1. 1
Abstract—This paper contains the various methodologies
developed to evaluate the impact of La Electricidad de Caracas
(EDC) investments on the quality of the electrical distribution
service. In order to do this, we analyze two of the three aspects in
the Venezuelan Electrical Distribution Service Quality Standards
(NCSD in Spanish): the Quality of the Technical Product and the
Quality of the Technical Service. The various methodologies are
designed to analyze circuits that have quality-related problems in
order to obtain the investments needed to minimize penalties,
while maintaining the highest possible level of revenues for the
company. Each quality aspect is thoroughly analyzed and
expressed in mathematical terms to support the computer model
Index Terms —Investments, Penalties, Quality, Regulation.
I. INTRODUCTION
A Electricidad de Caracas (EDC) is a private utility,
owned by the AES Corporation, which serves the
metropolitan area of the greater Caracas in Venezuela. It is a
vertically integrated company, serving about a million
customers, counting with about 2.949 km of underground
cables and 3.089 km of overhead wires, with voltages ranging
from 5 kV to 230 kV.
The work reported here [1] originated in the need
confronted by AES-EDC to develop some practical and simple
algorithm to assist in the decision making process, associated
to new power quality regulations, derived fines and
subsequent investments. It is a first approach to the solution of
a problem not fully solved in the literature.
The quality of the electrical distribution service is gaining
importance as customer needs evolve and the structure of the
sector changes. The nature of monopoly in the electric
distribution service, makes it necessary to implement proper
regulations. Several countries are now applying these
regulations [2], coinciding with restructuring processes across
the world.
The first stage of implementation of the Venezuelan
Electrical Distribution Service Quality Standards (NCSD in
_____________________________
E. Audiche, La Electricidad de Caracas AES, Caracas 1010-A, Venezuela
(e-mail: eduardo.audiche@aes.com).
J.F. Bermudez, Universidad Simón Bolívar, Caracas 1080, Venezuela (e-
mail: j.f.bermudez@ieee.org).
R.M. Luy, La Electricidad de Caracas AES, Caracas 1010-A, Venezuela
(e-mail: ricardo.luy@aes.com).
Spanish) came into force on August 23, 2004 [3].
These regulations approach the quality of electrical
distribution service from various points of view, such as
continuity of supply (Quality of Technical Service: duration
and number of interruptions); wave quality (Quality of
Technical Product: voltage level, quick voltage disturbances
and harmonic content); customer care (Quality of Commercial
Service: waiting period for new connections, delays in
problem-solving process, reconnections, billing errors, etc.).
These new regulations induce distribution companies to make
investments in order to maintain an adequate Quality of
Service level. Otherwise, sanctions will be imposed and this
could compromise the profitability of the business.
Meanwhile, the regulations should consider an adequate
level of profitability for distribution companies, while
establishing the commitment of setting adequate tariffs for end
users. However, because of this sudden change in the
regulations in Venezuela, distribution companies must
restructure themselves based on a model company, whose
efficiency allows for lower costs with maximum profitability,
if they are to successfully face the increasingly strict measures
imposed by the Regulator. It is difficult to find a balance
between the investments that a distribution company needs to
make to improve the power Quality and the fines that it is
willing to face if it does not meet the standards. From a merely
theoretical point of view, making the optimum level of
investment means knowing the cost involved in supplying
electricity with -or without- a certain degree of quality. In this
context, the AES-EDC company is attempting to find a tool
that will help to solve these significant paradigms. It also
needs to prioritize the investments that must be made with the
aim of guaranteeing coverage of demand, under reliable, safe
operating conditions, while avoiding potential sanctions. With
this goal in mind, we have developed a methodology to cover
all the quality-related aspects.
II. QUALITY OF THE TECHNICAL PRODUCT
A. Addressing voltage deviations with the use of capacitors.
In addition to increasing voltage levels, capacitors are
justified because they can reduce power losses [5]. This means
that lesser investment is required or that investments may be
postponed, and that energy is generated at a lower cost.
Figure 1 below shows how this improvement in voltage level
A Practical Formulation to Relate Power Quality,
Regulation, Penalties and Investments in the Caracas
(Venezuela) Metropolitan Area
L
1-4244-0288-3/06/$20.00 ©2006 IEEE
2006 IEEE PES Transmission and Distribution Conference and Exposition Latin America, Venezuela
Senior Member, IEEE, and R. M. LuyE. Audiche, Member, IEEE, J. F. Bermudez,

2. 2
is obtained by means of a phasor diagram [5].
Fig. 1. Phasor Diagram showing the effect of capacitors
IBANK is the capacitive reactive current injected the bank, IQ
is the inductive reactive current of the line, IP is the active
current of the line, I is the complex current without the effect
of the capacitor bank and INET is the complex current with the
effect of the condenser bank.
From this diagram, we can deduce that:
QP jIII −= (1)
BANKQPNET jIjIII +−= (2)
Assuming that L represents the length of the line, while R
and X are the resistance and reactance, respectively, per unit
length:
)( jXRLZ += (3)
Then, the voltage drop without the capacitor is:
IZV .=Δ (4)
Replacing both terms and ignoring the imaginary part:
)..( QP IXIRLV +=Δ (5)
Now, introducing the effect of the capacitor:
NETNET IZV .=Δ (6)
)...( BANKQPNET IXIXIRLV −+=Δ (7)
Subtracting equation (7) from equation (5):
NETONCONTRIBUTI VVV Δ−Δ=Δ (8)
BANKONCONTRIBUTI IXLV ..=Δ (9)
Where:
LLN
BANK
kV
k
I
3
var
= (10)
Where kvar is the capacity of the capacitor bank.
It must be pointed out that the dimension of expression (10) is
designed to introduce the capacitor bank capacity in kilo-Volt-
Ampere-Reactive and the line-line nominal voltage in kilo-
Volts. When we substitute the aforementioned expression in
equation (9), we have that:
XL
kV
k
V
LLN
ONCONTRIBUTI .
3
var
=Δ (11)
Equation (11) represents the increase in voltage produced
by the injection of the capacitor bank. Finally, in equation (12)
we obtain the value of the voltage drop with the effect of the
capacitor:
ONCONTRIBUTINET VVV Δ−Δ=Δ (12)
Now, we need to know the voltage increments produced by
capacitor bank on a percentage basis, given that the NCSD
establish maximum voltage variation levels in percentages.
Therefore, we will now calculate the drops in voltage as
percentages by repeating the analysis without the effect of the
capacitor bank and without this effect. We now start with
equation (5) and set the active and reactive current as a
function of the complex current and the power factor angle Φ:
)sincos(. Φ+Φ=Δ XRLIV (13)
Where:
LLNkV
kVA
I
3
= (14)
with kVA as the apparent power of the circuit. Then:
1000
0
LnNV
V
V
Δ
=Δ (15)
In order to be consistent with the previous development, we
will now introduce the value of the line-to-neutral nominal
voltage in kilo-Volts by adding a factor of 103
:
3
10
3
LL
Ln
N
N
kV
V =Δ (16)
Thus, when we substitute in equation (15):
)cos(
).(10 20
0 Φ+Φ=Δ XsenRL
kV
kVA
V
LLN
(17)
When we apply the same procedure to equation (11), we
obtain the value of the contribution of the capacitor bank as a
percentage:
XL
kV
k
V
LLN
ONCONTRIBUTI .
).(10
var
20
0 =Δ (18)
Finally:
ONCONTRIBUTINET VVV Δ−Δ=Δ 0
0
0
0
0
0 (19)
Using equation (19), we are able to determine the capacity
of the capacitor bank that should be installed if we set the
VB
IP
INET
I
-jIQ
j IBANk

3. 3
percentage of the required voltage variation (%ΔVNET) and we
know the existing variation in voltage (%ΔV). With this aim in
mind, we choose a normalized value of kvar for the bank and
we carry out the cost/benefit economic study. Once we decide
the capacity of the bank and the location where it will be
installed (usually at 2/3 of the total length of the feeder [6]),
we can then assess the determine in the system. We can also
indicate the amount of kW that is prevented from being lost in
the line. Thus, we can analyze the benefit of investing with the
added benefit of avoiding fines. This is all done using the Net
Present Value (NPV) methodology. Before entering into the
topic of investments, we will analyze losses in order to
ascertain the savings obtained by installing the capacitor bank.
The level of losses per phase in kW is obtained from the
Joule effect [5]:
3
2
10
.. LRI
Loss = (20)
Where:
I: Current per Phase =>
Φ
=
cos..3 LLNkV
kW
I
cosΦ : Power Factor => ]
var
.[1
kW
k
tg
TOTAL−
=Φ
R: Resistance in ohms per kilometer
L: Length of feeder in kilometers
We will now calculate the energy lost (kWh) throughout the
year using the following expression:
HoursofNLossFlossEner °= ...3 (21)
Where:
2
).(7.0).(3.0 FloadFloadFloss += (22)
Floss: Loss factor for mixed load
Fload: Load factor of the feeder
N° of Hours: 8760 corresponding to one-year period
In order to know the cost of losses, we have to multiply the
energy lost by the average energy price (PPE) [6]:
EnerPPECost fori .)()( = (23)
Now then, when we calculate the cost of energy losses
without the effect of the capacitor bank (Costi) and we find the
cost of energy losses with the effect of the capacitor bank
(Costf), we obtain the total savings in bolivars as a result of
reducing losses. This is:
fi CostCostSavings −= (24)
The cash flow per year will result from the losses and fines
that have been saved minus the operating and maintenance
costs of the bank. The savings in fines will keep increasing in
time because of their reiterative nature. The savings from
preventing losses will also increase because the load factor
goes up as the network load grows. As a result, we obtain a
present value that would tell us if the investment is
worthwhile. It must be pointed out that this investment is
based on the capacity (kvar) of the capacitor bank that is
selected, which in turn depends on the maximum level of
voltage variation that is allowed. This means that, if we invest
less than what is required for a smaller bank, we will be
penalized for lack of quality in the technical product,
providing that the measurements are always made at that
point.
III. QUALITY OF THE TECHNICAL SERVICE
The frequency of interruptions index (FMIK) and the index
measuring the duration of the interruption (TTIK) for Stage 3
of the NCSD [3], are the following:
j
n
i
j
kVAinst
ikVAfs
FMIK
∑ =
= 1
)( (25)
j
n
i
jj
J
kVAinst
iTfsikVAfs
TTIK
∑ =
= 1
)(.)(
(26)
Where kVAfs(i)j represents the nominal kVA out of supply
that correspond to the interruption i on the feeder j; kVAinstj
represents the total nominal kVA installed in feeder j; and
Tfs(i) corresponds to the time the nominal kVA remained out
of service during the interruption i of the feeder j.
A. Circuit sectioning with uniformly distributed loads.
We can discriminate the TTIK index [8] according to the
time employed to locate the failure (TL) and the time spent on
repairing the failure (TR) as follows:
j
n
i
jRjT
j
n
i
jLjT
J
kVAinst
iTikVAfs
kVAinst
iTikVAfs
TTIK
RL
∑∑ ==
+= 11
)(.)()(.)(
(27)
Introducing:
j
n
i
jT
kVAinst
ikVAfs
B
L
∑=
= 1
)(
(28)
j
n
i
jT
kVAinst
ikVAfs
C
R
∑=
= 1
)(
(29)
We obtain:
jRjLJ iTCiTBTTIK )(.)(. += (30)

4. 4
Figure 2 below shows N sectionings in a uniform circuit
(same load for each section):
Fig. 2. Uniform Circuit with N Sectionings.
Now then, with this arrangement, all the load is lost within
the time needed to locate a failure, but not, during the repair
stage, [8] when failure has been isolated, the amount of kVA
that was not being supplied is significantly reduced.
Consequently, if we know the average number of failures
per year in the circuit (F), the maximum demand of the circuit
in kVA (Dmax) and the installed capacity in kVA (Pinst), we
can rewrite the B expression in the following manner:
instP
DF
B
max.
≈ (31)
The reduction of the C factor will depend on the average
number of failures per year of the circuit (F) and this
reduction will vary depending on whether there is an
alternative feeder (AF) able to pick-up the load in the
sections downstream from the failure. Thus, we will identify
the following situations:
a) With interconnection:
kVAinst
kVAinst
NFC withAF
1
.≈ (32)
Therefore:
(33)
With TL and TR being the average time in hours to locate
and repair the failure.
b) Without interconnection:
If there is no interconnection, C factor will depend on where
the failure occurred. This means that, the farther away from
the source the failure is, the less load will be lost. If the failure
rate is the same across the circuit and there are equal loads in
each area, the failures in each area should also be equal to
F/N. Figure 3 below shows an example of this with 4 sections:
Fig. 3. Example of Lost of Load when there is no Alternative Feeder (AF)
Therefore, C factor will depend on the failure rate in each
area and on the load lost in each one.
If we assume N sections, we have that:
⎥
⎦
⎤
⎢
⎣
⎡
++++≈
N
N
NNNN
F
CwithoutAF ...
321 (34)
When we group the first and last term, the second (next-to-
last term), and so on, we have that:
( ) ( )
⎥⎦
⎤
⎢⎣
⎡
+
−+
+
−+
+
+
≈ ...
23121
N
N
N
N
N
N
N
F
CwithoutAF
(35)
Reducing:
⎥⎦
⎤
⎢⎣
⎡ +
=⎥⎦
⎤
⎢⎣
⎡
+
+
+
+
≈
N
NN
N
F
N
N
N
N
N
F
CwithoutAF
1
.
2
...
11 (36)
We then simplify:
⎥
⎦
⎤
⎢
⎣
⎡
+≈
N
FCwithoutAF
2
1
2
1
. (37)
Therefore:
RL
inst
T
N
FT
P
DF
TTIK .
2
1
2
1
..
. max
⎥
⎦
⎤
⎢
⎣
⎡
++≈ (38)
Now then, based on the above, we can construct two
functions: one for reducing the TTIK and another for investing
in sectioning. We can thus obtain an optimal investment value
for the number of sectionings in the circuit when we add both
curves and obtain the minimum value. It must be pointed out
that the solution of this equation will not necessarily result in
no penalties. The fines will depend on the limits set by the
regulator in the NCSD. Therefore, the optimal solution could
contemplate a fine that is acceptable to the utility. The
investment will be determined through the Net Present Value
(NPV) financial methodology. This process will allow us to
determine the profitability of the project and to make
decisions that will result in maximum benefits for the
company. The investment will correspond to the cost of one
sectioning times the number of sectionings that need to be
built:
NCI .sec= (39)
Where: CSecc: Cost of one sectioning
N: Number of sectionings
The net cash flow will result from the fines saved plus the
savings in the energy that would have not been sold if there
were no sectionings, minus the operating and maintenance
costs. So far, an attempt has been made to show how
reliability improves by means of sectionings in the circuit, but
N
TF
T
P
DF
TTIK
R
L
inst
.
.
. max
+≈

5. 5
this segmentation can be obtained with several manual or
automated elements. We will now present a methodology
designed to improve the interruption of service indexes
through the use of supplementary protection.
B. Application of Automatic Reclosers
In Figure 4 below, we assume a feeder equipped with
Reclosers in such a way that there are equal loads and equal
circuit lengths for each of the N sections [7]:
Fig. 4. Feeder Equipped with Automatic Reclosers
With this method, the time used to locate a failure will be
significantly reduced and the faulted section can be
automatically isolated. Similarly to the previous case, this
translates into a lower TTIK in the first addend of the equation
as follows:
a) With interconnection:
In this case, the Recloser automatically isolates the failure
and the circuit can recover the load, regardless of which
section the failure occurred at. Therefore, only the Nth part of
the load is lost. This means that expression B is now the
following:
N
F
kVAinst
kVAinst
NFB withAF =≈
1
. (40)
In addition, C factor remains the same as in the previous
case. Therefore, the TTIK is the following:
N
TF
N
TFTTIK RL
1
.
1
.. .+≈ (41)
b) Without interconnection:
Similarly to the previous case, B Factor will depend on the
section in which the failure occurred at. This means that the
greater the distance between the failure and the source, the less
load will be lost. If the failure rate is the same across the
circuit and the loads are the same in each area, the failures in
each area will also be equal to F/N, and we will have that:
⎥
⎦
⎤
⎢
⎣
⎡
++++≈
N
N
NNNN
F
BwithoutAF ...
321 (42)
When we apply the same reduction as in the previous case,
we obtain:
⎥
⎦
⎤
⎢
⎣
⎡
+≈
N
FBwithoutAF
2
1
2
1
. (43)
C factor remains unchanged and the find expression is as
follows:
⎟
⎠
⎞
⎜
⎝
⎛
++⎟
⎠
⎞
⎜
⎝
⎛
+≈
N
T
N
F
N
T
N
F
TTIK RLJ
2
1
2
1
2
1
2
1
.. (44)
In addition, since the Reclosers are automatic, the median
frequency of interruption FMIK is also reduced. This is
because the section with the failure is instantly isolated and,
given that the interruption is less than one (1) minute, it will
not be accounted for in those sections that automatically
recovered the load. According to equation (5) and recalling
that we are assuming a circuit with a uniformly distributed
load, the expression for FMIK, can be represented in two
different manners:
a) With interconnection:
The treatment is similar to the one given to the TTIK
because, since there is an alternative feeder, the circuit will
recover all the lost load after isolating the failure. Therefore,
the FMIK will count only the section with the failure,
according to the following equation:
kVA
kVA
NFFMIK
.
1
.≈ (45)
Therefore:
N
FFMIK
1
.≈ (46)
b) Without interconnection:
The result here is similar to the previous cases in which
there is no interconnection. The expression will depend on the
section in which the failure occurred. This means that, the
farther away from the source the failure is located, the lesser
the amount of load is lost. If the failure rate is the same across
the circuit and there are equal loads in all the areas, the
failures in each area will also be equal to F/N. Therefore, we
have that:
⎟
⎠
⎞
⎜
⎝
⎛
+=
⎥
⎦
⎤
⎢
⎣
⎡
+++
≈
N
F
kVA
kVA
N
N
kVA
N
kVA
N
N
F
FMIK
2
1
2
1
.
.....
2
.
1
(47)
It is important to remember that, in all the previous
expressions, N represents the number of sections in the circuit.
Therefore, when we speak of one (1) Recloser, we assume two
(2) sections (2N); when we have two (2) Reclosers, we assume
four (4) sections (4N), and so on.
It must be pointed out that, according to the Venezuelan
NCSD, the FMIK indicator will be used until the third stage
(12/31/07) of the process to compensate customers who
receive low-voltage service.
Those customers who receive medium- and high-voltage
service, will be controlled by means of the Frequency of
Interruption per User (FIU) index, which counts all the
interruptions lasting over one minute during the control
period, regardless of the amount of kVAs that were not
supplied [3.]

6. 6
Again, we have a reduction function of the TTIK and the
FMIK which can translate into a penalty function. This
generates a quality vs. cost graph, with a fine curve and an
investment curve.
The investment function is as follows:
RCNI .= (48)
Where:
I = Investment
N = Number of Reclosers
CR = Cost of one Recloser
When we calculate the NPV, we should consider, in the
cash flow, the savings from the absence of fines plus the
savings stemming from the energy that would not have been
sold if we had not made the investment in question, minus the
operating & maintenance costs.
This summary does not include other developments, such as
a Circuit with Recloser and Sectioner or Fuses in the
Branches; a Radial Circuit with Triangular Geometry; Failure
Signaling Equipment; Protected Conductors; and Cable
Replacement [1].
IV. CONCLUSIONS
Currently, there are no straightforward methods that allow us
to estimate the impact that certain investments have on the
quality of the electrical distribution service to some extent.
There is a void in the international literature on the subject.
This paper can be of value for power distribution companies
as Venezuelan electric utilities such as AES-EDC, because it
provides a tool for estimating the impact of investments on the
quality of the electrical distribution service according to the
new Venezuelan regulatory framework. These new regulations
will penalize distribution companies that deliver low-quality
energy and do not meet with the aforementioned regulations.
Regarding voltage variations, our conclusion is that AES-
EDC is, in practice, not violating the limits imposed.
Therefore, more investments can be channeled toward the two
remaining areas. However, the model provides the possibility
of evaluating two of the most important projects in this area.
The application of these projects has advantages in addition to
improving voltage, such as savings in losses (which makes
investing in voltage improvements very attractive for
increasing the profitability of the company).
Little research has been done regarding the impact of
investment on the Quality of Technical Service. We do not
know how to predict a reduction in the frequency and duration
of interruption indicators if investments are made.
Consequently, the model developed in this paper allows us to
know how the TTIK and the FMIK are improved once the
sectioning elements are included in the grid. At the same time,
we can determine which actions lead to the highest levels of
profitability for the business if there is zero investment and a
fine is paid. The results obtained with the model reveal the
need to study the effect of the investment before its is
executed because several runs can show that paying the fine
would be more advantageous than making the investment.
This type of decisions cannot be repeated indefinitely
because of obvious ethical reasons, such as the deterioration of
the grid, and because the utility would have an increasing
breach from the requirements of the Regulator. Nevertheless,
if we obtain this result, we could postpone the investment for a
specific period of time until we have more resources for that
end. Therefore, a major conclusion is that making an
investment is not always the most efficient option and that it is
sometimes better to pay the fine.
Another conclusion is that the frequency and time of
interruption problems are the most important cause of alert
signals as far as fines are concerned. Thus, they should be
considered as the first priority when it comes to making
investments. The assessment of the various projects had
positive results that represent the beginning of a new stage for
the company. Now, AES-EDC is capable of analyzing
investments so as to determine their impact on the quality of
the electrical distribution service before actually making those
investments.
Regarding the Technical Product, we can conclude that
frequent distortions and disturbances, such as harmonics and
rapid variations, represent a broad topic of study that is
anything but trivial. We have mentioned the fact that we
ignore how much the devices used to eradicate these problems
really reduce the disturbance effect. This means that, since we
do not know up to what level harmonics and/or rapid voltage
variations are reduced by the device to be purchased, we
cannot assess the feasibility of the investment summarized in
the profitability rendered by the Investment vs. Fine
comparison.
V. REFERENCES
Audiche, E. Methodology used to determine EDC Investments
on the basis of Electrical Distribution Service Quality
Standards. Universidad Simón Bolívar (USB). Electrical
Engineering Thesis. Caracas Venezuela, 2004.
Rivier,J. Quality of Service. Regulation and Investment
Optimization. Universidad Pontificia Comillas de Madrid.
Escuela Técnica Superior de Ingeniería (ICAI). Doctoral
Thesis, Chapter 5, Spain, Madrid, 1999.
Official Gazette of the Bolivarian Republic of Venezuela, N°
38.006, YEAR CXXXI, MONTH XI, August 23, 2004.
Canabal, C; Cadena, E. Technical Audit of Industrial Electrical
Power Systems. Gráficas Guarino, 1996.
“Applying Capacitors to the Distribution System” (In Spanish).
Item 6 Available at
http://www.ing.unlp.edu.ar/sispot/deeindex.htm.
IIE. Locating and Determining the Steps for Capacitors in
Derivation for Distribution Lines. September – October 2001)
“Efficient Distribution Costs In Venezuela” (In Spanish)
Section 2. Unit costs per SDT. FUNDELEC, MEM, Stone &
Webster Consultants. January 2002.
Naranjo, A. Distribution Systems. (Guidelines being prepared)
Last Version. Chapter 19. Caracas, Venezuela.
[1]
[2]
[3]
[4]
[5]
[6]
[7]

7. 7
Eduardo Audiche was born in Caracas,
Venezuela, in 1978. Obtained his degree in EE
from the Universidad Simón Bolívar, in March
2004. Since then he is with La Electricidad de
Caracas (AES Company), as a development
engineer in the area of Prices and Regulation.
Juan Bermudez was born in Caracas, Venezuela,
in 1947. PhD, is full professor of EE in the
Department of Conversion and Transportation of
Energy, Universidad Simón Bolívar, Caracas,
Venezuela.
Ricardo Luy was born in Vargas, Venezuela, in
1968. EE from the Universidad Simón Bolívar
1993, Master in Energetic Economy and
Environmental Politic, Fundación Bariloche,
Argentina 1999. Director of Prices and Regulation
in La Electricidad de Caracas (AES company).
This paper won the “2005 Student Prize Paper Award in Honor of T. Burke
Hayes” of the Power Engineering Society (IEEE-PES)