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in the next step, considering the best reconfiguration corresponding to tie switch 1 as the next base case, a similar process will be adopted for tie switch 2 and the respective optimal reconfiguration, and a corresponding total technical loss (I²R) will be obtained. Tie switch 2 will be selected by using the same procedure as adopted for selecting tie switch 1 while considering the remaining tie switches other than tie switch 1. In the above selection of tie switch 2, the load flow data obtained from the latest reconfiguration, i.e. the best reconfiguration corresponding to tie switch 1, will be used. The final reconfiguration obtained by practicing all the procedures adopted in the case of tie switch-1 will be considered as the best reconfiguration corresponding to tie switch 2.

      In the next step, the best reconfiguration corresponding to tie switch 2 will be considered as the base network and a similar process will be carried out for other remaining tie switches and their respective optimal configuration, and a corresponding total technical loss (I²R) will be obtained. The reconfiguration that will be obtained from the last step by practicing the above explained procedure will be considered as the optimal network reconfiguration.

      From the above explanation, it can be concluded that a large number of steps are required for obtaining each best reconfiguration corresponding to a particular tie switch. Hence the process of network reconfiguration becomes a complicated, combinatorial, non-differentiable, constrained optimization problem. There are even networks where millions of nodes are used. For such networks, investigating all possible options is impractical. The time required to calculate the total technical loss (I²R) is also too huge. Therefore, it is essential to develop some trick for reducing the number of steps involved and the time required for calculating technical loss. Hence, heuristic techniques are thought to be the most suitable techniques for the network reconfiguration process.

      The main objective while implementing network reconfiguration is to minimize the technical loss. Hence the objective function for the network reconfiguration problem is a loss function and is required to be minimized. While optimizing this objective function, different technical and non-technical constraints are required to be addressed, which will now be discussed.

      2.6.1 Objective Function

      The objective is to minimize the system total technical loss (I²R) described by:

       (2.1)

      where N_l = number of lines in the network r_l = resistance of the line l i_l = current flowing through line l

      2.6.2 Constraints

       1. Bus voltage limit:

       (2.2)

       2. Line limits:

      The current flowing through any line (i_l) should not exceed the current limit of that line (i_lmax).

       (2.3)

       3. Radiality:

      To ensure the radiality, the following assessment parameters are being used

       The number of loops while closing all different switches must be:

       (2.4)

      N_b = total number of branches

      N_bs = total number of buses

       Number of branches should be:

       (2.5)

      N_bs = number of buses

      N_s = number of sources

       All the loads should get a supply every time of reconfiguration.

      The use of heuristic approaches can reduce the complexity of the network reconfiguration problem. In this chapter, a heuristic approach has been used to solve network reconfiguration problems. The following points show the detail outlines of the used heuristic algorithm.

      2.6.3 Algorithm

      1 Read the system input data required for load flow.

      2 Run the load flow program for the distribution network and compute the power loss and voltages at various nodes.

      3 Calculate the differences in voltages ΔVtie(x) between the two buses across which different tie switches are placed to be connected; x = 1, 2, 3, … Stie, where Stie = number of tie switches.

      4 Form a table for the above calculated voltage differences for all of the tie switches.

      5 From the above table, select the tie switch for which the value of ΔVtie(x) is maximum. Suppose it is the tie switch ‘n’ such that (ΔVtie,max = ΔVtie(n)).

      6 Compare the value of the (ΔVtie,max) with a set threshold value (θ). If ΔVtie,max is greater than the threshold value, go to the next step, else stop.

      7 Compare the node voltages of the two nodes across which the tie switch ‘n’ is connected. Select the node with the smallest value. Let it be the node ‘m’ with node voltage Vm.

      8 Close the tie switch ‘n’ and simultaneously open the sectionalizing switch connected to node ‘m’.

      9 Run the load flow for the above reconfigured distribution network and compute the power loss. Let it be Ploss.

      10 In the next step, close the previously opened sectionalizing switch and open its adjacent sectionalizing switch within the same loop.

      11 Run the load flow for the above reconfigured distribution network and compute the power loss. Let it be P !loss.

      12 If P !loss ≥ Ploss, declare the present reconfiguration as the best reconfiguration corresponding to tie switch n, else replace Ploss by P !loss and go to step 10.

      13 i = number of iterations. If i < Stie then replace i by i + 1 and go to step 2 to repeat the program to find out the best reconfiguration corresponding to other tie switches, else go to next step.

      14 Consider the current reconfiguration as the optimal reconfiguration of the distribution network and run the load flow to calculate the total technical loss (I2R), individual bus voltages, and different line flows.

      15 Stop.

      At last, the total technical loss (I²R) obtained during the best reconfiguration corresponding to tie switch n (n = 1, 2,…, n) and normal case load flow will be compared. Among all these n + 1 cases, the case for which the total technical loss (I²R) obtained will be minimum will be adopted as the operational network.

      2.7 Conclusion

      The basic objective behind this chapter is to discuss a theft-handling mechanism for protecting various power equipment/appliances fitted in agricultural feeders during off-feed hours. The discussed method is based on network reconfiguration in which the normal topological structure of the distribution

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