ABSTRACT
A simple and efficient method for solving radial distribution networks is
presented. The proposed method involves only the evaluation of a simple
algebraic expression of receiving-end voltages. Computationally, the proposed
method using fuzzy logic is very efficient. The effectiveness of the proposed
method is demonstrated using some examples.
1. INTRODUCTION
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.
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.
2. OBJECTIVE
The objective of the capacitor
placement problem is to determine the locations and sizes of the capacitors so
that the power loss is minimized and annual savings are maximized.
Although some of these methods to solve
capacitor allocation problem are efficient, their efficiency 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.
3.
General description of Distribution System:
Distribution system is that part of the electric power system which connects the high voltage
transmission network to the low voltage consumer service point.
In any distribution system the power is distributed to
various uses through feeders, distributors and service mains. Feeders are conductors of large current carrying
capacity which carry the current in bulk to the feeding points. Distributors
are conductors from which the current is tapped of for the supply to the
consumer premises.
3.1 Basic Distribution Systems
There are two basic structures for distribution system
namely
(i) Radial distribution system
(ii) Ring main distribution system
(i) Radial distribution system:
If the distributor is connected to the supply
system on one end only then is system is said to be a radial distribution
system. In such a case the end of the distributor nearest to the generating station would be
heavily loaded and the consumers at the distance end of the distributor would
be subjected to large voltage variations as the load varies. The consumer is
dependent upon a single feeder so that a fault on any feeder or distributor
cuts off the supply to the consumers who are on the side of fault away from the
station.
(ii) Ring Main Distribution System:
Ring main employs a feeder which
covers the whole area of supply finally returns to the generating station. The
feeder is closed on itself. This arrangement is similar to two feeders in
parallel on different buses.
3.2
Distribution System
Losses
It has been established that 70% of the total losses occur in the primary and
secondary distribution system, while transmission and sub transmission lines
account for only 30% of the total losses. Distribution losses are 15.5% of the
generation capacity and target level is 7.5%. Therefore the primary and
secondary distribution must be properly planned to ensure losses within the
acceptability limits.
3.2.1
Factors Effecting
Distribution System Losses
1. Inadequate size of conductor,
2. Feeder Length,
3. Location of
Distribution Transformers,
4. Low Voltage,
5. Use of over rated
Distribution transformers,
6. Poor workmanship in fittings,
7. Low Power Factor
3.2.2.
Reduction of line losses:
The losses in Indian power system are on the higher side. So, the government of
India has decided to reduce the line losses and set a target for reduction of
T&D losses by 1% per annum in order to realize an overall reduction of 5%
in the national average.
Methods for the
reduction of line losses:
The following methods are adopted for reduction of distribution losses.
(1) HV distribution system ,
(2) Feeder reconfiguration,
(3) Reinforcement of the feeder
(4) Grading of conductor ,
(5) Construction of new substation,
(6) Reactive power compensation
(7) Installing Voltage regulators.
It is universally acknowledged that the voltage reactive
power control function plays a vital role in the distribution automation. The problem of reactive power compensation can be attempted
by providing static capacitors. The present practice to compensate reactive power component
is to increase reactive power by increasing the terminal voltage of the
generator or by increasing the field current of the synchronous machine
in condenser mode at generating stations. An alternate method for compensating
the reactive power is the use capacitors in distribution systems at customer
points.
There are two methods in capacitor compensation. They are
1. Series compensation. (Capacitors
are placed in series with line)
2. Shunt compensation. (Capacitors
are placed in parallel with load)
The fundamental function of capacitors whether they are in
series or in shunt in a power system is to generate reactive power to improve
power factor and voltage, there by enhancing the system capacity and reducing
losses. In series capacitors the reactive power is proportional to the square
of the load current where as in shunt capacitors it is proportional to the
square of the voltage.
For the capacitor placement problem,
approximate reasoning is employed in this manner:
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. Note that the terms, high and
low are linguistic descriptors which cannot be used to define rules in a
conventional ES.
4. Framework of Approach
Fig:-
Framework of Fuzzy Allocation System
4.1. FES IMPLEMENTATION
The FES contains a set of rules which are
developed from qualitative descriptions. In a FES, rules may be fired with some
degree using fuzzy inferencing; whereas, in a conventional ES, a rule is either
fired or not fired. 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 have been established. The inputs to the rules are the voltage and power
loss indices, and the output consequent is the suitability of capacitor
placement. The rules are summarized in the fuzzy decision matrix.
4.2 Selection of buses for capacitor placement using fuzzy
By invoking
the instruction fuzzy we got display of the fuzzy inference system (FIS) at the
top of window which shows the inputs, outputs and a central fuzzy rule processor.
In this case, the inputs are
1. Power Loss Index (PLI)
2. Nodal Voltage
The central
fuzzy rule processor contains the rules. The output is capacitor suitability
index (CSI) which indicates the location suitability for capacitor placement.
4.3 The input calculations
1. PLI : The power losses at all buses are calculated
and normalized between 0 and 1 such that, minimum power loss is zero and max
power loss is 1.
The formula is
2. Nodal
Voltage
The
per-unit nodal voltage is calculated from the load flow problem. The voltages
will be generally in range of 0.9 to 1.1.
4.3.1 Assigning of membership
functions
1. PLI The range of
this PLI is between 0 and 1. Triangular membership functions are assigned as
shown below
2. Nodal Voltage
The range of this is between 0.9 and 1.1. The combination of triangular
and trapezoidal membership functions are selected as shown in the figure
3. The Output (CSI)
The range of this is between 0 and 1. Triangular membership functions
are assigned shown below
4.3.2 DECISION MATRIX
4.3.3 RULE BASE
The rules defined in the fuzzy decision matrix are:
1.If
power loss is low and voltage is low then suitability is low- medium
2. If
power loss is low and voltage is low normal then suitability is low medium.
Etc.,
5.
CASE STUDY:
Case
Study Results of 15 Bus System
Capacitor Locations using FUZZY LOGIC
BUS
NO
PLI
VOLTAGE
CSI
NODE
SELECTED
2
0
0.9713
0.0940
———
3
0.3205
0.9567
0.3318
———
4
0.9602
0.9509
0.7500
4
5
0.1742
0.9499
0.2500
———
6
0.8000
0.9582
0.7500
6
7
0.8353
0.9560
0.7500
7
8
0.3267
0.9570
0.3370
———
9
0.1671
0.9680
0.2287
———
10
0.0313
0.9669
0.1972
———
11
0.9865
0.9500
0.7500
11
12
0.4612
0.9458
0.4505
———
13
0.2255
0.9445
0.2500
———
14
0.4119
0.9486
0.4051
———
15
1.0000
0.9484
0.7500
15
Here the candidate buses are selected based
on the CSI value. In this case CSI value is considered to be 0.75. Now the
buses 4,6,7,11,15 are selected as the candidate buses for minimum losses.
Voltage Profiles (before and after
compensation) at the Candidate Buses:
i)
At Bus 4
ii)
At
Bus 6
iii)
At Bus 7
iv)
At
Bus 11
v)
At
Bus 15
6. CONCLUSIONS
By implementing fuzzy logic the
optimal capacitor locations are determined for maximum loss reduction by using
matlab program. For identifying the bus locations for maximum loss reduction
are obtained using MATLAB in distribution systems. The results of the proposed
methods are almost identical and even better results are obtained with these
methods.
7. REFERENCES
1. S. Ghosh
and D. Das :”Method for load-flow solution of radial distribution networks”,
IEE proc-vol. 146,no 6,pp. 641-648, November,1999.
M.H.Haque,”
Capacitor placement in radial distribution systems for loss reduction”
IEE Proc.-Gener. Transm. Distrib., Vol. 146, No. 5,
September 1999V.K. Mehta, Rohit Mehta “principles
of power systems”, S.Chand & company Ltd, New Delhi,1st edn,1982.S.Rajasekaran,G.A.Vijayalakshmi
pai,”Neural Networks,Fuzzy logic and Genetic algorithms”,PHI
publications,New delhi,2005P.V. Prasad ,
S. Sivanagaraju and
N.Sreenivasulu,” A FUZZY-GENETIC
ALGORITHM FOR OPTIMAL CAPACITOR PLACEMENT IN RADIAL DISTRIBUTION SYSTEMS”, ARPN Journal VOL. 2,
NO. 3, JUNE 2007 IS.M.Amirthavalli,”Fuzzy
logic and neural networks”,scitech publications,Hyderabad,2nd
edn,2007
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