Proceedings of the 8th WSEAS International Conference on ELECTRIC POWER SYSTEMS, HIGH VOLTAGES, ELECTRIC MACHINES (POWER '08)

Monte Carlo Simulation to Evaluate the Reliability Improvement with

DG connected to Distribution Systems
FANGXING LI1 and NURA SABIR1
1
Department of Electrical Engineering and Computer Science
The University of Tennessee
1508 Middle Drive, Knoxville TN 37996
USA

Abstract: - This paper models the impact of distributed generation to distribution system reliability using a
comprehensive, sequential Monte Carlo simulation model. Since utility-connected distributed generation is
typically installed close to the consumers, it can reduce the current at the main feeder. Consequently, it
increases the chance that a stressed feeder can be reconfigured under a fault at a neighboring feeder. As a
comparison, it may be impossible to reconfigure feeder connection because reconfiguration will lead to line
overflow without distributed generators to supply part of the load. Test results from a system modified from
the IEEE 34-bus system are presented. It is shown that installation of distributed generators can improve the
distribution system reliability considerably.

Key-Words: - Distributed Generation, Distribution Reliability, Monte Carlo Simulation, Reconfiguration.

1 Introduction SAIDI indicates the time-span of the interruption for

Distribution system reliability is an important the average customer during a specified amount of
measure of utility performance. In order to quantify time. The formula for SAIDI is
the reliability of the distribution system metrics
SAIDI =
∑ Customer Interrupte d Duration (2)
known as reliability indices are used. The indices are Total Number of Customers Served
statistical collections of reliability data, they are
used as way to assess the effectiveness the However, CAIDI and ASAI can be obtained from
distribution system to supply power to the customer SAIFI and SAIDI, as shown below:
continually [1-2]. Reliability indices can be placed
SAIDI
in two categories, local indices or load point indices, CAIDI = (3)
and global or system indices. Load point indices SAIFI
measure the impact to the individual customer, 8760 − SAIDI
ASAI = (4)
while the system indices measure the overall 8760
reliability of the system [3]. This paper focuses on Therefore, this paper will focus on the
the system indices mainly from the utilities’ discussion of SAIFI and SAIDI since CAIFI and
viewpoint. Despite many different reliability indices, ASAI can be derived easily from SAIFI and SAIDI.
a survey [5] shows that there are four most popular On the other hand, there is an increasing interest
ones, System Average Interruption Frequency Index to install distributed generators (DGs) in the system.
(SAIFI), System Average Interruption Duration Typically the DG units are gas turbines powered by
Index (SAIDI), Customer Average Interruption synchronous generators, wind powered induction
Duration Index (CAIDI), and Average Service generators, fuel cells, hydro, and photovoltaic [6-7].
Availability Index (ASAI). The definition of these They offer various applications as well various
indices can be found in many literatures such as [1- benefits such as backup generation, peak shaving,
5] and briefly reviewed below. net metering, voltage support, energy-loss reduction,
SAIFI indicates how often an average customer release of system capacity and improvement in
experiences an interruption for a specific amount of reliability [6-8]. This research seeks to explore how
time. The formula for SAIFI is distributed generation will affect reliability. Some
recent work [6, 9] develops a model for evaluate the
SAIFI =
∑ Total Number of Customer Interrupted reliability impact from distributed generation based
Total Number of Customers Served (1) on average reliability data. However, this work
presents a comprehensive sequential Monte Carlo

ISSN: 1790-5117 177 ISBN: 978-960-474-026-0

Proceedings of the 8th WSEAS International Conference on ELECTRIC POWER SYSTEMS, HIGH VOLTAGES, ELECTRIC MACHINES (POWER '08)

simulation model to address line capacity limit, parameter called mean time to switch (MTTS),
time-varying load, and distributed generation. which is not addressed here since we consider the
This paper is organized as follows: Section 2 future distribution system will be highly automated
presents the basic algorithm to perform the and this automatic switching will significantly
distribution reliability evaluation with Monte Carlo reduced the interruption time such that it will not be
simulation (MCS); Section 3 presents the detailed classified as a sustained interruption. Therefore, it
comprehensive MCS simulation model considering does not affect SAIFI and SAIDI, which are two
line capacity limit, time-varying load and the indices related to sustained interruption. In addition,
distributed generation. Section 4 presents a test the focus of this paper is to compare the reliability
based on a system modified from the IEEE 34-bus indices with or without DGs. It is reasonable to have
distribution test system. Section 5 presents this assumption, which is applied to both cases (with
conclusions, and Section 6 provides some and without DG).
discussions about possible future works.
2.2 Artificial component operation history
A critical requirement in sequential Monte Carlo
2 Basic Model for Monte Carlo simulation is to create the artificial history of faults
Simulation for Distribution Reliability for each component. It is the applied to identify the
occurrence of contingencies and its impact to power
Reliability assessment for distribution system can be
supply.
based on analytical simulation or Monte Carlo
The artificial history is a two-state model, either
simulation (MCS). The former is for the average
the component is energized and in the up state or it
case (or year if the during of one year is considered)
is de-energized and in the down state. The up state
based on average component failure rate and
is referred to as the time to failure (TTF) and the
average repair/switch time. Hence, it gives the mean
down state is referred to as the time to repair (TTR)
value of reliability indices like SAIFI and SAIDI. As
or time-to-switch (TTS). Since here we assume
a comparison, MCS first creates an artificial,
switching is automatic and instantaneous, so only
random operational history which is also based on
TTF and TTR is considered. The transition between
the average component failure rate and average
the two states is referred to as the failure process
repair/switch time. However, since it generates an
[11]. As previously mentioned this process is
artificial history, variation of different cases (bad
random therefore there is a need to use random
years, average years, or good years) will all
variables. Random values are generated between
presented in the sample years of MCS, with different
[0,1] to calculate TTF and TTR for each component.
probability. Hence, it gives a probability distribution
of reliability indices, from which the mean value and ln (U i )
TTFi = − × 8760 hours (3)
the standard deviation can be obtained. λi
It should be noted that although Monte Carlo
TTRi = − ln (U i ) × MTTRi hours (4)
simulation may be performed non-sequentially via
some simplification [10], this work focuses on where λi =failure rate (1/yr)
sequentially MCS due to its strong modeling MTTRi=mean time to repair (hour)
capability.
In this section, first, the component model is Fig. 1 shows the typical up down operating
discussed. Second, the artificial random failure and history of components.
repair history of all components are presented.
Third, the impact to customer interruption is
presented. Here, the reconfiguration is considered.
However, the capacity limit of distribution feeders is
not considered in this Section.
1

TTF
2.1 Component Reliability Model TTR
The reliability-related parameters that describe the 0

characteristics of each component need to capture all Fig. 1: Component up down operating history
requirements critical to the systems reliability while
remaining as simple as possible. The two parameters It should be noted that multiple, overlapping
that are used in this model are the failure rate (λ) and failures at different component may occur, although
mean time to repair (MTTR). There is another very rarely. This work considers this case and the

ISSN: 1790-5117 178 ISBN: 978-960-474-026-0

Proceedings of the 8th WSEAS International Conference on ELECTRIC POWER SYSTEMS, HIGH VOLTAGES, ELECTRIC MACHINES (POWER '08)

impact of multiple, overlapping component failures searching algorithm are implemented based on the
will be considered jointly. For instance, if the algorithms described in [1].
system is already experiencing a fault and the The above process is applied to every hour. In
duration time is predicted to be four hours and then continuous hours, if there system state is the same
another fault is predicted with a duration time of (such as the same component is out of service), then
seven hours when the system has already been down the above process does not need to be repeated. The
for three hours, then duration time is extended by previous hour results will be simply used. In other
seven additional hours, instead of becoming words, the above process needs to be performed
operational after one more hour, the system will be only if the system state changes such as a fault
down for a total of 8 hours. occurs after the normal state or the repair is done
This is an advantage of MCS compared to the after the fault.
analytical simulation for an average case, which
typically consider a single component failure once a 2.3 Monte Carlo simulation procedure
time, and then accumulate the impact from each considering reconfiguration
individual component failure. Thus, analytical The generic process of Monte Carlo simulation can
simulation does not consider possible overlap of be briefly described as follows:
component failure duration. 1. Start with the first sample year.
2. An artificial, hourly history of faults is generated,
2.3 Customer interruption due to a as shown in Section 2.2.
component failure 3. Starting at time zero (first hour), identify location
When a component fails due to a sustained fault (as of the faults.
assumed here for illustrative purpose), a portion of 4. Apply the steps in Section 2.3 to identify the
the system will be out of service and the customers interrupted customers.
will experience an interruption. Assume the failed 5. Return to Step 2 until each hour in a year has
component, C, has a repair time of TTRC. The been analyzed.
typical process is described as follows [11]: 6. Perform an accounting to obtain the total
a. Fault isolation: An upstream search is performed interrupted customer-times and total interrupted
to find the nearest protection or reclosing device, customer-hours. Then, SAIFI and SAIDI can be
P, which operates to isolate the fault. calculated for this sample year.
b. Upstream isolation: If there is at least one 7. Return to Step 1 until pre-determined stopping
switching device between P and C, the one closest criteria is met, typically after a predefined
to C will be opened to isolate the faulted number of iterations such as 5000 times.
component. Since we assume all switches 8. Aggregate calculated reliability indices to
including this one, S, is automatic, no sustained produce probability distribution.
interruption will be experienced at customers 9. Repeat Steps 2-11 for the following sample year
between P and S. Although they will experience till reaching a pre-determined number of sample
momentary interruptions, this paper addresses the years.
indices related to sustained interruption (SAIFI
and SAIDI), which are more popularly adopted.
c. Downstream restoration through reconfiguration: 3 Comprehensive model of Monte
If there is an alternate power source through a
normally open switch (NOS) and there is another
Carlo simulation
The downstream restoration through reconfiguration
normally closed switch (NCS) between NOS and
has been an effective approach to minimize the
C, all components between two switches will not
impact of component failure and to improve system
experience a (sustained) interruption due to the
reliability. However, this is an increasing concern
assumption of automatic switching for
about whether the reconfiguration will lead to line
reconfiguration.
overload or not, especially in developing areas with
d. All isolated and unrestored components (including
more stressed distribution feeders. With a decreasing
load points) experience a sustained interruption of
line capacity margin, sometimes reconfiguration
TTRC.
may not be possible if reconfiguration may cause the
line flow violating the capacity limit. Therefore, a
In the above steps, upstream searching and
check of line capacity needs to be performed in the
downstream searching are needed. Details of the
simulation before the reconfiguration is performed.

ISSN: 1790-5117 179 ISBN: 978-960-474-026-0

Proceedings of the 8th WSEAS International Conference on ELECTRIC POWER SYSTEMS, HIGH VOLTAGES, ELECTRIC MACHINES (POWER '08)

Then, the check of line capacity calls the need and each load point has a different load curve with
of the actual chronological load model to assist with an associated peak load value and average load
the line capacity check. value. Load profiles vary from hour to hour, from
With distributed generators embedded in the day to day, from year to year, and from season to
feeders, it will reduce the line flow in general, since season. In addition to the load curve that is assigned
it can back feed a portion of the load from the to each load point there is a certain amount of
customer side. This will make reconfiguration more customers that are assigned. Since this data is not
possible, especially under the stressed feeders or the provided in the test system, the number of customers
peak load hours. at each load point is calculated based on the average
With these factors considered, the step C in value at the load point divided by a presumed 8kVA
Section 2.2 should be modified to include an for each customer. The load curves at each load
additional step to check whether the line flow (if point that were used for in this work are shown in
reconfigured) will violate the line capacity limit or Fig. 3. And the peak load and average load at all
not. Certainly, the actual model should be a line load points are shown in Table 1.
flow calculation. However, a full line flow for each Each system has a total of two 1MVA,
hourly simulation in MCS will be too costly in terms automatically controlled distributed generators each
of computational time. Therefore, a simplified load connected by a normally open switch.
flow is used. Basically, the losses will be ignored. The results are shown in Figs. 4-7. It is clearly
And, the line flow will be a topological search to shown that the installation of DG can reduce the
accumulate all loads. The accumulated load of the reliability indices by 20%, which is
main feeder (after pre-assumed reconfiguration) will (15) [7]

be used to verify whether the line flow limit will be 29

violated or not. Since line losses are typically 5-10%

28
(68) [2]

12 27

in distribution feeders, this should not have a

(34) [6]
1
11 24 26
25 30 31

significant impact to the result accuracy. Again, the 2

3 4 5 7 8 9
10
13 14
(30)
23
21 22
(5)
32

main focus of this paper is to look at the difference

Recloser [5]
Circuit [3] 33

Recloser
Breaker 20
6 15
(16) [8]

of reliability for two cases: with DG or without DG.

DG
34
DG 19
[1] (10) (33)

Then, any assumption equally applied to both cases

16 17 18 [4]

should not affect much of result accuracy. [ ] Load Point

( ) Number of
(23) [10]
35 n.o

With the above details, the proposed model Customer

44
36

becomes a comprehensive, sequential Monte Carlo (7) [15]

43

simulation model that address line capacity limit,

60 42
69 (10) [11]
41
59 46

time-varying load, and distributed generation, which

45 40 39

68 58 47 37
67 66 65 63 62 61 57 56 (17) 48 49 (11)

makes this work different from the previous works. Circuit

Recloser [14] [12]
38
Recloser

Breaker
64 50
55 (3) [9]
DG
DG 51
(8) [16] (2.5)
54 53 52 [13]

4 Test system and results Fig. 2: Test System Modified from the IEEE 34-
Figure 2 shows the test system that was modeled. node Test System
IEEE 34-bus distribution system was duplicated and
tied together using a normally open switch. This
configuration allows for each individual system to 1000

serve as a backup source if needed, which would 900

potentially improve reliability. This is a typical 800

configuration for many urban distribution systems. 700

Also, each feeder has a recloser around the mid- 600

Load KVA

point such that it can isolate the fault to smaller area. 500

The line reliability data is created based on typically 400

component reliability data given in [1]. 300

The test system is sufficiently small to permit 200

the execution of reliability calculations with 100

reasonable computation time but attempts to have 0

0 1000 2000 3000 4000 5000 6000 7000 8000 9000
enough detail to represent a practical system. The Time (hours)

system supplies different combinations of time

varying loads. The test system has 16 load points Fig. 3: Load Curves for 16 Load Points on Test
System

ISSN: 1790-5117 180 ISBN: 978-960-474-026-0

Proceedings of the 8th WSEAS International Conference on ELECTRIC POWER SYSTEMS, HIGH VOLTAGES, ELECTRIC MACHINES (POWER '08)

Table 1: Peak value, average value, and number of

customers of each load point
SAIDI without DG with Reconfiguration
0.35
Load Peak Load Average Load Number of
Point (KVA) (KVA) Customers 0.3

1 145.7 81.02 10
0.25
2 893 543.97 68
3 505 242.61 30 0.2

Probability
4 569 260.33 33 0.15

5 72.85 40.51 5 0.1

6 446.5 271.98 34
0.05
7 252.5 121.31 15
8 284.5 130.17 16 0
10 15 20 25 30 35 40 45 50 55
Time (hours)
9 48.57 27.01 3
297.67 181.32 23
Fig. 6: Probability distribution of SAIDI for the case
10
without DG
11 168.33 80.87 10
12 189.67 86.78 11 SAIDI with DG 1MVA
0.35
13 36.43 20.26 3
14 223.25 135.99 17 0.3

15 126.25 60.65 7 0.25

16 142.25 65.08 8
0.2
Probability

SAIFI without DG with Reconfiguration 0.15

0.1
0.3

0.05
0.25

0
0.2 10 15 20 25 30 35 40 45 50 55
Probability

Time (hours)

0.15 Fig. 7: Probability distribution of SAIDI for the case

0.1
with DG

0.05

0
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5
5 Conclusion
Time (hours) This work models the impact of distributed
Fig. 4: Probability distribution of SAIFI for the case generation to distribution system reliability. Since
without DG utility-connected distributed generation is typically
installed close to the consumers, it can reduce the
SAIFI with DG 1MVA current at the main feeder. Consequently, it
increases the chance that a stressed feeder can be
0.3 reconfigured under a fault at a neighboring feeder.
As a comparison, it may be impossible to
0.25
reconfigure feeder connection because
0.2 reconfiguration will lead to line overflow without
Probability

distributed generators to supply part of the load.

The reliability assessment in this work is carried
0.15

0.1 out with a comprehensive sequential Monte Carlo

simulation. The factors considered include time-
0.05
varying load model, reconfiguration possibility
0 check with a simplified load flow, the impact of DG
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5
TIme (hours) in improving the reliability since more
Fig. 5: Probability distribution of SAIFI for the case reconfiguration is possible because of DG’s back
with DG feed capability. This comprehensive, sequential

ISSN: 1790-5117 181 ISBN: 978-960-474-026-0

Proceedings of the 8th WSEAS International Conference on ELECTRIC POWER SYSTEMS, HIGH VOLTAGES, ELECTRIC MACHINES (POWER '08)

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ISSN: 1790-5117 182 ISBN: 978-960-474-026-0