International Journal of Scientific & Engineering Research, Volume 3, Issue 10, October-2012 1
ISSN 2229-5518
Studies have indicated that as much as 13% of total power generated is wasted in the form of losses at the distribution level [1]. Radial distribution systems are typically spread over large areas and are responsible for a significant portion of total power losses. Reduction of total power loss in distribution system is very essential to improve the overall efficiency of power delivery. This can be achieved by placing the optimal value of capacitors at proper locations in radial distribution systems. Capacitors are installed at strategic locations to reduce the losses and to maintain the voltages within the acceptable limits.
Although some of these methods to solve capacitor allocation problem are efficient, their efficacy relies entirely on the goodness of the data used. Fuzzy logic provides a remedy for any lack of uncertainty in the data. Fuzzy logic has the advantage of including heuristics and representing engineering judgments into the capacitor allocation optimization process. Furthermore, the solutions obtained from a fuzzy algorithm can be quickly assessed to determine their feasibility in being implemented in the distribution system.
Application of shunt capacitors to the primary distribution feeders is a common practice in most of the countries. The advantages anticipated include boosting the load level of the feeder so that additional loads can be carried by the feeder for the same maximum voltage drop, releasing a certain KVA at the substation that can be used to feed additional loads along other feeders and reducing power and energy losses in the feeder.
The objective of the capacitor placement problem is to determine the locations and sizes of the capacitors so that the power loss is minimized so that
loss reduction is maximized. Even though considerable amount of research work was done in
the area of optimal capacitor placement [2]-[15],
there is still a need to develop more suitable and effective methods for the optimal capacitor placement.
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H. Ng et al. [10] proposed the capacitor placement problem by using fuzzy approximate reasoning. In the first stage, the method proposed by H. Ng et al. [9] is adapted to determine the optimal capacitor locations using fuzzy logic.
Karaboga.D [16] proposed a new meta heuristic approach called artificial bee colony algorithm, It is inspired by the intelligent foraging behavior of honey bee swarm. In the second stage, the algorithm proposed by Karaboga.D [16] is adapted to determine the optimal capacitor sizes using artificial bee colony algorithm.
The proposed method is tested on 15, 34 and
69 bus test systems and results are obtained.
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modeled by fuzzy membership functions. A fuzzy inference system (FIS) containing a set of rules is then used to determine the capacitor placement suitability of each node in the distribution system.
The total
I 2 R loss (PL) in a distribution
Capacitors can be placed on the nodes with the
system having n number of branches is given by
n
highest suitability.
For the capacitor placement problem,
PL =
i 1
Ii Ri
(1)
approximate reasoning is employed in the following
manner: when losses and voltage levels of a distribution system are studied, an experienced
Here Ii is the magnitude of the branch current and Ri is the resistance of the ith branch respectively. The branch current can be obtained from the load flow solution. The branch current has two components, active component (Ia) and reactive component (Ir). The loss associated with the active and reactive components of branch currents can be written as
n
planning engineer can choose locations for capacitor installations, which are probably highly suitable. For example, it is intuitive that a section in a distribution system with high losses and low voltage is highly
ideal for placement of capacitors. Whereas a low loss
section with good voltage is not ideal for capacitor placement. A set of fuzzy rules has been used to determine suitable capacitor locations in a distribution system.
PLa Iai Ri
i 1
n
PLr Iri Ri
i 1
(2)
(3)
In the first step, load flow solution for the original system is required to obtain the real and reactive power losses. Again, load flow solutions are required to obtain the power loss reduction by compensating the total reactive load at every node of
the distribution system. The loss reductions are then,
linearly normalized into a [0, 1] range with the largest loss reduction having a value of 1 and the
Note that for a given configuration of a single source radial network, the loss PLa associated with the active component of branch currents cannot be minimized because all active power must be supplied
smallest one having a value of 0. Power Loss Index value for nth node can be obtained using equation (4).
lossreduction(n) lossreduction(min)
by the source at the root bus. However, supplying part of the reactive power demand locally can minimize the loss PLr associated with the reactive component of branch currents. This paper presents a
PLI (n)
lossreduction(max) lossreduction(min)
(4)
method that minimizes the loss due to the reactive component of the branch current by optimally placing the capacitors and thereby reduces the total loss in the distribution system.
This paper presents a fuzzy approach to determine suitable locations for capacitor placement. Two objectives are considered while designing a fuzzy logic for identifying the optimal capacitor locations. The two objectives are: (i) to minimize the real power loss and (ii) to maintain the voltage within the permissible limits. Voltages and power loss indices of distribution system nodes are
These power loss reduction indices along with
the p.u. nodal voltages are the inputs to the Fuzzy Inference System (FIS), which determines the node more suitable for capacitor installation.
In this paper, two input and one output variables are selected. Input variable-1 is power loss index (PLI) and Input variable-2 is the per unit nodal voltage (V). Output variable is capacitor suitability index (CSI). Power Loss Index range varies from 0 to
1, P.U. nodal voltage range varies from 0.9 to 1.1 and
Capacitor suitability index range varies from 0 to
1.Five membership functions are selected for PLI. They are L, LM, M, HM and H. All the five membership functions are triangular as shown in Figure 1. Five membership functions are selected for Voltage. They are L, LN, N, HN and H. membership
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functions are trapezoidal and triangular as shown in Figure 2. Five membership functions are selected for CSI. They are L, LM, M, HM and H. These five membership functions are also triangular as shown in Figure 3.
Figure 1. Membership function plot for P.L.I.
Figure 2. Membership function plot for p.u. nodal
voltage
Figure 3. Membership function plot for C.S.I.
For the capacitor allocation problem, rules are defined to determine the suitability of a node for capacitor installation. Such rules are expressed in the following form:
IF premise (antecedent), THEN conclusion (consequent) for determining the suitability of capacitor placement at a particular node, a set of
multiple antecedent fuzzy rules has been established. The inputs to the rules are the voltage and power loss indices and the output is the suitability of capacitor placement. The rules are summarized in the fuzzy decision matrix in Table I. The consequents of the rules are in the shaded part of the matrix.
Table I. Decision matrix for determining the optimal capacitor locations
4. OVERVIEW OF ARTIFICIAL BEE COLONY ALGORITHM (ABCA)
In the ABC algorithm [16], the colony of artificial bees contains three groups of bees: employed bees, onlookers and scouts. A bee going to the food source visited by it previously is named an employed bee and a bee waiting on the dance area for making decision to choose a food source is called an onlooker. A bee carrying out random search is called a scout.
In the ABC algorithm, first half of the colony consists of employed artificial bees and the second half constitutes the onlookers. For every food source, there is only one employed bee. In other words, the number of employed bees is equal to the number of food sources around the hive. The employed bee whose food source is exhausted by the employed and onlooker bees becomes a scout.
In the ABC algorithm, each cycle of the search consists of three steps: sending the employed bees onto the food sources and then measuring their nectar amounts; selecting of the food sources by the onlookers after sharing the information of employed bees and determining the nectar amount of the foods; determining the scout bees and then sending them onto possible food sources.
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At the initialization stage, a set of food source positions are randomly selected by the bees and their nectar amounts are determined. Then, these bees come into the hive and share the nectar information of the sources with the bees waiting on the dance area within the hive. At the second stage, after sharing the information, every employed bee goes to the food source area visited by her at the previous cycle since that food source exists in her memory, and then chooses a new food source by means of visual information in the neighborhood of the present one. At the third stage, an onlooker prefers a food source area depending on the nectar information distributed by the employed bees on the dance area. As the nectar amount of a food source increases, the probability with which that food source is chosen by an onlooker increases, too. Hence, the dance of employed bees carrying higher nectar recruits the onlookers for the food source areas with higher
and it becomes a scout, i.e., it will search for a new food source randomly. This tantamount to assigning a randomly generated food source (solution) to this scout and changing its status again from scout to employed. After the new location of each food source is determined, another iteration of ABC algorithm begins. The whole process is repeated again and again till the termination condition is satisfied.
The food source in the neighborhood of a particular food source using equation (6) is determined by altering the value of one randomly chosen solution parameter and keeping other parameters unchanged. This is done by adding to the current value of the chosen parameter the product of a uniform variate in [-1, 1] and the difference in values of this parameter for this food source and some other randomly chosen food source.
nectar amount. After arriving at the selected area, she chooses a new food source in the neighborhood of the
vij xij u(xij xkj )
(6)
one in the memory depending on visual information. Visual information is based on the comparison of food source positions. When the nectar of a food source is abandoned by the bees, a new food source is randomly determined by a scout bee and replaced
with the abandoned one.
In our model, at each cycle at most one scout goes outside for searching a new food source and the number of employed and onlooker bees were equal. The probability Pi of selecting a food source i is determined using the following expression:
where u is an uniform variate in [-1, 1]. If the resulting value falls outside the acceptable range for parameter j, it is set to the corresponding extreme value in that range.
5. ABC ALGORITHM FOR CAPACITOR SIZING PROBLEM
After identifying the n number of capacitor locations using fuzzy approach, the capacitor sizes in all these n capacitor locations are obtained by using the Artificial Bee Colony Algorithm (ABCA).The proposed artificial bee colony algorithm is
Pi SN
fiti
(5)
summarized as follows:
fitn
n1
Where fiti is the fitness of the solution represented by the food source i and SN is the total number of food sources. Clearly, with this scheme good food sources will get more onlookers than the bad ones. After all onlookers have selected their food sources, each of them determines a food source in the neighborhood of his chosen food source and computes its fitness. The best food source among all the neighboring food sources determined by the onlookers associated with a particular food source i and food source i itself, will be the new location of the food source i. If a solution represented by a particular food source does not improve for a
Step 1. Initially [SN x n] number of Bee population ( xij ) are generated randomly within the limits Qmax and Qmin where SN is the population size and n is the number of capacitors. Each row represents one possible solution to the optimal capacitor-sizing problem and the numbers of employed Bees are equal to onlooker Bees .
Step 2. By placing all the n capacitors of each Bee at the respective capacitor locations and load flow analysis is performed to find the total real power loss PL . The same procedure is repeated for the SN number of Bees. Evaluate fitness value for each Bee by using the equation (7),
1
predetermined number of iterations then that food source is abandoned by its associated employed bee
fitness(i)
1 powerloss(i)
(7)
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Step 3. Generate new population (solution) vij in the neighborhood of xij for employed bees using equation (6) and evaluate the fitness of them;
Step 4. Apply the greedy selection process between
xij and vij by comparing the fitness of them;
Step 5. Calculate the probability values Pi for the solutions xij by means of their fitness values using the equation (5);
Step 6. Produce the new population’s vij for the onlookers from the employed bee’s population, selected depending on Pi by applying roulette wheel selection process, and evaluate the fitness of all the onlooker bees;
Step 7. Apply the greedy selection process for the onlookers between xij and by comparing the fitness;
Step 8. Maximum fitness , Minimum fitness and average fitness values are calculated. Error is calculated using the equation
Error = (maximum fitness - average fitness)
If this error is less than a specified tolerance then go to Step 11
Step 9. The bee corresponding to minimum fitness is a scout and replace it with a new randomly produced solution xij for the scout bees using the following equation
The proposed algorithm is applied to 15-bus system [12]. Optimal capacitor locations are identified based on the C.S.I. values. For this 15- bus system, five optimal locations are identified. Capacitor sizes in the five optimal locations, total real power losses before and after compensation
xij Q min rand (0,1) * (Q max Q min)
(7)
Step 10. The iteration count is incremented and if iteration count is not reached maximum then go to step 2.
Step 11.The capacitor sizes corresponding to maximum fitness(Best Bee) gives the optimal capacitor sizes in n capacitor locations and the results are printed
Fuzzy approach is used to find the optimal capacitor locations and ABCA is used to find the optimal capacitor sizes for maximum loss reduction. Convergence criterion of ABCA is error must be less than 0.000000001.
The proposed algorithm is applied to 34-bus system [7]. Optimal capacitor locations are identified based on the C.S.I. values. For this 34-bus system, seven optimal locations are identified .Capacitor sizes in the seven optimal locations, total real power losses before and after compensations are shown in Table 3.
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The proposed algorithm is applied to 69-bus system [4]. Optimal capacitor locations are identified based on the C.S.I. values. For this 69-bus system, two optimal locations are identified. Capacitor sizes in the two optimal locations, total real power losses before and after compensation
are shown in Table 4.
Bus No. | Capacitor size in KVAR | |
61 | 1123 | |
64 | 207 | |
Total KVAR | 1330 | |
Total power loss in KW(before) | 225.0021 | |
Total power loss in KW(after) | 151.7069 | |
% of loss reduction | 32.57534 |
The results show that 50.052 % reduction in power loss for 15-bus system, 23 % reduction in power loss for 34-bus system and % reduction in power loss for 69-bus system is possible as shown in Tables 2, 3 and 4 respectively and bus voltages are also improved substantially.
In this paper, a two-stage methodology of finding the optimal locations and sizes of shunt capacitors for reactive power compensation of radial distribution systems is presented. Fuzzy approach is proposed to find the optimal capacitor locations and ABCA method is proposed to find the optimal capacitor sizes. Based on the simulation results, the following conclusions are drawn:
By installing shunt capacitors at all the potential locations, the total real power loss of the system has been reduced significantly and bus voltages are improved substantially. The proposed fuzzy approach is capable of determining the optimal capacitor locations based on the C.S.I. values. The proposed ABCA method iteratively searches the optimal capacitor sizes effectively for the maximum power loss reduction.
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