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.
Internal Guide D.RAGA LEELA M.Tech
Professor & H.O.D S.V.M.BHUVANAIKARAO M.E., F.I.E,Ph.D
Assistant Prof.
External Examiner
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 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
NEWTON-RAPHSON LOAD FLOW (NRLF) METHOD
14
1.9
CHAPTER 2 2
FACTS
2.1 FACTS CONTROLLERS 2.1.1SERIES CONNECTED CONTROLLERS
16 18 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
41
IEEE 14 BUS SYSTEM
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
IEEE 14 BUS LINE AND LOAD DATA
51 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 2.
14
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
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.
1
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
2
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
3
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.
4
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. 5
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.
6
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, sendingend and receiving-end node. Lines and transformers are represented by their πequivalent 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 loadflow problem is as follows:
7
● 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
8
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.
9
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:
10
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
11
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
12
is the jacobian matrix…………. (4) The elements of the Jacobian matrix can be calculated using the following equations
=
= +
=
………..(5)
13
Procedure for this iterative method is for the given system first the Y-bus matrix has to be formed.
Y=G+jB 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.
14
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
P
P
Calculate PK ,QK
P
P
P
P
∆PK = PK(Scheduled) - PK ; ∆QK (Scheduled) –QK K=1,2,3,…..n, K ≠ S
P
Determine max ∆P and max ∆Q
P= P+1
P
P
│ Max ∆P │ P
and│Max ∆Q │ > t (or) 0. 001
Solve for voltage corrections P
J1
P
∆P
P
J2
∆δ
= P
∆Q
P
J3
P
J4
∆│V │
VKP = VKP+1 + ∆ VKP ; δ KP+1 * ∆δ KP
VKP = VKP+1 ; δ KP+1 ,K=1,2,3,…..n, K ≠ S
Output voltage V angle δ at all buses, line flows and line
STOP
15
2. FLEXIBLE AC TRANSIMISSION SYSTEMS These are alternating current transmission systems incorporating power electronicbased 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
16
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
17
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)
18
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 nonconducting 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.
19
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.
20
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.
21
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 absorb system harmonics.
22
Figure 2.2.1 STATCOM layout
2.1.2.2 THYRISTOR CONTROLLED REACTOR (TCR) A
shunt-connected,
thyristor-controlled
inductor
whose
effect
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.
23
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 step change in the reactive power supplied to the system. Unlike shunt reactors, shunt capacitors cannot be switched continuously with variable firing angle control.
2.1.2.4 STATIC VAR COMPENSATOR (SVC) 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 var’s the thyristors-controlled or thyristors-switched reactor for absorbing reactive power and thyristors-switched capacitor for supplying the reactive power.
24
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, to allow bidirectional flow of real power between the series output terminals of the 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,
25
impedance, and angle or, alternatively, the real and reactive power flow in the line. The UPFC may also provide independently controllable shunt reactive compensation.
Figure 2.3 UPFC Lay out
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 there thermal capabilities.
Increase the system security through raising the transient stability limit.
Control of power flow as ordered.
Provide secure tie line connections.
Provide greater flexibility in setting new generation.
Reduce loop flows.
Reduce reactive power flows.
26
2.3 Comparison of various facts devices:
TABLE 1 FACTS DEVICE
TYPE OF CONNECTION
FUNCTION
Static var compensator
Shunt
Var compensation, steady state and dynamic stability
STATCOM
Shunt
Generating or absorbing the reactive power
SSSC
Series
Controlling transmitted
Static Synchronous Series
electric power by
Compensator
increasing or decreasing reactive voltage drop
TCSC
Series
Capacitive reactance
Thyristor Controlled
compensator in continuous
Series Capacitor
manner
UPFC
Two port
Terminal voltage control, phase angle regulation, series line compensation
RELATIVE IMPORTANCE OF CONTROLLABLE PARAMETERS
Control of the line impedance X (e.g., with a thyristor-controlled series capacitor) can provide a powerful means of current control.
When the angle is not large, which is often the case, control of X or the angle substantially provides the control of active power.
Control of angle, which in turn controls the driving voltage, provides a powerful 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 current flow, can increase or decrease the magnitude of current flow. Since the current flow lags
27
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 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 line voltage, 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 other line 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 and voltage regulation with a shunt controller can also provide a cost-effective means to control both the active and reactive power flow between the two systems.
28
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 output voltage 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 Fig.
Figure 3.1 structure of statcom
29
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 multibridge mode to reduce the harmonic level of the output current. Fig. below shows a single-phase equivalent circuit in which the STATCOM is controlled by changing 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 .
30
Figure 3.3 statcom
The STATCOM supplies reactive powers to the ac system if the magnitude of 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 can not provide active power to the AC system
31
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 to the AC system voltage. 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 device becomes 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 +/-90º 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 won’t 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 is proportional to the voltage difference between Vs and Vi.
3.2 MODELLING OF STATCOM Statcom
is ashumt connected reactive power compensation devic that is
capable of generating/obsorbing reactive power and in which the output can be varied to ocntrol the specfic parameters of an electric power system. It is in general a solid state switching converter capable of generating independatly 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 n fig above
32
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 π. The equation of power can be modulated by modulating the shunt reactive current I. The modeling of the statcom can be done in various methods 1. Variable suspectance 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 (Ambriz – Periz , Acha , and Fuerte – Esquivel , 2000 ). The equivalent circuit shown in figure is used to derive the SVC non-linear power equations and the linearised equations required by Newton’s 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
the state variable. 33
where
the
equivalent
susceptance
At the end of iteration (1), the variable shunt susceptance
is updated according
to
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 susceptance 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 • 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 • Small footprint
34
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. MATLAB’s built-in functions provide excellent tool for linear algebra computation, data analysis, signal processing, optimization, and numerical 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 3Dgraphics as well as for animation also, for those who can’t do without their FORTRAN or C courses, MATLAB even provides 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 lab’s language is very easy to learn and to use. There are several optional ‘toolboxes’ available from the developers
of the
MATLAB. These toolboxes are collections written for special applications such as symbolic computations, image processing, static’s control system design and Neural Networks. The basis 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.
35
4.2 MATLAB WINDOW On all UNIX system Macs, and pc, mat lab through three Basic windows, they are Command window: This is the main window it is characterized by MATLAB Command prompt ‘>>’: when you launch the application program, MATLAB puts you in this window. All commands, including those for running user written programs, are typed in this window at the MATLAB prompt. Graphics Window: The outputs of all graphic commands are typed in the command window and are flushed to the graphic or figure window, a separate grey window with white back ground colour. 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 programs in files called M-files. We can use any text editor to carry out these tasks. On the most systems, such as PC’s and Macs, MATLAB provides it’s built in editor. On
other
systems, you can invoke the edit window by typing the standard file editor command that at the MATLAB prompt following special character ‘!’. The exclamation 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 the screen, 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. It encompasses 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 dimensioning statements 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 between lower 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. 36
Output Display: the output of every command is displayed a screen unless MATLAB 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 output at once, without regard to the speed at which we read. Output format: Though computations inside the MATLAB are performed using the double precision, the appearance of floating point numbers on the screen is controlled by the output format in use. There are several different screen output formats. 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 three types for strong information M-files: M-files are standard ASCII text files, with an extension to the filename. 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 the filename. 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 C programs, with a Mex extension to the filename ,use of these files requires some experience with MATLAB and a lot of patience.
37
4.3 PROBLEM EVALUATION: 4.3.1 IEEE 5 BUS WITHOUT USING THE STATCOM The IEEE 5 BUS SYSTEM data
4
2 Figure 4.1 IEEE 5 bus
Mat lab results : for iter=4
Bus no. 1 2 3 4 5
TABLE 2
With out statcom Voltage magnitude Voltage angle 1.0600 0 1.0000 -2.0554 -4.6268 0.9873 0.9842 -4.9466 0.9717 -5.7563
38
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
Bus no. 1 2
With statcom Voltage magnitude Voltage angle 1.0600 0 1.0000 -2.0534
3
1.0000
-4.8379
4 5
0.9944 0.9752
-5.1073 -5.7975
Injected reactive power at bus no:3is QSVC = -0.2047 Mvar p.u
39
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
Bus no. 1
With statcom Voltage Voltage angle magnitude 1.0600 0
2
1.0000
-2.0549
3 4
1.0000 1.0000
-4.8355 -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. 40
4.3.2 IEEE 14 BUS SYSTEM IEEE 14 BUS SYSTEM
4.3.2.1 WITHOUT USING THE STATCOM
Figure 4.4 IEEE 14 bus
41
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
42
4.3.2.2USING SINGLE STATCOM
IEEE 14 BUS WITH USING THE SINGLE STATCOM
Figure 4.5 IEEE 14 bus with statocm
43
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
-7.0389
8
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
44
4.3.2.2USING MULTIPLE STATCOM
IEEE 14 BUS SYSTEM WITH MULTIPLE STATCOM
Figure 4.6 IEEE 14 bus with multiple statocm
45
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
46
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 along with 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).
47
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.
48
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 in Power System with Static Var Compensators,” Int. J. Electric Power and Energy Systems, vol. 19, no. 5, 1997, pp. 339–347. [3] N. G. Hingorani and Laszlo Gyugyi, “UNDERSTANDING FACTS”. [4] C. A. Ca˜nizares and Z. T. Faur, “Analysis of SVC and TCSC Controllers in Voltage Collapse,” IEEE Trans. on Power Systems, vol. 14, no. 1, February 1999, pp. 158–165. [5] C. A. Ca˜nizares. “Power Flow and Transient Stability Models of FACTS Controllers for Voltage and Angle Stability Studies”. In Proc. of IEEE/PES Winter Meeting, Singapore, January 2000. [6] G. Hingorani and L. Gyugi, Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems. IEEE Press, 1999. [7] Modern Power System Anaylsis., Dillon.P.kothari [8] C. A. Ca˜nizares, UWPFLOW: Continuation and Direct Methods to Locate Fold Bifurcation 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.
49
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
Bus code 1 2 3 4 5
Assumed bus voltage 1.06+j0.0 1.00+j0.0 1.00+j0.0 1.00+j0.0 1.00+j0.0
Generation slack 40 0 0 0
50
30 0 0 0
load 0 20 45 40 60
0 10 15 5 10
IEEE 14 BUS SYSTEM : LINE DATA Table 9 From bus
To bus
RESISTANCE
Reactance (p.u.)
()P.U)
Line charging (p.u.)
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
11
0.09498
0.1989
0.00
6
12
0.12291
0.25581
0.00
6
13
0.06615
0.13027
0.00
7
8
0.00
0.17615
0.00
7
9
0.00
0.11001
0.00
10
0.03181
0.08450
0.00
9
14
0.12711
0.27038
0.00
10
11
0.8205
0.19207
0.00
12
13
0.22092
0.19988
0.00
13
14
0.17903
0.34802
0.00
9
51
Load data IEEE 14 bus system Table 10 Bus no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
P Q Generated Generated (p.u.) (p.u.) 2.32 0.00 0.4 -0.424 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
P Load (P.U.) 0.00 0.2170 0.9420 0.4780 0.0760 0.1120 0.00 0.00 0.2950 0.0900 0.0350 0.0610 0.1350 0.1400
Q Load (P.U.) 0.00 0.1270 0.1900 0.00 0.0160 0.0750 0.00 0.00 0.1660 0.0580 0.0180 0.0160 0.0580 0.0500
52
BUS TYPE 2 1 2 3 3 2 3 2 3 3 3 3 3 2
Q Generated MAX(p.u.) 10.0 0.5 0.4 0.00 0.00 0.24 0.00 0.24 0.00 0.00 0.00 0.00 0.00 0.00
Q Generated MIN (p.u.) -10.0 -0.4 0.00 0.00 0.00 -0.06 0.00 -0.06 0.00 0.00 0.00 0.00 0.00 0.00
