A HIGH-PERFORMANCE FAULT LOCATION ALGORITHM FOR SHIPBOARD POWER SYSTEMS

1

A HIGH-PERFORMANCE FAULT LOCATION ALGORITHM FOR

SHIPBOARD POWER SYSTEMS

INTRODUCTION

1.1 History of Ship Power Systems (SPS)

The ship's electric power system was first installed on the USS Trenton in 1883, marking the

beginning of the use of electricity on naval ships. The system is designed to supply power to

247 lights, using direct current (DC) at a voltage of 110 volts.

Figure 1.1 USS Trenton

The history of the development of electric power systems on ships shows a significant

evolution along with increasingly complex operational and technological needs. In the beginning,

until 1914–1917, the ship's electric power system mainly used direct current (DC) to run the

motors and provide lighting. However, during World War I, alternating current (AC)-based

power systems with a voltage of 230 volts and a frequency of 60 Hz were introduced to naval

ships, which was a major step in the modernization of the ship's electrical system.

Another major change occurred after World War II, when the ship's electrical system

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continued to undergo significant improvements. One of the key changes is the adoption of a

4,160-volt high-voltage power system to accommodate the greater power needs of modern ships.

In addition, protective devices are being introduced to monitor important parameters in the

electric power system. The main function of these devices is to determine the optimal system

configuration in order to minimize damage to components, improve the continuity of the power

supply, and maintain the reliability of the system during operation.

In the early days, the protection of the electric power system was carried out using fuses.

However, over time, circuit breakers began to be added to improve the protection capabilities

and flexibility of the system. The end of the 20th century marked an important milestone with the

introduction of electronic solid-state-based overcurrent protective devices. The U.S. Navy

installed the device on a 4,160-volt power system on the Nimitz-class aircraft carriers, marking

the transition to a more advanced and reliable modern power system.

These innovations in electrical systems not only improve operational efficiency but also

provide better surveillance and protection capabilities to meet the challenges of harsh maritime

environments and complex mission demands.

1.2 Structure of SPS System

Power in a Ship Power System (SPS) is generated by several generators that are typically

placed in a ring configuration [1]-[7]. Typically, there are two types of loads in SPS: vital loads

and non-vital loads [1]-[5], [8], [9]. Navigation, communications, operations and weapons are

examples of vital loads while lighting and air-conditioning systems are part of non-vital loads

[1]-[4], [6], [8], [11]. SPS aims to supply energy for both types of loads. In fault conditions, the

system cannot supply electrical energy to the load. SPS requires a comprehensive protection

system to detect the exact location of faults and use several alternative paths to supply energy to

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undamaged loads]. It is important to note that the fault location mechanism does not have to be

as fast as the protective mechanism that disconnects in milliseconds. In contrast, fault location

algorithms capture fault data quickly and try to find faults in a short enough time to direct

electrical power to vital loads. There are three main protection schemes in power systems:

overcurrent, distance, and differential

Ship power systems use a three-phase generator that is in a ring configuration and

generally operates at 60 Hz to generate AC voltage for the system. The generator is in a ring

configuration to have an alternative path for the vital load of the different generators. He allows

the system to supply power to a vital load when the normal path of the main generator is

damaged or destroyed

Figure 1.2 shows a single line diagram of the SPS 11-bus . The system consists of four

three-phase main generators in a ring configuration that operate at 60 Hz. In this system, the vital

load has an alternative path in addition to the normal path of another generator to receive energy

from the source in a disturbance situation. The vital load uses Automatic Bus Transfer (ABT) or

Manual Bus Transfer (MBT) to select the wrong path to receive energy from the generator [1]-

[6], [8]. Under normal conditions the ABT/MBT connects the normal path to the load. When an

error occurs, the ABT/MBT disconnects the normal path and connects the alternate path.

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Figure 1.2 11-Bus SPS

1.3 Distance Protection and Its Drawbacks

Cable lengths in SPS are typically shorter (about 10–200 feet long [11]) than in large

distribution networks and thus small cable impedances (about 0.04/1000 feet

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[11].) Using proximity protection in short-duration power systems is impractical because the

impedance of the cables is too low to be detected with a small error. An improved spacing

scheme can be used to detect faults in short-length cables. The Active Impedance Estimation

(AIE) error location method [13] uses a high-frequency voltage on a bus in an electrical system

and measures the injected current followed by calculating the impedance at that frequency.

Higher frequencies add to the resolution of the cable impedance and make fault location easier in

the ship's power system. In the AIE method when the system is exposed to a fault, a short-

duration voltage will be used to find the visible system impedance of the injection bus and find

the fault. This method is only applied to radial distribution systems. This method uses the

measured impedance value to find errors [13], [15]. Although the available AIEs can distinguish

between distant and close-up faults, they can be used primarily in lateral branches where the

Thevenin equivalent impedance is equal to the cable impedance and proportional to the fault

distance. Thus, in interconnected systems, such as ship power systems with ring topology,

available active impedance estimation methods have topological limitations.

1.4 Overcurrent Protection and Its Drawbacks

Another conventional method of detection and location of faults is the overcurrent

scheme. The main power of the SPS is produced by several generators. Having multiple power

supplies leads to complex overcurrent protection in the system that requires a time delay to avoid

over-tripping [7]. Due to the short length of the cables, SPS is considered a highly coupled

electrical system; That is, if a fault occurs at a single point of the system and rapid detection and

isolation is not provided by the protection system, the fault will spread throughout the system in

a short time and can lead to catastrophic consequences [2]. So, just use

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Conventional overcurrent protection mechanisms are impractical in ship power systems due to

short wiring, time delay requirements, and multiple supplies, which complicates the scheme [7],

[11]. Overcurrent protection, however, can be used as a safety feature to enhance protection

capabilities in addition to other protection schemes.

1.5 Differential Protection and Its Drawbacks

Differential protection schemes, on the other hand, work well in systems with short wires.

Differential relays compare the inlet current to the protected equipment with the current leaving

the equipment. If these two currents are the same, as shown in figure 1.3(a), there is no error.

However, if these two currents are not the same, as shown in figure 1.3(b), which indicates that

there is a fault in the protected equipment, the relay trips [7], [11]. In this method, each piece of

equipment in the SPS requires a differential relay to find faults effectively. In addition, a

comprehensive communication system between all protected zones and related equipment is

required to cover the entire SPS, precisely. The vulnerability of communication systems to errors

greatly reduces the reliability of the system [9], [13]. In addition, this approach is expensive

because it requires many differential relays and a comprehensive communication infrastructure.

Figure 1.3(a) Differential Error Detection (No Error)

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Figure 1.3(b) Differential Error Detection (With Error)

1.6 Proposed Methods

There is a need to develop a more efficient fault location scheme to find all faults that

occur in the ship's power system at a low cost. This thesis introduces an economical and reliable

fault location scheme for SPS. This method requires the application of short-duration voltages

with high frequencies under fault conditions and observation of changes in the voltage and

current of the system bus due to faults. Changes in voltage and current at the measurement point

are indicators of location and magnitude of error. Different errors may have the same effect on

the voltage and current at the measurement point. In this case, multi-estimation occurs [14]. As

such, the system requires multiple voltage and/or measurement point applications to have a

unique data set for each fault. The goal is to minimize the number of applications and voltage

measurements and to find its optimal place in the system to uniquely identify each fault. In this

paper, a three-phase symmetrical fault is analyzed; However, the proposed method can be

generalized to other types of errors.

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CHAPTER 2 METHODOLOGY

2.1 Introduction

In this thesis, observations are made on the effect of any error on the voltage and/or

current of a particular set of measurements when a high-frequency voltage is applied to the

system on an injection bus. Relevant terms and definitions are given:

Injection bus: For convenience, here the term injection bus is called the bus where a high-frequency

voltage is applied. There may be several injection buses with different frequencies in SPS.

Measurement bus: The measurement bus is used to handle the bus where the voltage and/or current

is measured. It is important to mention that an injection bus may or may not be the same as a

measurement bus. In addition, more than one measurement bus can be used. In this sense, the

proposed approach generalizes the conventional method of error location of active impedance

estimation [1], [2].

Measurement set: The measurement set refers to the voltage and/or current measurement set on all

buses with specified injection, frequency, and Rfault buses . Measurement sets help compare

measurement results to find unique results and the best combination of injection and

measurement bus for fault locations.

Each error may have a different effect on the voltage or current of a particular

measurement bus. The goal of this paper is to find the optimal place for injection and the

measurement bus to have a unique set of measurements for each error. The unique measurement

is then referred to the specific fault to detect the exact location of the fault.

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Since SPS operates at 60 Hz, voltage applications and voltage/current measurements

must be applied at higher frequencies to avoid interference with the protection system. That is,

superpositions can be used for analysis because the fault location algorithm works separately

from the normal operation of the system. The fault location algorithm does not look at the

voltage generated by the main generator at 60 Hz but can still detect the error.

2.2 Proposed Error Location Algorithm

Suppose I is the bus number that has a voltage application, M is the bus number that has a

measurement, and F is the bus number that is faulty. Then, the ordered triple (I,M,F) represents

the fault detection observation. In this case, V→I,M,F represents the voltage vector of the

measurement bus when the injection is on the I bus, the measurement on the M bus, and the error

on the F bus. If F = 0 it indicates the initial value when there are no errors in the system. A

similar definition is used for I→I,M,F current measurements. The goal is to observe the values of

V→I,M,F and I→I,M,F for all faults, given the measurement and injection bus, and for comparing

value with normal values of current and voltage to see if the fault can be detected. The algorithm

starts from I=1, M=1 and applies a specific error to each bus and observes the voltage and

current changes on the measurement bus. For this purpose, the algorithm calculates ∆V→I,M,F if

I ≠ M, and ∆I→I,M,F if I = M; i.e.,

∆V→I,M,F = V→I,M,F − V→I,M,0

∆I→I,M,F = I→I,M,F − I→I,M,0.

Figures 2.1 and 2.2 show the magnitude and phase angle of V →I,M,F for the simulation

system described in figure 1.2 when I = 10, M = 9, Rfault = 1e−3, and f = 1000Hz for

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different F values (1 ≤ F ≤ 11.) The error sequence with an impedance of Rfault = 1e−3

is applied to different system nodes as shown in the figure and the effect is observed. Figures 2.3

and 2.4 show the magnitude and angle of the I→I,M,F phase for the simulated system when

I = 2, M = 2, Rfault = 1e−3, and f = 1000Hz for different F values (1 ≤ F ≤ 11.) Note

that if I = M, the algorithm considers the current value whereas for I ≠ M considers the

voltage value.

Figure 2.1 The magnitude of V→I,M,F when I = 10, M = 9, Rfault = 1e−3, and f =

1000Hz for different F values

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Figure 2.2 Phase angle →V I,M,F when I = 10, M = 9, Rfault = 1e−3, and f = 1000Hz

for different F values

Figure 2.3 The magnitude of I→I,M,F when I = 2, M = 2, Rfault = 1e−3, and f =

1000Hz for different F values

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Figure 2.4 Phase angle I→I,M,F when I = 2, M = 2, Rfault = 1e−3, and f =

1000Hz for different F values

In a ship's power system if

V→I,M,F−V→I,

M,0

∆V→I,

M,F

I→I,M,F−I→I,

M,0

∆ I → Me

, M, F

||V→

Me,

M,0

| = |

Me,M,0

| or |

|

I→I,M,

0

| = | | <

Me,M,0

|

0.001, ∆V→ and ∆I→ are difficult to detect. Table 2.1 shows the simulation results for the

system presented in figure 1.2 when I = 10, M = 9, Rfault = 1e−3, and f = 1000Hz. The

numbers in Table 2.1 are F-values that indicate which buses are damaged. The highlighted

numbers indicate which bus errors cannot be detected with the selected measurement and

injection buses. In other words,

Error cannot be detected when the relative value | ∆V→ %| = |∆V→

I,M,F |

= |V→I,M,F−V→I,M,0| Lebih

Kecil

I, M, F

|

V→I,M,0

|

|V→I,M,0|

from 0.001 and/or |

∆I→ %| = |∆I→

I,M,F |

=

|

I→I,M,F−I→I,M,0|

less than 0.001.

I, M, F

|I→I,M,0|

13

|I→I,M,0|

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Table 2.1 Detectable and undetectable bus faults when I = 10, M = 9, Rfault = 1e−3, and

f = 1000Hz

Until

#

1 2 3 4 5 6 7 8 9 10 11

Delta

V/I

0.06 0.066 0.02 0.0008 0.069 0.025 0.023 0.064 0.07 0.01 0.0009

The algorithm checks all possible combinations with different values for M, I, and F to

find the optimal bus for injection and measurement that can detect all faults (various fault

impedances.) If one injection and measurement is insufficient to cover the entire system, the

system requires more injection and/or measurement buses to cover all faults. The proposed

approach looks for injection buses and measurements that result in the lowest number of

undetected errors (location and impedance.) Error not detected when

|∆V→

I,M,F

%|

< 0.001,

or

|∆I→I,M,F%|

< 0.001.

Thus, the algorithm finds the case that has the lowest number of undetected errors

with

|∆V→

I,M,F

%|

< 0.001, or |∆I→I,M,F %| < 0.001. For convenience, if the number

of undetected errors is 0 or 1, an injection measurement set consisting of an injection bus and a

selected measurement is selected. Then, the algorithm will check if these cases cause unique

changes to

|∆V→

I,M,F

%|

or

|∆I→I,M,F%|for

different errors. If

|∆V→

I,M,F

%|

or

|

∆I→I,M,F%|

having the same results for different errors (i.e., those that differ less than 0.001,) the

system faces multi-estimation. To check this, the algorithm evaluates

∆V→

I , M , F

%

or

∆I→I,M,F

% for all fault conditions (location and impedance) to find similar pairs (i.e.,

those that differ less than 0.001,) voltage change vectors ∆V→I,M,F % and the

current change vectors ∆I→I,M,F %, given a set of injections and

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measurement bus. In the event of similarities, the injection measurement set cannot offer unique

results for different errors. In this case the system observes multi-estimation.

The next step is to iterate on the algorithm for different combinations of injection and

measurement buses along with (and possibly their frequencies) to find the optimal bus for

injection and measurement in order to cover all errors with the minimum number of injection and

measurement buses and to avoid multi-estimation. The proposed algorithm is depicted in the

flowchart figure 2.5.

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Figure 2.5 Algorithm finds the best injection and measurement placement

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2.3 Error Location Algorithm Using Channel Current Measurement

So far, current measurement is only considered when the injection bus and the

measurement are the same. When the injection and metering buses are different, multiple lines

can be connected to the metering bus with different currents on each channel. Therefore, one

must determine which line is used for measurement. In this thesis, channel current measurements

are used to find faults based on the difference in measured current in faulty and non-faulty

systems. Using the results from voltage and current measurements helps reduce the number of

measuring equipment for the fault location leading to the lowest number of undetected faults. For

this purpose, one needs to measure the current on all the channels connected to the measurement

bus to see which one has the highest variation for the various faults being considered.

Since each bus connects multiple lines together and each of these lines has a different

flow, it is important to know which line to use for the fault location that results in the lowest

undetected error. Start with the naming of the paths connected to each measurement bus from 1

to n where n is the number of lines connected to the selected measurement bus. Note that for a

bus with two channels, only one current measurement is taken because the line has the same

current when the load current is ignored. This procedure is repeated for all measurement buses

(figure 2.6); that is, all power system buses. In the proposed method, the algorithm measures the

current on all channels connected to the measurement bus for different injection buses and

defective buses, then proceeds to the next measurement bus and repeats the same procedure for

the lines connected to that bus until it covers all the measurement buses (the entire system bus.)

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Figure 2.6 11-Bus SPS

Suppose I is the number of the bus that has a voltage application (injection bus), B is the

number of the measurement bus, M is the number of lines connected to the measurement bus B,

and F is the number of the defective bus. In this case I→I,B,M,F represents the current vector

measured on the measurement bus B. If F = 0 it indicates a value that is not false; that is, when

there is no error in the system. The purpose is to observe the value of I→I,B,M,F for all errors,

remember the measurement, and to compare its value with the normal value of the current to see

if the error can be detected. The algorithm starts from B=1, I=1, M=1 and applies certain

errors to each

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and observe the current changes in the measurement bus. For this purpose, the algorithm calculates

∆I→

I,B,M,F

;

That is

∆I→I,B,M,F = I→I,B,M,F − I→I,B,M,0.

In a ship's power system, an error cannot be detected when the relative value

of |∆I→

I,B,M,F

%|

which is the same as |∆I→I,B,M,F| = |I→I,B,M,F−I→I,B,M,0|, less than 0.001.

|Me→I,B,M,0| |ME→ME,B,M,0|

The algorithm checks all possible combinations with different values for, I, B, M, and F

to find the optimal bus for injection and optimal line current measurement that can observe all

errors (various fault impedances.) If one injection bus and measurement bus are insufficient to

cover the entire system, the system requires more injection and/or current measurement buses

from the measurement bus or even more measurement buses to cover all faults. The proposed

approach seeks a set of injection and measurement buses that results in the lowest number of

undetected errors (location and impedance.) An error is not detected when

|∆I→I,B,M,F %| < 0.001. The algorithm evaluates all injection buses and measurements to

cover the entire system.

Once the algorithm finds the case that has the lowest number of undetected errors with

|

∆I→

I,B,M,F

%|

< 0.001, it will check if these cases cause unique changes to

|∆I→I,B,M,F

%|for

different faults with the selected measurement and injection bus. If

|∆I→

I,B,M,F

%|

having the same results for different errors (i.e., those that differ less than 0.001,) the system

faces multi-estimation. To check this, the algorithm evaluates

∆I→

I,B,M,F

%

for all fault

conditions (location and impedance) to find similar pairs (i.e., those that differ less than 0.001,)

of current change vectors

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∆I→

I,B,M,F

%,

given a set of injection and measurement buses. One has to iterate on the algorithm

to

Combinations of different injection and measurement buses (and possibly with different injection

frequencies) to find the optimal bus for injection and measurement in order to cover all errors

with the minimum number of injection and measurement buses and to avoid multi-estimation.

The proposed algorithm is illustrated in the flowchart figure 2.7.

Figure 2.7 Algorithm finds the best injection and measurement placement by Using Current

21

Measurement

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ARTICLE 3

INJECTION FREQUENCY EFFECT

3.1 Introduction

Using standard error analysis, one can find ∆V and ∆I for the proposed fault location

algorithm based on the Zbus matrix elements. To find the relationship between the

injection frequency and the location of the fault, one needs to trace the effect of the frequency in

the Zbus matrix element. For this purpose one needs to develop a Zbus matrix.

3.2 Background Impedance Matrix

The bus impedance matrix is an important tool for the fault analysis of the power system [1].

There are various ways to find the system impedance matrix. The inversion of the reception

matrix is more suitable for small systems. In the proposed method, the target is to obtain a

mathematical relationship between frequency and impedance; However, inversion makes it too

difficult to keep track of relationships. In addition, for large systems, the inversion of the

admission matrix becomes very time-consuming.

The bus impedance matrix can also be directly found from the structure of the power system

[1]. To build an impedance matrix directly, one starts with a simple 1×1 impedance matrix

between the bus and the reference node and then modifies this simple network by adding the bus

and the next line between the buses one by one.

To understand how to modify the Zbus impedance matrix, consider the notations h, i, j, and k

for the existing bus and m and n for the new bus, respectively, as shown in Cases 1 to 4 depicted

in figures 3.1 to 3.4 below. There are four different cases that can be utilized in modifying

Zbus.

Case 1. Added a Zbus branch between the reference node and the new bus m

bu

s

23

un

til

To update Zorig's original impedance matrix when there is an impedance (Z)

bus 𝑏

added between the reference node (0) and the new bus (m), one needs to add rows and columns

to Zorig with the values in equation (3.1) [1].

Ne

w

Bus

(3.1)

Figure 3.1 Case 1. Added Zb branch between the reference node and the new bus m

Case 2. Added Zb branch between the existing k bus and the new m bus

To update the original impedance matrix Zorig when there is a new bus (m)

connected via Eg to the existing bus (k) equation (3.2) can be used [1].

Ne

w

Bus

(3.2)



Z orig





0

bus

⁝ 

0 

0



0 

Zb







Z

k1

Z1k

From

orig

W

it

h

2k

until ⁝





Zk 2…ZKnZkk 

Eg



W

it

h

Nk

W

it

W

it

24

Figure 3.2 Case 2. Added Zb branch between the existing k bus and the new m bus

Case 3. Adding a Zb branch between existing k buses to a reference node

In this case there is an impedance of Zb between bus k (existing bus) and bus (0)

(reference node). To get Znew , one needs to add a temporary bus (m) connected via

Zb to the k bus (figure 3.3), then one needs to repeat case 2 and then delete the m row and m

column with Kron reduction. To use the Kron reduction to find every elemental equation (3.3) is

used [1].

Zhi

(new)

=

Zhi

−

zh

(N+1)Z(N+1)

i

Zkk+Zb

(3.3)

Figure 2.3 Case 3. Adding a Zb branch between existing k buses to a reference node

bu

s

25

bu

s



Case 4. Add Zb branch between existing j bus to existing k bus

To get the Znew original impedance matrix for this case one needs to form

The matrix uses equation (3.4) [1].

New Z

 

Ori

g

Bus

kol.j  kol.k 

(3.4)

bus baris. j 

baris.k

Zth, jk  Zb 

Figure 3.4 Case 4. Add Zb branch between existing j bus to existing k bus

where Zth,jk = Zjj + Zkk − 2Zjk and then delete the n rows and n columns by the Kroon

reduction [1].

By knowing how to modify Zbus using these four cases, one can find Zbus from the

system. The Zbus impedance matrix can be obtained starting from a single bus connected

through a branch impedance to a reference node and then extending this simple network, based

on the system topology and the four cases mentioned above, to modify the Zbus and find a

large system impedance matrix. This approach was used in chapter 3.3 to find the relationship

between the frequency of injection and the location of the error.

Z

26

3.3 Effect of Injection Frequency on Fault Location

In SPS, the wires are resistive, inductive and in the form of RL which makes the

impedance of each wire equal to Z = R + jLω. Note that ω = 2πf which makes ω depends

on the frequency of injection. Therefore, the impedance of the cable also depends on the

frequency. The resistance (R) and inductance (L) of the cable are also related to the length of the

cable in the SPS. That is, R = rl where r is the resistance per mile and l is the length of the

cable. With the same approach, L = al where a is the inductance per mile and l is the length of

the cable. Under the assumption that the same cable is used across the SPS, the values for a and r

remain the same for the entire system and the only parameter that changes is the length which

makes R and L different for each cable. Let each element of Zbus be represented by the

complex number Zij =

Rij + jωLij. Then, Zij can be converted to Zij = Ψl where Ψ ∈ C1 is a constant complex

number and equal to Ψ = r + jωa. In addition, one can consider R = rl = const = K. By

Considering this can write:

�

Z = R + jLω = L

(�

�

+ jω) =

al

(K +

jω)

𝐿

=

KC(ω)l

To the

Since K is considered a constant and a is the same inductance per mile for all the wires used in

SPS, there are only two variables in this equation which are l and ω.

In the proposed approach, the algorithm is supposed to look at the ∆V and ∆I values

to find the location of the fault in the system. Using standard error analysis, an observant change

in bus voltage on bus h (when an error occurs on bus p) can be described as:

Z (h, p)

27

∆Vh = Z(p, p)

+ R

× Vpref

erro

r

28

where Z(h,p) is the (h,p) entrée of the impedance matrix and Z(p,p) is the Thevenin

Impedance system visible from the p bus, and Vpref is the prefault voltage at the fault point in

the system. As shown in the equation, one needs to look for the impedance matrix (Zbus) to

find ∆Vh. Since the proposed algorithm is related to injection and measurement frequencies, one

needs to find the relationship between the impedance matrix and frequency to find the right

frequency to get the best results and find the unique values of ∆V and ∆I for each error. This

will then lead to finding the exact location of the fault for different Rfault values.

One can find Zbus by finding Ybus and flipping it, but this is inconvenient because

making it impossible for one to track the effect of frequency in the formulation of the fault site.

For this reason, the Zbus direct building algorithm is used to precisely find its relationship with

injection frequency. In the process of searching for Zbus it seems that all these matrix elements

have a(K + jω) in their numerator. Note that the Kron subtraction in this process will maintain

this value in the numerator of each Zbus element. As mentioned, for the analysis of the error

one needs to look at the values of ∆V and ∆I to find the exact location of the error. Because

every element of Zbus has

KC(ω) = a(K + jω), one can reset the equation as:

KC(ω)ZC(h, p)

∆Vh = KC(ω)ZC(p, p) +

R

where ZC(h, p) and ZC(p, p) are the elements of the Zbus

matrix.

KC(ω)

× Vpref

Similarly, for current measurements since ∆Vh is available for each h in the grid

according to the fault analysis of a standard power system, the change in channel current can be

erro

r

29

expressed as:

30

∆ Forward = ∆Vh −

∆Vu

Zhu

= × (∆Vh − ∆Vu)

1

Zhu =

H

u

−1

=Y(h, u)

∆Yehu = y(h, u) × (∆wu − ∆wow)

where H is the measurement bus and U is the adjacent bus connected to H by the Hu transmission line,

Zhu is the line impedance and Y(h, u) is the (h, u) entrée of the acceptance matrix. Because Ybus

=

1

Zbu

s

It seems that all of these matrix elements have 1

(K+jω)

in their numerator. Note that Kron

The subtraction in this process will maintain this value in the numerator of each Ybus element.

As mentioned, for error analysis one needs to look at the ∆V and ∆I values to find the exact

location of the

error. Because every element of

Ybus

Have

1

KC(ω) =1

a(K+jω) , one can rearrange the equation as:

∆ Forward

1

=KC(ω

)

YC(h, u) ×

(∆Vu

− ∆Vh)

where YC(h, u) is the element of Ybus × matrix KR(ω).

From the above equation it can be concluded that if the Rfault is a small value, the

frequency will not have a critical effect on the ∆V and ∆I values and the location of the fault,

but if the Rfault is large, one can get a higher ∆V and ∆I by increasing the frequency.

3.4 Reference

�

31

[1] Grainger, J. J., & Stevenson, W. D. Analysis of energy systems (Vol. 621). New York:

McGraw- Hill., 1994.

32

CHAPTER 4

SIMULATION RESULTS

4.1 Introduction

The 11-bus SPS in Figure 1.2 is considered a case study. The proposed algorithm is

applied to this system in Matlab/Simulink to find the minimum number of injections and

measurements and the best place for them to cover all errors in the network. The algorithm

checks all possible places for measurements and injections to see which errors are covered and

which are not.

4.2 Simulation Results for f=1000Hz

Table 4.1 shows the number of errors (occurring on the bus) that were not detected for the

selected M and I values. The algorithm is also capable of showing which errors are not covered

in each case (numbers in parentheses). Table 4.1 shows the results when Rfault = 1e−4 and

f = 1000Hz in both injections and measurements. For example, based on Table 4.1, if we have

an injection on bus 2 and a measurement on bus 3, we have two undetected errors that are on bus

6 and bus 9.

Table 4.1 Results of the application of the proposed approach when Rfault = 1e−4

and f = 1000Hz

33

M→

ME

↓

1 2 3 4 5 6

11

(11)

7

(3,4,5,7,8,10,11)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

24

(4,6,9,11)

2

(4,11)

2

(6,9)

2

(6,9)

4

(4,6,9,11)

9

(1,3,4,5,7,8,9,10,11)

32

(4,11)

2

(4,11)

2

(6,9)

8

(1,2,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

41

(11)

1

(11)

8

(2,5,6,7,8,9,10,11)

7

(2,5,6,7,8,9,10)

1

(11)

1

(11)

55

(4,7,8,10,11)

5

(4,7,8,10,11)

3

(7,8,10)

3

(7,8,10)

7

(1,2,3,4,6,9,11)

5

(4,7,8,10,11)

62

(4,11)

3

(3,4,11) 0 0 2

(4,11)

10

(1,2,3,4,5,7,8,9,10,11)

72

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

83

(4,10,11)

3

(4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

92

(4,11)

3

(3,4,11) 0 0 2

(4,11)

3

(3,4,11)

10 2

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

11 0 0 6

(2,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10) 0 0

Table 4.1 Results of the application of the proposed approach when Rfault = 1e−4

and f = 1000Hz

34

M→

ME

↓

7 8 9 10 11

16

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

6

(2,3,4,6,9,11)

7

(2,5,6,7,8,9,10)

24

(4,6,9,11)

4

(4,6,9,11)

9

(1,3,4,5,6,7,8,10,11)

4

(4,6,9,11)

2

(6,9)

32

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

8

(1,2,5,6,7,8,9,10)

41

(11)

1

(11)

1

(11)

1

(11)

9

(1,2,3,5,6,7,8,9,10))

59

(1,2,3,4,6,8,9,10,11)

8

(1,2,3,4,6,7,9,11)

5

(4,7,8,10,11)

8

(1,2,3,4,6,7,9,11)

3

(7,8,10)

62

(4,11)

2

(4,11)

3

(3,4,11)

2

(4,11) 0

710

(1,2,3,4,5,6,8,9,10,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11) 0

84

(3,4,10,11)

9

(1,2,3,4,5,6,7,9,11)

3

(4,10,11)

9

(1,2,3,4,5,6,7,9,11))

1

(10)

92

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,10,11)

2

(4,11) 0

10 3

(3,4,11)

3

(3,4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,11) 0

11 0 0 0 0 10

(1,2,3,4,5,6,7,8,9,10)

31

Table 4.1 shows that there are some cases with the lowest number (0 or 1) of undetected

errors. Zero indicates that the measurements on the M bus can observe all system faults when

the injection is performed on the I bus. If there are no zeros in the table, the system will consider

more than one injection bus and/or measurement to observe all possible desired errors.

Furthermore, the case with the lowest number of undetected errors should be checked for multi-

estimation. In other words, these cases must prove that they have a unique effect on the

measurement chosen for each error. If the measurements for multiple errors are the same, multi-

estimation has occurred, since these errors are not recognizable to each other and thus increase

the number of undetected errors. In our simulations, there are no cases in Table 4.1 that involve

multi-estimation. The highlighted sections in the table show cases that require multi-estimation.

Tables 4.2, 4.3, 4.4, and 4.5 show that assuming a higher Rfault for a system with the

same value for frequency (1000 Hz) the results will change slightly. In this case some cases

involve multi-estimation.

Table 4.2 Results of the application of the proposed approach when Rfault = 1e−3

and f = 1000Hz

32

M→

ME

↓

1 2 3 4 5 6

11

(11)

7

(3,4,5,7,8,10,11)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

24

(4,6,9,11)

2

(4,11)

2

(6,9)

2

(6,9)

4

(4,6,9,11)

9

(1,3,4,5,7,8,9,10,11)

32

(4,11)

2

(4,11)

2

(6,9)

8

(1,2,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

41

(11)

1

(11)

8

(2,5,6,7,8,9,10,11)

7

(2,5,6,7,8,9,10)

1

(11)

1

(11)

55

(4,7,8,10,11)

5

(4,7,8,10,11)

3

(7,8,10)

3

(7,8,10)

7

(1,2,3,4,6,9,11)

5

(4,7,8,10,11)

62

(4,11)

3

(3,4,11) 0 0 2

(4,11)

10

(1,2,3,4,5,7,8,9,10,11)

72

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

83

(4,10,11)

3

(4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

92

(4,11)

3

(3,4,11) 0 0 2

(4,11)

3

(3,4,11)

10 2

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

11 0 0 6

(2,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10) 00

Table 4.2 Results of the application of the proposed approach when Rfault = 1e−3

and f = 1000Hz

33

M→

ME

↓

7 8 9 10 11

16

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

6

(2,3,4,6,9,11)

7

(2,5,6,7,8,9,10)

24

(4,6,9,11)

4

(4,6,9,11)

9

(1,3,4,5,6,7,8,10,11)

4

(4,6,9,11)

2

(6,9)

32

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

8

(1,2,5,6,7,8,9,10)

41

(11)

1

(11)

1

(11)

1

(11)

9

(1,2,3,5,6,7,8,9,10))

59

(1,2,3,4,6,8,9,10,11)

8

(1,2,3,4,6,7,9,11)

5

(4,7,8,10,11)

8

(1,2,3,4,6,7,9,11)

3

(7,8,10)

62

(4,11)

2

(4,11)

3

(3,4,11)

2

(4,11) 0

710

(1,2,3,4,5,6,8,9,10,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11) 0

84

(3,4,10,11)

9

(1,2,3,4,5,6,7,9,11)

3

(4,10,11)

9

(1,2,3,4,5,6,7,9,11))

1

(10)

92

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,10,11)

2

(4,11) 0

10 3

(3,4,11)

3

(3,4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,11) 0

11 0 0 0 0 10

(1,2,3,4,5,6,7,8,9,10)

Table 4.3 Results of the application of the proposed approach when Rfault = 1e−2

and f = 1000Hz

34

M→

ME

↓

1 2 3 4 5 6

12

(1,11)

8

(1,3,4,5,7,8,10,11)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

25

(2,4,6,9,11)

3

(2,4,11)

3

(2,6,9)

3

(2,6,9)

5

(2,4,6,9,11)

10

(1,2,3,4,5,7,8,9,10,11)

31

(11)

1

(11)

2

(6,9)

8

(1,2,5,6,7,8,9,10)

1

(11)

1

(11)

40 0 7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10) 0 0

56

(4,5,7,8,10,11))

6

(4,5,7,8,10,11)

4

(5,7,8,10)

4

(5,7,8,10)

8

(1,2,3,4,5,6,9,11)

6

(4,5,7,8,10,11)

63

(4,6,11)

4

(3,4,6,11)

1

(6)

1

(6)

3

(4,6,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

73

(4,7,11)

3

(4,7,11)

1

(7)

1

(7)

4

(3,4,7,11)

3

(4,7,11)

83

(4,10,11)

3

(4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

93

(4,9,11)

4

(3,4,9,11)

1

(9)

1

(9)

3

(4,9,11)

4

(3,4,9,11)

10 3

(4,10,11)

3

(4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

11 1

(11)

1

(11)

8

(2,5,6,7,8,9,10,11)

9

(1,2,5,6,7,8,9,10,11)

1

(11)

1

(11)

Table 4.3 Results of the application of the proposed approach when Rfault = 1e−2

and f = 1000Hz

35

M→

ME

↓

7 8 9 10 11

17

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

7

(1,2,3,4,6,9,11)

8

(1,2,5,6,7,8,9,10)

25

(2,4,6,9,11)

5

(2,4,6,9,11)

10

(1,2,3,4,5,6,7,8,10,11)

5

(2,4,6,9,11)

3

(2,6,9)

31

(11)

1

(11)

1

(11)

1

(11)

8

(1,2,5,6,7,8,9,10)

40 0 0 0 9

(1,2,3,5,6,7,8,9,10)

510

(1,2,3,4,5,6,8,9,10,11)

9

(1,2,3,4,5,6,7,9,11)

6

(4,5,7,8,10,11)

9

(1,2,3,4,5,6,7,9,11)

4

(5,7,8,10)

63

(4,6,11)

3

(4,6,11)

4

(3,4,6,11)

3

(4,6,11)

1

(6)

711

(1,2,3,4,5,6,7,8,9,10,11)

4

(3,4,7,11)

3

(4,7,11)

4

(3,4,7,11)

1

(7)

84

(3,4,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

3

(4,10,11)

8

(1,2,3,4,6,7,9,11))

1

(10)

93

(4,9,11)

3

(4,9,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

3

(4,9,11)

1

(9)

10 4

(3,4,10,11)

4

(3,4,10,11)

3

(4,10,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

1

(10)

11 1

(11)

1

(11)

1

(11)

1

(11)

11

(1,2,3,4,5,6,7,8,9,10,11)

Table 4.4 Results of the application of the proposed approach when Rfault = 1e−1

and f = 1000Hz

36

M→

ME

↓

1 2 3 4 5 6

13

(1,4,11)

8

(1,3,4,5,7,8,10,11)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

26

(2,3,4,6,9,11)

4

(2,3,4,11)

3

(2,6,9)

3

(2,6,9)

6

(2,3,4,6,9,11)

10

(1,2,3,4,5,7,8,9,10,11)

33

(3,4,11)

3

(3,4,11)

9

(1,2,3,5,6,7,8,9,10)

9

(1,2,3,5,6,7,8,9,10)

3

(3,4,11)

3

(3,4,11)

42

(4,11)

2

(4,11)

10

(1,2,4,5,6,7,8,9,10,11)

9

(1,2,4,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

57

(3,4,5,7,8,10,11)

7

(3,4,5,7,8,10,11)

4

(5,7,8,10)

4

(5,7,8,10)

8

(1,2,3,4,5,6,9,11)

7

(3,4,5,7,8,10,11)

64

(3,4,6,11)

4

(3,4,6,11)

1

(6)

1

(6)

4

(3,4,6,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

74

(3,4,7,11)

4

(3,4,7,11)

1

(7)

1

(7)

4

(3,4,7,11)

4

(3,4,7,11)

85

(3,4,8,10,11)

5

(3,4,8,10,11)

2

(8,10)

2

(8,10)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

94

(3,4,9,11)

4

(3,4,9,11)

1

(9)

1

(9)

4

(3,4,9,11)

4

(3,4,10,11)

10 4

(3,4,10,11)

4

(3,4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

4

(3,4,10,11)

11 1

(11)

1

(11)

9

(1,2,5,6,7,8,9,10,11)

9

(1,2,5,6,7,8,9,10,11)

1

(11)

1

(11)

Table 4.4 Results of the application of the proposed approach when Rfault = 1e−1

and f = 1000Hz

37

M→

ME

↓

7 8 9 10 11

17

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

7

(1,2,3,4,6,9,11)

8

(1,2,5,6,7,8,9,10)

26

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

10

(1,2,3,4,5,6,7,8,10,11)

6

(2,3,4,6,9,11)

3

(2,6,9)

33

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

9

(1,2,3,5,6,7,8,9,10)

42

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,10)

510

(1,2,3,4,5,6,8,9,10,11)

9

(1,2,3,4,5,6,7,9,11)

7

(3,4,5,7,8,10,11)

9

(1,2,3,4,5,6,7,9,11)

4

(5,7,8,10)

64

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

1

(6)

711

(1,2,3,4,5,6,7,8,9,10,11)

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

1

(7)

85

(3,4,8,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

5

(3,4,8,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

2

(8,10)

94

(3,4,9,11)

4

(3,4,9,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

4

(3,4,9,11)

1

(9)

10 4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

1

(10)

11 1

(11)

1

(11)

1

(11)

1

(11)

11

(1,2,3,4,5,6,7,8,9,10,11)

Table 4.5 Results of the implementation of the proposed approach when

Rfault =

1 and f = 1000Hz

38

M→

I↓ 1 2 3 4 5 6

14

(1,3,4,11)

8

(1,3,4,5,7,8,10,11)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

26

(2,3,4,6,9,11)

4

(2,3,4,11)

3

(2,6,9)

3

(2,6,9)

6

(2,3,4,6,9,11)

10

(1,2,3,4,5,7,8,9,10,11)

33

(3,4,11)

3

(3,4,11)

9

(1,2,3,5,6,7,8,9,10)

9

(1,2,3,5,6,7,8,9,10)

3

(3,4,11)

3

(3,4,11)

42

(4,11)

2

(4,11)

10

(1,2,4,5,6,7,8,9,10,11)

9

(1,2,4,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

57

(3,4,5,7,8,10,11)

7

(3,4,5,7,8,10,11)

4

(5,7,8,10)

4

(5,7,8,10)

8

(1,2,3,4,5,6,9,11)

7

(3,4,5,7,8,10,11)

64

(3,4,6,11)

4

(3,4,6,11)

1

(6)

1

(6)

4

(3,4,6,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

74

(3,4,7,11)

4

(3,4,7,11)

1

(7)

1

(7)

7

(2,3,4,6,7,9,11)

4

(3,4,7,11)

85

(3,4,8,10,11)

5

(3,4,8,10,11)

2

(8,10)

2

(8,10)

8

(2,3,4,6,8,9,10,11)

5

(3,4,8,10,11)

94

(3,4,9,11)

4

(3,4,9,11)

1

(9)

1

(9)

4

(3,4,9,11)

4

(3,4,9,11)

10 4

(3,4,10,11)

4

(3,4,10,11)

1

(10)

1

(10)

7

(2,3,4,6,9,10,11)

4

(3,4,10,11)

11 1

(11)

1

(11)

9

(1,2,5,6,7,8,9,10,11)

9

(1,2,5,6,7,8,9,10,11)

1

(11)

1

(11)

Table 4.5 Results of the implementation of the proposed approach when

Rfault =

1 and f = 1000Hz

39

M→

I↓ 7 8 9 10 11

17

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

7

(1,2,3,4,6,9,11)

8

(1,2,5,6,7,8,9,10)

26

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

10

(1,2,3,4,5,6,7,8,10,11)

6

(2,3,4,6,9,11)

3

(2,6,9)

33

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

9

(1,2,3,5,6,7,8,9,10)

42

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,10)

510

(1,2,3,4,5,6,8,9,10,11)

9

(1,2,3,4,5,6,7,9,11)

7

(3,4,5,7,8,10,11)

9

(1,2,3,4,5,6,7,9,11)

4

(5,7,8,10)

64

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

1

(6)

711

(1,2,3,4,5,6,7,8,9,10,11)

7

(2,3,4,6,7,9,11)

4

(3,4,7,11)

7

(2,3,4,6,7,9,11)

1

(7)

88

(2,3,4,6,8,9,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

5

(3,4,8,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

2

(8,10)

94

(3,4,9,11)

4

(3,4,9,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

4

(3,4,9,11)

1

(9)

10 7

(2,3,4,6,9,10,11)

8

(1,2,3,4,6,9,10,11)

4

(3,4,10,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

1

(10)

11 1

(11)

1

(11)

1

(11)

1

(11)

11

(1,2,3,4,5,6,7,8,9,10,11)

40

This algorithm is also applied to systems with Rfault = 1 and f = 1000Hz. As shown

in Table 4.5, in this scenario all cases that have the lowest number of undetected faults suffer

from multi-estimation (highlighted figure). That is, for higher Rfaults, the combination of

injection and measurement buses with f = 1000Hz cannot cover all fault locations unless

multiple injection and measurement buses are selected. This requires the algorithm to run at a

higher frequency (f=7000Hz.)

4.3 Simulation Result for f=7000Hz

The algorithm repeats all the steps with f = 7000Hz for different Rfault values

(1e−4, 1e−3, 1e−2, 1e−1, and 1) to minimize the number of multi-estimates. Each Rfault

will generate a table similar to Table 4.1 showing the number of undetected errors for each case

(Tables 4.6, 4.7, 4.8, .49, and 4.10).

Table 4.6 Results of the implementation of the proposed approach when Rfault =

1e−4 and f = 7000Hz

41

M→

I↓ 1 2 3 4 5 6

11

(11)

7

(3,4,5,7,8,10,11)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

24

(4,6,9,11)

2

(4,11)

2

(6,9)

2

(6,9)

4

(4,6,9,11)

9

(1,3,4,5,7,8,9,10,11)

32

(4,11)

2

(4,11)

2

(6,9)

8

(1,2,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

41

(11)

1

(11)

8

(2,5,6,7,8,9,10,11)

7

(2,5,6,7,8,9,10)

1

(11)

1

(11)

55

(4,7,8,10,11)

5

(4,7,8,10,11)

3

(7,8,10)

3

(7,8,10)

7

(1,2,3,4,6,9,11)

5

(4,7,8,10,11)

62

(4,11)

3

(3,4,11) 0 0 2

(4,11)

10

(1,2,3,4,5,7,8,9,10,11)

72

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

83

(4,10,11)

3

(4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

92

(4,11)

3

(3,4,11) 0 0 2

(4,11)

3

(3,4,11)

10 2

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

11 0 0 6

(2,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10) 0 0

Table 4.6 Results of the implementation of the proposed approach when Rfault =

1e−4 and f = 7000Hz

42

M→

ME

↓

7 8 9 10 11

16

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

6

(2,3,4,6,9,11)

7

(2,5,6,7,8,9,10)

24

(4,6,9,11)

4

(4,6,9,11)

9

(1,3,4,5,6,7,8,10,11)

4

(4,6,9,11)

2

(6,9)

32

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

8

(1,2,5,6,7,8,9,10)

41

(11)

1

(11)

1

(11)

1

(11)

9

(1,2,3,5,6,7,8,9,10))

59

(1,2,3,4,6,8,9,10,11)

8

(1,2,3,4,6,7,9,11)

5

(4,7,8,10,11)

8

(1,2,3,4,6,7,9,11)

3

(7,8,10)

62

(4,11)

2

(4,11)

3

(3,4,11)

2

(4,11) 0

710

(1,2,3,4,5,6,8,9,10,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11) 0

84

(3,4,10,11)

9

(1,2,3,4,5,6,7,9,11)

3

(4,10,11)

9

(1,2,3,4,5,6,7,9,11))

1

(10)

92

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,10,11)

2

(4,11) 0

10 3

(3,4,11)

3

(3,4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,11) 0

11 0 0 0 0 10

(1,2,3,4,5,6,7,8,9,10)

Table 4.7 Results of the implementation of the proposed approach when Rfault =

1e−3 and f = 7000Hz

43

M→

ME

↓

1 2 3 4 5 6

11

(11)

7

(3,4,5,7,8,10,11)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

24

(4,6,9,11)

2

(4,11)

2

(6,9)

2

(6,9)

4

(4,6,9,11)

9

(1,3,4,5,7,8,9,10,11)

32

(4,11)

2

(4,11)

2

(6,9)

8

(1,2,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

41

(11)

1

(11)

8

(2,5,6,7,8,9,10,11)

7

(2,5,6,7,8,9,10)

1

(11)

1

(11)

55

(4,7,8,10,11)

5

(4,7,8,10,11)

3

(7,8,10)

3

(7,8,10)

7

(1,2,3,4,6,9,11)

5

(4,7,8,10,11)

62

(4,11)

3

(3,4,11) 0 0 2

(4,11)

10

(1,2,3,4,5,7,8,9,10,11)

72

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

83

(4,10,11)

3

(4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

92

(4,11)

3

(3,4,11) 0 0 2

(4,11)

3

(3,4,11)

10 2

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

11 0 0 6

(2,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10) 0 0

Table 4.7 Results of the implementation of the proposed approach when Rfault =

1e−3 and f = 7000Hz

44

M→

I↓ 7 8 9 10 11

16

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

6

(2,3,4,6,9,11)

7

(2,5,6,7,8,9,10)

24

(4,6,9,11)

4

(4,6,9,11)

9

(1,3,4,5,6,7,8,10,11)

4

(4,6,9,11)

2

(6,9)

32

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

8

(1,2,5,6,7,8,9,10)

41

(11)

1

(11)

1

(11)

1

(11)

9

(1,2,3,5,6,7,8,9,10))

59

(1,2,3,4,6,8,9,10,11)

8

(1,2,3,4,6,7,9,11)

5

(4,7,8,10,11)

8

(1,2,3,4,6,7,9,11)

3

(7,8,10)

62

(4,11)

2

(4,11)

3

(3,4,11)

2

(4,11) 0

710

(1,2,3,4,5,6,8,9,10,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11) 0

84

(3,4,10,11)

9

(1,2,3,4,5,6,7,9,11)

3

(4,10,11)

9

(1,2,3,4,5,6,7,9,11))

1

(10)

92

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,10,11)

2

(4,11) 0

10 3

(3,4,11)

3

(3,4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,11) 0

11 0 0 0 0 10

(1,2,3,4,5,6,7,8,9,10)

Table 4.8 Results of the implementation of the proposed approach when Rfault =

1e−2 and f = 7000Hz

45

M→

ME

↓

1 2 3 4 5 6

11

(11)

7

(3,4,5,7,8,10,11)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

24

(4,6,9,11)

2

(4,11)

2

(6,9)

2

(6,9)

4

(4,6,9,11)

9

(1,3,4,5,7,8,9,10,11)

32

(4,11)

2

(4,11)

2

(6,9)

8

(1,2,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

41

(11)

1

(11)

8

(2,5,6,7,8,9,10,11)

7

(2,5,6,7,8,9,10)

1

(11)

1

(11)

55

(4,7,8,10,11)

5

(4,7,8,10,11)

3

(7,8,10)

3

(7,8,10)

7

(1,2,3,4,6,9,11)

5

(4,7,8,10,11)

62

(4,11)

3

(3,4,11) 0 0 2

(4,11)

10

(1,2,3,4,5,7,8,9,10,11)

72

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

83

(4,10,11)

3

(4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

92

(4,11)

3

(3,4,11) 0 0 2

(4,11)

3

(3,4,11)

10 2

(4,11)

2

(4,11) 0 0 3

(3,4,11)

2

(4,11)

11 0 0 6

(2,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10) 0 0

Table 4.8 Results of the implementation of the proposed approach when Rfault =

1e−2 and f = 7000Hz

46

M→

ME

↓

78910 11

16

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,11)

6

(2,3,4,6,9,11)

7

(2,5,6,7,8,9,10)

24

(4,6,9,11)

4

(4,6,9,11)

9

(1,3,4,5,6,7,8,10,11)

4

(4,6,9,11)

2

(6,9)

32

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

8

(1,2,5,6,7,8,9,10)

41

(11)

1

(11)

1

(11)

1

(11)

9

(1,2,3,5,6,7,8,9,10))

59

(1,2,3,4,6,8,9,10,11)

8

(1,2,3,4,6,7,9,11)

5

(4,7,8,10,11)

8

(1,2,3,4,6,7,9,11)

3

(7,8,10)

62

(4,11)

2

(4,11)

3

(3,4,11)

2

(4,11) 0

710

(1,2,3,4,5,6,8,9,10,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11) 0

84

(3,4,10,11)

9

(1,2,3,4,5,6,7,9,11)

3

(4,10,11)

9

(1,2,3,4,5,6,7,9,11))

1

(10)

92

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,10,11)

2

(4,11) 0

10 3

(3,4,11)

3

(3,4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,11) 0

11 0 0 0 0 10

(1,2,3,4,5,6,7,8,9,10)

Table 4.9 Results of the application of the proposed approach when Rfault = 1e−1

and f = 7000Hz

47

M→

ME

↓

1 2 3 4 5 6

12

(1,11)

8

(1,3,4,5,7,8,10,11)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

25

(2,4,6,9,11)

3

(2,4,11)

3

(2,6,9)

3

(2,6,9)

5

(2,4,6,9,11)

10

(1,2,3,4,5,7,8,9,10,11)

33

(3,4,11)

3

(3,4,11)

3

(3,6,9)

9

(1,2,3,5,6,7,8,9,10)

3

(3,4,11)

3

(3,4,11)

42

(4,11)

2

(4,11)

9

(2,4,5,6,7,8,9,10,11)

8

(2,4,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

56

(4,5,7,8,10,11)

6

(4,5,7,8,10,11)

4

(5,7,8,10)

4

(5,7,8,10)

8

(1,2,3,4,5,6,9,11)

6

(4,5,7,8,10,11)

63

(4,6,11)

4

(3,4,6,11)

1

(6)

1

(6)

3

(4,6,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

73

(4,7,11)

3

(4,7,11)

1

(7)

1

(7)

4

(3,4,7,11)

3

(4,7,11)

84

(4,8,10,11)

4

(4,8,10,11)

2

(8,10)

2

(8,10)

5

(3,4,8,10,11)

4

(4,8,10,11)

93

(4,9,11)

4

(3,4,9,11)

1

(9)

1

(9)

3

(4,9,11)

4

(3,4,9,11)

10 3

(4,10,11)

3

(4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

11 1

(11)

1

(11)

8

(2,5,6,7,8,9,10,11)

9

(1,2,5,6,7,8,9,10,11)

1

(11)

1

(11)

Table 4.9 Results of the application of the proposed approach when Rfault = 1e−1

and f = 7000Hz

48

M→

ME↓ 7 8 9 10 11

17

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

7

(1,2,3,4,6,9,11)

8

(1,2,5,6,7,8,9,10)

25

(2,4,6,9,11)

5

(2,4,6,9,11)

10

(1,2,3,4,5,6,7,8,10,11)

5

(2,4,6,9,11)

3

(2,6,9)

33

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

9

(1,2,3,5,6,7,8,9,10)

42

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,10)

510

(1,2,3,4,5,6,8,9,10,11)

9

(1,2,3,4,5,6,7,9,11)

6

(4,5,7,8,10,11)

9

(1,2,3,4,5,6,7,9,11)

4

(5,7,8,10)

63

(4,6,11)

3

(4,6,11)

4

(3,4,6,11)

3

(4,6,11)

1

(6)

711

(1,2,3,4,5,6,7,8,9,10,11)

4

(3,4,7,11)

3

(4,7,11)

4

(3,4,7,11)

1

(7)

85

(3,4,8,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

4

(4,8,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

2

(8,10)

93

(4,9,11)

3

(4,9,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

3

(4,9,11)

1

(9)

10 4

(3,4,10,11)

4

(3,4,10,11)

3

(4,10,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

1

(10)

11 1

(11)

1

(11)

1

(11)

1

(11)

11

(1,2,3,4,5,6,7,8,9,10,11)

Table 4.10 Results of the implementation of the proposed approach when

Rfault =

1 and f = 7000Hz

49

M→

ME

↓

1 2 3 4 5 6

14

(1,3,4,11)

8

(1,3,4,5,7,8,10,11)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

26

(2,3,4,6,9,11)

4

(2,3,4,11)

3

(2,6,9)

3

(2,6,9)

6

(2,3,4,6,9,11)

10

(1,2,3,4,5,7,8,9,10,11)

33

(3,4,11)

3

(3,4,11)

9

(1,2,3,5,6,7,8,9,10)

9

(1,2,3,5,6,7,8,9,10)

3

(3,4,11)

3

(3,4,11)

42

(4,11)

2

(4,11)

10

(1,2,4,5,6,7,8,9,10,11)

9

(1,2,4,5,6,7,8,9,10)

2

(4,11)

2

(4,11)

57

(3,4,5,7,8,10,11)

7

(3,4,5,7,8,10,11)

4

(5,7,8,10)

4

(5,7,8,10)

8

(1,2,3,4,5,6,9,11)

7

(3,4,5,7,8,10,11)

64

(3,4,6,11)

4

(3,4,6,11)

1

(6)

1

(6)

4

(3,4,6,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

74

(3,4,7,11)

4

(3,4,7,11)

1

(7)

1

(7)

4

(3,4,7,11)

4

(3,4,7,11)

85

(3,4,8,10,11)

5

(3,4,8,10,11)

2

(8,10)

2

(8,10)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

94

(3,4,9,11)

4

(3,4,9,11)

1

(9)

1

(9)

4

(3,4,9,11)

4

(3,4,9,11)

10 4

(3,4,10,11)

4

(3,4,10,11)

1

(10)

1

(10)

4

(3,4,10,11)

4

(3,4,10,11)

11 1

(11)

1

(11)

9

(1,2,5,6,7,8,9,10,11)

9

(1,2,5,6,7,8,9,10,11)

1

(11)

1

(11)

Table 4.10 Results of the implementation of the proposed approach when

Rfault =

1 and f = 7000Hz

50

M→

ME

↓

7 8 9 10 11

17

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

8

(1,3,4,5,7,8,10,11)

7

(1,2,3,4,6,9,11)

8

(1,2,5,6,7,8,9,10)

26

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

10

(1,2,3,4,5,6,7,8,10,11)

6

(2,3,4,6,9,11)

3

(2,6,9)

33

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

9

(1,2,3,5,6,7,8,9,10)

42

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,7,8,9,10)

510

(1,2,3,4,5,6,8,9,10,11)

9

(1,2,3,4,5,6,7,9,11)

7

(3,4,5,7,8,10,11)

9

(1,2,3,4,5,6,7,9,11)

4

(5,7,8,10)

64

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

1

(6)

711

(1,2,3,4,5,6,7,8,9,10,11)

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

1

(7)

85

(3,4,8,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

5

(3,4,8,10,11)

10

(1,2,3,4,5,6,7,8,9,11)

2

(8,10)

94

(3,4,9,11)

4

(3,4,9,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

4

(3,4,9,11)

1

(9)

10 4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

11

(1,2,3,4,5,6,7,8,9,10,11)

1

(10)

11 1

(11)

1

(11)

1

(11)

1

(11)

11

(1,2,3,4,5,6,7,8,9,10,11)

51

The algorithm compares all of these tables together to find the optimal bus for injection

and measurement to find the unique location of the error with minimal multi-estimation. Table

4.10 shows the results for Rfault = 1 when f = 7000Hz. This table is compared with other

tables at f = 7000Hz for different Rfaults to find the optimal measurement and injection

location. Cases with circles have the lowest number of undetected errors for all possible

Rfaults that do not involve multi-estimation.

The optimal injection measurement set for the system analyzed in this paper requires two

injections and two measurements to cover all errors (1e−4, 1e−3, 1e−2, 1e−1, and 1) in the

system. By comparing the table for f = 7000Hz it is shown that the first injection should be on

bus 6 with the measurement on bus 3. The second injection and measurement pair can be one of

these cases: I = 9, M = 3, or I = 11, M = 1, or I = 11, M = 2, or I = 11, M = 5, or

I = 11, M = 6, or I = 11, M = 7, or I = 11, M = 8, or I = 11, M = 9, or I = 11, M = 10.

4.4 Error Location Results Using Channel Current Measurement

Since each bus connects multiple lines together and each of these lines has a different

flow, one needs to know which line is used for the fault location and which lane produces the

lowest undetected error.

The 11-bus SPS in figure 4.1 is considered a case study. In this image each row has a

number that is used for the current measurement. The proposed algorithm is applied to this

system in Matlab/Simulink to find the minimum number of injections and measurements and the

best place for them to cover all errors in the network. The algorithm checks all possible places

for measurements and injections to see which errors are covered and which are not. The

proposed algorithm is tested for Rfault = 1 and Rfault = 1e−3 for f = 1000Hz and

f = 7000Hz. In this section, each table shows the results for current and voltage

52

Measurement. In this section, the circle in the table shows cases with better results for current

measurements than voltage measurements. The highlighted table shows cases that require multi-

estimation.

Figure 4.1 11-Bus SPS

53

4.5 Current Measurement Results for Rfault = 1e−3 and f = 1000Hz

Table 4.11 Voltage and current measurements for Bus-1 when Rfault = 1e−3 and f =

1000Hz

Msr

Inj

Bus-1

Voltase Current

Bus-1 Bus-1-Line-1 Bus-1-Line-2 Bus-1-Line-3 Bus-1-Line-4

Until

-1

10

(2,3,4,5,6,7,8,

9,10,11)

1

(11)

7

(2,5,6,7,8,9,10

)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,1

1)

Until

-2

4

(4,6,9,11)

4

(4,6,9,11)

2

(6,9)

4

(4,6,9,11)

4

(4,6,9,11)

Until

-3

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Until

-4

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Until

-5

5

(4,7,8,10,11)

5

(4,7,8,10,11)

3

(7,8,10)

5

(4,7,8,10,11)

5

(4,7,8,10,11)

Until

-6

2

(4,11)

2

(4,11)

02

(4,11)

2

(4,11)

Until

-7

2

(4,11)

2

(4,11)

03

(3,4,11)

2

(4,11)

Until

-8

3

(4,10,11)

3

(4,10,11)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

Until

-9

2

(4,11)

2

(4,11)

02

(4,11)

2

(4,11)

Until

-10

2

(4,11)

2

(4,11)

03

(3,4,11)

2

(4,11)

Until

-11 00000

Table 4.12 Voltage and current measurements for Bus-2 when Rfault = 1e−3 and f =

1000Hz

54

Msr

Inj

Bus-2

Voltase Current

Bus-2 Bus-2-Line-1 Bus-2-Line-2 Bus-2-Line-3 Bus-2-Line-4

Bus-

1

7

(3,4,5,7,8,10

,11)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,11

)

4

(3,4,7,11)

7

(3,4,5,7,8,10,1

1)

Bus-

2

10

(1,3,4,5,6,7,

8,9,10,11)

2

(4,11)

4

(4,6,9,11)

9

(1,3,4,5,7,8,9,

10,11)

9

(1,3,4,5,6,7,8,1

0,11)

Bus-

3

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

4

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Bus-

5

(4,7,8,10,11)

5

(4,7,8,10,11)

5

(4,7,8,10,11)

3

(4,7,11)

5

(4,7,8,10,11)

Bus-

6

3

(3,4,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

7

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

8

3

(4,10,11)

3

(4,10,11)

3

(4,10,11)

3

(4,10,11)

3

(4,10,11)

Bus-

9

3

(3,4,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

10

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

11 0 0 0 0 0

Table 4.13 Voltage and current measurements for Bus-3 when Rfault = 1e−3 and f =

1000Hz

55

Msr

Inj

Bus-3

Voltase Current

Bus-3 Bus-3-Line-1 Bus-3-Line-2 Bus-3-Line-3

Bus-

1

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

Bus-

2

(6,9)

2

(6,9)

2

(6,9)

2

(6,9)

Bus-

3

10

(1,2,4,5,6,7,8,9,10,11)

2

(6,9)

2

(4,11)

8

(1,2,5,6,7,8,9,10)

Bus-

4

8

(2,5,6,7,8,9,10,11)

8

(2,5,6,7,8,9,10,11)

1

(11)

8

(1,2,6,7,8,9,10,11)

Bus-

5

3

(7,8,10)

3

(7,8,10)

3

(7,8,10)

3

(7,8,10)

Bus-

60 0 0 0

Bus-

70 0 0 0

Bus-

8

1

(10)

1

(10)

1

(10)

1

(10)

Bus-

90 0 0 0

Bus-

10 0 0 0 0

Bus-

11

6

(2,6,7,8,9,10)

6

(2,6,7,8,9,10)

07

(2,5,6,7,8,9,10)

Table 4.14 Voltage and current measurements for Bus-4 when Rfault = 1e−3 and f =

1000Hz

56

Msr

Inj

Bus-4

Voltase Current

Bus-4 Bus-4-Line-1 Bus-4-Line-2 Bus-4-Line-3

Bus-

1

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

Bus-

2

(6,9)

2

(6,9)

2

(6,9)

2

(6,9)

Bus-

3

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

Bus-

4

10

(1,2,3,5,6,7,8,9,10,11)

7

(2,5,6,7,8,9,10)

8

(2,5,6,7,8,9,10,11)

9

(1,2,3,5,6,7,8,9,10)

Bus-

5

3

(7,8,10)

3

(7,8,10)

3

(7,8,10)

3

(7,8,10)

Bus-

60 0 0 0

Bus-

70 0 0 0

Bus-

8

1

(10)

1

(10)

1

(10)

1

(10)

Bus-

90 0 0 0

Bus-

10 0 0 0 0

Bus-

11

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

Table 4.15 Voltage and current measurements for Bus-5 when Rfault = 1e−3 and f =

1000Hz

57

Msr

Inj

Bus-5

Voltase Current

Bus-5 Bus-5-Line-1 Bus-5-Line-2 Bus-5-Line-3

Bus-

1

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

Bus-

2

4

(4,6,9,11)

4

(4,6,9,11)

4

(4,6,9,11)

4

(4,6,9,11)

Bus-

3

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

4

1

(11)

1

(11)

1

(11)

1

(11)

Bus-

5

10

(1,2,3,4,6,7,8,9,10,

11)

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

Bus-

6

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

7

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

8

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

Bus-

9

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

10

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

11 0 0 0 0

Table 4.16 Voltage and current measurements for Bus-6, Bus-7, and Bus-8 when Rfault =

1e−3

and f=1000Hz

58

Measu

rement

Inj

Bus-6 Bus-7 Bus-8

Voltase Current Voltase Current Voltase Current

Bus-1 7

(3,4,5,7,8,1

0,11)

3

(3,4,11)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,

11)

Bus-2 9

(1,3,4,5,7,8,

9,10,11)

6

(3,4,7,9,10,

11)

4

(4,6,9,11)

4

(4,6,9,11)

4

(4,6,9,11)

4

(4,6,9,11)

Bus-3 2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-4 1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Bus-5 5

(4,7,8,10,11

)

3

(4,7,11)

9

(1,2,3,4,6,8,

9,10,11)

9

(1,2,3,4,6,8,

9,10,11)

8

(1,2,3,4,6,7,

9,11)

8

(1,2,3,4,6,

7,9,11)

Bus-6 10

(1,2,3,4,5,7,

8,9,10,11)

10

(1,2,3,4,5,7,

8,9,10,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-7 2

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,

8,9,10,11)

10

(1,2,3,4,5,6,

8,9,10,11)

3

(3,4,11)

3

(3,4,11)

Bus-8 3

(4,10,11)

3

(4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

10

(1,2,3,4,5,6,

7,9,10,11)

9

(1,2,3,4,5,

6,7,9,11)

Bus-9 3

(3,4,11)

3

(3,4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-10 2

(4,11)

2

(4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-11 0 0 0 0 0 0

Table 4.17 Voltage and current measurements for Bus-9, Bus-10, and Bus-11 when Rfault

= 1e−3 and f = 1000Hz

59

Measu

rement

Inj

Bus-9 Bus-10 Bus-11

Voltase Current Voltase Current Voltase Current

Bus-1

7

(3,4,5,7,8,1

0,11)

7

(3,4,5,7,8,1

0,11)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,1

1)

7

(2,5,6,7,8,9

,10)

7

(2,5,6,7,8,9

,10)

Bus-2

9

(1,3,4,5,6,7,

8,10,11)

9

(1,3,4,5,6,7,

8,10,11)

4

(4,6,9,11)

4

(4,6,9,11)

2

(6,9)

2

(6,9)

Bus-3 2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

8

(1,2,5,6,7,8

,9,10)

8

(1,2,5,6,7,8

,9,10)

Bus-4 1

(11)

1

(11)

1

(11)

1

(11)

9

(1,2,3,5,6,7

,8,9,10)

9

(1,2,3,5,6,7

,8,9,10)

Bus-5

5

(4,7,8,10,11

)

5

(4,7,8,10,11

)

8

(1,2,3,4,6,7

,9,11)

8

(1,2,3,4,6,7

,9,11)

3

(7,8,10)

3

(7,8,10)

Bus-6 3

(3,4,11)

3

(3,4,11)

2

(4,11)

2

(4,11) 0 0

Bus-7 2

(4,11)

2

(4,11)

3

(3,4,11)

3

(3,4,11) 0 0

Bus-8 3

(4,10,11)

3

(4,10,11)

9

(1,2,3,4,5,6

,7,9,11)

9

(1,2,3,4,5,6

,7,9,11)

1

(10)

1

(10)

Bus-9

10

(1,2,3,4,5,6,

7,8,10,11)

10

(1,2,3,4,5,6,

7,8,10,11)

2

(4,11)

2

(4,11) 0 0

Bus-10 2

(4,11)

2

(4,11)

10

(1,2,3,4,5,6

,7,8,9,11)

10

(1,2,3,4,5,6

,7,8,9,11)

0 0

Bus-11 0 0 0 0

10

(1,2,3,4,5,6

,7,8,9,10)

10

(1,2,3,4,5,6

,7,8,9,10)

60

4.6 Current Measurement Results for Rfault = 1 and f = 1000Hz

Table 4.18 Voltage and current measurements for Bus-1 when Rfault = 1 and f = 1000Hz

Msr

Inj

Bus-1

Voltase Current

Bus-1 Bus-1-Line-1 Bus-1-Line-2 Bus-1-Line-3 Bus-1-Line-

4

Bus-

1

11

(1,2,3,4,5,6,7,8

,9,10,11)

4

(1,3,4,11)

10

(1,2,4,5,6,7,8,9,

10,11)

7

(1,2,3,4,6,9,11

)

8

(1,3,4,5,7,8,1

0,11)

Bus-

2

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

5

(2,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

Bus-

3

(3,4,11)

3

(3,4,11)

11

(1,2,3,4,5,6,7,8,

9,10,11)

3

(3,4,11)

3

(3,4,11)

Bus-

4

2

(4,11)

2

(4,11)

7

(1,6,7,8,9,10,11

)

2

(4,11)

2

(4,11)

Bus-

5

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,

11)

6

(4,5,7,8,10,11)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,

11)

Bus-

6

4

(3,4,6,11)

4

(3,4,6,11)

3

(4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

Bus-

7

4

(3,4,7,11) 4

(3,4,7,11)

3

(4,7,11)

7

(2,3,4,6,7,9,11

)

4

(3,4,7,11)

Bus-

8

5

(3,4,8,10,11) 5

(3,4,8,10,11)

4

(4,8,10,11)

8

(2,3,4,6,8,9,10

,11)

5

(3,4,8,10,11)

Bus-

9

4

(3,4,9,11)

4

(3,4,9,11)

3

(4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

Bus-

10

4

(3,4,10,11) 4

(3,4,10,11)

3

(4,10,11)

7

(2,3,4,6,9,10,1

1)

4

(3,4,10,11)

Bus-

11

1

(11)

1

(11)

7

(1,2,5,6,7,9,11)

1

(11)

1

(11)

Table 4.19 Voltage and current measurements for Bus-2 when Rfault = 1 and f =

1000Hz

61

Msr

Inj

Bus-2

Voltase Current

Bus-2 Bus-2-Line-1 Bus-2-Line-2 Bus-2-Line-3 Bus-2-Line-4

Bus-

1

8

(1,3,4,5,7,8,

10,11)

8

(1,3,4,5,7,8,10

,11)

8

(1,3,4,5,7,8,10

,11)

8

(1,3,4,5,7,8,10

,11)

8

(1,3,4,5,7,8,10,1

1)

Bus-

2

11

(1,2,3,4,5,6,

7,8,9,10,11)

4

(2,3,4,11)

6

(2,3,4,6,9,11)

10

(1,2,3,4,5,7,8,

9,10,11)

10

(1,2,3,4,5,6,7,8,

10,11)

Bus-

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

4

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

5

7

(3,4,5,7,8,10

,11)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,11)

Bus-

6

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

9

(1,3,4,5,6,7,8,

10,11)

4

(3,4,6,11)

Bus-

7

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

Bus-

8

5

(3,4,8,10,11)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

Bus-

9

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

9

(1,3,4,5,7,8,9,10

,11)

Bus-

10

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

Bus-

11

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Table 4.20 Voltage and current measurements for Bus-3 when Rfault = 1 and f =

1000Hz

62

Msr

Inj

Bus-3

Voltase Current

Bus-3 Bus-3-Line-1 Bus-3-Line-2 Bus-3-Line-3

Bus-

1

8

(1,2,5,6,7,8,9,

10)

8

(1,2,5,6,7,8,9,10)

10

(1,2,4,5,6,7,8,9,10,11)

8

(1,2,5,6,7,8,9,10)

Bus-

2

3

(2,6,9)

3

(2,6,9)

5

(2,4,6,9,11)

3

(2,6,9)

Bus-

3

11

(1,2,3,4,5,6,7,

8,9,10,11)

9

(1,2,3,5,6,7,8,9,1

0)

11

(1,2,3,4,5,6,7,8,9,10,1

1)

9

(1,2,3,5,6,7,8,9,10

)

Bus-

4

10

(1,2,4,5,6,7,8,

9,10,11)

10

(1,2,4,5,6,7,8,9,1

0,11)

10

(1,2,4,5,6,7,8,9,10,11)

10

(1,2,4,5,6,7,8,9,10

,11)

Bus-

5

4

(5,7,8,10)

4

(5,7,8,10)

6

(4,5,7,8,10,11)

4

(5,7,8,10)

Bus-

6

1

(6)

1

(6)

3

(4,6,11)

1

(6)

Bus-

7

1

(7)

1

(7)

3

(4,7,11)

1

(7)

Bus-

8

2

(8,10)

2

(8,10)

4

(4,8,10,11)

2

(8,10)

Bus-

9

1

(9)

1

(9)

3

(4,9,11)

1

(9)

Bus-

10

1

(10)

1

(10)

3

(4,10,11)

1

(10)

Bus-

11

9

(1,2,5,6,7,8,9,

10,11)

9

(1,2,5,6,7,8,9,10,

11)

9

(1,2,5,6,7,8,9,10,11)

9

(1,2,5,6,7,8,9,10,1

1)

Table 4.21 Voltage and current measurements for Bus-4 when Rfault = 1 and f =

1000Hz

63

Msr

Inj

Bus-4

Voltase Current

Bus-4 Bus-4-Line-1 Bus-4-Line-2 Bus-4-Line-3

Bus-

1

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10

)

Bus-

2

3

(2,6,9)

3

(2,6,9)

3

(2,6,9)

3

(2,6,9)

Bus-

3

9

(1,2,3,5,6,7,8,9,10)

9

(1,2,3,5,6,7,8,9,1

0)

9

(1,2,3,5,6,7,8,9,10

)

9

(1,2,3,5,6,7,8,9,

10)

Bus-

4

11

(1,2,3,4,5,6,7,8,9,10

,11)

9

(1,2,4,5,6,7,8,9,1

0)

10

(1,2,4,5,6,7,8,9,10

,11)

10

(1,2,3,4,5,6,7,8,

9,10)

Bus-

5

4

(5,7,8,10)

4

(5,7,8,10)

4

(5,7,8,10)

4

(5,7,8,10)

Bus-

6

1

(6)

1

(6)

1

(6)

1

(6)

Bus-

7

1

(7)

1

(7)

1

(7)

1

(7)

Bus-

8

2

(8,10)

2

(8,10)

2

(8,10)

2

(8,10)

Bus-

9

1

(9)

1

(9)

1

(9)

1

(9)

Bus-

10

1

(10)

1

(10)

1

(10)

1

(10)

Bus-

11

9

(1,2,5,6,7,8,9,10,11)

9

(1,2,5,6,7,8,9,10,

11)

9

(1,2,5,6,7,8,9,10,1

1)

9

(1,2,5,6,7,8,9,10

,11)

Table 4.22 Voltage and current measurements for Bus-5 when Rfault = 1 and f =

1000Hz

64

Msr

Inj

Bus-5

Voltase Current

Bus-5 Bus-5-Line-1 Bus-5-Line-2 Bus-5-Line-3

Bus-

1

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

Bus-

2

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

Bus-

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

4

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

5

11

(1,2,3,4,5,6,7,8,9,

10,11)

8

(1,2,3,4,5,6,9,11)

8

(1,2,3,4,5,6,9,11)

8

(1,2,3,4,5,6,9,11)

Bus-

6

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

Bus-

7

(2,3,4,6,7,9,11)

7

(2,3,4,6,7,9,11)

7

(2,3,4,6,7,9,11)

7

(2,3,4,6,7,9,11)

Bus-

8

(2,3,4,6,8,9,10,11

)

8

(2,3,4,6,8,9,10,1

1)

8

(2,3,4,6,8,9,10,1

1)

8

(2,3,4,6,8,9,10,1

1)

Bus-

9

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

Bus-

10

7

(2,3,4,6,9,10,11)

7

(2,3,4,6,9,10,11)

7

(2,3,4,6,9,10,11)

7

(2,3,4,6,9,10,11)

Bus-

11

1

(11)

1

(11)

1

(11)

1

(11)

Table 4.23 Voltage and current measurements for Bus-6, Bus-7, and Bus-8 when Rfault = 1

and

f = 1000Hz

65

Measu

remen

t

Inj

Bus-6 Bus-7 Bus-8

Voltase Current Voltase Current Voltase Current

Bus-1 8

(1,3,4,5,7,8,

10,11)

8

(1,3,4,5,7,8,

10,11)

7

(1,2,3,4,6,9,

11)

7

(1,2,3,4,6,9,

11)

7

(1,2,3,4,6,9,

11)

7

(1,2,3,4,6,

9,11)

Bus-2 10

(1,2,3,4,5,7,

8,9,10,11)

10

(1,2,3,4,5,7,

8,9,10,11)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,

11)

Bus-3 3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-4 2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-5 7

(3,4,5,7,8,1

0,11)

7

(3,4,5,7,8,1

0,11)

10

(1,2,3,4,5,6,

8,9,10,11)

10

(1,2,3,4,5,6,

8,9,10,11)

9

(1,2,3,4,5,6,

8,9,11)

9

(1,2,3,4,5,

6,8,9,11)

Bus-6 11

(1,2,3,4,5,6,

7,8,9,10,11)

11

(1,2,3,4,5,6,

7,8,9,10,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

Bus-7 4

(3,4,7,11)

4

(3,4,7,11)

11

(1,2,3,4,5,6,

7,8,9,10,11)

11

(1,2,3,4,5,6,

7,8,9,10,11)

7

(2,3,4,6,7,9,

11)

7

(2,3,4,6,7,

9,11)

Bus-8 5

(3,4,8,10,11

)

5

(3,4,8,10,11

)

8

(2,3,4,6,8,9,

10,11)

8

(2,3,4,6,8,9,

10,11)

11

(1,2,3,4,5,6,

7,8,9,10,11)

10

(1,2,3,4,5,

6,7,8,9,11

)

Bus-9 4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

Bus-10 4

(3,4,10,11)

4

(3,4,10,11)

7

(2,3,4,6,9,1

0,11)

7

(2,3,4,6,9,1

0,11)

8

(1,2,3,4,6,9,

10,11)

7

(2,3,4,6,9,

10,11)

Bus-11 1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Table 4.24 Voltage and current measurements for Bus-9, Bus-10, and Bus-11 when Rfault

= 1

and f=1000Hz

66

Measu

remen

t

Injecti

abov

e

Bus-9 Bus-10 Bus-11

Voltase Current Voltase Current Voltase Current

Bus-1

8

(1,3,4,5,7,8,

10,11)

8

(1,3,4,5,7,

8,10,11)

7

(1,2,3,4,6,9,

11)

7

(1,2,3,4,6,9,

11)

8

(1,2,5,6,7,8,

9,10)

8

(1,2,5,6,7,8,

9,10)

Bus-2

10

(1,2,3,4,5,6,

7,8,10,11)

9

(1,2,3,4,5,

6,7,10,11)

5

(2,3,4,6,11)

5

(2,3,4,6,11)

3

(2,6,9)

3

(2,6,9)

Bus-3 3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

9

(1,2,3,5,6,7,

8,9,10)

9

(1,2,3,5,6,7,

8,9,10)

Bus-4 2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

6

(4,5,6,7,8,9)

6

(1,5,6,7,8,9)

Bus-5 4

(7,8,10,11)

3

(7,10,11)

5

(5,6,7,9,11)

5

(5,6,7,9,11)

4

(5,7,8,10)

4

(5,7,8,10)

Bus-6 4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

1

(6)

1

(6)

Bus-7 4

(3,4,7,11)

4

(3,4,7,11)

5

(2,6,7,9,11)

5

(2,6,7,9,11)

1

(7)

1

(7)

Bus-8

5

(3,4,8,10,11

)

5

(3,4,8,10,

11)

10

(1,2,3,4,5,6,

7,8,9,11)

10

(1,2,3,4,5,6,

7,8,9,11)

2

(8,11)

2

(8,11)

Bus-9

11

(1,2,3,4,5,6,

7,8,9,10,11)

10

(1,2,3,4,5,

6,7,8,9,11

4

(3,4,9,11)

4

(3,4,9,11)

1

(9)

1

(9)

Bus-10 4

(3,4,10,11)

4

(3,4,10,11

)

11

(1,2,3,4,5,6,

7,8,9,10,11)

11

(1,2,3,4,5,6,

7,8,9,10,11)

1

(10)

1

(10)

Bus-11 1

(11)

1

(11)

1

(11)

1

(11)

11

(1,2,3,4,5,6,

7,8,9,10,11)

11

(1,2,3,4,5,6,

7,8,9,10,11)

67

4.7 Current Measurement Results for Rfault = 1e−3 and f = 7000Hz

Table 4.25 Voltage and current measurements for Bus-1 when Rfault = 1e−3 and f =

7000Hz

Msr

Inj

Bus-1

Voltase Current

Bus-1 Bus-1-Line-1 Bus-1-Line-2 Bus-1-Line-3 Bus-1-Line-4

Until

-1

10

(2,3,4,5,6,7,8,9,1

0,11)

1

(11)

7

(2,5,6,7,8,9,10

)

6

(2,3,4,6,9,11)

7

(3,4,5,7,8,10,

11)

Until

-2

4

(4,6,9,11)

4

(4,6,9,11)

2

(6,9)

4

(4,6,9,11)

4

(4,6,9,11)

Until

-3

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Until

-4

1

(11)

1

(11)

2

(9,11)

1

(11)

1

(11)

Until

-5

5

(4,7,8,10,11)

5

(4,7,8,10,11)

3

(7,8,10)

5

(4,7,8,10,11)

5

(4,7,8,10,11)

Until

-6

2

(4,11)

2

(4,11)

02

(4,11)

2

(4,11)

Until

-7

2

(4,11)

2

(4,11)

03

(3,4,11)

2

(4,11)

Until

-8

3

(4,10,11)

3

(4,10,11)

1

(10)

4

(3,4,10,11)

3

(4,10,11)

Until

-9

2

(4,11)

2

(4,11)

02

(4,11)

2

(4,11)

Until

-10

2

(4,11)

2

(4,11)

03

(3,4,11)

2

(4,11)

Until

-11 0 0 1

(9) 0 0

Table 4.26 Voltage and current measurements for Bus-2 when Rfault = 1e−3 and f =

7000Hz

68

Msr

Inj

Bus-2

Voltase Current

Bus-2 Bus-2-Line-1 Bus-2-Line-2 Bus-2-Line-3 Bus-2-Line-4

Bus-

1

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,

11)

Bus-

2

10

(1,3,4,5,6,7,8,9

,10,11)

2

(4,11)

4

(4,6,9,11)

9

(1,3,4,5,7,8,9,

10,11)

9

(1,3,4,5,6,7,8,

10,11)

Bus-

3

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

4

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Bus-

5

(4,7,8,10,11)

5

(4,7,8,10,11)

5

(4,7,8,10,11)

4

(4,7,10,11)

5

(4,7,8,10,11)

Bus-

6

3

(3,4,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

7

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

8

3

(4,10,11)

3

(4,10,11)

3

(4,10,11)

3

(4,10,11)

3

(4,10,11)

Bus-

9

3

(3,4,11)

3

(3,4,11)

2

(4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

10

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

11 0 0 0 0 0

Table 4.27 Voltage and current measurements for Bus-3 when Rfault = 1e−3 and f =

7000Hz

69

Msr

Inj

Bus-3

Voltase Current

Bus-3 Bus-3-Line-1 Bus-3-Line-2 Bus-3-Line-3

Bus-

1

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

Bus-

2

(6,9)

2

(6,9)

2

(6,9)

2

(6,9)

Bus-

3

10

(1,2,4,5,6,7,8,9,10,11)

2

(6,9)

2

(4,11)

8

(1,2,5,6,7,8,9,10)

Bus-

4

8

(2,5,6,7,8,9,10,11)

8

(2,5,6,7,8,9,10,11)

1

(11)

8

(1,2,6,7,8,9,10,11)

Bus-

5

3

(7,8,10)

3

(7,8,10)

3

(7,8,10)

3

(7,8,10)

Bus-

60 0 0 0

Bus-

70 0 0 0

Bus-

8

1

(10)

1

(10)

1

(10)

1

(10)

Bus-

90 0 0 0

Bus-

10 0 0 0 0

Bus-

11

6

(2,6,7,8,9,10)

6

(2,6,7,8,9,10)

07

(2,5,6,7,8,9,10)

Table 4.28 Voltage and current measurements for Bus-4 when Rfault = 1e−3 and f =

7000Hz

70

Msr

Inj

Bus-4

Voltase Current

Bus-4 Bus-4-Line-1 Bus-4-Line-2 Bus-4-Line-3

Bus-

1

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

Bus-

2

(6,9)

2

(6,9)

2

(6,9)

2

(6,9)

Bus-

3

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

Bus-

4

10

(1,2,3,5,6,7,8,9,10,11)

7

(2,5,6,7,8,9,10)

8

(2,5,6,7,8,9,10,11)

9

(1,2,3,5,6,7,8,9,10)

Bus-

5

3

(7,8,10)

3

(7,8,10)

3

(7,8,10)

3

(7,8,10)

Bus-

60 0 0 0

Bus-

70 0 0 0

Bus-

8

1

(10)

1

(10)

1

(10)

1

(10)

Bus-

90 0 0 0

Bus-

10 0 0 0 0

Bus-

11

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

7

(2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

Table 4.29 Voltage and current measurements for Bus-5 when Rfault = 1e−3 and f =

7000Hz

71

Msr

Inj

Bus-5

Voltase Current

Bus-5 Bus-5-Line-1 Bus-5-Line-2 Bus-5-Line-3

Bus-

1

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

Bus-

2

4

(4,6,9,11)

4

(4,6,9,11)

4

(4,6,9,11)

4

(4,6,9,11)

Bus-

3

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

4

1

(11)

1

(11)

1

(11)

1

(11)

Bus-

5

10

(1,2,3,4,6,7,8,9,10,11)

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

Bus-

6

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

7

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

8

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

Bus-

9

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

10

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

11 0 0 0 0

Table 4.30 Voltage and current measurements for Bus-6, Bus-7, and Bus-8 when Rfault =

1e−3

and f=7000Hz

72

Msr

Inj

Bus-6 Bus-7 Bus-8

Voltase Current Voltase Current Voltase Current

Bus-

1

7

(3,4,5,7,8,

10,11)

7

(3,4,5,7,8,1

0,11)

6

(2,3,4,6,9,11

)

6

(2,3,4,6,9,11

)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,1

1)

Bus-

2

9

(1,3,4,5,7,

8,9,10,11)

9

(1,3,4,5,7,8,

9,10,11)

4

(4,6,9,11)

4

(4,6,9,11)

4

(4,6,9,11)

4

(4,6,9,11)

Bus-

3

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

4

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Bus-

5

(4,7,8,10,1

1)

4

(4,7,10,11)

9

(1,2,3,4,6,8,

9,10,11)

9

(1,2,3,4,6,8,

9,10,11)

8

(1,2,3,4,6,7

,9,11)

8

(1,2,3,4,6,7

,9,11)

Bus-

6

10

(1,2,3,4,5,

7,8,9,10,1

1)

10

(1,2,3,4,5,7,

8,9,10,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

7

2

(4,11)

2

(4,11)

10

(1,2,3,4,5,6,

8,9,10,11)

10

(1,2,3,4,5,6,

8,9,10,11)

3

(3,4,11)

3

(3,4,11)

Bus-

8

3

(4,10,11)

3

(4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

10

(1,2,3,4,5,6

,7,9,10,11)

9

(1,2,3,4,5,6

,7,9,11)

Bus-

9

3

(3,4,11)

3

(3,4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

10

2

(4,11)

2

(4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

11 0 0 0 0 0 0

Table 4.31 Voltage and current measurements for Bus-9, Bus-10, and Bus-11 when Rfault

= 1e−3 and f = 7000Hz

73

Msr

Instr

uctio

ns

Bus-9 Bus-10 Bus-11

Voltase Current Voltase Current Voltase Current

Bus-

1

7

(3,4,5,7,8,1

0,11)

7

(3,4,5,7,8,10

,11)

6

(2,3,4,6,9,

11)

6

(2,3,4,6,9,11)

7

(2,5,6,7,8,

9,10)

7

(2,5,6,7,8,

9,10)

Bus-

2

9

(1,3,4,5,6,7

,8,10,11)

9

(1,3,4,5,6,7,

8,10,11)

4

(4,6,9,11)

4

(4,6,9,11)

2

(6,9)

2

(6,9)

Bus-

3

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

8

(1,2,5,6,7,

8,9,10)

8

(1,2,5,6,7,

8,9,10)

Bus-

4

1

(11)

1

(11)

1

(11)

1

(11)

9

(1,2,3,5,6,

7,8,9,10)

9

(1,2,3,5,6,

7,8,9,10)

Bus-

5

(4,7,8,10,1

1)

5

(4,7,8,10,11)

8

(1,2,3,4,6,

7,9,11)

8

(1,2,3,4,6,7,9

,11)

3

(7,8,10)

3

(7,8,10)

Bus-

6

3

(3,4,11)

3

(3,4,11)

2

(4,11)

2

(4,11) 0 0

Bus-

7

2

(4,11)

2

(4,11)

3

(3,4,11)

3

(3,4,11) 0 0

Bus-

8

3

(4,10,11)

3

(4,10,11)

9

(1,2,3,4,5,

6,7,9,11)

9

(1,2,3,4,5,6,7

,9,11)

1

(10)

1

(10)

Bus-

9

10

(1,2,3,4,5,6

,7,8,10,11)

10

(1,2,3,4,5,6,

7,8,10,11)

2

(4,11)

2

(4,11) 0 0

Bus-

10

2

(4,11)

2

(4,11)

10

(1,2,3,4,5,

6,7,8,9,11)

10

(1,2,3,4,5,6,7

,8,9,11)

0 0

Bus-

11 0 0 0 0

10

(1,2,3,4,5,

6,7,8,9,10)

10

(1,2,3,4,5,

6,7,8,9,10)

74

4.8 Current Measurement Results for Rfault = 1 and f = 7000Hz

Table 4.32 Voltage and current measurements for Bus-1 when Rfault = 1 and f = 7000Hz

Mr

s.

R

Inj

Bus-1

Voltase Current

Bus-1 Bus-1-Line-1 Bus-1-Line-2 Bus-1-Line-3 Bus-1-Line-4

Until

-1

11

(1,2,3,4,5,6,7,

8,9,10,11)

4

(1,3,4,11)

8

(1,2,5,6,7,8,9,

10)

7

(1,2,3,4,6,9,11

)

8

(1,3,4,5,7,8,10

,11)

Until

-2

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

3

(2,6,9)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

Until

-3

3

(3,4,11)

3

(3,4,11)

6

(2,3,4,6,9,11)

3

(3,4,11)

3

(3,4,11)

Until

-4

2

(4,11)

2

(4,11)

5

(2,4,6,9,11)

2

(4,11)

2

(4,11)

Until

-5

7

(3,4,5,7,8,10,

11)

7

(3,4,5,7,8,10,1

1)

4

(5,7,8,10)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,1

1)

Until

-6

4

(3,4,6,11)

4

(3,4,6,11)

1

(6)

4

(3,4,6,11)

4

(3,4,6,11)

Until

-7

4

(3,4,7,11)

4

(3,4,7,11)

1

(7)

4

(3,4,7,11)

4

(3,4,7,11)

Until

-8

5

(3,4,8,10,11)

5

(3,4,8,10,11)

2

(8,10)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

Until

-9

4

(3,4,9,11)

4

(3,4,9,11)

1

(9)

4

(3,4,9,11)

4

(3,4,9,11)

Until

-10

4

(3,4,10,11)

4

(3,4,10,11)

1

(10)

4

(3,4,10,11)

4

(3,4,10,11)

Until

-11

1

(11)

1

(11)

4

(2,6,9,11)

1

(11)

1

(11)

Table 4.33 Voltage and current measurements for Bus-2 when Rfault = 1 and f =

7000Hz

75

Msr

Inj

Bus-2

Voltase Current

Bus-2 Bus-2-Line-

1Bus-2-Line-2 Bus-2-Line-3 Bus-2-Line-4

Bus-

1

8

(1,3,4,5,7,8,

10,11)

8

(1,3,4,5,7,8,1

0,11)

8

(1,3,4,5,7,8,10

,11)

8

(1,3,4,5,7,8,10

,11)

8

(1,3,4,5,7,8,10,

11)

Bus-

2

11

(1,2,3,4,5,6,

7,8,9,10,11)

4

(2,3,4,11)

6

(2,3,4,6,9,11)

10

(1,2,3,4,5,7,8,

9,10,11)

10

(1,2,3,4,5,6,7,8

,10,11)

Bus-

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

4

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

5

7

(3,4,5,7,8,10

,11)

7

(3,4,5,7,8,10,

11)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,1

1)

7

(3,4,5,7,8,10,1

1)

Bus-

6

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

Bus-

7

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

Bus-

8

5

(3,4,8,10,11)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

Bus-

9

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

Bus-

10

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

Bus-

11

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Table 4.34 Voltage and current measurements for Bus-3 when Rfault = 1 and f =

7000Hz

76

Msr

Inj

Bus-3

Voltase Current

Bus-3 Bus-3-Line-1 Bus-3-Line-2 Bus-3-Line-3

Until

-1

8

(1,2,5,6,7,8,9,10

)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

Until

-2

3

(2,6,9)

3

(2,6,9)

3

(2,6,9)

3

(2,6,9)

Until

-3

11

(1,2,3,4,5,6,7,8,9

,10,11)

9

(1,2,3,5,6,7,8,9,10

)

5

(3,4,6,9,11)

9

(1,2,3,5,6,7,8,9,10

)

Until

-4

10

(1,2,4,5,6,7,8,9,1

0,11)

10

(1,2,4,5,6,7,8,9,10

,11)

5

(2,4,6,9,11)

10

(1,2,4,5,6,7,8,9,10

,11)

Until

-5

4

(5,7,8,10)

4

(5,7,8,10)

4

(5,7,8,10)

4

(5,7,8,10)

Until

-6

1

(6)

1

(6)

1

(6)

1

(6)

Until

-7

1

(7)

1

(7)

1

(7)

1

(7)

Until

-8

2

(8,10)

2

(8,10)

2

(8,10)

2

(8,10)

Until

-9

1

(9)

1

(9)

1

(9)

1

(9)

Until

-10

1

(10)

1

(10)

1

(10)

1

(10)

Until

-11

9

(1,2,5,6,7,8,9,10,

11)

9

(1,2,5,6,7,8,9,10,1

1)

4

(2,6,9,11)

9

(1,2,5,6,7,8,9,10,1

1)

Table 4.35 Voltage and current measurements for Bus-4 when Rfault = 1 and f =

7000Hz

77

Msr

Inj

Bus-4

Voltase Current

Bus-4 Bus-4-Line-1 Bus-4-Line-2 Bus-4-Line-3

Until

-1

8

(1,2,5,6,7,8,9,10

)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

8

(1,2,5,6,7,8,9,10)

Until

-2

3

(2,6,9)

3

(2,6,9)

3

(2,6,9)

3

(2,6,9)

Until

-3

9

(1,2,3,5,6,7,8,9,1

0)

9

(1,2,3,5,6,7,8,9,10)

9

(1,2,3,5,6,7,8,9,10)

9

(1,2,3,5,6,7,8,9,10)

Until

-4

11

(1,2,3,4,5,6,7,8,9

,10,11)

9

(1,2,4,5,6,7,8,9,10)

10

(1,2,4,5,6,7,8,9,10,

11)

10

(1,2,3,4,5,6,7,8,9,1

0)

Until

-5

4

(5,7,8,10)

4

(5,7,8,10)

4

(5,7,8,10)

4

(5,7,8,10)

Until

-6

1

(6)

1

(6)

1

(6)

1

(6)

Until

-7

1

(7)

1

(7)

1

(7)

1

(7)

Until

-8

2

(8,10)

2

(8,10)

2

(8,10)

2

(8,10)

Until

-9

1

(9)

1

(9)

1

(9)

1

(9)

Until

-10

1

(10)

1

(10)

1

(10)

1

(10)

Until

-11

9

(1,2,5,6,7,8,9,10,

11)

9

(1,2,5,6,7,8,9,10,1

1)

9

(1,2,5,6,7,8,9,10,1

1)

9

(1,2,5,6,7,8,9,10,1

1)

Table 4.36 Voltage and current measurements for Bus-5 when Rfault = 1 and f =

7000Hz

78

Msr

Inj

Bus-5

Voltase Current

Bus-5 Bus-5-Line-1 Bus-5-Line-2 Bus-5-Line-3

Bus-

1

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

7

(1,2,3,4,6,9,11)

Bus-

2

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

Bus-

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Bus-

4

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Bus-

5

11

(1,2,3,4,5,6,7,8,9,10,11)

8

(1,2,3,4,5,6,9,11)

8

(1,2,3,4,5,6,9,11)

8

(1,2,3,4,5,6,9,11)

Bus-

6

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

Bus-

7

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

Bus-

8

5

(3,4,8,10,11)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

5

(3,4,8,10,11)

Bus-

9

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

Bus-

10

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

Bus-

11

1

(11)

1

(11)

1

(11)

1

(11)

Table 4.37 Voltage and current measurements for Bus-6, Bus-7, and Bus-8 when Rfault = 1

and

f=7000Hz

79

M

rs.

r

Inj

Bus-6 Bus-7 Bus-8

Voltase Current Voltase Current Voltase Current

Until

-1

8

(1,3,4,5,7,8

,10,11)

8

(1,3,4,5,7,8,

10,11)

7

(1,2,3,4,6,9

,11)

7

(1,2,3,4,6,9

,11)

7

(1,2,3,4,6,9,1

1)

7

(1,2,3,4,6,

9,11)

Until

-2

10

(1,2,3,4,5,7

,8,9,10,11)

10

(1,2,3,4,5,7,

8,9,10,11)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,1

1)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,

11)

Until

-3

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

Until

-4

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

Until

-5

7

(3,4,5,7,8,1

0,11)

7

(3,4,5,7,8,1

0,11)

10

(1,2,3,4,5,6

,8,9,10,11)

10

(1,2,3,4,5,6

,8,9,10,11)

9

(1,2,3,4,5,6,8

,9,11)

9

(1,2,3,4,5,

6,8,9,11)

Until

-6

11

(1,2,3,4,5,6

,7,8,9,10,1

1)

11

(1,2,3,4,5,6,

7,8,9,10,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

Until

-7

4

(3,4,7,11)

4

(3,4,7,11)

11

(1,2,3,4,5,6

,7,8,9,10,11

)

11

(1,2,3,4,5,6

,7,8,9,10,11

)

4

(3,4,7,11)

4

(3,4,7,11)

Until

-8

5

(3,4,8,10,1

1)

5

(3,4,8,10,11

)

5

(3,4,8,10,1

1)

5

(3,4,8,10,1

1)

11

(1,2,3,4,5,6,7

,8,9,10,11)

10

(1,2,3,4,5,

6,7,8,9,11)

Until

-9

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

4

(3,4,9,11)

Until

-10

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

4

(3,4,10,11)

Until

-11

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

1

(11)

Table 4.38 Voltage and current measurements for Bus-9, Bus-10, and Bus-11 when Rfault

= 1

and f=7000Hz

80

Mr

s. r

Inj

Bus-9 Bus-10 Bus-11

Voltase Current Voltase Current Voltase Current

Until

-1

8

(1,3,4,5,7,8,

10,11)

8

(1,3,4,5,7,8,1

0,11)

7

(1,2,3,4,6,9,1

1)

7

(1,2,3,4,6,9,1

1)

8

(1,2,5,6,7,

8,9,10)

8

(1,2,5,6,7,

8,9,10)

Until

-2

10

(1,2,3,4,5,6,

7,8,10,11)

10

(1,2,3,4,5,6,7

,8,10,11)

6

(2,3,4,6,9,11)

6

(2,3,4,6,9,11)

3

(2,6,9)

3

(2,6,9)

Until

-3

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

3

(3,4,11)

4

(1,2,3,10)

9

(1,2,3,10)

Until

-4

2

(4,11)

2

(4,11)

2

(4,11)

2

(4,11)

10

(1,2,3,4,5,

6,7,8,9)

10

(1,2,3,4,5,

6,7,8,9)

Until

-5

7

(3,4,5,7,8,1

0,11)

7

(3,4,5,7,8,10,

11)

9

(1,2,3,4,5,6,7

,9,11)

9

(1,2,3,4,5,6,7

,9,11)

4

(5,7,8,10)

4

(5,7,8,10)

Until

-6

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

4

(3,4,6,11)

1

(6)

1

(6)

Until

-7

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

4

(3,4,7,11)

1

(7)

1

(7)

Until

-8

5

(3,4,8,10,11

5

(3,4,8,10,11

5

(5,7,8,9,11)

5

(5,7,8,9,11)

2

(8,11)

2

(8,11)

Until

-9

11

(1,2,3,4,5,6,

7,8,9,10,11)

11

(1,2,3,4,5,6,7

,8,9,10,11)

4

(3,4,9,11)

4

(3,4,9,11)

1

(9)

1

(9)

Until

-10

4

(3,4,10,11)

4

(3,4,10,11)

11

(1,2,3,4,5,6,7

,8,9,10,11)

11

(1,2,3,4,5,6,7

,8,9,10,11)

1

(10)

1

(10)

Until

-11

1

(11)

1

(11)

1

(11)

1

(11)

9

(1,3,5,6,7,

8,9,10,11

9

(1,3,5,6,7,

8,9,10,11

As shown in the table, current measurements can provide better results with fewer undetected

buses and less multi-estimation over voltage measurements.

81

CHAPTER 5

CONCLUSION

Conclusion

In this thesis, a new method for locating faults in the ship's power system is proposed

using the applied voltage and the voltage/current measured when a fault occurs in the system.

The system is tested for all possible buses for injection and measurement and the optimal point

leading to the minimum number of injections and measurements in the system is found. The

proposed approach generalizes the Active Impedance Estimation (AIE) error location method

where the injection and measurement do not have to be in the same location. Also, it was shown

that by increasing the frequency of multi-estimation injections was significantly reduced. The

proposed approach is a reliable and economical method that can find fault locations in the ship's

power system with a minimum number of injections and measurements.

82

LIFE

Pedram Jahanmard was born in 1990 in Iran. He received his BS in Electrical

Engineering from Azad Islamic University, Najafabad, Esfahan, Iran in 2013. His current

research interests include Fault Location, Ship Power Systems, Protection, Intelligent Networks,

and Micronetworks.

A HIGH-PERFORMANCE FAULT LOCATION ALGORITHM FOR SHIPBOARD POWER SYSTEMS

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