A novel multi-objective modified symbiotic organisms search algorithm for optimal allocation of distributed generation in radial distribution system


This article presents a novel optimization technique to allocate distributed generation (DG) units optimally in radial distribution system (RDS). Three renewable type DG units (such as wind turbine, solar photovoltaic and biomass system) have been integrated in the RDS. In this regard, an optimization problem is formulated considering multiple technical and economic objectives of the DG planning. A new metaheuristic, namely multi-objective modified symbiotic organisms search (MOMSOS), is proposed to solve this optimal DG allocation problem. A chaos-based cross-over operator is introduced in the parasitism phase of the proposed MOMSOS to enhance diversity in the population. The proposed MOMSOS is equipped with hierarchical non-dominated sorting technique which is superior to the existing fast non-dominated sorting strategy in terms of computational complexity. An adaptive penalty function is utilized for constraint handling. The proposed algorithm is tested on some CEC 2009 benchmark test problems to ensure its global optimization capability. Furthermore, performance of the proposed MOMSOS is validated on 69-node RDS and the obtained results are compared with other well-established multi-objective optimization algorithms.

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Vector of chaotic variables

\(f_{i}\), \(f_{i}^{\text{min} }\), \(f_{i}^{\text{max} }\) :

ith objective function and its minimum and maximum values, respectively

\(f_{k}^{i}\), \(f_{k}^{j}\) :

Values of the kth objective at points i and j, respectively

\(g_{j}\), \(h_{j}\) :

jth equality and inequality constraint, respectively

loc, P :

Location and size of DG units, respectively

n :

Planning period

\({\text{pf}}_{{{\text{DG}}ik}}\) :

Operating power factor of the ith DG unit at the kth hour

r :

Discount rate

\(t_{k}\) :

Duration of the kth load level

\(z_{\text{c}}\), \(z_{\text{s}}\) :

Vector of control and state variables, respectively

\({\text{BF}}_{1} ,{\text{BF}}_{2}\) :

Benefit factors

\(C_{{{\text{inst}\_\text{DG}}i}}\) :

Installation cost of the ith DG unit

\({\text{CInst}}_{\text{annual}}\) :

Annual installation cost of the DG units

\(C_{{{\text{om}\_\text{DG}}i}}\) :

Operation and maintenance cost of the ith DG unit

\({\text{COM}}_{\text{annual}}\) :

Annual operation and maintenance cost of the DG units

\(C_{\text{fuel}}\), \(C_{\text{env}}\) :

Fuel cost and environmental pollution cost, respectively

\(C_{\text{f}}\) :

Fuel cost of thermal power plant

\(E_{\text{loss}}\) :

Total annual energy loss

FE, maxFE:

Function evaluation count and its maximum value, respectively

\(I_{i}\) :

Current flowing in the ith branch

\(K_{i}\), \(E_{i}\), \(R_{i}\) :

Emission intensity, equivalent environmental value and imposed penalty price, respectively, of the ith pollutant


Lower and upper bound of control variables, respectively

M :

Number of objectives

N :

Size of the ecosystem

\(N_{\text{br}}\) :

Number of branches of the network

\(N_{\text{DG}}\) :

Number of DG units

\(N_{\text{n}}\) :

Total number of nodes in the network

\(N_{\text{p}}\) :

Number of pollutants

PF, \(\left| {\text{PF}} \right|\) :

Approximated Pareto front and the number of points on the approximated Pareto front, respectively

\(P_{Djk}\), \(Q_{Djk}\) :

Active and reactive power load, respectively, at the jth node at the kth hour

\(P_{{{\text{DG}}ik}}\), \(Q_{{{\text{DG}}ik}}\) :

Active and reactive power generation, respectively, of the ith DG unit at the kth hour

\(P_{{{\text{DG}}ik}}^{\text{min} }\), \(P_{{{\text{DG}}ik}}^{\text{max} }\) :

Minimum and maximum active power generation, respectively, of the ith DG unit at the kth hour

\(P_{\text{loss}}^{k}\), \(Q_{\text{loss}}^{k}\) :

Active and reactive power loss, respectively, at the kth load level

\(P_{{{\text{sub}}\_k}}\), \(Q_{{{\text{sub}}\_k}}\) :

Net active and reactive power supplied, respectively, by the substation at the kth hour

\(R_{i}\) :

Resistance of the ith branch

S :

Size of the final Pareto set

TPF, \(\left| {\text{TPF}} \right|\) :

The true Pareto front and the number of points on the true Pareto front, respectively

\(V_{i}^{k}\), \(V_{i}^{{k,{\text{spec}}}}\) :

Voltage of the ith node at the kth hour and its specified value, respectively

\(V_{i}^{k,\text{min} }\), \(V_{i}^{k,\text{max} }\) :

Minimum and maximum limit of the ith node voltage, respectively, at the kth hour

\(n_{\text{eq}}, \, n_{\text {ineq}}\) :

Number of equality and inequality constraints, respectively


Artificial bee colony


Annual electricity purchase cost


Annual interest


Annual investment and operating cost


Biomass, photovoltaic and wind turbine, respectively

C :

C metric


Capital recovery factor


Distributed generation


Genetic algorithm


Hierarchical non-dominated sorting


Inverted generational distance


Multi-objective modified SOS


Multi-objective PSO


Multi-objective SOS


Mutual vector


Non-dominated sorting GA II


Optimal DG allocation


Particle swarm optimization


Reliability test system


Symbiotic organisms search


Spacing metric


Total voltage deviation


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Correspondence to Subhodip Saha.

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See Tables 6 and 7.

Table 6 Installation and operational cost of different types of DGs
Table 7 Emission intensities of pollutant gases and their cost

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Saha, S., Mukherjee, V. A novel multi-objective modified symbiotic organisms search algorithm for optimal allocation of distributed generation in radial distribution system. Neural Comput & Applic (2020). https://doi.org/10.1007/s00521-020-05080-6

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  • Distributed generation
  • Multi-objective optimization
  • Non-dominated sorting
  • Symbiotic organisms search