A Multimachine Power System for Educational Purposes*

Jacob Efrain Diaz LavariegaManuel Garcıa Lopez

Instituto Politecnico NacionalUnidad Profesional Adolfo Lopez Mateos

Carrera de Ingenierıa ElectricaCiudad de Mexico

Abstract— In this paper a multimachine power system isevaluated in order to be used for educational purposes. It iscommon that the absence of resources for analyzing of powersystems is cause of frustrating thesis works or researches inundergraduate studies or even in graduate levels. This problemarises from the difficulty for understanding or creating modelsof power systems elements such as transformers, synchronousmachines, transmission lines, loads, etc. In this work, an inter-connected power system is evaluated in order to be included instudies in which the intention is not the power system by itself,but improvings in electrical protections, transformer models, ortransmission lines. The multimachine power system presentedin this work can be used to analyze electrical phenomenacaused for operation conditions, or in works which purpose is todesign no conventional primary controls (neurofuzzy and fuzzycontrol, for example). The results obtained for the proposedmultimachine power system were tested in PSCAD that is adigital tool for analyzing electrical power systems, this tool isflexible with Fortran code that the user includes with the mainsource code (in language Fortran too).

Index Terms— Electrical powers system components, educa-tion, models .

I. INTRODUCTION

From our experience, we have found that it is common thatstudents in undergraduate level do not have resources to testmathematical models of powers systems components (trans-formers, transmission lines, synchronous machines, etc.),electrical phenomena, to implement ideas or writing thesis inelectrical field. Trends in jobs offers and demand of electricalengineers in power systems present a challenge to institutionsin the electrical field. The level in which electrical topicsare taught in classrooms has been exceeded by technologyand advances in electrical field. For this, it is important toprovided students with elements and tools that help them tosucceed in their objectives and ideas.

The multimachine power system studied in present work,has been used as an example for modal studies in very largesystems [1], and it has been used to examine how electrome-chanical oscillations can affect the stability of interconnectedelectrical power systems [2][3][4]. In addition to these works,this power system has been used in the design of noconventional primary controls (automatic voltage regulatorand power system stabilizer) [5]. However, when parametersand variables can be found in these references, they are notfocused in how this system performs in nominal state. Even

*Los autores agradecen al Instituto Politecnico Nacional la infraestructuray recursos proveıdos para la elaboracion de este trabajo

when this system is presented for educational purposes, itsimplementation in analysis digital tools requires to be testedand verified in order to know if the system is respondingaccording the parameters that have been introduced to thedigital tool.

In this work, the parameters presented in [2] are used forevaluating the interconnected power system in Fig. 1. Thework in [1] do not present time simulation longer that 10 sec.,it is focused in an excellent modal analysis; however, thereare studies that require longer time simulations. In this work,our intention is to observe if with the provided parameters,it is possible to obtain stable longer time simulation.

II. SYSTEM CONFIGURATION

In Fig. 1, the line diagram of what is named Two AreaSystem is presented. It is designed to be symmetrical withtwo areas: area 1 and area 2 are located to the left andto the right, respectively, of bus 101. Each area containstwo synchronous machine of 900 MVA and 20 kV . Eachgenerator transformer has an impedance of 0+j0.0167 perunit on 22/230 kV base, and has an off-nominal ratio of 1.0.Each load transformer has an impedance of 0+j0.005 per uniton 230/115 kV base, and has an off-nominal ratio of 1.0.

Fig. 1. Two area power system [2]

The transmission system nominal voltage is 230 kV. Theline lengths are shown in Fig. 1. The parameters are in perunit on 100 MVA, 230 kV base.

III. NORMAL STATE OPERATION

The normal state of a power system means that all vari-ables of the system are in normal range and any equipment

is no overloaded, and it can be said that the system isoperating in a secure manner [1]. For normal state operationtest, the loads in nodes 4 and 14, are defined as follows:Pnodo14 = 1765MW , Pnodo4 = 976MW , and Qnodo14 =Qnodo4 = 100MVAR, the time response of the powersystem in a simulation of 40 sec. in shown in Fig. 2.

Fig. 2. Power Flow from area 1 to area 2 with P = 1765MW in node14

With this load conditions, the power system must transfer400 MW from area 1 to area 2 [2]. However, even when thiscondition is fulfilled during early operation, the system tendsto be unstable at the last of its operation as it is shown inFig 2. As it was mentioned early, the established load initialconditions were taken into account for a modal analysis, it ispossible that, during simulation, some oscillation mode getscloser to the right complex plane taking to power system tothis oscillatory conditions.

In order to observe if this system has a stable behavior,a new operation point is considered. The load in node 14 isreadjusted to a new value, reactive powers remain withoutchange, and active power is set to Pnodo14 = 1620MW . Theresults are shown in Fig. 3, the power system has a stableperformance, and the sum of active powers on line 1 andline 2 indicates that the load transferred from area 1 to area2 has a value of 330 MW.

Fig. 3. Power Flow from area 1 to area 2 with P = 1620MW in node14

IV. TRANSIENT STATE OPERATION

In order to evaluate if the power system is stable to atransient failure, a three phase fault to ground is programmedon line 1, the fault has 3 cycles of duration. During thefault, line 1 is released, after the transient event, the line is

recovered. This fault is applied on t = 10 sec., active andreactive powers are shown in Fig. 4. The behavior of powerson lines shows that the system is stable.

Fig. 4. Active and reactive powers on line 1 and 2

V. CONCLUSIONS

In this work a power system for educational purposes hasbeen presented, from the tests for this system, it was observedthat during a normal state operation a stable response isobtained when the load buses have a lower load comparedwith the load proposed in references. In the load operationpoint, active and reactive powers show that the system isstable when a three phase fault occurs on line 1 of the system.

If the reader requires the power system presented in thiswork for her/his studies, please write to jediazl@ipn.mx inorder to obtain full data, and additional information.

REFERENCES

[1] P. Kundur, Power Systems Stability and Control, Ed. McGraw Hill,Inc. 1994

[2] G.J. Rogers, Power System Oscillations,Kluwer Academic Publishers,U.S.A.2000.

[3] M. Klein and G. J. Rogers and S. Moorty and P. Kundur,Analyticalinvestigation of factors influencing power system stabilizers perfor-mance,IEEE Transactions on Energy Conversion vol. 7, num. 3, Sep1992.

[4] M. Klein and G. J. Rogers and P. Kundur, A fundamental study ofinter-area oscillations in power systems,IEEE Transactions on PowerSystems, vol. 6, num. 3, Aug 1991.

[5] Diaz Lavariega Jacob Efrain and Manuel Garcia Lopez, Desempenode un regulador-estabilizador neurodifuso en un sistema multi-maquinas,Reunion Internacional de Otono &C 2014-2015, IEEE.

Jacob Efraın Dıaz Lavariega nacio enla Ciudad de Oaxaca, Mexico. Es ingenieroelectrico por el Instituto Tecnologico deOaxaca (1999), candidato a doctor y maestroen ciencias de la ingenierıa electrica (2007y 2001, respectivamente) por el InstitutoPolitecnico Nacional. Recibio el Premioa la Excelencia en 1998 y 1999 durante

sus estudios de posgrado de maestrıa, graduandose con

mencion honorıfica. Actualmente trabaja en la Academiade Electronica en la carrera de Ingenierıa Electrica delIPN-ESIME-ZAC, Ciudad de Mexico. Su interes actual deinvestigacion es la aplicacion de tecnicas de inteligenciaartificial al control de los sistemas electricos de potencia.E-mail: jediazl@ipn.mx

Manuel Garcıa Lopez es ingeniero electricista por laESIME Zacatenco-IPN, candidato a doctor y maestroen ciencias de la ingenierıa electrica por la SEPI-ESIME Zacatenco-IPN. Actualmente es profesor titularde tiempo completo del Departamento Academicode Ingenierıa Electrica de la ESIME Zacatenco. Susprincipales areas de interes son Electronica de Potencia,accionamientos de maquinas de corriente directa ycorriente alterna y compensadores estaticos de vars.E-mail:manuelgalo@hotmail.com