power system stability study using modelica · power system stability study using modelica thomas...

POWER SYSTEM STABILITY STUDY USING MODELICA

Thomas Oyvang∗, Dietmar Winkler and Bernt LieTelemark University College

Faculty of Technology3901 Porsgrunn

Norway

Gunne John HegglidSkagerak Energi AS

Norway

ABSTRACT

This paper is concerned with power system modeling using the Modelica language in comparisonto a traditional simulation tool. Though most common power system simulation tools are com-putationally efficient and reasonably user-friendly, they have a closed architecture. Thus, there ismotivation to use an open-source modeling language to describe electric networks, such as Model-ica. A well-established benchmark for power system studies was analyzed. Regarding the voltageas a function of time, a reasonable agreement was found between the simulation results of the usedsimulation tools for long-term voltage stability. However, a comparison of faster electromechanicalmechanisms, such as rotor angle stability, demands more detailed models in the Modelica tool.

Keywords: Power system modeling and control, PSS R©E, Modelica, Dymola, Voltage stability, Ro-tor angle stability, Frequency stability

NOMENCLATUREP Active power [W]S Apparent power [VA]AV R Automatic Voltage RegulatorGOV Governorδ Load angleOLTC On-Load Tap-ChangerOXL Over eXcitation LimiterPSS Power System StabilizerQ Reactive power [VAr]f System frequency [Hz]V Voltage [V]

INTRODUCTIONThe modeling of power system components andnetworks is important for planning and operat-ing electric networks, as they provide insight intohow the power system will respond to both chang-

∗Corresponding author: Phone: +47 3557 5155 Fax: +473557 5401 E-mail:[email protected]

ing power demand and to various types of distur-bances.Traditional tools for power system modelingare usually tied to a certain time frame (e.g., 1 secto 15 min) depending on the phenomenon being in-vestigated. Different time frames often limit the ap-plicability and/or validity of the models to a specifickind of study [1]. A broad range of time constantsresults in specific domain tools for simulations. Tra-ditionally, simulation of stability in power systemshas been constrained to tools developed specificallyfor this purpose, as PSS R©E, EUROSTAG and Pow-erFactory [2]. Though most of these tools are com-putationally efficient and reasonably user-friendly,they have a closed architecture in which it is diffi-cult to view or change most of the component mod-els. The implementation of new network compo-nent models in PSS R©E requires editing of the FOR-TRAN source code. PSS R©E has the capability toexport a linearized representation of the system forfurther analysis, but the full nonlinear representation

Proceedings from The 55th Conference on Simulation and Modelling (SIMS 55), 21-22 October, 2014. Aalborg, Denmark

120

remains hidden to the user. Thus, there is motivationto use an open-source modeling language, such asModelica, to describe electric networks.In this paper, power system modeling was per-formed using the Modelica language with the toolDymola [3] as well as PSS R©E, to analyze stabil-ity. PSS R©E is one of the most widely used com-mercial programs of its type. Modelica effectivelyallows multi-domain modeling, including electrical,mechanical, and control systems. Thus, this paperpresents power system stability simulations from ananalysis of a simple power system to compare mod-eling tools.The paper is organized as follows. Section 2 pro-vides a brief overview of phenomena within powersystem stability. Section 3 introduces and describesthe test system, and the simulation results are pre-sented in Section 4. The results of the simulationsare discussed in Section 5, and conclusions and fu-ture perspectives are presented in Section 6.

POWER SYSTEM STABILITY AND CON-TROLTwo important highly nonlinear characteristics ofpower system stability are two pairs of strongly con-nected variables: reactive power Q and voltage V ,and active power P and power angle δ . The powerangle is often referred to as the load angle and as-sociated with the system frequency f . These vari-ables need to be monitored and controlled withincertain limits to secure stable power system opera-tion [1]. The TSO (Transmission System Operator)Statnett gives functional requirements in the powersystem [4] and has the overall supervision respon-sibility and physical control as regards Norway‘spower system. TSO ensures normally a power gridfrequency of 50 Hz (or 314.16 rad/s) ±2% and avoltage interval of ±10% according too [5]. Thesystem frequency of an interconnected power sys-tem has the same value everywhere in the system;in other words, it is independent of the location. Asimilar "‘system voltage" does not exist the voltageamplitude depends strongly on the local situation inthe system. Power system stability is understood asthe ability to regain an equilibrium state after beingsubjected to a physical disturbance, and it can be di-vided into:

• Voltage stability

• Rotor angle stability

• Power imbalance (frequency stability)

Different types of disturbances are classified in theliterature [1]. Only the large disturbances given inTable 1 will be addressed in this paper. Determi-nation of large-disturbance stability requires exam-ination of the nonlinear dynamic performance of asystem over a period of time sufficient to captureinteractions between the devices to be investigated.To manage these stability phenomena, synchronousgenerators in power systems are often protected orcontrolled by devices, such as an automatic volt-age regulator (AVR), power system stabilizer (PSS),turbine governor (GOV) and over-excitation limiter(OXL). A simplified control structure for these dif-ferent devices is illustrated in Figure 1 and willonly be presented here briefly. The turbine gover-nor controls either the speed or output power accord-ing to a preset active power-frequency characteristic(droop control). This control is achieved by open-ing/closing control valves to regulate the water-flow(e.g., hydropower) through the turbine, forcing thegenerator to rotate, converting mechanical energyinto electricity. The excitation (or field) current re-quired to produce the magnetic field inside the gen-erator is provided by the exciter and controlled by anAVR. The AVR is designed to automatically main-tain a constant voltage; it may be a simple "feed-forward" design or may include negative feedbackcontrol loops and implemented as a PI or PID con-troller. The AVR, in cooperation with the PSS, reg-ulates the generator terminal voltage by controllingthe amount of current supplied to the generator fieldby the exciter.

Figure 1: Single generator voltage and frequencycontrol


121

10-BUS TEST SYSTEMThis paper presents the results from an analysis of asimple 10-bus1 power system described in [1]. Typ-ically nominal SI-voltage levels are used in simula-tions. The system is a well-established benchmarkfor exploring voltage stability issues [6]. This smallsystem shares some of its characteristics with theNordic system studied in [7]. In both systems, mostgeneration occurs in a remote area that is connectedto a main load area through five transmission lines.In addition to voltage stability, the frequency and ro-tor angle stability will also be visualized in this pa-per. The system has three synchronous hydro-powergenerators; one generator is connected to a slack-bus to represent inter-area power exchange. Bothgenerators 1 and 2 are remote generators that supplypower to the loads through five parallel feeders, andgenerator 3 is a local generator. A one-line diagramof the test system that will be used to illustrate someof the mechanisms of power system instability in atime simulation is shown in Figure 2.

Figure 2: 10 bus case (BPA test system [1]).

The purpose of the simulations is to visualize howthe generators in a power system respond when amomentary disturbance occurs in the power balancebetween the electrical power consumed in the sys-tem, the mechanical power delivered by the tur-bines, and the equivalent power from the slack-bus.The simulations were performed in Dymola [3] andcompared with PSS R©E Dynamic Simulation mod-ule [8] . An overview of simulations and counter-measures2 carried out in this paper is shown in Ta-ble 1.

1In an electrical power system the bus is an electrical junc-tion (node) where conductors terminate. It is usually made ofcopper bar.

2After an disturbance, measures are taken by different con-trol components to stabilize voltage, frequency and rotor oscil-lations.

Test model constructed using PSS R©E andDymola

Power system parameters can be given in Interna-tional System of measurement (SI) or per-unit sys-tem (pu). The pu system is used in power systemmodeling in which each parameter is expressed as adecimal fraction of its respective base. A minimumof two base quantities is required to completely de-fine a pu system. For example, apparent power Sand voltage V are fixed and then the current andimpedance (or admittance) set arbitrarily. The pubases used in the models developed in this paperwere both "system base" (100 MVA) and a different"machine base".

PSS R©E

The dynamic simulations of PSS R©E are based onpower-flow calculations in steady-state. The equip-ment used in dynamic simulations needs to be de-fined in power-flow. The main skeleton of PSS R©Econtains logic for data input, output, numerical inte-gration, and electric network solutions but containsno logic related to differential equations for specificequipment [9]. The equipment used in this paperincluded standard PSS R©E models and was definedin so-called subroutines in PSS R©E. The model sub-routines are called whenever the main skeleton logicneeds numerical values of time derivatives. Dy-namic models that are used for developing the testsystem are listed in Table 2. The models in PSS R©Eare restricted to block diagrams with input and out-puts (casual), whereas in Modelica models can beacasual.

Dymola

Larsson [7, 10] created the freely available powersystem library ObjectStab, which is intended forpower system stability simulations written in Model-ica, a general-purpose object-oriented modeling lan-guage. The "Electric Power Library" (EPL) [10]in Dymola by Modelon AB was used to developthe test system in this paper. The EPL containsmodels of standard power system components, in-cluding the control of generators, exciters for syn-chronous machines (generators), and turbine GOVs.To investigate the stability phenomena in this pa-per, some additional components were made. An


122

Table 1: SimulationsCase Stability Countermeasures/Devices Disturbance

A1 Voltage Tap changer and OXL at G2 and G3 Loss of line

A2 Voltage Tap changer and OXL at G3 Loss of line

B Rotor angle Power system stabilizer 3-phase fault and line trip

C Frequency Governor/Tie-line/load shedding power imbalance

IEEE ST1A bus-fed thyristor excitation system withPSS and OXLs with inverse-time characteristics wasbuilt with logic blocks in Modelica. The ST1A hasa PSS using only generator speed as the input sig-nal. This stabilizer is simpler than the one used inPSS R©E, which uses both speed and active power asthe input. The ST1A was setup similar to a tran-sient stability analysis of a power system in Kun-dur [1]. An On-Load Tap-Changer (OLTC) wasalso created as an state machine based on [11].Generator G1 was modeled as an infinite bus (volt-age with a constant amplitude and phase) and gen-erators G2 and G3 using 6th-order models. Theloads at bus 8 and bus 11 were modeled as con-stant impedance. The load at bus 11 was connectedthrough the OLTC at T6. The GOVs were imple-mented as PI controllers (first-order transfer func-tions with limiter) using speed and power as refer-ence values (set points).

For the comparison with PSS R©E, some parame-ters needed to be correlated in EPL. This was donemainly at the transformer ratio and transmissionline parameters (resistance, inductance, and capac-itance).

SIMULATIONSThe simulations are designed to visualize the threemain stability phenomena within power systems.Voltage instability/collapse is a major security con-cern for power system operation. This phenomenonis often preceded by a slow process of load restora-tion and limitation in generators reactive power sup-ply, after some initial disturbances [12]. If each busin a system elevating both the voltage (V) and re-active power (Q) after a disturbance the system isvoltage-stable. On the other hand, if the voltage de-creases and reactive power increases at one or morebuses we have voltage instability. This phenomenoncan be seen in case A1 in Figure 3 (only Dymola)

and case A2 in Figure 4 (Dymola and PSS R©E). Adisconnect between one of the five parallel lines oc-curred in the simulation at 100 s. At approximately115 s, the short-term dynamics including the gen-erator electromechanical and load recovery dynam-ics settled. As the voltage at bus 11 was below theOLTC deadband, its internal timer started. As seenfrom the figures, the OLTC reacted and slightly in-creased the voltage at bus 11 (secondary side) anddecreased the voltage at bus 10 (primary side). InFigure 3, OXLs were implemented at G3 (at 140seconds) and G2 (at 160 seconds). Bus 10 exhib-ited voltage instability until the OXL started to limitthe reactive power after 140 seconds. In Figure 4,the OXL was only implemented at generator 3. TheOXL limited the field voltage by ramping down thefield voltage (or current), ensuring that G3 did notoverheat. Consequently, the necessary voltage sup-port was not dispatched locally and a power system"blackout" occurred. The use of a tap-changer asa countermeasure is often referred to as secondaryvoltage control. Another countermeasure for voltageinstability is load shedding, but it is not presented inthis case.

As seen in Figure 3, similar trend was observed forboth PSS R©E and Dymola. However, the voltage be-fore disturbance was not the same due to how thepower system was constructed in the different simu-lation tools. Also the OXL characteristic in PSS R©E(MAXEX1) was slightly more complex than thatimplemented with EPL.

Rotor angle stability

In Figures 5 and Figure 6, the rotor angle stabilityphenomena and countermeasures are visualized byshowing the speed deviation in pu from synchronousspeed of generator G3 with and without stabilizer


123

Table 2: Test system in PSS R©E and DymolaEquipment PSSE Dymola

Governor G1 (Slack bus) GENCLS Infinite bus

Governor G2 and G3 GENROU 6-th order dq

Exciter G2 and G3 SEXS IEEE ST1A

Overexcitation limiter at G3 MAXEX1 Inverse-time characteristic with ramping

Overexcitation limiter at G2 None Constant maximum limit

Transformer tap changer at bus 11 OLTC1T OLTC

Power system stabilizer at G2 PSS2A Simplified PSS

Load at bus 8 and 11 Constant impedance Impedance (Load at nominal voltage)

Figure 3: Case A1: Voltage instability at bus 10 withOXL implemented both at G2 and G3

during a large disturbance. Rotor angle 3 stability isthe ability of interconnected synchronous machinesof a power system to remain in synchronism. PSSprovided supplemental damping to the oscillation ofsynchronous machine rotors through the generatorexcitation as shown in Figure 1. A fundamental fac-tor in this problem is the manner in which the poweroutputs of synchronous machines vary as their rotorsoscillates.The effect of this positive damping after an large dis-turbance in the grid can be seen in figure 5, wherePSS is applied to the excitation system at G3.

As mentioned, PSS R©E is using the PSS2A stabi-lizer measuring both speed and active power as in-put. This gives a greater positive damping by the sta-bilizer compared to the one in EPL with only speedas input. Also the generator oscillation behavior

3the derivative of rotor angle is equal to the rotor angularvelocity in [rad/s]

Figure 4: Case A2: Voltage level due to tap-changertransformer T6 with results from both Dymola andPSS R©E

and amplitude are different due to different gover-nor models. In both cases the stabilizer will lowerthe time for the system to settle in non oscillatingstate.

Frequency stability

If a large load is suddenly connected (disconnected)to the system, or if a generating unit is suddenlydisconnected, a long-term distortion occurs in thepower balance, changing the frequency in the sys-tem. In Figure 7 the frequency stability phenom-ena is visualized in Dymola by showing the rotor-dynamic oscillation at G2. In real-life applications,generators are protected against frequency instabil-ity by disconnecting equipment before a severe haz-ard. However, this protection was not implementedhere and the simulations are only a theoretical ap-proach for visualizing this phenomenon. When the


124

Figure 5: Rotor oscillations at G3 in PSS R©E

Figure 6: Rotor oscillations at G3 in Dymola

turbine generators are equipped with governing sys-tems following a change in total power demand (orloss of a generator), the system is not able to returnto the initial frequency on its own without any addi-tional action. In Figure 7, generator G3 was discon-nected from the system at 103 seconds. The G2 isnow oscillating due to the generator rotor-dynamics.This rotor oscillation is a good representation of thefrequency instability that would occur in the 10-bussystem. The 10-bus system is now in power im-balance transferring more power through the slack-bus trying to stabilize the system. This is often ref-ered to tie-line power. After 130 seconds the load atbus 11 was disconnected (load shedding) making thefrequency equilibrate after approximately 160 sec-onds. Simulation in this case is done only with Dy-mola. How the infinte bus are constructed in EPLand PSS R©E are different causing the system to be-have differently.

DISCUSSIONThe simulations in Dymola were carried out withtransient initialisation and simulations due to un-

Figure 7: Case C in Dymola: Showing rotor-dynamic behavior at G2 influencing the grid fre-quency after an disturbance at time 103 seconds (os-cillation starts) and countermeasure applied at 130seconds.

certainty with the parameters of the power systemand control components. There are two initialisationmodes, transient (state variables with default-values)and steady-state. When choosing transient initialisa-tion, no specific initial equations are defined. Thistype of transient simulation is only possible withfeedback within the controllers. Periodically drivensystems tend towards a periodic solution after sometime. To get the periodic solution (after about 20second simulation time in this paper) the initial lim-its of governor and AVR need to be greater than inbalanced situations. Simulating transmission linesin steady-state was not possible in EPL due to someinitializing problems.

The EPL’s complexity (fully represents the actualphysics of the components) demands the user toimplement a huge amount of accurate parameters.Building a stable power system in the EPL with onlylimited knowledge of parameters is challenging, assome initial values need to be set explicitly to avoidguessing from the tool side. A real-life power sys-tem application with known parameters is recom-mended when comparing simulation tools with theEPL. When creating a large system model in Dy-mola, it is typically easier to build the system modelthrough the composition of subsystem models thatcan be tested in isolation. However, connectingthese well-posed subsystems together to create thefull scale large power system may lead to instabilityand unwanted oscillations. A balanced power sys-tem, well posed initial equations, and accurate pa-rameter values are of crucial importance to running


125

transient power system simulations in Dymola.

The main advantages of using Modelica as a mod-eling language is the readability and re-usability ofthe code. Models within this library are based on aclear set of equations rather than a set of diagramsas in the PSS R©E tool. In this sense the library has adidactic intention. FORTRAN is considered a pro-cedural language (i.e., you tell the computer whatto do step-by-step), whereas Modelica is a declara-tive language. Thus, rather than developing sourcecode that lists a set of steps to follow in order tosolve a problem, you only have to describe the math-ematical structure of your problem [13]. The disad-vantage is longer execution times compared to theFORTRAN model. For example, in long term sim-ulations as shown in case A2, PSS R©E use less than3 second computation time on the 180 second sim-ulation, while Dymola uses about 20 seconds on thesame calculation (without the transient initializationprocess). For example if you want to simulate a stateutility network (where the number of buses will be inthousands) you will need a robust software such asPSS R©E. But if you want to execute a system withless number of buses and do in depth analysis youcan use EPL and Dymola.

The different complexity of models used in PSS R©Eand Dymola affect the results. For example, theGOV used in the EPL is a PI control done as a trans-fer function block, whereas in PSS R©E the Hydro-Turbine Governor (HYGOV) models both the GOVand hydraulic systems. This HYGOV model is amore complex structure than the EPL model. How-ever, visualizing the stability phenomena in this pa-per, the controllers made in EPL had promising re-sults compared to PSS R©E. As seen in the long-termvoltage stability simulations, this difference has alimited impact. A detailed hydraulic system modellike HYGOV and an infinite bus such as GENCLSin PSS R©E should be created with the EPL.However, the modeling detail required for any givenstudy depends on the scope of the study and thesystem characteristics [1]. A Hydro Power Library(HPL) is also available [14]. The EPL could becombined with the HPL in Dymola to also includewaterway components and droop control.

CONCLUSIONRegarding the voltage as a function of time, a rea-sonable agreement was found between the simula-tion results obtained using Dymola and PSS R©E forlong-term voltage stability. However, a comparisonof faster electromechanical mechanisms, such as ro-tor angle demands, requires more detailed models inEPL. In this paper, PSS R©E was clearly the fastestsimulator. However, PSS R©E has an closed architec-ture in which it is difficult to view or change mostof the component models. Using an open-sourcemodel with didactic intention for describing electricnetworks, such as Modelica, could be preferable forin-depth power system studies.

ACKNOWLEDGMENTThe financial support from Statkraft ASA of thePhD study of the first author is greatly acknowl-edged. The practical support from Jan Petter Haugli,Statkraft ASA is likewise acknowledged.

REFERENCES[1] Prabha Kundur. Power System Stability and

Control. McGraw-Hill Professional, 1994.ISBN: 007035958X.

[2] Luigi Vanfretti, Tetiana Bogodorova, andMaxime Baudette. “A Modelica Power Sys-tem Component Library for Model Validationand Parameter Identification”. In: Proceed-ings of the 10th International Modelica Con-ference, March 10-12, 2014, Lund, Sweden(2014). DOI: 10.3384/ecp140961195.

[3] Dassault Systèms. Dymola. URL: http://www.dymola.com.

[4] Statnett. FIKS Funksjonskrav i Kraftsys-temet/Functional requirements in the powersystem. Tech. rep. Statnett, 2012.

[5] Ministry of Petroleum and Energy (OED).Forskrift om leveringskvalitet i kraftsystemetNorwegian Water Resources and EnergyDirectorate (NVE). 2004. URL: http :/ / lovdata . no / dokument / SF /forskrift/2004-11-30-1557.


126

[6] Go Bong. “Voltage stability enhancement viamodel predictive control.” ProQuest Disser-tations and Theses, , 173. Dissertation. TheUniversity of Wisconsin, Madison, 2008.

[7] Mats Larsson. “Coordinated Voltage Controlin Electric Power Systems”. PhD thesis. LundUniversity, 2000.

[8] Siemens. PSSE Dynamic Simulation mod-ule. URL: http : / / w3 . siemens .com / smartgrid / global / en /products - systems - solutions /software - solutions / planning -data - management - software /planning-simulation/pages/pss-e.aspx#.

[9] Siemens. Program Application Guide: Vol-ume II PSSE 33.4 Siemens.

[10] Larsson. “ObjectStab-an educational tool forpower system stability studies”. In: IEEETransactions On Power Systems 19.1 (2004),pp. 56–63. DOI: 10.1109/TPWRS.2003.821001.

[11] P.W. Sauer and M.A. Pai. “A comparison ofdiscrete vs. continuous dynamic models oftap-changing-under-load transformers”. In:Proceedings of NSF/ECC Workshop on Bulkpower System Voltage Phenomena - III: Volt-age Stability, Security and Control, Davos,Switzerland (1994).

[12] A stable finite horizon model predictive con-trol for power system voltage collapse pre-vention. 2011, pp. 7105–7110. DOI: 10 .1109/CDC.2011.6161396.

[13] Michael M. Tiller. Modelica by Example. Xo-gency, Web. 2014. URL: http://book.xogeny.com.

[14] Modelon. Hydro Power Library (HPL). URL:http : / / www . modelon . com /products / modelica - libraries /hydro-power-library/.


127

power system stability study using modelica · power system stability study using modelica thomas...

Documents