Simulink model for examining dynamic interactions involving electro-mechanical oscillations in distribution systems

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1 University of Wollongong Research Online Faculty of Engineering an Information Sciences - Papers: Part A Faculty of Engineering an Information Sciences 205 Simulink moel for examining ynamic interactions involving electro-mechanical oscillations in istribution systems Dothinka Ranamuka Rallage University of Wollongong, ssrr987@uowmail.eu.au Ashish P. Agalgaonkar University of Wollongong, ashish@uow.eu.au Kashem M. Muttai University of Wollongong, kashem@uow.eu.au Publication Details D. Ranamuka, A. P. Agalgaonkar & K. M. Muttai, "Simulink moel for examining ynamic interactions involving electro-mechanical oscillations in istribution systems," in Power Engineering Conference (AUPEC), 205 Australasian Universities, 205, pp. -6. Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW Library: research-pubs@uow.eu.au

2 Simulink moel for examining ynamic interactions involving electromechanical oscillations in istribution systems Abstract In Australian meium voltage (MV) istribution networks, the majority of embee local generation (LG) uses synchronous machine base technology. LG units with a synchronous generator can easily be ispatche an controlle to provie or absorb reactive power an thereby locally supporting the system voltage an increasing the voltage stability margin. The fast response from a synchronous machine base LG unit exciter will ensure fast voltage recovery. This will significantly improve the transient voltage stability. Also, the synchronous machine base LG units can provie inertial support to the system. Furthermore, some of these LG technologies work as stanby power supplies all over the worl. However, there can be ynamic interactions between nearby synchronous machine base LG units leaing to significant rotor swings. It is mainly because of (a) low inertia coefficient associate with the machines an (b) the operation of excitation system eteriorates the amping of oscillations that follow the first rotor swing after the perturbation where a fast responing excitation system can reuce the amping torue component. This paper emonstrates moelling MV istribution systems using MATLAB-SimuLink an conventional moelling techniue for investigating inter-unit electro-mechanical oscillations in nearby LG units. Keywors oscillations, mechanical, electro, involving, interactions, ynamic, examining, moel, systems, simulink, istribution Disciplines Engineering Science an Technology Stuies Publication Details D. Ranamuka, A. P. Agalgaonkar & K. M. Muttai, "Simulink moel for examining ynamic interactions involving electro-mechanical oscillations in istribution systems," in Power Engineering Conference (AUPEC), 205 Australasian Universities, 205, pp. -6. This conference paper is available at Research Online:

3 Simulink Moel for Examining Dynamic Interactions Involving Electro-Mechanical Oscillations in Distribution Systems D. Ranamuka, Stuent Member, IEEE, A. P. Agalgaonkar, Senior Member, IEEE, K. M. Muttai, Senior Member, IEEE Abstract--In Australian meium voltage (MV) istribution networks, the majority of embee local generation (LG) uses synchronous machine base technology. LG units with a synchronous generator can easily be ispatche an controlle to provie or absorb reactive power an thereby locally supporting the system voltage an increasing the voltage stability margin. The fast response from a synchronous machine base LG unit exciter will ensure fast voltage recovery. This will significantly improve the transient voltage stability. Also, the synchronous machine base LG units can provie inertial support to the system. Furthermore, some of these LG technologies work as stanby power supplies all over the worl. However, there can be ynamic interactions between nearby synchronous machine base LG units leaing to significant rotor swings. It is mainly because of (a) low inertia coefficient associate with the machines an (b) the operation of excitation system eteriorates the amping of oscillations that follow the first rotor swing after the perturbation where a fast responing excitation system can reuce the amping torue component. This paper emonstrates moelling MV istribution systems using MATLAB-SimuLink an conventional moelling techniue for investigating inter-unit electro-mechanical oscillations in nearby LG units. Inex Terms--istribution systems; electro-mechanical oscillations; interactions; local generation. NOMENCLATURE MV Meium voltage LG Local generation F Stator magnetomotive force F 2 Rotor magnetomotive force Ψ Resultant of the vector aition of F an F 2 a, b, c Phase-a, b an c of a three phase system v Stator voltage on rotor o-reference frame (-axis r s Stator wining resistance i Stator wining current on rotor o-reference frame (-axis x Sub-transient reactance (-axis i Stator wining current on rotor o-reference frame (-axis The authors are with the Australian Power Quality an Reliability Centre, School of Electrical, Computer an Telecommunications Engineering, University of Wollongong, New South Wales 2522 Australia. ( ssrr987@uowmail.eu.au; ashish@uow.eu.au; kashem@uow.eu.au) E Voltage behin the sub-transient inuctance (axis v Stator voltage on rotor o-reference frame (axis x Sub-transient reactance (-axis E Voltage behin the sub-transient inuctance (axis λ Sub-transient flux linkage (-axis λ Steay state flux linkage (-axis L Sub-transient inuctance (-axis λ Sub-transient flux linkage (-axis λ Steay state flux linkage (-axis L Sub-transient inuctance (-axis ω e Synchronous spee T o Sub-transients time constant (-axis E f Fiel wining voltage x Steay state reactance (-axis T o Sub-transients time constant (-axis x Steay state reactance (-axis T em Electro-mechanical torue H Inertia coefficient ω r Rotor spee ω b Base value for spee per unitization where f b is the electrical freuency of the system T mech Mechanical torue T amp Frictional an winage torue δ Rotor angle ω rm Prime mover spee P Number of poles Y system Amittance matrix of the istribution system n Number of buses in the istribution system I. INTRODUCTION N the meium voltage active istribution networks, the I small to meium scale synchronous machine base local generators which normally have low inertia coefficient are primarily utilize for active voltage control (normal-sate) in the system enabling an excitation system []. However, it may lea to not only the interactions among local generation units an voltage regulating evices; but also interactions among the nearby local generation units []-[4]. Therefore, it is necessary

4 to investigate an analyse those interactions an their impact on the system electric variables in orer to etermine whether any supplementary control is reuire or not. The electrical power generate by a synchronous generator is eual to the mechanical power applie by the prime mover, when the associate losses are assume zero. In the steay state, output electrical power balances the input mechanical power. Also, the associate mechanical torue is in the irection of rotor rotation, while the electrical torue (comprising synchronising torue component ealing with machine synchronism an amping torue component ealing with amping rotor oscillations) is applie to the shaft by the generator is in a irection opposite to the rotor rotation. If the generator system is perturbe, the output electrical power of the generator can change rapily, while the input mechanical power is relatively slow to change. Due to this ifference in response times, there can be temporary unbalance between output electrical power an input mechanical power. Due to this power unbalance, there can be a ifference in torue applie to the shaft leaing to rotor acceleration or eceleration. When the rotor spee is change, the relative rotor angle is change causing rotor swings an instability [5]. A fast excitation system ais to eliminate transient instability within the first swing following large perturbations by managing a sufficient synchronizing torue component. However, the operation of excitation system eteriorates the amping of oscillations that follow the first rotor swing after the perturbation; because a fast responing excitation system can reuce the amping torue component. Therefore, it is clear that the operation of an excitation system can significantly contribute to small signal instability of a power system, especially where low inertia machines are ominant because the low values of inertia coefficient will increase the values of both natural freuency of oscillations an amping coefficient. This is the motivation for the work associate with this paper. This paper is base on ynamic moelling of synchronous machine base LG units an MV istribution systems for such interaction stuies using MATLAB-SimuLink an conventional moelling techniue. The main interest is for transients of the electro-mechanical oscillations among the local generation units, where roun rotor machines are common in MV istribution level. Using this moel, the impact of machine inertia, excitation system an its tune parameters, on-line ajustment in voltage reference value for excitation system an network strength on inter-unit oscillations can be investigate an analyze. Moelling using MATLAB-SimuLink helps esign supplementary control when reuire, since MATLAB is rich with variety of control tool boxes (such as robust-control tool box), which can easily be linke to the SimuLink. The paper is organise as follows. Section II etails moeling active istribution systems for the interaction stuies using MATLAB-SimuLink; an Section III contains a case stuy, which emonstrates the moeling aspects an possible electro-mechanical oscillations among synchronous machine base LG units proviing primary voltage control in normalstate. The Section IV inclues the concluing remarks. II. MODELING DISTRIBUTION SYSTEMS WITH LOCAL GENERATION USING MATLAB-SIMULINK The etail moelling of electric power systems an machines using MATLAB-SimuLink presente in [6]. Since, the main interest is for transients of the electro-mechanical oscillations an the associate interactions, the fast electromagnetic transients are neglecte. Also, the representation of network retains only a subset of the network buses where the generation an loa behaviour are of interest, hence overall moelling task is base on integrating the conventional transient moel for embee synchronous generators into the localise static network moel. In this case, the simplifie transient moel is use for the embee synchronous generators in which the changes in stator - flux linkages are neglecte. This approach enhances the moelling task, especially in case of istribution systems with large set of electric variables which lea to inherently varying operating points resulting into more complex simulations. The overall moelling task inclues (i) ynamic moelling of synchronous generators using the transient moel, (ii) etail moelling of excitation system an (iii) expressing all voltages an currents in a common reference frame (i.e., synchronously rotating reference frame) an writing all the network euations. While moelling synchronous generators uring the transient perio the amper winings can be assume to be no longer active, where overall mathematical moel inclues (i) stator wining euations, (ii) rotor wining euations, (iii) torue euation an (iv) rotor motion euation as etaile in the following sections. Fig. shows a iagrammatic representation of rotor angle an stator magnetomotive force, F an the rotor magnetomotive force, F 2. By funamental efinition, the rotor angle is the angle between F 2 an the resultant of the vector aition of F an F 2, ψ [5]. F ψ b c a Fig.. Diagrammatic representation of rotor angle. F 2 a rotor angle Over the years, experience on power system simulation has shown that the most synchronous generators can aeuately be represente by a moel that is base on an euivalent iealise machine with one or two sets of amper winings, besies the fiel wining [7]. Damper winings in the euivalent machine moel can be use to represent physical armortisseur winings ω r c b

5 or the amping effects of ey currents in the soli iron portion of the rotor poles. Amortisseur winings are bars which are foun in the rotor of synchronous machines. These bars are short circuite similar to the rotor winings in a suirrel cage machine. The function of these winings is to ampen the torsional oscillations in the rotor that may occur as a result of loa fluctuations. They are also known as amper winings. A general circuit representation of iealise machine moel of the synchronous machine is shown in Fig. 2. It is note that the changes in stator flux linkages i.e., the time erivative terms in the stator voltage euations are usually small in comparison to the voltage behin transient inuctances. Therefore, those terms in the stator voltage euations can be omitte. ω r amper wining fiel wining amper wining rotor -axis rotor angle -axis stator Fig. 2. Diagrammatic circuit representation of iealise machine moel of the synchronous machine. The parameters in the following euations of the synchronous generator (machine) are on per unit basis. A. Stator Wining Euations v = r s.i x.i + E v = r s.i + x.i + E λ = λ L E = ω e. λ,.( i ), λ = λ L.( i ) E = ω e. λ B. Rotor Wining Euations To. t To. t b a c ( 0) ( E ) + E = E f ( x x ).i ( E ) + E = ( x x ).i ( 02) C. Torue Euation T em = { E.i + E.i + ( x x ).i. i } ( 03) D. Rotor Motion Euation 2H. δe = t ( ω ω ) r ( ωr ωe ), ωr =.ωrm e / ωb = Tem + Tmech Tamp t P 2 ( 04) E. Moelling Excitation System An accurate moelling of an excitation system as epicte in [8], [9] is essential. Most of the moern excitation systems are of the ac-rotary or ac-static type. Compare to ac-rotary type exciters, the ac-static excitation systems are more compact an have much uicker response time. Most ac-static type exciters raw their primary power from a local ac bus an use controlle rectification to provie an ajustable c excitation to the fiel wining of the synchronous generator. Such bus fe systems are epenent on the availability of the ac voltage, which coul be aversely affecte by nearby faults. There are number of stability issues in which the excitation system plays an important role. On the other han, the wie variety of esign arrangements of excitation systems makes the task of efining generic moels ifficult. However, mathematical expressions associate with principal components of all excitation systems can be aeuate to represent the characteristics of an excitation system. The armature wining usually has a small number of turns compare to the fiel wining as such; the small resistance an inuctance of the armature wining are often neglecte. Since, some intene application of these computer moels inclues large signal variations, limits an non-linearities are consiere as important characteristics to be moelle. Also, the output voltage of the exciter is typically a non-linear function of the fiel an armature currents. In case of saturation, typically, two values of the saturation function are given. Using those two values, a useful region of the saturation curve about the normal operating conition (i.e., operating point) can be approximate by an exponential function. The value of exciter output voltage that prouces rate open circuit stator voltage on its air-gap line is chosen as the voltage base. Accoringly, the base value for the exciter fiel current is calculate. Then, with this per unit system, the exciter s fiel current an voltage euations are re-written. F. Moeling Distribution Network with LG units A typical MV istribution system with synchronous machine base LG units is shown in Fig. 3. MV OLTC Gri Substation SVR LG Units SVR3 SVR2 LG Units Tie-line2 Tie-line Fig. 3. Representative MV istribution system topology with LG units. In moelling the test network, voltage phasor angle of infinite bus is conventionally chosen as the reference phasor for the rotor angles an angles of other bus voltages. Next, the time erivative terms of the stator flux linkages are omitte from the stator voltage euations by simplifying the respective transient moels of the synchronous generators.the resultant stator voltage euations will be algebraic in nature. Hence, CB

6 algebraic loops will be originate, if the algebraic stator euations an those of the static network moel are to be solve separately. In orer to avoi algebraic loops involving the network euations an the euations of the stator, all respective euations ought to be properly combine. An algebraic loop in a Simulink moel occurs when a signal loop exists with only irect feethrough blocks within the loop. Algebraic loops are further iscusse in the Simulink Users Guie [0]. In orer to avoi such algebraic loops from computational perspective; combinatorial euations nee to be written. Therefore the stator voltage euations nee to be transforme into the synchronously rotating reference frame whose -axis is aligne with the reference phasor as given by (05) an (06), where the transforme terms are now enote with aitional prefix, e [6]. However, the transformation of the stator euations in the rotor reference frame to the synchronously rotating frame of the network involves the time varying rotor angle. If the effective stator impeances in the -axis an -axis are the same, in other wors there is no rotor saliency; the resulting impeance in the synchronously rotating frame will not be a function of the time varying rotor angle. The sub-transient saliency of many machines is usually very small. Moreover, where simpler moels are esirable, the transient saliency can also be neglecte. v jv = r s v jv j = e e e v jv = ( i ji ) x.i jx.i + ( E je ) e e j e e ( v jv ), ( i ji ) = e ( i ji ) e e e e j ( i ji ) x.i jx.i + e ( E je ) ( 05) If transient saliency is ignore, incorporating the stator voltage euations into the static network moel will be straightforwar as given by (06). e e v jv = e e j ( r + x )( i ji ) + e ( E je ) ( 06) s Euation (06) can be moelle using a Thevenin s euivalent as shown in Fig. 4. Next, the bus amittance matrix incluing the transient impeances of the generators, Y system is erive as given by (07), where total number of buses eual to n. I r s +jx MV Distribution System V Fig. 4. Thevenin s euivalent circuit for machine transient moel. E ~ LG unit e e generator bus i ji = ( Ysystem ) e e network bus i n n ji n generator bus E je e e network bus v jv n ( 07) If the injecte current are subjecte to loa or fault currents; accoringly the corresponing rows an columns in Y system matrix shoul be gyrate. Finally, the set of euations in complex variables are rewritten as a set of euations of real variables with twice the orer in the form as given by (08) [6]. For large MV power systems, network reuction methos can appropriately be aopte for minimizing the computational buren. ( A ja ) = ( G + jb) ( A ja ) 2 n A = G A2 2 B n n n B A3 G 2n 2n A4 2n 3 4 n ( 08) G. Overall Moel in MATLAB-SimuLink The transient moels of synchronous generators are implemente in MATLAB-SimuLink maintaining initialisation parameters in orer to minimise the start-up transients. For the excitation system moel, integrators instea of transfer function blocks are use to moel the components. It allows initialising the states of excitation system with the outputs from trim function to keep the start-tup transients of the simulation a minimum level. The output from trim function can be use as initial values to get a uick simulation start at the esire operating point. The istribution system euations given by (08) are implemente using matrix gain MATLAB- SimuLink blocks. Outputs of the network block are the injecte currents from the generators. For istribution systems with many noes, application of per unit system woul be beneficial. Then, the parameters of the generators have also to be expresse using the per unit system, appropriately. Finally, the overall SimuLink moel which comprises the static network moel an transient moels of the LG units incluing excitation system moels is appropriately simulate for investigating the interactions between the LG units operate in voltage control moe. A MATLAB script is use for loaing system parameters, setting up ifferent case-stuy conitions, carrying out moal analysis an plotting results. Eigen values can be erive from the SimuLink moel by efining the respective inputs an outputs with inport/outport blocks in place of the source/sink blocks, linmo an eig functions. The participation factors reuire for moel analysis can simply be erive using a MATLAB Coe. The moel analyses are not etaile in this paper.

7 III. CASE STUDY The test system topology shown in Fig. 5 is use for emonstrative simulation case stuy in this paper. Similar topological combinations can freuently be seen in Australian MV istribution networks, for example in coal mine areas where coal seam gases are use to generate power locally in nearby coal mine sites. For the excitation system moel, IEEE Type- excitation system is use. The ata propose in [9] for small local generator units an their controls are aopte for the simulation case stuies. The simulate system ata are shown in Table I, where mechanical torue of the generator, LG is varie in small steps (of 0. pu) up-own-up at t = 7.5 s, 5 s an 22.5 s, respectively for generating the small perturbations. The simulate rate capacity of LG an LG2 are.5 MVA an.0 MVA, respectively. Power System MV 4 R 3 +jx 3 Fig. 5. Test system topology. Power Line 3 R +jx Mine-/Site-: LG ~ ~ 2 R 2 +jx 2 Mine-/Site-2: LG2 Local Loa Bus TABLE I SIMULATED TEST SYSTEM DATA Line: -3 Impeance /(pu) Line: 2-3 Impeance /(pu) Line: 3-4 Impeance /(pu) Local Loa Amittance /(pu) j j j j0.6 The following case stuy shows the possibility of occurring inherent oscillations among LG units in istribution systems, a worst case, when the LG units are also utilize for primary voltage control enabling an excitation system. The Fig. 6 (a) shows the rotor angle swings between LG an LG2, where Fig. 6 (b) shows the terminal voltage of each LG unit controlle by the excitation system. Rotor Angle (LG-LG2) Terminal Voltage (LG & LG2) pu Time (s) (a) Time (s) (b) Fig. 6 (a) Rotor angle swings between LG an LG2 units, an (b) Terminal voltage of LG an LG2 units. The variation of rotor angle of LG unit is shown Fig. 7. Rotor Angle (LG) Time (s) Fig. 7 Rotor angle variation of LG unit. The variation of rotor angle of LG2 unit is shown Fig. 8. Rotor Angle (LG2) Time (s) Fig. 8 Rotor angle variation of LG2 unit. IV. CONCLUSION In this paper, ynamic moelling of synchronous machine base LG units an MV istribution systems for interaction stuies involving electro-mechanical oscillations are etaile. The MATLAB-SimuLink is use for eveloping an simulating the moels. The motivation behin this work is to observe the respective interactions in case of the low inertia LG units which are also utilize for primary voltage control (normal-sate) in the istribution systems enabling an excitation system. The overall moelling task is base on integrating the conventional transient moel for LG units into the localise static network moel. This approach enhances the istribution system moelling task, since istribution systems are normally subjecte to large set of electric variables which lea to inherently varying operating points causing simulations more complex. The impact of machine inertia, excitation system an its tune parameters an network strength on inter-unit oscillations can be investigate in etail using this moel. The emonstrative test simulation case stuy reveals that there can be interactions among synchronous machine base LG units which are utilize for primary voltage control in the istribution systems, leaing to significant electro-mechanical oscillations. V. REFERENCES [] D. Ranamuka, A. P. Agalgaonkar, an K. M. Muttai, On-line Voltage Control in Distribution Systems with Multiple Voltage Regulating Devices, IEEE Trans. Sustainable Energy, vol. 5, no. 2, pp , Apr [2] D. Ranamuka, A. P. Agalgaonkar, an K. M. Muttai, Investigating the Operation of Multiple Voltage Regulators an DG in a Distribution Feeer, Energy Proceia, vol. 4, pp , Mar [3] D. Ranamuka, A. P. Agalgaonkar, an K. M. Muttai, Dynamic Ajustment of OLTC Parameters using Voltage Sensitivity while utilizing DG for Volt/VAr Support, in Proc. 204 IEEE/PES General Meeting an Conference, pp. -8. [4] D. Ranamuka, A. P. Agalgaonkar, an K. M. Muttai, Mitigating Tapchanger Limit Cycles in Moern Electricity Networks Embee with

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