# Power loss minimisation in distribution networks using fuzzy approach for system configuration

10 October 2017

Studies indicate that as much as 13% of total generated power is wasted in the form of line loss at the distribution level [1]. One important area in which operating techniques of controlling distribution system losses are being applied is the area of network reconfiguration.

Network reconfiguration refers to the closing and opening of switches in a power distribution system in order to alter the network topology, and thus the flow of power from the substation to the customers. Operating costs are reduced, while still meeting all of the system constraints.

There are two major distribution configurations, radial configuration and loop configuration, and two types of switches that are normally closed (sectionalising switches) and normally open (tie switches).

In response to a fault, some of the normally closed switches would be opened in order to isolate the faulted network branches. At the same time, a number of normally open switches would be closed in order to transfer part or all of the isolated branches to another feeder or to another branch of the same feeder. All switches would be restored to their normal positions after removal of the fault.

Most of the recent work on reconfiguration has used branch exchange and loop-cutting methods [2]. The branch exchange and loop-cutting methods were discussed in [3] and [4] respectively. Distribution system reconfiguration for loss reduction was proposed by Merlin and Back [5] and then improved later by Shirmohammadi and HW Hong [4]. Liu et al [6], Jung et al [7] and Augugliaro et al [8] have proposed artificial-intelligence-based application in a minimum loss reconfiguration.

FV Gomes [9] has presented a heuristic reconfiguration algorithm for large distribution systems. It was improved by D Das [10], who presented an algorithm for network reconfiguration based on the heuristic rules and fuzzy multiobjective approach. In [11] and [12], network reconfiguration for loss reduction was produced using simulation algorithm and genetic algorithm, respectively.

This paper presents a method to minimise real power-line losses in a medium voltage distribution network, based on heuristic rules and fuzzy multi-objective approach, accounting for different distribution system constraints.

## Distribution network modelling and optimsation

Realistic mathematical representations for each of the system components are needed in order to achieve accurate and meaningful results from the power flow study. Detailed models for distribution system components such as line sections, shunt elements, and loads can be found in [13].

The objective of optimisation is to seek values for a set of parameters that maximise or minimise objective functions subjected to certain constraints. A choice of values for the set of parameters that satisfy all constraints is called a ‘feasible solution’. Optimisation includes both maximisation and minimisation problems. Any maximisation problem can be converted into minimisation problem by taking the negative of the objective function, and vice versa.

In general, the problem tackled in this paper is minimisation problem. The minimisation problem can be defined as follows [14]:

Given

**1. Optimisation in fuzzy environment**

The main purpose of fuzzy logic is to map an input space to an output space, and the primary mechanism for doing this is a list of ‘If-Then’ statements, which is called rules. All rules are evaluated in parallel, and the order of the rules is unimportant. The rules themselves are useful because they refer to variables and the adjectives that describe those variables. Before we can build a system that interprets rules, we have to define all the terms we plan on using and the adjectives that describe them. When there are multiple objectives to be satisfied simultaneously, a compromise has to be made to get the best solution. In this work, the solution methodology for the multi-objective optimisation in fuzzy framework is based on the maximum minimum principle.

**2. Distribution system constraints**

Not every configuration is a feasible solution to the network reconfiguration problem. So it is necessary to specify which states are accepted and which ones are not, these involves the below stated constraints:

*Topological constraints*

The studied network is structured as meshed and operated as redial network with the possibility of connecting and disconnecting the network branches by tie switches and sectionalising switches respectively. This involves that loops are not allowed and each bus in the network should be connected via at least one path to the substation.*Electrical constraints*

The state of a power system network must satisfy Kirchhoff’s voltage and current laws. The formulation of these constraints is treated in the power flow solution which is part from the proposed algorithm.*Operational constraints*

Each line in the system has a certain thermal limitation which restricts the maximum allowable current through it. In general, these physical limitations can be controlling bus voltages, line currents and feeder load balancing.*Load constraints*

The system has to supply the power demanded by each customer recognising any voltage deviation limits.

**3. Problem formulation**

The network reconfiguration problem can be given as a multiple objectives nonlinear combinatorial optimisation problem subjected to constraints that involve finding the optimal or best solution out of a set of possible alternatives. It can be completely characterised by the search space and the constrained objective function. If the load profile for a distribution network is known, then a radial configuration for the network which minimises the network losses and satisfies the distribution network constraints can be obtained. The problem can be described in the following equation:

**4. Search space**

The search space for this problem is the set of all possible network configurations. Once the general layout of the distribution network is specified, the specific topology is determined by the status of each of the switches in the system. Specifying the open/closed status of each switch completely characterises the topology of the network.

The current configuration ‘U’ can be represented by the following vector:

Where:

*ui:* Individual switch states, where ‘u’ = 1or 0 indicates that switch ‘i’ is closed or open respectively;

*ns:* The total number of tie and sectionalising switches in the system;

*S:* The search space, the space of all possible configurations ‘U’.

**5. Proposed algorithm**

The proposed algorithm starts with existing radial configuration, do the calculations needed for power flow, real power loss and voltage across tie switches while checking the system constrains. If all loops changed into radial feeders, and all constraints are satisfied with no more real power loss reduction could be achieved then procedure is completed. The flow chart for network reconfiguration using the proposed algorithm is shown in Figure 1:

**6. Algorithm accuracy test**

The proposed algorithm has been tested on two test networks, Baran [15] and Wu [10] to check its accuracy. Below tests were applied:

- Power flow solution test;
- Loop identifying test;
- System reconfiguration test;
- Overall algorithm test.

The test results showed excellent results with negligible error. Tables 1 through 4 show the test results.

**7. Implementation of the proposed algorithm**

The proposed algorithm was applied to a practical network from CCED (Qantra Shark network). Below is a detailed description for the studied network.

## Circuit description

A 22kv underground network with total length of 12.8165 km, consisting of 49 branches and serving 45 distribution transformers with total installed capacity of 14.4 MVA and percentage loading of about 80%, 50% and 20% as maximum, average and minimum respectively. It is served by one substation through eight feeders.

The network has 45 sectionalising switches, and 4 tie switches. In the base configuration shown in Figure 2, the normally open switches are S46, S47, S48, and S49 and the normally closed switches are S1 to S45. The main customer types are residential. A constant power model is considered to be the most suitable to represent the behaviour of the customer loads. Customer loads are included in the study as spot loads with average power factor of 0.8, 0.82 and 0.85 for maximum, average and minimum load respectively.

All cables are 18/30 KV, 3×240 mm2 Aluminum Conductors, XLPE Insulated, Steel Tape Armoured, and PVC Sheathed. According to IEC 502/1994 Standard and national standard applicable in CCED, the current capacity is 349 A. For all networks, the base values are 11KVand 10 MVA for voltage and apparent power respectively.

The suggested algorithm was applied under three different cases representing the typical maximum, average and minimum recorded load percentages with different system constrains for each.

**Case (a)**

Load percentage of 80% subjected to the following operating states:

- a1- Branch current loading index of 1.0, 1.15 p.u. and load balancing index among feeders of 0.1,0.5 p.u. as minimum and maximum limits respectively;
- a2 -Branch current loading index of 1.0, 1.15 p.u. and load balancing index among feeders of 0.05, 0.25 p.u. as minimum and maximum limits respectively;
- a3 -Branch current loading index of 0.8, 1.0 p.u. and load balancing index among feeders of 0.1 ,0.5 p.u. as minimum and maximum limits respectively;
- a4- Branch current loading index of 0.8, 1.0 p.u. and load balancing index among feeders of 0.05, 0.25 p.u. as minimum and maximum limits respectively.

Cases (b) and (c) are similar to case (a) but with load percentages of 50% and 20% respectively.

Figure 2 shows the base configuration for the studied network. Power loss reduction from applying the algorithm on the studied network for all operating states has been summarised in Table 5.

The voltage profiles for base and suggested configurations for cases (a), (b) and (c) shown in figures 3 through 8. The results for the cases a3 and a4 were found the same as the cases a1 and a2 respectively. Similarly b3, b4 and c3, c4 were found the same as b1, b2 and c1, c2 respectively.

The power loss reduction and system constrains verification for the studied network in the specified operating cases was summarised in figures 9 through 12. Table 6 summarises the results of the base and final suggested configurations for the three operating cases.

## Conclusions

- Proposed algorithm has been tested two test systems from literature and one practical system. It shows almost zero error on the test systems and improved results on the practical system.
- It has been shown that the Fuzzy Set Theory (FST) and heuristic rules can be used successfully to find the configuration of a three-phase power distribution network which minimises the overall real power losses of the system while satisfying the system constrains. A maximum real power loss reduction of 8.49% has been achieved.
- It is not a must that the variation in operational constraints limits result in a new solution
- The percentage in loss reduction in Qantra Shark network in operating states (a1), (b1) and (c1) are 8.49%, 6.41% and 8.13% respectively which means that different values of real power loss reduction could be achieved in different load percentages for the same operational constraints limits. This encourages the implementation of the algorithm in the real time operation mode.
- The reduction in the real power loss in Qantra Shark network is low compared to that of test cases. This due to the limited number of tie switches in the topological or layout structure of all networks in CCED.
- To maximise the real power loss reduction, the network structure should be performed in such a way that one can relieve loads to other feeders or even to the same feeder. This requires a sufficient number of tie switches in different locations. The locations of the suggested new tie switches can be selected with the help of the suggested program to minimise the power loss.

**Authors:**

*Pat Moriarty BE, CEng of CDGA Engineering Consultants Ltd*

* Sameh M.M.A. Noufal, MSc, CEng, MAEE of CDGA Engineering Consultants Ltd*

*Pat Moriarty is a UCC graduate and Sameh Ahmed Nofal is a graduate of Helwan University and Tabbin Institute in Egypt. CDGA Engineering Consultants Ltd has a wide international consultancy business in Africa, South East Asia and Middle East. Pat Moriarty leads the CDGA team on these, while Sameh Ahmed is part of the team working in the Middle East.*

*CDGA Engineering Consultants Ltd is a consultancy firm based in Cork and with representation in United Arab Emirates and Bulgaria. The company is an Engineers Ireland Continuing Professional Development (CPD) Accredited Employer.*

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15. M. E. Baran and F. F. Wu, “Network reconfiguration in distribution systems for loss reductoin, “IEEE Trans. Power Syst., vol. 4, no. 3, pp. 1401-1407, Aug. 1989.

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