Learning Center
Plans & pricing Sign in
Sign Out

Optimal Placement of Distributed Generation Using Particle Swarm


Optimal Placement of Distributed Generation Using Particle Swarm ...

More Info
									             Optimal Placement of Distributed Generation Using
                        Particle Swarm Optimization
               Wichit Krueasuk                                           Weerakorn Ongsakul
      Department of Electrical Engineering                       School of Environment, Resources and
        Faculty of Engineering Sripatum                        Development, Asian Institute of Technology
         University, Bangkok, Thailand                                  Pathumthani, Thailand
           E-mail:                                   E-mail:

                  ABSTRACT                                    Optimal placement of DG (OPDG) in distribution
                                                              network is an optimization problem with continuous and
This paper proposes a particle swarm optimization             discrete variables. Many researchers have used
(PSO) algorithm for optimal placement of distributed          evolutionary methods for finding the optimal DG
generation (DG) in a primary distribution system to           placement [6]-[9].
minimize the total real power loss. The PSO provides a
population-based search procedure in which individuals        In fact, three types of DG are considered as follows:
called particles change their positions with time. During     Type 1: DG is capable of supplying only real power;
flight, each particle adjusts its position according to its   Type 2: DG is capable of supplying only reactive power;
own experience, and the experience of neighboring             Type 3: DG is capable of supplying real power but
particles, making use of the best position encountered by     consuming proportionately reactive power.
itself and its neighbors. Initially, the algorithm randomly
generates the particle positions representing the size and    In [10], a Newton-Raphson algorithm based load flow
location of DG. Each particle will move from its current      program is used to solve the load flow problem. The
position using the velocity and the distance from current     methodology for optimal placement of only one DG type
best local and global solution reached. The velocity          1 is proposed. Moreover, the heuristic search requires
consists of inertia of the particle, memory, and              exhaustive search for all possible locations which may
cooperation between particles. The proposed PSO               not be applicable to more than one DG. Therefore, in
algorithm is used to determine optimal sizes and              this paper, PSO method is proposed to determine the
locations of multi-DGs. Three types of DG are                 optimal location and sizes of multi-DGs to minimize the
considered and the distribution load flow is used to          total real power loss of the distribution systems.
calculate the exact loss. Test results indicate that PSO
                                                              The organization of this paper is as follows. Section 2
method can obtain better results than the simple
                                                              addresses the problem formulation. The DG type and
heuristic search method on the 33-bus and 69-bus radial
                                                              heuristic search method are explained in Section 3. The
distribution systems. The PSO can obtain maximum loss
                                                              PSO algorithm is represented in Section 4. A PSO
reductions for each of three types of optimally placed
                                                              computation procedure on for the OPDG problem is
multi-DGs. Moreover, voltage profile improvement and
                                                              given in Section 5. Simulation result on the test systems
branch current reduction are obtained.
                                                              are illustrated in Section 6. Then, the conclusion is given
                                                              in Section 7.
Keywords- Distributed Generation, DG types, Optimal
DG size, Particle Swarm Optimization
                                                              2.        PROBLEM FORMULATION
                                                              The real power loss reduction in a distribution system is
                                                              required for efficient power system operation. The loss
Distributed Generation (DG) is a small generator spotted
                                                              in the system can be calculated by equation (1) [11],
throughout a power system network, providing the
                                                              given the system operating condition,
electricity locally to load customers [1]. DG can be an
alternative for industrial, commercial and residential                    n    n
applications. DG makes use of the latest modern                    PL = ∑∑ Aij ( Pi Pj + Qi Q j ) + Bij (Qi Pj − Pi Q j )   (1)
technology which is efficient, reliable, and simple                      i =1 j =1

enough so that it can compete with traditional large
generators in some areas [2] [3].                             where,
                                                                                      Rij cos (δ i −δ j )
Placement of DGs is an interesting research area due to                       Aij =
                                                                                            VV j
economical reason. Distributed generation systems (such
as fuel cells, combustion engines, microturbines, etc) can                            Rij sin (δ i −δ j )
                                                                              Bij =
reduce the system loss and defer investment on                                              VV j
transmission and distribution expansion. Appropriate
size and optimal locations are the keys to achieve it [4]     where, Pi and Qi are net real and reactive power injection
[5].                                                          in bus ‘i’ respectively, Rij is the line resistance between
bus ‘i’ and ‘j’, Vi and δi are the voltage and angle at bus                                             wind turbines, induction generator is used to produce
‘i’ respectively                                                                                        real power and the reactive power will be consumed in
                                                                                                        the process [12]. The amount of reactive power they
The objective of the placement technique is to minimize                                                 require is an ever increasing function of the active power
the total real power loss. Mathematically, the objective                                                output. The reactive power consumed by the DG (wind
function can be written as:                                                                             generation) in simple form can be given as in equation
                                                N SC                                                    (9) as in the case of [13]
         Minimize               PL =            ∑ Loss                     k
                                                                                                                                QDG = − ( 0.5 + PDG )
                                                k =1                                                                                             2
Subject to power balance constraints
                      N                                N                                                The loss equation will be modified. After following the
                     ∑ PDGi = ∑ PDi + PL
                     i =1                           i =1
                                                                                                  (3)   similar methodology of the first two types, optimal DG
                                                                                                        size can be found by solving equation (10).

                                                        ≤ Vi ≤ Vi
                                            min                                             max
voltage constraints:              Vi                                                              (4)        0.0032 Aii PDGi + PDGi [1.004 Aii + 0.08 Aii QDi − 0.08Yi ] +
                                                                                                             ( X i − Aii PDi ) = 0
current limits:                        I ij ≤ I ij                                                (5)
                                                                                                        Equation (10) gives the amount of real power that a DG
where: Lossk is distribution loss at section k, NSC is                                                  should produce when located at but ‘i’, so as to obtain
total number of sections, PL is the real power loss in the                                              the minimum system loss whereas the amount of
system, PDGi is the real power generation DG at bus i,                                                  reactive power that it consumes can be calculated from
PDi is the power demand at bus i.                                                                       equation (9).

3.          DG TYPE AND HEURISTIC METHODLOGY                                                            4.           PARTICLE SWARM OPTIMIZATION
                                                                                                        Particle swarm optimization (PSO) is a population-based
3.1.        DG TYPE 1                                                                                   optimization method first proposed by Kennedy and
                                                                                                        Eberhart in 1995, inspired by social behavior of bird
Certain type of DGs like photovoltaic will produce real
                                                                                                        flocking or fish schooling [16]. The PSO as an
power only. To find the optimal DG size at but ‘i’, when
                                                                                                        optimization tool provides a population-based search
it supplies only real power, the necessary condition for
                                                                                                        procedure in which individuals called particles change
minimum loss is
                                                                                                        their position (state) with time. In a PSO system,
                                            n                                                           particles fly around in a multidimensional search space.
                                       ∑( A P − B Q )
                                 1                                                                (6)
     Pi = PDGi − PDi = −                                ij        j                ij   j
                                                                                                        During flight, each particle adjusts its position according
                                 Aii    j =1                                                            to its own experience (This value is called Pbest), and
                                        j ≠i
                                                                                                        according to the experience of a neighboring particle
                                                                                                        (This value is called Gbest),made use of the best position
From equation (6), we obtain the following relationship:
                                                                                                        encountered by itself and its neighbor (Figure 1).

                          ∑( A P − B Q )
                    1                                                                             (7)
     PDGi = PDi −                      ij       j            ij            j
                    Aii   j =1
                          j ≠i

Equation (7) gives the optimal DG size for each bus so
as to minimize the total real power loss.

3.2.        DG TYPE 2

For synchronous condenser DG, it provides only reactive                                                        Figure 1: Concept of a searching point by PSO
power to improve voltage profile. To determine the
optimal DG placement, we again differentiate the loss                                                   This modification can be represented by the concept of
equation on either side with respect to Qi. The optimal                                                 velocity. Velocity of each agent can be modified by the
DG size for every bus in the system is given by equation                                                following equation:
                                                                                                        vid+1 = ωvid + c1rand ×( pbestid − sid ) + c2rand × ( gbestd − sid ) (11)
                                                                                                         k        k                         k                           k

                                                    ∑(A Q                           + Bij Pj )
                            1                                                                     (8)
             QDGi   = QDi −                                           ij       j
                            Aii                     j =1                                                Using the above equation, a certain velocity, which
                                                    j ≠i
                                                                                                        gradually gets close to pbest and gbest can be calculated.
3.3.        DG TYPE 3                                                                                   The current position (searching point in the solution
                                                                                                        space) can be modified by the following equation:
Here, we consider that the DG will supply real power
and in turn will absorb reactive power. In case of the
         s id+ 1 = s id + v id+ 1 , i = 1, 2 , ..., n ,
           k         k      k
                                                                    (12)                                                Start

                                  d = 1, 2 , ..., m                                                              Input system data

where    s k is current searching point, s k +1 is modified                                                  Calculate the original loss
                                                                                                              using Bw-Fw Sweep (2)

searching point, v k is current velocity, v k +1 is modified
                                                                                                                  Initialize particle

velocity of agent i, v pbest is velocity based on pbest,                                                            population (3)

vgbest is velocity based on gbest,                        n is number of                                     Calculate the total loss (4)

particles in a group, m is number of members in a                                                            Record Pbest (5),Gbest(6)

particle, pbesti is pbest of agent i, gbesti is gbest of the
group, ωi is weight function for velocity of agent i, ci
                                                                                                                  Update particle
                                                                                                              position and velocity (7)

is weight coefficients for each term.
                                                                                                        No      Check the stopping
                                                                                                                   criterion (8)
The following weight function is used:
                                                                                       Particle Swarm
                                  ωmax − ωmin                                           Optimization
                 ωi = ωmax −
                                                                                                               Print out location and
                                                   .k               (13)                                           size of DG (9)

where, ωmin and ωmax are the minimum and maximum
weights respectively. k and kmax are the current and                            Figure 2: PSO-OPDG computational procedure
maximum iteration. Appropriate value ranges for C1 and
C2 are 1 to 2, but 2 is the most appropriate in many
cases. Appropriate values for ωmin and ωmax are 0.4 and                    6.       SIMULATION RESULTS
0.9 [17] respectively.
                                                                           The distribution test systems are the 33 bus [18] and 69
                                                                           bus [19] systems. The 33 bus system has 32 sections
5.       PSO PROCEDURE                                                     with the total load 3.72 MW and 2.3 MVar shown in
                                                                           Figure 3. The original total real power loss and reactive
The PSO-based approach for solving the OPDG problem                        power loss in the system are 221.4346 kW and 150.1784
to minimize the loss takes the following steps:                            kVar, respectively. The 69 bus system has 68 Sections
                                                                           with the total load of 3.80 MW and 2.69 MVar, shown in
Step 1: Input line and bus data, and bus voltage limits.                   Figure 4. The original total real and reactive power
Step 2: Calculate the loss using distribution load flow                    losses of the system are 230.0372 kW and 104.3791
         based on backward-forward sweep.                                  kvar, respectively. For PSO parameters, population
Step 3: Randomly generates an initial population (array)                   size=200, Maximum generation (kmax) = 100. The
         of particles with random positions and velocities                 maximum number of DG is 3 for each type.
         on dimensions in the solution space. Set the
         iteration counter k = 0.
Step 4: For each particle if the bus voltage is within the
         limits, calculate the total loss in equation (1).
         Otherwise, that particle is infeasible.
Step 5: For each particle, compare its objective value
         with the individual best. If the objective value is
         lower than Pbest, set this value as the current
         Pbest, and record the corresponding particle
         position.                                                         Figure 3: The 33 bus radial distribution system.
Step 6: Choose the particle associated with the minimum
         individual best Pbest of all particles, and set the
         value of this Pbest as the current overall best
Step 7: Update the velocity and position of particle using
       (11) and (12) respectively.
Step 8: If the iteration number reaches the maximum
       limit, go to Step 9. Otherwise, set iteration index k
       = k + 1, and go back to Step 4.
Step 9: Print out the optimal solution to the target
       problem. The best position includes the optimal
       locations and size of DG or multi-DGs, and the
       corresponding fitness value representing the
       minimum total real power loss.

                                                                           Figure 4: The 69 bus radial distribution system.
   Table 1: PSO result of the 69 bus test system
      Total real power loss    Min       Avg.      Max

                              80.1933   95.4714   203.2326
      Average Time (sec.)               5.6341

For DG type 1, the convergence characteristic of the best
solution of PSO is shown in Figure 5. Figure 6 shows the
total real power loss from 100 trials of PSO-OPDG. The
average CPU time is 5.6341 second.

                                                             Figure 6: The total loss distribution from 100 trials of a
                                                             69 bus test system

                                                             The improvement in the voltage profile after optimally
                                                             placing the DGs is shown in Figure 7. Without DG, the
                                                             bus no. 64 has the lowest voltage of 0.8891 p.u. and the
                                                             bus voltage has improved to 0.9453 p.u. after installing

Figure 5: Convergence characteristic of the 69 bus test

For the 33 and 69 bus systems, in Tables 2-4, the PSO
can obtain the same optimal size and location as the
heuristic search [10] for one types 1-3 DG. For the 33
bus system, one type-1 DG can reduce the total real and
reactive power loss by 47.49% & 43.12% compared to
28.29% & 27.55% and 26.01% & 23.05% for DG types
2 and 3, respectively. For three type-1 DGs, they can
further reduce the real and reactive power loss by
65.60% & 64.73% compared to 34.56% & 34.24% and
24.66% & 22.03% for DG types 2 and 3, respectively. In
the 69 bus system, three type-1 DGs can reduce the real      Figure 7: Bus voltage before and after DG Installation
and reactive power loss by 69.19% & 65.81% compared          for DG type-1.
to 35.53% & 33.78% and 29.71% & 29.13% for DG
types 2 and 3, respectively.

Table 2: Optimal DG placement for DG type 1
Table 3: Optimal DG placement for DG type 2

Table 4: Optimal DG placement for DG type 3

7.       CONCLUSION                                               generation: definitions, benefits and issues,”
                                                                  Energy Policy 33, pp787-798, 2005.
In this paper, a particle swarm optimization for optimal    [4]   William Rosehart and Ed Nowicki, “Optimal
placement of multi-DGs is efficiently minimizing the              Placement of Distributed Generation,” 14th
total real power loss satisfying transmission line limits         PSCC, Sevilla, 24-28 June 2002.
and constraints. The methodology is fast and accurate
                                                            [5]   Caisheng Wang and M. Hashem Nehrir,
in determining the sizes and locations. DG regulating
                                                                  “Analytical   Approaches     for    Optimal
bus voltage will be considered in future research work.
                                                                  Placement of Distributed Generation Sources
                                                                  in Power Systems,” IEEE Transactions on
8.       ACKNOWLEDGEMENT                                          Power Systems, vol.19, no.4, pp2068-2076,
The authors would like to thank Dr. Keerati
Chayakulkheeree, Head of Department of Electrical           [6]   T.Niknam, A.M. Ranjbar, A.R. Sirani,
Engineering of Sripatum University for his guidance in            BMozafari and A. Ostadi, “Optimal Operation
PSO programming.                                                  of Distribution System with Regard to
                                                                  Distributed Generation : A Comparison of
                                                                  Evolutionary Methods,” IEEE Conference
REFERENCES                                                        IAS 2005, pp2690-2696, 2005.
[1]      Thomas Ackermann, GÖran Andersson and              [7]   N.Mithulananthan, Than Oo and Le Van Phu,
         Lennart SÖder, “Distributed generation: a                “Distributed Generator Placement in Power
         definition,” Electric Power Systems Research             Distribution System Using Genetic Algorithm
         57, pp195-204, 2001.                                     to      Reduce        Losses,”      Thammasat
                                                                  Int.J.Sc.Tech.,vol.9,no.3,     July-September,
[2]      W.El-Khattam , M.M.A.Salama, “Distributed
                                                                  pp55-62, 2004.
         generation technologies, definitions and
         benefits,” Electric Power Systems Research         [8]   Andrew Keane and Mark O’Malley, “Optimal
         71, pp119-128, 2004.                                     Allocation of Embedded Generation on
                                                                  Distribution Networks,” IEEE Transactions
[3]      G.Pepermans, J.Driesen, D.Haeseldonckx,
                                                                  on Power System, vol.20, no.3, August,
         R.Belmans, and W.D’haeseleer, “Distributed
                                                                  pp1640-1646, 2005.
[9]    Kyu-Ho Kim, Yu-Jeong Lee,Sang-Bong                             Mr. Wichit Krueasuk received his
       Rhee, Sang-Kuen Lee and Seok-Ku You,                           B.Eng from Sripatum University,
       “Dispersed Generator Placement using Fuzzy-                    Thailand,    degrees  in electrical
       GA in Distribution System,” IEEE                               engineering, in 2000.
       Conference, pp1148-1152, 2002.                                 Currently, he is a faculty member of
[10]   Naresh Acharya, Pukar Mahat, and N.             Sripatum University and also he is pursuing his
       Mithulanathan, “An analytical approach for      M.Eng. at AIT, Thailand. His research interest includes
       DG allocation in primary distribution           the optimization and Artificial Intelligence (AI)
       network,” International Journal of Electrical   application to distribution system, and energy
       Power & Energy System, to be published.         management systems.
[11]   I.O. Elgerd, Electric Energy System Theory:
       an Introduction. McGraw Hill., 1971.                           Dr. Weerakorn Ongsakul received his
[12]   M. Ermis, H. B. Eratn, M. Demirekler, B. M.                    B.Eng. from Chulalongkorn University,
       Saribatir, Y. Uctung, M. E. Sezer etal,                        Thailand, M.S. and Ph.D. from Texas
       “Various Induction Generator Scheme for                        A&M University, USA, all degrees in
       Wind Power Electricity Generation,” Electric                   electrical engineering, in 1988, 1991
       Power Systems Research, vol.23, pp71-83,                       and 1994 respectively.
       1992.                                           Currently he is an Associate Professor at AIT,
[13]   DTI, “Network Performance Benefits of           Bangkok Thailand. His research interest includes AI
       Energy Storage for a Large Wind Farm,”          applications to power systems, parallel processing    applications, power system operation & control, and
       s/pdfs/kel002460000.pdf/, 2004.                 power system restructuring.
[14]   W.D. Stevenson, Elements of Power System
       Analysis. Tokyo: 3rd ed., McGraw Hill
       Kogakush, Ltd., 1975.
[15]   Hadi Saadat, Power System           Analysis.
       Singapore: McGraw Hill, 1999.
[16]   Kennedy J and Eberhart R, “Particle Swarm
       Optimizer,” IEEE International Conference
       on Neural Networks (Perth, Australia), IEEE
       Service Center Piscataway, NJ, IV, pp1942-
       1948, 1995.
[17]   Eberhart, R.C. and Shi, Y, “Comparing
       inertial weights and Constriction factor in
       particle Swarm optimization,” proceeding of
       the 2000 International Congress on
       Evaluationing Computation, San Diego,
       California, IEEE Service Center, Piscataway,
       NJ, pp84-88, 2000.
[18]   M.A. Kashem, V. Ganapathy, G.B. Jasmon
       and M.I. Buhari, “A Novel Method for Loss
       Minimization in Distribution Networks,”
       proceeding of International Conference on
       Electric    Utility    Deregulation   and
       Restructuring and Power Technologies,
       pp251-255, 2000.
[19]   M.E. Baran and F.F. Wu, “Optimal Sizing of
       Capacitor Placed on Radial Distribution
       Systems,” IEEE Trans,Vol. PWRD-2, pp735-
       743, 1989.

To top