International Journal of Scientific & Engineering Research Volume 2, Issue 4, April-2011 1

ISSN 2229-5518

Distributed Generation Planning Optimization

Using Multiobjective Evolutionary Algorithms

Mahmood Sheidaee, Mohsen Kalantar

Abstract— In this paper, a method to determine the size - location of Distributed Generations (DGs) in distribution systems based on multi objective performance index is provided considering load models. We will see that load models affect the location and the optimized size of Distributed Generations in distributed systems significantly. The simulation studies are also done based on a new multi objective evolutionary algorithm. The proposed method has a mechanism to keep the diversity to overcome the premature convergence and the other problems. A hierarchical clustering algorithm is used to provide a manageable and representative Pareto set for decision maker. In addition, fuzzy set theory is used to extract the best solution. Comparing this method with the other methods shows the superiority of proposed method. Furthermore, this method can easily

satisfy other purposes with little development and extension.

Index Termsc Distributed generation, Distribution systems, Load models, Strength Pareto Evolutionary Algorithm.

—————————— • ——————————

1 INTRODUCTION

ptimization was used to reconstruct electricity in- dustry and looked for the best location for distri- buted products. Development in technology and
client requirements to have cheap electric power and reli- able one caused more motivation in distributed genera- tion .Discussion about reliability and maintaining prevent the penetration of DG resources in the distribution sys- tems.
In [1] one approach was described based on genetic algo-

2 LOAD MODELS AND IMPACT INDICES

To determine different load model effects on distributed generation planning, 37-bus distribution system will be studied (appendix 1)[7]. The effect of load models depends on voltage, means residential, industrial and commercial, will be studied in different planning scenarios. Load model defined as followed.
rithm for multistage planning of distribution systems op-
timizations. In this work, it's expressed as a mathematical

Pi P0i Vi

/ Qi Q0i Vi

(1)
model and algorithmic one and also tested with real sys- tems. In [2] – [5], it was studied on load models that are usable for power flow and dynamic studies. This study was done on load models depended on frequency or vol- tage. During the recent years, studies on evolutionary algorithm have shown that these methods don’t have the difficulties of classical methods. In principle, multiple Pareto optimal solutions can be found in one single run. This paper has discussed on load model effects in location and size planning and distributed generation optimiza- tion. We can see that the load models affect on location and size planning of DGs in distribution network. For the purpose of studying on load models, its delivered loca- tion and size planning for single DG, its assumed that the regarded DG has enough capacity. The proposed method is general and it can be used for case of multiple DG in the network with increasing some variables.
This paper also suggested a new Strength Pareto Evolu- tionary Algorithm (SPEA) based approach for solving the problem. The diversity-preserving mechanism embedded in the search algorithm makes it effective in exploring the problem space and capable of finding widely different solutions. A hierarchical clustering technique is imple- mented to provide a representative and manageable Parto-optimal set. Also, a fuzzy-based mechanism has used the best solution for extraction.
Where Pi and Qi are active and reactive power at bus i, P0i and Q0i are active and reactive power operating point in bus I, Vi is voltage in bus i and a and are active and reactive power exponents. In a constant power model conventionally used in power flow studied a = = 0 is assumed. The values of the real and reactive exponents used in the present paper for industrial, residential and commercial loads are given in Table 1 [7].

TABLE 1

EXPONENT VALUES

Load Type

a

Constant

0

0

Industrial

0.18

6.00

Residential

0.92

4.04

Commercial

1.51

3.40

During studying residential, it’s assumed that 38-bus systems just has residential load. It's assumed that for industrial and commercial load, all loads are a kind of industrial and commercial. In real situations, loads aren’t exactly residential, commercial and industrial, so the mixture load class should be foreseen for distribution system. There are different ideas for studying DG effects in distribution systems .One of this idea is different

IJSER © 2011 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 2, Issue 4, April-2011 2

ISSN 2229-5518

indices evaluation on the purpose of effect description on distribution system because of DG during maximum power production. These indices are

1) Active and Reactive Power Loss Indices (ILP and ILQ):

b) Search external Pareto set for the nondominated individuals and emit all dominated individuals from the set.

c) If the amount of the individuals externally stored in

[PLDG ]

[QLDG ]

the Pareto set exceeds a prespecified maximum size,

ILP

[PL ]

X 100 / ILQ

[QL ]

X 100

(2)
reduce the set by means of clustering.

Step 3) Fitness assignment: Calculate the amount of

Where PLDG and QLDG are total loss of active and reactive power distribution system with DG, PL and QL are total loss of active and reactive power of total system without DG in the distribution network.

2) Voltage Profile Index (IVD): One of the advantage of proper location and size of the DG is the improvement in voltage profile.




v V - V

fitness values of individuals in both external Pareto set and the population as follows.

a) Assign appropriate each individual s strength amount in external set. The strength amount is proportional to the number of individuals covered by that individual.

b) The fitness of each individual in population is equal to the sum of the strengths of all external Pareto solutions which dominate that individual.

IVD

max n

1

i X 100

(3)

Step 4) Selection: combine the population and external


i 2

\ 1 )

3) MVA Capacity Index (IC): This informational index gives information in the field of system necessities for promoting transmission line.

set individuals. Choose two individuals randomly and compare their fitness. Choose the best one and copy in a mating pool.

Step 5) Crossover and Mutation: do the crossover and mutation according to new population production probabilities.


v S Step 6) Ending: check the ending criteria if all things are

n ij

being done finish the work else substitute the old

IC maxi 2 CS

\

ij )

(4)
population with the new one and go to step2.
In this paper, time searching will be stopped if the generation counter exceeds its maximum number.
In some cases, the Pareto optimal set is extremely big or

3 PROPOSED APPROACH

Recently evolutionary algorithm showed that this algorithm can be effective for removing old method problems [8]. The main element method of SPEA is

1) External set: It’s a set of Pareto optimal solutions. These solutions were recorded externally and continuously be updated. Finally recorded solutions show Pareto optimal front.

2) Strength of a Pareto optimal solution: It is an assigned

real value SE[0,1) for each individual in the external set.
The strength of an individual is proportional to the
number of individuals covered by it.

3) Fitness of population individuals: Fitness of each individual in population is the sum of the strengths of all

has extra solutions. An average linkage based hierarchical clustering algorithm is used to reduce the Pareto set. We want to change P given set which its size exceeds the maximum allowable size N to P* set with size of N. Algorithm is such as following [8].

Step 1) Give primary amount to set C. each member of

P means a distinct cluster.
Step 2) if the number of clusters N, go to Step 5, else
go to Step 3.

Step 3) Calculate all the pairs of clusters distance. The

distance dc of two clusters C1, C2 E C is given as the
average distance between pairs of individuals across the
two clusters

1

external Pareto optimal solutions by which it is covered.
The strength of a Pareto optimal solution is at the same time its fitness.
Algorithm is in the following steps [8].

d c

n1n

2:d (i1 , i2 )

2 i1Ec1,i2Ec2

(5)

Step 1) primary amounts: produce population and make empty external Pareto optimal set.

Step 2) updating external set: External Pareto optimal set is updated as following:

a) Search population for the nondominated individuals and copy them in the external pareto set.

Where n1 and n2 are clusters individuals of C1 and C2.
Function d shows Euclidian distance between i1 and i2.

Step 4) Determine two clusters that have minimum dc distance. Combine these clusters into a larger one. Go to Step 2.

Step 5) find centroid for each cluster and choose the nearest individual to the centroid as agent and emit other individuals from the cluster.

IJSER © 2011 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 2, Issue 4, April-2011 3

ISSN 2229-5518

Step 6) Compute the reduced nondominated set P* by uniting the representatives of the clusters.
As soon as having the Pareto optimal set of nondominated solution, the proposed approach presents one solution as the best compromise solution. Each objective function of the i-th solution is represented by a membership function J.i defined as
Where 1" is a binary random number, r is a random
number rE[0,1], gmax is maximum number of generations
and is a positive constant that is desirable. = 5 is
selected. This operator gives a value x’iE[ai,bi] such that
the probability of returning a value close to xi increases as
the algorithm advances. This makes uniform search in the initial stages where t is small and for later stages is so local.

r

Fi

1

max

- Fi

Fi Fi

min

min

max

(6)

5 MULTIOBJECTIVE BASED FORMULATION

i

Fi

max

- Fi

0

F

min i

Fi Fi

Fi F max

Multiobjective index for evaluating distribution systems operation on purpose of DG location and size planning with load models, considers all previously mentioned
For each nondominated solution, the normalized membership function J.k is
indices by strategically giving a weight. The multiobjective index operation on basis of SPEA algorithm is according to (10).

Nobj

2: k

IMO

( 1

.ILP +

2 .ILQ +

3 .IC +

4 .IVD )

(10)

k i 1

(7)

These weights are because of giving the corresponding

M Nobj

2:2: k

k 1 i 1

where M is the number of nondominated solutions. The best solution is the one that has more J.k.
.

4 IMPLEMENTATION OF THE PROPOSED APPROACH

Because of Binary representation problems when search space has wide dimension, the proposed approach has been implemented using Real Coded Genetic Algorithm (RCGA). Decision variable xi has real amount within limit
of ai and bi (xiE[ai,bi]). The RCGA mutation and crossover
operators RCGA is like this.
Crossover: A blend crossover operator (BLX-a) has been
employed in this paper. This operator will choose one number randomly from the interval [xi a(yi - xi) , yi + a(yi - xi)], where xi and yi are the ith parameter values of the parent solutions and xi < yi. Because of ensure the balance between exploitation and exploration from search
space, a = 0.5 is chosen.
importance to each impact indices. Table 2 identifies used
amount for the weights with regarding normal operation analysis [7].

TABLE 2

INDICES WEIGHTS

Indices

op

ILP

0.40

ILQ

0.20

IC

0.25

IVD

0.15

Multiobjective function (10) can be minimized with regarding to various operational constraints to satisfy the electrical requirements for distribution network. These limitations are:

1) Power Conservation Limits: The algebraic sum of all input and output powers, such as distribution network total losses and power generated from DG, which should be equal with zero. (NOL = no of lines)

n NOL

Mutation: Nonuniform mutation was used here. In this

Pss (i, V )

2: (PD (i, V )) + 2: Ploss (V ) - PDGi

(11)
operator, new amount x’i of parameter xi produced after mutation in t time.

i 2 n 1

2) Distribution Line Capacity Limits: Transmission capability in each line should be equal with thermal

rxi + 6(t , bi - xi )if , -r 0

x

(8)
capacity.

xi - 6(t , bi - xi ) if ,-r 1

S (i, j) S (i, j)

(12)

v v1- t

6(t, y )

y 1 - r \

\

gmax )

)

(9)

3) Voltage Drop Limits: voltage drop should base on voltage regulation that DISCO gives.

IJSER © 2011 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 2, Issue 4, April-2011 4

ISSN 2229-5518


V1 - V j

6Vmax

(13)

Fig. 1. Impact indices and IMO with DG size-location pair for constant load

If voltage and MVA limits in system buses for a par- ticular size and location, accept that pair for next genera- tion, else this size and location will be ignored and re- jected. Size and location should be had minimum IMO.

6 SIMULATION RESULTS

The multiobjective index based analysis is carried out on
37-bus test systems as given in the Appendix [7]. A DG size
is considered in a practical range (0–0.63 p.u.). It's assumed
that DG is operated at unity p.f.. This assumption has two reasons:

1) Usually when the DG has unity power factor, has maximum profit because the cost of active power is higher. Use at unity power factor cause to have maximum capaci- ty.

2) Used models in this paper are simple and more atten- tion is for voltage changes dependence of load models.

The using method hasn’t been limited by DG models and it's general. First bus was chose as feeder of electric power from network and the rest buses are regarded as DG location. On all optimization runs, the population size and maximum number of generations were selected as 200 and
500, respectively. The Pareto optimal set maximum size
includes 20 solutions. The crossover and mutation proba-
bilities were selected as 0.9 and 0.01, respectively. For 37-
bus system, variation of impact indices and IMO have been
shown with DG size and location in figure 3-7 for constant,
industrial, residential, commercial and mixed load models.
The value of IVD for all load models is near zero. It shows
that voltage profile improves with present DG.
We can see from Figs. (1) – (5) that the indices ILP, ILQ,
IC and IMO achieve values greater than zero and smaller
than one, indicating the positive impact of DG placement
in the system. Fig. 1 shows that values of IC, ILP and ILQ for buses 2-4 as IC<ILP<ILQ and for buses 6-8 like ILQ<ILP<IC. Figure 2 shows the value of optimum DG size, IMQ and its components for all buses for industrial
load model. So load models affect on solutions.

Fig. 2. Impact indices and IMO with DG size-location pair for industrial load

The solution obtained using constant power load models may not be feasible for industrial load. A similar and significant effect of load models can be easily be observed from the Figs. (3) – (5) for residential commercial and mixed load models. The differences in values of DG size, IMO and its components are significant, showing that the load models effects are important for suitable planning of size and location. Table
3 summarizes the optimal DG size-location pairs, IMO along with its components for each kind of load. From Table 3, the optimal size-location for constant load model (0.6299 p.u. – bus 14) is different with industrial load model (0.63 p.u. – bus 14) residential load model (0.4672 p.u. – bus 14) commercial load model (0.4419 p.u. – bus

14) and mixed load (0.5113 p.u. – bus 32). Similarly IMO and other effective indices for optimal DG location-size are different.

Fig. 3. Impact indices and IMO with DG size-location pair for residential load

IJSER © 2011 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 2, Issue 4, April-2011 5

ISSN 2229-5518

Fig. 4. Impact indices and IMO with DG size-location pair for commercial load

Fig. 5. Impact indices and IMO with DG size-location pair for mixture load

The probable DG location-sizes may be little (because of constraints), but the number of candidate solution are fairly large to suggest the application of SPEA. The differences in values of DG size, IMO and its components are significant for load models, showing that the load models effects are important for suitable planning of size and location. The values of QLDG and PLDG related to optimal size –location for any kind of load model have been shown in table 4, although the values of QLDG and PLDG for nonconstant load models (industrial – residential
– commercial and mixture) aren’t different but their difference is significant when compared to constant load model.

TABLE 4

COMPARISON OF SYSTEM POWER LOSSES AT OPTIMAL LOCATION OF DG WITH LOAD MODELS

6.3 Conclusion

The general analysis includes load models is proposed for location–size of distributed generation planning in multiob- jective optimization in distribution systems. The multiobjec- tive criteria depends on system operation indices is used in this work. It was seen that while regarding load models, there will be changed in DG location and size. The overall value of multiobjective index (IMO) changed during charge model changing.
Also in this paper, we suggested a new method based on Pareto evolutionary algorithm and used for DGs location – size planning problem. This problem formulized as a mul- tiobjective optimization problem, A diversity preserving mechanism for finding widely different Pareto optimal solu- tions was used. A hierarchical clustering technique is im- plemented to provide a representative and manageable Pa- reto optimal set without destroying the characteristics of the trade-off front and a fuzzy based mechanism is used for finding the best compromise solution. The result shows that the suggestive method for multiobjective optimization prob- lem is useful, because multiple Pareto optimal solutions are found during simulation. Since the proposed approach does not impose any limitation on the number of objectives, its extension to include more objectives is a straightforward process.

APPENDIX

Fig. 6 shows the 37-bus test system.

TABLE 3

IMPACT INDICES COMPARISON FOR PENETRATION

OF DG WITH LOAD MODELS

Indices

Constant

Industrial

Residential

Commercial

Mixture

ILP

0.7078

0.6517

0.7459

0.7756

0.7526

ILQ

0.7035

0.6449

0.7383

0.7685

0.7551

IC

0.9913

0.9671

0.9570

0.9476

0.9478

IVD

0.0687

0.0634

0.0661

0.0653

0.0696

IMO

0.6823

0.6409

0.6952

0.7106

0.6994

Location

14

14

14

14

32

Size

0.6299

0.63

0.4672

0.4419

0.5113

IJSER © 2011 http://www.ijser.org

International Journal of Scientific & Engineering Research Volume 2, Issue 4, April-2011 6

ISSN 2229-5518

REFERENCES

[1]. V. Miranda, J. V. Ranito, and L. M. Proenca, “Genetic algorithms in optimal multistage distribution network planning,” IEEE Trans. Power Syst., vol. 9, no. 4, Nov. 1994, pp. 1927–1933.

[2]. C. Concordia and S. Ihara, “Load representation in power sys- tems stability studies,” IEEE Trans. Power App. Syst., vol. PAS-

101, no. 4, Apr. 1982, pp. 969–977.

[3]. IEEE Task Force on Load Representation for Dynamic Perfor- mance, “Bibliography on load models for power flow and dy- namic performance simulation,” IEEE Trans. Power Syst., vol.

10, no. 1, Feb. 1995, pp. 523–538.

[4]. IEEE Task Force on Load Representation for Dynamic Perfor- mance, “Load representation for dynamic performance analy- sis,” IEEE Trans. Power Syst., vol. 8, no. 2, May 1993, pp. 472–

482.

[5]. IEEE Task Force on Load Representation for Dynamic Perfor-

Fig. 6. 37-bus test system

mance, “Standard load models for power flow and dynamic performance simulation,” IEEE Trans. Power System, vol. 10, no. 3, Aug. 1995, pp. 1302–1313.

[6]. C. A. C. Coello, “A comprehensive survey of evolutionary based multiobjective optimization techniques,” Knowledge and Information Systems, vol. 1, no. 3, 1999, pp. 269–308.

[7]. E D. Singh, D. Singh, K. S. Verma, “Multiobjective Optimization for DG Planning With Load Models,” IEEE Trans. Power Syst., vol. 24, no. 1, Feb. 2009, pp. 427-436.

[8]. M. A. Abido, “Environmental/Economic Power Dispatch Using

Multiobjective Evolutionary Algorithms,” IEEE Trans. Power

Syst., vol. 18, no. 4, Nov.2003, pp. 1529–1537.

[9]. C. M. Huang, H. T. Yang, and C. L. Huang, “Bi-Objective power

dispatch using fuzzy satisfaction-maximizing decision ap- proach,” IEEE Trans. Power Syst., vol. 12, Nov. 1997, pp. 1715–

1721.

[10]. D. B. Das and C. Patvardhan, “New multi-objective stochastic

search technique for economic load dispatch,” Proc. Inst. Elect. Eng.-Gen. Transm. Dist., vol. 145, no. 6, 1998, pp. 747–752.

[11]. M. E. Baran and I. M. El-Markabi, “A multiagent-based dis-

patching scheme for distributed generators for voltage support on distribution feeders,” IEEE Trans. Power Syst., vol. 22, no. 1, Feb. 2007, pp. 52–59.

[12]. E. G. Carrano, L. A. E. Soares, R. H. C. Takahashi, R. R. Saldan-

na, and O. M. Neto, “Electric distribution network multiobjec-

tive design using a problem-specific genetic algorithm,” IEEE Trans. Power Del., vol. 21, no. 2, Apr. 2006, pp. 995–1005.

IJSER © 2011 http://www.ijser.org