Optimal DG Placement and Sizing in Distribution Systems Using Imperialistic Competition Algorithm Arash Mahari and Ebrahim Babaei, Member, IEEE Faculty of Electrical and Computer Engineering University of Tabriz Tabriz, Iran E-mails:
[email protected];
[email protected] Abstract— Distributed Generation (DG) sources are becoming more noticeable in distribution systems, due to the increasing demands for electrical energy. Location and size of DG sources have effectively impact on the power losses in a distribution network. In this paper, imperialistic competition algorithm (ICA) is used for optimal locating and sizing of DG on distribution systems. The cost function is based on minimizing network power losses. Optimal sizing and allocation result in better voltage regulation. The performance analysis is executed on 33 and 69 bus systems with different scenarios to present the efficiency of the proposed method in comparison with other algorithms. Keywords— Distributed generation; optimal optimal sizing; imperialistic competition algorithm
placement;
I. INTRODUCTION DG sources are becoming more important in distribution systems, recently, due to the growth demands for electrical energy. DG is 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 [1]. There are some reasons for increasingly developing of DG using in electrical networks. One of the main reasons is that it is easy to find sites for small generators and the generator in small ranges, down to 10 kW, is available due to latest technologies. The other reason is about DG units distance to customers, which is very short, in comparison with conventional units, so the transmission and distribution costs and power losses will reduce. In DG units, it is easier to use some new sources of energy, such as wind and solar energy and so on. In order to obtain the mentioned advantages, DG size and place has to be optimized. Researchers have presented many interesting algorithms and solutions, as some of the solutions, which referred in [2] as analytical approaches [3] numerical programming and heuristic [4, 5]. Some researches are based on evolutionary algorithms. In [6] the DG allocation problem is solved using artificial bee colony. Combination of particle swarm optimization and genetic algorithm to solve DG placement problem is given in [7]. Each method has their benefits and defect based on data and system being speculated. Generally, the allocation and sizing problem formulation of distributed generation is nonlinear, stochastic, and mixinteger.In all formulations, the objective function is to minimize the real power losses with improving voltage
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profile; while satisfying all constraints equations in terms of voltage and power. In this paper, a new optimization approach, using ICA, is developed to determine the optimal DG unit location, size, and power factor, in order to reduce the total system real power losses, as much as possible. Sample 33-bus and 69-bus systems are examined as test cases with different load scenarios. The results expose that the ICA is effective, fast, and capable of handling complex nonlinear mix-integer optimization problems. II. PROBLEM FORMULATION One most important benefit of spreading out DG unit in distribution networks is to reduce the total system power losses, as much as possible, while fulfills operating constraints. In other words, DG unit application problem is defined as finding the optimum size and location of DG unit, to satisfy the considered objective function subordinate to equality and inequality constraints. In this paper, the objective function is based on active power losses reduction in network. The powerflow analysis method used in DG unit problem has impact on reliability, flexibility, and accuracy of results. Hence, the overall optimization algorithm accuracy is mostly dependent on power flow analysis. In other words, the power-flow analysis is a basic part of the DG unit solution algorithm. Due to this, Backward-Forward Sweep Load Flow Algorithm is applied in this paper. DG unit application is mixed integer nonlinear optimization problem. The formulations are as follows: •
The objective function is based minimizing the system real power losses:
• n
Objective Function = min ∑ (I i ) 2 .ri
(1)
i =o
where Ii and ri are current and resistance of ith line. •
To satisfy the system power demand, the following two linear equation must be satisfied:
Psys + PDG = Pd + Ploss
(2)
Q sys + Q DG = Qd + Q loss
(3)
where:
Psys and Qsys are active and reactive power obtained from main system. PDG and Q DG are active and reactive power supplied by DG units. Pd
and Q d are total system active and reactive power demand.
Ploss and Q loss are total system active and reactive power losses. •
The system voltage should be between the limits, which is, 1±5% of the nominal voltage value:
V min ≤ V sysi ≤ V max
(4)
where V sysi is the voltage at ith bus, and V min and V max are minimum and maximum allowable voltage of system, respectively. •
The thermal capacity limits of the network’s feeder lines should be considered:
| I i |≤| I irated |
(5)
where I irated is the rated current of ith line. •
S
≤S
DG i
≤S
DG max
DG DG ≤ pf i DG ≤ pf max pf min
A. Generating Initial Empires
At the beginning of the algorithm, an initial population called countries should be created. In an N-dimensional optimization problem, the position of the ith country is defined as, Country i = [ p i1 , p i2 , p i3 ,..., p iN var ] where i=1, 2, 3, ..., Ncountriy. Ncountriy is total number of the countries. The objective function of the countries can be set up by evaluating the function at the [ p i1 , p i2 , p i3 ,..., p iN var ] variables. Then the cost of the ith country is as follows:
cost i = f (country i ) = f ( p1 , p 2 , p3 ,..., p N var )
Discrete inequality constricts for DG size and power factor must satisfied as following equations :
DG min
in is inversely proportional to its cost function. Then the colonies transfer toward their pertinent imperialist and the position of the imperialists will be updated if any of the colonies has better position than the imperialist. In the next step, the imperialistic competition begins among imperialists, and through this competition, the weak empires are eliminated. The imperialistic competition will progressively lead to a growth in the power of powerful empires and a reduction in the power of weaker ones. At the end, the weak empires that are not able to make their position better will be collapsed. These competitions between the empires will cause all the countries to converge to a state in which there exists only one empire in the world and all the other countries are colonies of this empire [11].
(6)
(7)
In this paper, the practical concern about DG size and power factor is considered. Since the DG unit’s size and pf are considered as discrete values and treated initially in the proposed method, the preciseness of the results is promised. The preselected (discrete) DG unit sizes are from 10%–80% of the total system demands (i.e. Pd), approximated to integer values with 25 kW steps. The DG unit’s pf (lead or lag) is set to operate at practical values [8] that is, unity, 0.95, 0.90, 0.85 and 0.8 close to the best result. Furthermore, the operating DG unit’s pf must be different from the load of bus at which the DG-unit is placed [9]. III. IMPERIALISTIC COMPETITION ALGORITHM Atashpaz Gargari and Lucas introduced the ICA, which is inspired by imperialistic competitions [10]. As other evolutionary algorithms, the ICA starts with an initial population, which is called countries. Some of the countries, which have the minimum costs, are selected to be foremost imperialists. The other countries become the colonies of these imperialists. The colonies are shared between the imperialists based on the imperialists’ power. The power of an imperialist
(8)
where cost i is the cost of the ith country. Then Nimperialist of the most powerful countries are chosen to create empires. The remaining Ncoloniy countries will be the colonies of these empires. In the next step, the colonies must be divided among the imperialists based on their strength. The imperialists’ strength is inversely proportional to their cost value in an optimization problem. The initial number of colonies of an empire is straight proportional to its power. To do this, the normalized costs of the empires are defined as (9)
C n = max{c i } − c n i
where c n is the cost of the nth imperialist and C n is its normalized cost. The normalized power of each imperialist is defined by
pn =
Cn
(10)
N im p
∑C
i
i =1
Then the initial number of colonies of an empire will be
NC n = round { p n .(N colony )}
(11)
where NC n is the initial number of colonies of the nth empire.
For each imperialist, NC n of the colonies are randomly selected and are donated to it. These colonies together with their imperialist set up the nth empire.
x θ
d Fig. 2. Single line diagram of 69-bus system
Fig. 1. Movement of colonies toward relevant imperialist
B. Moving the Colonies toward Their Imperialists In this step, the colonies start to move toward their relevant imperialists. This movement is shown in Fig.1., In which the colony moves toward the imperialist by x units. In this paper x is a random variable with uniform distribution. Then for x we have x ∈U (0 , β × d )
(12)
To search various points around the imperialist, a random amount of deviation is supplemented to the direction of movement. Figure shows the act of moving a colony toward its related imperialist in the new direction. In Fig.1, θ is a random angle between ( −γ , γ ) where γ is the parameter that adjusts the deviation from the straight direction toward imperialist. Then for θ we have
θ ∈ U (−γ , γ )
(13)
C. Updating Positions of the Imperialists During the prior step, it is possible for a colony to obtain a position, which has lower cost than that of the imperialist. In such occasion, the positions of the imperialist and colony with better position must be changed. Then the previous imperialist as other colonies of this empire move toward the location of the new imperialist. D. Calculating Absolute Power of an Empire The absolute power of an empire related to the both power of the imperialist and the power of its colonies. Also colonies have impact on power of empire it is mainly affected by the power of the imperialist the best country of the empire. The absolute power of an empire is defined as TC n =Cost (imperialist n ) + ξ mean{Cost (colonies of empire n )}
(14)
where TC n is the absolute power of the nth empire and ξ is a positive factor which is assumed to be less than 1 in this paper. In fact, ξ depicts the role of the colonies in calculating the absolute power of an empire.
E. Imperialistic Competition In this step, the imperialistic competition starts and all the empires attempt to take possession of the colonies from other empires. This competition is simulated by choosing the weakest colony of the weakest empire and competes against each other to possess this weak colony and add it to they own empire and enhance their power. Each of the empires will have a probability of taking possession of this colony based on their absolute powers; so, the powerful empires have more chance to possess the mentioned colony. F. Eliminating the Powerless Empires The powerless empires will breakdown in the imperialistic competition. Various standards can be defined for breakdown mechanism. In this paper, an empire is supposed breakdown when it has no colony and loose all of its colonies.
G. Convergence After some imperialistic competitions, all the empires will breakdown and just the most powerful one remains. All of the countries that they were colonies of other imperialist is now the under possession of this empire. At the end all of the colonies have the same positions and costs and there is not any difference between the colonies and their imperialist in other word all the world is just one powerful country. In such a case, the algorithm stops and this position is the best position.
IV.APPLICATION OF ICA FOR DG PLACING PROBLEM Tuning parameters of optimization algorithms has great impact on the performance of the algorithm. Not being trapped in local extrema, and fast converge are such outcomes of setting the parameters properly. The ICA has few but effective controlled parameters. In this paper, the initial population (initial countries) is 100 and there is 10 initial imperialists in all test cases. As suggested in [10], the assimilation coefficient set to be 2 and assimilation angle coefficient is set to (π/4). Revolution rate is 0.7 to govern not trapping in local extrema.
TABLE I. SUMMARY OF 69-BUS SYSTEM (SCENARIO1, 2) Load scenario
∑ kW
∑ kV Ar
loss
loss
|Vmin|,P.u. |Vmax|,P.u.
∑S
Load
, KV A
I
II
224.94
560.53
102.35
253.59
0.9091 1.0000
0.8559 1.0000
4660.20
6990.30
560.53 kW (Table I) while the real power loss after installing optimal DG unit is 53.37 kW (Table II). The active loss reduced about 90%, and the minimum voltage of the system is within acceptable limits.
C. Third case study In third case study, the properness of the presented algorithm on placing more than one DG unit is mentioned. In this case, two DG units are considered to be located on 69-bus test system on both load scenarios (scenario 1, 2). Table III show the results in detail. As mentioned in Table III, in third TABLE II. SIMULATION RESULTS OF ICA ON 69-BUS SYSTEM (SCENARIO 1,2) Load scenario I II Optimal DG location(bus)
61
61
0.8(lead)
0.8(lead)
2250
3250
23.05
53.37
14.52
36.68
|Vmin|,P.u.
0.9731
0.9583
|Vmax|,P.u.
1.0000
1.0000
Optimal PF Optimal DG size(kVA)
Fig. 3. Single line diagram of 33-bus system
V. RESULTS The proposed algorithm was examined on two 33-bus (Fig.3) and 69-bus (Fig.4) radial system to ensure the validity of ICA. The test on 69-bus system was on two load scenarios and one load scenario about 33-bus test system. In each case placing one and two DG are examined two check the validity of algorithm on placing more than one DG unit. 69-bus system load values obtained from [12] and 33-bus data obtained from [13]. The second scenario on 69-bus test system represents the same system with 50% increased in system loads. The results were compared with results obtained from other methods. In addition, the proposed ICA algorithm results are obtained after 50 independent runs for various test cases. This means that, the initial population (countries) was generated randomly and independent from previous runs.
∑ kW loss ∑ kV Ar loss
TABLE III. SIMULATION RESULTS OF ICA FOR THIRD CASE Load scenario I II Optimal DG 61 16 17 61 location(bus) Optimal PF 0.8(lead) 0.85(lead) 0.85(lead) 0.8(lead) Optimal DG size(kVA) 2000 750 1000 3250
∑ kW loss ∑ kVAr loss |Vmin|,P.u. |Vmax|,P.u.
system
B. Second case study The second case study system is the same as previous one, however the loads of system increase 50% (scenario2). In this case, the validity of presented algorithm to placing the optimum DG unit is considered on highly loaded systems. In this case, the active power losses before the DG placing was
16.36
8.47
18.40
0.9925 1.003
0.9914 1.001
TABLE IV. SUMMARY OF 33-BUS SYSTEM 33-bus
∑ kW A. First case study The first case study is a radial distribution system with the total load of 3809.16 kW, 2694.6 kVAr (scenario1), 69-bus as it is shown in Fig.3. The real power losses in the system is 224.94 kW and the reactive power losses is 102.35 kVAr (Table I) .The results for optimal allocation and sizing problems of DG using ICA is described in Table II. The location, DG size, DG PF, the active power losses, the reactive power losses and minimum and maximum voltage of system is shown in Table II. The active power losses lessen down to the 89% of the system without any DG.
7.97
∑ kV Ar
loss
211
loss
143.03
|Vmin|,P.u.
0.9038
|Vmax|,P.u.
1.0000
∑ S Load , kV A
4369.34
TABLE V. SIMULATION RESULTS OF ICA FOR 33-BUS SYSTEM DG 1 DG 2 DG Optimal DG location (bus) 6 30 13 0.8 0.8 0.9 Optimal PF (lead) (lead) (lead) Optimal DG size(kVA) 3100 1550 925 68.08 29.15 kW loss
∑ ∑ kV ar
|Vmin|,P.u. |Vmax|,P.u.
loss
54.94
21.11
0.9581 1.001
0.9804 1.006
this study, effect of optimal DG placement on active and reactive power losses and voltage profile will be considered.
TABLE VI. COMPARISON OF LOSSES REDUCTION USING DIFFERENT ALGORITHMS Feeder system
33-bus
69-bus(scenario 1)
Analytic[14]
47.3%
62.9%
ABC[6]
48.2%
63%
GA[15]
44.8%
62.9%
Modified ABC[16]
48.2%
63%
ICA
67.7%
89%
The run time, number of iteration and output variance will be analyzed.
A. Active power loss reduction The objective function of this paper is about reduction of real power losses. In other words, the optimal allocation and sizing is based on losses reduction. Table VI shows the result of this method in comparison with other methods. As shown the ICA has best result between others methods such as ABC or analytic method.
B. Voltage Profile As Fig. 4 Shows, the voltage profile in all cases is within allowable limits. However, after adding DG not only the buses voltages satisfy voltage constraints but also become flatter and almost 1(pu) (especially with 2 DG unit) in all systems.
C. Reactive Power Losses Reduction Fig. 4. Voltage profile (A) 69-bus scenario1 (B) 69-bus scenario2 (C) 33-bus
case study the real power losses decrease about 96.5% in load scenario1 and 97% in load scenario 2.
D. Forth case study In last study case, the algorithm is applied on 33-bus system to check its performance on different test systems. In this system, the total load power is 4369.4 kVA. The real power losses are about is 211kW and reactive power loss is 143.03 kVAr (Table IV). The best DG location shown in Table V. Placing one DG cause real power losses to lessen down to 68.08 (kW) and placing two optimal DG cause the active loss to be 29.35 (kW). In both cases, the minimum and maximum voltages are satisfying voltage limit constraint. VI. RESULTS ANALYSIS In the following subsections, performance of the algorithm is analyzed in different conditions and for different cases. In
In all study cases, the reactive power losses reduced as well as active power. As shown in Fig. 5, the reactive power reduced in all cases at least 61% in worst case, which is 33-bus system with one DG unit. These results declare that also the objective function was based on real power loss reduction, the reactive power loss reduced as well.
D. Output Variance Output variance is one of indicators declare the results validity. For comparing different methods variances calculated for the fifty independent runs. As result, the output variances for GA and PSO are 0.0986 and 0.02134 respectively [7], and about ABC it’s almost 1.14e-5 [6] however variance in ICA is zero in all study cases. Having zero variance shows that the ICA is more efficient than other optimization methods. Conclusion E. Convergence Characteristic
This arises from the searching and assimilation method of ICA as separate, the all population in some empires. This fast
convergence characteristic causes less run time than other methods. Fig.6 shows the convergence characteristic of method on 69-bus system on both load scenario 1, 2. As shown in both cases, the algorithm reaches the best solution in less than 25 iteration (iteration is named one decade in ICA).
Reactive power loss (kVAr)
300 default 1 DG unit 2 DG unit
250 200
Also the objective function was based on active loss reduction, other parameters improved after adding DG unit(s) as well.
•
Practical concerns about of DG-unit sizes and power factors are considered in the presented technique.
•
The ICA has best result in placing more than one DG unit system as in placing only one unit.
•
The algorithm converges in less than 25 iterations, and has so little run time due to converge characteristic.
•
The output variance is zero in all cases.
150 100
REFERENCES
50
[1]
0
[2]
69-bus(1)
69-bus(2)
33-bus
Fig. 5. Reactive power losses reduction in different cases
[3] [4] [5] [6]
[7]
[8]
Fig. 6. Convergence characteristic of ICA on 1st and 2nd study cases
[9]
This paper, proposed a method to solve the mixed-integer nonlinear DG allocation and sizing optimization problem, using ICA. The objective function was based on minimizing the total system active power losses, by satisfying various system constraints. The algorithm is tested on the two 69-bus and 33-bus radial distribution feeder systems in different cases with different load scenarios.
[10]
The ICA-based proposed technique has some significant advantages over other techniques. The following important points should be considered about this solution:
[13]
•
The results about active and reactive losses reduction are best in comparison with other methods.
•
Voltage profile improved after adding optimal DG unit(s) to system and all the voltages become within allowable limits.
•
•
The validity of algorithm on different load scenarios was verified.
[11] [12]
[14] [15] [16]
[17]
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