A number of considerations were made for problem formulation featured separately hereafter, targeting the following operational issues:

1) Brief shut down improved in several ways, including the following:

a) Reduce faults—such as power tapings, tree lowering, tree fall, creatures’ movements, arresters, tour duties, and so on;

b) Reclosing quickly;

c) Reduce the number of consumers’ disturbance by using downstream recloser.

2) Distribution Line Reclosers

In this kind of recloser arrangement, the strategy is to minimize recloser time because it is based on the time delay required to extinguish the fault. Table 1 provides an overview of how recloser types and set-up work together with reclosing schemes. These standard ratings were important to guide all sectors of power systems.

The reclosing technique design was meant to have at most three delays. For all types of reclosers the power fault condition completely would have subsequent opening and closing the affected area three times to check whether the fault was able to clear itself. It is only the permanent faults, which normally open or cut off after the third delay to safe guard the power system apparatus. The time values provided are considered to be within the minimum accepted range for the purpose of setting a recloser depending on criteria applicable to the designer.

Firefly MATLAB coding for this work uses instantaneous values of 15 sec for period B and 30 sec for period C. These are time delays meant to safeguard especially transformers from stressing currents which are abnormally very high during transients.

Considering the costs incurred in an event that transient and permanent faults or “non-technical power occurs”. The objective cost function of transient faults were calculated as (1)

w ENS = min ∑ r = 1 n     P r T r C r (1)

where C r , P r and T r are load based cost of energy, consumed power and recovery period in seconds during short-lived failures. C r is subject to recloser settings and brief power cut off caused by the operation:

This model aims to reduce the cost and increase the system reliability with recloser’ optimization model given by Equation (2). This equation describes amount of power transferred during a blackout in a distribution network.

E h = ∑ 0 9     kVA I ∗ t r = P ∗ t (2)

In which, t r is operation time of the recloser, P is transferred power and E h , kW sec of the lost supply. kVA ∗ t r is the thermal energy required to melt a specific fuse element; taken as recloser dead-time. Using reclosing philosophy as shown in (3)

ENS = kVA ∗ t 1 + 0.01 ∗ kVA ∗ t 2 + 0.06 ∗ kVA ∗ t 3 (3)

where ENS is Energy not served during reclosing operation.

kVA = Transformer rating or size, t 1 , t 2 and t 3 time interval for reclosing period. The work aimed at optimizing savings in cost of energy, according to formulation in Equation (4)

min f ( x ) = E N S = d i t 1 + 0.11 d i t 2 + 0.06 d i t 3 (4)

where,

d i = D j F k L m R ( t ) C C r (5)

subject to;

0.5 ≤ t r ≤ 45.9 ;

75 ≤ D j ≤ 400 ;

0 ≤ F k ≤ 1 ;

R ( t ) ≥ R 0

In which D_i is upstream supply for the model nine zones, F_k is rate of failure over the length of line, L_m is downstream length of line, t_r fault clearance time based on recloser operation in 3 shots, C is accumulated recloser cost of operation and maintenance, C_r is cost of blackout per Kilowatt while R(t) is the rate of failure.

Considering single recloser device, the total everyday device operation and maintenance cost is given by:

C r o m = ξ ∗ CENS (6)

ξ ∗ CENS = min ( f ( C r o m ) ) (7)

R ( t ) ≥ R 0 (8)

ENS max ≥ ENS ≥ ENS min (9)

In which CENS is unserved energy cost resukting from reclosing operation as a protective measure for feeders. Thus R(t) is the probability of success (reliability) index of a distribution system, under a given recloser constraints. R₀(t) is the occurrence or reliability index projection compels, hence the location based energy savings realized according to the formualtion for the radial network.

Parameters in the vector settings included power, current, distance and time. These parameters are equated such that: x₁ is per kilometer detection period, based on standard setting of the recloser x₂ is downstream length of line in kilometer. And x₃ is upstream length of line in kilometer. The per kilometer detection period along feeders is approximated as two second per kilometer. Parameters in the vector i.e. power, current and time are set and equated as;

x 2 = ∑ i = 1 9     L i (10)

x 3 = ∑ i = 1 9     L j (11)

L i = 5.6 , 7.4 , 10.4 , 13.2 , 16.7 , 19.9 , 22.5 , 24.5 , 26.1 (12)

L j = 26.1 , 25.4.22.5 , 19.9.16.7 , 13.2 , 10.4 , 7.4 , 5.6 (13)

g 1 = x 2 / ( x 2 + x 3 ) x 1 (14)

where g₁ is time taken to locate fault, while x₁ is standard setting for detection period, i.e. two seconds per kilometer. Equation (14) shows feeder’s switching time. Post fault switching period for individual feeder is given as per Equation (15) while Equation (16) illustrates period taken to clear faults. Demand based un-served energy during the blackout is shown in Equation (17) and the Per kVA, per zone rate of failure is given by Equation (18), In which D is downstream demand. Protective equipment cost of maintenance and operation is formulated in Equation (19) and the cost savings for unserved demand modeled as shown in Equation (20)

g 2 = g 1 + 15   s (15)

g 3 = g 2 + 30   s (16)

C r = $   1 / kVA (17)

g 4 = g 1 D + 0.11 D g 2 + 0.06 D g 3 (18)

g 5 = 0.008 D (19)

g 6 = $   0.008 / kVA (20)

CENS = min ( C r ∗ ∑ ​ ( g 1 g 2 g 3 g 4 g 5 g 6 ) ) (21)

The limits for these vector parameters include:

0.5 ≤ x 1 ≤ 45 ; 80 ≤ D ≤ 1800 ; 0 ≤ g 5 ≤ 1 and 1 ≤ x 3 ≤ 26

ENS_max is the highest outage and expressed by considering the recloser operation in terms of fault location time, which is given by;

“ Faultlocationtime ” = x 1 / ⌊ x 1 + x 2 ⌋ ∗ “ Reclosersettime ”

where, x₁ and x₂ are downstream and upstream distances to the faulted area. Fault location is the place where a short circuit current occur. The distance is measured from the sub-station recloser position. Fault location time for faulted area was calculated using Equation (13).

Step 1: Initialization of algorithm parameters.

Step 2: Creation of first population using: X j , i = X j . i L + rand ( X j , i U + X j , i L )

(In which j and i are integers ranging from 1 to n and N respectively i.e. count of decision variables).

Step 3: Objective Function Computation using: f ( X ) , X = ( x 1 , ⋯ , x N ) T .

Step 4: Iterative FA parameter definition for attractiveness (β), randomization (α) and coefficient of light absorption (γ).

Step 5: Firefly attraction, in which attractiveness depends on distance, such that: d a , b exp [ − γ d a , b 2 ] .

Step 6: Light Intensity Update as per the created and computed solution.

Step 7: Limiting violation to both inequality and equality constraints.

Step 8: finding current best out of rated fireflies.

Step 9: Report result.

Step 10: Screen printout optimum solution based on firefly with highest light intensity.

Step 11: time plotting of iterations/time vs., light intensity.

Step 12: Stop.

Application of this pseudo code to the formulated problem is illustrated in the diagram of Figure 1.

The data for the firefly algorithm coding utilized a radial network. This network has values including: downstream load power demands symbolized as d, distances where transformers are placed and their kVA values, the reliability ratings of each line and is based on power demand of the section.

1) Network Zones and Parameters

For each of the nine zones, three parameters are considered for data inputs, as tabulated in Table 2. These include maximum kVA, downstream network length (km) and line failure rates.

2) Fault Location Time for 9 Zones

Once a faulty occurs on the downstream network, it takes time for the system to detect and locate. The data in Table 3 shows the time taken by system, to locate the faults.

Table 3 and Table 4 values were used to develop matrices for reclosing coefficient. Reclosing coefficient values were useful for optimization technique developed in firefly algorithm. Basically, all the zones’ distances are stretched for different kilometers along the network. Fault location and clearing time are solved using Equations (11) and (13) respectively. At first, fault location and clearing times are shorter and increases downstream. As long as the recloser is closer to the upstream distribution system, it is made to have a shorter time to locate and clear the fault once it occurs along the proposed radial line.

Tabulated results (Table 5), have each column’s input variables, as per the model system of radial network. Levels of reliability are inversely proportional to zonal span. Distance depended detection-period, for faults establish the clearance times in which distance is referenced to location of upstream recloser. This criterion implies longer clearing periods for furthest zone 9. Zone 9 has higher CENS, as compared to zone 8 that possesses less operation, maintenance and kVA * t costs, hence lowering the cost savings. A methodology to evaluate the economic advantages of using reclosers in power distribution system permitting. Self-operative procedures were discussed in [9].

The economic advantage contradicted the capital and the operational consumptions against the investment funds because of the decrease with the expense of energy not served. The use of a single recloser was obviously expensive compared to using two. The cost of capital investment for several reclosers became much beneficial to an extent that 40% of power was saved in a techno-economic assessment. Simulated result in this work realized a higher benefit of 43.3%.

During power outages, derivation of equations based on un-served energy gives sufficient problem formulation for non-technical losses. Animal based power interruptions and illegal tapings contribute to transients causing blackouts. The plotted results of unserved energy cost savings is illustrated in Figure 2. These results indicate downstream CENS, with automatic optimization of upstream reclosing, as per the scheme of protection modeled in Equation (2). The plots imply that power transfer for upstream loads is higher in each zone.

Difference in cost of un-served energy varies from zone 1 to zone 9, based on simulated models, with significant variations. Figure 3 illustrates 3D distribution of cost of energy not served and demand distribution, in same plot. Both maximum and minimum values are illustrated for reclosed feeder zones, according to the simulation, as opposed to generation of un-served energy costs.

To attest on results generated in this work, the reviewed publication [11] had a 40% savings for recloser placement. This previous work demonstrated recloser placement in a rural distribution network with a radial setting. Tradition formulation, recloser placement developed was on two levels. The problem was to optimize recloser placement. The first level, recloser allocation was reliability estimation of SAIFI and CAIDI in smaller areas within the feeder network. Estimation of reliability indices was on assumption that customers were evenly distributed. To some extent, second level placement was exact location employing simulation technique based on Roy Billiton Test System (RBTS).

In [15], optimal recloser placement in fault condition was based on design to cost methodology. The formulation was based on matrix tables available which could be used to determine maximum number of reclosers in the network. Cost benefit analysis was done and payback was possible within a yearly period. The results were that cost benefit factor was greater than 1 (one). This translated to benefit greater than cost when reclosers were distributed in a radial system.

Having analyzed these two techniques, the proposed technique appears to be an improvement in comparison. 43.3% savings which could be calculated in

every interruption is a better idea. The cost benefit analysis which runs for a year could be tedious work compared to the proposed method so far. This cost benefit factor kept the real unknown.