.A. Rahman, S.R.A. Rahim, and I. Musirin, “Optimal allocation and sizing of embedded generators,” in Proc. 2004 National Power and Energy Conference, pp. 288-294. W. El-Khattam, K. Bhattacharya, Y. Hegazy, and M.M.A. Salama, “Optimal investment planning for distributed generation in a competitive electricity market,” IEEE Trans. Power Systems, vol. 19, pp. 1674-1684, August 2004. A. Keane and M. O'Malley, “Optimal allocation of embedded generation on distribution networks,” IEEE Trans. Power Systems, vol. 20, pp. 1640-1646, August 2005. X. Yu, X. Xiong, and Y. Wu, “A PSO-based approach to optimal capacitor placement with harmonic distortion consideration,” Electric Power Systems Research 71, 2004, pp. 27–33.
6
