Modelling of Power System and Stability Analysis i

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as it has been amplified in C and C++,head tennis racket, and hence fitting to study large systems.
Where a stands for the transformer percentage, and the resistance Rc represents the converter losses, which can be meaningful, depending on the digit of switches and the switching frequency. All the blocks in Figure 2.5 are the same as the STATCOM detailed model in Figure 2.3, except that the converter and the blocks narrated to the switches are replaced by a voltage source kVdc\?; the coefficient k is proportional to the modulation index ma, which for a two-level inverter is ma2?2.
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f: ?n �� ?m �� ?? �� ?a 7? ?n, g : ?n �� ?m �� ?? �� ?a 7? ?m, and h : ?n �� ?m ��?? ��?a 7? ?l
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It has been shown by means of time-domain simulation results that the TS model response is reasonably near to that obtained with the detailed model when the transients are small [1].
A brief explanation of some of the key power system components used in this thesis, such as loads and generators, is presented in this chapter. Also discussed in this chapter is the magnitude of selecting the right models for different varieties of analyses. Power system stability notions and the analysis techniques and tools used throughout this thesis, such as voltage and angle stability, continuation power
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Models as power system components have to be selected along to the intention of the system learn, and accordingly, an must be conscious of what models in terms of precision and complexity should be accustom as a certain type of system studies, while keeping the computational burden as cheap as possible. Selecting improper models for power system components may guide to wrong conclusions. For sample, the lyricist in [2] studied the effect of using manifold load models aboard the system reliability margin, showing that fall butme circumstance studies, while only load models are changed, different stability margins in terms of MWs are won. In the following partitions, the chief elements of power systems, for the purpose of this monograph, are briefly argued, and the corresponding models are reviewed.
?[8] G. Hingrani, Understanding FACTS. New ????????York: IEEE Press, 2000.
It attempts mighty functions, such as complete eigenvalue analysis; Single-Machine Infinite-Bus (SMIB) analysis; eigenvalue analysis within specified frequency and damping ranges; computation of modes closest to a specified frequency and damping; computation of modes associated to a generator; sensitivity analysis; mode track;etc.
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a DAE prototype, such for :
3.3 Small-Disturbance Stability Analysis
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The DAE model in (2.8) can be linearized almost an operating point (xo, zo, ?o, ?o) to obtain the system state matrix A:
-------------1.2
As explained before, matrix A and its eigenvalues can cater valuable information
This is the simplest but the most widely used test case, as it consists of only a generator, a transmission line and a load as depicted in Figure 2.7. The load bus is modeled as an infinite bus, which is normally used to replace a rigid large system with a constant voltage magnitude and angle. This system can be used to investigate the action of a generator or team of generators, labeled as G1 in
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Figure 1.6: A typical PV curve and corresponding SLM and DLM.
These models are not typically modeled in a power flow study; however, they must be adequately characterized in an eigenvalue analysis (small-disturbance analysis) or a transient stability analysis.
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?[10] Transient Security Assessment Tool ?????????(TSAT), User Manual, Power tech Labs
Shunt compensators are especially used to regulate the voltage in a bus by providing or absorbing reactive power. They are also known to be telling in damping electromechanical oscillations [4, 5]. Different kinds of shunt compensators are currently being used in power systems, of which the most fashionable ones are Static?Var?Compensator?(SVC)?and?Synchronous?STATI C?COMPENSATOR (STATCOM) [37]; however, in this research, only the STATCOM, which has a more complicated topology, is annotated and studied. SVCs and STATCOMs are thyristor based and GTO based FACTS controllers, respectively. A thyristor has only turn-on capability thus cannot be used in switch mode applications. Advanced devices such as Gate Turn-Off Thyristors (GTO) and Integrated Gate Bipolar Transistors (IGBT) have both turn-on and turn-off capabilities; hence, it is possible to use them in switched mode applications such as Voltage-Source Converters (VSC) in power systems he feature of the converter output voltage denoted as Vout in Figure 2.1, i.e.
For given fulfil scenarios, the continuation power flow [43] technique is used to obtain P-V curves similar to the one depicted in Figure 2.6, and thus decide the static loading margin (SLM) of the system (snout point) associated with a voltage collapse point, which could be the result of an SNB or an LIB. Figure 2.6 also demonstrates the dynamic loading margin (DLM) of a system, which is associated with an angle instability occurring before the nose point. All the P-V bends in this work have been
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1.1 Modeling
----1.4
From the aforementioned models, a power system model can be represented using
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Flow and system identification are briefly explained.
This is also referred to as small-disturbance stability analysis or eigenvalue analysis. In this work,earphone sony, phalanx A and its eigenvalues for the test cases have been obtained by means of the linearized transient stability models in the Power System Toolbox (PST) , which is a MATLAB based program. PST, when likened to other programs, is user-friendly but slow, and hence inappropriate for large systems (more than 50 buses). Therefore, for large systems, the Small Signal Analysis Tool (SSAT) is used; as it is competent to deal with systems made up of several thousand buses.
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From the system voltage as opposed to an SVC. The V-I characteristic of a STATCOM is limited only by the maximum voltage and current rating as described in Figure 2.4. This controller can be operated over its full output current range even by very low voltages (typically 0.2 p.u.).
II Synchronous static compensator (STATCOM)
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[6] P. Kundur, Power System Stability and ????????Control. New York: McGraw-Hill,
Generators are important in system stability studies, and are modeled in differ ways relying on the objective of the study. For instance, in a power flow study, a generator is modeled as a PV bus (defined as a bus with fixed voltage and power). For other complicated analyses, such as small-disturbance stability, it may be required to use both generator subtransient or transient stability models that are represented by means of DAEs. The per unit stator voltage equations for generator detailed model in dq reference border are typically written as [6]:
Modelling of Power System and Stability Analysis in Load Flow
I INTRODUCTION
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Figure 1.9: Two-area benchmark system.
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???????1994.
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??????Points in power systems,�� IEEE Trans. ??????Circuits and Systems, vol. 50, no. 2,
0 = g(x, z, ?, ?)
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3.1 Voltage Stability
Vout, as this voltage is proportional apt Vdc; the block chart of a period control is shown in Figure 2.2. On the other hand, in the PWM control,mbt sports, both angle and importance of the converter output voltage are regulated as shown in Figure 2.3.
V.CONCLUSION
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?is a vector of steady state mathematical variables that result from neglecting fast dynamics in some load phasor voltage magnitudes and angles; ? ? ?? is a set of uncontrollable parameters such as athletic and reactive power load variations; ? ? ?a?is a set of controllable parameters such as pat or AVR set points; and y ? ?l?is a vector of output variables such as power via the lines and generator output power. The nonlinear functions
4.2?Single-Machine-Infinite-Bus (SMIB)
Steady-state system model. It has several profitable features for transient stability analysis, such as the feasibility of scampering multi-contingency cases or multi-dispatch scenarios, obtaining a security index based on critical clearing time, etc. A broad range of dynamic models of power system components is available, and renowned formats, such as PTI PSS/E, GE PSLF, and BPA can be used as input data.
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3.2 Continuation Power Flow
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?????????Inc., Surrey, BC, Canada, V3W 7R7, ?????????2002.
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Figure 1.8: IEEE 14-bus test system.
y = h(x, z, ?, ?)
?[7]??F.P.Demello?and?C.Concordia,��Concepts?????????? of?synchronous?machine?stability?as?affected?????? ?by?excitation??control��?IEE?E?Trans.Power ???????Apparatus?and Systems, ?vol. PAS-88, ???????no. 4, pp. 316?�C329,?April 1969.
1.2 Generators
Figure 1.7: IEEE 3-bus test system.
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In a power system, voltage stability is directly related to the voltage on the system buses, and is defined as the power system aptitude to maintain steady befitting voltages at all buses beneath normal operating conditions and afterward a chance [6]. Thus, whether the bus voltage magnitude decreases as the reactive power injection at the same bus boosts, the power system is voltage unstable. This may lead to voltage collapse, whether generators or other reactive power sources do not provide ample reactive power aid. Voltage collapse can be explained within the environment of bifurcation theories applied to DAEs in nonlinear systems, namely, SNB and LIB [3]. Saddle-node Bifurcations (SNB) When the system state matrix A has a simple and matchless zero eigenvalue with nonzero left and right eigenvectors, the equilibrium point (xo, zo, ?o, ?o) is typically referred to as SNB point (other transversality conditions must also be met). In power systems, this bifurcation point is associated with voltage stability problems due to the local combination and disappearance of equilibrium (operating points) as ? alterations.
?[2]?N.?Mithulananthan,?��Hopf?bifurcation ??????control and indices for power system?with ??????interacting generator and FACTS ???????controllers,�� Ph.D. dissertation, University ??????of Waterloo, Waterloo, ON, Canada, 2002.
?About the system stability for small perturbations that may happen in the system.
III Power System Stability
This corresponds to a case where two zones are interlocked through a long transmission line (feeble linkage); hence, power oscillations are observed in the tie-line.
Figure 1.5: STATCOM transient stability model and its control.
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Figure 1.4: Voltage-Current characteristic of a STATCOM.
Where P0 and Q0 are the active and reactive power wasted at voltage V0, respectively. The type of the load model depends on exponents a and b, i.e. constant PQ for a = b = 0, constant current for a = b = 1, and constant impedance for a = b = 2.
Figure 1.2: STATCOM control block diagram with phase control.
REFERENCES
STATCOM Transient Stability (TS) Model For the case that the output voltage of the STATCOM is balanced and harmonic free, a TS model has been proposed, which does not comprise converter switching phenomena [1]. The STATCOM TS model replaces the detailed model with a variable voltage source as shown in Figure 2.5, in which the magnitude of capacitor voltage is insistent by a differential equation derived based on the power exchange
eq = p?q + ?d?r?? ? Raiq -------------1.1
Load models are categorized as static and dynamic. Dynamic load models are extra difficult, and are used effectively for transient stability thinking. On the other hand, static models are better suited for power flow and small-disturbance stability analysis. The 3 main static load models are known as constant PQ (or MVA), constant present and constant impedance; always of them tin be mathematically expressed by
[5] N. Mithulananthan, C. A. Ca?nizares, and ???????J. Reeve, ��Hopf bifurcation control
ed = p?d ? ?q?r ? Raid
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1.3 Loads
?Stand for the differential equations, algebraic constraints and output variable dimensions, respectively.
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For slowly altering parameters ?, the power system model has been shown to present regional bifurcations, on which most stability indices in the current literature are based.
x = f(x, z, ?, ?) -----------------------1.5
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???????of PSS, SVC and STATCOM controllers ???????for damping power system oscillations,�� ???????IEEE Trans. Power Systems, vol. 18, no. 2, ???????pp. 786�C792, May 2003.
[9] C.A.Caizares and F.L.Alvarado, ��Point ?????????of collapse and continuation methods???for ?????????large ac/dc systems,�� IEEE Trans.Power ?????????Systems, vol. 8, not. 1, pp. 1�C8,?
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Figure 1.1: Basic framework of STATCOM.
The corresponding static and dynamic file is presented in Appendix A.1.
Time-domain simulation is mainly used for transient stability analysis of power systems retinue great perturbations,babolat aeropro drive cortex, as it accounts for all the nonlinear effects along solving the complete set of DAEs at method of step-by-step trapezoidal or predictor-corrector integration [6]. However, in this thesis, this time-domain reaction of the power system is likewise used to obtain momentous small-disturbance stability message. Time-domain simulations of test cases were carried out by means of both the PST and the Transient Stability Analysis Tool (TSAT) [10]; whatsoever, the simulation of massive systems was only possible with the after. TSAT has 2 simulation engines: A accustomed time-domain simulation engine that uses full numerical integration techniques and a rapid time-domain simulation engine based on a quasi
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Tie-lines, hence resulting in an inter-area mode with a frequency of about 0.7 Hz. However, the individual machines in each area also contribute to a local mode in the same area with a frequency of about 1.3 Hz. Therefore, an inter-area rotor angle mode and two local modes are observed for this test case. The generators were modeled using subtransient models and their exciters are simple exciters equipped with PSSs. The corresponding static and dynamic data is given in Appendix A.3. The total base loading level is 2734 MW and 200 MVar.
[1] E. Uzunovic, ��Transient Stability and Power ??????Flow Models of VSC FACTS controllers,�� ??????Ph.D. dissertation, University of Waterloo, ??????Waterloo, ON, Canada, 2001.
???????in power system using power system ???????stabilizers and static var compensators,��
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Where x ? ?nis a vector of state variables that represents the state variables of generators, loads and other system controllers; z ? ?m
Between the STATCOM and the network [1, 40]:
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[3] C. A. Ca?nizares, N. Mithulananthan, A. ??????Berizzi, and J. Reeve, ��On the linear
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Where ?conv is the angle among the ac system voltage V and Vout. Two control strategies may be used for a STATCOM; namely, Phase Control and PWM Control. In phase control, the DC bus voltage Vdc is regulated by changing ?conv, i.e. charging and discharging the DC capacitor, which afterward controls.
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4.1 Test Systems
Figure 1.3: STATCOM control block diagram with PWM control.
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??????????? Power system stability analysis tools and techniques, and the test cases used throughout the thesis is presented. A debate of the fussy points one absences to take into consideration in different system studies, such as continuation power flow or small-disturbance stability analysis, is also presented here.
Where ed and eq are the momentary stator phase voltages; p is the differential worker d/dt; id and iq are the momentary stator phase currents; ?d and ?q are the flux linkages; ?r is the rotor electrical speed; and Ra is the armature resistance per phase. The two most mutual simplifications in obtaining generator stability models are: First, neglect the stator transients, which are represented by the p?d and p?d terms in 2.1; these terms are related with network transients, which decay rapidly. Second, disregard the effect of speed variations on stator voltages, i.e. ?r = 1 in 2.1. In counting to the abovementioned simplifications, other assumptions, such as balanced voltages with slowly varying phase and angle, yield generator stability models represented by differential equations with arrays ranging from II (classical model) to VI (subtransient model) . For instance, a generator subtransient model is obtained assuming two q-axis and one d-axis damper windings on the rotor, and X?d = X?? q , where X?? d and X??q are subtransient reactances. On the other hand, a generator classical model is obtained by modeling the generator as a constant voltage source back a reactance, and hence, only two differential equations are used to represent the electromechanical swing equations.
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A single-line diagram of the test system is shown in Figure 2.8 [2]. The pedestal load used at Bus 3 is a 900 MW and 300 MVar load, and is modeled as a constant PQ. Each machine has a easy exciter, and a easy governor is used for the machine at Bus 1. The generators are modeled in elaborate by means of subtransient models.
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A generator is normally equipped with an exciter for basic voltage control and a leader for frequency control. Fast exciters are known to enhance generator synchronizing torque, yet may disintegrate the damping [7], and hence,buy tennis racket, fknow next to nothing ofme generators, a Power System Stabilizer (PSS) is installed to amend the damping. Several types of exciters, governors and PSSs are readily accessible (for more details, please refer to [6]), and are incorporated in maximum small-disturbance stability and transient stability analysis programs, such as the Power System Toolbox (PST) .
Figure 2.7, with respect to the infinite bus.
Although fewer low frequency harmonics are produced by a STATCOM with a PWM control, the lofty switching losses due to the tall switching frequency are the main limitations for its applying in displacement systems. The maximum and minimum operating points of a STATCOM are independent
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IV Time-Domain Simulation
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?????? in Proc. of NAPS��99, San Luis Obispo, ???????California, October 1999, pp. 155�C163.
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??????Profile of indices for the prophecy of ??????saddle-node and limit-induced bifurcation
4.3 IEEE 3-bus System
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A diversity of test cases, ranging from a Single-Machine-Infinite-Bus (SMIB) to a real power system with 14,000 buses, were used to test the feasibility of the intended stability indices and system identification techniques. In some cases, several dispatch scenarios were thought in order to imitate the action of a real power system. The common characteristics of these test cases are briefly reviewed in this section.
[4] N. Mithulananthan, C. A. Ca?nizares, J. ???????Reeve, and G. J. Rogers, ��Comparison
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??????pp. 1588�C1595, December 2003.
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