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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 margins for such a
self-regulation. If vo l tage 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 variescontinuously. That is, the amount of power divided by the power companies
must be equal to that of consumers 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 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 F ACTS
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
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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 denote the characteristic impedance and electrical distance.
Note that peak power transfer capability is
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 sat isfactory voltage profi le under varying load
c o n d i t i o n s a nd 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
un-damped power oscillations.
4. The increases in load levels are accompanied by higher reactive powerconsumption 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.
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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 instabilityis 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.
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 voltageinstability 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.
The following conventional corrective actions are possible;
Reserve reactive support must be used, i.e. switched shunt capacitors and
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SVC
Network control actions coordinate system LTCs, recluse lines automatically, useHVDC station reactive power control capabilities.
Load control: automatic under voltage load shedding or operator initiated load
Shedding. Generator control action: remove generation to mit igate a transmissionsystem 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. Thisform of voltage instability is the long recognized problem of induction motorinstability. Induction motor instability is an increasing problem as transmissionsystem 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.
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1.5 LOAD FLOW STUDIES
1.5 INTRODUCTION TO LOAD-FLOW
Load-flow studies are probably the most common of all power system analysiscalculations. 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
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equivalent models.
Voltage magnitude and phase-angle at one bus, which is the reference point for therest 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:
at any bus there are four quantities of interest: V, , P, and Q.
if any two of these quantities are specified, the other two must not be specifiedotherwise 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 loadflow solution gives the bus voltages and phase angles, hence the power injection at all
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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 o p e r a t i o n of the existing one for varying demand. `
These analyses require number of load flow solutions under both normal andabnormal (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 behavior 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 arefixed at a particular value over a suitable period of time. E.g. half an hour or
monthly, depending upon data.
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 through theload 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 Vand real power PG corresponding to its ratings is specified. It is required to
find out the reactive power generation QG and the phase angle of the bus. It isalso known as the Generator bus or voltage-controlled bus.
Slack/Swing or reference bus: Here the voltage magnitude V and phase angle is specified. This will take care of the additional power generation requiredand 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 must bespecified. Usually, an angle of = 0 is used at the slack bus and all other busangles 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, twovariables are specified at each bus and the remaining variables are obtained through
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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 (upperand 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.
1.8 CLASSICAL LOAD FLOW METHODS:
These are classified as:
1. GaussSeidel method2. Fast-Decoupled-Load-Flowmethod.
3. NewtonRaphson method
1.8.1Gauss-Siedal Method:
In numerical algebra, the GaussSeidel method, also known as the Liebmannmethod 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 Value of x:
Where,
Then A can be decomposed into a lower triangular component L*, and a strictly upper
triangular component U:
A=L+U
Where,
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The system of linear equations may be rewritten as:
The GaussSeidel method is an iterative technique that solves the left hand side of thisexpression 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 belowsome tolerance. The element-wise formula for the GaussSeidel method is extremelysimilar 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 orderof the original equations .The convergence properties of the GaussSeidel method aredependent 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 GaussSeidel method sometimes converges even if these conditions are notsatisfied.
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 longexecution time.
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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
Pand n-equations for reactive power11 injection Qi. . (1) (2)
..... (3)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 Pis and number of knownQis. In the above conditions number of known Pis are n-1 and the number of knownQis 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 () at all the buses except slack (i.e. n-1) and bus voltages (V) at loadbus (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: 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
is the Jacobian Matrix...(4)The elements of the Jacobian matrix can be calculated using the following equations
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(5)
Procedure for this iterative method is for the given system first the Y-bus matrix hasto be formed.
Where,
Y is a bus admittance matrix
G is real part of Y-bus matrix
B is imaginary part of Y-bus
Y= G+j B
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 = 0) at slack bus fixed, assume voltagemagnitude and power angles at PQ buses and at all PV buses. Generally flat voltagestart will be used.
2. Compute i Pfor all buses except slack bus and i Q for all PQ buses using Eq. (3). Ifall 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).
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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.
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CHAPTER 2
FLEXIBLE AC TRANSIMISSION SYSTEMS
These are alternating current transmission systems incorporating power
electronic- based and other static controllers to enhance controllabil ity 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 FACTSThe 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 varioustransmission 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 an 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, becausepower is electronically controlled, the HVDC line can be used to its full thermal
capacity if 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 flowcan in fact be limited to its rated limit under contingency conditions when this
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line is expected to carry more power due to the loss of a parallel line.
Fig 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
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, thedifferent main types of FACTS devices are described:
Shunt connected controllers Series connected controllers Combined series-series controllers Combined series-shunt controllers
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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 seriescontroller 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)
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) isconnected across a series capacitor. When the TCR firing angle is 180 degrees, the
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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 theseries capacitor impedance.
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 withoutfiring 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.
Figure 2.1.3 SSSCThe SSSC may include transiently rated energy storage or energy
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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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reactance is varied in a continuous manner by partial-conduction control of the
thyristor valve.
Figure 2.2.2 TCR
Layout
TCR is a subset of SVC in which conduction time and hence, current in shunt
reactor is controlled by a thyristor-based AC switch with firing control.
2.1.2.3 THYRISTOR SWITCHED REACTOR (TSC)
Figure 2.2.3 TCSC Layout
A shunt-connected, thyristor-switched inductor whose effective reactance
is varied in a stepwise manner by full- or zero-conduction operation of the
thyristor valve.
TSR is made up of several shunt-connected inductors which are switched in
and out by thyristor switches without any firing angle.
TSC is also a subset of SVC in which thyristors based ac switches are used to
switch in and out shunt capacitors units, in order to achieve the required stepchange in the reactive power supplied to the system. Unlike shunt reactors, shunt
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capacitors cannot be switched continuously with variable firing angle control.
2.1.2.4 STATIC VAR COMPENSATOR
A shunt-connected static var generator or absorber whose output is adjusted
to exchange capacitive or inductive current so as to maintain or control specific
parameters of the electrical power system (typically bus voltage).SVC is based
of thyristors without the gate turn-off capability. SVC is considered by some as a
lower cost alternative to STATCOM.
This is a general term for a thyristors-controlled or thyristors-switched
reactor, and/or thyristors-switched capacitor or combination. SVC is based on
thyristors without the gate turn-off capability. It includes separate equipment for
leading and lagging vars the thyristors-controlled or thyristors-switched reactor forabsorbing reactive power and thyristors-switched capacitor for supplying thereactive power.
2.1.3 COMBINED SERIES-SHUNT CONTROLLERS
This could be combination of separate shunt and series controllers, which are
controlled in a coordinated manner, or a Unified Power Flow Controller with
series and shunt elements in principle, combined shunt and series controllers inject
current into the system with shunt part of controller and voltage in series in the
line with series part of controller. However, when the shunt and series controllers
are unified, there can be real power exchange between the series and shunt
controllers via the power link.
In principle, combined shunt and series controllers inject current into
the system with the shunt part of the controller and voltage in series in the line with
the series part of the controller. However, when the shunt and series
controllers are unified, there can be a real power exchange between the series and
shunt controllers via the power link.
COMBINED SERIES-SERIES CONTROLLERS
This could be a combination of separate series controllers, which
are controlled in a coordinated manner, in a multi line transmission system.
The real power transfer capability of the unified series-series controller, referred to
as interline power flow controller, makes it possible to balance both the real and
reactive power flow in the lines and thereby maximize the utilization of the
transmission system.
2.1.4 UNIFIED POWER FLOW CONTROLLER (UPFC)
A combination of static synchronous compensator (STATCOM) and a
static series compensator (SSSC) which are coupled via a common dc link, toallow bidirectional flow of real power between the series output terminals of the
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SSSC and the shunt output terminals of the STATCOM, and are controlled
to provide concurrent real and reactive series line compensation without an
external electric energy source. The UPFC, by means of angularly unconstrained
series voltage injection, is able to control, concurrently or selectively, the
transmission line voltage,impedance, and angle or, alternatively, the real andreactive power flow in the line. The UPFC may also provide independently
controllable shunt reactive compensation.
Figure 2.3 UPFC Layout
This is a complete controller for controlling active and reactive power
control through the line, as well as line voltage control.
In UPFC, which combines a STATCOM and an SSSC, the active power
for the series unit is obtained from the line itself via the shunt unit STATCOM; the
latter is also used for voltage control with control of its reactive power. This is a
complete controller for controlling active and reactive power control through the
line, as well as line voltage control. Additional storage such as a superconducting
magnet connected to the dc link via an electronic interface would provide the means
of further enhancing the effectiveness of the UPFC. As mentioned before, the
controlled exchange of real power with an external source, such as storage, is
much more effective in control of system dynamics than modulation of the power
transfer within a system.
2.2 BENEFITS OF FACTS CONTROLLERS
Increase the loading capability of lines to their thermal capabilities. Increase the system security through raising the transient stability limit. Control of power flow as ordered. Provide secure tie line connections.
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Provide greater flexibility in setting new generation. Reduce loop flows. Reduce reactive power flows.2.3 Comparison of various facts devices:
TABLE
FACTS DEVICE TYPE OF
CONNECTION
FUNCTION
Static Var compensator Shunt Var compensation, steady
state and dynamic stability
STATCOM Shunt Generating or absorbingthe reactive power
SSSC
Static Synchronous Series
Compensator
Series Controlling transmitted
electric power by increasing
or decreasing reactive
voltage drop
TCSC
Thyristor Controlled
Series Capacitor
Series Capacitive reactance
compensator in continuous
manner
UPFC Twoport Terminal voltage control,
phase angle regulation, seriesline compensation
RELATIVE IMPORTANCE OF CONTROLLABLE PARAMETERS
Control of the line impedance X (e.g., with a thyristor-controlled seriescapacitor)can provide a powerful means of current control.
when the angle is not large, which is often the case, control of X or theangle substantiallyprovides the control of active power.
Control of angle, which in turn controls the driving voltage, provides apowerful means of controlling the current flow and hence active power flow
when the angle is not large.
Injecting a voltage in series with the line, and perpendicular to the currentflow, can increase or decrease the magnitude of current flow. Since the current
flow lags the driving voltage by 90 degrees, this means injection of reactive
power in series, can provide a powerful means of controlling the current, and
hence the active power when the angle is not large.
Injecting voltage in series with the line and with any phase angle with respect
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to the driving voltage can control the magnitude and the phase of the line
current. This means that injecting a voltage phasor with variable phase angle can
provide a powerful means of precisely controlling the active and reactive power
flow. This requires injection of both active and reactive power in series.
Because the per unit line impedance is usually a small fraction of the linevoltage, the MVA rating of a series controller will often be a small fraction of
the throughput line MAVA.
When the angle is not large, controlling the magnitude of one or the otherline voltages can be a very cost-effective means for the control of reactive power
flow through the interconnection.
Combination of the line impedance control with a series controller andvoltage regulation with a shunt controller can also provide a cost-effective
means to control both the active and reactive power flow between the twosystems.
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CHAPTER 3
STATIC COMPENSATOR(STATCOM)
It is a device connected in derivation, composed of a coupling transformer
that serves of link between the electrical power system and the voltage
synchronous controller (VSC) that generates the voltage wave comparing it to
the one of the electric system to realize the exchange of reactive power. The
control system of the STATCOM adjusts at each moment the inverse voltage so
that the current injected in the network is in quadrature to the network voltage, in
these conditions P=0 and Q=0.
Static synchronous compensator (STATCOM) is a voltage-source
converter based device, which converts a DC input voltage into an AC outputvoltage in order to compensate the active and reactive needs of the system.
STATCOM has better characteristics than SVC; when the system voltage drops
sufficiently to force the STATCOM output to its ceiling, its maximum reactive
power output will not be affected by the voltage magnitude. Therefore, it exhibits
constant current characteristics when the voltage is low under the limit.
A schematic diagram and STATCOM characteristic are shown in Figures below
Figure 3.1 structure of statcom
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Figure 3.2 Typical VI characteristics of stat COM
Thus, when operating at its voltage limits, the amount of reactive power
compensation provided by the STATCOM is more than the most-common
compensating FACTS controller, namely the Static Var Compensator (SVC). This
is because at a low voltage limit, the reactive power drops off as the square of
the voltage for the SVC, where Mvar=f(BV2), but drops off linearly with the
STATCOM, where Mvar=f(VI). This makes the reactive power controllability of
the STATCOM superior to that of the SVC, particularly during times of system
distress.
3.1 STATCOM OPERATING PRINCIPLE
The STATCOM generates a balanced 3-phase voltage whose magnitude and
phase can be adjusted rapidly by using semiconductor switches. The STATCOM is
composed of a voltage-source inverter with a dc capacitor, coupling transformer,
and signal generation and control circuit.
The voltage source inverter for the transmission STATCOM operates in
multi- bridge mode to reduce the harmonic level of the output current. Fig. below
shows a single-phase equivalent circuit in which the STATCOM is controlled bychanging the phase angle between the inverter output voltage and the bus voltage at
the common point connection point. The inverter voltage Vi is assumed to be in
phase with the ac terminal voltage Vt .
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Figure 3.3 statcom
The STATCOM supplies reactive powers to the ac system if the magnitudeof Vi is greater than that of Vt. It draws reactive power from the ac system if the
magnitude of Vt is greater than that if Vi.
There can be a little active power exchange between the STATCOM and
the EPS. The exchange between the inverter and the AC system can be
controlled adjusting the output voltage angle from the inverter to the voltage
angle of the AC system. This means that the inverter cannot provide active power
to the AC system form the DC accumulated energy if the output voltage of the
inverter goes before the voltage of the AC system. On the other hand, the inverter
can absorb the active power of the AC system if its voltage is delayed in respect tothe AC system voltage.
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Using the classical equations that describe the active and reactive power
flow in a line in terms of Vi and Vs, the transformer impedance (which can be
assumed as ideal) and the angle difference between both bars, we can define P and
Q. The angle between the Vs and Vi in the system is d. When the STATCOM
operates with d=0 we can see how the active power send to the system devicebecomes zero while the reactive power will mainly depend on the voltage module.
This operation condition means that the current that goes through the transformer
must have a +/-90 phase difference to Vs. In other words, if Vi is bigger than Vs,
the reactive will be send to the STATCOM of the system (capacitive operation),
originating a current flow in this direction. In the contrary case, the reactive will be
absorbed from the system through the STATCOM (inductive operation) and the
current will flow in the opposite direction. Finally if the modules of Vs and Vi are
equal, there wont be nor current nor reactive flow in the system.
Thus, we can say that in a stationary state Q only depends on the
module difference between Vs and Vi voltages. The amount of the reactive power isproportional to the voltage difference between Vs and Vi.
3.2 MODELLING OF STATCOM:
Statcom is a shunt connected reactive power compensation device that is
capable of generating/absorbing reactive power and in which the output can be
varied to control the specific parameters of an electric power system. It is in general
a solid state switching converter capable of generating independently
controllable reactive power at its output terminal.
The statcom is placed in the bus m and is represented by a shunt
reactive current source is as shown in fig below
Figure 3.4 statcom under variable susceptance model
With the statcom the output power Pe of the machine can be written and is
positive when oscillates in between zero and .
The equation of power can be modulated by modulating the shunt reactive current I.
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The modeling of the statcom can be done in various methods
1. Variable susceptance method
2. Firing angle method
3. Transformer tapping and firing angle method
3.2.1 Shunt Variable Susceptance Model:
In practice the SVC can be seen as an adjustable reactance with either firing angle limits. The equivalent circuit shown in figure is used to derive the SVC non-
linear power equations and the linearised equations required by Newtons method.
With reference to the figure , the current drawn by the SVC is
And the reactive power drawn by the SVC which is also the reactive power injected
at bus k, is The linearised equations is given where the equivalent susceptanceis to be taken the state variable.
The changing susceptance represents the total SVC susceptance necessary to
maintain the nodal voltage magnitude at the specified value.
Once the level of compensation has been computed then the thyristor
firing angle can be calculated. However, the additional calculation requires an
iterative solution because the SVC s u s c e p t a n c e and thyristor firing angle are
non linearly related.
3.3 TYPICAL STATCOM APPLICATIONS
Utilities with weak grid knots or fluctuating reactive loads
Unbalanced loads
Arc furnaces
Wind farms
Wood chippers
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Welding operations
Car crushers & shredders
Industrial mills
Mining shovels & hoists
Harbor cranes
3.4 MAIN ADVANTAGES OF STATCOM
Continuous and dynamic voltage control
High dynamic and very fast response time
Enables grid code compliance
Maximum reactive current over extended voltage range
High efficiency
Single phase control for unbalanced loads
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CHAPTER 4
INTRODUCTION TO MATLAB
4.1 INTRODUCTION
MATLAB is a software package for high-performance numerical
computation and visualization it provides an interactive environment with
hundred of built-in function for its own high level programming language. The
name MAT LAB stands for MATrix laboratory.
MATLABs built-in functions provide excellent tool for linear
algebra computation, data analysis, signal processing, optimization, andnumerical solutions of ODES, quadrature, and many type of scientific
computation. Most of these functions use state-of-the art algorithm. These are
numerous functions for 2-D and 3- D-graphics as well as for animation also, for
those who cant do without their FORTRAN or C courses, MATLAB evenprovides an external interface to fun those programs from within MATLAB even
provides an external interface to fun those programs from within MATLAB. The
user however is not limited to the built-in functions, he can write his own
function in the MATLAB language once written, and these functions behave just
like the built in functions MAT labs language is very easy to learn and to use.
There are several optional toolboxes available from the developers ofthe MATLAB. These toolboxes are collections written for special applications
such as symbolic computations, image processing, statics control system designand Neural Networks. The basic building block of MATLAB is the matrix. The
fundamental data type is the array. Vectors, scalars, real matrices and complex
matrices are all automatically handled as special cases of the basic data-type.
What is more, you almost never have to declare the dimensions of the matrix.
MATLAB simply loves matrices and matrix operations. The built in functions are
optimized for vectors operations. Consequently, vectorised commands or
commands or codes run much fast in mat lab.
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4.2 MATLAB WINDOW:
On all UNIX system Macs, and pc, mat lab through three Basic windows, they are:
Command w i n d o w : This is the main window it is characterized by MATLABCommand prompt >>: when you launch the application program, MATLAB
puts you i n th is window. All commands , including those fo r runn ing
user wr i t t en programs, are typed in this window at the MATLAB prompt.
Graphics Window: The outputs of all graphic commands are typed in thecommand window and are f l u s h e d t o the graphic or figure window, a
separate grey window with white back ground c o l o r . The user can create as
many figure windows, as the system memory will allow.
Edit Window: This is where you edit, write, create, and save your own programsin files called M-files. We can use any text editor to carry out these tasks. On the
most systems, such as PCs and Macs, MATLAB provides its built in editor. Onother systems, you can invoke the edit window by typing the standard file editor
command that at the MATLAB prompt following special character !. Theexclamation character prompts MATLAB to return the control temporarily to
the local operation system, which executes the commands following the !character. After editing is completed, the control is returned to MATLAB.
Input-Output: MATLAB supports interactive computation taking input from thescreen, and flushing the output to the screen. In addition, it can read input files and
write output files. The following features hold for all forms of input-output.
Data Type: The fundamental data type in MATLAB is the array. Itencompasses several distinct data objects, integer, double, matrices, character
string, and cells. In most cases, however, we never have to worry about the data
type or the data object declaration. For example there is no need to declare variable,
MATLAB automatically sets the variable to be real.
Dimensioning: Dimensioning is automatic in MATLAB. No dimensioningstatements are required for vectors or arrays. We can find the dimensions of an
existing matrix or a vector with size and length commands.
Case sensitivity: MATLAB is case sensitive, that is, it differentiates betweenlower case and upper case letters. Thus a and an are different variables. Most
MATLAB commands and built-in function calls are typed in lower case letters. We
can turn case sensitivity on and off with case sensitive command.
Output Display: the output of every command is displayed a screen unlessMATLAB is directed otherwise. A semicolon at the end of a command
suppress the screen output, expect for the graphics and on-line help command. The
following facilities are providing for controlling the screen output.
Paged Output: To direct the MATLAB to show one screen of output at a time,type more on the MATLAB prompt. Without it, MATLAB flushes the entire
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output at once, without regard to the speed at which we read.
Output format: Though computations inside the MATLAB are performed usingthe double precision, the appearance of floating point numbers on the screen is
controlled by the output format in use. There are several different screen outputformats.
Command History: MATLAB severs previously typed commands in buffer.These commands can be called with the up arrow key .This helps in editing
previous commands. You can also recall previous command by typing the first few
characters and then pressing the up-arrow key. On most UNIX systems,
MATLAB command line editor also understands the standard maces key
buildings.
FILE TYPE:MATLAB has 3 types for strong information:
M-files: M-files are standard ASCII text files, with an extension to thefilename. There are low types of these files: script files and functions. Most
programs we write in MATLAB are saved as M-files. All built-in function
in MATLAB are M-files, most of which reside on our computer in
precompiled format. Some built in function are provided with secure code in
readable M-file so they can be copied and modified.
Mat-files: Mat-files are binary data-files with mat extensions to thefilename. Mat fills are created by MATLAB can read. Can be loaded into
MATLAB with the load command.
Mex-files are MATLAB: Mat files callable FORTRAN and Cprograms, with a Mex extension to the filename; u s e of these files
requires some experience with MATLAB and a lot of patience.
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4.3 PROBLEM EVALUATION:
4.3.1 IEEE 5 BUS WITHOUT USING THE STATCOM
The IEEE 5 BUS SYSTEM Data
Figure 4.1 IEEE 5bus
Mat lab Results:
TABLE 2
For iteration =4Without Statcom
Bus no. Voltage magnitude Voltage angle
1 1.0600 0
2 1.0000 -2.0554
3 0.9873 -4.6268
4 0.9842 -4.9466
5 0.9717 -5.7563
4
2
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4.3.1.1 IEEE 5 BUS USING WITH SINGLE STATCOM SINGLE STATCOM
Figure 4.2 IEEE 5 bus with statcom
Mat lab results with single statcom
The statcom is placed at the bus no:3 .At the bus 3 we are placing the statcom
for maintaining the voltage stability. TABLE 3
With Statcom
Bus no. Voltage magnitude Voltage angle
1 1.0600 0
2 1.0000 -2.0534
3 1.0000 -4.8379
4 0.9944 -5.1073
5 0.9752 -5.7975
Injected reactive power at bus no:3is QSVC = -0.2047 Mvar p.u
4
2
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4.3.1.2 USING THE MULTIPLE STATCOM
Figure 4.3 IEEE 5 bus with Multiple Statcom
Mat lab results:Table 4
for iter=5 multiple statcom
With Multiple Statcom
Bus no. Voltagemagnitude
Voltage angle
1 1.0600 0
2 1.0000 -2.0549
3 1.0000 -4.8355
4 1.0000 -5.2094
5 0.9771 -5.8262
Injected reactive power at bus no: 3 and 4are QSVC = -0.0180 and -0.2331 Mvar
p.u.
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4.3.2 IEEE 14 BUS SYSTEM IEEE 14 BUS SYSTEM
4.3.2.1 WITHOUT USING THE STATCOM
Figure 4.4 IEEE 14bus
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MAT LAB RESULTS
Ieee 14 bus without using the statcom
Mat lab results without using the statcom for iter=12
TABLE 5
Bus no Voltage magnitude VM Voltage angle VA
1 1.0600 0
2 1.0000 0.6486
3 1.0000 -3.3780
4 0.9900 -7.2978
5 0.9956 -6.2474
6 1.000 -17.1069
7 0.9895 -16.2977
8 1.0000 -16.4584
9 0.9853 -20.2564
10 0.9812 -21.4684
11 0.9865 -20.0745
12 0.9881 -19.1840
13 0.9807 -19.6256
14 0.9648 -22.3504
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4.3.2.2USING SINGLE STATCOM
IEEE 14 BUS WITH USING THE SINGLE STATCOM
Figure 4.5 IEEE 14 bus with statcom
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Mat lab results by placing the single statcom at bus 14 for iter=12
TABLE 6
Bus no Voltage magnitude VM Voltage angle VA
1 1.0600 0
2 1.0000 1.3388
3 1.0000 -1.4316
4 1.0047 -3.7057
5 1.0089 -3.0453
6 1.0000 -7.8704
7 0.9930 -7.03898 1.0000 -7.0389
9 0.9838 -8.8289
10 0.9786 -8.9877
11 0.9854 -8.5796
12 0.9866 -8.9359
13 0.9872 -9.2189
14 1.0000 -11.0470
Injected reactive power at bus no:4 is QSVC = -0.2221 Mvar p.u
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4.3.2.2USING MULTIPLE STATCOM
IEEE 14 BUS SYSTEM WITH MULTIPLE STATCOM
Figure 4.6 IEEE 14 bus with multiple statocm
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TABLE 7
Mat lab results for multi statcom at bus 4 and 14 for iter=17
Bus no Voltage magnitude VM Voltage angle VA
1 1.0600 0
2 1.0000 1.3415
3 1.0000 -1.4435
4 1.0000 -3.6365
5 1.0060 -3.0054
6 1.0000 -7.8546
7 0.9911 -6.9891
8 1.0000 -6.9891
9 0.9822 -8.7840
10 0.9733 -8.9477
11 0.9848 -8.5506
12 0.9866 -8.9214
13 0.9872 -9.2057
14 1.0000 -11.0426
Injected reactive power at bus no:4 and 14 are QSVC = 0.1133 and -0.2280 Mvar
p.u
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5. CONCLUSION:
In this thesis, various aspects regarding voltage stability have been presented
and the importance to maintain voltage profile has been discussed.
Various concepts regarding the FACTS technology and the important features of
some of the FACTS devices have been presented. The Newton Raphson method has
been presented to solve the power flow problem in the power system with static
synchronous compensator (STATCOM). In this thesis we had discussed about the
STATCOM modeling and analysis when connected to a bus and made it to maintain a
flat voltage profile of the full range of operation when there is a need. There by the
reactive power compensation was successfully done in the particular transmission
whenever it is required.
The power flow and the voltage profile in various transmission lines alongwith and without the placement of STATCOM in a specific transmission line is
obtained in order to improve the system performance by using the load flow studies
using MAT lab software.
Hence our objective to maintain voltage stability have been successfully
achieved with the incorporation of Static Synchronous Compensator (STATCOM).
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FUTURE SCOPE
The project has been performed on a 5-bus and 14 bus power system using
Newton raphson method with a single and multiple STATCOMs.
However, it can be extended to any bus system with single and multiple
STATCOMs if necessary. Along with this thesis optimization can also be done.
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Bibliography:
[1] IEEE FACTS working group 15.05.15, FACTS Application, December 1995.
[2] M. J. Lautenberg, M. A. Pai, and K. R. Padiyar, Hopf Bifurcation Control inPower System with Static Var Compensators, Int. J. Electric Power and EnergySystems, vol. 19, no. 5, 1997, pp. 339347.
[3] N. G. Hingorani and Laszlo Gyugyi, UNDERSTANDINGFACTS.
[4] C. A. Canizares and Z. T. Faur, Analysis of SVC and TCSC Controllers inVoltage Collapse, IEEE Trans. on Power Systems, vol. 14, no. 1, February 1999, pp.15865.
[5] C. A. Canizares. Power Flow and Transient Stability Models of FACTSControllers for Voltage and Angle Stability Studies. In Proc. of IEEE/PES WinterMeeting, Singapore, January 2000.
[6] G. Hingorani and L. Gyugi, Understanding FACTS: Concepts and Technology of
Flexible AC Transmission Systems. IEEE Press, 999.
[7] Modern Power System Anaylsis., Dillon.P.kothari
[8] C. A. Canizares, UWPFLOW: Continuation and Direct Methods to Locate FoldBifurcation in AC/DC/FACTS Power Systems. University of Waterloo, November
1999
[9] Ambriz-Perez, H. (2000)Advanced SVC Models for Newton-Raphson Load Flow
and Newton Optimal Power Flow Studies. IEEE Trans. On Power Systems, vol.15,
No:1, February 2000, pp 129-136.
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APPENDIX
IEEE 5 BUS SYSTEM
IEEE 5 bus system load and line data of the system
Impedance and line charging
Bus code impedance line charging
1-2 0.02+j0.06 0+j0.030
1-3 0.08+j0.24 0+j0.025
2-3 0.06+j0.18 0+j0.020
2-4 0.06+j0.18 0+j0.020
2-5 0.04+j0.18 0+j0.015
3-4 0.01+j0.18 0+j0.010
4-5 0.08+j0.24 0+j0.025
Table 8
Buscode
Assumedbusvoltage
Generation load
1 1.06+j0.0 slack 0 0
2 1.00+j0.0 40 30 20 10
3 1.00+j0.0 0 0 45 15
4 1.00+j0.0 0 0 40 5
5 1.00+j0.0 0 0 60 10
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LINE DATA
IEEE 14 BUS SYSTEMS:
Table 9
From bus To bus RESISTANCE(P.U)
Reactance (p.u.) Line
charging
1 3 0.04699 0.19797 0.0438
1 4 0.05811 0.17632 0.0374
1 5 0.05695 0.17388 0.034
2 1 0.01938 0.05917 0.0528
2 5 0.05403 0.22304 0.0492
3 4 0.06701 0.17103 0.0346
4 5 0.01335 0.04211 0.0128
4 7 0.00 0.20912 0.00
4 9 0.00 0.55618 0.00
5 6 0.00 0.25202 0.00
6 1
0.09498 0.1989 0.00
6 1
0.12291 0.25581 0.00
6 1
0.06615 0.13027 0.00
7 8 0.00 0.17615 0.00
7 9 0.00 0.11001 0.00
9 1
0.03181 0.08450 0.00
9 1
0.12711 0.27038 0.00
10 1
0.8205 0.19207 0.00
12 1
0.22092 0.19988 0.00
13 1
0.17903 0.34802 0.00
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Load data IEEE 14 bus system
Table 10
Busno.
PGenerated
(p.u.)
QGenerated
(p.u.)
PLoad
(P.U.
QLoad
(P.U.
BUSTYPE
QGenerated
MAX(p.u.
QGenerated
MIN1 2.32 0.00 0.00 0.00 2 10.0 -10.02 0.4 -0.424 0.2170 0.1270 1 0.5 -0.4
3 0.00 0.00 0.9420 0.1900 2 0.4 0.00
4 0.00 0.00 0.4780 0.00 3 0.00 0.005 0.00 0.00 0.0760 0.0160 3 0.00 0.006 0.00 0.00 0.1120 0.0750 2 0.24 -0.067 0.00 0.00 0.00 0.00 3 0.00 0.008 0.00 0.00 0.00 0.00 2 0.24 -0.06
9 0.00 0.00 0.2950 0.1660 3 0.00 0.0010 0.00 0.00 0.0900 0.0580 3 0.00 0.0011 0.00 0.00 0.0350 0.0180 3 0.00 0.0012 0.00 0.00 0.0610 0.0160 3 0.00 0.0013 0.00 0.00 0.1350 0.0580 3 0.00 0.0014 0.00 0.00 0.1400 0.0500 2 0.00 0.00