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A novel multi-objective PSO for electrical distribution system planning incorporating distributed generation

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This paper presents a novel particle swarm optimization (PSO) based multi-objective planning approach for electrical distribution systems incorporating distributed generation (DG). The proposed strategy can be used for planning of both radial and meshed networks incorporating DG. The DG plays an important role in the distribution system planning due to its increasing use motivated by reduction of power loss, voltage profile improvement, meeting future load demand, and optimizing the use of non-conventional energy sources etc. The overall approach consists of two multi-objective planning stages. In the first stage, a contingency-based multi-objective planning is used to optimize the number of feeders and their routes, and the number and location of the sectionalizing switches. In the second stage, the optimum siting and sizing of the DG units is determined for the networks obtained in the first stage by another multi-objective optimization. The multiple objectives of the first planning stage are: (i) minimization of the total installation and operational cost, and (ii) maximization of network reliability. The reliability of the distribution network is evaluated by a reliability index, i.e., contingency-load-loss index (CLLI), defined as the ratio of the average non-delivered load due to failure of all branches, taken one at a time, to the total load. The objectives for the second stage optimization are the DG penetration level and the total power loss. A set of non-dominated solutions/networks is obtained by simultaneous minimization of the conflicting objectives (at each stage) using the Pareto-optimality principle based trade-off analysis. A novel multi-objective PSO (MOPSO) is proposed for solving these optimization problems using a technique for selection and assignment of leaders/guides for efficient search of the non-dominated solutions. The selection of the leaders makes use of the available non-dominated and dominated solutions. The proposed planning algorithm is tested for the static and expansion planning of typical 100-node and 21-node distribution systems, respectively. The computer simulation results are critically evaluated. The performance of the algorithm is compared with that of the popular Strength Pareto Evolutionary Algorithm-2 (SPEA2)-based PSO and few other existing MOPSO techniques by means of statistical tests to highlight the efficacy of the proposed scheme.

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C IO :

total installation and operational cost ($)

\(C^{I_{b}}\ (C^{R})\) :

branch installation (conductor replacement) cost per unit length ($/km)

\(C^{M_{b}}\) :

annual branch maintenance cost ($/km/year)

l j :

length of branch j in km

C V :

total cost of energy losses ($/year)

t a :

total planning time (in years)

\(C^{I_{s}}\ (C^{M_{s}})\) :

substation Installation (maintenance) cost ($)

\(C^{I_{\mathit{Sw}}}\) :

installation cost of a sectionalizing switch ($)

\(C^{I_{\mathit{bkr}}}\ (C^{I_{T}})\) :

installation cost of a circuit breaker (tie line) ($)

N b (N e ):

number of new (existing) branches in the network

N s (N Sw ):

number of substations (sectionalizing switches)

N F (N loop ):

number of feeders (loops)

y j :

a binary variable (=1 if conductors are to be replaced; =0 otherwise)

D F :

discount factor (\(D_{F}=\frac{1}{(1+u)^{t_{a}}};u\) is interest rate)


contingency-load-loss index

NDL avg :

average non-delivered load

NDL i :

non-delivered load due to fault in branch i

L total (ϑ):

total load (load loss factor)

\(P_{\mathit{total}}^{l}(P_{i}^{l})\) :

total real power loss (real power loss in branch i)

Ψ(R i ):

DG penetration index (active power rating of the i-th DG)

\(N_{\mathit{DG}}\ (n_{i}^{\mathit{DG}})\) :

number (site/node of the i-th DG unit) of DG units

iter :

superscript denoting iteration number

\(PV_{i\theta}^{\mathit{iter}}\ (X_{i\theta}^{\mathit{iter}})\) :

velocity (position) of i-th particle in the θ-th dimension in iteration iter

φ1 (φ2):

learning constants (1.5–2.5)

r1 (r2):

random number ∈[0,1]

\(\mathit{pbest}_{i\theta}^{\mathit{iter}}\) :

best position of the i-th particle in the θ-th dimension in iteration iter

\(\mathit{nbest}_{i\theta}^{\mathit{iter}}\) :

neighborhood best of the i-th particle in the θ-th dimension in iteration iter

w :

inertia weight

N loop :

number of loops

\(Z_{i}^{s}\ (Z_{i}^{e})\) :

start (end) zone for tie branch of i-th loop

\(n_{F_{i}}\ (N_{\mathit{Sw}}^{F_{i}})\) :

number of load nodes (switches) in feeder F i

n :

number of load nodes served by the substation


circuit breaker


feeder branch


tie-line with switch (normally open)


sectionalizing switch in feeder branch (normally closed)




node/load point

Bold numeral:

branch conductor size

Italic numeral:

node number


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Ganguly, S., Sahoo, N.C. & Das, D. A novel multi-objective PSO for electrical distribution system planning incorporating distributed generation. Energy Syst 1, 291–337 (2010).

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