International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 10, October 2015)
Planning of the Electric Power Distribution Systems Securing
Maximum Reliability at Constrained Budget
Prof.Dr.Ahmed R. Abul'Wafa1, Shazly Nasser Fahmy2, Dr. Aboul’Fotouh El’Garably 3
1
Electric Power and Machines Dept.Ain Shams University, Cairo, Egypt
Electric Power and Machines Dept. El’Shorouk Academy, Cairo, Egypt
2,3
Abstract— It is evident that electric utilities all over world
are facing an increasing number of complaints about
distribution systems reliability. High levels of continuity and
quality are the two characteristics that customers expect and
demand. Therefore distribution systems reliability increase
constitutes one of the most important issues in the studies of
the power distribution systems. The purpose of this paper is
to study the distribution systems reliability increase using a
decision making process based on both incremental cost and
incremental benefits criteria. This paper uses A Mathematical
Programming Language (AMPL) software to build an
algorithm to optimize the customer oriented reliability
indices, which is measured by System Average Interruption
Duration Index (SAIDI). The objective function of AMPL is to
minimize SAIDI for a distribution system through several
alternatives corresponding to different system configurations.
Five alternatives for minimizing of SAIDI will be applied to
the test system. Investments for proposed alternatives are
constrained by a limited budget. Reliability parameters of the
system components are obtained through simulation of the
different system configuration on NEPLAN software. These
parameters values are introduced in the AMPL data file.
Minimal cut sets technique (MCs) is used to explore the path
from each load point to the supply source. These MCs are
used to build the objective function and the constraints in
AMPL optimization model file. The procedure is illustrated
by application on Feeder 4 of Bus 6 of RBTS as test system.
Net Present Value (NPV) will be used to capitalize the cost of
energy interruption (ECOST), used with capital budgeting to
calculate the net cost for the optimal investment.
Investment cost for each alternative.
Maximum budget available for the utility.
The number of investment alternatives.
The annual outage time of main feeder
corresponding to each load point.
The annual outage time of lateral distribution
feeder connecting to its load point.
The number of main feeder component sections
corresponding to each load.
The failure rate of main feeder component
sections corresponding to each load point.
The repair time of main feeder component
sections corresponding to each load point.
The decrease of failure rate for main feeder
component sections corresponding to each load
point at available investment alternatives x z.
The decrease of repair time for main feeder
component sections corresponding to each load
point at available investment alternatives x z.
The failure rate for lateral distribution feeder
connecting to its load point.
The repair time for lateral distribution feeder
connecting to its load point.
Annual expected interruption cost over the time
period of project ($/yr).
Keywords— AMPL, Cut Set, NEPLAN, NPV, SAIDI.
Nomenclature
Optimal investment cost.
Failure rate for component i in a cut set.
Repair time for component i in a cut set.
Number of components in a cut set.
Average failure rate of load point j.
SAIDI
Repair time of load point j.
Annual outage time of load point j.
EENS
ECOST
TCC
RBTS
Number of customers of each load point j.
Number of load point in the system.
Binary decision variable for each alternative.
280
Number of time periods which is equal to 15
year.
Discount rate which is equal to 10%.
System Average Interruption Duration Index
(hr/cust.yr ).
Expected energy not supplied (Kwh/yr).
Annual expected interruption cost ($/yr).
Total Capital Cost ($).
Roy Billinton Test System.
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 10, October 2015)
MFSs
SF5Ss
SF6Ss
MCs
D.S
MTS
ATS
TR
LD
OHL
UGC
“Ref. [8]” addresses the problem of resource allocation
on multiple cloud platforms formulated as a mixed integer
non-linear programming problem (MINLP). The paper
optimizes scheduling of bag of tasks applications and
workflows under the deadline constraint. The optimization
models implemented in AMPL modelling language allow
us to apply leading solvers such as Cbc and CPLEX. “Ref.
[9]” deals in a unique combination with the aspects of
model-building and solving real world-optimization
problems. It treats in a systematic way all major modelling
languages and model language software used to solve
mathematical optimization problems. In the midst 1980s,
when, for instance, AMPL or XPress-MP appeared, the
software developers were already trying to improve on
previous designs, by taking advantage of faster computers
and better computing environments. “Ref. [10]” provides a
framework for quantifying the reliability impacts of
different projects as measured by Customer-Minutes of
Interruption (CMI) avoided ($/CMI). The changes in
expected reliability and associated benefit-cost analyses
were quantified for all of the project options. These are
assembled and ranked according to increasing dollars spent
per CMI purchased. The most cost-effective option is to
automate the switches on Feeders.
Minimal cut sets technique (MCs) [11] is used to explore
the path from each load point to the supply source. These
MCs are used to build the objective function and the
constraints in AMPL optimization Model file. However,
since we are using student edition of AMPL only allowing
up to 300 constraints, this paper make use of the
Reliability-network-equivalent approach [2] to handle the
test system in two steps. In the first step, each sub-feeder is
transferred into an equivalent lateral distribution section
with its reliability equivalent [2]. Secondly, load points on
the sub-feeder are attached to its equivalent lateral section
allowing calculation of load points and system reliability
indices SAIDI [1].
Net Present Value (NPV) [12] will be used to capitalize
the cost of energy interruption (ECOST), used with capital
budgeting to calculate the net cost for the optimal
investment.
Main feeder sections of Feeder 4.
Main sections of a sub-feeder F5.
Main sections of a sub-feeder F6.
Minimal cut sets technique.
Disconnects switching.
Mechanical transfer switch.
Automatic transfer switch.
A step-down transformer.
Lateral distributor.
Overhead lines.
Underground cables.
I.
INTRODUCTION
The electrical power distribution system is the final stage
in electricity delivery to end users. The most important
function of a modern electric power system is to provide
electric power to its customer at the lowest possible cost
and with an acceptable level of reliability. Also, reliability
is one of the major factors for planning, designing,
operating and maintaining electric power system [1]. Since
distribution systems account for up to 80 % of all customer
reliability problems, improving distribution reliability is the
key to improve customer reliability [2].
The System Average Interruption Duration Index
(SAIDI) was used to predict the system reliability [3]. The
reliability of power distribution networks can be improved
by reducing the power supply outage duration. In order to
achieve these improvements, in this paper a number of
investment alternatives corresponding to different system
configurations is applied to a test Feeders 4 of Bus6 of
RBTS distribution system [4]. The paper uses the
mathematical programming language (AMPL) software [5]
to reach optimal expected value of SAIDI under budget
constraint.
AMPL is used extensively in many fields of power
system optimization. “Ref. [6]” uses Mixed-integer
quadratic, quadratically constrained, a solver in AMPL as a
second-order cone programming models of distribution
system reconfiguration. Each model can be reliably and
efficiently solved to optimality using AMPL commercial
software. In the course of deriving each model, original
quadratically constrained and second-order cone
approximations were obtain to power flow in radial
networks. “Ref. [7]” presents a complete, quadratic
programming formulation of the standard thermal unit
commitment problem in power generation planning,
together with a novel iterative optimization algorithm,
based on AMPL software for its solution.
II.
DISTRIBUTION SYSTEM RELIABILITY EVALUATION
The reliability of a distribution system can be described
using two sets of reliability parameters. These are the load
point reliability indices and the system reliability indices
[1].
281
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 10, October 2015)
A. Load point reliability indices
The component reliability data of failure rate (λ), outage
time (r) can be used to determine the reliability indices for
the load points [13]. The average failure rate indicates the
number of failures a load point will experience during a
given period of time. The average outage time is the
average duration of failure at the load point. The average
annual outage time (u) is the average total duration of
outage in a year experienced at the load point. These
reliability indices are expected values and represent the
long-run average value.
The solver actually finds an optimal solution to the
problem by reading in the intermediate file produced by
AMPL and applying an appropriate algorithm.
B. System Reliability Indices
Additional reliability indices will be calculated in order
to obtain an overall representation of the systems
performance and their reliability. This paper will
concentrate on SAIDI to measure the reliability
improvements. The mathematical equation for SAIDI is
shown in Eq. (4). Optimization of The customer oriented
index was considered in [1; 13].
SAIDI =
Fig. (1) Function diagram of AMPL modeling language.
III.
AMPL MODELING LANGUAGE
B. Mathematical Programming Solvers
By default the AMPL student edition uses, as solver,
MINOS 5.5, but if the users want to use CPLEX as solver,
they should define CPLEX as their solver using (option
solver cplex ;). CPLEX Solver is used in this paper as– it is
used for solving linear optimization programs (LP’s) and
integer optimization programs (IP’s). It will not solve
nonlinear optimization programs (NLP’s).
The AMPL is an algebraic modeling language for
describing and solving high-complexity problems for largescale mathematical computation and large-scale problems
[5]. It is also, a powerful modeling language for linear,
non-linear, and mixed integer non-linear optimization
problems in discrete or continuous variables.
A. Function Operation of AMPL
A function diagram of how AMPL is operating is shown
in Fig. 1 [14]. To start, AMPL needs a model file, which
describes many of variables, objectives, constraints and
relationships without referring to specific data. AMPL also,
needs a data file for the mathematical model. The model
and data files are fed into the AMPL program, which put
them into an intermediate form that can be read by a solver.
C. AMPL Advantages
One particular advantage of AMPL is the symmetry of
its syntax to the mathematical registration of optimization
problems. An algebraic modelling language allows one to
easily specify and understand objective functions,
constraints and logical relationships among variables.
282
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 10, October 2015)
Familiarity is one of the major advantages of algebraic
modelling languages (i.e. the input format for a math
program in AMPL is more suitable with the way that we
express it on paper). Another advantage is their
applicability to a particularly wide variety of linear,
nonlinear and integer programming models. A modelling
language is designed to express the modeller’s form in a
way that can serve as direct input to a computer system.
Then the translation to the algorithm’s form can be
performed entirely by computer.
IV.
Minimize
Subject to
The objective function can be expressed mathematically
as:
SAIDI =
The constraint can be expressed mathematically as
shown in Eq. (6). The annual outage time of load point can
be expressed mathematically for AMPL software in
constraint part as following:
MINIMAL CUT SET METHOD
In many complex systems, the reliability of the system
can be computed through the reliability of the components
along with the system’s structure function. If the exact
reliability is too difficult to compute explicitly, reliability
bounds might be achievable based on Minimal Cut Sets
technique (MCs). MCs are the collections of the smallest
component sets that are required to fail in order to fail the
system. MCs can be applied to systems with simple as well
as complex configurations and is a very suitable technique
for the reliability analysis of power distribution systems
[11].
MCs are used to explore the path from each load point to
the supply source. Main sections of a sub-feeder (ex.
SF5Ss) are common part of MCs of any load point on that
feeder. The lateral and distribution transformer of that load
point is to be shunted to SF5Ss or SF6Ss as appropriate.
These MCs are used to build the objective function and the
constraints in AMPL optimization Model file.
V.
SAIDI
VI.
CASE STUDY
The proposed algorithm is illustrated by application on
Feeder 4 of Bus 6 of RBTS as test system. Fig. 2 [2]
represents Bus 6 of RBTS system. The transformers
reliability, customer data, and lines reliability data of feeder
four are extracted from [4, 15].
MCs are used to explore the path from each load point to
the supply source. Main sections of a sub-feeder (ex.
SF5Ss) are common part of MCs of any load point on that
feeder. The lateral and distribution transformer of that load
point is to be shunted to SF5Ss or SF6Ss as appropriate.
These MCs are used to build the objective function and the
constraints in AMPL optimization Model file.
As the student edition of AMPL is limited to 300
constraints, the test system of RBTS is truncated to main
feeder F4 with two sub feeders F5, and F6. The main
sections of the sub-feeders F5, and F6 (SF5Ss, and SF6Ss)
respectively, are given in Table 1.
MATHEMATICAL ALGORITHM
The objective function of AMPL is to minimize SAIDI
for a distribution system given a limited budget and a
number of investment alternatives corresponding to
different system configurations. The constraint for the
objective function is that the cost for all introduced
investment alternatives must be choosing between equal to
or below the maximum budget. In addition to, the annual
outage time of load point can be used for AMPL software
in constraint part.
The role of AMPL technique comes to select the
optimum alternative system configurations which achieve
the minimization of SAIDI. The optimization of SAIDI is
expressed mathematically as:
283
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 10, October 2015)
TABLE I.
MINIMUM CUT SETS OF SUB FEEDER
Sub feeder
F5
F6
Main sections of a sub-feeder
{L53},{L54},{L56},{L57},{L58}
{L50},{L51},{L52}
The reliability parameters of the sub feeders are given in
Table 2, the new system (Feeder 4 of Bus 6 of RBTS, with
F7 excluded) is shown in Fig. 3.
Fig. (2) Practical Distribution of Bus 6 of RBTS.
Fig. (3) Practical Distribution of Bus 6 of RBTS.
284
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 10, October 2015)
A. Introduction of one manual D.S on Each Main Feeder
Segment: A first alternative or improvement scheme is the
provision of twelve disconnects switching (D.S) at
judicious points along the main OHL feeder. The total
isolation and switching time are designed to be 1 hour.
B. Introduction of two manual D.S on Each Main Feeder
Segment: A second alternative or improvement scheme is
the provision of a dual D.S on each main feeder segment
provided with an alternative power supply. The radial
structure of the standby power is developed on the basis of
the radial structure of the single-loop in order to improve
reliability [4]. The total isolation and switching time are
designed to be 1 hour.
C. Using two Mechanical Transfer Switch (MTS) for OHL
Feeder: The second alternative (2) is used with a
replacement of a manual disconnecting switch to MTS with
a specific value of switching time. The total isolation and
switching time of MTS is 9 minute.
D. Using two Automatic Transfer Switch (ATS) for OHL
Feeder: The second alternative (2) is used with a
replacement of a manual disconnecting switch to ATS
which has a more suitable value of switching time. The
total isolation and switching time of ATS is 5 second.
E. Using two Automatic Transfer Switch (ATS) for UGC
Feeder: The fourth alternative (4) of ATS is used with a
replacement of an overhead line to an underground cable
with a failure rate of 0.04 f/yr. and a repair time of 30 hour.
Suggested alternatives, corresponding investment and
associated action are given in Table 4.
TABLE II.
DISTRIBUTION SUB FEEDER’S RELIABILITY DATA
Sub feeder
F5/ SF5Ss
F6/ SF6Ss
Reliability data of main sections of
sub-feeder
λ (f/yr)
r (hr)
u (hr/yr)
0.8645
5
4.3225
0.5525
5
2.7625
Now, final MCs are given in Table III. Main feeder (F4)
sections (MFSs) include L35, L36, L37, L38, L39, L40,
L42, L44, L45, L46, L48, and L49 and load point branches
may be either connected to it either with a lateral
distributor (LD) and a step-down transformer (TR) or with
a step down transformer (TR) only as detailed in Table 3.
TABLE III.
MINIMUM CUT SETS FOR EACH LOAD POINT
Number of load point
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
VII.
Minimum cut set
{MFSs}, {TR}
{MFSs}, {TR}
{MFSs}, {TR}
{MFSs}, {TR}
{MFSs}, {TR}
{MFSs}, {TR}, {LD41}
{MFSs}, {TR}, {LD43}
{MFSs}, {TR}
{MFSs}, {TR}, {LD47}
{MFSs}, {TR}
{MFSs}, {TR}, {SF6Ss}
{MFSs}, {TR}, {SF6Ss}
{MFSs}, {TR}, {SF6Ss}
{MFSs}, {TR}, {SF5Ss}
{MFSs}, {TR}, {SF5Ss}, {LD55}
{MFSs}, {TR}, {SF5Ss}
{MFSs}, {TR}, {SF5Ss}
{MFSs}, {TR}, {SF5Ss}
TABLE IV.
THE INVESTMENT ALTERNATIVES NUMBERS, COST, AND ACTION
Investment
alternatives, Ninv
A
INVESTMENT ALTERNATIVES
During an operating and a planning period, the
distribution system operator (DSO) may face some
identified alternatives to improve supply reliability to
customers (decrease the expected SAIDI or other indices of
reliability as much as possible). Each alternative is requires
certain investment to realize. However the total allocated
budget is limited and defined.
The objective function of reliability improvement
alternatives in an optimization problem (minimization of
SAIDI) subjected to the constraint: The investment in any
alternatives must be equal to or below the maximum budget
of $6000000. The alternatives to be implemented in this
work are as following:
285
Investment,
($)
550,000
B
1,150,000
C
1,725,000
D
2,300,000
E
6,500,000
Associated action
Introduction one manual
D.S on each main feeder
segment.
Introduction two manual
D.S on each main feeder
Segment.
Introduction two (MTS)
for OHL feeder.
Introduction two (ATS)
for OHL feeder.
Introduction two (ATS)
for UGC feeder.
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 10, October 2015)
VIII.
This paper uses AMPL software to build an algorithm to
optimize SAIDI for a distribution system given a limited
budget and a number of investment alternatives
corresponding to different system configurations. Five
alternatives for optimizing of SAIDI were applied to the
test system. The procedure is illustrated by application on
Feeder 4 of Bus 6 of RBTS test system. Reliability
parameters of the system components needed for the
AMPL Data file are obtained through simulation of the
different system configuration on NEPLAN software.
INVESTMENT NET PRESENT VALUE
Net present value (NPV) approach is used to capitalize
the annual expected interruption cost over a time period T
of project [11]. Adding investment to capitalized ECOST
to get total capital cost (TCC) of the project alternative
given by Eq. (11).
REFERENCES
IX.
[1]
RESULTS
The objective function of AMPL is to minimize SAIDI
for a distribution system given a limited budget and a
number of investment alternatives corresponding to
different system configurations. AMPL selects the best
configurations from the available alternatives having
minimum SAIDI and satisfying constraints. AMPL outputs
include the corresponding SAIDI, EENS, ECOST, and
TCC as shown in Table 5. The binary variable =1 (output
of AMPL), indicates acceptance of project alternative and
=0, means rejection of project alternative.
[2]
[3]
[4]
[5]
TABLE V.
INVESTMENT ALTERNATIVES DECISION, EENS, ECOST, TCC, AND
SAIDI
Alter
EENS
(Kwh/yr)
ECOST
($/yr)
TCC
($)
SAIDI
(hr/cust.yr)
[6]
SAIDI
(NEPLAN)
(hr/cust.yr)
A
1
36096.1
360,961
3,295,500
8.73942
8.73457
B
1
21894.8
175,159
2,482,270
5.2952
5.29447
C
1
16262.8
97,577
2,467,180
3.7846
3.787365
D
1
15285.3
45,830.1
2,648,590
3.5182
3.523868
E
0
26550.2
265,502
8,519,430
4.9152
4.95929
[7]
[8]
[9]
[10]
AMPL chooses project alternative 4) as the optimum one
to implement. However it is left to DSO to choose another
project alternative for implementation from the accepted
ones, since alternative 3) for example, produce only 7.57%
increase of in SAIDI but with a reduction of 6.85% in the
total capital cost.
X.
[11]
[12]
[13]
CONCLUSION
[14]
This paper studies planning of electric power
distribution systems securing maximum reliability to
customers at constrained budget allocated to the utility.
[15]
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