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This paper presents a reconfiguration of electric power distribution network based on the symbiotic organism search algorithm (SOS). The goal here is to come out with an optimal reconfiguration of a power distribution network that minimises the active power losses for a good power flow. This method is applied to IEEE 33 bus and the results show a significant reduction of active power losses. The execution time for this algorithm is found to be smaller compared to other metaheuristic algorithms.

The growth of the demand of electrical energy is of a great challenge for the entire society. This calls for optimization of the production, the distribution and the use of electrical energy. The extension of a distribution power network being difficult and costly, it is necessary to optimize the management of the energy in order to ensure the satisfaction of customers, reduce the production cost and increase the income.

There are several technics of optimization of power distribution network. Ahmed Ould Nagi [

Let consider a simple linear network represented bellow

The objective is to minimize the joule losses by a proper reconfiguration of the network. The objective function is therefore:

min f = min ( P t , l o s s ) (1)

with P t , l o s s , total active losses.

The apparent power carried by a branch, must be less than the maximal apparent power that branch can accept. The amplitude on a nod should be in the accepted range.

These constraints are express by:

S i ≤ S i , max (2)

V i , min ≤ V i ≤ V i , max (3)

The following equations enable us to calculate the power flow.

P i + 1 = P i − r i P i 2 + Q i 2 V i 2 – P L i + 1 (4)

Q i + 1 = Q i − x i P i 2 + Q i 2 V i 2 – Q L i + 1 (5)

P i + 1 = P i − r i P i 2 + Q i 2 V i 2 – P L i + 1 (6)

V i + 1 2 = V i 2 − 2 ( r i P i + x i Q i ) + ( r i 2 + x i 2 ) P i 2 + Q i 2 V i 2

with:

P_{i}: active power on nod i.

Q_{i}: reactive power on node i.

P_{i}_{+1:} active power on nod i + 1.

Q_{i}_{+1:} reactive power on node i + 1.

r_{i}: resistance of branch i.

x_{i}: reactance of branch i.

V_{i}: real mean value of the voltage on node i.

V_{i}_{+}_{1}: real mean value of the voltage on node i + 1.

S_{i}: apparent power on node i.

The total losses are expressed by the relation:

P T , l o s s = ∑ i = 0 n − 1 P i 2 + Q i 2 V i 2 r i (7)

The goal of the reconfiguration being to minimize the active power losses during the power flow, the problem is stated as follow:

min ∑ i = 0 n − 1 P i 2 + Q i 2 V i 2 r i (8)

Equations (2) and (3) are the constraints.

The reconfiguration hold on the following rules:

- All the load must be fed if not at least most of them.

- The reconfiguration of the network should be radial.

- The network islinear.

If we consider a network of n switches we arrive at the following vector:

X = [ x 0 x 1 x 2 x 3 x 4 ⋯ x n − 1 ]

The symbiotic organism search algorithm is a new algorithm develop by [

Mutualism is a social system between the members of a same Professional branch. It is a lasting and complementary relation between two groups of plants, animals or human being.

Commensalism is an association of different species living in such a way that one of them depends on the others without any ham.

Parasitism is linked to predation. In that system, two organisms live together, one feeding himself at the cost of the other.

The detailed flow chart of the symbiotic organism search algorithm is presented at

STEP 1:

Initialisation of the ecosystem

At this level we determine the size of the ecosystem and the initial organism

STEP 2:

Phase de mutation phase

Ze select at random an organism X_{j} such that. X j ≠ X i Determine the mutual vector (X_{i} + X_{j})/2. Determine two random number situated between 1 and 2. Modify the organisms X_{i} and X_{j} taking into account the mutual vector Ze obtain X_{in} and X_{jnov}. Calculate the value of the fitness function of each new organism and compare them.

STEP 3:

Phase of commensalism

STEP 4:

Phase of parasitism

The optimization code are written with Matlab. The characteristics of the computer used are: processor of 1.4 GHz, memory RAM of 2 Go, OS 64 bite WINDOWS 8.

The result obtained is a 37 elements line matrix. Each element correspond to the state of a switch between two nods. We start by calculating the total lose from the initial configuration. The optimization, give us the best organism witch correspond to the best configuration.

Initially the state of the switches are: from S1 to S32 “ON” and S33, S35, S36, S37 “OFF”.

The rMS of the voltage at nod 0 is 12.66 kV and the active power and reactive powers are respectively 3715 kW and 2300 kVAr.

The characteristics of the network are found in

The initial binary code or organism is

From S1 to S31 “1” and from S32 to S37 “0”.

1) The total loses are: 203,15 kW

The optimal organism which reduce the losses and enable the majority of customers to remain connected is

2) The total losses are: 175,3337 kW

The summary table is the following

We obtain the following graph

Before the optimization, the open switches are S22, S23, S24, S30, S31, S32, S33, S34, S35, S37 the others are closed. This configuration allows for an active power loss of about 203.15 kW. After the implementation of the SOS algorithm the power loss is reduce to 175.3337 kW

A novel approach based on symbiotic organism search algorithm has been implemented for the optimization of the distribution of electricity in a power network. The implementation was carried out on an IEEE 33 Bus system. The

Before the reconfiguration | After the reconfiguration | ||||
---|---|---|---|---|---|

State of the switch | Total losses (kW) | State of the switch | Total losses (kW) | ||

S32, S33, S34, S35, S36, S37 | OFF | 203,15 | S22, S23, S24, S30,S31, S32, S33, S34, S35, S37 | OFF | 175.3337 |

De S1 à S31 | ON | Other switches | ON |

Element | Initial state | GA | SOS |
---|---|---|---|

Open switch | S32, S33, S34, S35, S36, S37 | S15, S25, SS31, S33, S34, S35 | S22, S23, S24, S30,S31, S32, S33, S34, S35, S37 |

Losses (kW) | 203.15 | 194.6427 | 175,3337 |

Number of itiration | 100 | 100 | |

Execution time (s) | 25.63080 | 0.259030 |

Bus to bus | Section resistance(Ω) | Section reactance(Ω) | End bus real load ( kW) | End bus reactive load (kVAr) | Bus to bus | Section resistance(Ω) | Section reactance(Ω) | End bus real load ( kW) | End bus reactive load (kVAr) | Bus to bus | Section resistance(Ω) | Section reactance(Ω) | End bus real load ( kW) | End bus reactive load (kVAr) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0 - 1 | 0.0922 | 0.0470 | 100 | 60 | 13 - 14 | 0.5910 | 0.5260 | 60 | 10 | 25 - 26 | 0.2842 | 0.1447 | 60 | 25 |

1 - 2 | 0.4930 | 0.2511 | 90 | 40 | 14 - 15 | 0.7463 | 05450 | 60 | 20 | 26 - 27 | 1.0590 | 0.9337 | 60 | 20 |

2 - 3 | 0.3660 | 0.1864 | 120 | 80 | 15 - 16 | 0.2890 | 1.7210 | 90 | 20 | 27 - 28 | 0.8042 | 0.7006 | 120 | 70 |

3 - 4 | 0.3811 | 0.1941 | 60 | 30 | 16 - 17 | 0.7320 | 0.5740 | 90 | 40 | 28 - 29 | 0.5075 | 0.2585 | 200 | 600 |

4 - 5 | 0.8190 | 0.7070 | 60 | 20 | 1 - 18 | 0.1640 | 0.1565 | 90 | 40 | 29 - 30 | 0.9744 | 0.9630 | 150 | 70 |

5 - 6 | 0.1872 | 0.6188 | 200 | 100 | 18 - 19 | 1.5042 | 1.3554 | 90 | 40 | 30 - 31 | 0.3105 | 0.3619 | 210 | 100 |

6 - 7 | 0.7114 | 0.2351 | 200 | 100 | 19 - 20 | 0.4095 | 0.4784 | 90 | 40 | 31 - 32 | 0.3410 | 0.5302 | 60 | 40 |

7 - 8 | 1.0300 | 0.7400 | 60 | 20 | 20 - 21 | 0.7089 | 0.9373 | 90 | 40 | 7 - 20 | 2 | 2 | ||

8 - 9 | 1.0440 | 0.7400 | 60 | 20 | 2 - 22 | 0.4512 | 0.3083 | 90 | 50 | 8 - 14 | 2 | 2 | ||

9 - 10 | 0.1966 | 0.0650 | 45 | 30 | 22 - 23 | 0.8980 | 0.7091 | 420 | 200 | 11 - 21 | 2 | 2 | ||

10 - 11 | 0.3744 | 0.1238 | 60 | 35 | 23 - 24 | 0.8960 | 0.7011 | 420 | 200 | 17 - 32 | 0.5 | 0.5 | ||

11 - 12 | 1.4680 | 1.1550 | 60 | 35 | 5 - 25 | 0.2030 | 0.1034 | 60 | 25 | 24 - 28 | 0.5 | 0.5 | ||

12 - 13 | 0.5416 | 0.7129 | 120 | 80 |

simulations led to an optimal reconfiguration that minimizes the active power loss. The comparison of this algorithm with other metaheuristic algorithm such as GA, proves it superiority in losses reduction and short execution time.

In further work, we may consider combination of GA and SOS or another metaheuristic algorithm.

Boum, A.T., Ndjependa, P.R. and Bisse, J.N. (2017) Optimal Reconfiguration of Power Distribution Systems Based on Symbiotic Organism Search Algorithm. Journal of Power and Energy Engineering, 5, 1-9. https://doi.org/10.4236/jpee.2017.511001

PGSA: Plant growth simulation algorithm

SOS: Symbiotic organism search algorithm

GA: Genetic algorithm