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The distribution system provides power to the end users from a set of distribution feeders, which are normally configured radially due to a protection point of view. Two types of switches, i.e. sectionalizing switches and tie switches are placed in every distribution network. During normal operations, sectionalize switches are kept closed and tie switches are kept open. In case of any requirements related to protection coordination or reconfigurations, these switches play the dominant roles.

Since many sectionalizing switches and tie switches may be present in a distribution network, the task of reconfiguration becomes complex due to huge possible combinations of these switches. Hence the task of reconfiguration becomes a complicated combinatorial, non-differentiable, constrained optimization problem. A huge amount of time is required for calculating network losses during all the different possible combinations. Thus to reduce the time and the number of steps involved, heuristic methods are mostly being used by different researchers across the globe for reconfiguration of the radial distribution system.

Let us try to understand the methodology through an example. Assume that the methodology is being applied to an IEEE 33-bus radial distribution test system, as shown in Figure 2.2. In this figure the dotted lines represent the tie switches and the solid lines represent the sectionalizing switches.

Figure 2.2 IEEE 33-bus radial distribution system.

There are 33 buses, 32 sectionalizing switches, and 5 tie switches. Suppose the total loads connected to the network are (3715 + j2300) kVAh. The tie switches (33, 34, 35, 36, and 37) are normally kept open and the sectionalizing switches (1–32) are normally kept closed. Using this normal configuration, load flow will be carried out to calculate the total technical loss (I²R), individual bus voltages, and different line flows. By using the load flow data, the voltage across all tie switches will be computed, which will be equal to the voltage difference between the two buses across which that tie switch is connected. Suppose that the total technical loss obtained through the normal case load flow is 150 kW. Similarly, voltages across different tie switches can be calculated using load flow data, as shown in Table 2.1.

Table 2.1 Voltage difference across all open tie switches after first switching.

S. No.	Tie switch number	Voltage difference across tie switch
1	33	0.071
2	34	0.027
3	35	0.085
4	36	0.023
5	37	0.058

Now, let us consider that the loss obtained, i.e. 150 kW, is too high and there is scope for a loss reduction for which network reconfiguration is selected. The basic task required in network reconfiguration is to alter topological structures of the network by changing the status of the tie and sectionalizing switches. At the start any one tie switch will be closed. However, whenever the tie switch is closed, one loop will be formed in the network, which will violate the network operational constraint, i.e. radiality. Hence, to eradicate this violation, any sectionalizing switch of the network that is essentially part of the loop formed must be opened. Further, while opening the sectionalizing switch, care must be taken that every node is getting a supply. After opening the sectionalizing switch, the load flow will be run for the restructured case. The total technical loss (I²R), individual bus voltages, and different line flows for this restructured case will be observed. From the observed data, it must be verified that the current flow through none of the line is violating the thermal limit of the line.

As per the proposed methodology, any one of the tie switches is closed and one of the sectionalizing switches constituting the loop is made open in the first step. Generally, the tie switch across which the voltage difference is highest among all the tie switches and is also more than a specified value is preferred to be closed first. For example, in the network shown in Table 2.1, tie switch 36 will be closed first as the voltage difference across it is highest among all the ties switches. Similarly, the sectionalizing switch that is opened first is the one that is connected to any one bus between the two supporting buses of the tie switch; generally the bus with the lower voltage is preferred. The reconfigured network obtained with the closing of the tie switch and opening of the sectionalizing switch will be considered as the base case for running the load flow. Suppose x₁ is the total technical loss (I²R) taking place in the network for the first base case, as obtained from the load flow. In the next step, the presently open sectionalizing switch will be closed and its adjacent sectionalizing switch in the same loop will be open. For this second reconfiguration, again the load flow will be run and the above parameters will be observed while checking for all different constraints explained above. Suppose the total technical loss (I²R) obtained in this case is x₂. If x₂ is greater than x₁, then the first reconfiguration will be the best reconfiguration corresponding to tie switch 1. However, if x₂ is less than x₁, then similar steps will be repeated by closing the presently opened sectionalizing switch while simultaneously opening the next adjacent sectionalizing switch within the same loop. This process will be repeated until a reconfiguration is obtained for which the value of the total technical loss (I²R) is more than its current previous value. Suppose the process continued for nth number of sectionalizing switches in the loop and xn is the corresponding technical loss (I²R). Let this xn obtained from nth reconfigurations is found to be more than its previous value, i.e. xn-₁. Then the process will be stopped and (n – 1)th reconfigurations will be considered as the best reconfiguration corresponding to tie switch 1.

Now 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.