VOLTAGE STABILITY ENHANCEMENT BY USING STATCOM A Project Report Submitted in Partial Fulfillment Of Requirements for the Degree of BACHELOR OF TECHNOLOGY IN ELECTRICAL AND ELECTRONICS ENGINEERING By YANDRAPRAGADA SRIHARI 07505A0201 Under the Esteemed Guidance of D. RAGA LEELA M.Tech Assistant Professor DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING PRASAD V. POTLURI SIDDHARTHA INSTITUTE OF TECHNOLOGY (Affiliated to JNTU Kakinada, Approved by AICTE, New Delhi) KANURU, VIJAYAWADA-520007 APRIL, 2010.
Transcript
VOLTAGE STABILITY ENHANCEMENT BY USING STATCOM
A Project Report Submitted in Partial Fulfillment Of Requirements for the Degree of
BACHELOR OF TECHNOLOGY IN
ELECTRICAL AND ELECTRONICS ENGINEERING By
YANDRAPRAGADA SRIHARI 07505A0201
Under the Esteemed Guidance of
D. RAGA LEELA M.Tech Assistant Professor
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING
PRASAD V. POTLURI SIDDHARTHA INSTITUTE OF TECHNOLOGY
(Affiliated to JNTU Kakinada, Approved by AICTE, New Delhi)
KANURU, VIJAYAWADA-520007
APRIL, 2010.
PRASAD V. POTLURI SIDDHARTHA INSTITUTE OF
TECHNOLOGY (Affiliated to JNTU Kakinada, Approved by AICTE, New Delhi)
KANURU, VIJAYAWADA-520007.
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
Certificate
This is to certify that the project work entitled “VOLTAGE STABILITY
ENHANCEMENT BY USING STATCOM” that is being Submitted by
YANDRAPRAGADA SRIHARI in Partial fulfillment of the requirements for the award of
BACHELOR OF TECHNOLOGY in ELECTRICAL & ELECTRONICS ENGINEERING by
Jawaharlal Nehru Technological University is a record of bonafide work carried out by them
under our guidance and supervision. The results embodied in this report have not been submitted
to any other University or Institute for the award of any degree or diploma.
I express my profound sense of gratitude and sincere thanks to Sri D.RAGA LEELA
M.Tech., Assistant professor, Department of Electrical and Electronics Engineering, for initiating
me into this work and guiding me in the successful completion of this project.
I express my thanks to Sri Prof. Dr.S.V.M.BHUVANAIKARAO M.E.,F.I.E,Ph.D, Head of
the Department of Electrical and Electronics Engineering, for providing all the facilities in the
Department.
We are thankful to our Principal Dr.K.SRINIVASU, M.Tech., P.h.D, for providing an
excellent environment in our college and helping us at all points for achieving our task.
Finally we thank to our faculty, E.E.E Department for imparting good knowledge to us
throughout our course.
Last, but not least, I take this opportunity to thank all the people who aided me in the
completion of the project work, directly or indirectly, for their continuous encouragement and
extended services.
Finally, I would like to thank my parents, for their support and encouragement, which
helped me to complete this project with full enthusiasm.
PROJECT ASSOCIATE
YANDRAPRAGADA SRIHARI
Acknowledgements
I express my profound sense of gratitude and sincere thanks to Sri D.RAGA LEELA
M.Tech., Assistant professor, Department of Electrical and Electronics Engineering, for initiating me
into this work and guiding me in the successful completion of this project.
I express my thanks to Sri Prof. Dr.S.V.M.BHUVANAIKARAO M.E.,F.I.E,Ph.D, Head of
the Department of Electrical and Electronics Engineering, for providing all the facilities in the
Department.
We are thankful to our Principal Dr.K.SRINIVASU, M.Tech., P.h.D, for providing an
excellent environment in our college and helping us at all points for achieving our task.
Finally we thank to our faculty, E.E.E Department for imparting good knowledge to us
throughout our course.
Last, but not least, I take this opportunity to thank all the people who aided me in the
completion of the project work, directly or indirectly, for their continuous encouragement and
extended services.
Finally, I would like to thank my parents, for their support and encouragement, which
helped me to complete this project with full enthusiasm.
PROJECT ASSOCIATES….
YANDRAPRAGADA SRIHARI
BODDU ADILAKSHMI
MOHAMMAD ABDUL AZEEZ
MADASU VENKATESWARA RAO
SAJJA PRUDHVI NATH
MANDA EMYELU
ABSTRACT
In recent years, power demand has increased substantially while the expansion of
power generation and transmission has been severely limited due to the limited resources
and environmental restrictions. As a consequence, some transmission lines are heavily
loaded and the system stability becomes a power transfer-limiting factor. Flexible AC
transmission systems (FACTS) controllers have been mainly used for solving various power
system steady state control problems and function of power flow control.
Among the different variants of facts devices, static compensator are proposed as the
most adequate due to they can supply required reactive current even at low values of bus
voltage and also for the real power modulation.
A more flexible model may be realized by representing the STATCOM as a variable
voltage source for which the magnitude and phase angle may be adjusted using suitable
algorithm, to satisfy a specified voltage magnitude at the point of connection with AC
network.
The STATCOM will be represented by a synchronous voltage source with maximum
and minimum voltage magnitude limits and also it is represented as a voltage source for the
full range of operation.
This paper aims to verify the capability of statcom in improving voltage regulation in
the transmission systems and the statcom is included in Newton raphson model and
simulated study is implemented by MAT lab.
CONTENTS PAGE NO.
1.1. INTRODUCTION 1
1.2. FLOW OF POWER IN AC SYSTEM 2
1.3. AC SYSTEM SCENARIO 3
1.4. PROBLEM OF VOLTAGE STABILITY 4
1.4.1. VOLTAGE STABILITY ENHANCEMENT 5
1.5 LOAD FLOW STUDIES 7
1.6 LOAD FLOW 8
1.7 BUS CLASSIFICATION 9
1.8 LOAD FLOW METHODS 10
1.8.1Gauss–Seidel method 10
1.8.2 Fast-Decoupled-Load-Flow method. 11
1.8.3 Newton–Raphson method. 12
1.9 NEWTON-RAPHSON LOAD FLOW (NRLF) METHOD 14
CHAPTER 2
2 FACTS 16
2.1 FACTS CONTROLLERS 18
2.1.1SERIES CONNECTED CONTROLLERS 18
2.1.1.1Thyristor controlled series capacitor(TCSC) 19
2.1.1.2Thyristor switched series capacitor(TSSC) 20
2.1.1.3Static synchronous series compensator(SSSC) 20
2.1.2 SHUNT CONNECTED CONTROLLERS 22
2.1.2.1Static synchronous compensator(STATCOM) 22
2.1.2.2Thyristor controlled reactor(TCR) 23
2.1.2.3Thyristor switched reactor(TSC) 24
2.1.2.4Static var compensator(SVC) 24
2.1.3COMBINED SERIES SHUNT CONTROLLERS 25
2.1.4UNIFIED POWER FLOW CONTROLLERS 25
2.2 BENEFITS OF FACTS DEVICES 26
2.3 COMPARISON OF VARIOUS FACTS DEVICES 28
2.4 RELATIVE IMPORTANCE OF CONTROLLABLE PARAMETERS 29
CHAPTER 3
3 STATCOM 29
3.1 OPERATING PRINCIPLE 30
3.2 MODELLING OF STATCOM 32
3.2.1SHUNT VARIABLE SUSPECTANCE METHOD 33
3.3 TYPICAL APPLICATIONS OF STATCOM 34
3.4 MAIN ADVANTAGES OF STATCOM 34
CHAPTER 4
4 MATLAB 35
4.1 INTRODUCTION TO MAT LAB 35
4.2 MAT LAB WINDOW 36
4.3 PROBLEM EVALUATION 38
4.3.1 IEEE 5 BUS SYSTEM 38
4.3.1 USING WITHOUT STATCOM 38
4.3.2 USING SINGLE STATCOM 39
4.3.3 USING MULTIPLE STATCOM 40
4.3.2 IEEE 14 BUS SYSTEM 41
4.3.2.1 USING WITHOUT STATCOM 41
4.3.2.2 USING SINGLE STATCOM 43
4.3.2.3 USING MULTIPLE STATCOM 45
CHAPTER 5
5 CONCLUSION 47
BIBLIOGRAPHY 49
APPENDIX 50
IEEE 5 BUS LINE AND LOAD DATA 51
IEEE 14 BUS LINE AND LOAD DATA 52
LIST OF FIGURES:
1.1 POWER FLOW IN PARALLEL PATHS 12
2.1.1 TCSC LAYOUT 19
2.1.2 TSSC LAYOUT 20
2.1.3 SSSC LAYOUT 21
2.2.1 STATCOM LAYOUT 23
2.2.2 TCR LAYOUT 24
2.2.3 TCSC LAYOUT 24
2.3 UPFC LAYOUT 26
3.1 STRUCTURE OF STATCOM 29
3.2 TYPICAL VI CHARACTERISTICS FOF STATCOM 30
3.3 STATCOM 31
3.4 STATCOM UNDER VARIABLE SUSPECTANCE METHOD 33
4.1 IEEE 5 BUS SYSTEM 38
4.2 IEEE 5 BUS SYSTEM WITH SINGLE STATCOM 39
4.3 IEEE 5 BUS SYSTEM WITH MULTIPLE STATCOM 40
4.4 IEEE 14 BUS SYSTEM 41
4.5 IEEE 14 BUS SYSTEM WITH SINGLE STATCOM 43
4.6 IEEE 14 BUS SYSTEM WITH MULTIPLE STATCOM 45
LIST OF TABLES
1. COMPARISION IF DIFFERENT FACTS DEVICES 14
2. MAT LAB RESULTS OF IEEE 5 BUS WITHOUT USING STATCOM 38
3. MAT LAB RESULTS IEEE 5 BUS WITH USING SINGLE STATCOM 39
4. MAT LAB RESULTS 5 BUS WITH USING MULTIPLE STATCOM 40
5. MAT LAB RESULTS IEEE 14 BUS WITHOUT USING STATCOM 42
6. MAT LAB RESULTS 14 BUS WITH USING SINGLE STATCOM 44
7. MAT LAB RESULTS 14 BUS WITH USING MULTIPLE STATCOM 46
8. LINE AND LOAD DATA FO IEEE 5 BUS SYSTEM 50
9. LINE DATA FO IEEE 14 BUS SYSTEM 51
10. LOAD DATA FO IEEE 14 BUS SYSTEM 52
1
INTRODUCTION
Electric power plays an exceedingly important role in the life of community
and in the development of various sectors of economy
Infact the modern economy is very dependent on the electricity as a basic
input. This in turn has led to increase in the number of power stations and their
capacities and consequent increase in the power transmission line that connect the
generating station to the load centers.
Most if not all of the worlds, electric power systems are widely
interconnected. We need these interconnections because, apart from delivery, the
purpose of transmission network is to pool power plants and load centers in order to
minimize the total power generation capacity and cost. Transmission interconnections
enable taking advantage of diversity of loads, availability of sources, and full price in
order to supply electricity to the loads at minimum cost with a required reliability.
Transmission is often an alternative to the new generation resource. One cannot be
sure about what the optimum balance is between ge4neration and transmission unless
the system planners use advanced methods of analysis which integrate transmission
planning into an integrated value-based transmission/generation planning scenario.
Hence, we need to incorporate some control mechanism in order to increase the power
transfer capability and enhance the controllability.
On the other hand, as power transfer grow, the power system becomes
increasingly more complex to operate and the system can become less secure for
riding through the major outages. It may lead to large power flows with inadequate
control, excessive reactive power in various parts of the system, large dynamic swings
between different parts of the system and bottlenecks, and thus the full potential of
transmission interconnections can not be utilized.
The power systems of today largely, care mechanically controlled. The
problem with mechanical devices is that control cannot be initiated frequently,
because these mechanical devices tend to wear out very quickly compared to static
devices.
2
1.2 FLOW OF POWER IN AN AC SYSTEM
At present, many transmission facilities confront one or more limiting network
parameters plus inability to direct power flow at will.
In ac power systems, given the insignificant electrical storage, the electrical
generation and load must balance all the times. To some extent, the electrical system
is self-regulating. If generation is less than load, the voltage and frequency drop, and
there by the load, goes down to equal the generation minus the transmission losses.
However, there is only a few percent margin for such a self-regulation. If voltage is
propped up with reactive power support, them the load will go up, and consequently
frequency will keep dropping, and the system will collapse. Alternatively, if there is
inadequate reactive power, the system can have voltage collapse.
The basic requirement of power system is to meet the demand that varies
continuously. That is, the amount of power divided by the power companies must be
equal to that of consumer’s need.
The power transmitted over an AC transmission line is a function of the line
impedance, the magnitude of the sending and receiving and voltages and the phase
angle voltages between voltages. The compensators have been provided to control any
one of the function variable.
Traditional techniques of reactive line compensation and step like voltage
adjustment are generally used to alter these parameters to achieve power transmission
control. Fired and mechanically switched shunt and series reactive compensation are
employed to modify the natural impedance characteristics of transmission line in
order to establish the desired effective impedance between the sending and receiving
ends to meet power transfer requirements. Voltage regulating and phase shifting
transformers with mechanical tap changing gears are also used to minimize voltage
variation and control power flow. These conventional methods provide adequate
3
control under steady state and slowly changing conditions, but are largely ineffective
in handling dynamic disturbance.
The power systems can be effectively utilized with prudent use of FACTS
technology on a selective, as needed basis.
FACTS technology opens up new opportunities for controlling power and
enhancing the usable capacity of present, as well as new and upgraded lines. These
opportunities arise through the ability of FACTS controllers to control the interrelated
parameter that govern the operation of transmission systems. These constraints cannot
be overcome while maintaining the required system reliability, by mechanical means
with lowering the usable transmission capacity. By providing added flexibility,
FACTS controllers can enable a line to carry power closer to its thermal ratings.
Mechanical switches need to be supplemented by rapid-response power electronics.
In this scenario, the FACTS technology opens up new opportunity to control
the power by controlling the initial parameter that governs the operation of
transmission system.
1.3 AC SYSTEM SCENARIO Flow in AC lines is generally uncontrollable. As a result of the lack of control
in AC lines the following disadvantages are present in AC systems:
1. The power flow in AC lines (except short lines of lengths below 150 km) is
limited by stability considerations. The expression for power flow in a lossless
AC line with voltage magnitude v at sending and receiving end is given by:
Zc and θ denote the characteristic impedance and electrical distance. Note
that peak power transfer capability is
4
The normal power flow in a line is kept much below the peak value. This
margin (or reserve) is required to maintain system security under contingency
conditions. The fact implies that the lines may operate normally at power
levels much below their thermal limits.
2. The AC transmission network requires dynamic reactive power control to
maintain satisfactory voltage profile under varying load conditions and
transient disturbances. The voltage profile of a long line with the two ends
maintained at voltage magnitude v for different loading conditions.
3. AC lines while providing synchronizing (restoring) torque for oscillating
generator rotors may contribute negative damping torque which results in
undamped power oscillations.
4. The increases in load levels are accompanied by higher reactive power
consumption in the line reactances. In case of mismatch in the reactive power
balance in the system, this can result in voltage instability and collapse.
Recent developments involving deregulation and restructuring of Power industry,
are aimed at isolating the supply of electrical energy (a product) from the service
involving transmission from generating stations to load centers. This approach is
feasible only if the operation of AC transmission lines is made flexible by introducing
fast acting high power solid-state controllers using thyristor or GTO valves. This led
to the development of FACTS technology.
1.4 PROBLEM OF VOLTAGE STABILITY
Voltage stability is the ability of a power system to maintain adequate voltage
magnitude so that when the system nominal load is increased, the actual power
transferred to that load will increase. The main cause of voltage instability is the
inability of the power system to meet the demand for reactive power. Voltage
instability s the cause of system voltage collapse, in which the system voltage decays
to a level from which it is unable to recover. Voltage collapse may lead to partial or
full power interruption in the system.
5
There are two types of voltage stability based on simulation time; static
voltage stability and dynamic voltage stability. Static analysis involves
computationally less extensive than dynamic analysis. Static voltage stability is ideal
for the bulk of studies in which a voltage stability limit for many pre-contingency and
post-contingency cases must be determined. Providing adequate reactive power
support at the appropriate location solves voltage instability problems. There are
many reactive compensation devices used by the utilities for this purpose, each of
which has its own characteristics and limitations. However, the utility would like to
achieve this with the most beneficial compensation device.
Voltage stability is one of the biggest problems in power systems. Engineers
and researchers have met with the purpose of discussing and trying to consolidate a
definition regarding to voltage stability, besides proposing techniques and
methodologies for their analysis. Most of these techniques are based on the search of
the point in which the system’s Jacobin becomes singular; this point is referred as the
point of voltage collapse or maximum load ability point. The series and shunt
compensation are able to increase the maximum transfer capabilities of power
network .Concerning to voltage stability, such compensation has the purpose of
injecting reactive power to maintain the voltage magnitude in the nodes close to the
nominal values, besides, to reduce line currents and therefore the total system losses.
At the present time, thanks to the development in the power electronics devices, the
voltage magnitude in some node of the system can be adjusted through sophisticated
and versatile devices named FACTS. One of them is the static synchronous
compensator (STATCOM).
1.4.1. VOLTAGE STABILITY ENHANCEMENT
Voltage stability (instability/collapse) is a totally different form of power
system dynamic problem. Contrary to the loss of electromechanical stability, voltage
instability is a possible consequence of progressive increase in load until the point of
collapse is reached, beyond which little can be done except to prepare for system
restoration. The collapse phenomenon is typically slow, over several minutes,
depending on the time-varying behavior of the loads.
6
The following conventional corrective actions are possible;
• Reserve reactive support must be used, i.e. switched shunt capacitors and
SVCs.
• Network control actions: coordinate system LTCs, recluse lines
automatically, use
HVDC station reactive power control capabilities.
• Load control: automatic under voltage load shedding or operator initiated
load
Shedding.
• Generator control action: remove generation to mitigate a transmission
system overload, add local generation or trade real power for reactive power on
critical generation.
FACTS studies on easing voltage instability problems have been confined, so
far, to the application of the SVC and the more recent alternative, the STATCOM.
A more difficult form of voltage instability, sometimes referred to as
“transient voltage instability” is becoming an increasing problem. This form of
voltage instability is the long recognized problem of “induction motor instability”.
Induction motor instability is an increasing problem as transmission system becomes
more heavily loaded. Following a system fault, certain induction motors may either be
already stalled or absorb a disproportional high reactive power compared with active
power in their recovery to operating speed. In the absence of established solutions,
certain FACTS devices (like the STATCOM), which are fast acting and have the
potential for high short time overload ratings, may be helpful.
7
1.5 LOAD FLOW STUDIES
1.5 INTRODUCTION TO LOAD-FLOW
Load-flow studies are probably the most common of all power system analysis
calculations. They are used in planning studies to determine if and when specific
elements will become overloaded. Major investment decisions begin with
reinforcement
Strategies based on load-flow analysis. In operating studies, load-flow analysis is used
To ensure that each generator runs at the optimum operating point; demand will be
met
Without overloading facilities; and maintenance plans can proceed without
undermining
The security of the system.
The objective of any load-flow program is to produce the following
information:
• Voltage magnitude and phase angle at each bus.
• Real and reactive power flowing in each element.
• Reactive power loading on each generator.
The above objectives are achieved by supplying the load-flow program with
the Following information:
• Branch list of the system connections i.e., the impedance of each element, sending-
end and receiving-end node. Lines and transformers are represented by their π-
equivalent models.
• Voltage magnitude and phase-angle at one bus, which is the reference point for the
rest of the system.
• Real power generated and voltage magnitude at each generator bus.
• Real and reactive power demanded at each load bus.
The foregoing information is generally available since it either involves
readily Known data (impedances etc.) or quantities which are under the control of
power system
Personnel (active power output and excitation of generators.) Simply stated the load-
flow problem is as follows:
8
● at any bus there are four quantities of interest: │V│, θ, P, and Q.
● If any two of these quantities are specified, the other two must not be specified
otherwise we end up with more unknowns than equations.
1.6 Load Flow Load flow solution is a solution of the network under steady state condition
subjected to certain inequality constraints under which the system operates. These
constraints can be in the form of load magnitude, bus voltages, reactive power
generation of the generators, tap settings of a tap-changing transformer etc. The load
flow solution gives the bus voltages and phase angles, hence the power injection at all
the buses and power flow through interconnecting transmission lines can be easily
calculated. Load flow solution is essential for designing a new power system as well
as for planning an extension or operation of the existing one for varying demand. `
These analyses require number of load flow solutions under both normal and
abnormal (outage of transmission line or outage of some generators) operating
conditions. Load flow solution also gives the initial state of the system when the
transient behaviour of the system is to be studied. The load flow solution of the power
system mainly requires the following calculations/steps:
1. Formulation of equations for the given network
2. Suitable mathematical technique for the solution of the equations
Under steady state condition, the network equations will be in the form of
simple algebraic equations. The loads and generations are continuously changing in a
real power system, but for solving load flow it is assumed that loads and generations
are fixed at a particular value over a suitable period of time. E.g. half an hour or
monthly etc depending upon data
9
1.7 Bus Classification
In a power system each bus or node is associated with four quantities, real and
reactive powers, bus voltage magnitudes and its phase angles. In a load flow solution
two out of four quantities are specified and the remaining two are to be calculated
through the solution of the equations. The buses are classified into the following three
types depending upon the quantities specified.
PQ bus: At this bus the real and reactive components of power are specified. It is
desired to find out the voltage magnitude V and phase angle δ through the load flow
solution. Voltage at load bus can be allowed to vary within a prescribed value e.g.
5%. It is also known as the load bus.
PV bus: Here the voltage magnitude corresponding to the generator voltage V and
real power PG corresponding to its ratings is specified. It is required to find out the
reactive power generation QG and the phase angle δ of the bus. It is also known as the
Generator bus or voltage-controlled bus.
Slack/Swing or reference bus: Here the voltage magnitude V and phase angle δ is
specified. This will take care of the additional power generation required and
transmission losses. It is required to find the real and reactive power generations (PG,
QG) at this bus.
This is called the slack (or swing, or reference) bus and since P and Q are
unknown, │V│ and θ must be specified. Usually, an angle of θ = 0 is used at the
slack bus and all other bus angles are expressed with respect to slack.
Load flow solution can be achieved by any iterative methods. There are many
kinds of iterative methods but as per the literature review the Newton-Raphson
method is normally applied. In the load flow problem as explained above, two
variables are specified at each bus and the remaining variables are obtained through
load flow solutions.
The additional variables to be specified for load flow solution are the tap settings of
regulating transformers, capacitances, resistances etc. If the specified variables are
allowed to vary in a region constrained by practical considerations (upper and lower
limits of real and reactive generations, bus voltage limits and range of transformer tap
settings), these results in load flow solutions each pertaining to one set of values of
specified variables.
10
1.8 CLASSICAL LOAD FLOW METHODS:
These are classified as:
1. Newton–Raphson method.
2. Fast-Decoupled-Load-Flow method.
3. Gauss–Seidel method
1.8.1Gauss Siedal Method:
In numerical algebra, the Gauss–Seidel method, also known as the Liebmann
method or the method of successive displacement, is an iterative method used to solve
a linear system of equations. It is named after the German mathematicians Carl
Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobian
method. Though it can be applied to any matrix with non-zero elements on the
diagonals, convergence is only guaranteed if the matrix is either diagonally dominant,
or symmetric and positive definite.
Description
Given a square system of n linear equations with unknown x:
Where
Then A can be decomposed into a lower triangular component L*, and a strictly upper
triangular component U:
A=L+U
Where
The system of linear equations may be rewritten as:
11
The Gauss–Seidel method is an iterative technique that solves the left hand side of
this expression for x, using previous value for x on the right hand side. Analytically,
this may be written as:
However, by taking advantage of the triangular form of L*, the elements of x(k+1)
can be computed sequentially using forward substitution:
The procedure is generally continued until the changes made by iteration are below
some tolerance. The element-wise formula for the Gauss–Seidel method is extremely
similar to that of the Jacobian method.
The computation of xi(k+1) uses only the elements of x(k+1) that have already
been computed, and only the elements of x(k) that have yet to be advanced to iteration
k+1. This means that, unlike the Jacobian method, only one storage vector is required
as elements can be overwritten as they are computed, which can be advantageous for
very large problems.
However, unlike the Jacobian method, the computations for each element cannot
be done in parallel. Furthermore, the values at each iteration are dependent on the
order of the original equations .The convergence properties of the Gauss–Seidel
method are dependent on the matrix A. Namely, the procedure is known to converge
if either:
A is symmetric positive-definite, or
A is strictly or irreducibly diagonally dominant.
The Gauss–Seidel method sometimes converges even if these conditions are not
satisfied
1.8.2 Fast Decoupled Load Flow Method:
It is a reliable and fastest method in obtaining convergence
This method with branches of high (r/x) rations could not solve problems with regard
to non-convergence and long execution time
12
1.8.3 Newton-Raphson load flow (NRLF) Method Calculation of Jacobian
For an N-bus power system there will be n equations for real power injection i
P and n-equations for reactive power11 injection Qi .
= = I =1 , 2, 3, …….,N
The number of equations to be solved depends upon the specifications we
have. If the total number of buses is n and number of generator buses is m then the
number of equations to be solved will be number of known Pi’s and number of known
Qi’s. In the above conditions number of known Pi’s are n-1 and the number of known
Qi’s are (n-m), therefore the total number of simultaneous equations will be 2*n-m-1,
and number of
unknown quantities are also 2*n-m-1. Unknowns to be calculated are power angles
(δ) at all the buses except slack (i.e. n-1) and bus voltages (V) at load bus (i.e. n-m).
The following method known as Newton- Raphson method is used for solving
=
the unknown quantities. The problem formulation is as follows: = (specified) = (specified)
Real power terms will be calculated for all the buses except slack bus and reactive power terms will be calculated for all load buses. In the above equation
And
13
is the jacobian matrix…………. (4)
The elements of the Jacobian matrix can be calculated using the following equations
=
= -
+
= ………..(5)
14
Procedure for this iterative method is for the given system first the Y-bus matrix has
to be formed.
Y = G + j B Where
Y is a bus admittance matrix
G is real part of Y-bus matrix
B is imaginary part of Y-bus matrix
The resistance and reactance of each line have been given for any system from which
the admittance matrix can be formed.
1.9 Iterative Algorithm for N-R Method
1. With voltage and angle (usually δ = 0 ) at slack bus fixed, assume voltage
magnitude and power angles at PQ buses and δ at all PV buses. Generally flat voltage
start will be used.
2. Compute i ΔP for all buses except slack bus and i ΔQ for all PQ buses using Eq.
(3). If all the values are less than the prescribed tolerance, stop the iterations.
3. If the convergence criterion is not satisfied, evaluate elements of the jacobian using
Eq. (5)
4. Solve the Eq. (2) for correction vector.
5. Update voltage angles and magnitudes by adding the corresponding changes to the
previous values and return to step 2.
15
START
Input primitive network, slack bus No. Real and
Reactive power at all buses except the slack bus, slack
bus voltage magnitude and phase angle, no of buses
Form bus Admittance Matrix Y bus
Assume bus Voltage E K (0) , K=1,2,3,…..n, K ≠ S
Set Iteration count P = 0
Calculate PKP ,QK
P
∆PKP = PK(Scheduled) - PK
P ; ∆QKP(Scheduled) –QK
P
K=1,2,3,…..n, K ≠ S
Determine max ∆PP and max ∆QP
│ Max ∆PP │
and│Max ∆QP │ > t
(or) 0. 001
Solve for voltage corrections =
∆PP
∆QP
J1P J2
P J3
P J4P
∆ δ ∆│V │
VKP = VK
P+1 + ∆ VKP ; δ K
P+1 * ∆δ K
P
VKP = VK
P+1 ; δ KP+1 ,K=1,2,3,…..n, K ≠ S
Output voltage V angle δ at all buses, line flows and line
STOP
P= P+1
16
2. FLEXIBLE AC TRANSIMISSION SYSTEMS
These are alternating current transmission systems incorporating power electronic-
based and other static controllers to enhance controllability and increase power
transfer capability. FACTS do not indicate a particular controllers but a host of
controllers which the system planner can choose based on both technical
considerations and cost benefit analysis.
OBJECTIVES OF FACTS The main objectives of introducing FACTS are:
1. Regulation of power flows in prescribed transmission routes.
2. Secure loading of lines nearer their contributing to emergency control
3. Prevention of cascading outages by contributing to emergency control
4. Improving the stability of the system.
Power Flow in Parallel Paths
Consider a very simple case of power flow through two parallel paths
(possibly corridors of several lines) from a surplus generation area, shown as an
equivalent generator on the left, to a deficit generation area on the right. Without any
control, power flow is based on the inverse of the various transmission line
impedances. Apart from ownership and contractual issues over which lines carry how
much power, it is likely that the lower impedance line may become overloaded and
thereby limit the loading on both paths even though the higher impedance path is fully
loaded. There would not be and incentive to upgrade current capacity of the
overloaded path, because this would further decrease the impedance and the
investment would be self-defeating particularly if the higher impedance path already
has enough capacity.
Fig (b) shows the same two paths, but one of these has HVDC transmission.
With HVDC, power flows as ordered by the operator, because with HVDC power
electronics converters power is electronically controlled. Also, because power is
electronically controlled, the HVDC line can be used to its full thermal capacity if
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adequate converter capacity is provided. Furthermore, an HVDC line, because of its
high-speed control, can also help the parallel ac transmission line to maintain stability.
However, HVDC is expensive for general use, and is usually considered when long
distances are involved, such as the Pacific DC Inter tie on which power flows as
ordered by the operator.
As alternative FACTS controllers, fig(c) and (d) show one of the transmission
lines with different types of series types FACTS controllers. By means of controlling
impedance, or series injection of appropriate voltage a FACTS controller can control
the power flow as required. Maximum power flow can in fact be limited to its rated
limit under contingency conditions when this line is expected to carry more power
due to the loss of a parallel line.
1.1 Power flow in parallel paths a) ac power flow with parallel paths b) power flow control with hvdc c) power
flow control with variable impedance d) power flow control with variable phase angle
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2.1 FACTS CONTROLLERS
A power Electronic based system and other static equipment that provide
control of one or more AC transmission system parameters.
FACTS devices or controllers are used for the dynamic control of voltage,
impedance and phase angle of high voltage AC transmission lines. Below, the
different main types of FACTS devices are described:
Shunt connected controllers
Series connected controllers
Combined series-series controllers
Combined series-shunt controllers
2.1.1 SERIES CONNECTED CONTROLLERS
The series controller could be variable impedance, such as capacitor, reactor etc
(or) power electronics based variable source (or) a combination of these. In principle,
all series controllers inject voltage in series with the line. The series controller could
be variable impedance, such as capacitor, reactor, etc., or power electronics based
variable source of main frequency, sub synchronous and harmonic frequencies to
serve the desired need. In principle, all series controllers inject voltage in series with
the line. Even variable impedance multiplied by the current flow through it, represents
an injected series voltage in the line. As long as the voltage is in phase quadrature
with the line current, the series controller only supplies or consumes variable reactive
power. Any other phase relationship will involve handling of real power as well.
i. Thyristors controlled series capacitor(TCSC)
ii. Thyristor switched series capacitor(TSSC)
iii. Static synchronous series compensator(SSSC)
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2.1.1.1 THYRISTOR CONTROLLED SERIES CAPACITOR (TCSC)
A capacitive reactance compensator which consists of a series capacitor bank
shunted by a thyirstor-controlled reactor in order to provide a smoothly variable series
capacitive reactance. The TCSC may be a single, large unit, or may consist of several
equal or different-sized smaller capacitors in order to achieve a superior performance.
Figure 2.1.1 TCSC Layout
The TCSC is based on thyristors without the gate turn-off capability. It is an
alternative to SSSC above and like an SSSC, it is a very important FACTS controller.
A variable reactor such as a Thyristors-controlled reactor (TCR) is connected across a
series capacitor. When the TCR firing angle is 180 degrees, the reactor becomes non-
conducting and the series capacitor has its normal impedance. As the firing angle is
advanced from 180 degrees to less than 180 degrees, the capacitive impedance
increases. At the other end, when the TCR firing angle is 90 degrees, the reactor
becomes fully conducting, and the total impedance becomes inductive, because the
reactive impedance is designed to be much lower than the series capacitor impedance.
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2.1.1.2. THYRISTOR SWITCHED SERIES CAPACITOR (TSSC)
A capacitive reactance compensator which consists of a series capacitor bank
shunted by a thyristor-switched reactor to provide a stepwise control of series
capacitive reactance.
Figure 2.1.2 TSSC LAYOUT
Instead of continuous control of capacitive impedance, this approach of
switching inductors at firing angle of 90 degrees or 180 degrees but without firing
angle control, could reduce cost and losses of the controller.
It is reasonable to arrange one of the modules to have thyristors control, while
others could be thyristors switched
2.1.1.3 STATIC SYNCHRONOUS SERIES CAPACITOR (SSSC)
A static synchronous generator operated without an external electric energy
source as a series compensator whose output voltage is in quadrature with, and
controllable independently of, the line current for the purpose of increasing or
decreasing the overall reactive voltage drop across the line and thereby controlling the
transmitted electric power.
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Figure 2.1.3 SSSC
The SSSC may include transiently rated energy storage or energy absorbing
devices to enhance the dynamic behavior of the power system by additional
temporary active power compensation, to increase or decrease momentarily, the
overall active (resistive) voltage drop across the line. SSSC is one the most important
FACTS controllers.
It is like a STATCOM, except that the output ac voltage is in series with the
line. It can be based on a voltage-sourced converter or current-sourced converter.
Without an extra energy source, SSSC can only inject a variable voltage, which is 90
degrees leading or lagging the current.
Usually the injected voltage in series would be quite small compared to the
line voltage, and the insulation to ground would be quite high. With and appropriate
insulation between the primary and the secondary of the transformer, the converter
equipment is located at the ground potential unless the entire converter equipment is
located on a platform duly insulated from ground.
Battery- storage or superconducting magnetic storage can also be connected to
a series controller to inject a voltage vector of variable angel in series with the line.
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2.1.2 SHUNT CONNECTED CONTROLLERS
Shunt controllers may be variable impedance, such as capacitor, reactor, etc., or
power electronics based variable source, or a combination of these. In principle all
shunt controllers inject current into the system at the point of connection. Examples of
shunt connected controllers. As in the case of series controllers, the shunt controllers
may be variable impedance, variable source, or a combination of these. In principle,
all shunt controllers inject current into the system at the point of connection. Even
variable shunt impedance connected to the line voltage causes a variable current flow
and hence represents injection of current into the line. As long as the injected current
is in phase quadrature with the line voltage, the shunt controller only supplies or
consumes variable reactive power. Any other phase relationship will involve handling
of real power as well.
i. Static synchronous compensator(STATCOM)
ii. Thyristor controlled reactor(TCR)
iii. Thyristor switched reactor(TSC)
iv. Static var compensator(SVC)
2.1.2.1 STATIC SYNCHRONOUS COMPENSATOR (STATCOM) A static synchronous generator operated as a shunt-connected static var
compensated whose capacitive or inductive output current can be controlled
independent of the AC system voltage. It can be based on a voltage-sourced or
current-sourced converter. For the voltage-sourced converter, its AC output voltage is
controlled such that it is just right for the required reactive current flow for any AC
bus voltage DC capacitor voltage is automatically adjusted to serve as a voltage
source for the converter. STATCOM can be designed to also act as an active filter to
