Reconfiguration of electrical distribution system using ACO methodology

Abstract

Reconfiguration of Distribution system during a contingency is a composite problem. The switching of loads between adjacent feeders to relieve the system from contingency could lead a trouble to the radiality of the system. These switching also lead to further overloading of the system feeders. To overcome from such a situation an algorithm based on ant colony optimization is presented to keep the system safe and maintain its radiality. The Ant Colony Optimization is a probabilistic approach which will seek the shortest path to switch the loads during the overload contingency while minimizing the power loss and maintaining the radiality of the system. To have the practical applicability, the algorithm is tested on the IEEE 30 bus system using the MI-Power software.

Keywords

Ant colony optimization power loss minimization pheromone intensity electrical distribution system

1 Introduction

Reconfiguration of a system is a composite problem weather it is done during the normal conditions or abnormal conditions. The reconfiguration has to be done while taking in to consideration of various parameters. These parameters when been breached could lead to the results which are quite unhealthy for the overall functioning of the system. These parameters could be voltage limits of buses, current capacity of the lines, feeder capability to sustain loads etc. During contingency period like faults in distribution lines, overloading of distribution feeders etc. the reconfiguration of distribution system while keeping these parameters within limits is a slickest procedure. When a contingency occur on a system e.g. overloading of the distribution system the power loss in the system get increased. The abruptly switching of loads could further lead to the increase in the power losses occurring in the system. To overcome this problem a sophisticated approach has to be developed which could be able to handle such a situation. Another problem associated with the reconfiguration of distribution system under such a condition is that during the switching some of the loads could be left off from the supply due to which the radiality of the system gets affected.

To solve the reconfiguration problem a number of approaches are used by the scholars and some of them are reviewed in the literature survey. Raimundo F. Sampaio, Lucas Silveira Melo, Ruth P.S. Leão, Giovanni Cordeiro Barroso, and José Roberto Bezerra as in [1] apply an approach based on the multiagent system with the help of intelligent electronic devices. An algorithm is formed by dividing the agents in to four groups i.e. feeder, substation, branch and equipment. In this approach, the customers are defined by the objective function W_i but are differentiated from the priority customers. Also in this approach, the voltage profile limit and power loss of the system are not considered as an essential objective function. Leandro T. Marques, Alexandre C. B. Delbem, and João Bosco A. London as in [2] restore the distribution system with consideration on the priority customers by using the remote control switches and applying the soft computing. The graph analysis is used to implement the approach while using the tree structure with their nodes and depths. The concentration of this approach is mainly on the fast recovery of the system but it does not consider the specific parameter of power loss reduction which overall govern the whole restoration strategy. Bo Chen, Chen Chen, Jianhui Wang, and Karen L. Butler-Purry as in [3] apply the self healing approach using the tree topology on the IEEE 123 bus system. The objective function is defined to maximise the restored energy while considering the constraint on DG’s and system considered. The approach on the occurrence of a fault, distribute the whole system in to the microgrids which if are possible; on the basis of their power capability; able to restore all the loads. Also these microgrids are not in radial form, hence if any single source of power goes out of service its branch will remain without power. Anmar Arif, Zhaoyu Wang, Jianhui Wang, and Chen Chen as in [4] use the linear programming based on the mixed integer to restore the distribution system in two stages. The second stage i.e. restoration of system is mainly affected by the first approach in which the damage parts are repaired first while the switches are put on the off mode. This strategy will eventually lead to the slower restoration of customers. In the restoration mode too the algorithm does not consider the reduction in power losses which will financially affect the whole strategy. Juan Camilo López, John F. Franco, Marcos J. Rider, and Rubén Romero as in [5] apply two stage non linear integer programming using the mixed integers to restore the unbalanced distribution system by the help of power injecting through DG’s. The objective function is defined with minimization of the cost related to switching and zones without power. The objective function is very well defined with the short coming of its relation to the minimization of power losses which occurred during the restoration strategy. Bo Chen, Chen Chen, Jianhui Wang, and Karen L. Butler-Purry as in [6] restore the system under the cold loading with the help of mixed integer linear programming while designing it as spanning tree. The DG’s are used to inject the power where necessary for restoration processes. A detailed objective function is defined which takes in to account of various system parameters but a lot of assumption were taken in the beginning which at the difficult time make the restoration algorithm ineffective. Yin Xu, Chen-Ching Liu, Kevin P. Schneider, and Dan T. Ton as in [7] apply greedy algorithm for placement of remote control switches for the effective restoration of the system. The restoration algorithm considers placing the minimum number of remotely controlled switches but with the constraint that only one switching operation of loads should take place. In such a situation, if necessary switching of loads with the feeder is required for effective restoration the algorithm will not work. Also the number of switching should be dependent on the power losses, voltage profile and other necessary factors of the system. Jônatas Boás Leite, and José Roberto Sanches Mantovani as in [8] use the multiagent to prepare a self healing system for the restoration of system. The algorithm on the basis of voltage profile, total time taken for switching and current capacity of lines restores the system with minimum switching of loads. The switches do have knowledge of the current capacity of the loads but the power loss with the switching of loads and load balancing between the feeders are not addressed. Lei Sun, Can Zhang, Zhenzhi Lin, Fushuan Wen, Yusheng Xue, Md. Abdus Salam, and Swee Peng Ang as in [9] apply graph theory approach to restore the loads under black start by dividing whole network in to small networks thus rapidly providing the power to all loads. In this process it is assumed that all the small networks formed have the power source available in their zones which has the capability to provide power to all loads which is quite impractical. Chen Yuan, Mahesh S. Illindala, and Amrit S. Khalsa as in [10] apply the restoration strategy by modifying the viterbi algorithm. The main aim of the approach is to minimize the switching operation for the transfer of loads and maintaining the radiality of the system. To implement the approach the algorithm works on the binary system denominations but does not refer to the important system constraints comprising of voltage and current. Adi Botea, Jussi Rintanen, and Debdeep Banerjee as in [11] the heuristic methodology is used to apply A* search approach for implementation of restoration algorithm. Load balancing among feeders & node voltage deviation are taken as indices but the approach does not include minimization of power loss for final solution. Lucas S. M. Guedes, and Adriano C. Lisboa as in [13] with the use of subdivision of feasible set by the branch-exchange technique in tree structure apply the multi-objective heuristic approach while considering the current capacity of lines & power loss reduction as major factors but as a necessary objective function do not incorporate the feeder load balancing. Juan Li, Xi-Yuan Ma, Chen-Ching Liu and Kevin P. Schneider as in [14] apply Spanning tree search algorithms to find thecandidate restoration strategies by modeling microgrids as virtual feeders and representing the distribution system as a spanning tree but the objective function are not clearly defined & for large distribution system this approach become more complex. A.Y. Abdelaziz, R.A. Osama, and S.M. El-Khodary as in [12] apply hyper cube ant colony optimization technique for the power loss reduction with constraint on the node voltage deviation & line current capacity taken within its limits rather taking them as a part of the restoration strategy. On the basis of the literature survey it is inferred that the approach is to be used which is much simpler in its application while taking the direct concise of the objective function. Since one or more objective function is not been taken in to the above approaches, the ACO methodology is being used to directly reduce the overall power losses of the system with simple application through probabilistic output. The research paper is categorized in different sections. In Section 2 brief details of ACO methodology is introduced where the working details of the approach is discussed. In Section 3 ACO’s algorithm is explained for its application to electrical distribution system reconfiguration. The system modelling of IEEE 30-bus distribution and results are discussed in Section 4. The validation of the results by comparing it with different approaches is also done in Section 4. The conclusion is given in Section 5.

2 Ant colony system optimization

M. Dorigo, and L.M. Gambardella as in [15] and M. Dorigo, M. Birattari, and T. Stutzle as in [16] developed ant colony optimization which is based on the foraging nature of ants. Being a random population algorithm ACO contains artificial ants as agents which simulates the same mechanism as found in the real ants. It imitates the cooperation and learning strategies of ants to discover the optimal solution. Ants are the special species who during their hunt for their food keep on pushing to find the shortest path between their nest and food source. During their search the ants keep on depositing the pheromone trail; a chemical substance; through which it can be able to find their way back home. Being a chemical substance pheromone has the propensity to get evaporated with time. With reference to above factor, to maintain a certain path which heads to food source, it has to be deposited again and again. Suppose that there are several ways to the food source. When an ant reach nest with food, other ants start following that ant path with the help of pheromone level. The ant which takes the shortest path from nest to food source will have the largest pheromone level concentration in comparison with the other paths and hence all ants will start taking this single path. This scenario is explained in the Fig. 1. As described in the Fig. 1, the ant starts making pheromone trail from the food source to the nest. With the other ants also starting their tour and reaching food source from different paths also make their individual pheromone trail, as shown in Fig. 1. Since the length of the path-b is less than path-a and path-c, more and more ants start following path-b. With the discovery of the shortest path the pheromone level on this path will get high in concentration which will attracts more ants. Hence finally from Fig. 1 it is seen that pheromone level on other two paths start evaporating and path-b is selected as the most optimal path to reach the foodsource.

Fig.1

Ants food search pattern.

Ant colony optimization uses the same cycle as used by the ants in real life to achieve the optimal solution. The ACO’s cycle as described in Fig. 2, shows the flow of information in the ACOalgorithm.

First the pheromone trail is initialized to obtain the optimal solution. Than the solution is build on the basis of the pheromone trail. The pheromone trail is updated again towards the newly found solution. Certain state transition rules are used to implement the above mentioned cycle to implement ACO are given in Equation (1),

$\begin{matrix} P_{K} (i, j) = \frac{{[τ (i, j)]}^{α} {[η (i, j)]}^{β}}{\sum_{m \in J_{K (i)}} {[τ (i, m)]}^{α} {[η (i, m)]}^{β}}; \forall j \in J_{K (i)} \\ = 0; otherwise \end{matrix}$ (1)

where

P_K(i,j) = ant movement probability from node i to j,

τ (i, j)= deposition of pheromone between node i & j,

η (i, j)= heuristic desirability of path between node i & j,

J_{K (i)} = nodes to be visited by ant k starting from node i,

α, β= constants.

Fig.2

ACO’s cycle.

Equation (2) is used to update the pheromones, which changes the pheromone intensity trail between node i & j on the basis of factor inversely proportional to the pheromone change in the equation. $τ (i, j) = (1 - ρ) τ (i, j) + ρ \sum Δ τ_{ij}^{k}$ (2) $\begin{matrix} Δ τ_{ij}^{k} = 1 / Gk & when K^{th} ant tour between nodes (i, j) \\ = 0 & otherwise \end{matrix}$ (3)

On the basis of the probabilistic Equations (2) & (3), ACO algorithm is constructed for its implementation to restore electrical distribution system during overload contingency.

3 Ant colony system optimization

For the restoration of distribution system from the overload contingency the power loss occurring in the system is taken as the objective function for this study. The P_lossk is taken as heuristic factor G_k which will determine the intensity of the pheromone trail for the various path calculated by Equation (4).

Hence

$\begin{matrix} Δ τ_{ij}^{k} = 1 / Plossk when K^{th} ant tour between nodes (i, j) \\ = 0; otherwise \end{matrix}$ (4)

The constraints are taken for the Algorithm is radiality of distribution system and flow through transmission lines. The planned algorithm for the implementation of ACO is described in Fig. 3.

Fig.3

ACO algorithm.

According to the algorithm in Fig. 3, the system first checks for the overloading contingency by running the load flow analysis. After that if the overloading exists the first iteration will be initiated by the algorithm. First counter for the ants is started to select the open switch and obtain the loop. The selection is done by taking the heuristic desirability factor inversely proportional to the P_lossk. After the selection of open switch the counter of ants is started to select the close switch. When counter for all ants is completed than the system checks for the overload contingency. If the contingency still exist the system update the pheromone trail for the open switch and again run the algorithm till the system is revive from the overloading contingency.

4 System modeling & results

With the use of Mi-Power software, the distribution system is devised as shown in Fig. 4. is It contains a mixture of customers like residential, commercial, industrial etc. The 30 bus electrical distribution system contains three service zones. The supply is fetched through six feeders (Fd₁, Fd₂, Fd₃, Fd₄, Fd₅ and Fd₆ as shown in model). Distribution lines (Total no. = 41) connect these service zones with tie switches (Total no. = 34, normally open) & sectionalizing switches (Total no. = 7, normally closed), connected between the buses and distribution lines. The network is simulated by Mi-Power software. For design purposes, Mi-Power software is a high end comprehensive analysis platform for design & simulation of generation, transmission and distribution power systems. After the occurrence of the overloading on the system the voltages of bus 8 & 28 goes below the minimum limit. Also the line flows exceed on distribution lines between bus 1-2 & bus 1–3.

Fig.4

30-Bus Distribution System.

In the proposed study, to restore the system, calculations are done to select the first tie switch. For this first ants are used to find the correct open switch (NO) to be closed for a respective zone, through which the loads from the overloaded zones could be transferred to the feeder having adequate margin to give supply to these loads without getting overloaded by itself. The probability is calculated according to the Equation (1) while taking the power loss across the switches as the objective function. The calculation of probability for each switch is provided in Table 1.

Table 1

Probability calculations for Tie-switch selection

Tie Switch No.	η (i, j)	[η (i, j)] ^β	P_K(i,j)	Rank
Tie switch 1(BUS 27–28)	0.0362	0.0434	0.1321	1
Tie switch 2 (BUS 9–10)	0.0299	0.0392	0.1195	6
Tie switch 3 (BUS 6–10)	0.0319	0.0407	0.1237	4
Tie switch 4 (BUS 10–17)	0.0308	0.0401	0.1219	5
Tie switch 5 (BUS 10–20)	0.0353	0.0426	0.1297	2
Tie switch 6 (BUS 4–12)	0.0327	0.0419	0.1258	3
Tie switch 7 (BUS 23-24)	0.0293	0.0389	0.1187	7

On analyzing the Table 1, the highest probability is that of tie switch 1 (b/w bus 27&28). Hence Tie switches 1 which tie-up feeder 1(Fd₁) and feeder 3(Fd₃) is selected. Now the loop is selected between feeder 1 and feeder 3 in which the selection of the line switch is made based on the power loss occurring while opening the line switch. The ants are moved to find the normal close line switch to open.

The probability to calculate the line switch is given in Table 2. The first column gives the buses on which the line switches are installed, the second column gives the value of η (i, j), in the fourth column the probability is calculated.

Table 2

Probability calculations for Line-switch selection

Line Switch No.	η (i, j)	[η (i, j)] ^β	P_K(i,j)	Rank
Line switch 1 (BUS 1–3)	0.0259	0.0405	0.0609	10
Line switch 2 (BUS 1-2)	0.0253	0.0400	0.0604	11
Line switch 3 (BUS 3-4)	0.0294	0.0432	0.0641	6
Line switch 4 (BUS 2–5)	0.0277	0.0417	0.0628	8
Line switch 5 (BUS 2–6)	0.0265	0.0409	0.0615	9
Line switch 6 (BUS 2–4)	0.0286	0.0428	0.0634	7
Line switch 7 (BUS 4–6)	0.0427	0.0468	0.0661	3
Line switch 8 (BUS 6–28)	0.0332	0.0473	0.0679	2
Line switch 9 (BUS 6–8)	0.0304	0.0449	0.0648	5
Line switch 10 (BUS 8–28)	0.0341	0.0486	0.0688	1
Line switch 11 (BUS 7-5)	0.0451	0.0614	0.0757	8
Line switch 12 (BUS 7-6)	0.0317	0.0457	0.0652	4

On the basis of the calculation of probability above it is found that the line switch 10 between bus 8 and bus 28 is selected. After the final switching of loads, the total power loss is found as 14.4175 kW.

After the application of ACO algorithm the bus voltages come within limit & the overall voltage profile of distribution system is improved.

Figure 5, shows the comparison between the bus voltages before & after the reconfiguration. In Fig. 5, validation of the algorithm is also done by comparing it with the genetic algorithm approach as applied in [17].

Fig.5

Comparison & validation of bus voltage.

Figure 6 elaborates the difference between the loadings on the distribution line. It is clearly seen that after the application of ACO algorithm the distribution system line loading is improved from 145.5% overloading on line 1 between bus 1-2 to 94.3% and 134.1% overloading on line 2 between bus 1–3 to 91.2%. Similarly the overloading improved on the distribution lines 3, 4, 5, 6, 8, 10 etc.

Fig.6

Comparison of line flow.

The final comparison is drawn by comparing the reduction in the real power losses. In Fig. 7, it is seen that there is substantial reduction in the power loss occurring in the system from 17.9605 kW to 14.4175 kW, after the application of ACO algorithm.

Fig.7

Comparison of real power losses.

For the validation of the applied ACO algorithm, the reduction in real power losses in percentage is done. In Fig. 8, the results are validated by comparing the percentage reduction in real power losses with approach applied in [18]. It is seen that the percentage reduction in real power losses by ACO algorithm is 19.72% where as it is only 17.41% by the hybrid GA-PSO algorithm as in [18].

Fig.8

Validation of reduction of real power losses.

5 Conclusion

In the proposed work an Ant Colony Optimization based methodology is successfully devised to relieve the electrical distribution system from the overload contingency. The real power loss reduction is taken care as the main objective of the problem which validates its novelty towards the power saving of the system even during the switching of loads. The Mi-power software is used to simulate the IEEE 30 bus distribution system. The algorithm is capable of resolving the overload contingency while keeping the bus voltage within limits. The distribution line flows are maintained. The validation of results is done with the appropriate approaches applied on the same system. There is a significant reduction in the real power losses which shows a promising future prospect for the implementation of aforementionedalgorithm.

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