IMPACT OF DISTRIBUTED GENERATION ON VOLTAGE PROFILE OF DISTRIBUTION
NETWORKS
Mohammed Osama AlRuwaili
B.S., Gonzaga University, 2010
PROJECT
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL AND ELECTRONIC ENGINEERING
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
FALL
2011
IMPACT OF DISTRIBUTED GENERATION ON VOLTAGE PROFILE OF DISTRIBUTION
NETWORKS
A Project
by
Mohammed Osama AlRuwaili
Approved by:
__________________________________, Committee Chair
Mohammad Vaziri, Ph.D., P.E
__________________________________, Second Reader
Fethi Belkhouche, Ph.D.
____________________________
Date
ii
Student: Mohammed Osama AlRuwaili
I certify that this student has met the requirements for format contained in the University format manual,
and that this project is suitable for shelving in the Library and credit is to be awarded for the Project.
__________________________, Graduate Coordinator
Preetham B. Kumar, Ph.D.
Department of Electrical and Electronic Engineering
iii
________________
Date
Abstract
of
IMPACT OF DISTRIBUTED GENERATION ON VOLTAGE PROFILE OF DISTRIBUTION
NETWORKS
by
Mohammed Osama AlRuwaili
This project provides the results of a study conducted to assess the impacts of the “wind
generation variability” on the voltage profile in a small-scale radial distribution system. The
power network has been modeled using one of the well-known simulation programs used by the
industry known as Powerworld®. The study takes into account the irregular behavior of the wind
patterns and focuses on effects of wind generation at variable penetration levels on the voltage
profile of a 13-bus radial distribution system. The assessment introduces two unique scenarios. In
one scenario, the wind-generation farms are connected to a remote location with a critical voltage
profile. The intensity of wind penetration is fluctuated methodically to evaluate the influence on
the grid’s voltage profile. The Smallest Singular Value of Jacobian (SSVJ) analysis of the power
flow Jacobian matrix is applied to further assess the networks voltage profile. This method has
been favored and utilized as an index for evaluating voltage profiles by the industry as well as the
utilities. Simulation results along with recommendation and suggestions for improvements in
each scenario have been provided.
______________________ , Committee Chair
Mohammad Vaziri, Ph.D., P.E.
_______________________
Date
iv
ACKNOWLEDGMENTS
Thanks and appreciation to King Abdullah Bin Abdulaziz and the Ministry of Higher
Education in Riyadh, The Kingdom of Saudi Arabia for providing me with the comprehensive
support and financial funding to pursue my undergraduate and graduate studies in the United
States of America.
I would like to extend my sincere thanks to my family for their encouragement and
assistance that helped me in various methods.
My deepest thanks to, Dr. Mohammad Vaziri, for guiding and directing the process of
this paper, and for correcting various versions of this paper with attention and care. I express my
thanks to the Chair of the Electrical Engineering department, Dr. Suresh Vadhva, at California
State University, Sacramento (CSUS) for extending his support. Thanks and appreciation to Dr.
Fethi Belkhouche and Dr. Preetham Kumar for their helpful support. I would also thank my
Institution and my faculty members.
v
TABLE OF CONTENTS
Page
Acknowledgments..................................................................................................................... v
List of Figures ........................................................................................................................ vii
Chapter
1. INTRODUCTION .............................................................................................................. 1
2. PERFORMANCE INDICATORS ..................................................................................... 3
3. SINGULAR VALUE DECOMPOSITION ....................................................................... 5
The Smallest Singular Value in Power Systems .......................................................... 8
Utilization of the Singular Value Decomposition ....................................................... 10
4. THE RADIAL DISTRIBUTION GRID ........................................................................... 12
Simulation Results ..................................................................................................... 14
5. CONCLUSION ................................................................................................................. 22
References ............................................................................................................................... 23
vi
LIST OF FIGURES
Figures
Page
1.
Figure 1 Electricity Grid Schematic [22] .................................................................. 13
2.
Figure 2 13-Bus Network, with Wind Farms at Buses 7, 10, & 11 ........................... 14
3.
Figure 3 Voltage Profile at Critical Locations (No Wind)......................................... 15
4.
Figure 4 SSV Index of the Network (No Wind) ........................................................ 15
5.
Figure 5 Voltage Profile at Critical Locations (No Wind)......................................... 16
6.
Figure 6. SSV Index of the Network (No Wind) ....................................................... 17
7.
Figure 7 Voltage Profile at Critical Locations (With Wind) ..................................... 17
8.
Figure 8 SSV Index of the Network (With Wind) ..................................................... 18
9.
Figure 9 Voltage Profile at Critical Locations (With Wind) ..................................... 19
10.
Figure 10. SSV Index of the Network (With Wind) .................................................. 20
11.
Figure 11. Illustration of the Impact of Reversed Power Flow .................................. 21
12.
Figure 12 Illustration of the Total Power Loss in all Four Scenarios ........................ 21
vii
1
Chapter 1
INTRODUCTION
Modern power system networks consist of various types of generators, and loads
interconnected to significantly intricate and large transmission and distribution systems. As the
electric power demand increases, the complexity of the power network rises. Due to hard to
control reasons such as economics and environmental factors, the expansion of generation
capacities has become a difficult task for the electric utilities. Such situations can cause stressful
operating events especially during peak loading conditions. As a result, electric utilities have
adapted the idea of expanding and developing renewable distributed generations (DG’s) such as
wind farms and Photo Voltaic (PV) establishments to generate electricity. To assist the power
system in serving the peak load, the wind turbines for example, can be used as small power
generators that are connected to the distribution system or directly at the customer’s site [1].
Since the primary fuel of wind turbines is air, which is free, they are considered cheap and clean
energy resources. However, they may require fairly high initial costs compared to generators
using fossil fuel. The output power of a wind turbine generally depends on its size and where it is
located. Recently, manufacturers produce wind turbines that provide rated output power ranging
between hundreds of Watts to few Mega Watts (MW). Due to the intermittent behavior of wind,
known as “wind variability”, it would be difficult to have an accurate prediction of the output
power from wind turbines. Therefore, such a phenomenon could result in a challenging impact on
the reliability of the power network and on the steadiness of the voltage magnitude. For instance,
if the wind generation drops rapidly, then it would produce an immediate voltage drop effect at
the end of a feeder. In contrast, a sudden increase in wind speed would cause a voltage rise at the
high generation point. Consequently, the compliance of the power grid to the new grid codes and
to the system’s regulation should be carefully evaluated and considered during the feasibility
2
studies. The main focus of this paper is to provide an understanding of the impact of wind
generation on the voltage magnitude and profile in a small-scale distribution network. For this
purpose, a distribution system has been structured and modeled using Powerworld®. The study
evaluates and simulates a 13-bus network that contains both fossil fueled base generation units as
well as wind generation. Wind farms are connected at separate and strategic locations in the
distribution system for the analysis. To assess the performance of the power network and to
evaluate the behavior of the voltage profile, the method of the SSV of the Jacobian matrix (SSVJ)
is used. This index has been preferred by the industry as a performance indicator for the radial
distribution networks. Brief explanations about the most important performance indicators that
are used by many electric utilities around the world as well as the details for the method of SSVJ
will be presented in the following sections.
3
Chapter 2
PERFORMANCE INDICATORS
Electric companies use sophisticated power flow programs that are intended to study the
capabilities of large interconnected power systems. Hence, essential data is collected regarding
the operation of potential power networks and their impact on the present power systems [5].
Based on the information that is obtained, transmission and distribution design engineers are able
to detect the power network’s weaknesses such as excessive loading conditions and abnormal
voltages due to various loading and generation patterns. Variability in solar or wind generation
levels are good examples of generation patterns known to cause abnormal voltages during certain
periods. The variability of these renewable power resources has made the prediction and the
analysis of the performance of power networks more challenging and a primary concern for
engineers and researchers. Use of performance indices has been known to assist investigators to
determine the system’s closeness to a probable collapse. There are various types of performance
indices that have different uses. The performance index that is used in this paper utilizes the
method of the smallest singular value (SSV). Nevertheless, few of the other important indices are
also briefly described in the following chapters [3].
A. MVAR Power Reserve and Support
Principally, reactive power support is an important concept in power systems because as
a general rule most systems are known to be inductive nature [1]. From a voltage profile stand
point; the reactive power support that is provided by generators is greatly essential. Therefore,
reactive power reserves that are automatically activated serve as critical voltage profile indices
[3], with the assumption that the power network is close to collapse when major generating units
reach their reactive limits, and there is no other significant sources of reactive power support.
4
B. Voltage Drop
The “voltage drop” assessing technique is based on the theory that states that the voltage
drops as the demand on the power system increases causing added voltage drops in the grid.
Accuracy of the voltage profile and calculations of voltage drops will depend on accuracy of
modeling the system elements, especially the devices that compensate for reactive support such as
the Capacitors and the Static VAR Compensators (SVCs). It should be noted that in many cases,
compensation of reactive power is a requirement to sustain the voltage at a specific level while
delivering the desired real power via the distribution or transmission network.
C. Variable Steady State Margin Index
Initially, Venikov proposed an analysis to assess the voltage profile of the power system
by making use of the power flow Jacobian matrix [4]. Later, that method has been developed to
offer an indicator that is based on a special set of equations which are applied to the determinant
of the Jacobian. Then, that indicator is normalized to range between Zero and 1.0, where 0.0
represents the critical point of the power network.
D. Smallest Singular Value
To comprehend a straightforward analysis of a large power network, the Smallest
Singular Values (SSV) or minimum Eigen values have been utilized because of the usefulness of
the square orthogonal decomposition of the Jacobian of the power flow matrix. This paper will
first introduce general facts and fundamentals regarding the SSV decomposition of a matrix.
Then, it will propose a procedure of how the SSV decomposition method is going to be applied as
the primary tool to analyze our power network.
5
Chapter 3
SINGULAR VALUE DECOMPOSITION
The SVD decomposition as a valuable factorization can be determined for any given
matrix. One of the most useful aspects of the SVD of a matrix is that it provides a numerically
reliable method for determining the rank of a matrix. The rank of a matrix is the number of
nonzero singular values of that matrix. The smallest singular value can provide a measure of a
matrix’s L2 distance from a matrix of a lower rank. A considerably useful application of the SVD
is that it can be used to determine the least-squared solution to a system of linear equations Ax =
b. A description of such a solution can be found in [23]. In such an application, a large condition
number for matrix A indicates how sensitive the given system is to noise.
Typically, the Singular Value Decomposition (SVD) is employed to determine the rank
of a matrix. . A usful indicator that is obtained from a complete SSV decomposition of the power
flow Jacobian matrix may be applied to assess the voltage profile analysis [6]. In power networks,
the utilization of this indicator has been presented by Thomas and Tiranuchit in [8], [9], and [10].
If J is a real squared n-by-n matrix, then the singular value decomposition may be written
as [7]:
where
and
are the singular vectors that represent the columns in the n-by-n U and V
matrices respectively as in (2) and (3), and
is the singular value in matrix E as in (4):
6
Matrix E has the same size as matrix J, and has zeroes as its elements except possibly on
its main semi-axes. The singular values of matrix J are precisely the lengths of the diagonals of
matrix E, and they are generally sorted so that
. Matrix E may be
defined by the following equation, where I = 1, 2, …, n.[6]:
When matrix J has a rank (r) that is less or equal to (n), then its singular values are the
square roots of the positive Eigenvalues of matrix J multiplied by its transpose as in (J*JT), that is
also the positive Eigenvalues of (JT*J) [6]. In that sense, when
matrix J, then
is the ith singular value of
are the ith left and right singular vectors of matrix J respectively.
and
The meaning of the Eigenvalues is the characteristic polynomial or characteristic
equation from either one of the matrices
or
. The rank of matrix J is equivalent to the
degree of the characteristic equation [13]. Now, assume that
matrices
or
. Also, let matrix
are the Eigenvalues of
signify the n-by-n diagonal matrix with
denoting its diagonal elements. The link between the Eigenvalues and the singular values of
matrix M could be illustrated by the following relation [6]:
Acknowledging equation 1, which states that
decomposition of
or
, we may derive the Eigen
. However, first, it may be valuable to regard that matrices U and V
hold singular vectors which could always be selected to be perpendicular to each other. Thus,
those vectors assure that
, and
, where (I) here is an n-by-n identity matrix
[13]. That is to say, matrices U and V are orthogonal when they contain real elements and unitary
when they contain imaginary elements. Taking into consideration one of the key matrix properties
7
which states that
[14], the Eigen decomposition is derived as illustrated by
the following equations [6]:
Also,
In the process of calculating the singular value decomposition, we could imagine how
large the computations could be when analyzing large power networks. The size of the power
flow Jacobian matrix of a particular power network is directly proportional to its number of buses
or nodes. Thus, the larger the power system, the more complicated the SVD computations
become. Therefore, multiple scholars such as P. A. Lof, T. Smed, G. Andersson, and D. J. Hill in
[6], also Y. H. Hong, C. T. Pan, and W. W. Lin in [11] have proposed fast calculation algorithms
for the singular value decomposition. Those methods are valid for both small and large power
systems. For instance, the authors in [11] use the Lower/Upper (LU) factorization theory to
estimate the SSV of the Jacobian,
, which is proposed to be equal to the product
of the SSV of the lower matrix, (L), of the Jacobian by the maximum singular value of the upper
matrix, (U), of the Jacobian where
.
However, in this paper, we are going to directly compute the singular value matrix, E, by
utilizing the pre-built mathematical tools in MATLAB®, which is a fast software for numerical
computing and matrix manipulation. Primarily, in MATLAB®, we are going to employ the
command (SVD) which uses certain routines known as the LAPACK routines in order to execute
the singular value decomposition [12]. After that we are going to straightforwardly detect the
8
SSV of the Jacobian. The importance of the SSV of the power flow Jacobian matrix is described
in details in the following section.
THE SMALLEST SINGULAR VALUE IN POWER SYSTEMS
The study of the relationship of the SSV to the voltage profile problems has become an
essential area of research. One of the objectives of G. H. Golub and C. F. Van Loan studies in [7]
verify that the SSV of a matrix J (n-by-n) is a measure of the length in the Euclidean-norm, l2norm, between matrix J and the set of all rank-deficient matrices, which have a rank r that is less
than n. Additionally, the authors in [15] illustrate that one of the advantages of singular values is
that they are rather insensitive of perturbations in the matrix elements while the Eigenvalues of a
particular unsymmetrical matrices are very sensitive noting that:
In order to employ the above-mentioned theories on power networks, it is necessary to
first establish a linearized relation between the real and imaginary powers at nodes versus voltage
magnitudes and node angles [6]. That relationship may be discovered by the power flow Jacobian
matrix which is defined by the following equation [5], and [6], where Vi is the voltage magnitude
at bus , and
is the angle of Vi at bus :
In equation (11),
first node,
is the number of nodes/buses in the power network. The
, is considered as the slack bus. Matrix J is defined by the following [5]:
9
The Jacobian matrix J contains the real and the imaginary power flow equations
and
respectively and they are defined in the following polar format, where Y is the
admittance matrix, Vi and Vn are the voltage magnitudes at buses and n respectively, and
and
are the node angles at buses and n respectively:
The power flow Jacobian matrix defines principle data regarding the voltage magnitude
and angle at each node in addition to the node’s real and imaginary power flow. In theory, the
SSV of the Jacobian,
, is a measure of how close to singularity is the Jacobian [6].
Therefore, in case the SSV is equivalent to zero, then the power flow Jacobian matrix is singular
and as a result, the power flow solution cannot be obtained. The singularities in the Jacobian
matrix of the system’s dynamic equations are corresponded to the Bifurcation points [16], which
predict how the system becomes unstable. A singular Jacobian matrix could be interpreted as an
infinite sensitivity of the power flow solution to small disturbance in the parameter values [6].
10
That is when the value of a parameter passes through a static bifurcation point or a critical point;
the power network will experience a qualitative change in the nature of the solution.
UTILIZATION OF THE SINGULAR VALUE DECOMPOSITION
In this section, essential interpretations for the SSV and the consequent left and right
singular vectors are made. The main analyses, theories, and interpretations that are presented in
this section were proposed by P. A. Lof, T. Smed, G. Andersson, and D. J. Hill in [6].
The effect on the change in the phase angle,
voltage,
, and the change in magnitude of a bus
, from a small change in the real and reactive power injections can be introduced by
the following formula:
From the above formula, the inverse of the SSV of the power flow Jacobian will therefore
be a sign of the largest change in the state variables due to a small disturbance. In the
following,
,
, and
are the last columns in matrices U, V, and E respectively,
now let:
Then,
In addition, for the ith column of the unitary matrices, U and V, the following formulas
follow [18]:
11
Where,
,
[19], bearing in mind that
when the power
flow Jacobian is singular.
Now that we have gone through an analysis of the singular value decomposition theory
and considering the above formulas, the following interpretations may be derived for the SSV and
the corresponding right and left singular vectors [6]:
1. The SSV,
, is an indicator of the proximity to the steady state stability limit.
2. The right singular vector,
, which corresponds to
, is an indicator of sensitive voltage
magnitudes and their angles.
3. The left singular vector,
, which corresponds to
, is an indicator of the most sensitive
direction for changes of active and reactive power injections.
12
Chapter 4
THE RADIAL DISTRIBUTION GRID
This section provides a description and a general understanding of the proposed power
network including its connections, generation units, and impedances. The power network in our
case study is an adjusted 13-bus radial distribution network that is formed using Powerworld®
[1], [21].
Distribution power systems work as one of the essential final portion of the grid for
transporting power to end-users. Figure 1 shows a sample illustration of how power is generated
and then transmitted through transmission and distribution networks to finally reach the end users
such as homes, farms, and factories [22]. It also shows how the power is supplied to the
distribution networks via the connectivity of distributed generations such as solar panels, wind
farms, and other small to medium sized generators. The low-voltage distribution network in this
paper represents the point where the power is taken, through a substation, from the high-voltage
transmission network until it reaches the end users. Consequently, the power transmitted from the
transmission network is estimated and then connected to the distribution system using
Powerworld®. The end users are exemplified by loads of different capacities. The final network
model is a representation of modern radial distribution networks that are adaptive to the
assessment and evaluation of new concepts.
13
Figure 1: Electricity Grid Schematic. [22]
The single-line diagram in figure 1 demonstrates the 13-bus distribution network that is
used in the power system analysis. The distribution network used in this analysis represents a
typical substation through a small-scale radial distribution network in order to amplify various
impacts. The distribution network consists of two generators that are connected at busses 1 and 4.
The generation at bus 1 represents the power that is supplied by the transmission network through
a substation. The sending end voltage, where these generators are connected, is set to 1 P.U. by
the actions of the Automatic Voltage Regulators (AVR) connected at busses 1 and 4. The
14
generators supply power to a total of 6 load points through 50/7.2 kV transformers. The load
points have various values that were set up arbitrarily to add together to a total maximum load
capacity of 125 MW. The voltage level at the load points is 7.2 kV.
Figure 2: 13-Bus Network, with Wind Farms at Buses 7, 10, & 11
SIMULATION RESULTS
A. Case Scenario# 1
The main objective of the first scenario is to evaluate the voltage profile of the network
when no wind farms are connected and bus voltage regulation is not applied. The distribution grid
is supplied with power from the substation at bus# 1 (Slack Bus), and from the hydro generator
connected at bus# 4. Figure 3 demonstrates the load profile and the corresponding voltage profile
of the critical nodes at busses 6 7, 8, and 9. At peak load, bus# 6 had a voltage magnitude value of
15
(0.918 PU), that is approximately an %8 voltage drop, and bus# 7 had a voltage magnitude value
of (0.937 PU), which is approximately a %6 voltage drop. One of the solutions to fix the
excessive voltage drop issue at busses 6 and 7 is to apply voltage regulation at bus# 5 [2]. Hence,
that setting is proposed scenario#2. Figure 4 presents the load profile and the consequent
calculated SSVJ index values for system. We observe that at peak load, the network’s SSVJ index
140
1
120
0.98
100
0.96
80
0.94
60
0.92
40
20
Bus 7
Bus 9
0.88
0.86
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
0
0.9
Total Load
Bus 8
Bus 6
Bus Voltage (P.U.)
Load Demand (MW)
reached (10.51), which indicates the proximity to the steady state stability limit [6].
Time (hr)
Figure 3: Voltage Profile at Critical Locations (No Wind)
10.65
Load Demand (MW)
120
10.6
100
80
10.55
60
10.5
40
10.45
20
Total Load
SSVJ Index
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
0
Time (hr)
Figure 4: SSV Index of the Network (No Wind)
B. Case Scenario# 2
10.4
Smallest Singular Value Index
140
16
The key intention in this scenario is to assess the voltage profile of the distribution
network after applying voltage regulation functions at bus#5 only. Since the voltage magnitudes
at busses 6 and 7 dropped below %5 in the first scenario, we assume that applying voltage
regulation at bus# 5 would result in the enhancement of the voltage magnitudes at busses 6 and 7.
Figure 5 demonstrates the simulation results of the load profile and the corresponding voltage
magnitudes of the critical nodes at busses 6, 7, 8, and 9. We observe that at peak load, bus# 6 had
a voltage magnitude value of (0.979 PU), and bus#7 had a voltage magnitude value of (0.995
PU). Those outcomes show that the voltage magnitudes at busses 6 and 7 have improved due to
the bus voltage regulation at bus#5.
140
1.02
1.01
1
100
0.99
80
0.98
0.97
60
0.96
0.95
40
20
Bus 7
Bus 9
0.94
0.93
0.92
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
0
Total Load
Bus 8
Bus 6
Bus Voltage (P.U.)
Load Demand (MW)
120
Time (hr)
Figure 5: Voltage Profile at Critical Locations (No Wind)
Figure 6 illustrates the load profile and the corresponding calculated SSVJ index values
for the system. The simulation results illustrate that the voltage regulation has actually enhanced
the SSVJ index value at the peak load compared to scenario#1and hence verifying the usefulness
of this index for analyses of system voltage profiles. At peak load, the SSVJ index value was
recorded as (11.02).
140
Load Demand (MW)
120
100
80
60
40
20
Total Load
SSVJ Index
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
0
11.16
11.14
11.12
11.1
11.08
11.06
11.04
11.02
11
10.98
10.96
10.94
Smallest Singular Value Index
17
Time (hr)
Figure 6: SSV Index of the Network (No Wind)
C. Case Scenario# 3
In this case scenario, three wind farms are connected at busses 7, 8, and 9. The wind
farms provide a maximum total power of 35 MW. The wind generation follows a methodical
pattern as in [1], and is varied from 0% to 75% of the total connected load in the network. Also,
in this case scenario, bus voltage regulation is still functioning at bus#5. Figure 7 demonstrates
the simulation results of the voltage magnitudes at busses 6, 7, 8, and 9. In the figure, we notice
that at the peak load, the voltage magnitude at bus#6 dropped below 5% to reach (0.948 PU),
140
Wind
Bus 8
Bus 6
100
80
60
40
20
0
1.02
1.01
1
0.99
0.98
0.97
0.96
0.95
0.94
0.93
0.92
0.91
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
Load Demand (MW)
120
Total Load
Bus 7
Bus 9
Time (hr)
Figure 7: Voltage Profile at Critical Locations (With Wind)
Bus Voltage (P.U.)
where in the other hand, the voltage magnitude at bus%7 was at a value of (0.980 PU).
18
Figure 8 shows the load profile and the corresponding calculated SSVJ index values for
the system. In the figure, the simulation results illustrate that the SSVJ index value of (10.995) at
peak load was lower than its counterpart in case scenario# 2. We also observed that the voltage
regulation at bus#5 did not provide a very good enhancement in the voltage magnitude at bus#6.
Thus, one possible solution to improve the voltage magnitude at bus#6 is to apply a bus voltage
11.15
120
100
80
11.1
Total Load
Wind
SSVJ Index
11.05
60
11
40
10.95
20
0
Smallest Singular Value Index
140
10.9
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
Load Demand (MW), Wind Power (MW)
regulation at that bus. Hence, that setting is proposed in case scenario# 4.
Time (hr)
Figure 8: SSV Index of the Network (With Wind)
D. Case Scenario# 4
The main objective of this scenario is to improve the voltage magnitude at bus# 6, taking
into account that wind farms are still connected to the grid. To do so, one possible approach is to
apply bus voltage regulation at bus#6 in addition to the existing voltage regulation at bus#5.
Then, An assessment of the voltage profile and calculations of the SSVJ index values of the
distribution network are performed. Figure 9 shows the simulation results of the voltage
magnitudes at busses 6, 7, 8, and 9. In the figure, we observe that at the peak load, the voltage
magnitude at bus#6 has enhanced to record a value of (1.004 PU), where in the other hand, the
voltage magnitude at bus#7 was at a value of (0.978PU). Hence, applying the additional voltage
19
regulation at bus#6 has substantially improved the voltage magnitude at that bus compared to
120
Total Load
Bus 7
Bus 9
Wind
Bus 8
Bus 6
100
1.02
1.01
1
80
0.99
60
0.98
40
0.97
20
0.96
0
0.95
Bus Voltage (P.U.)
140
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
Load Demand (MW), Wind Power (MW)
case scenario# 3.
Time (hr)
Figure 9: Voltage Profile at Critical Locations (With Wind)
Figure 10 presents the load profile and the corresponding calculated SSVJ index values
for the system. In the figure, the simulation results illustrate that the SSVJ index value at peak
load was (25.837), which is lower than its counterpart in all of the previous case scenarios. The
lowest SSVJ index value was (24.357) and was recorded at time (17:00). However, even the
lowest SSVJ index value was still way higher than the lowest SSVJ index values in the all of the
previous case scenarios as well. Thus, the voltage regulation at bus#6 did not only improve the
overall voltage magnitudes at that bus, but it also increased the SSVJ index values of the
distribution network. That means that the overall quality of the steady state stability limit has also
improved.
26.2
120
26
100
25.8
Total Load
Wind
SSVJ Index
80
25.6
60
25.4
40
25.2
20
25
0
Smallest Singular Value Index
140
24.8
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
Load Demand (MW), Wind Power (MW)
20
Time (hr)
Figure 10: SSV Index of the Network (With Wind)
E. Special Case Scenario
In cases where the networks experiences high DG penetration and low demand, high bus
voltages may occur at the points where the DG’s are connected. This phenomenon could happen
due to the reversed power flow that is caused by the DG’s [2]. In the distribution network in
figure 1, one case where the high voltage incident may happen is when the network has low load
profile, and the wind farms at busses 7, 8 or 9 are injecting high power to the system causing
reversed power flows. To further illustrate this phenomenon, figure 10 shows an extraction of
case scenario# 3, but with low load profile and higher DG penetrations. The figure provides an
analysis of the voltage profile at the DG bus# 7 only. We could observe that the reversed power
flow starts occurring around 2:00 AM causing a high voltage condition at the DG bus# 7. For the
specified period of time in figure 6, the SSV index value reached (11.52) at (1:00 AM), and
reached a maximum value of (11.59) at (4:00 AM). Those values are higher in average compared
to their counterparts in case scenario# 3. In [2], M. Vaziri and K. Tran propose multiple possible
solutions to high voltage incidents caused by the DG’s. Some of those solutions include
conversion of distribution voltage to higher levels, moving the voltage regulators to different
locations, or to change their base and compensation settings.
21
1.065
40
1.06
35
1.055
30
25
1.05
20
1.045
15
1.04
Total Load
10
Wind
5
Bus Voltage (P.U.)
Total Load Demand, & Wind Power (MW)
45
1.035
Bus 7
0
1.03
1:00
2:00
Time (hr)
3:00
4:00
Figure 11: Illustration of the Impact of Reversed Power Flow
As the renewable distributed generations were connected to the different busses, we have
observed that there were significant reductions in the total power loss in the network as the total
load demand was increasing. That is, the contribution of the wind farm’s power reduced the
power lost within the distribution feeders. Figure 11 shows a comparison between the total power
losses in all four case scenarios.
3.5
Total Ploss Scenario#1
Total Power Loss (MW)
3
Total Ploss Scenario#2
2.5
Total Ploss Scenario#3
2
Total Ploss Scenario#4
1.5
1
0.5
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0:00
0
Time (hr)
Figure 12: Illustration of the Total Power Loss in all Four Scenarios
22
Chapter 5
CONCLUSION
A 13 bus radial distribution system with 4 different scenarios of wind generation profile
and loading was studied to investigate the effects of wind variability on the system voltage
profile. Computer simulations using Powerworld program were conducted and the results were
compared with the SSV analysis. For each scenario, the SSV of the Jacobian power flow matrix
were calculated and analyzed. The SSV index analysis was used to examine the networks
performance. The index values improved with the proposed solutions through out the case
scenarios. The assessments showed the most enhancements in the steady state stability limit in
case scenario# 4, where the distribution network needed bus voltage regulation at busses 5 and 6.
The scenarios demonstrated that when renewable distribution generations are connected to
particular busses, then the voltage magnitudes at those busses will improve as predicted by the
theoretical concepts. However, renewable distribution generation at high penetration levels may
also cause high voltage conditions and/or interfere in the functioning process of the existing line
voltage regulators as shown in case scenario# 3. That is, even when renewable distribution
generations are connected to the grid, we still have to be aware of the overall functionality of the
existing voltage regulation systems on the grid in order to avoid unwanted voltage magnitude
drops or rises. It should also be noted that at situation when the distributed generation is suddenly
disconnected from the grid, it may cause a considerable drop in the voltage profile at the critical
locations [2]. In that case, is it necessary to arrange preexisting solutions to overcome such
incidents when they occur. In [2], the authors introduce multiple essential methods to solve
voltage regulation problems such as installing capacitors on feeders with distributed generations
or using autotransformers that have under load tap changers.
23
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