asics bargain Modelling of Power System and Stabil

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Modelling of Power System and Stability Analysis in Load Flow
I INTRODUCTION
??????????? Power system stability analysis tools and techniques, and the test cases used throughout the dissertation is presented. A dispute of the critical points one needs to take into consideration in assorted system studies, such as continuation power flow or small-disturbance stability analysis, is also presented here.
1.1 Modeling
Models for power system components have to be selected along to the purpose of the system study, and hence, one must be conscious of what models in terms of accuracy and complexity should be used for a certain type of system studies, while reserving the computational burden as low as possible. Selecting unsuitable models for power system components may lead to incorrect conclusions. For example, the founder in [2] studied the effect of using assorted load models on the system stability margin, showing that for some case studies, when only load models are changed, different stability margins in terms of MWs are obtained. In the retinue sections, the main units of power systems, for the purpose of this thesis, are briefly discussed, and the corresponding models are reviewed.
1.2 Generators
Generators are important in system stability studies, and are modeled in another ways depending 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 complex analyses, such as small-disturbance stability, it may be required to use either 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 skeleton are typically written as [6]:
ed = p?d ? ?q?r ? Raid
eq = p?q + ?d?r?? ? Raiq -------------1.1
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Where ed and eq are the momentary stator phase voltages; p namely the differential operator d/dt; id and iq are the instantaneous stator phase currents; ?d and ?q are the flux linkages; ?r is the rotor electrical speed; and Ra namely the armature resistance per phase. The two most common simplifications in obtaining generator stability models are: First, omit the stator temporaries,Indian Flights market to be third largest in Ten years_4466, which are represented by the p?d and p?d terms in 2.1; these terms are associated with web transients, which decay quickly. Second, neglect the efficacy of speed variations above stator voltages, i.e. ?r = 1 in 2.1. In increase to the abovementioned simplifications, additional speculations, such as poised voltages with slowly varying phase and angle, yield generator stability models represented by differential equations with arrays ranging from II (classic prototype) apt VI (subtransient model) . For example, a generator subtransient model is acquired assuming two q-axis and 1 d-axis damper roundabouts on the rotor, and X?d = X?? q , where X?? d and X??q are subtransient reactances. On the additional hand, a generator classical model is got by modeling the generator as a constant voltage source back a reactance, and hence, only two differential equations are accustom apt represent the electromechanical wag equations.
A generator is normally equipped with an exciter for primary voltage control and a governor for frequency control. Fast exciters are known to enhance generator synchronizing torque, but may corrode the damping [7], and hence, fhardly everme generators, a Power System Stabilizer (PSS) is installed to amend the damping. Several types of exciters, governors and PSSs are readily available (for more details, amuse refer to [6]), and are merged in most small-disturbance stability and transient stability analysis programs, such as the Power System Toolbox (PST) .
These models are no typically modeled in a power stream learn; however, they have to be adequately represented in an eigenvalue thinking (small-disturbance analysis) or a transient stability analysis.
1.3 Loads
Load models are categorized as static and dynamic. Dynamic load models are more complicated, and are used mainly for transient stability analysis. On the other hand, static models are better suited for power flow and small-disturbance stability analysis. The three cardinal static load models are known as constant PQ (or MVA), constant present and constant impedance; all of them can be mathematically expressed by
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-------------1.2
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Where P0 and Q0 are the active and reactive power consumed 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.
II Synchronous static compensator (STATCOM)
Shunt compensators are especially used to regulate the voltage in a bus by providing or preoccupying reactive power. They are also known to be efficacious in damping electromechanical oscillations [4, 5]. Different kinds of shunt compensators are currently creature used in power systems, of which the most popular 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 explained and studied. SVCs and STATCOMs are thyristor based and GTO based FACTS controllers, respectively. A thyristor has only turn-on skill accordingly cannot be used in alternate mode petitions. 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 feasible to use them in switched mode petitions such as Voltage-Source Converters (VSC) in power systems he feature of the converter output voltage denoted as Vout in Figure 2.1,hermes kelly bag, i.e.
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.
------1.3
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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 ultimately controls.
Vout, as this voltage is proportional to Vdc; the block diagram of a phase control is shown in Figure 2.2. On the other hand, in the PWM control, both angle and magnitude of the converter output voltage are regulated as shown in Figure 2.3.
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Although less low frequency harmonics are produced by a STATCOM with a PWM control, the tall switching losses due to the high switching frequency are the main constraints for its application in transmission systems. The maximum and minimum operating points of a STATCOM are independent
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Figure 1.1: Basic structure of STATCOM.
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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 most voltage and current rating as depicted in Figure 2.4. This controller can be manipulated over its full output current range even at quite low voltages (typically 0.2 p.u.).
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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
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Figure 1.2: STATCOM control block figure with phase control.
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Figure 1.3: STATCOM control block diagram with PWM control.
Figure 1.4: Voltage-Current characteristic of a STATCOM.
Between the STATCOM and the network [1, 40]:
----1.4
Where a stands for the transformer ratio, and the resistance Rc represents the converter losses, which can be premonitory, depending on the number of switches and the switching frequency. All the blocks in Figure 2.5 are the same as the STATCOM careful model in Figure 2.3, except that the converter and the blocks related to the switches are replaced by a voltage source kVdc\?; the coefficient k is proportional to the modulation concordance ma, which for a two-level inverter is ma2?2.
It has been shown by means of time-domain simulation results that the TS model response is reasonably close to that obtained with the detailed model when the transients are small [1].
Figure 1.5: STATCOM transient stability model and its control.
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III Power System Stability
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From the aforementioned models, a power system model can be represented using
a DAE model, such as :
x = f(x, z, ?, ?) -----------------------1.5
0 = g(x, z, ?, ?)
y = h(x, z, ?, ?)
Where x ? ?nis a vector of state variables that represents the state variables of generators, loads and other system controllers; z ? ?m
?is a vector of steady state algebraic variables that outcome from neglecting fast dynamics in some load phasor voltage magnitudes and angles; ? ? ?? is a set of uncontrollable parameters such as lively and reactive power load variations; ? ? ?a?is a set of controllable parameters such as tap 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
f: ?n �� ?m �� ?? �� ?a 7? ?n, g : ?n �� ?m �� ?? �� ?a 7? ?m, and h : ?n �� ?m ��?? ��?a 7? ?l
?Stand for the differential equations, algebraic constraints and output variable measurements, respectively.
The DAE model in (2.8) can be linearized almost an operating point (xo, zo, ?o, ?o) to obtain the system state matrix A:
-----1.6
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For slowly varying parameters ?, the power system model has been shown to present local bifurcations, on which most stability indices in the current literature are based.
3.1 Voltage Stability
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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 ability to nourish steady prepossessing voltages by entire buses below normal operating conditions and after a chance [6]. Thus, whether the bus voltage importance decreases as the reactive power injection at the same bus boosts, the power system is voltage unstable. This may guide to voltage breakdown, whether generators or other reactive power sources do not invest enough reactive power support. Voltage collapse can be annotated among the environment of bifurcation theories applied to DAEs in nonlinear systems, is, SNB and LIB [3]. Saddle-node Bifurcations (SNB) When the system state matrix A has a simple and unique zero eigenvalue with nonzero left and right eigenvectors, the balance 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 deserving to the regional merger and wane of equilibrium (operating points) as ? alterations.
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3.2 Continuation Power Flow
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For given dispatch scenarios, the continuation power flow [43] technique is used to obtain P-V curves alike to the one depicted in Figure 2.6, and thus determine the static loading margin (SLM) of the system (neb 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 ahead the nostril point. All the P-V curves in this work have been
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Figure 1.6: A typical PV curve and corresponding SLM and DLM.
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as it has been developed in C and C++, and hence appropriate to study large systems.
3.3 Small-Disturbance Stability Analysis
As explained before, matrix A and its eigenvalues can provide valuable information
?About the system stability for small perturbations that may happen in the system.
This is also referred to as small-disturbance stability analysis or eigenvalue analysis. In this go, matrix A and its eigenvalues for the test cases have been obtained by method of the linearized transient stability models in the Power System Toolbox (PST) , which is a MATLAB based agenda. PST, when compared to other programs, is user-friendly but slow, and hence inappropriate for great systems (more than 50 buses). Therefore, for great systems, the Small Signal Analysis Tool (SSAT) is used; as it is capable to handle with systems made up of several thousand buses.
It attempts powerful 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 trace;etc.
IV Time-Domain Simulation
Time-domain simulation is effectively used for transient stability analysis of power systems emulating large perturbations, as it accounts for all the nonlinear effects by solving the complete set of DAEs by means of step-by-step trapezoidal or predictor-corrector integration [6]. However, in this thesis, this time-domain reaction of the power system is also used to obtain important 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]; however, the simulation of large systems was only feasible with the after. TSAT has two simulation engines: A conventional time-domain simulation engine namely uses full numerical integration techniques and a quick time-domain simulation engine based on a quasi
Steady-state system model. It has several useful features for transient stability analysis, such as the likelihood of sprinting multi-contingency cases or multi-dispatch scenarios, obtaining a security index based on critical removing period, etc. A broad scope of dynamic models of power system components is accessible, and renowned formats, such as PTI PSS/E, GE PSLF, and BPA can be used as input file.
4.1 Test Systems
A variety 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 possibility of the proposed stability indices and system identification techniques. In some cases, several fulfil scenarios were thought in order to follow the action of a real power system. The common specifics of these test cases are briefly reiterated in this section.
4.2?Single-Machine-Infinite-Bus (SMIB)
This is the simplest but the most warmhearted 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 stiff large system with a constant voltage magnitude and angle. This system can be used to investigate the action of a generator or group of generators,Das Monk are AOK_2571, named as G1 in
Figure 2.7,tods shoes Teen Drug Rehabilitation_1009, with esteem to the infinite bus.
4.3 IEEE 3-bus System
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This corresponds to a case where two districts are connected through a long displacement line (languid linkage); hence, power oscillations are observed in the tie-line.
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Figure 1.7: IEEE 3-bus test system.
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A single-line diagram of the test system is shown in Figure 2.8 [2]. The found load used at Bus 3 is a 900 MW and 300 MVar load, and is modeled as a constant PQ. Each machine has a simple exciter,puma shoes ferrari, and a simple ruler is used for the machine at Bus 1. The generators are modeled in detail by means of subtransient models.
The corresponding static and dynamic data is presented in Appendix A.1.
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Figure 1.8: IEEE 14-bus test system.
Figure 1.9: Two-area benchmark system.
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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 absolute base loading class is 2734 MW and 200 MVar.
V.CONCLUSION
A terse explanation of some of the opener power system components used in this thesis, such as loads and generators, is presented in this chapter. Also discussed in this part is the magnitude of selecting the right models for different kinds of analyses. Power system stability conceptions and the analysis techniques and tools used throughout this thesis, such as voltage and angle stability, continuation power
Flow and system identification are briefly explained.
REFERENCES
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[1] E. Uzunovic, ��Transient Stability and Power ??????Flow Models of VSC FACTS controllers,�� ??????Ph.D. dissertation, University of Waterloo, ??????Waterloo, ON, Canada, 2001.
?[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.
[3] C. A. Ca?nizares, N. Mithulananthan, A. ??????Berizzi, and J. Reeve, ��On the linear
??????Profile of indices for the forecast of ??????saddle-node and limit-induced bifurcation
??????Points in power systems,�� IEEE Trans. ??????Circuits and Systems, vol. 50, no. 2,
??????pp. 1588�C1595, December 2003.
[4] N. Mithulananthan, C. A. Ca?nizares, J. ???????Reeve, and G. J. Rogers, ��Comparison
???????of PSS,asics sale, SVC and STATCOM controllers ???????because damping power system oscillations,�� ???????IEEE Trans. Power Systems, vol. 18, no. 2, ???????pp. 786�C792, May 2003.
[5] N. Mithulananthan, C. A. Ca?nizares, and ???????J. Reeve, ��Hopf bifurcation control
???????in power system using power system ???????stabilizers and static var compensators,��
?????? in Proc. of NAPS��99, San Luis Obispo, ???????California, October 1999, pp. 155�C163.
[6] P. Kundur, Power System Stability and ????????Control. New York: McGraw-Hill,
???????1994.
?[7]??F.P.Demello?and?C.Concordia,��Concepts?????????? of?synchronous?machine?reliability?for?affected??? ????at?excitation??control��?IEE?E?Trans.Power ???????Apparatus?and Systems, ?vol. PAS-88, ???????no. 4, pp. 316?�C329,?April 1969.
?[8] G. Hingrani, Understanding FACTS. New ????????York: IEEE Press, 2000.
[9] C.A.Caizares and F.L.Alvarado, ��Point ?????????of collapse and continuation means???for ?????????large ac/dc systems,�� IEEE Trans.Power ?????????Systems, vol. 8, no. 1, pp. 1�C8,?
?[10] Transient Security Assessment Tool ?????????(TSAT), User Manual, Power tech Labs
?????????Inc., Surrey, BC, Canada, V3W 7R7, ?????????2002.
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