joão manoel lenz, and airam teresa zago romcy sausen a

Regular Article

Alcedir Luis Finkler*, Luana Obregon, Mauricio de Campos, Paulo Sérgio Sausen,João Manoel Lenz, and Airam Teresa Zago Romcy Sausen

A SIMULINK implementation of a vector shiftrelay with distributed synchronous generator forengineering classes

https://doi.org/10.1515/eng-2021-0066received December 15, 2020; accepted April 12, 2021

Abstract: In recent years, the concerns regarding globalwarming have encouraged an increase in research onrenewable energy and distributed generation. Differentrenewable resources are currently being used, and bioe-nergy is one among them. Biogas can be produced viadigesters, and its energy is converted into electricity andinjected into the electrical power system for supplyingto meet the local or distant demands. Nevertheless, thegeneration of electricity via biogas on the consumer sidebrings new problems and challenges to the power systemcontroller. Protection devices, such as a vector shift relay,are one of the most important components needed toconnect a bioenergy system using synchronous genera-tors into the mains. Although distributed synchronousgenerators are widely used and simulated in softwaretools, especially in MATLAB/SIMULINK, there is still agap in technical literature detailing how to design ormodel a Vector Shift Relay. In view of this subject’s impor-tance, this article aims to assist students, researchers, andengineers by proposing a step-by-step method on how tomodel and implement a vector shift relay in MATLAB/SIM-ULINK, although the methodology may easily be used inother simulation tools. A review of the topic is presentedalong with a detailed description of all needed blocks andexpected results.

Keywords: distributed generation, loss of mains, islandingdetection, synchronous machine, electrical engineering

1 Introduction

Economic growth has a straightforward relationship tothe necessity of energy expansion. A higher percentageof renewable energy (RE) sources has been encouragedby worries about global warming [1]. Every day, theimportance of the research about RE resources as wellas the importance of addressing this issue as electricalengineering discipline is growing [2]. To meet thisrequirement, the students and researchers need to beprepared to find, understand, and solve new problemson this subject. The engineers need to be able to solveproblems about the use of the devices to convert the REinto electrical energy and share with the electrical powersystem [3]. This sharing is done with the use of generatorsconnected to the consumer facilities, known as distrib-uted generation (DG) [4]. There is a current demand ofgraduate specialization courses on DG, and universitiesshould address this gap.

Lectures of DG courses, either in undergrad or grad-uate classes, can be performed with the support ofhardware-based or software-based experiments. Hardware-based experiments are restricted due to concerns ofsecurity and cost. For the hardware-based laboratories,some difficulties can be listed as follows: for securityconcerns, the students are requested to perform specifictests following step-by-step procedures and are not beingallowed to try different proposals; there is the necessity ofspace availability for the equipment that usually con-strains the use of the equipment for a couple of students;and for the hardware experimental implementation thesystem is greatly simplified [5]. On the other hand, withthe use of software programs, the students can perform thesimulation of any scenario without risk of damage. Thestudents can be induced to perform any “what-if” type oftest and to learn by their own experiences [6]. Amongthe software programs used in research about electricalpower systems, the utilization of MATLAB/SIMULINK is

* Corresponding author: Alcedir Luis Finkler, Instituto FederalFarroupinha-IFFAR, Industrial Processes and Control Group, SantaRosa-RS, Brazil, e-mail: [email protected] Obregon, Mauricio de Campos, Paulo Sérgio Sausen, JoãoManoel Lenz, Airam Teresa Zago Romcy Sausen: Mathematical andComputacional Modeling Graduate Program, Universidade Regionaldo Noroeste do Estado do Rio Grande do Sul-UNIJUI, Ijui, Brazil

Open Engineering 2021; 11: 677–688

Open Access. © 2021 Alcedir Luis Finkler et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0International License.

https://doi.org/10.1515/eng-2021-0066

mailto:[email protected]

swiftly growing [7]. Classes and methodologies that defyand motivate students to apply their multidisciplinaryknowledge into solving real problems are becoming moreimportant, especially using computer simulation [3]. Tocapture the interest of the students, real problems tend tobe more attractive. So, related to the worries about RE,which scenario could be proposed? What kind of troublescan be handled by the students?

Regarding RE, the energy produced with biogasobtained by the anaerobic digestion is becoming moreattractive [1]. The biogas is converted to electricity usinga gas engine as primary machine coupled to a synchro-nous or asynchronous generator [8,9]. Despite the bene-fits of the DGs, their use has some associated risks. Whena DG is installed in a consumer facility, due to somefailure in the transmission line, there is a risk of a fractionof this line losing the connection with the main grid. Inthis case, the local load could be fed by the DG, and this isknown as an unintentional islanding event [10]. Theunintentional islanding operation can bring many trou-bles with respect to the quality of the energy issues andalso puts the staff, working in the distribution line, atrisk [11]. The detection of an unintentional islandingevent is known as anti-islanding protection [12]. InBrazil, one of the biggest companies that works withthe electrical distribution is the Companhia Paranaense

de Energia, COPEL. This company follows the standardNTC 9,05,200 [13] to guide the DGs to connect parallelto the grid. In its October 2018 revision, it is defined thatthe DG should use an anti-islanding method, suggestingthe use of vector shift relay, or, also known as vectorshift relays or vector surge relays (ANSI 78V). So, un-intentional islanding detection is a quite important issuefor the feasibility of the use of synchronous machineswith biogas engines. Besides that, the studies related toislanding detection supply to the students of electricalengineering a good view of some issues related to theDGs as follows: worries about safety of the maintenancestaff; worries about voltage and frequency stability; and apossibility to exercise the knowledge about control andprotection of power systems.

Even though MATLAB/SIMULINK is being used asa powerful tool for the power system analysis, in itslibraries there is non pre-built block with a vector shiftrelay. In a research with the key words most used in articlesabout anti-islanding detection the following (“islanding”and “vector shift,” “islanding” and “vector surge,”“islanding” and “vector jump,” “loss of mains” and “vectorshift,” “loss of mains” and “vector surge,” “loss of mains”and “vector jump”) were found as listed in Table 1.

Current literature regarding the use of vector shiftrelays, given in Table 1, does not go into the details of

Table 1: Articles found related to vector shift relays

Title Author Software∗

Protection & control strategy for effectively interconnecting and islanding distributed energyresources during grid disturbances [28]

Xavier (2019) ∗∗

Implications for the rate of change of frequency on an isolated power system [29] O’Donovan et al. (2019) ∗∗

Islanding detection during intended island operation of nested microgrid [30] Laaksonen andHovila (2018)

PSCAD

Wide area phase angle measurements for islanding detection – An adaptive nonlinearapproach [31]

Liu et al. (2016) DigSilent

Grid code compatible islanding detection schemes using traditional passive methods [32] Laaksonen (2016) PSCADSynchrophasor-based islanding detection for distributed generation systems usingsystematic principal component analysis approaches [33]

Guo et al. (2015) ∗∗

Islanding detection based on probabilistic PCA with missing values in PMU data [34] Liu et al. (2014) ∗∗

A study on anti-islanding detection algorithms for grid-tied photovoltaic systems [35] Banu et al. (2014) SIMULINKA composite method for islanding detection based on vector shift and frequencyvariation [36]

Hou et al. (2010) PSCAD

Dispersed generation in MV networks: performance of anti-islanding protections [37] Delfanti et al. (2010) DigSilentDesign and implementation of an anti-islanding protection strategy for distributedgeneration involving multiple passive protection [38]

Foss and Leppik (2009) ∗∗

A practical method for assessing the effectiveness of vector surge relays for distributedgeneration applications [39]

Freitas et al. (2005) ∗∗

False operation of vector surge relays [40] Freitas and Wilsun (2004) ∗∗

∗ Software used in the simulations.∗∗ Not informed.

678 Alcedir Luis Finkler et al.

how to implement it from scratch when using a softwarethat does not contain this type of protection device in itsdefault library, nor how to design it when applied to asynchronous generator. Simulation software is a powerfultool to help students, engineers, and researchers studythese systems, and it is used to overcome the difficultiesof safety, cost, and space that exist in implementing DGexperiments. Thus, this article, giving complete step-by-step modeling of a vector shift relay applied in distributedbioenergy systems, is proposed and demonstrated inMATLAB/SIMULINK.

The organization of this article is done as follows: inSection 2 is first done a review about the standardsrelated to the islanding detection, so that this informationguides in choosing the components to the proposed dia-gram as well as their settings. After this, a second sub-section is used to do a review about the vector shift relayworking principle and to explain its implementation inMATLAB/SIMULINK. Later, each subsection is used todescribe in detail each of the others blocks necessary tothe simulation. Within each subsection, some sugges-tions of problems and possible research to be performedwith the students are presented. Conclusion is given inSection 3.

2 Performing the simulation

In the simulation of a vector shift relay, the excitationsystem and the speed governor have a key function onthe circuit and can significantly affect the obtained results.Thus, dedicated subsections are written for them. For aclear understanding, this section is divided into seven sub-sections. Each of them brings the most relevant informa-tion for better understanding and addresses some possiblediscussions to be carried on with the students in theclasses.

2.1 Standards related to islanding detection

A well-established regulatory framework is needed inorder to make the DG systems feasible and attractive tothe investors [14]. One of the most important standardsfor handling this issue is the IEEE 1547-2018 standard. Toguarantee the safety of workers who operate the energydistribution grid, the IEEE 1547-2018 standard states that,as soon as a loss of DG connection with the intercon-nected power system occurs, the DG must be able to

detect this loss and automatically disconnect the gene-rator from the system in less than 2 s [15]. The IEEE1547.6, in the chapter “7.1.2 DR Electric power generationtechnologies,” classifies generator units into three types:induction generators, synchronous generators, and inver-ters [16]. Among these, the most concerning are the syn-chronous generators because they have frequency andvoltage controllers that allow these generators to continueoperating with nominal voltage and frequency values ofthe local grid, even after loss of connection with thesystem. Furthermore, the IEEE 1547.1 standard definestest procedures to be performed with anti-islanding pro-tection devices to ensure safe operation [17]. In some coun-tries, as an example of Brazil, the distribution companiesmake their standards to guide the requirements to connectthe DGs. One of the biggest distribution energy companiesin Brazil, called Companhia Paranaense de Energia,COPEL, has the standard NTC 905200 [13] to guide theDGs to connect parallel to the grid at the low voltage. Inthe revision of October 2018, it is defined that the DGshould use an anti-islanding method, suggesting the useof vector shift relay (ANSI 78V), but, it is not informed ofthe setting value to this protection device. The designerresponsible for the project, who connects the DG on thegrid, has to define the values to be set on the protectionrelays. It implies a huge responsibility on the designers.How could the designer know the correct settings for thisdevice? Would it be possible for the students to develop aprocedure to help the engineers to quickly access thesesettings for the vector shift relays?

2.2 Working principle of vector shift relays

Islanding detection can be performed quickly using vectorshift relays [18]. The vector shift relays available in themarket measure the voltage of each phase and computethe duration of each cycle of the grid. Then, the duration ofthe last period is compared with the duration of the pre-vious period. An increase or decrease in the duration of theperiod would be identified as a vector shift causing therelay to act. Thus, the typical settings for this protectionranges from 2° to 20° [19].

The basic principle of operation of a vector shift relaycan be explained with the help of Figure 1 [19]. In thisdiagram, ĒI represents the internal voltage of the syn-chronous machine, VΔ ̄ represents the voltage drop inthe reactance of the synchronous machine Xd as a func-tion of the current Īs, V̄T represents the voltage at thecoupling point between the generator and the grid,

A SIMULINK implementation of a vector shift relay with distributed synchronous generator 679

known as the point of common coupling (PCC), and ĪGrrepresents the current flowing from the grid. CB is theswitch that will be used to disconnect the grid, thusallowing the generator to supply the islanded load. VSRelay represents the switch that must be connected to thegenerator output to disconnect it when the anti-islandcircuit detects loss of connection to the grid.

In ref. [19], it is demonstrated that during the periodin which the DG operates in parallel to the grid, the loadconnected to the PCC will be fed by +Ī Īs Gr. The internalvoltage of the machine ĒI will be at a displacement angleto the voltage at PCC represented by V̄T. The angle betweenĒI and V̄T is known as the load angle, which is representedby θ. When a loss of connection to the grid occurs, simu-lated by the opening of the switch CB, the load will beexclusively fed by Īs; thus, the voltage at the PCC will be

represented by ′V̄T. In this case, there is a change in the loadangle. This change is represented by θΔ . Figure 2a repre-sents the voltage vectors before the opening of the CBswitch, whereas Figure 2b represents the voltage vectorsafter the opening of the switch. This displacement in theangle of the voltage at the PCC is called the vector shift.

The change in the load angle of the machine can beeasily assessed by measuring the displacement in thephase of the voltage at PCC. Therefore, this displacement

is proportional to the change in the load angle. Figure 3illustrates the voltage at the PCC immediately after theopening of the CB switch. For the purpose of simulation,the single line diagram of Figure 1 was implemented inSIMULINK, as illustrated in Figure 4.

The generator G1 is connected to the infinite busthrough the switch CB. Parallely connected to the G1there is the local load. The vector shift relay is also illu-strated. For simulation purposes, as the analysis wouldbe done in symmetrical faults, it is considered that themeasures for the vector shift relay are being performed ina single phase. The configuration of the G1 and of theblock of “Excitation and speed governor” is done inSections 2.3 and 2.4.

A single line diagram of Figure 4 is shown in Figure 5.The subsystem used to simulate the vector shift relay

block of Figure 4 is illustrated in Figure 6.In this simulation, the systemwas considered balanced,

and only one phase was analyzed. This subsystem takes thevoltage of the phase “a” as a reference and applies it to theblock “zero crossing.” Thus, this block gives an impulse ofunity each time the voltage crosses to zero. After this, the“off delay” block is applied to solve any problems associatedwith the time step of the simulation. This signal is applied toan “AND” port to check if the crossing occurred during theraising period or the falling period. Therefore, it will onlycompute the zero crossing in the raising period. For a betterunderstanding of the diagram in Figure 6, a flowchart isillustrated in Figure 7. At the point “A” of Figure 6, thereis a zero crossing signal reference for the beginning of eachcycle. This signal is applied to four synchronized subsys-tems. The first one, at each falling edge will capture thecurrent crossing time. This information will be available atthe point “C.” But, before the current time is updated, thesecond subsystem will save the last crossing time at therising edge in “B.” A subtraction of the current time from

Figure 1: Basic diagram of a single generator connected parallel tothe grid [19].

Figure 2: Vector phase diagram: (a) load angle before islanding; (b)displacement in the loading angle during islanding [41].

Figure 3: Voltage measured at PCC in the cycle of islandingevent [41].


the last time will be done putting at the point “D” the infor-mation of the duration of each full cycle. In a similar way,the duration of each cycle will be updated at “F” as well asthe duration of the past cycle will be stored in “E.” Thedifference between this time duration is available at “G.”This difference will be divided by the duration of the last

cycle to calculate the percentage variation of the cycle time,which is available at “H.” Once a full cycle corresponds toa 360°, the variation in degrees can be obtained by multi-plying the percentage by 360. This information is availableat “I.” The RMS value of the voltage measured at input 1 isdivided by the phase voltage. In “K” there is the voltagemeasured in percentage. This value is compared to a refer-ence, in this case, 90% and, if the voltage of the phase isgreater than this, the signal at “L” will be one. Otherwise, ifthe voltage is smaller, the signal will be zero disabling thevector shift relay. Another condition is implemented in “J”where a unity step is applied after 1.5 s. This has the functionto disable the vector shift relay during the initial transientperiod of simulation. Past the transient period of simulation,if the voltage is greater than 90%, the module of the infor-mation of the phase displacement will be available in “M.”This value will be compared to a triggering value adjusted inthe input 2. If the measured value is greater than the trig-gering value, the output 3 will become high at “O.” Thisinformation can be used to stop the simulation. At theoutput 1 will be available the information about the phasedisplacement measured in the instant where the simulationwas stopped. In the output 2, point “N,”will be available the

Figure 4: Diagram of DG connected parallel to the grid.

Figure 5: Single line diagram of DG connected parallel to the grid.


information about the time that the simulation was stopped.So, time information available at the output two can be usedto compare with the time that CB switch was set to open.With these, the duration that the vector shift relay spent tofeel the loss of main can be captured.

For good accuracy of the results, the time step for thesimulation must be considered. For a frequency of 50 Hz,if an accuracy of ∘0. 2 is desired, the time step should notbe greater than ×

−1 10 5.

2.3 Excitation control

In the IEEE 1547.1, section “5.7.1 Unintentional islandingtest,” the test procedures to ensure the action of the anti-islanding detection device are described. In the section“5.7.2.5 Comments,” it is emphasized that, the character-istics of the fuel rate (speed governor) and of the excita-tion devices must be considered during the unintentionalislanding test procedure [15]. So, these should be consid-ered in the simulation.

The excitation control is composed of componentssuch as the automatic voltage regulator (AVR), reactivecurrent compensation, and power system stabilizer andlimiters. The IEEE Std 421.5-2016 “Recommended Practicefor Excitation System Models for Power System StabilityStudies,” has a collection of the most used excitationsystems in synchronous machines. The excitation systemcan be classified into three groups according to the cur-rent source to the field winding as Type DC, Type AC, andType ST. Each of them is further divided into different

topologies according to their implemented functions,giving a total of 43 different excitation systems. A sampledata for each of them is provided in the Annex H of thestandard [20]. The AVR ST1A was selected for this article.Students could also be challenged into researching theadvantages and disadvantages of each topology throughsimulation.

Another important device to be studied is the reactivepower controller. It can be used to ensure a predefinedpower factor (PF) value or a predefined reactive powervalue. For the PF, there is a trouble that needs to behandled about the nonlinear function. Some normaliza-tion methods are presented in the IEEE Std 421.5-2016[20]. As defined in the IEEE 1547-2018, chapter 5.3.1, inthe general case, the DG should be set to work with aconstant PF equal to one [15]. For this simulation, a“VAR type 2,” as presented in the IEEE Std 421.5-2016,was considered with reactive power set to zero. The para-meters used were available at the Annex H of the IEEE Std421.5-2016 [20].

The excitation diagram implemented in the sub-system “Excitation and speed governor” of Figure 4 isillustrated in Figure 8.

By convention, the generator is considered with alagging PF when it is supplying the reactive power, andleading PF when it is consuming reactive power. Manyresearch studies are done comparing the effects of a gen-erator working with unity PF or lagging PF [21]. Related tothis topic, the students can be encouraged to change thecontrol from the reactive power control to PF control. Thestudents can also be encouraged to perform some

Figure 6: Diagram of the proposed vector shift relay implementation in SIMULINK.


experiments by changing the PF of the generator amongunity PF, lagging PF, and leading PF to check the effectsof these in the voltage of the PCC. The students can beasked to implement all the limiters in the excitation

control as over and under voltage, maximum andminimumreactive power, and all others suggested in the IEEE Std421.5-2016 [20].

2.4 Speed governor

Considering the DG working with biogas, the mostcommon topology is the use of a gas engine with a syn-chronous generator. For its proper operation, the speed ofthe synchronous machine has to be controlled. The syn-chronous machine can work attached to the distributiongrid or islanded, and the speed governor must maintaina constant speed of the machine even in the case ofislanding [22]. For this purpose, the two main methodsused to control the speed of the generators, only based onlocal measurements, with no need of communication, areisochronous mode and droop mode. In the isochronousmode, the speed of the generator is kept constant from noload to full load, which is recommended for islandedoperation. In case of parallel operation, if two generatorsare settled to isochronous mode, they will fight by theload and some of them will be switched off. In the droopmode, the speed is decreased as the load is increased in aproportional scale known as droop coefficient. For theoperation parallel with the utility grid (infinite bus), themachines are usually set in droop mode. The usual speeddroop coefficient is between 3 and 5% [8,23].

For this simulation purpose, the model used for thespeed governor is illustrated in Figure 9 as a droop con-trol. As inputs of the controller, a summing block willcompare the reference speed (wref) with the measuredspeed of the shaft of the generator (wm). A second addingblock compares the measured active power (Peo)with thecommanded power (Pcommand). So, the control will tryto increase the speed of the shaft until the measured powermatches the commanded power with an error defined bythe droop characteristics. The speed error will be appliedto the control block. The dynamics of the actuator and ofthe gas engine are described in ref. [8,9]. For simulationpurposes, the models and parameters of the control,actuator, and engine were used as described in ref. [9].The parameters are available in the Appendix.

Some tasks to the students regarding speed governorcan be to analyze the different speed droop settings asreference [24]. What would be the effects of a higher orlower droop setting? Another option to defy the studentscould be to improve the research about nonlinear methodsto adjust the droop as developed in ref. [25]. As the iso-chronous mode is more appropriate for islanded operation

Figure 7: Flowchart of the vector shift relay implemented inSIMULINK.


and the speed droop mode more appropriate for grid tieoperation, an automatic switching method is proposed inref. [23]. As soon as an islanding event is detected, the gene-rator is switched from droop mode to isochronous mode.Some research to improve this method can be proposed.

2.5 Synchronous machine

The SIMULINK has the block “Synchronous machine-p.u.standard” in its library. In the simulation described here,it was considered a salient pole machine of 31,300 VA,50 Hz, and 400 V. The parameters of the synchronousgenerator were set based on ref. [22] and are availablein the Appendix. In MATLAB/SIMULINK, for the simula-tion of the synchronous machine is also necessary to addthe “powergui” block. On this simulation, it was set todiscrete solver with a time step of ×

−1 10 s2 .

2.6 Infinite bus

On the settings of the infinite bus a point to be handledis the internal impedance or, the short-circuit level.Some different scenarios can be simulated considering

the generators installed in the rural, urban, or suburbanareas. The distance between the generator and the dis-tribution transformer will directly affect the circuit char-acteristics. A research about the minimum and maximumlength as well as the minimum and maximum short-cir-cuit level and the typical X/R relation for each differentscenario is done in ref. [26] and could be used to supportthe simulations. With this information, the students canbe defied to experiment the DG in different conditions. Asthe coverage of all possible topologies is beyond the focusof this article, for the proposed example, the check box ofinternal impedance and short-circuit level of the infinitebus are unchecked. The phase-to-phase voltage is definedas 400 V and the frequency as 50 Hz.

2.7 Simulation discussion

Once everything is set as described, the simulation can beperformed. The switch CB illustrated in Figure 4 is used tosimulate any event that would make the DG islanded withthe load. In the IEEE 1547.1, in section “5.7.2 Uninten-tional islanding test for synchronous generators” a pro-cedure to be followed to ensure the proper operation ofthe unintentional islanding protection is described [17].On this standard, there is a step-by-step procedure explaining

Figure 8: Excitation control diagram of the synchronous generator with ST1A and VAR Type 2.

Figure 9: Speed control of the synchronous generator.


how to choose the values to set the load and what conditionswould be needed to simulate to ensure the proper operationof the anti-islanding device.

The phase displacement measured at the output 1 ofthe subsystem illustrated in Figure 6 can be plotted usingthe “Scope” block from SIMULINK. If more than onesimulation need to be plotted in the same graphic, a“To Workspace” block from SIMULINK can be used. Asan example, four simulations were performed. In the firstone, the local load was set with the same power as thesettled power in the DG ( =PL PG1.00 ). A second simula-tion was performed with the local load settled at 95% ofthe power settled in the DG ( =PL PG0.95 ). Similarly, athird with 90% ( =PL PG0.90 ) and a fourth with localload settled as 85% of the power settled in the DG( =PL PG0.85 ) were performed. For all these simulations,the CB switch was set to open with 18 s. The simulationrunning time was set to 20 s. The phase displacementangle, obtained as a result of these four simulations isillustrated in Figure 10. For this plot, the time was decre-mented from 18, thus, the time illustrated in the graphicsmeans the time after CB opening. As illustrated in Figure4, the triggering angle of the vector shift relay was set at1.5 degrees, so, for the simulations with a power mis-match equal to 0%, 5%, and 10%, the relay was not trig-gered. In the simulation with a power mismatch of 15%,the phase displacement observed was greater than thetriggering angle settled value, so, the vector shift relayhas actuated. Once the vector shift relay act, the phasedisplacement at this moment will be stored in the output1 of the subsystem as illustrated in Figure 4. The time that

this trip had occurred will be stored in the output 2. Thus,with this information, it is possible to determine howlong it took for the system to detect the islanding. Theoutput 3 of the subsystem of Figure 6 will be used to stopthe simulation.

This scenario was organized considering the studieswith focus in the methods of vector shift relay to detectthe unintentional islanding switching off the DG as soonas possible. In the case the user intends to analyze theoperation of an islanded DG system, it is recommended tothe students to do a review of the IEEE 1547.4 thatdescribes all the tests to be performed to ensure theproper operation for some islanded area [27].

3 Conclusion

This article presented a vector shift relay implementationin MATLAB/SIMULINK with all components necessaryto its simulation as a proposal for DG lectures to electricalengineering courses and researches. The choice of eachcomponent and all settings are justified based on stan-dards or referenced articles. For each topic, possiblechallenges and difficulties for the students to researchare related. Thus, the objective here was to providea tool to help students and engineers in improvingtheir self-learning abilities, problem solving, and ana-lysis of DG systems. Finally, this article aims to contri-bute with a step-by-step orientation to students andengineers about unintentional islanding detection withvector shift relays applied to synchronous machine, spe-cially due to the lack of technical literature and guideson this subject.

Acknowledgments: The authors would like to thank theInstituto Federal Farroupilha, IFFar, for their support andincentive to professional qualification, and in particular,the Institutional Qualification Incentive Program (PIIQP).The authors would like to thank the Brazilian NationalResearch Council (CNPq) for providing a scholarship.The authors would like to thank Prof. A. M. Kulkarniand Kaustav Dey from Indian Institute of Technology,Bombay, for their attention and cooperation in the develop-ment of this study.

Conflict of interest: Authors state no conflict of interest.

Data availability statement: All data generated or ana-lysed during this study are included in this publishedarticle.

Figure 10: Phase displacement signal at output of the vector shiftrelay block.


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Appendix

The parameters suggested for the simulations are avail-able at Table A.

Table A: Parameters for simulation

Parameter Value Unit

Ra 0.003 puXd 1.8 pu

X ′d 0.3 pu

X ″d 0.23 pu

Xq 1.7 pu

X ″q 0.25 pu

T ′d 0.8274 Seconds

T ″d 0.0232 Seconds

T ′d0 5 Seconds

T ″d0 0.03 Seconds

T ″q 0.0293 Seconds

T ″q0 0.07 Seconds

H 3 SecondsT 1 0.01 DimensionlessT 2 0.02 DimensionlessT 3 0.2 DimensionlessT 4 0.25 DimensionlessT 5 0.009 DimensionlessTmin 0 puTmax 1.1 puTD 0.024 Seconds


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